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<!--XBRL document created with Toppan Merrill Bridge  11.4.0.1 -->
<!--Based on XBRL 2.1-->
<!--Created on: 8/19/2026 9:06:07 PM-->
<!--Modified on: 8/19/2026 9:06:07 PM-->
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    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityTaxIdentificationNumber" xlink:label="dei_EntityTaxIdentificationNumber" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressAddressLine1" xlink:label="dei_EntityAddressAddressLine1" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_Security12bTitle" xlink:label="dei_Security12bTitle" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_SecurityExchangeName" xlink:label="dei_SecurityExchangeName" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityWellKnownSeasonedIssuer" xlink:label="dei_EntityWellKnownSeasonedIssuer" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityVoluntaryFilers" xlink:label="dei_EntityVoluntaryFilers" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityInteractiveDataCurrent" xlink:label="dei_EntityInteractiveDataCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Current assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and Cash Equivalent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and cash equivalents</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedCashCurrent" xlink:label="us-gaap_RestrictedCashCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RestrictedCashCurrent" xlink:to="us-gaap_RestrictedCashCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RestrictedCashCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Restricted Cash, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RestrictedCashCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Restricted cash</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsReceivableNetCurrent" xlink:label="us-gaap_AccountsReceivableNetCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableNetCurrent" xlink:to="us-gaap_AccountsReceivableNetCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, after Allowance for Credit Loss, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts receivable, net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts receivable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PrepaidExpenseCurrent" xlink:label="us-gaap_PrepaidExpenseCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PrepaidExpenseCurrent" xlink:to="us-gaap_PrepaidExpenseCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PrepaidExpenseCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Prepaid Expense, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PrepaidExpenseCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Prepaid expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InventoryNet" xlink:label="us-gaap_InventoryNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryNet" xlink:to="us-gaap_InventoryNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InventoryNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventory, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InventoryNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventory</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommodityContractAssetCurrent" xlink:label="us-gaap_CommodityContractAssetCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommodityContractAssetCurrent" xlink:to="us-gaap_CommodityContractAssetCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommodityContractAssetCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commodity Contract Asset, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommodityContractAssetCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commodity derivative assets, current</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssetsCurrent" xlink:label="us-gaap_OtherAssetsCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherAssetsCurrent" xlink:to="us-gaap_OtherAssetsCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherAssetsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Assets, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherAssetsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other current assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsCurrent" xlink:label="us-gaap_AssetsCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsCurrent" xlink:to="us-gaap_AssetsCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Assets, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_AssetsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total current assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OilAndGasPropertyFullCostMethodNetAbstract" xlink:label="us-gaap_OilAndGasPropertyFullCostMethodNetAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OilAndGasPropertyFullCostMethodNetAbstract" xlink:to="us-gaap_OilAndGasPropertyFullCostMethodNetAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OilAndGasPropertyFullCostMethodNetAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Full Cost Method, Property and Equipment, after Accumulated Depletion [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OilAndGasPropertyFullCostMethodNetAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural gas properties and equipment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProvedOilAndGasPropertySuccessfulEffortMethod" xlink:label="us-gaap_ProvedOilAndGasPropertySuccessfulEffortMethod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProvedOilAndGasPropertySuccessfulEffortMethod" xlink:to="us-gaap_ProvedOilAndGasPropertySuccessfulEffortMethod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProvedOilAndGasPropertySuccessfulEffortMethod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Successful Efforts Method, Property and Equipment, Proved Property, before Accumulated Depreciation, Depletion, Amortization, and Impairment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProvedOilAndGasPropertySuccessfulEffortMethod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Developed properties</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnprovedOilAndGasPropertySuccessfulEffortMethod" xlink:label="us-gaap_UnprovedOilAndGasPropertySuccessfulEffortMethod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_UnprovedOilAndGasPropertySuccessfulEffortMethod" xlink:to="us-gaap_UnprovedOilAndGasPropertySuccessfulEffortMethod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_UnprovedOilAndGasPropertySuccessfulEffortMethod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Successful Efforts Method, Property and Equipment, Unproved Property, before Accumulated Depreciation, Depletion, Amortization, and Impairment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_UnprovedOilAndGasPropertySuccessfulEffortMethod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Undeveloped properties</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamPropertyBeforeAccumulatedDepreciationDepletionAmortizationAndImpairment" xlink:label="bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamPropertyBeforeAccumulatedDepreciationDepletionAmortizationAndImpairment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamPropertyBeforeAccumulatedDepreciationDepletionAmortizationAndImpairment" xlink:to="bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamPropertyBeforeAccumulatedDepreciationDepletionAmortizationAndImpairment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamPropertyBeforeAccumulatedDepreciationDepletionAmortizationAndImpairment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Successful Efforts Method, Property and Equipment, Midstream Property, before Accumulated Depreciation, Depletion, Amortization, and Impairment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamPropertyBeforeAccumulatedDepreciationDepletionAmortizationAndImpairment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Successful Efforts Method, Property and Equipment, Midstream Property, before Accumulated Depreciation, Depletion, Amortization, and Impairment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamPropertyBeforeAccumulatedDepreciationDepletionAmortizationAndImpairment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Midstream assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OilAndGasPropertySuccessfulEffortMethodAccumulatedDepreciationDepletionAndAmortization" xlink:label="us-gaap_OilAndGasPropertySuccessfulEffortMethodAccumulatedDepreciationDepletionAndAmortization" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OilAndGasPropertySuccessfulEffortMethodAccumulatedDepreciationDepletionAndAmortization" xlink:to="us-gaap_OilAndGasPropertySuccessfulEffortMethodAccumulatedDepreciationDepletionAndAmortization_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OilAndGasPropertySuccessfulEffortMethodAccumulatedDepreciationDepletionAndAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Successful Efforts Method, Property and Equipment, Accumulated Depreciation, Depletion, and Amortization</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_OilAndGasPropertySuccessfulEffortMethodAccumulatedDepreciationDepletionAndAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accumulated depreciation, depletion, and amortization</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OilAndGasPropertySuccessfulEffortMethodNet" xlink:label="us-gaap_OilAndGasPropertySuccessfulEffortMethodNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OilAndGasPropertySuccessfulEffortMethodNet" xlink:to="us-gaap_OilAndGasPropertySuccessfulEffortMethodNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OilAndGasPropertySuccessfulEffortMethodNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Successful Efforts Method, Property and Equipment, after Accumulated Depreciation, Depletion, Amortization, and Impairment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_OilAndGasPropertySuccessfulEffortMethodNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total natural gas properties, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentOtherNet" xlink:label="us-gaap_PropertyPlantAndEquipmentOtherNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentOtherNet" xlink:to="us-gaap_PropertyPlantAndEquipmentOtherNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentOtherNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment, Other, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentOtherNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other property, plant, and equipment, net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentOtherNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other property and equipment, net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentOtherNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other property, plant, and equipment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DepositsAssetsNoncurrent" xlink:label="us-gaap_DepositsAssetsNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DepositsAssetsNoncurrent" xlink:to="us-gaap_DepositsAssetsNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DepositsAssetsNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deposits Assets, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DepositsAssetsNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deposits</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Goodwill" xlink:label="us-gaap_Goodwill" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Goodwill" xlink:to="us-gaap_Goodwill_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Goodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_Goodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommodityContractAssetNoncurrent" xlink:label="us-gaap_CommodityContractAssetNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommodityContractAssetNoncurrent" xlink:to="us-gaap_CommodityContractAssetNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommodityContractAssetNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commodity Contract Asset, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommodityContractAssetNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commodity derivative assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssetsNoncurrent" xlink:label="us-gaap_OtherAssetsNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherAssetsNoncurrent" xlink:to="us-gaap_OtherAssetsNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Assets, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other noncurrent assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Assets" xlink:label="us-gaap_Assets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Assets" xlink:to="us-gaap_Assets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Assets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_Assets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities and Equity [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities, mezzanine equity, and equity</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesCurrentAbstract" xlink:label="us-gaap_LiabilitiesCurrentAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesCurrentAbstract" xlink:to="us-gaap_LiabilitiesCurrentAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities, Current [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Current liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsPayableAndAccruedLiabilitiesCurrent" xlink:label="us-gaap_AccountsPayableAndAccruedLiabilitiesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsPayableAndAccruedLiabilitiesCurrent" xlink:to="us-gaap_AccountsPayableAndAccruedLiabilitiesCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsPayableAndAccruedLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Payable and Accrued Liabilities, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_AccountsPayableAndAccruedLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts payable and accrued liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_AccountsPayableAndAccruedLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AccountsPayableAndAccruedLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts payable and accrued liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationContingentConsiderationLiabilityCurrent" xlink:label="us-gaap_BusinessCombinationContingentConsiderationLiabilityCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationContingentConsiderationLiabilityCurrent" xlink:to="us-gaap_BusinessCombinationContingentConsiderationLiabilityCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationContingentConsiderationLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Contingent Consideration, Liability, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationContingentConsiderationLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contingent consideration payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLiabilitiesCurrent" xlink:label="us-gaap_DerivativeLiabilitiesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeLiabilitiesCurrent" xlink:to="us-gaap_DerivativeLiabilitiesCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Liability, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commodity derivative liabilities, current</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccruedIncomeTaxesCurrent" xlink:label="us-gaap_AccruedIncomeTaxesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccruedIncomeTaxesCurrent" xlink:to="us-gaap_AccruedIncomeTaxesCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccruedIncomeTaxesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued Income Taxes, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccruedIncomeTaxesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income taxes payable to related party</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_PayableToAffiliatesSubsidiariesAssociatesAndJointVenturesCurrent" xlink:label="bkv_PayableToAffiliatesSubsidiariesAssociatesAndJointVenturesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_PayableToAffiliatesSubsidiariesAssociatesAndJointVenturesCurrent" xlink:to="bkv_PayableToAffiliatesSubsidiariesAssociatesAndJointVenturesCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_PayableToAffiliatesSubsidiariesAssociatesAndJointVenturesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying amount as of the balance sheet date of the unpaid sum of the known and estimated amounts payable to BPPUS for the BKV-BPP Power Joint Venture Transaction.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_PayableToAffiliatesSubsidiariesAssociatesAndJointVenturesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payable To Affiliates, Subsidiaries, Associates, And Joint Ventures, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_PayableToAffiliatesSubsidiariesAssociatesAndJointVenturesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payable to BPPUS for the BKV-BPP Power Joint Venture Transaction</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NotesPayableCurrent" xlink:label="us-gaap_NotesPayableCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NotesPayableCurrent" xlink:to="us-gaap_NotesPayableCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NotesPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes Payable, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NotesPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Current portion of Temple I Loan Agreements</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_CurrentPortionOfLongTermDebtNet" xlink:label="bkv_CurrentPortionOfLongTermDebtNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_CurrentPortionOfLongTermDebtNet" xlink:to="bkv_CurrentPortionOfLongTermDebtNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_CurrentPortionOfLongTermDebtNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of long-term debt classified as other, payable within one year or the operating cycle, if longer.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_CurrentPortionOfLongTermDebtNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Current Portion Of Long-Term Debt, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_CurrentPortionOfLongTermDebtNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Current portion of long-term debt, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLiabilitiesCurrent" xlink:label="us-gaap_OtherLiabilitiesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherLiabilitiesCurrent" xlink:to="us-gaap_OtherLiabilitiesCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Liabilities, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other current liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesCurrent" xlink:label="us-gaap_LiabilitiesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesCurrent" xlink:to="us-gaap_LiabilitiesCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total current liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetRetirementObligationsNoncurrent" xlink:label="us-gaap_AssetRetirementObligationsNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetRetirementObligationsNoncurrent" xlink:to="us-gaap_AssetRetirementObligationsNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetRetirementObligationsNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Retirement Obligations, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetRetirementObligationsNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset retirement obligations</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AssetRetirementObligationsNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset retirement obligations, long-term</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLiabilitiesNoncurrent" xlink:label="us-gaap_DerivativeLiabilitiesNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeLiabilitiesNoncurrent" xlink:to="us-gaap_DerivativeLiabilitiesNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeLiabilitiesNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Liability, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeLiabilitiesNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commodity derivative liabilities</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_PayableToAffiliatesSubsidiariesAssociatesAndJointVenturesNoncurrent" xlink:label="bkv_PayableToAffiliatesSubsidiariesAssociatesAndJointVenturesNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_PayableToAffiliatesSubsidiariesAssociatesAndJointVenturesNoncurrent" xlink:to="bkv_PayableToAffiliatesSubsidiariesAssociatesAndJointVenturesNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_PayableToAffiliatesSubsidiariesAssociatesAndJointVenturesNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of payables to affiliates, subsidiaries, associates and joint venture, classified as noncurrent.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_PayableToAffiliatesSubsidiariesAssociatesAndJointVenturesNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payable To Affiliates, Subsidiaries, Associates, And Joint Ventures, NonCurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_PayableToAffiliatesSubsidiariesAssociatesAndJointVenturesNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payable to BPPUS for the BKV-BPP Power Joint Venture Transaction</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:label="us-gaap_DeferredIncomeTaxLiabilitiesNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:to="us-gaap_DeferredIncomeTaxLiabilitiesNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DeferredIncomeTaxLiabilitiesNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Income Tax Liabilities, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DeferredIncomeTaxLiabilitiesNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred tax liability, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermNotesPayable" xlink:label="us-gaap_LongTermNotesPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermNotesPayable" xlink:to="us-gaap_LongTermNotesPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes Payable, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncurrent portion of Temple I Loan Agreements</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_LongTermDebtNet" xlink:label="bkv_LongTermDebtNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_LongTermDebtNet" xlink:to="bkv_LongTermDebtNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_LongTermDebtNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of long-term debt classified as other, payable after one year or the operating cycle, if longer.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_LongTermDebtNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_LongTermDebtNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-term debt, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLiabilitiesNoncurrent" xlink:label="us-gaap_OtherLiabilitiesNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherLiabilitiesNoncurrent" xlink:to="us-gaap_OtherLiabilitiesNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherLiabilitiesNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Liabilities, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherLiabilitiesNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other noncurrent liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_OtherLiabilitiesNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Liabilities" xlink:label="us-gaap_Liabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_Liabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Liabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_Liabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommitmentsAndContingencies" xlink:label="us-gaap_CommitmentsAndContingencies" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommitmentsAndContingencies" xlink:to="us-gaap_CommitmentsAndContingencies_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commitments and Contingencies</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commitments and contingencies (Note 16)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityAbstract" xlink:label="us-gaap_TemporaryEquityAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityAbstract" xlink:to="us-gaap_TemporaryEquityAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TemporaryEquityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TemporaryEquityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Mezzanine equity</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount" xlink:to="us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redeemable Noncontrolling Interest, Equity, Carrying Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending balance, Mezzanine Equity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning balance, Mezzanine Equity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityAbstract" xlink:label="us-gaap_EquityAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityAbstract" xlink:to="us-gaap_EquityAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EquityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockholders' equity</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockValue" xlink:label="us-gaap_CommonStockValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockValue" xlink:to="us-gaap_CommonStockValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Value, Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock, $0.01 par value; 500,000 authorized shares; 96,872 and 84,600 shares issued and outstanding as of December 31, 2025 and 2024, respectively</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TreasuryStockCommonValue" xlink:label="us-gaap_TreasuryStockCommonValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TreasuryStockCommonValue" xlink:to="us-gaap_TreasuryStockCommonValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TreasuryStockCommonValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Treasury Stock, Common, Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_TreasuryStockCommonValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Treasury stock, shares at cost; 214 shares as of December 31, 2025 and 2024</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalPaidInCapital" xlink:label="us-gaap_AdditionalPaidInCapital" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdditionalPaidInCapital" xlink:to="us-gaap_AdditionalPaidInCapital_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional Paid in Capital</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional paid-in capital</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RetainedEarningsAccumulatedDeficit" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RetainedEarningsAccumulatedDeficit" xlink:to="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Retained Earnings (Accumulated Deficit)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Retained earnings</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquity" xlink:label="us-gaap_StockholdersEquity" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_StockholdersEquity_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity, Attributable to Parent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockholdersEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV's interest in BKV-BPP Power</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_StockholdersEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total stockholders' equity</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterest" xlink:label="us-gaap_MinorityInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MinorityInterest" xlink:to="us-gaap_MinorityInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MinorityInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity, Attributable to Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MinorityInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_MinorityInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling interest in BKV-BPP Power</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:to="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity, Including Portion Attributable to Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending balance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning balance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total equity</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAndStockholdersEquity" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities and Equity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total liabilities, mezzanine equity, and equity</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockParOrStatedValuePerShare" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockParOrStatedValuePerShare" xlink:to="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Par or Stated Value Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock par value (in USD per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesAuthorized" xlink:label="us-gaap_CommonStockSharesAuthorized" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockSharesAuthorized" xlink:to="us-gaap_CommonStockSharesAuthorized_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Shares Authorized</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock, authorized (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesIssued" xlink:label="us-gaap_CommonStockSharesIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockSharesIssued" xlink:to="us-gaap_CommonStockSharesIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Shares, Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock, issued (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesOutstanding" xlink:label="us-gaap_CommonStockSharesOutstanding" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockSharesOutstanding" xlink:to="us-gaap_CommonStockSharesOutstanding_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Shares, Outstanding</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending balance (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning balance (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock, outstanding (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TreasuryStockCommonShares" xlink:label="us-gaap_TreasuryStockCommonShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TreasuryStockCommonShares" xlink:to="us-gaap_TreasuryStockCommonShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TreasuryStockCommonShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Treasury Stock, Common, Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_TreasuryStockCommonShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending Balance (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_TreasuryStockCommonShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning Balance (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TreasuryStockCommonShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Treasury stock, at cost (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementAbstract" xlink:label="us-gaap_IncomeStatementAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeStatementAbstract" xlink:to="us-gaap_IncomeStatementAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeStatementAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Statement [Abstract]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProductOrServiceAxis" xlink:label="srt_ProductOrServiceAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProductOrServiceAxis" xlink:to="srt_ProductOrServiceAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProductOrServiceAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Product and Service [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ProductOrServiceAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Product and Service [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProductsAndServicesDomain" xlink:label="srt_ProductsAndServicesDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProductsAndServicesDomain" xlink:to="srt_ProductsAndServicesDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProductsAndServicesDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Product and Service [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ProductsAndServicesDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Product and Service [Domain]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_NaturalGasNGLAndOilMember" xlink:label="bkv_NaturalGasNGLAndOilMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_NaturalGasNGLAndOilMember" xlink:to="bkv_NaturalGasNGLAndOilMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_NaturalGasNGLAndOilMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural Gas, NGL, And Oil</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_NaturalGasNGLAndOilMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural Gas, NGL, And Oil [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_NaturalGasNGLAndOilMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural gas, NGL, and oil sales</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NaturalGasMidstreamMember" xlink:label="us-gaap_NaturalGasMidstreamMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NaturalGasMidstreamMember" xlink:to="us-gaap_NaturalGasMidstreamMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NaturalGasMidstreamMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural Gas, Midstream [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NaturalGasMidstreamMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Midstream revenues</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_PowerRevenuesMember" xlink:label="bkv_PowerRevenuesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_PowerRevenuesMember" xlink:to="bkv_PowerRevenuesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_PowerRevenuesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information relating to Power revenues.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_PowerRevenuesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Power Revenues [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_PowerRevenuesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Power revenues</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_MarketingMember" xlink:label="bkv_MarketingMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_MarketingMember" xlink:to="bkv_MarketingMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_MarketingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Marketing</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_MarketingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Marketing [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_MarketingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Marketing revenues</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_Section45QTaxCreditsMember" xlink:label="bkv_Section45QTaxCreditsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_Section45QTaxCreditsMember" xlink:to="bkv_Section45QTaxCreditsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_Section45QTaxCreditsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Section 45Q Tax Credits</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_Section45QTaxCreditsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Section 45Q Tax Credits [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_Section45QTaxCreditsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Section 45Q tax credits</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_OtherRevenueMember" xlink:label="bkv_OtherRevenueMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_OtherRevenueMember" xlink:to="bkv_OtherRevenueMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_OtherRevenueMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Revenue</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_OtherRevenueMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Revenue [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_OtherRevenueMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Revenue</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenuesAbstract" xlink:label="us-gaap_RevenuesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevenuesAbstract" xlink:to="us-gaap_RevenuesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RevenuesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenues [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RevenuesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenues and other operating income</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Revenues" xlink:label="us-gaap_Revenues" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Revenues" xlink:to="us-gaap_Revenues_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Revenues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenues</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_Revenues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total revenues, net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_Revenues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenues and other income</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeGainLossOnDerivativeNet" xlink:label="us-gaap_DerivativeGainLossOnDerivativeNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeGainLossOnDerivativeNet" xlink:to="us-gaap_DerivativeGainLossOnDerivativeNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeGainLossOnDerivativeNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative, Gain (Loss) on Derivative, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeGainLossOnDerivativeNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative gains (losses), net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DerivativeGainLossOnDerivativeNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative gains, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnSaleOfBusiness" xlink:label="us-gaap_GainLossOnSaleOfBusiness" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GainLossOnSaleOfBusiness" xlink:to="us-gaap_GainLossOnSaleOfBusiness_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GainLossOnSaleOfBusiness_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) on Disposition of Business</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_GainLossOnSaleOfBusiness_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on sale of business</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GainLossOnSaleOfBusiness_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on sale of business</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnSaleOfOtherAssets" xlink:label="us-gaap_GainLossOnSaleOfOtherAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GainLossOnSaleOfOtherAssets" xlink:to="us-gaap_GainLossOnSaleOfOtherAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GainLossOnSaleOfOtherAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) on Disposition of Other Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GainLossOnSaleOfOtherAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gains (losses) on sales of assets, net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_GainLossOnSaleOfOtherAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on sales of assets</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_RevenuesAndOtherOperatingIncome" xlink:label="bkv_RevenuesAndOtherOperatingIncome" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_RevenuesAndOtherOperatingIncome" xlink:to="bkv_RevenuesAndOtherOperatingIncome_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_RevenuesAndOtherOperatingIncome_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenues and Other Operating Income</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_RevenuesAndOtherOperatingIncome_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenues and Other Operating Income</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_RevenuesAndOtherOperatingIncome_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Corporate and Other revenues and other operating income</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="bkv_RevenuesAndOtherOperatingIncome_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total revenues and other operating income</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingExpensesAbstract" xlink:label="us-gaap_OperatingExpensesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingExpensesAbstract" xlink:to="us-gaap_OperatingExpensesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingExpensesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Expenses [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingExpensesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating expenses</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_LeaseOperatingAndWorkover" xlink:label="bkv_LeaseOperatingAndWorkover" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_LeaseOperatingAndWorkover" xlink:to="bkv_LeaseOperatingAndWorkover_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_LeaseOperatingAndWorkover_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lease Operating And Workover</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_LeaseOperatingAndWorkover_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lease Operating And Workover</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_LeaseOperatingAndWorkover_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lease operating and workover</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_FuelCommodityCosts" xlink:label="bkv_FuelCommodityCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_FuelCommodityCosts" xlink:to="bkv_FuelCommodityCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_FuelCommodityCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fuel commodity costs incurred that are directly related to goods produced and sold and services rendered during the reporting period.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_FuelCommodityCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fuel commodity costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_FuelCommodityCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fuel commodity costs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UtilitiesOperatingExpensePurchasedPower" xlink:label="us-gaap_UtilitiesOperatingExpensePurchasedPower" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_UtilitiesOperatingExpensePurchasedPower" xlink:to="us-gaap_UtilitiesOperatingExpensePurchasedPower_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_UtilitiesOperatingExpensePurchasedPower_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Utilities Operating Expense, Purchased Power</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_UtilitiesOperatingExpensePurchasedPower_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchased power</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TaxesExcludingIncomeAndExciseTaxes" xlink:label="us-gaap_TaxesExcludingIncomeAndExciseTaxes" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TaxesExcludingIncomeAndExciseTaxes" xlink:to="us-gaap_TaxesExcludingIncomeAndExciseTaxes_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TaxesExcludingIncomeAndExciseTaxes_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Taxes, Miscellaneous</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TaxesExcludingIncomeAndExciseTaxes_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Taxes other than income</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_GatheringAndTransportationCosts" xlink:label="bkv_GatheringAndTransportationCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_GatheringAndTransportationCosts" xlink:to="bkv_GatheringAndTransportationCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_UtilitiesOperatingExpenseMaintenanceOperationsAndOtherCostsAndExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Utilities Operating Expense, Maintenance, Operations, and Other Costs and Expenses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_UtilitiesOperatingExpenseMaintenanceOperationsAndOtherCostsAndExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Power operating and maintenance</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">General and Administrative Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Corporate and Other general and administrative</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">General and administrative</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherGeneralExpense" xlink:to="us-gaap_OtherGeneralExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_OtherGeneralExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Corporate and Other other operating expenses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherGeneralExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other operating expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingExpenses" xlink:label="us-gaap_OperatingExpenses" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Expenses</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Income (Loss)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income (loss) from operations</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherIncomeAndExpensesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Income and Expenses [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherIncomeAndExpensesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other income (expense)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1" xlink:label="us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Contingent Consideration, Change in Contingent Consideration, Liability, Increase (Decrease)</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseNonoperating" xlink:label="us-gaap_InterestExpenseNonoperating" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InterestExpenseNonoperating_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Expense, Nonoperating</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_InterestExpenseNonoperating_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest expense, net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_InterestExpenseNonoperating_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest expense</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeInterest" xlink:label="us-gaap_InvestmentIncomeInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentIncomeInterest" xlink:to="us-gaap_InvestmentIncomeInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InvestmentIncomeInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment Income, Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InvestmentIncomeInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest income</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on early extinguishment of debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on early extinguishment of debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on extinguishment of debt</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherNonoperatingIncome" xlink:label="us-gaap_OtherNonoperatingIncome" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherNonoperatingIncome_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Nonoperating Income</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherNonoperatingIncome_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other income</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income (loss) before income taxes</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income tax benefit (expense)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income tax expense (benefit)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProfitLoss" xlink:label="us-gaap_ProfitLoss" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProfitLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net income (loss)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_ProfitLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net income (loss)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ProfitLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net income (loss)</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less: net income attributable to noncontrolling interest</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EarningsPerShareAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Earnings Per Share [Abstract]</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerShareBasic" xlink:to="us-gaap_EarningsPerShareBasic_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Earnings Per Share, Basic</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Basic (in USD per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareDiluted" xlink:label="us-gaap_EarningsPerShareDiluted" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerShareDiluted" xlink:to="us-gaap_EarningsPerShareDiluted_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Earnings Per Share, Diluted</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Diluted (in USD per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract" xlink:to="us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted Average Number of Shares Outstanding, Diluted [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted average number of common shares outstanding:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:to="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted Average Number of Shares Outstanding, Basic</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Basic (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Basic weighted average common shares outstanding (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted Average Number of Shares Outstanding, Diluted</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Diluted (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Diluted weighted average of common shares outstanding (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfCashFlowsAbstract" xlink:label="us-gaap_StatementOfCashFlowsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementOfCashFlowsAbstract" xlink:to="us-gaap_StatementOfCashFlowsAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementOfCashFlowsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Statement of Cash Flows [Abstract]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditFacilityAxis" xlink:label="us-gaap_CreditFacilityAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CreditFacilityAxis" xlink:to="us-gaap_CreditFacilityAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CreditFacilityAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Credit Facility [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CreditFacilityAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Credit Facility [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditFacilityDomain" xlink:label="us-gaap_CreditFacilityDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CreditFacilityDomain" xlink:to="us-gaap_CreditFacilityDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CreditFacilityDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Credit Facility [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CreditFacilityDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Credit Facility [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevolvingCreditFacilityMember" xlink:label="us-gaap_RevolvingCreditFacilityMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevolvingCreditFacilityMember" xlink:to="us-gaap_RevolvingCreditFacilityMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RevolvingCreditFacilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revolving Credit Facility [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RevolvingCreditFacilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revolving Facility</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_RevolvingCreditFacilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temple Revolving Facility</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TempleTermLoanFacilityMember" xlink:label="bkv_TempleTermLoanFacilityMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_TempleTermLoanFacilityMember" xlink:to="bkv_TempleTermLoanFacilityMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TempleTermLoanFacilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temple Term Loan Facility</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_TempleTermLoanFacilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temple Term Loan Facility [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_TempleTermLoanFacilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temple Term Loan Facility</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash flows from operating activities:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustments to reconcile net income (loss) to net cash provided by operating activities:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DepreciationDepletionAndAmortization" xlink:label="us-gaap_DepreciationDepletionAndAmortization" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DepreciationDepletionAndAmortization" xlink:to="us-gaap_DepreciationDepletionAndAmortization_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DepreciationDepletionAndAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Depreciation, Depletion and Amortization</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DepreciationDepletionAndAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Depreciation, depletion, amortization, and accretion</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensation" xlink:label="us-gaap_ShareBasedCompensation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensation" xlink:to="us-gaap_ShareBasedCompensation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Payment Arrangement, Noncash Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity-based compensation expense</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:to="us-gaap_DeferredIncomeTaxExpenseBenefit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Income Tax Expense (Benefit)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred income tax expense (benefit)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total deferred income tax expense (benefit)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrealizedGainLossOnDerivatives" xlink:label="us-gaap_UnrealizedGainLossOnDerivatives" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_UnrealizedGainLossOnDerivatives_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unrealized Gain (Loss) on Derivatives</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_UnrealizedGainLossOnDerivatives_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unrealized (gains) losses on derivatives, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentForContingentConsiderationLiabilityOperatingActivities" xlink:label="us-gaap_PaymentForContingentConsiderationLiabilityOperatingActivities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentForContingentConsiderationLiabilityOperatingActivities" xlink:to="us-gaap_PaymentForContingentConsiderationLiabilityOperatingActivities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentForContingentConsiderationLiabilityOperatingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payment for Contingent Consideration Liability, Operating Activities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_PaymentForContingentConsiderationLiabilityOperatingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement of contingent consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PaymentForContingentConsiderationLiabilityOperatingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement of contingent consideration</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_PaymentsForThePurchaseOfPutOptions" xlink:label="bkv_PaymentsForThePurchaseOfPutOptions" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_PaymentsForThePurchaseOfPutOptions" xlink:to="bkv_PaymentsForThePurchaseOfPutOptions_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_PaymentsForThePurchaseOfPutOptions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments For The Purchase Of Put Options</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_PaymentsForThePurchaseOfPutOptions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments For The Purchase Of Put Options</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="bkv_PaymentsForThePurchaseOfPutOptions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments for the purchase of put options</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ProceedsFromCallOptionSales" xlink:label="bkv_ProceedsFromCallOptionSales" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ProceedsFromCallOptionSales" xlink:to="bkv_ProceedsFromCallOptionSales_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ProceedsFromCallOptionSales_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds From Call Option Sales</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ProceedsFromCallOptionSales_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds From Call Option Sales</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ProceedsFromCallOptionSales_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from the sale of call options</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalizedComputerSoftwareImpairments1" xlink:label="us-gaap_CapitalizedComputerSoftwareImpairments1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CapitalizedComputerSoftwareImpairments1" xlink:to="us-gaap_CapitalizedComputerSoftwareImpairments1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CapitalizedComputerSoftwareImpairments1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capitalized Computer Software, Impairments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CapitalizedComputerSoftwareImpairments1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Write-off of capitalized software costs</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_GainLossOnSaleOfAssets" xlink:label="bkv_GainLossOnSaleOfAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_GainLossOnSaleOfAssets" xlink:to="bkv_GainLossOnSaleOfAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_GainLossOnSaleOfAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of gain (loss) on sale or disposal of assets, including but not limited to property, plant, and equipment; intangible assets; and equity in securities of subsidiaries or equity method investee.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_GainLossOnSaleOfAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) On Sale Of Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="bkv_GainLossOnSaleOfAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">(Gains) losses on sale of assets, net</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_GainLossOnDispositionOfAssetsTransactionCosts" xlink:label="bkv_GainLossOnDispositionOfAssetsTransactionCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_GainLossOnDispositionOfAssetsTransactionCosts" xlink:to="bkv_GainLossOnDispositionOfAssetsTransactionCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_GainLossOnDispositionOfAssetsTransactionCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) On Disposition Of Assets, Transaction Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_GainLossOnDispositionOfAssetsTransactionCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) On Disposition Of Assets, Transaction Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_GainLossOnDispositionOfAssetsTransactionCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Transaction costs from sale of business</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherNoncashIncomeExpense" xlink:label="us-gaap_OtherNoncashIncomeExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherNoncashIncomeExpense" xlink:to="us-gaap_OtherNoncashIncomeExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherNoncashIncomeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Noncash Income (Expense)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_OtherNoncashIncomeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:to="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity, Increase (Decrease) in Operating Capital [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Changes in operating assets and liabilities:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:to="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Accounts Receivable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts receivable, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInAccountsReceivableRelatedParties" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivableRelatedParties" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInAccountsReceivableRelatedParties" xlink:to="us-gaap_IncreaseDecreaseInAccountsReceivableRelatedParties_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivableRelatedParties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Accounts Receivable, Related Parties</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivableRelatedParties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts receivable, related party</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:to="us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Accounts Payable and Accrued Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts payable and accrued liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:label="us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:to="us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Other Operating Assets and Liabilities, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other changes in operating assets and liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net cash provided by operating activities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net cash provided by operating activities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash flows from investing activities:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireOtherProductiveAssets" xlink:label="us-gaap_PaymentsToAcquireOtherProductiveAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToAcquireOtherProductiveAssets" xlink:to="us-gaap_PaymentsToAcquireOtherProductiveAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsToAcquireOtherProductiveAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to Acquire Other Productive Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_PaymentsToAcquireOtherProductiveAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset acquisition</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_CashAcquiredFromJointVentureFormation" xlink:label="bkv_CashAcquiredFromJointVentureFormation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_CashAcquiredFromJointVentureFormation" xlink:to="bkv_CashAcquiredFromJointVentureFormation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_CashAcquiredFromJointVentureFormation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash Acquired From Joint Venture Formation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_CashAcquiredFromJointVentureFormation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash Acquired From Joint Venture Formation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_CashAcquiredFromJointVentureFormation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash acquired in consolidation of BKV-BPP Cotton Cove</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:to="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to Acquire Property, Plant, and Equipment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capital expenditures</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromDivestitureOfBusinesses" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinesses" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromDivestitureOfBusinesses" xlink:to="us-gaap_ProceedsFromDivestitureOfBusinesses_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinesses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Divestiture of Businesses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinesses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from sale of business</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleOfOilAndGasPropertyAndEquipment" xlink:label="us-gaap_ProceedsFromSaleOfOilAndGasPropertyAndEquipment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromSaleOfOilAndGasPropertyAndEquipment" xlink:to="us-gaap_ProceedsFromSaleOfOilAndGasPropertyAndEquipment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromSaleOfOilAndGasPropertyAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Sale of Oil and Gas Property and Equipment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromSaleOfOilAndGasPropertyAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from sales of assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromInsuranceSettlementInvestingActivities" xlink:label="us-gaap_ProceedsFromInsuranceSettlementInvestingActivities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromInsuranceSettlementInvestingActivities" xlink:to="us-gaap_ProceedsFromInsuranceSettlementInvestingActivities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromInsuranceSettlementInvestingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Insurance Settlement, Investing Activities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromInsuranceSettlementInvestingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from insurance claim</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:label="us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_PaymentsForProceedsFromOtherInvestingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other investing activities, net</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromIssuanceInitialPublicOffering" xlink:label="us-gaap_ProceedsFromIssuanceInitialPublicOffering" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromIssuanceInitialPublicOffering" xlink:to="us-gaap_ProceedsFromIssuanceInitialPublicOffering_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromIssuanceInitialPublicOffering_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Issuance Initial Public Offering</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromIssuanceInitialPublicOffering_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from issuance of common stock in initial public offering, net of underwriting discounts and commissions</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:to="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Issuance of Common Stock</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from issuance of common stock, net of underwriting discounts and commissions</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt" xlink:label="us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt" xlink:to="us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Issuance of Other Long-Term Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds on long-term debt</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfDebtIssuanceCosts" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsOfDebtIssuanceCosts" xlink:to="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments of Debt Issuance Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payment of debt issuance costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payment of debt issuance costs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RepaymentsOfLinesOfCredit" xlink:label="us-gaap_RepaymentsOfLinesOfCredit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RepaymentsOfLinesOfCredit" xlink:to="us-gaap_RepaymentsOfLinesOfCredit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RepaymentsOfLinesOfCredit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments of Lines of Credit</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_RepaymentsOfLinesOfCredit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments on Temple Term Loan Facility</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RepaymentsOfSeniorDebt" xlink:label="us-gaap_RepaymentsOfSeniorDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RepaymentsOfSeniorDebt" xlink:to="us-gaap_RepaymentsOfSeniorDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RepaymentsOfSeniorDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments of Senior Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_RepaymentsOfSeniorDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments on Temple I Loan Agreements</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromIssuanceOfSecuredDebt" xlink:label="us-gaap_ProceedsFromIssuanceOfSecuredDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromIssuanceOfSecuredDebt" xlink:to="us-gaap_ProceedsFromIssuanceOfSecuredDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromIssuanceOfSecuredDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Issuance of Secured Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromIssuanceOfSecuredDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds under RBL Credit Agreement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RepaymentsOfSecuredDebt" xlink:label="us-gaap_RepaymentsOfSecuredDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RepaymentsOfSecuredDebt" xlink:to="us-gaap_RepaymentsOfSecuredDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RepaymentsOfSecuredDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments of Secured Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_RepaymentsOfSecuredDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments on RBL Credit Agreement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RepaymentsOfUnsecuredDebt" xlink:label="us-gaap_RepaymentsOfUnsecuredDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RepaymentsOfUnsecuredDebt" xlink:to="us-gaap_RepaymentsOfUnsecuredDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RepaymentsOfUnsecuredDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments of Unsecured Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_RepaymentsOfUnsecuredDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payment on term loan agreement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RepaymentsOfNotesPayable" xlink:label="us-gaap_RepaymentsOfNotesPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RepaymentsOfNotesPayable" xlink:to="us-gaap_RepaymentsOfNotesPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RepaymentsOfNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments of Notes Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_RepaymentsOfNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments on notes payable to related party</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RepaymentsOfNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from sales of assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_RepaymentsOfNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments of notes payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromNotesPayable" xlink:label="us-gaap_ProceedsFromNotesPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromNotesPayable" xlink:to="us-gaap_ProceedsFromNotesPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Notes Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from notes payable from related party</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromRelatedPartyDebt" xlink:label="us-gaap_ProceedsFromRelatedPartyDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromRelatedPartyDebt" xlink:to="us-gaap_ProceedsFromRelatedPartyDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromRelatedPartyDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Related Party Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromRelatedPartyDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds on Power Plant Loan</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RepaymentsOfRelatedPartyDebt" xlink:label="us-gaap_RepaymentsOfRelatedPartyDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RepaymentsOfRelatedPartyDebt" xlink:to="us-gaap_RepaymentsOfRelatedPartyDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RepaymentsOfRelatedPartyDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments of Related Party Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_RepaymentsOfRelatedPartyDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payment on Power Plant Loan</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromLongTermLinesOfCredit" xlink:label="us-gaap_ProceedsFromLongTermLinesOfCredit" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromLongTermLinesOfCredit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Long-Term Lines of Credit</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromLongTermLinesOfCredit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from draws on credit facilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RepaymentsOfLongTermLinesOfCredit" xlink:label="us-gaap_RepaymentsOfLongTermLinesOfCredit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RepaymentsOfLongTermLinesOfCredit" xlink:to="us-gaap_RepaymentsOfLongTermLinesOfCredit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RepaymentsOfLongTermLinesOfCredit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments of Long-Term Lines of Credit</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_RepaymentsOfLongTermLinesOfCredit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments on credit facilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfStockIssuanceCosts" xlink:label="us-gaap_PaymentsOfStockIssuanceCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsOfStockIssuanceCosts" xlink:to="us-gaap_PaymentsOfStockIssuanceCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsOfStockIssuanceCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments of Stock Issuance Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_PaymentsOfStockIssuanceCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments of deferred offering costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PaymentsOfStockIssuanceCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments of stock issuance costs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfDebtExtinguishmentCosts" xlink:label="us-gaap_PaymentsOfDebtExtinguishmentCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsOfDebtExtinguishmentCosts" xlink:to="us-gaap_PaymentsOfDebtExtinguishmentCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsOfDebtExtinguishmentCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payment for Debt Extinguishment or Debt Prepayment Cost</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_PaymentsOfDebtExtinguishmentCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt extinguishment costs</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_PaymentsForDistributionToNoncontrollingInterests" xlink:label="bkv_PaymentsForDistributionToNoncontrollingInterests" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_PaymentsForDistributionToNoncontrollingInterests" xlink:to="bkv_PaymentsForDistributionToNoncontrollingInterests_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_PaymentsForDistributionToNoncontrollingInterests_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash outflow for distributions to noncontrolling interests.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_PaymentsForDistributionToNoncontrollingInterests_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments for Distribution To Noncontrolling Interests</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="bkv_PaymentsForDistributionToNoncontrollingInterests_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distributions to noncontrolling interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:label="us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:to="us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payment, Tax Withholding, Share-Based Payment Arrangement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net share settlements, equity-based compensation</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToMinorityShareholders" xlink:label="us-gaap_PaymentsToMinorityShareholders" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToMinorityShareholders" xlink:to="us-gaap_PaymentsToMinorityShareholders_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsToMinorityShareholders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to Noncontrolling Interests</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_PaymentsToMinorityShareholders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash distributions to noncontrolling interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromMinorityShareholders" xlink:label="us-gaap_ProceedsFromMinorityShareholders" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromMinorityShareholders" xlink:to="us-gaap_ProceedsFromMinorityShareholders_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromMinorityShareholders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Noncontrolling Interests</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromMinorityShareholders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash contributions from noncontrolling interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:label="us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:to="us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from (Payment for) Other Financing Activity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other financing activities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net cash provided by (used in) financing activities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect" xlink:to="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Excluding Exchange Rate Effect, Including Discontinued Operation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net increase (decrease) in cash, cash equivalents, and restricted cash</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash, cash equivalents, and restricted cash, beginning of period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total cash, cash equivalents, and restricted cash</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash, cash equivalents, and restricted cash, end of period</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SupplementalCashFlowInformationAbstract" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SupplementalCashFlowInformationAbstract" xlink:to="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Supplemental Cash Flow Information [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash payments for:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestPaidNet" xlink:label="us-gaap_InterestPaidNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestPaidNet" xlink:to="us-gaap_InterestPaidNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InterestPaidNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Paid, Excluding Capitalized Interest, Operating Activity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InterestPaidNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxesPaidNet" xlink:label="us-gaap_IncomeTaxesPaidNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxesPaidNet" xlink:to="us-gaap_IncomeTaxesPaidNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Taxes Paid, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income tax</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income tax</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:label="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:to="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash Flow, Noncash Investing and Financing Activities Disclosure [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-cash investing and financing activities:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssued1" xlink:label="us-gaap_StockIssued1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssued1" xlink:to="us-gaap_StockIssued1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssued1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssued1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity issued as consideration for acquisition</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ConversionOfMezzanineEquityToCommonStockUponInitialPublicOffering" xlink:label="bkv_ConversionOfMezzanineEquityToCommonStockUponInitialPublicOffering" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ConversionOfMezzanineEquityToCommonStockUponInitialPublicOffering" xlink:to="bkv_ConversionOfMezzanineEquityToCommonStockUponInitialPublicOffering_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ConversionOfMezzanineEquityToCommonStockUponInitialPublicOffering_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion Of Mezzanine Equity To Common Stock Upon Initial Public Offering</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ConversionOfMezzanineEquityToCommonStockUponInitialPublicOffering_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion Of Mezzanine Equity To Common Stock Upon Initial Public Offering</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ConversionOfMezzanineEquityToCommonStockUponInitialPublicOffering_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion of mezzanine equity to common stock upon initial public offering</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ConversionOfEquityBasedCompensationToCommonStockUponInitialPublicOffering" xlink:label="bkv_ConversionOfEquityBasedCompensationToCommonStockUponInitialPublicOffering" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ConversionOfEquityBasedCompensationToCommonStockUponInitialPublicOffering" xlink:to="bkv_ConversionOfEquityBasedCompensationToCommonStockUponInitialPublicOffering_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ConversionOfEquityBasedCompensationToCommonStockUponInitialPublicOffering_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion Of Equity-Based Compensation To Common Stock Upon Initial Public Offering</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ConversionOfEquityBasedCompensationToCommonStockUponInitialPublicOffering_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion Of Equity-Based Compensation To Common Stock Upon Initial Public Offering</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ConversionOfEquityBasedCompensationToCommonStockUponInitialPublicOffering_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Conversion of equity-based compensation to common stock upon initial public offering</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_IncomeTaxDeconsolidation" xlink:label="bkv_IncomeTaxDeconsolidation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_IncomeTaxDeconsolidation" xlink:to="bkv_IncomeTaxDeconsolidation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_IncomeTaxDeconsolidation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Tax Deconsolidation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_IncomeTaxDeconsolidation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Tax Deconsolidation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_IncomeTaxDeconsolidation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income tax deconsolidation</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ReclassificationOfDeferredOfferingCosts" xlink:label="bkv_ReclassificationOfDeferredOfferingCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ReclassificationOfDeferredOfferingCosts" xlink:to="bkv_ReclassificationOfDeferredOfferingCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ReclassificationOfDeferredOfferingCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reclassification Of Deferred Offering Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ReclassificationOfDeferredOfferingCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reclassification Of Deferred Offering Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ReclassificationOfDeferredOfferingCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reclassification of deferred offering costs to additional paid-in capital upon initial public offering</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ChangeInExpendituresIncurredButNotYetPaid" xlink:label="bkv_ChangeInExpendituresIncurredButNotYetPaid" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ChangeInExpendituresIncurredButNotYetPaid" xlink:to="bkv_ChangeInExpendituresIncurredButNotYetPaid_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetRetirementObligationLiabilitiesIncurred" xlink:label="us-gaap_AssetRetirementObligationLiabilitiesIncurred" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetRetirementObligationLiabilitiesIncurred" xlink:to="us-gaap_AssetRetirementObligationLiabilitiesIncurred_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetRetirementObligationLiabilitiesIncurred_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Retirement Obligation, Liabilities Incurred</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetRetirementObligationLiabilitiesIncurred_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities incurred</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AssetRetirementObligationLiabilitiesIncurred_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additions to asset retirement obligations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:to="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Right-of-Use Asset Obtained in Exchange for Operating Lease Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lease liabilities arising from obtaining right-of-use assets</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_IncreaseDecreaseInAccruedOfferingCosts" xlink:label="bkv_IncreaseDecreaseInAccruedOfferingCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_IncreaseDecreaseInAccruedOfferingCosts" xlink:to="bkv_IncreaseDecreaseInAccruedOfferingCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_IncreaseDecreaseInAccruedOfferingCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) In Accrued Offering Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_IncreaseDecreaseInAccruedOfferingCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) In Accrued Offering Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_IncreaseDecreaseInAccruedOfferingCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (decrease) in accrued equity transaction costs</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_AdjustmentOfMinorityOwnershipPuttableSharesToRedemptionValue" xlink:label="bkv_AdjustmentOfMinorityOwnershipPuttableSharesToRedemptionValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_AdjustmentOfMinorityOwnershipPuttableSharesToRedemptionValue" xlink:to="bkv_AdjustmentOfMinorityOwnershipPuttableSharesToRedemptionValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_AdjustmentOfMinorityOwnershipPuttableSharesToRedemptionValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustment Of Minority Ownership Puttable Shares To Redemption Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AdjustmentOfMinorityOwnershipPuttableSharesToRedemptionValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustment Of Minority Ownership Puttable Shares To Redemption Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_AdjustmentOfMinorityOwnershipPuttableSharesToRedemptionValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustment of minority ownership puttable shares to redemption value</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_AdjustmentOfEquityBasedCompensationToRedemptionValue" xlink:label="bkv_AdjustmentOfEquityBasedCompensationToRedemptionValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_AdjustmentOfEquityBasedCompensationToRedemptionValue" xlink:to="bkv_AdjustmentOfEquityBasedCompensationToRedemptionValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_AdjustmentOfEquityBasedCompensationToRedemptionValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustment Of Equity-Based Compensation To Redemption Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AdjustmentOfEquityBasedCompensationToRedemptionValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustment Of Equity-Based Compensation To Redemption Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_AdjustmentOfEquityBasedCompensationToRedemptionValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustment of equity-based compensation to redemption value</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_RedemptionOfSharesIssuedInSettlementOfEquityBasedCompensationImpact" xlink:label="bkv_RedemptionOfSharesIssuedInSettlementOfEquityBasedCompensationImpact" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_RedemptionOfSharesIssuedInSettlementOfEquityBasedCompensationImpact" xlink:to="bkv_RedemptionOfSharesIssuedInSettlementOfEquityBasedCompensationImpact_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_RedemptionOfSharesIssuedInSettlementOfEquityBasedCompensationImpact_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption of Shares Issued In Settlement of Equity-based Compensation Impact</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_RedemptionOfSharesIssuedInSettlementOfEquityBasedCompensationImpact_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption of Shares Issued In Settlement of Equity-based Compensation Impact</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_RedemptionOfSharesIssuedInSettlementOfEquityBasedCompensationImpact_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Impact of redemption of shares issued in settlement of equity-based compensation and other on additional paid-in capital, common stock, and treasury stock</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment" xlink:label="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment" xlink:to="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Accretion to Redemption Value, Adjustment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accretion of Class B Units to redemption value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accretion of Class B Units to redemption value</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TemporaryEquityDistributionPayable" xlink:label="bkv_TemporaryEquityDistributionPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_TemporaryEquityDistributionPayable" xlink:to="bkv_TemporaryEquityDistributionPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TemporaryEquityDistributionPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Distribution Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_TemporaryEquityDistributionPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Distribution Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_TemporaryEquityDistributionPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distributions payable to noncontrolling interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfStockholdersEquityAbstract" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="us-gaap_StatementOfStockholdersEquityAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Statement of Stockholders' Equity [Abstract]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementEquityComponentsAxis" xlink:label="us-gaap_StatementEquityComponentsAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementEquityComponentsAxis" xlink:to="us-gaap_StatementEquityComponentsAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementEquityComponentsAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Components [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StatementEquityComponentsAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Components [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityComponentDomain" xlink:label="us-gaap_EquityComponentDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityComponentDomain" xlink:to="us-gaap_EquityComponentDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityComponentDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Component [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EquityComponentDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Component [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockMember" xlink:label="us-gaap_CommonStockMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockMember" xlink:to="us-gaap_CommonStockMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CommonStockMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TreasuryStockCommonMember" xlink:label="us-gaap_TreasuryStockCommonMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TreasuryStockCommonMember" xlink:to="us-gaap_TreasuryStockCommonMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TreasuryStockCommonMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Treasury Stock, Common [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TreasuryStockCommonMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Treasury</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalPaidInCapitalMember" xlink:label="us-gaap_AdditionalPaidInCapitalMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdditionalPaidInCapitalMember" xlink:to="us-gaap_AdditionalPaidInCapitalMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional Paid-in Capital [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional Paid-In Capital</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RetainedEarningsMember" xlink:label="us-gaap_RetainedEarningsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RetainedEarningsMember" xlink:to="us-gaap_RetainedEarningsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RetainedEarningsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Retained Earnings [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RetainedEarningsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Retained Earnings</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoncontrollingInterestMember" xlink:label="us-gaap_NoncontrollingInterestMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NoncontrollingInterestMember" xlink:to="us-gaap_NoncontrollingInterestMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NoncontrollingInterestMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling Interest [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NoncontrollingInterestMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling Interest</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TemporaryEquityComponentsAxis" xlink:label="bkv_TemporaryEquityComponentsAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_TemporaryEquityComponentsAxis" xlink:to="bkv_TemporaryEquityComponentsAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TemporaryEquityComponentsAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity Components</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_TemporaryEquityComponentsAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity Components [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_TemporaryEquityComponentsAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity Components [Axis]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TemporaryEquityComponentsDomain" xlink:label="bkv_TemporaryEquityComponentsDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_TemporaryEquityComponentsDomain" xlink:to="bkv_TemporaryEquityComponentsDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TemporaryEquityComponentsDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity Components [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_TemporaryEquityComponentsDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity Components [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_TemporaryEquityComponentsDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity Components [Domain]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_EquityBasedCompensationMember" xlink:label="bkv_EquityBasedCompensationMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_EquityBasedCompensationMember" xlink:to="bkv_EquityBasedCompensationMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_EquityBasedCompensationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity-Based Compensation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_EquityBasedCompensationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity-Based Compensation [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_EquityBasedCompensationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity-Based Compensation</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:label="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Stockholders' Equity [Roll Forward]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_NetIncomeLossIncludingPortionAttributableToNoncontrollingInterestExcludingTemporaryEquityNetIncome" xlink:label="bkv_NetIncomeLossIncludingPortionAttributableToNoncontrollingInterestExcludingTemporaryEquityNetIncome" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_NetIncomeLossIncludingPortionAttributableToNoncontrollingInterestExcludingTemporaryEquityNetIncome" xlink:to="bkv_NetIncomeLossIncludingPortionAttributableToNoncontrollingInterestExcludingTemporaryEquityNetIncome_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_NetIncomeLossIncludingPortionAttributableToNoncontrollingInterestExcludingTemporaryEquityNetIncome_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The consolidated profit or loss for the period, net of income taxes, including the portion attributable to the noncontrolling interest.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_NetIncomeLossIncludingPortionAttributableToNoncontrollingInterestExcludingTemporaryEquityNetIncome_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest Excluding Temporary Equity Net Income</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_NetIncomeLossIncludingPortionAttributableToNoncontrollingInterestExcludingTemporaryEquityNetIncome_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net income (loss)</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_RedemptionOfCommonStockIssuedUponVestingOfEquityBasedCompensationShares" xlink:label="bkv_RedemptionOfCommonStockIssuedUponVestingOfEquityBasedCompensationShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_RedemptionOfCommonStockIssuedUponVestingOfEquityBasedCompensationShares" xlink:to="bkv_RedemptionOfCommonStockIssuedUponVestingOfEquityBasedCompensationShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_RedemptionOfCommonStockIssuedUponVestingOfEquityBasedCompensationShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption Of Common Stock Issued Upon Vesting Of Equity-based Compensation, Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_RedemptionOfCommonStockIssuedUponVestingOfEquityBasedCompensationShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption Of Common Stock Issued Upon Vesting Of Equity-based Compensation, Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_RedemptionOfCommonStockIssuedUponVestingOfEquityBasedCompensationShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption of common stock issued upon vesting of equity-based compensation (in shares)</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_RedemptionOfCommonStockIssuedUponVestingOfEquityBasedCompensation" xlink:label="bkv_RedemptionOfCommonStockIssuedUponVestingOfEquityBasedCompensation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_RedemptionOfCommonStockIssuedUponVestingOfEquityBasedCompensation" xlink:to="bkv_RedemptionOfCommonStockIssuedUponVestingOfEquityBasedCompensation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_RedemptionOfCommonStockIssuedUponVestingOfEquityBasedCompensation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption of Common Stock Issued Upon Vesting of Equity-based Compensation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_RedemptionOfCommonStockIssuedUponVestingOfEquityBasedCompensation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption of Common Stock Issued Upon Vesting of Equity-based Compensation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_RedemptionOfCommonStockIssuedUponVestingOfEquityBasedCompensation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption of common stock issued upon vesting of equity-based compensation</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_AdjustmentsToAdditionalPaidInCapitalAdjustmentOfMinorityOwnershipPuttableSharesToRedemptionValue" xlink:label="bkv_AdjustmentsToAdditionalPaidInCapitalAdjustmentOfMinorityOwnershipPuttableSharesToRedemptionValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_AdjustmentsToAdditionalPaidInCapitalAdjustmentOfMinorityOwnershipPuttableSharesToRedemptionValue" xlink:to="bkv_AdjustmentsToAdditionalPaidInCapitalAdjustmentOfMinorityOwnershipPuttableSharesToRedemptionValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_AdjustmentsToAdditionalPaidInCapitalAdjustmentOfMinorityOwnershipPuttableSharesToRedemptionValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustments To Additional Paid In Capital, Adjustment Of Minority Ownership Puttable Shares To Redemption Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AdjustmentsToAdditionalPaidInCapitalAdjustmentOfMinorityOwnershipPuttableSharesToRedemptionValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustments To Additional Paid In Capital, Adjustment Of Minority Ownership Puttable Shares To Redemption Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_AdjustmentsToAdditionalPaidInCapitalAdjustmentOfMinorityOwnershipPuttableSharesToRedemptionValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustment of minority ownership puttable shares to redemption value</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_AdjustmentsToAdditionalPaidInCapitalAdjustmentOfEquityBasedCompensationToRedemptionValue" xlink:label="bkv_AdjustmentsToAdditionalPaidInCapitalAdjustmentOfEquityBasedCompensationToRedemptionValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_AdjustmentsToAdditionalPaidInCapitalAdjustmentOfEquityBasedCompensationToRedemptionValue" xlink:to="bkv_AdjustmentsToAdditionalPaidInCapitalAdjustmentOfEquityBasedCompensationToRedemptionValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_AdjustmentsToAdditionalPaidInCapitalAdjustmentOfEquityBasedCompensationToRedemptionValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustments To Additional Paid In Capital, Adjustment Of Equity Based Compensation To Redemption Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AdjustmentsToAdditionalPaidInCapitalAdjustmentOfEquityBasedCompensationToRedemptionValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustments To Additional Paid In Capital, Adjustment Of Equity Based Compensation To Redemption Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_AdjustmentsToAdditionalPaidInCapitalAdjustmentOfEquityBasedCompensationToRedemptionValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustment of equity-based compensation to redemption value</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoncontrollingInterestIncreaseFromSubsidiaryEquityIssuance" xlink:label="us-gaap_NoncontrollingInterestIncreaseFromSubsidiaryEquityIssuance" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NoncontrollingInterestIncreaseFromSubsidiaryEquityIssuance" xlink:to="us-gaap_NoncontrollingInterestIncreaseFromSubsidiaryEquityIssuance_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NoncontrollingInterestIncreaseFromSubsidiaryEquityIssuance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling Interest, Increase from Subsidiary Equity Issuance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NoncontrollingInterestIncreaseFromSubsidiaryEquityIssuance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contributions from noncontrolling interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoncontrollingInterestDecreaseFromDeconsolidation" xlink:label="us-gaap_NoncontrollingInterestDecreaseFromDeconsolidation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NoncontrollingInterestDecreaseFromDeconsolidation" xlink:to="us-gaap_NoncontrollingInterestDecreaseFromDeconsolidation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NoncontrollingInterestDecreaseFromDeconsolidation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling Interest, Decrease from Deconsolidation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_NoncontrollingInterestDecreaseFromDeconsolidation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Changes due to consolidation of BKV-BPP Cotton Cove</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_AccretionToRedemptionValue" xlink:label="bkv_AccretionToRedemptionValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_AccretionToRedemptionValue" xlink:to="bkv_AccretionToRedemptionValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_AccretionToRedemptionValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accretion To Redemption Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AccretionToRedemptionValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accretion To Redemption Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_AccretionToRedemptionValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accretion of Class B Units to redemption value</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_StockRedeemedDuringPeriodSharesEmployeeStockPurchasePlan" xlink:label="bkv_StockRedeemedDuringPeriodSharesEmployeeStockPurchasePlan" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_StockRedeemedDuringPeriodSharesEmployeeStockPurchasePlan" xlink:to="bkv_StockRedeemedDuringPeriodSharesEmployeeStockPurchasePlan_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_StockRedeemedDuringPeriodSharesEmployeeStockPurchasePlan_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Redeemed During Period, Shares, Employee Stock Purchase Plan</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_StockRedeemedDuringPeriodSharesEmployeeStockPurchasePlan_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Redeemed During Period, Shares, Employee Stock Purchase Plan</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_StockRedeemedDuringPeriodSharesEmployeeStockPurchasePlan_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption of common stock issued from employee stock purchase plan (in shares)</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_StockRedeemedDuringPeriodValueEmployeeStockPurchasePlan" xlink:label="bkv_StockRedeemedDuringPeriodValueEmployeeStockPurchasePlan" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_StockRedeemedDuringPeriodValueEmployeeStockPurchasePlan" xlink:to="bkv_StockRedeemedDuringPeriodValueEmployeeStockPurchasePlan_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_StockRedeemedDuringPeriodValueEmployeeStockPurchasePlan_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Redeemed During Period, Value, Employee Stock Purchase Plan</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_StockRedeemedDuringPeriodValueEmployeeStockPurchasePlan_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Redeemed During Period, Value, Employee Stock Purchase Plan</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="bkv_StockRedeemedDuringPeriodValueEmployeeStockPurchasePlan_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption of common stock issued from employee stock purchase plan</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:to="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, New Issues</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:to="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, New Issues</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common stock</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TreasuryStockRetiredCostMethodAmount" xlink:label="us-gaap_TreasuryStockRetiredCostMethodAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TreasuryStockRetiredCostMethodAmount" xlink:to="us-gaap_TreasuryStockRetiredCostMethodAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TreasuryStockRetiredCostMethodAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Treasury Stock, Retired, Cost Method, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_TreasuryStockRetiredCostMethodAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares repurchased with reverse stock split</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_NoncontrollingInterestDistributionsToNoncontrollingInterestHolders" xlink:label="bkv_NoncontrollingInterestDistributionsToNoncontrollingInterestHolders" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_NoncontrollingInterestDistributionsToNoncontrollingInterestHolders" xlink:to="bkv_NoncontrollingInterestDistributionsToNoncontrollingInterestHolders_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_NoncontrollingInterestDistributionsToNoncontrollingInterestHolders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling Interest, Distributions to Noncontrolling Interest Holders</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_NoncontrollingInterestDistributionsToNoncontrollingInterestHolders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling Interest, Distributions to Noncontrolling Interest Holders</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="bkv_NoncontrollingInterestDistributionsToNoncontrollingInterestHolders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Distributions to noncontrolling interest</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ReclassificationsOfTemporaryToPermanentEquityShares" xlink:label="bkv_ReclassificationsOfTemporaryToPermanentEquityShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ReclassificationsOfTemporaryToPermanentEquityShares" xlink:to="bkv_ReclassificationsOfTemporaryToPermanentEquityShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ReclassificationsOfTemporaryToPermanentEquityShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reclassifications of Temporary To Permanent Equity, Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ReclassificationsOfTemporaryToPermanentEquityShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reclassifications of Temporary To Permanent Equity, Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ReclassificationsOfTemporaryToPermanentEquityShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Mezzanine equity conversion (in shares)</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ReclassificationsOfTemporaryToPermanentEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reclassifications of Temporary to Permanent Equity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ReclassificationsOfTemporaryToPermanentEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Mezzanine equity conversion</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:to="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity-based compensation</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedStockSharesIssuedNetOfSharesForTaxWithholdings" xlink:label="us-gaap_RestrictedStockSharesIssuedNetOfSharesForTaxWithholdings" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RestrictedStockSharesIssuedNetOfSharesForTaxWithholdings" xlink:to="us-gaap_RestrictedStockSharesIssuedNetOfSharesForTaxWithholdings_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RestrictedStockSharesIssuedNetOfSharesForTaxWithholdings_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Restricted Stock, Shares Issued Net of Shares for Tax Withholdings</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RestrictedStockSharesIssuedNetOfSharesForTaxWithholdings_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock issued upon vesting of RSUs, net of shares withheld for income taxes (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedStockValueSharesIssuedNetOfTaxWithholdings" xlink:label="us-gaap_RestrictedStockValueSharesIssuedNetOfTaxWithholdings" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RestrictedStockValueSharesIssuedNetOfTaxWithholdings" xlink:to="us-gaap_RestrictedStockValueSharesIssuedNetOfTaxWithholdings_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RestrictedStockValueSharesIssuedNetOfTaxWithholdings_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Restricted Stock, Value, Shares Issued Net of Tax Withholdings</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RestrictedStockValueSharesIssuedNetOfTaxWithholdings_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock issued upon vesting of RSUs, net of shares withheld for income taxes</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:label="us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:to="us-gaap_IncreaseDecreaseInTemporaryEquityRollForward_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInTemporaryEquityRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Temporary Equity [Roll Forward]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_IncreaseDecreaseInTemporaryEquityRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Mezzanine Equity</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquitySharesOutstanding" xlink:label="us-gaap_TemporaryEquitySharesOutstanding" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquitySharesOutstanding" xlink:to="us-gaap_TemporaryEquitySharesOutstanding_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TemporaryEquitySharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Shares Outstanding</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_TemporaryEquitySharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending balance, Mezzanine Equity (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_TemporaryEquitySharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning balance, Mezzanine Equity (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TemporaryEquitySharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Mezzanine equity, outstanding (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:label="us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:to="us-gaap_TemporaryEquityCarryingAmountAttributableToParent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TemporaryEquityCarryingAmountAttributableToParent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Carrying Amount, Attributable to Parent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_TemporaryEquityCarryingAmountAttributableToParent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending balance, Mezzanine Equity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_TemporaryEquityCarryingAmountAttributableToParent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning balance, Mezzanine Equity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TemporaryEquityCarryingAmountAttributableToParent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carrying amount</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityNetIncome" xlink:label="us-gaap_TemporaryEquityNetIncome" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityNetIncome" xlink:to="us-gaap_TemporaryEquityNetIncome_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TemporaryEquityNetIncome_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Net Income</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TemporaryEquityNetIncome_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net income</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_RedemptionOfTemporaryEquityIssuedUponVestingOfEquityBasedCompensationShares" xlink:label="bkv_RedemptionOfTemporaryEquityIssuedUponVestingOfEquityBasedCompensationShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_RedemptionOfTemporaryEquityIssuedUponVestingOfEquityBasedCompensationShares" xlink:to="bkv_RedemptionOfTemporaryEquityIssuedUponVestingOfEquityBasedCompensationShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_RedemptionOfTemporaryEquityIssuedUponVestingOfEquityBasedCompensationShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption of Temporary Equity Issued Upon Vesting of Equity-based Compensation, Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_RedemptionOfTemporaryEquityIssuedUponVestingOfEquityBasedCompensationShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption of Temporary Equity Issued Upon Vesting of Equity-based Compensation, Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_RedemptionOfTemporaryEquityIssuedUponVestingOfEquityBasedCompensationShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption of common stock issued upon vesting of equity-based compensation (in shares)</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_RedemptionOfTemporaryEquityIssuedUponVestingOfEquityBasedCompensationValue" xlink:label="bkv_RedemptionOfTemporaryEquityIssuedUponVestingOfEquityBasedCompensationValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_RedemptionOfTemporaryEquityIssuedUponVestingOfEquityBasedCompensationValue" xlink:to="bkv_RedemptionOfTemporaryEquityIssuedUponVestingOfEquityBasedCompensationValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_RedemptionOfTemporaryEquityIssuedUponVestingOfEquityBasedCompensationValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption of Temporary Equity Issued Upon Vesting of Equity-based Compensation, Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_RedemptionOfTemporaryEquityIssuedUponVestingOfEquityBasedCompensationValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption of Temporary Equity Issued Upon Vesting of Equity-based Compensation, Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_RedemptionOfTemporaryEquityIssuedUponVestingOfEquityBasedCompensationValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption of common stock issued upon vesting of equity-based compensation</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TemporaryEquityIssuedSharesShareBasedPaymentArrangementAfterForfeiture" xlink:label="bkv_TemporaryEquityIssuedSharesShareBasedPaymentArrangementAfterForfeiture" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_TemporaryEquityIssuedSharesShareBasedPaymentArrangementAfterForfeiture" xlink:to="bkv_TemporaryEquityIssuedSharesShareBasedPaymentArrangementAfterForfeiture_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TemporaryEquityIssuedSharesShareBasedPaymentArrangementAfterForfeiture_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Issued, Shares, Share-Based Payment Arrangement, after Forfeiture</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_TemporaryEquityIssuedSharesShareBasedPaymentArrangementAfterForfeiture_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Issued, Shares, Share-Based Payment Arrangement, after Forfeiture</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_TemporaryEquityIssuedSharesShareBasedPaymentArrangementAfterForfeiture_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock issued upon vesting of RSUs, net of shares withheld for income taxes (in shares)</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TemporaryEquityIssuedValueShareBasedPaymentArrangementAfterForfeiture" xlink:label="bkv_TemporaryEquityIssuedValueShareBasedPaymentArrangementAfterForfeiture" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_TemporaryEquityIssuedValueShareBasedPaymentArrangementAfterForfeiture" xlink:to="bkv_TemporaryEquityIssuedValueShareBasedPaymentArrangementAfterForfeiture_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TemporaryEquityIssuedValueShareBasedPaymentArrangementAfterForfeiture_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Issued, Value, Share-Based Payment Arrangement, after Forfeiture</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_TemporaryEquityIssuedValueShareBasedPaymentArrangementAfterForfeiture_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Issued, Value, Share-Based Payment Arrangement, after Forfeiture</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_TemporaryEquityIssuedValueShareBasedPaymentArrangementAfterForfeiture_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common stock issued upon vesting of RSUs, net of shares withheld for income taxes</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TemporaryEquityMinorityOwnershipPuttableSharesToRedemptionValueAdjustment" xlink:label="bkv_TemporaryEquityMinorityOwnershipPuttableSharesToRedemptionValueAdjustment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_TemporaryEquityMinorityOwnershipPuttableSharesToRedemptionValueAdjustment" xlink:to="bkv_TemporaryEquityMinorityOwnershipPuttableSharesToRedemptionValueAdjustment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TemporaryEquityMinorityOwnershipPuttableSharesToRedemptionValueAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Minority Ownership Puttable Shares to Redemption Value, Adjustment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_TemporaryEquityMinorityOwnershipPuttableSharesToRedemptionValueAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Minority Ownership Puttable Shares to Redemption Value, Adjustment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_TemporaryEquityMinorityOwnershipPuttableSharesToRedemptionValueAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustment of minority ownership puttable shares to redemption value</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_AdjustmentOfEquityBasedCompensationToRedemptionValueDecreaseToEquity" xlink:label="bkv_AdjustmentOfEquityBasedCompensationToRedemptionValueDecreaseToEquity" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_AdjustmentOfEquityBasedCompensationToRedemptionValueDecreaseToEquity" xlink:to="bkv_AdjustmentOfEquityBasedCompensationToRedemptionValueDecreaseToEquity_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_AdjustmentOfEquityBasedCompensationToRedemptionValueDecreaseToEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustment Of Equity-Based Compensation To Redemption Value, Decrease To Equity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AdjustmentOfEquityBasedCompensationToRedemptionValueDecreaseToEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustment Of Equity-Based Compensation To Redemption Value, Decrease To Equity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="bkv_AdjustmentOfEquityBasedCompensationToRedemptionValueDecreaseToEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustment of equity-based compensation to redemption value</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TemporaryEquityRedeemedDuringPeriodValueEmployeeStockPurchasePlan" xlink:label="bkv_TemporaryEquityRedeemedDuringPeriodValueEmployeeStockPurchasePlan" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_TemporaryEquityRedeemedDuringPeriodValueEmployeeStockPurchasePlan" xlink:to="bkv_TemporaryEquityRedeemedDuringPeriodValueEmployeeStockPurchasePlan_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TemporaryEquityRedeemedDuringPeriodValueEmployeeStockPurchasePlan_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Redeemed During Period, Value, Employee Stock Purchase Plan</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_TemporaryEquityRedeemedDuringPeriodValueEmployeeStockPurchasePlan_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Redeemed During Period, Value, Employee Stock Purchase Plan</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="bkv_TemporaryEquityRedeemedDuringPeriodValueEmployeeStockPurchasePlan_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption of common stock issued from employee stock purchase plan</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues" xlink:label="us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues" xlink:to="us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OilAndGasExplorationAndProductionIndustriesDisclosuresTextBlock" xlink:label="us-gaap_OilAndGasExplorationAndProductionIndustriesDisclosuresTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OilAndGasExplorationAndProductionIndustriesDisclosuresTextBlock" xlink:to="us-gaap_OilAndGasExplorationAndProductionIndustriesDisclosuresTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OilAndGasExplorationAndProductionIndustriesDisclosuresTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Supplemental Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OilAndGasExplorationAndProductionIndustriesDisclosuresTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Supplemental Oil and Gas Disclosures (unaudited)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:label="us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:to="us-gaap_BasisOfAccountingPolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BasisOfAccountingPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Basis of Accounting, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BasisOfAccountingPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Basis of Presentation</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:label="us-gaap_PriorPeriodReclassificationAdjustmentDescription" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:to="us-gaap_PriorPeriodReclassificationAdjustmentDescription_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PriorPeriodReclassificationAdjustmentDescription_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reclassification, Comparability Adjustment [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PriorPeriodReclassificationAdjustmentDescription_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reclassification</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityPolicyTextBlock" xlink:label="us-gaap_StockholdersEquityPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityPolicyTextBlock" xlink:to="us-gaap_StockholdersEquityPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquityPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockholders' Equity, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockholdersEquityPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Offering Costs and Treasury Stock</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UseOfEstimates" xlink:label="us-gaap_UseOfEstimates" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_UseOfEstimates" xlink:to="us-gaap_UseOfEstimates_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_UseOfEstimates_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Use of Estimates, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_UseOfEstimates_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Significant Judgments and Accounting Estimates</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConsolidationPolicyTextBlock" xlink:label="us-gaap_ConsolidationPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConsolidationPolicyTextBlock" xlink:to="us-gaap_ConsolidationPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConsolidationPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consolidation, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConsolidationPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Principles of Consolidation</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xlink:label="us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xlink:to="us-gaap_ComprehensiveIncomePolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ComprehensiveIncomePolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive Income, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ComprehensiveIncomePolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive Income (Loss)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationsPolicy" xlink:label="us-gaap_BusinessCombinationsPolicy" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationsPolicy" xlink:to="us-gaap_BusinessCombinationsPolicy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationsPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationsPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combinations</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_AssetAcquisitionPolicyPolicyTextBlock" xlink:label="bkv_AssetAcquisitionPolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_AssetAcquisitionPolicyPolicyTextBlock" xlink:to="bkv_AssetAcquisitionPolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_AssetAcquisitionPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Policy</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AssetAcquisitionPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_AssetAcquisitionPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisitions</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:label="us-gaap_CashAndCashEquivalentsPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:to="us-gaap_CashAndCashEquivalentsPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashAndCashEquivalentsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and Cash Equivalents, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashAndCashEquivalentsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and Cash Equivalents</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:label="us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:to="us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and Cash Equivalents, Restricted Cash and Cash Equivalents, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Restricted Cash</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InventoryPolicyTextBlock" xlink:label="us-gaap_InventoryPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryPolicyTextBlock" xlink:to="us-gaap_InventoryPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InventoryPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventory, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InventoryPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventory</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPolicyTextBlock" xlink:label="us-gaap_IncomeTaxPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxPolicyTextBlock" xlink:to="us-gaap_IncomeTaxPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeTaxPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Tax, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeTaxPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Taxes</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OilAndGasPropertiesPolicyPolicyTextBlock" xlink:label="us-gaap_OilAndGasPropertiesPolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OilAndGasPropertiesPolicyPolicyTextBlock" xlink:to="us-gaap_OilAndGasPropertiesPolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OilAndGasPropertiesPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas Properties Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OilAndGasPropertiesPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural Gas Properties</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_MidstreamAssetsPolicyPolicyTextBlock" xlink:label="bkv_MidstreamAssetsPolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_MidstreamAssetsPolicyPolicyTextBlock" xlink:to="bkv_MidstreamAssetsPolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_MidstreamAssetsPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Midstream Assets, Policy</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_MidstreamAssetsPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Midstream Assets, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_MidstreamAssetsPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Midstream Assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:label="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:to="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Property and Equipment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetRetirementObligationsPolicy" xlink:label="us-gaap_AssetRetirementObligationsPolicy" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetRetirementObligationsPolicy" xlink:to="us-gaap_AssetRetirementObligationsPolicy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetRetirementObligationsPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Retirement Obligation [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetRetirementObligationsPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Retirement Obligations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeLeasesPolicyTextBlock" xlink:label="us-gaap_LesseeLeasesPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeLeasesPolicyTextBlock" xlink:to="us-gaap_LesseeLeasesPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeLeasesPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Leases [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeLeasesPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Leases</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueRecognitionPolicyTextBlock" xlink:label="us-gaap_RevenueRecognitionPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevenueRecognitionPolicyTextBlock" xlink:to="us-gaap_RevenueRecognitionPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RevenueRecognitionPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RevenueRecognitionPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue Recognition</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativesPolicyTextBlock" xlink:label="us-gaap_DerivativesPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativesPolicyTextBlock" xlink:to="us-gaap_DerivativesPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativesPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivatives, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativesPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Financial Instruments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TradeAndOtherAccountsReceivablePolicy" xlink:label="us-gaap_TradeAndOtherAccountsReceivablePolicy" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:to="us-gaap_FairValueOfFinancialInstrumentsPolicy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:label="us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:to="us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:to="us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConsolidationVariableInterestEntityPolicy" xlink:to="us-gaap_ConsolidationVariableInterestEntityPolicy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConsolidationVariableInterestEntityPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consolidation, Variable Interest Entity, Policy [Policy Text Block]</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EarningsPerSharePolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Earnings Per Share, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EarningsPerSharePolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Income (Loss) Per Common Share</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Recently Adopted Accounting Standards and Accounting Pronouncements Not Yet Adopted</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:to="us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Restrictions on Cash and Cash Equivalents [Table Text Block]</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:label="us-gaap_PropertyPlantAndEquipmentTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:to="us-gaap_PropertyPlantAndEquipmentTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetAcquisitionTable" xlink:label="us-gaap_AssetAcquisitionTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetAcquisitionTable" xlink:to="us-gaap_AssetAcquisitionTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetAcquisitionTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition [Table]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetAcquisitionTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetAcquisitionAxis" xlink:label="us-gaap_AssetAcquisitionAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetAcquisitionAxis" xlink:to="us-gaap_AssetAcquisitionAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetAcquisitionAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetAcquisitionAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetAcquisitionDomain" xlink:label="us-gaap_AssetAcquisitionDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetAcquisitionDomain" xlink:to="us-gaap_AssetAcquisitionDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetAcquisitionDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetAcquisitionDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition [Domain]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_BedrockAcquisitionMember" xlink:label="bkv_BedrockAcquisitionMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_BedrockAcquisitionMember" xlink:to="bkv_BedrockAcquisitionMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_BedrockAcquisitionMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bedrock Acquisition</label>
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    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TempleIiAcquisitionMember" xlink:label="bkv_TempleIiAcquisitionMember" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TempleIiAcquisitionMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to acquisition of  Temple II, combined-cycle gas turbine and steam turbine power plant.</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetAcquisitionLineItems" xlink:label="us-gaap_AssetAcquisitionLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetAcquisitionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetAcquisitionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition [Line Items]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock" xlink:label="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock" xlink:to="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business combination</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetAcquisitionTableTextBlock" xlink:label="us-gaap_AssetAcquisitionTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetAcquisitionTableTextBlock" xlink:to="us-gaap_AssetAcquisitionTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetAcquisitionTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetAcquisitionTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:label="us-gaap_ScheduleOfDebtInstrumentsTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:to="us-gaap_ScheduleOfDebtInstrumentsTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfDebtInstrumentsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Long-Term Debt Instruments [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfDebtInstrumentsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Long-Term Debt Instruments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionTableTextBlock" xlink:label="us-gaap_DebtInstrumentRedemptionTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentRedemptionTableTextBlock" xlink:to="us-gaap_DebtInstrumentRedemptionTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentRedemptionTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument Redemption</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:label="us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis [Table Text Block]</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SubsequentEventMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent Event</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems" xlink:label="us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems" xlink:to="us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsidiary of Limited Liability Company or Limited Partnership [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsidiary of Limited Liability Company or Limited Partnership [Line Items]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByParent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:to="us-gaap_MinorityInterestOwnershipPercentageByParent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByParent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsidiary, Ownership Percentage, Parent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByParent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage owned by parent</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:to="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsidiary, Ownership Percentage, Noncontrolling Owner</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage owned by noncontrolling members</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_AssetAcquisitionVotingEquityInterestAcquiredPercentage" xlink:label="bkv_AssetAcquisitionVotingEquityInterestAcquiredPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_AssetAcquisitionVotingEquityInterestAcquiredPercentage" xlink:to="bkv_AssetAcquisitionVotingEquityInterestAcquiredPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_AssetAcquisitionVotingEquityInterestAcquiredPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Voting Equity Interest Acquired, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AssetAcquisitionVotingEquityInterestAcquiredPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Voting Equity Interest Acquired, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_AssetAcquisitionVotingEquityInterestAcquiredPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset acquisition, voting equity interest acquired, percentage</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfOperatingSegments" xlink:label="us-gaap_NumberOfOperatingSegments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NumberOfOperatingSegments" xlink:to="us-gaap_NumberOfOperatingSegments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Operating Segments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of operating segments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfReportableSegments" xlink:label="us-gaap_NumberOfReportableSegments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NumberOfReportableSegments" xlink:to="us-gaap_NumberOfReportableSegments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Reportable Segments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of reportable segments</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_NumberOfOperatingSegmentsOtherThanReportableSegments" xlink:label="bkv_NumberOfOperatingSegmentsOtherThanReportableSegments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_NumberOfOperatingSegmentsOtherThanReportableSegments" xlink:to="bkv_NumberOfOperatingSegmentsOtherThanReportableSegments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_NumberOfOperatingSegmentsOtherThanReportableSegments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of operating segments other the segments reported by the entity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_NumberOfOperatingSegmentsOtherThanReportableSegments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Operating Segments Other Than Reportable Segments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:label="us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:to="us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsidiary or Equity Method Investee, Sale of Stock, Type [Table]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsidiary or Equity Method Investee, Sale of Stock, Type [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsidiarySaleOfStockAxis" xlink:label="us-gaap_SubsidiarySaleOfStockAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsidiarySaleOfStockAxis" xlink:to="us-gaap_SubsidiarySaleOfStockAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Stock [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Stock [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SaleOfStockNameOfTransactionDomain" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Stock [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Stock [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IPOMember" xlink:label="us-gaap_IPOMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IPOMember" xlink:to="us-gaap_IPOMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IPOMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">IPO [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IPOMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">IPO</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OverAllotmentOptionMember" xlink:label="us-gaap_OverAllotmentOptionMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OverAllotmentOptionMember" xlink:to="us-gaap_OverAllotmentOptionMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OverAllotmentOptionMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Over-Allotment Option [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OverAllotmentOptionMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Over-Allotment Option</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_PublicOfferingMember" xlink:label="bkv_PublicOfferingMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_PublicOfferingMember" xlink:to="bkv_PublicOfferingMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_PublicOfferingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Public Offering</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_PublicOfferingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Public Offering [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_PublicOfferingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Public Offering</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsidiarySaleOfStockLineItems" xlink:label="us-gaap_SubsidiarySaleOfStockLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_SubsidiarySaleOfStockLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsidiarySaleOfStockLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsidiary, Sale of Stock [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SubsidiarySaleOfStockLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsidiary, Sale of Stock [Line Items]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:to="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Stock, Number of Shares Issued in Transaction</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">IPO shares (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares issued in transaction (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SaleOfStockPricePerShare" xlink:label="us-gaap_SaleOfStockPricePerShare" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SaleOfStockPricePerShare" xlink:to="us-gaap_SaleOfStockPricePerShare_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SaleOfStockPricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Stock, Price Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SaleOfStockPricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of stock, price per share (in USD per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:label="us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:to="us-gaap_SaleOfStockConsiderationReceivedOnTransaction_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SaleOfStockConsiderationReceivedOnTransaction_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Stock, Consideration Received on Transaction</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SaleOfStockConsiderationReceivedOnTransaction_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aggregate purchase price</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_SaleOfStockNumberOfDaysFollowingInitialPublicOfferingThreshold" xlink:label="bkv_SaleOfStockNumberOfDaysFollowingInitialPublicOfferingThreshold" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_SaleOfStockNumberOfDaysFollowingInitialPublicOfferingThreshold" xlink:to="bkv_SaleOfStockNumberOfDaysFollowingInitialPublicOfferingThreshold_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_SaleOfStockNumberOfDaysFollowingInitialPublicOfferingThreshold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale Of Stock, Number Of Days Following Initial Public Offering, Threshold</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_SaleOfStockNumberOfDaysFollowingInitialPublicOfferingThreshold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale Of Stock, Number Of Days Following Initial Public Offering, Threshold</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_SaleOfStockNumberOfDaysFollowingInitialPublicOfferingThreshold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of days following initial public offering, threshold</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TemporaryEquityConversionShares" xlink:label="bkv_TemporaryEquityConversionShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_TemporaryEquityConversionShares" xlink:to="bkv_TemporaryEquityConversionShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TemporaryEquityConversionShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Conversion, Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_TemporaryEquityConversionShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Conversion, Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_TemporaryEquityConversionShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary equity, conversion, shares (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredOfferingCosts" xlink:label="us-gaap_DeferredOfferingCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredOfferingCosts" xlink:to="us-gaap_DeferredOfferingCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentAxis" xlink:label="us-gaap_DebtInstrumentAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentAxis" xlink:to="us-gaap_DebtInstrumentAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument [Axis]</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentNameDomain" xlink:label="us-gaap_DebtInstrumentNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentNameDomain" xlink:to="us-gaap_DebtInstrumentNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Name [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Name [Domain]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_RBLCreditAgreementMember" xlink:label="bkv_RBLCreditAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_RBLCreditAgreementMember" xlink:to="bkv_RBLCreditAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_RBLCreditAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">RBL Credit Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_RBLCreditAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">RBL Credit Agreement [Member]</label>
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    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_SeniorUnsecuredNotesDue2030Member" xlink:label="bkv_SeniorUnsecuredNotesDue2030Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_SeniorUnsecuredNotesDue2030Member" xlink:to="bkv_SeniorUnsecuredNotesDue2030Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_SeniorUnsecuredNotesDue2030Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Senior Unsecured Notes Due 2030</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_SeniorUnsecuredNotesDue2030Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Senior Unsecured Notes Due 2030 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_SeniorUnsecuredNotesDue2030Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2030 Senior Notes (7.50%)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeAxis" xlink:label="us-gaap_LongtermDebtTypeAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongtermDebtTypeAxis" xlink:to="us-gaap_LongtermDebtTypeAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongtermDebtTypeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Type [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongtermDebtTypeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Type [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeDomain" xlink:label="us-gaap_LongtermDebtTypeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongtermDebtTypeDomain" xlink:to="us-gaap_LongtermDebtTypeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongtermDebtTypeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Type [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongtermDebtTypeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Type [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SeniorNotesMember" xlink:label="us-gaap_SeniorNotesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SeniorNotesMember" xlink:to="us-gaap_SeniorNotesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SeniorNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Senior Notes [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SeniorNotesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Senior Notes</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentLineItems" xlink:label="us-gaap_DebtInstrumentLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentLineItems" xlink:to="us-gaap_DebtInstrumentLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument [Line Items]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_WorkingCapitalSurplusNet" xlink:label="bkv_WorkingCapitalSurplusNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_WorkingCapitalSurplusNet" xlink:to="bkv_WorkingCapitalSurplusNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_WorkingCapitalSurplusNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Working Capital Surplus, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_WorkingCapitalSurplusNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Working Capital Surplus, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_WorkingCapitalSurplusNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Working capital surplus, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativePremiumPaid" xlink:label="us-gaap_DerivativePremiumPaid" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativePremiumPaid" xlink:to="us-gaap_DerivativePremiumPaid_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativePremiumPaid_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative, Premium Paid</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativePremiumPaid_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative, premium paid</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentFaceAmount" xlink:label="us-gaap_DebtInstrumentFaceAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentFaceAmount" xlink:to="us-gaap_DebtInstrumentFaceAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Face Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt instrument, face amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Principal amount</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:to="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Interest Rate, Stated Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt instrument, interest rate, stated percentage</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromIssuanceOfLongTermDebt" xlink:label="us-gaap_ProceedsFromIssuanceOfLongTermDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromIssuanceOfLongTermDebt" xlink:to="us-gaap_ProceedsFromIssuanceOfLongTermDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromIssuanceOfLongTermDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Issuance of Long-Term Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromIssuanceOfLongTermDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net proceeds on long-term debt</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireProductiveAssets" xlink:label="us-gaap_PaymentsToAcquireProductiveAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToAcquireProductiveAssets" xlink:to="us-gaap_PaymentsToAcquireProductiveAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsToAcquireProductiveAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to Acquire Productive Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PaymentsToAcquireProductiveAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_PaymentsToAcquireProductiveAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetAcquisitionConsiderationTransferredTransactionCost" xlink:label="us-gaap_AssetAcquisitionConsiderationTransferredTransactionCost" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetAcquisitionConsiderationTransferredTransactionCost" xlink:to="us-gaap_AssetAcquisitionConsiderationTransferredTransactionCost_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetAcquisitionConsiderationTransferredTransactionCost_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Consideration Transferred, Transaction Cost</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetAcquisitionConsiderationTransferredTransactionCost_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capitalized transaction costs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:to="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment [Table]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:label="us-gaap_PropertyPlantAndEquipmentByTypeAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:to="us-gaap_PropertyPlantAndEquipmentByTypeAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentByTypeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Lived Tangible Asset [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentByTypeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Lived Tangible Asset [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:label="us-gaap_PropertyPlantAndEquipmentTypeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:to="us-gaap_PropertyPlantAndEquipmentTypeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentTypeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Lived Tangible Asset [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentTypeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Lived Tangible Asset [Domain]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_CompressorAndMeterStationsMember" xlink:label="bkv_CompressorAndMeterStationsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_CompressorAndMeterStationsMember" xlink:to="bkv_CompressorAndMeterStationsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_CompressorAndMeterStationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Compressor And Meter Stations</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_CompressorAndMeterStationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Compressor And Meter Stations [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_CompressorAndMeterStationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Compressor And Meter Stations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PipelinesMember" xlink:label="us-gaap_PipelinesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PipelinesMember" xlink:to="us-gaap_PipelinesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PipelinesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Pipelines [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PipelinesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Pipelines</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentLineItems" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentLineItems" xlink:to="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment [Line Items]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:label="us-gaap_PropertyPlantAndEquipmentUsefulLife" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:to="us-gaap_PropertyPlantAndEquipmentUsefulLife_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentUsefulLife_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment, Useful Life</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentUsefulLife_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, plant and equipment, useful life (in years)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BuildingMember" xlink:label="us-gaap_BuildingMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BuildingMember" xlink:to="us-gaap_BuildingMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BuildingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Building [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BuildingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Buildings</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_PlantFacilityMember" xlink:label="bkv_PlantFacilityMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_PlantFacilityMember" xlink:to="bkv_PlantFacilityMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_PlantFacilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Plant Facility</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_PlantFacilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Plant Facility [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_PlantFacilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Plant facility</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_CarbonCaptureUtilizationAndSequestrationMember" xlink:label="bkv_CarbonCaptureUtilizationAndSequestrationMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_CarbonCaptureUtilizationAndSequestrationMember" xlink:to="bkv_CarbonCaptureUtilizationAndSequestrationMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_CarbonCaptureUtilizationAndSequestrationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carbon Capture, Utilization, And Sequestration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_CarbonCaptureUtilizationAndSequestrationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carbon Capture, Utilization, And Sequestration [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_CarbonCaptureUtilizationAndSequestrationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Carbon capture, utilization, and sequestration</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_FurnitureFixturesEquipmentVehiclesAndOtherMember" xlink:label="bkv_FurnitureFixturesEquipmentVehiclesAndOtherMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_FurnitureFixturesEquipmentVehiclesAndOtherMember" xlink:to="bkv_FurnitureFixturesEquipmentVehiclesAndOtherMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_FurnitureFixturesEquipmentVehiclesAndOtherMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Furniture, Fixtures, Equipment, Vehicles, And Other</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_FurnitureFixturesEquipmentVehiclesAndOtherMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Furniture, Fixtures, Equipment, Vehicles, And Other [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_FurnitureFixturesEquipmentVehiclesAndOtherMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Furniture, fixtures, equipment, vehicles, and other</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ComputerHardwareAndSoftwareMember" xlink:label="bkv_ComputerHardwareAndSoftwareMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ComputerHardwareAndSoftwareMember" xlink:to="bkv_ComputerHardwareAndSoftwareMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ComputerHardwareAndSoftwareMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Computer Hardware And Software</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ComputerHardwareAndSoftwareMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Computer Hardware And Software [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ComputerHardwareAndSoftwareMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Computer hardware and software</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LeaseholdImprovementsMember" xlink:label="us-gaap_LeaseholdImprovementsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LeaseholdImprovementsMember" xlink:to="us-gaap_LeaseholdImprovementsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LeaseholdImprovementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Leasehold Improvements [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LeaseholdImprovementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Leasehold improvements</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis" xlink:label="srt_RangeAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RangeAxis" xlink:to="srt_RangeAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RangeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Statistical Measurement [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_RangeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Statistical Measurement [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember" xlink:label="srt_RangeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RangeMember" xlink:to="srt_RangeMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RangeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Statistical Measurement [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_RangeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Statistical Measurement [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MinimumMember" xlink:label="srt_MinimumMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_MinimumMember" xlink:to="srt_MinimumMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_MinimumMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_MinimumMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MaximumMember" xlink:label="srt_MaximumMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_MaximumMember" xlink:to="srt_MaximumMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_MaximumMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_MaximumMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseExpense" xlink:label="us-gaap_OperatingLeaseExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseExpense" xlink:to="us-gaap_OperatingLeaseExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Lease, Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lease expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfProductInformationTable" xlink:label="us-gaap_ScheduleOfProductInformationTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfProductInformationTable" xlink:to="us-gaap_ScheduleOfProductInformationTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfProductInformationTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Nature of Operation, Product Information, Concentration of Risk [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProductInformationLineItems" xlink:label="us-gaap_ProductInformationLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProductInformationLineItems" xlink:to="us-gaap_ProductInformationLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProductInformationLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Product Information [Line Items]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnbilledContractsReceivable" xlink:label="us-gaap_UnbilledContractsReceivable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_UnbilledContractsReceivable" xlink:to="us-gaap_UnbilledContractsReceivable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_UnbilledContractsReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unbilled Contracts Receivable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_UnbilledContractsReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">unbilled revenues</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAxis" xlink:label="us-gaap_BusinessAcquisitionAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionAxis" xlink:to="us-gaap_BusinessAcquisitionAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessAcquisitionAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain" xlink:label="us-gaap_BusinessAcquisitionAcquireeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionAcquireeDomain" xlink:to="us-gaap_BusinessAcquisitionAcquireeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionAcquireeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessAcquisitionAcquireeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination [Domain]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_BKVBPPPowerLLCMember" xlink:label="bkv_BKVBPPPowerLLCMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_BKVBPPPowerLLCMember" xlink:to="bkv_BKVBPPPowerLLCMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_BKVBPPPowerLLCMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV-BPP Power, LLC</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_BKVBPPPowerLLCMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV-BPP Power, LLC [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_BKVBPPPowerLLCMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV-BPP Power, LLC</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bkv_BKVBPPPowerLLCMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV-BPP Power</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_CounterpartyNameAxis" xlink:label="srt_CounterpartyNameAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_CounterpartyNameAxis" xlink:to="srt_CounterpartyNameAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_CounterpartyNameAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Counterparty Name [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_CounterpartyNameAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Counterparty Name [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RepurchaseAgreementCounterpartyNameDomain" xlink:label="srt_RepurchaseAgreementCounterpartyNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RepurchaseAgreementCounterpartyNameDomain" xlink:to="srt_RepurchaseAgreementCounterpartyNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_RepurchaseAgreementCounterpartyNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Counterparty Name [Domain]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_BanpuPowerUSCorporationBPPUSMember" xlink:label="bkv_BanpuPowerUSCorporationBPPUSMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_BanpuPowerUSCorporationBPPUSMember" xlink:to="bkv_BanpuPowerUSCorporationBPPUSMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_BanpuPowerUSCorporationBPPUSMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Banpu Power US Corporation ("BPPUS")</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_BanpuPowerUSCorporationBPPUSMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Banpu Power US Corporation ("BPPUS") [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_BanpuPowerUSCorporationBPPUSMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BPPUS</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis" xlink:to="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment, Nonconsolidated Investee [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment, Nonconsolidated Investee [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xlink:label="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xlink:to="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment, Nonconsolidated Investee [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment, Nonconsolidated Investee [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:label="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:to="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment, Name [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment, Name [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_EquityMethodInvesteeNameDomain" xlink:label="srt_EquityMethodInvesteeNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_EquityMethodInvesteeNameDomain" xlink:to="srt_EquityMethodInvesteeNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_EquityMethodInvesteeNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment, Name [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_EquityMethodInvesteeNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment, Name [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfFinancialPositionLocationActivityCapitalizationAxis" xlink:label="us-gaap_StatementOfFinancialPositionLocationActivityCapitalizationAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementOfFinancialPositionLocationActivityCapitalizationAxis" xlink:to="us-gaap_StatementOfFinancialPositionLocationActivityCapitalizationAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementOfFinancialPositionLocationActivityCapitalizationAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Statement of Financial Position Location, Activity, Capitalization [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfFinancialPositionLocationActivityCapitalizationDomain" xlink:label="us-gaap_StatementOfFinancialPositionLocationActivityCapitalizationDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementOfFinancialPositionLocationActivityCapitalizationDomain" xlink:to="us-gaap_StatementOfFinancialPositionLocationActivityCapitalizationDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementOfFinancialPositionLocationActivityCapitalizationDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Statement of Financial Position Location, Activity, Capitalization [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementLocationAxis" xlink:label="us-gaap_IncomeStatementLocationAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeStatementLocationAxis" xlink:to="us-gaap_IncomeStatementLocationAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeStatementLocationAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Statement of Income Location, Balance [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementLocationDomain" xlink:label="us-gaap_IncomeStatementLocationDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeStatementLocationDomain" xlink:to="us-gaap_IncomeStatementLocationDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeStatementLocationDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Statement of Income Location, Balance [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherOperatingIncomeExpenseMember" xlink:label="us-gaap_OtherOperatingIncomeExpenseMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherOperatingIncomeExpenseMember" xlink:to="us-gaap_OtherOperatingIncomeExpenseMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherOperatingIncomeExpenseMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Operating Income (Expense) [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherOperatingIncomeExpenseMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other operating expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireBusinessesGross" xlink:label="us-gaap_PaymentsToAcquireBusinessesGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToAcquireBusinessesGross" xlink:to="us-gaap_PaymentsToAcquireBusinessesGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsToAcquireBusinessesGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to Acquire Businesses, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PaymentsToAcquireBusinessesGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to acquire businesses, gross</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:label="us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:to="us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Consideration Transferred, Equity Interest, Share Issued, Number of Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consideration transferred, equity interest, (in shares)</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_BusinessCombinationEquityConsiderationLockUpPeriod" xlink:label="bkv_BusinessCombinationEquityConsiderationLockUpPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_BusinessCombinationEquityConsiderationLockUpPeriod" xlink:to="bkv_BusinessCombinationEquityConsiderationLockUpPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_BusinessCombinationEquityConsiderationLockUpPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Equity Consideration Lock-Up Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_BusinessCombinationEquityConsiderationLockUpPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Equity Consideration Lock Up Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_BusinessCombinationEquityConsiderationLockUpPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity consideration lock-up period</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_BusinessCombinationAggregateConsideration" xlink:label="bkv_BusinessCombinationAggregateConsideration" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_BusinessCombinationAggregateConsideration" xlink:to="bkv_BusinessCombinationAggregateConsideration_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_BusinessCombinationAggregateConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Aggregate Consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_BusinessCombinationAggregateConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Aggregate Consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_BusinessCombinationAggregateConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business combination, aggregate consideration</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_JointVentureOwnershipPercentageOfNoncontrollingInterest" xlink:label="bkv_JointVentureOwnershipPercentageOfNoncontrollingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_JointVentureOwnershipPercentageOfNoncontrollingInterest" xlink:to="bkv_JointVentureOwnershipPercentageOfNoncontrollingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_JointVentureOwnershipPercentageOfNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Joint Venture, Ownership Percentage of Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_JointVentureOwnershipPercentageOfNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Joint Venture, Ownership Percentage of Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_JointVentureOwnershipPercentageOfNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of noncontrolling interest</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInCashPercentage" xlink:label="bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInCashPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInCashPercentage" xlink:to="bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInCashPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInCashPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Consideration Transferred, Liabilities Paid In Cash, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInCashPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Consideration Transferred, Liabilities Paid In Cash, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInCashPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business combination, consideration transferred, cash, percentage</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInEquityPercentage" xlink:label="bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInEquityPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInEquityPercentage" xlink:to="bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInEquityPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInEquityPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Consideration Transferred, Liabilities Paid In Equity, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInEquityPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Consideration Transferred, Liabilities Paid In Equity, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInEquityPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business combination, consideration transferred, equity interest,</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebt" xlink:label="us-gaap_LongTermDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebt" xlink:to="us-gaap_LongTermDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total debt, net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LongTermDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-term debt, net</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_BusinessCombinationConsiderationTransferredPercent" xlink:label="bkv_BusinessCombinationConsiderationTransferredPercent" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_BusinessCombinationConsiderationTransferredPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Consideration Transferred, Percent</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionSharePrice" xlink:to="us-gaap_BusinessAcquisitionSharePrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionSharePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Price Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessAcquisitionSharePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business combination, price per share</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_BusinessCombinationThresholdConsecutiveTradingDays" xlink:label="bkv_BusinessCombinationThresholdConsecutiveTradingDays" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_BusinessCombinationThresholdConsecutiveTradingDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Threshold Consecutive Trading Days</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_BusinessCombinationThresholdConsecutiveTradingDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business combination, convertible, threshold consecutive trading days</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:to="us-gaap_BusinessCombinationAcquisitionRelatedCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationAcquisitionRelatedCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Acquisition-Related Cost, Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationAcquisitionRelatedCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquisition-related cost, expense</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:label="us-gaap_EquityMethodInvestmentOwnershipPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:to="us-gaap_EquityMethodInvestmentOwnershipPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestmentOwnershipPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment, Ownership Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EquityMethodInvestmentOwnershipPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity method investment, ownership percentage</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_EarningsPerShareAttributableToMajorityStockholdersBasic" xlink:label="bkv_EarningsPerShareAttributableToMajorityStockholdersBasic" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_EarningsPerShareAttributableToMajorityStockholdersBasic" xlink:to="bkv_EarningsPerShareAttributableToMajorityStockholdersBasic_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_EarningsPerShareAttributableToMajorityStockholdersBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Earnings Per Share, Attributable to Majority Stockholders, Basic</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_EarningsPerShareAttributableToMajorityStockholdersBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Earnings Per Share, Attributable to Majority Stockholders, Basic</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_EarningsPerShareAttributableToMajorityStockholdersBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Basic (in USD per share)</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_EarningsPerShareAttributableToMajorityStockholdersDiluted" xlink:label="bkv_EarningsPerShareAttributableToMajorityStockholdersDiluted" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_EarningsPerShareAttributableToMajorityStockholdersDiluted" xlink:to="bkv_EarningsPerShareAttributableToMajorityStockholdersDiluted_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_EarningsPerShareAttributableToMajorityStockholdersDiluted_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Earnings Per Share, Attributable to Majority Stockholders, Diluted</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_EarningsPerShareAttributableToMajorityStockholdersDiluted_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Earnings Per Share, Attributable to Majority Stockholders, Diluted</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_EarningsPerShareAttributableToMajorityStockholdersDiluted_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Diluted (in USD per share)</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_EarningsPerShareAttributableToCommonStockholdersBasic" xlink:label="bkv_EarningsPerShareAttributableToCommonStockholdersBasic" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_EarningsPerShareAttributableToCommonStockholdersBasic" xlink:to="bkv_EarningsPerShareAttributableToCommonStockholdersBasic_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_EarningsPerShareAttributableToCommonStockholdersBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Earnings Per Share, Attributable to Common Stockholders, Basic</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_EarningsPerShareAttributableToCommonStockholdersBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Earnings Per Share, Attributable to Common Stockholders, Basic</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_EarningsPerShareAttributableToCommonStockholdersBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Basic (in USD per share)</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_EarningsPerShareAttributableToCommonStockholdersDiluted" xlink:label="bkv_EarningsPerShareAttributableToCommonStockholdersDiluted" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_EarningsPerShareAttributableToCommonStockholdersDiluted" xlink:to="bkv_EarningsPerShareAttributableToCommonStockholdersDiluted_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_EarningsPerShareAttributableToCommonStockholdersDiluted_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Earnings Per Share, Attributable to Common Stockholders, Diluted</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_EarningsPerShareAttributableToCommonStockholdersDiluted_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Earnings Per Share, Attributable to Common Stockholders, Diluted</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_EarningsPerShareAttributableToCommonStockholdersDiluted_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Diluted (in USD per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:label="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:to="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination [Table]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RestatementAxis" xlink:label="srt_RestatementAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RestatementAxis" xlink:to="srt_RestatementAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RestatementAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revision of Prior Period [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RestatementDomain" xlink:label="srt_RestatementDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RestatementDomain" xlink:to="srt_RestatementDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RestatementDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revision of Prior Period [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RestatementAdjustmentMember" xlink:label="srt_RestatementAdjustmentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RestatementAdjustmentMember" xlink:to="srt_RestatementAdjustmentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RestatementAdjustmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revision of Prior Period, Adjustment [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_RestatementAdjustmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Adjustments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionLineItems" xlink:label="us-gaap_BusinessAcquisitionLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionLineItems" xlink:to="us-gaap_BusinessAcquisitionLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessAcquisitionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination [Line Items]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_BKVBPPPowerJointVentureMember" xlink:label="bkv_BKVBPPPowerJointVentureMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_BKVBPPPowerJointVentureMember" xlink:to="bkv_BKVBPPPowerJointVentureMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_BKVBPPPowerJointVentureMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV-BPP Power Joint Venture</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_BKVBPPPowerJointVentureMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV-BPP Power Joint Venture [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_BKVBPPPowerJointVentureMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV-BPP Power</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_BanpuPublicCompanyLimitedBanpuMember" xlink:label="bkv_BanpuPublicCompanyLimitedBanpuMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_BanpuPublicCompanyLimitedBanpuMember" xlink:to="bkv_BanpuPublicCompanyLimitedBanpuMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_BanpuPublicCompanyLimitedBanpuMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Banpu Public Company Limited (Banpu)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_BanpuPublicCompanyLimitedBanpuMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Banpu Public Company Limited (Banpu) [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_BanpuPublicCompanyLimitedBanpuMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Banpu</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_NetAssetsAttributableToCommonShareholders" xlink:label="bkv_NetAssetsAttributableToCommonShareholders" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_NetAssetsAttributableToCommonShareholders" xlink:to="bkv_NetAssetsAttributableToCommonShareholders_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_NetAssetsAttributableToCommonShareholders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Assets Attributable To Common Shareholders</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_NetAssetsAttributableToCommonShareholders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Assets Attributable To Common Shareholders</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_NetAssetsAttributableToCommonShareholders_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net assets attributable to common shareholders</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_NetAssetsAttributableToMajorityShareholder" xlink:label="bkv_NetAssetsAttributableToMajorityShareholder" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_NetAssetsAttributableToMajorityShareholder" xlink:to="bkv_NetAssetsAttributableToMajorityShareholder_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_NetAssetsAttributableToMajorityShareholder_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Assets Attributable To Majority Shareholder</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_NetAssetsAttributableToMajorityShareholder_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Assets Attributable To Majority Shareholder</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_NetAssetsAttributableToMajorityShareholder_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net assets attributable to Banpu</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV-BPP Power net income (loss) attributable to common shareholders</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net income (loss) including accretion of Class B Units to redemption value</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_NetIncomeLossAvailableToMajorityStockholders" xlink:label="bkv_NetIncomeLossAvailableToMajorityStockholders" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_NetIncomeLossAvailableToMajorityStockholders" xlink:to="bkv_NetIncomeLossAvailableToMajorityStockholders_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersBasic" xlink:label="bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersBasic" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted Average Number of Shares Outstanding, Attributable to Majority Stockholders, Basic</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted Average Number of Shares Outstanding, Attributable to Majority Stockholders, Basic</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Basic (in shares)</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersDiluted" xlink:label="bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersDiluted" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersDiluted_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted Average Number of Shares Outstanding, Attributable to Majority Stockholders, Diluted</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersDiluted_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted Average Number of Shares Outstanding, Attributable to Majority Stockholders, Diluted</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersDiluted_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Diluted (in shares)</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_AssetAcquisitionDepositForAcquisition" xlink:label="bkv_AssetAcquisitionDepositForAcquisition" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_AssetAcquisitionDepositForAcquisition" xlink:to="bkv_AssetAcquisitionDepositForAcquisition_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_AssetAcquisitionDepositForAcquisition_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Deposit For Acquisition</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AssetAcquisitionDepositForAcquisition_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Deposit For Acquisition</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_AssetAcquisitionDepositForAcquisition_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deposit for acquisition</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_PaymentsToAcquireProductiveAssetsPaymentsOfDebt" xlink:label="bkv_PaymentsToAcquireProductiveAssetsPaymentsOfDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_PaymentsToAcquireProductiveAssetsPaymentsOfDebt" xlink:to="bkv_PaymentsToAcquireProductiveAssetsPaymentsOfDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_PaymentsToAcquireProductiveAssetsPaymentsOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to Acquire Productive Assets, Payments Of Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_PaymentsToAcquireProductiveAssetsPaymentsOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to Acquire Productive Assets, Payments Of Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_PaymentsToAcquireProductiveAssetsPaymentsOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments of debt</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_AssetAcquisitionConsiderationTransferredEquityInterestShareIssuedNumberOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Consideration Transferred, Equity Interest, Share Issued, Number Of Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AssetAcquisitionConsiderationTransferredEquityInterestShareIssuedNumberOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Consideration Transferred, Equity Interest, Share Issued, Number Of Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_AssetAcquisitionConsiderationTransferredEquityInterestShareIssuedNumberOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares of BKV Corporation's common stock (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_GasAndOilAreaDevelopedNet" xlink:label="srt_GasAndOilAreaDevelopedNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_GasAndOilAreaDevelopedNet" xlink:to="srt_GasAndOilAreaDevelopedNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_GasAndOilAreaDevelopedNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Developed Acreage, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_GasAndOilAreaDevelopedNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and gas, developed acreage, net</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetAcquisitionConsiderationTransferredEquityInterestIssuedAndIssuable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity issued as consideration for acquisition</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AssetAcquisitionConsiderationTransferredEquityInterestIssuedAndIssuable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total stock consideration</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetAcquisitionConsiderationTransferred_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Consideration Transferred</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetAcquisitionConsiderationTransferred_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total consideration</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consideration:</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_AssetAcquisitionPricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Price Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AssetAcquisitionPricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Price Per Share</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetAbstract" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AssetAcquisitionRecognizedAssetAcquiredReceivableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Recognized Asset Acquired, Receivable, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_AssetAcquisitionRecognizedAssetAcquiredReceivableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts receivable, net</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_AssetAcquisitionRecognizedAssetAcquiredCommodityDerivativeAssetsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Recognized Asset Acquired, Commodity Derivative Assets, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AssetAcquisitionRecognizedAssetAcquiredCommodityDerivativeAssetsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Recognized Asset Acquired, Commodity Derivative Assets, Current</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AssetAcquisitionRecognizedAssetAcquiredCommodityDerivativeAssetsNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Recognized Asset Acquired, Commodity Derivative Assets, Noncurrent</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AssetAcquisitionRecognizedLiabilityAssumedAccountsPayableAndAccruedLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Recognized Liability Assumed, Accounts Payable And Accrued Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="bkv_AssetAcquisitionRecognizedLiabilityAssumedAccountsPayableAndAccruedLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts payable and accrued liabilities</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_AssetAcquisitionRecognizedLiabilityAssumedCommodityDerivativeLiabilitiesCurrent" xlink:label="bkv_AssetAcquisitionRecognizedLiabilityAssumedCommodityDerivativeLiabilitiesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_AssetAcquisitionRecognizedLiabilityAssumedCommodityDerivativeLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Recognized Liability Assumed, Commodity Derivative Liabilities, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AssetAcquisitionRecognizedLiabilityAssumedCommodityDerivativeLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Recognized Liability Assumed, Commodity Derivative Liabilities, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="bkv_AssetAcquisitionRecognizedLiabilityAssumedCommodityDerivativeLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commodity derivative liabilities, current</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_AssetAcquisitionRecognizedLiabilityAssumedOtherLiabilityCurren" xlink:label="bkv_AssetAcquisitionRecognizedLiabilityAssumedOtherLiabilityCurren" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_AssetAcquisitionRecognizedLiabilityAssumedOtherLiabilityCurren" xlink:to="bkv_AssetAcquisitionRecognizedLiabilityAssumedOtherLiabilityCurren_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_AssetAcquisitionRecognizedLiabilityAssumedOtherLiabilityCurren_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset, Acquisition, Recognized Liability Assumed, Other Liability, Curren</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AssetAcquisitionRecognizedLiabilityAssumedOtherLiabilityCurren_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset, Acquisition, Recognized Liability Assumed, Other Liability, Curren</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="bkv_AssetAcquisitionRecognizedLiabilityAssumedOtherLiabilityCurren_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other current liabilities</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_AssetAcquisitionRecognizedLiabilityAssumedAssetRetirementObligations" xlink:label="bkv_AssetAcquisitionRecognizedLiabilityAssumedAssetRetirementObligations" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_AssetAcquisitionRecognizedLiabilityAssumedAssetRetirementObligations" xlink:to="bkv_AssetAcquisitionRecognizedLiabilityAssumedAssetRetirementObligations_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AssetAcquisitionRecognizedLiabilityAssumedAssetRetirementObligations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Recognized Liability Assumed, Asset Retirement Obligations</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="bkv_AssetAcquisitionRecognizedLiabilityAssumedAssetRetirementObligations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset retirement obligations</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_AssetAcquisitionRecognizedLiabilityAssumedOtherNoncurrentLiabilities" xlink:label="bkv_AssetAcquisitionRecognizedLiabilityAssumedOtherNoncurrentLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_AssetAcquisitionRecognizedLiabilityAssumedOtherNoncurrentLiabilities" xlink:to="bkv_AssetAcquisitionRecognizedLiabilityAssumedOtherNoncurrentLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_AssetAcquisitionRecognizedLiabilityAssumedOtherNoncurrentLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Recognized Liability Assumed, Other Noncurrent Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AssetAcquisitionRecognizedLiabilityAssumedOtherNoncurrentLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Recognized Liability Assumed, Other Noncurrent Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="bkv_AssetAcquisitionRecognizedLiabilityAssumedOtherNoncurrentLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other noncurrent liabilities</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_AssetAcquisitionRecognizedAssetAcquiredToLiabilityAssumedExcessLess" xlink:label="bkv_AssetAcquisitionRecognizedAssetAcquiredToLiabilityAssumedExcessLess" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AssetAcquisitionRecognizedAssetAcquiredToLiabilityAssumedExcessLess_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Recognized Asset Acquired to Liability Assumed, Excess (Less)</label>
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    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TempleCreditFacilitiesMember" xlink:label="bkv_TempleCreditFacilitiesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_AssetAcquisitionConsiderationTransferredGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase price</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_NumberOfHomesPoweredByEnergyGenerated" xlink:label="bkv_NumberOfHomesPoweredByEnergyGenerated" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_NumberOfHomesPoweredByEnergyGenerated_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Homes Powered by Energy Generated</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property taxes payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and gas production and other taxes payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsNet" xlink:label="us-gaap_AssetsNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsNet" xlink:to="us-gaap_AssetsNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total net assets acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_AssetsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ChaffeeMember" xlink:label="bkv_ChaffeeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ChaffeeMember" xlink:to="bkv_ChaffeeMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ChaffeeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Chaffee</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ChaffeeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Chaffee [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ChaffeeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Chaffee</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ChaffeeAndRepsolOilAndGasMidstreamSystemMember" xlink:label="bkv_ChaffeeAndRepsolOilAndGasMidstreamSystemMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ChaffeeAndRepsolOilAndGasMidstreamSystemMember" xlink:to="bkv_ChaffeeAndRepsolOilAndGasMidstreamSystemMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ChaffeeAndRepsolOilAndGasMidstreamSystemMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Chaffee And Repsol Oil And Gas Midstream System</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ChaffeeAndRepsolOilAndGasMidstreamSystemMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Chaffee And Repsol Oil And Gas Midstream System [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ChaffeeAndRepsolOilAndGasMidstreamSystemMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Chaffee And Repsol Oil And Gas Midstream System</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ChelseaMember" xlink:label="bkv_ChelseaMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ChelseaMember" xlink:to="bkv_ChelseaMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ChelseaMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Chelsea</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ChelseaMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Chelsea [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ChelseaMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Chelsea</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StatementGeographicalAxis" xlink:label="srt_StatementGeographicalAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_StatementGeographicalAxis" xlink:to="srt_StatementGeographicalAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_StatementGeographicalAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Geographical [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_StatementGeographicalAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Geographical [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_SegmentGeographicalDomain" xlink:label="srt_SegmentGeographicalDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_SegmentGeographicalDomain" xlink:to="srt_SegmentGeographicalDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_SegmentGeographicalDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Geographical [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_SegmentGeographicalDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Geographical [Domain]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_NortheastPennsylvaniaMember" xlink:label="bkv_NortheastPennsylvaniaMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_NortheastPennsylvaniaMember" xlink:to="bkv_NortheastPennsylvaniaMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_NortheastPennsylvaniaMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Northeast Pennsylvania</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_NortheastPennsylvaniaMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Northeast Pennsylvania [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_NortheastPennsylvaniaMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Northeast Pennsylvania</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProductiveOilWellsNumberOfWellsWithMultipleCompletionsGross" xlink:label="srt_ProductiveOilWellsNumberOfWellsWithMultipleCompletionsGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProductiveOilWellsNumberOfWellsWithMultipleCompletionsGross" xlink:to="srt_ProductiveOilWellsNumberOfWellsWithMultipleCompletionsGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProductiveOilWellsNumberOfWellsWithMultipleCompletionsGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Gross Productive Well, Multiple Completions, Number</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ProductiveOilWellsNumberOfWellsWithMultipleCompletionsGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gross wells</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProductiveOilWellsNumberOfWellsWithMultipleCompletionsNet" xlink:label="srt_ProductiveOilWellsNumberOfWellsWithMultipleCompletionsNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProductiveOilWellsNumberOfWellsWithMultipleCompletionsNet" xlink:to="srt_ProductiveOilWellsNumberOfWellsWithMultipleCompletionsNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProductiveOilWellsNumberOfWellsWithMultipleCompletionsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Net Productive Well, Multiple Completions, Number</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ProductiveOilWellsNumberOfWellsWithMultipleCompletionsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net wells</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProvedDevelopedReservesBOE1" xlink:label="srt_ProvedDevelopedReservesBOE1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProvedDevelopedReservesBOE1" xlink:to="srt_ProvedDevelopedReservesBOE1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProvedDevelopedReservesBOE1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Developed Reserve, Quantity, Energy</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ProvedDevelopedReservesBOE1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proved reserves (Bcfe)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="srt_ProvedDevelopedReservesBOE1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proved developed reserves (energy)</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_GainLossOnDispositionOfBusinessTransactionCosts" xlink:label="bkv_GainLossOnDispositionOfBusinessTransactionCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_GainLossOnDispositionOfBusinessTransactionCosts" xlink:to="bkv_GainLossOnDispositionOfBusinessTransactionCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_GainLossOnDispositionOfBusinessTransactionCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) On Disposition Of Business, Transaction Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_GainLossOnDispositionOfBusinessTransactionCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) On Disposition Of Business, Transaction Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_GainLossOnDispositionOfBusinessTransactionCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Transaction costs from sale of business</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TempleILoanAgreementsMember" xlink:label="bkv_TempleILoanAgreementsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_TempleILoanAgreementsMember" xlink:to="bkv_TempleILoanAgreementsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TempleILoanAgreementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temple I Loan Agreements</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_TempleILoanAgreementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temple I Loan Agreements [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_TempleILoanAgreementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temple I Loan Agreements</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NotesPayableOtherPayablesMember" xlink:label="us-gaap_NotesPayableOtherPayablesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NotesPayableOtherPayablesMember" xlink:to="us-gaap_NotesPayableOtherPayablesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NotesPayableOtherPayablesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes Payable, Other Payables [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NotesPayableOtherPayablesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Notes Payable, Other Payables</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecuredDebtMember" xlink:label="us-gaap_SecuredDebtMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SecuredDebtMember" xlink:to="us-gaap_SecuredDebtMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SecuredDebtMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Secured Debt [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SecuredDebtMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Secured Debt</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditMember" xlink:label="us-gaap_LineOfCreditMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LineOfCreditMember" xlink:to="us-gaap_LineOfCreditMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LineOfCreditMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line of Credit [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LineOfCreditMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line of Credit</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtCurrent" xlink:label="us-gaap_LongTermDebtCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtCurrent" xlink:to="us-gaap_LongTermDebtCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Current Maturities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long term debt, current</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentCarryingAmount" xlink:label="us-gaap_DebtInstrumentCarryingAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentCarryingAmount" xlink:to="us-gaap_DebtInstrumentCarryingAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-term debt, gross</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:to="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line of Credit Facility, Maximum Borrowing Capacity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum credit commitment</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_LongTermDebtPrincipalAmount" xlink:label="bkv_LongTermDebtPrincipalAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_LongTermDebtPrincipalAmount" xlink:to="bkv_LongTermDebtPrincipalAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_LongTermDebtPrincipalAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Principal Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_LongTermDebtPrincipalAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Principal Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="bkv_LongTermDebtPrincipalAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total debt, net</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_LongTermDebtPrincipalValueCurrentMaturities" xlink:label="bkv_LongTermDebtPrincipalValueCurrentMaturities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_LongTermDebtPrincipalValueCurrentMaturities" xlink:to="bkv_LongTermDebtPrincipalValueCurrentMaturities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_LongTermDebtPrincipalValueCurrentMaturities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Principal Value, Current Maturities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_LongTermDebtPrincipalValueCurrentMaturities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Principal Value, Current Maturities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_LongTermDebtPrincipalValueCurrentMaturities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less: current portion of long-term debt</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_LongTermDebtPrincipalValueExcludingCurrentMaturities" xlink:label="bkv_LongTermDebtPrincipalValueExcludingCurrentMaturities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_LongTermDebtPrincipalValueExcludingCurrentMaturities" xlink:to="bkv_LongTermDebtPrincipalValueExcludingCurrentMaturities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_LongTermDebtPrincipalValueExcludingCurrentMaturities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Principal Value, Excluding Current Maturities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_LongTermDebtPrincipalValueExcludingCurrentMaturities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Principal Value, Excluding Current Maturities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="bkv_LongTermDebtPrincipalValueExcludingCurrentMaturities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total long-term debt, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtNoncurrent" xlink:label="us-gaap_LongTermDebtNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtNoncurrent" xlink:to="us-gaap_LongTermDebtNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Excluding Current Maturities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total long-term debt, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPeriodAxis" xlink:label="us-gaap_DebtInstrumentRedemptionPeriodAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentRedemptionPeriodAxis" xlink:to="us-gaap_DebtInstrumentRedemptionPeriodAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentRedemptionPeriodAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Redemption, Period [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentRedemptionPeriodAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Redemption, Period [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:label="us-gaap_DebtInstrumentRedemptionPeriodDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:to="us-gaap_DebtInstrumentRedemptionPeriodDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentRedemptionPeriodDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Redemption, Period [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentRedemptionPeriodDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Redemption, Period [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:label="us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:to="us-gaap_DebtInstrumentRedemptionPeriodTwoMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentRedemptionPeriodTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Redemption, Period Two [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentRedemptionPeriodTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2028</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DebtInstrumentRedemptionPeriodTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Redemption, Period Two</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPeriodFourMember" xlink:label="us-gaap_DebtInstrumentRedemptionPeriodFourMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentRedemptionPeriodFourMember" xlink:to="us-gaap_DebtInstrumentRedemptionPeriodFourMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentRedemptionPeriodFourMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Redemption, Period Four [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentRedemptionPeriodFourMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Redemption, Period Four</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPeriodFiveMember" xlink:label="us-gaap_DebtInstrumentRedemptionPeriodFiveMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentRedemptionPeriodFiveMember" xlink:to="us-gaap_DebtInstrumentRedemptionPeriodFiveMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentRedemptionPeriodFiveMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Redemption, Period Five [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentRedemptionPeriodFiveMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Redemption, Period Five</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredFinanceCostsGross" xlink:label="us-gaap_DeferredFinanceCostsGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredFinanceCostsGross" xlink:to="us-gaap_DeferredFinanceCostsGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DeferredFinanceCostsGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Issuance Costs, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DeferredFinanceCostsGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Outstanding unamortized debt issuance costs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:label="us-gaap_DebtInstrumentInterestRateEffectivePercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:to="us-gaap_DebtInstrumentInterestRateEffectivePercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentInterestRateEffectivePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Interest Rate, Effective Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentInterestRateEffectivePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt instrument, interest rate, effective percentage</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:label="us-gaap_DebtInstrumentRedemptionPricePercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:to="us-gaap_DebtInstrumentRedemptionPricePercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentRedemptionPricePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Redemption Price, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentRedemptionPricePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt instrument, redemption price, percentage</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPricePercentageOfPrincipalAmountRedeemed" xlink:label="us-gaap_DebtInstrumentRedemptionPricePercentageOfPrincipalAmountRedeemed" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentRedemptionPricePercentageOfPrincipalAmountRedeemed" xlink:to="us-gaap_DebtInstrumentRedemptionPricePercentageOfPrincipalAmountRedeemed_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentRedemptionPricePercentageOfPrincipalAmountRedeemed_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Redemption Price, Percentage of Principal Amount Redeemed</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentRedemptionPricePercentageOfPrincipalAmountRedeemed_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt instrument, redemption price, percentage of principal amount redeemed</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_DebtInstrumentRedemptionThreshold" xlink:label="bkv_DebtInstrumentRedemptionThreshold" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_DebtInstrumentRedemptionThreshold" xlink:to="bkv_DebtInstrumentRedemptionThreshold_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_DebtInstrumentRedemptionThreshold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Redemption, Threshold</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_DebtInstrumentRedemptionThreshold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Redemption, Threshold</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_DebtInstrumentRedemptionThreshold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt instrument, redemption, threshold</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionTable" xlink:label="us-gaap_DebtInstrumentRedemptionTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentRedemptionTable" xlink:to="us-gaap_DebtInstrumentRedemptionTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentRedemptionTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument Redemption [Table]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentRedemptionTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument Redemption [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPeriodOneMember" xlink:label="us-gaap_DebtInstrumentRedemptionPeriodOneMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentRedemptionPeriodOneMember" xlink:to="us-gaap_DebtInstrumentRedemptionPeriodOneMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentRedemptionPeriodOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Redemption, Period One [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentRedemptionPeriodOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPeriodThreeMember" xlink:label="us-gaap_DebtInstrumentRedemptionPeriodThreeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentRedemptionPeriodThreeMember" xlink:to="us-gaap_DebtInstrumentRedemptionPeriodThreeMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentRedemptionPeriodThreeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Redemption, Period Three [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DebtInstrumentRedemptionPeriodThreeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2029 and thereafter</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionLineItems" xlink:label="us-gaap_DebtInstrumentRedemptionLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentRedemptionLineItems" xlink:to="us-gaap_DebtInstrumentRedemptionLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentRedemptionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Redemption [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentRedemptionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Redemption [Line Items]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_BKVUpstreamMidstreamMember" xlink:label="bkv_BKVUpstreamMidstreamMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_BKVUpstreamMidstreamMember" xlink:to="bkv_BKVUpstreamMidstreamMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_BKVUpstreamMidstreamMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV Upstream Midstream</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_BKVUpstreamMidstreamMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV Upstream Midstream [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_BKVUpstreamMidstreamMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV Upstream Midstream</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity" xlink:label="us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity" xlink:to="us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line of Credit Facility, Current Borrowing Capacity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Borrowing base amount</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_LineOfCreditFacilityAggregateElectedCommitment" xlink:label="bkv_LineOfCreditFacilityAggregateElectedCommitment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_LineOfCreditFacilityAggregateElectedCommitment" xlink:to="bkv_LineOfCreditFacilityAggregateElectedCommitment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_LineOfCreditFacilityAggregateElectedCommitment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line Of Credit Facility, Aggregate Elected Commitment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_LineOfCreditFacilityAggregateElectedCommitment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line Of Credit Facility, Aggregate Elected Commitment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_LineOfCreditFacilityAggregateElectedCommitment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Elected commitment amount</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LettersOfCreditOutstandingAmount" xlink:label="us-gaap_LettersOfCreditOutstandingAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LettersOfCreditOutstandingAmount" xlink:to="us-gaap_LettersOfCreditOutstandingAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LettersOfCreditOutstandingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Letters of Credit Outstanding, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LettersOfCreditOutstandingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Outstanding letters of credit</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:label="us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:to="us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line of Credit Facility, Remaining Borrowing Capacity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Remaining borrowing capacity</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:to="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Basis Spread on Variable Rate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Credit spread adjustment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditFacilityCommitmentFeeAmount" xlink:label="us-gaap_LineOfCreditFacilityCommitmentFeeAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LineOfCreditFacilityCommitmentFeeAmount" xlink:to="us-gaap_LineOfCreditFacilityCommitmentFeeAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LineOfCreditFacilityCommitmentFeeAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line of Credit Facility, Commitment Fee Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LineOfCreditFacilityCommitmentFeeAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commitment fee amount</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_LineOfCreditFacilityCovenantTermsMinimumHedgedProjectedProductionFromProvedDevelopedReservesSubsequent24MonthsPercentage" xlink:label="bkv_LineOfCreditFacilityCovenantTermsMinimumHedgedProjectedProductionFromProvedDevelopedReservesSubsequent24MonthsPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_LineOfCreditFacilityCovenantTermsMinimumHedgedProjectedProductionFromProvedDevelopedReservesSubsequent24MonthsPercentage" xlink:to="bkv_LineOfCreditFacilityCovenantTermsMinimumHedgedProjectedProductionFromProvedDevelopedReservesSubsequent24MonthsPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_LineOfCreditFacilityCovenantTermsMinimumHedgedProjectedProductionFromProvedDevelopedReservesSubsequent24MonthsPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line Of Credit Facility, Covenant Terms, Minimum Hedged Projected Production From Proved, Developed Reserves, Subsequent 24 Months, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_LineOfCreditFacilityCovenantTermsMinimumHedgedProjectedProductionFromProvedDevelopedReservesSubsequent24MonthsPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line Of Credit Facility, Covenant Terms, Minimum Hedged Projected Production From Proved, Developed Reserves, Subsequent 24 Months, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_LineOfCreditFacilityCovenantTermsMinimumHedgedProjectedProductionFromProvedDevelopedReservesSubsequent24MonthsPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum hedged projected production from proved, developed reserves, subsequent 24 months, percentage</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_LineOfCreditFacilityCovenantTermsMinimumCurrentRatio" xlink:label="bkv_LineOfCreditFacilityCovenantTermsMinimumCurrentRatio" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_LineOfCreditFacilityCovenantTermsMinimumCurrentRatio" xlink:to="bkv_LineOfCreditFacilityCovenantTermsMinimumCurrentRatio_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_LineOfCreditFacilityCovenantTermsMinimumCurrentRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line of Credit Facility, Covenant Terms, Minimum Current Ratio</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_LineOfCreditFacilityCovenantTermsMinimumCurrentRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line of Credit Facility, Covenant Terms, Minimum Current Ratio</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_LineOfCreditFacilityCovenantTermsMinimumCurrentRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum current ratio</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_LineOfCreditFacilityCovenantTermsMaximumNetLeverageRatio" xlink:label="bkv_LineOfCreditFacilityCovenantTermsMaximumNetLeverageRatio" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_LineOfCreditFacilityCovenantTermsMaximumNetLeverageRatio" xlink:to="bkv_LineOfCreditFacilityCovenantTermsMaximumNetLeverageRatio_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_LineOfCreditFacilityCovenantTermsMaximumNetLeverageRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line of Credit Facility, Covenant Terms, Maximum Net Leverage Ratio</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_LineOfCreditFacilityCovenantTermsMaximumNetLeverageRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line of Credit Facility, Covenant Terms, Maximum Net Leverage Ratio</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_LineOfCreditFacilityCovenantTermsMaximumNetLeverageRatio_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum net leverage ratio</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredFinanceCostsNet" xlink:label="us-gaap_DeferredFinanceCostsNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredFinanceCostsNet" xlink:to="us-gaap_DeferredFinanceCostsNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Issuance Costs, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Outstanding unamortized debt issuance costs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd" xlink:label="us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd" xlink:to="us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Line of Credit Facility, Interest Rate at Period End</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective interest rate</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_BNACLoanAgreementMember" xlink:label="bkv_BNACLoanAgreementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_BNACLoanAgreementMember" xlink:to="bkv_BNACLoanAgreementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_BNACLoanAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BNAC Loan Agreement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_BNACLoanAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BNAC Loan Agreement [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_BNACLoanAgreementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BNAC Loan Agreement</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_BKVBPPPowerCreditFacilityMember" xlink:label="bkv_BKVBPPPowerCreditFacilityMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_BKVBPPPowerCreditFacilityMember" xlink:to="bkv_BKVBPPPowerCreditFacilityMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_BKVBPPPowerCreditFacilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV-BPP Power Credit Facility</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_BKVBPPPowerCreditFacilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV-BPP Power Credit Facility [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_BKVBPPPowerCreditFacilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV-BPP Power Credit Facility</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromIssuanceOfSeniorLongTermDebt" xlink:label="us-gaap_ProceedsFromIssuanceOfSeniorLongTermDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromIssuanceOfSeniorLongTermDebt" xlink:to="us-gaap_ProceedsFromIssuanceOfSeniorLongTermDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromIssuanceOfSeniorLongTermDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Issuance of Senior Long-Term Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromIssuanceOfSeniorLongTermDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from issuance of senior long-term debt</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_DebtInstrumentMinimumNetWorthRequirement" xlink:label="bkv_DebtInstrumentMinimumNetWorthRequirement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_DebtInstrumentMinimumNetWorthRequirement" xlink:to="bkv_DebtInstrumentMinimumNetWorthRequirement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_DebtInstrumentMinimumNetWorthRequirement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Minimum Net Worth Requirement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_DebtInstrumentMinimumNetWorthRequirement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Minimum Net Worth Requirement</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_DebtInstrumentMinimumNetWorthRequirement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum net worth requirement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RepaymentsOfDebt" xlink:label="us-gaap_RepaymentsOfDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RepaymentsOfDebt" xlink:to="us-gaap_RepaymentsOfDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RepaymentsOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments of Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RepaymentsOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments of debt</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_DebtInstrumentCollateralHeldPercent" xlink:label="bkv_DebtInstrumentCollateralHeldPercent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_DebtInstrumentCollateralHeldPercent" xlink:to="bkv_DebtInstrumentCollateralHeldPercent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_DebtInstrumentCollateralHeldPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Collateral Held, Percent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_DebtInstrumentCollateralHeldPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Collateral Held, Percent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_DebtInstrumentCollateralHeldPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Collateral held, percent</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_BridgeportMember" xlink:label="bkv_BridgeportMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_BridgeportMember" xlink:to="bkv_BridgeportMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_BridgeportMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bridgeport</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_BridgeportMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bridgeport [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_BridgeportMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bridgeport</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentProvedPropertyAccumulatedDepreciationDepletionAmortizationAndImpairment" xlink:label="bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentProvedPropertyAccumulatedDepreciationDepletionAmortizationAndImpairment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentProvedPropertyAccumulatedDepreciationDepletionAmortizationAndImpairment" xlink:to="bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentProvedPropertyAccumulatedDepreciationDepletionAmortizationAndImpairment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentProvedPropertyAccumulatedDepreciationDepletionAmortizationAndImpairment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Successful Efforts Method, Property and Equipment, Proved Property, Accumulated Depreciation, Depletion, Amortization, and Impairment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentProvedPropertyAccumulatedDepreciationDepletionAmortizationAndImpairment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Successful Efforts Method, Property and Equipment, Proved Property, Accumulated Depreciation, Depletion, Amortization, and Impairment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentProvedPropertyAccumulatedDepreciationDepletionAmortizationAndImpairment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accumulated depreciation, depletion, amortization, and impairment</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_OilAndGasProvedPropertyDepreciationDepletionAmortizationAndAccretion" xlink:label="bkv_OilAndGasProvedPropertyDepreciationDepletionAmortizationAndAccretion" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_OilAndGasProvedPropertyDepreciationDepletionAmortizationAndAccretion" xlink:to="bkv_OilAndGasProvedPropertyDepreciationDepletionAmortizationAndAccretion_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_OilAndGasProvedPropertyDepreciationDepletionAmortizationAndAccretion_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Property, Depreciation, Depletion, Amortization, and Accretion</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherDepreciationAndAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Depreciation and Amortization</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleOfOtherPropertyPlantAndEquipment" xlink:label="us-gaap_ProceedsFromSaleOfOtherPropertyPlantAndEquipment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromSaleOfOtherPropertyPlantAndEquipment" xlink:to="us-gaap_ProceedsFromSaleOfOtherPropertyPlantAndEquipment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromSaleOfOtherPropertyPlantAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Sale of Other Property, Plant, and Equipment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromSaleOfOtherPropertyPlantAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from sales of assets</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_FeesFromSaleOfPropertyPlantAndEquipment" xlink:label="bkv_FeesFromSaleOfPropertyPlantAndEquipment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_FeesFromSaleOfPropertyPlantAndEquipment" xlink:to="bkv_FeesFromSaleOfPropertyPlantAndEquipment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_FeesFromSaleOfPropertyPlantAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fees From Sale Of Property, Plant, And Equipment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_FeesFromSaleOfPropertyPlantAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fees From Sale Of Property, Plant, And Equipment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bkv_FeesFromSaleOfPropertyPlantAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fees</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnSaleOfProperties" xlink:label="us-gaap_GainLossOnSaleOfProperties" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GainLossOnSaleOfProperties" xlink:to="us-gaap_GainLossOnSaleOfProperties_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GainLossOnSaleOfProperties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) on Sale of Properties</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_GainLossOnSaleOfProperties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain on sale of properties</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalizedComputerSoftwareAdditions" xlink:label="us-gaap_CapitalizedComputerSoftwareAdditions" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CapitalizedComputerSoftwareAdditions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capitalized Computer Software, Additions</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CapitalizedComputerSoftwareAdditions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capitalized computer software, additions</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:label="us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:to="us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquired Finite-Lived Intangible Assets, Weighted Average Useful Life</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Estimated useful life</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:label="us-gaap_FinitelivedIntangibleAssetsAcquired1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:to="us-gaap_FinitelivedIntangibleAssetsAcquired1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinitelivedIntangibleAssetsAcquired1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets Acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinitelivedIntangibleAssetsAcquired1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible assets acquired</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AmortizationOfIntangibleAssets" xlink:label="us-gaap_AmortizationOfIntangibleAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AmortizationOfIntangibleAssets" xlink:to="us-gaap_AmortizationOfIntangibleAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AmortizationOfIntangibleAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization of Intangible Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AmortizationOfIntangibleAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:to="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset, Expected Amortization, Year One</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization expense for intangible assets</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_CompressorStationMember" xlink:label="bkv_CompressorStationMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_CompressorStationMember" xlink:to="bkv_CompressorStationMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_CompressorStationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Compressor Station</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_CompressorStationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Compressor Station [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_CompressorStationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Compressor station</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_MeterStationMember" xlink:label="bkv_MeterStationMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_MeterStationMember" xlink:to="bkv_MeterStationMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_MeterStationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Meter Station</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_MeterStationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Meter Station [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_MeterStationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Meter station</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_OilAndGasSuccessfulEffortsMethodPropertyPlantAndEquipmentMidstreamAssetsAccumulatedDepreciation" xlink:label="bkv_OilAndGasSuccessfulEffortsMethodPropertyPlantAndEquipmentMidstreamAssetsAccumulatedDepreciation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_OilAndGasSuccessfulEffortsMethodPropertyPlantAndEquipmentMidstreamAssetsAccumulatedDepreciation" xlink:to="bkv_OilAndGasSuccessfulEffortsMethodPropertyPlantAndEquipmentMidstreamAssetsAccumulatedDepreciation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_OilAndGasSuccessfulEffortsMethodPropertyPlantAndEquipmentMidstreamAssetsAccumulatedDepreciation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Successful Efforts Method, Property, Plant and Equipment, Midstream Assets, Accumulated Depreciation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_OilAndGasSuccessfulEffortsMethodPropertyPlantAndEquipmentMidstreamAssetsAccumulatedDepreciation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Successful Efforts Method, Property, Plant and Equipment, Midstream Assets, Accumulated Depreciation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="bkv_OilAndGasSuccessfulEffortsMethodPropertyPlantAndEquipmentMidstreamAssetsAccumulatedDepreciation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accumulated depreciation</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_OilAndGasSuccessfulEffortsMethodPropertyPlantAndEquipmentMidstreamAssetsNet" xlink:label="bkv_OilAndGasSuccessfulEffortsMethodPropertyPlantAndEquipmentMidstreamAssetsNet" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_OilAndGasSuccessfulEffortsMethodPropertyPlantAndEquipmentMidstreamAssetsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Successful Efforts Method, Property, Plant and Equipment, Midstream Assets, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_OilAndGasSuccessfulEffortsMethodPropertyPlantAndEquipmentMidstreamAssetsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Successful Efforts Method, Property, Plant and Equipment, Midstream Assets, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="bkv_OilAndGasSuccessfulEffortsMethodPropertyPlantAndEquipmentMidstreamAssetsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Midstream assets, net</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_FurnitureFixturesEquipmentAndVehiclesMember" xlink:label="bkv_FurnitureFixturesEquipmentAndVehiclesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_FurnitureFixturesEquipmentAndVehiclesMember" xlink:to="bkv_FurnitureFixturesEquipmentAndVehiclesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_FurnitureFixturesEquipmentAndVehiclesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Furniture, Fixtures, Equipment, and Vehicles</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_FurnitureFixturesEquipmentAndVehiclesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Furniture, Fixtures, Equipment, and Vehicles [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_FurnitureFixturesEquipmentAndVehiclesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Furniture, fixtures, equipment, and vehicles</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SoftwareAndSoftwareDevelopmentCostsMember" xlink:label="us-gaap_SoftwareAndSoftwareDevelopmentCostsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SoftwareAndSoftwareDevelopmentCostsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Software and Software Development Costs [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SoftwareAndSoftwareDevelopmentCostsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Computer software</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LandMember" xlink:label="us-gaap_LandMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LandMember" xlink:to="us-gaap_LandMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LandMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Land [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LandMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Land</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConstructionInProgressMember" xlink:label="us-gaap_ConstructionInProgressMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConstructionInProgressMember" xlink:to="us-gaap_ConstructionInProgressMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConstructionInProgressMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Construction in Progress [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConstructionInProgressMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Construction in process</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentOther" xlink:label="us-gaap_PropertyPlantAndEquipmentOther" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentOther" xlink:to="us-gaap_PropertyPlantAndEquipmentOther_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentOther_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment, Other, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentOther_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, plant and equipment, gross</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentOtherAccumulatedDepreciation" xlink:label="us-gaap_PropertyPlantAndEquipmentOtherAccumulatedDepreciation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentOtherAccumulatedDepreciation" xlink:to="us-gaap_PropertyPlantAndEquipmentOtherAccumulatedDepreciation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentOtherAccumulatedDepreciation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment, Other, Accumulated Depreciation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentOtherAccumulatedDepreciation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accumulated depreciation</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueOptionQuantitativeDisclosuresTable" xlink:label="us-gaap_FairValueOptionQuantitativeDisclosuresTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueOptionQuantitativeDisclosuresTable" xlink:to="us-gaap_FairValueOptionQuantitativeDisclosuresTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueOptionQuantitativeDisclosuresTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Option, Disclosures [Table]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueOptionQuantitativeDisclosuresTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Option, Disclosures [Table]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_DevonBarnettAcquisitionMember" xlink:label="bkv_DevonBarnettAcquisitionMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_DevonBarnettAcquisitionMember" xlink:to="bkv_DevonBarnettAcquisitionMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_DevonBarnettAcquisitionMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Devon Barnett Acquisition</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_DevonBarnettAcquisitionMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Devon Barnett Acquisition [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_DevonBarnettAcquisitionMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Devon Barnett Acquisition</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Hierarchy and NAV [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Hierarchy and NAV [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Hierarchy and NAV [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Hierarchy and NAV [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel2Member" xlink:label="us-gaap_FairValueInputsLevel2Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueInputsLevel2Member" xlink:to="us-gaap_FairValueInputsLevel2Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Inputs, Level 2 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Significant Other Observable Inputs (Level 2)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueOptionQuantitativeDisclosuresLineItems" xlink:label="us-gaap_FairValueOptionQuantitativeDisclosuresLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueOptionQuantitativeDisclosuresLineItems" xlink:to="us-gaap_FairValueOptionQuantitativeDisclosuresLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueOptionQuantitativeDisclosuresLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Option, Quantitative Disclosures [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueOptionQuantitativeDisclosuresLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Option, Quantitative Disclosures [Line Items]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_DerivativeLiabilitiesNonPerformanceRiskAdjustment" xlink:label="bkv_DerivativeLiabilitiesNonPerformanceRiskAdjustment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_DerivativeLiabilitiesNonPerformanceRiskAdjustment" xlink:to="bkv_DerivativeLiabilitiesNonPerformanceRiskAdjustment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_DerivativeLiabilitiesNonPerformanceRiskAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Liabilities, Non-Performance Risk Adjustment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_DerivativeLiabilitiesNonPerformanceRiskAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Liabilities, Non-Performance Risk Adjustment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_DerivativeLiabilitiesNonPerformanceRiskAdjustment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commodity derivative liability</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtFairValue" xlink:label="us-gaap_LongTermDebtFairValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtFairValue" xlink:to="us-gaap_LongTermDebtFairValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebtFairValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Fair Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermDebtFairValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-term debt, fair value</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:to="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel3Member" xlink:label="us-gaap_FairValueInputsLevel3Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueInputsLevel3Member" xlink:to="us-gaap_FairValueInputsLevel3Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Inputs, Level 3 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Significant Unobservable Inputs (Level 3)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentRiskAxis" xlink:label="us-gaap_DerivativeInstrumentRiskAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeInstrumentRiskAxis" xlink:to="us-gaap_DerivativeInstrumentRiskAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeInstrumentRiskAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Instrument [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeInstrumentRiskAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Instrument [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeContractTypeDomain" xlink:label="us-gaap_DerivativeContractTypeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeContractTypeDomain" xlink:to="us-gaap_DerivativeContractTypeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeContractTypeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Contract [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeContractTypeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Contract [Domain]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_NaturalGasDerivativesMember" xlink:label="bkv_NaturalGasDerivativesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_NaturalGasDerivativesMember" xlink:to="bkv_NaturalGasDerivativesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_NaturalGasDerivativesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural Gas Derivatives</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_NaturalGasDerivativesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural Gas Derivatives [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_NaturalGasDerivativesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural gas derivatives</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_NaturalGasLiquidsNglDerivativesMember" xlink:label="bkv_NaturalGasLiquidsNglDerivativesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_NaturalGasLiquidsNglDerivativesMember" xlink:to="bkv_NaturalGasLiquidsNglDerivativesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_NaturalGasLiquidsNglDerivativesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural Gas Liquids (NGL) Derivatives</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_NaturalGasLiquidsNglDerivativesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural Gas Liquids (NGL) Derivatives [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_NaturalGasLiquidsNglDerivativesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">NGL derivatives</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_NaturalGasBasisSwapDerivativeMember" xlink:label="bkv_NaturalGasBasisSwapDerivativeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_NaturalGasBasisSwapDerivativeMember" xlink:to="bkv_NaturalGasBasisSwapDerivativeMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_NaturalGasBasisSwapDerivativeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural gas basis swaps</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_NaturalGasBasisSwapDerivativeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural Gas Basis Swap Derivative [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_NaturalGasBasisSwapDerivativeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural gas basis swaps</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_PowerDerivativesMember" xlink:label="bkv_PowerDerivativesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_PowerDerivativesMember" xlink:to="bkv_PowerDerivativesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_PowerDerivativesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Power Derivatives</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_PowerDerivativesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Power Derivatives [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_PowerDerivativesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Power derivatives</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative instruments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:to="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_LiabilityAndEquityClassAxis" xlink:label="bkv_LiabilityAndEquityClassAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_LiabilityAndEquityClassAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liability And Equity Class</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_LiabilityAndEquityClassAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liability And Equity Class [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_LiabilityAndEquityClassAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liability And Equity Class [Axis]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_LiabilityAndEquityClassDomain" xlink:label="bkv_LiabilityAndEquityClassDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_LiabilityAndEquityClassDomain" xlink:to="bkv_LiabilityAndEquityClassDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_LiabilityAndEquityClassDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liability And Equity Class [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_LiabilityAndEquityClassDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liability And Equity Class [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_LiabilityAndEquityClassDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liability And Equity Class [Domain]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ContingentConsiderationMember" xlink:label="bkv_ContingentConsiderationMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ContingentConsiderationMember" xlink:to="bkv_ContingentConsiderationMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ContingentConsiderationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contingent Consideration</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_MinorityOwnershipMember" xlink:to="bkv_MinorityOwnershipMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_MinorityOwnershipMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minority Ownership [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_MinorityOwnershipMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minority Ownership</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeMember" xlink:label="us-gaap_DerivativeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivatives</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationRollForward" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationRollForward" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationRollForward" xlink:to="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationRollForward_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis, Unobservable Input Reconciliation [Roll Forward]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis, Unobservable Input Reconciliation [Roll Forward]</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisWithUnobservableInputs_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis with Unobservable Inputs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisWithUnobservableInputs_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Balance, end of period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisWithUnobservableInputs_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Balance, beginning of period</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationSettlements" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationSettlements" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationSettlements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative settlements</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_FairValueNetDerivativeAssetLiabilityRecurringBasisUnobservableInputReconciliationRealizedGainLossIncludedInEarnings_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Net Derivative Asset (Liability), Recurring Basis, Unobservable Input Reconciliation, Realized Gain (Loss) Included In Earnings</label>
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    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_FairValueNetDerivativeAssetLiabilityRecurringBasisUnobservableInputReconciliationUnrealizedGainLossIncludedInEarnings" xlink:label="bkv_FairValueNetDerivativeAssetLiabilityRecurringBasisUnobservableInputReconciliationUnrealizedGainLossIncludedInEarnings" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityAndEquityValueGrantDateFairValueOfEquityBasedCompensation" xlink:label="bkv_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityAndEquityValueGrantDateFairValueOfEquityBasedCompensation" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityAndEquityValueGrantDateFairValueOfEquityBasedCompensation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability And Equity, Value, Grant Date Fair Value of Equity-Based Compensation</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityAndEquitySettlements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of settlements of liability and equity, measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityAndEquitySettlements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability And Equity, Settlements</label>
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    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityAndEquityRealizedGainLossIncludedInEarnings" xlink:label="bkv_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityAndEquityRealizedGainLossIncludedInEarnings" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityAndEquityRealizedGainLossIncludedInEarnings_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability And Equity, Realized Gain (Loss) Included In Earnings</label>
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    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityAndEquityValueChangeInFairValueMarketValue" xlink:label="bkv_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityAndEquityValueChangeInFairValueMarketValue" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_MeasurementInputCommodityPriceCorrelationMember" xlink:label="bkv_MeasurementInputCommodityPriceCorrelationMember" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_MeasurementInputCommodityPriceCorrelationMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Power and natural gas price correlation</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_WeightedAverageMember" xlink:to="srt_WeightedAverageMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeAssetLiabilityNetMeasurementInput_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Measurement Input</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable" xlink:label="us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Instruments, Gain (Loss) [Table]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Instruments, Gain (Loss) [Table]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_CounterpartyTwoMember" xlink:label="bkv_CounterpartyTwoMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_CounterpartyTwoMember" xlink:to="bkv_CounterpartyTwoMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_CounterpartyTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Counterparty Two</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_CounterpartyTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Counterparty Two [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_CounterpartyTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Counterparty Two</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommodityContractMember" xlink:label="us-gaap_CommodityContractMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommodityContractMember" xlink:to="us-gaap_CommodityContractMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommodityContractMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commodity Contract [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommodityContractMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commodity Contract</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_EarlyTerminatedCommodityContractMember" xlink:label="bkv_EarlyTerminatedCommodityContractMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_EarlyTerminatedCommodityContractMember" xlink:to="bkv_EarlyTerminatedCommodityContractMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_EarlyTerminatedCommodityContractMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Early Terminated Commodity Contract</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_EarlyTerminatedCommodityContractMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Early Terminated Commodity Contract [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_EarlyTerminatedCommodityContractMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Early Terminated Commodity Contract</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_A2026PutOptionsMember" xlink:label="bkv_A2026PutOptionsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_A2026PutOptionsMember" xlink:to="bkv_A2026PutOptionsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_A2026PutOptionsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026 Put Options</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_A2026PutOptionsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026 Put Options [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_A2026PutOptionsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026 Put Options</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_PriceIndexAxis" xlink:label="bkv_PriceIndexAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_PriceIndexAxis" xlink:to="bkv_PriceIndexAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_PriceIndexAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Price-Index</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_PriceIndexAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Price-Index [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_PriceIndexAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Price-Index [Axis]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_PriceIndexDomain" xlink:label="bkv_PriceIndexDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_PriceIndexDomain" xlink:to="bkv_PriceIndexDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_PriceIndexDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Price-Index [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_PriceIndexDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Price-Index [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_PriceIndexDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Price-Index [Domain]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_HenryHubIndexMember" xlink:label="bkv_HenryHubIndexMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_HenryHubIndexMember" xlink:to="bkv_HenryHubIndexMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_HenryHubIndexMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Henry Hub Index</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_HenryHubIndexMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Henry Hub Index [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_HenryHubIndexMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Henry Hub Index</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:label="us-gaap_DerivativeInstrumentsGainLossLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:to="us-gaap_DerivativeInstrumentsGainLossLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeInstrumentsGainLossLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Instruments, Gain (Loss) [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeInstrumentsGainLossLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Instruments, Gain (Loss) [Line Items]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationContingentConsiderationLiability" xlink:label="us-gaap_BusinessCombinationContingentConsiderationLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationContingentConsiderationLiability" xlink:to="us-gaap_BusinessCombinationContingentConsiderationLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationContingentConsiderationLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Contingent Consideration, Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_BusinessCombinationContingentConsiderationLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contingent consideration</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeNumberOfInstrumentsHeld" xlink:label="us-gaap_DerivativeNumberOfInstrumentsHeld" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeNumberOfInstrumentsHeld" xlink:to="us-gaap_DerivativeNumberOfInstrumentsHeld_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeNumberOfInstrumentsHeld_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative, Number of Instruments Held</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeNumberOfInstrumentsHeld_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of instruments held</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_DerivativeNumberOfCounterparties" xlink:label="bkv_DerivativeNumberOfCounterparties" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_DerivativeNumberOfCounterparties" xlink:to="bkv_DerivativeNumberOfCounterparties_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_DerivativeNumberOfCounterparties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative, Number Of Counterparties</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_DerivativeNumberOfCounterparties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of counterparties</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeNonmonetaryNotionalAmount" xlink:label="us-gaap_DerivativeNonmonetaryNotionalAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeNonmonetaryNotionalAmount" xlink:to="us-gaap_DerivativeNonmonetaryNotionalAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeNonmonetaryNotionalAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative, Nonmonetary Notional Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeNonmonetaryNotionalAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative, nonmonetary notional amount</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_DerivativeGainLossOnDerivativeSettledNet" xlink:label="bkv_DerivativeGainLossOnDerivativeSettledNet" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_DerivativeGainLossOnDerivativeSettledNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative, Gain (Loss) on Derivative, Settled, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_DerivativeGainLossOnDerivativeSettledNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (loss) on settled derivatives, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OpenOptionContractsWrittenPremiums" xlink:label="us-gaap_OpenOptionContractsWrittenPremiums" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OpenOptionContractsWrittenPremiums" xlink:to="us-gaap_OpenOptionContractsWrittenPremiums_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OpenOptionContractsWrittenPremiums_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative, Premium Received</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OpenOptionContractsWrittenPremiums_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from the sale of call options</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAverageFloorPrice" xlink:label="us-gaap_DerivativeAverageFloorPrice" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeAverageFloorPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted average floor price (in USD per unit)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable" xlink:label="us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable" xlink:to="us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Values Derivatives, Balance Sheet Location, by Derivative Contract Type [Table]</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommodityMember" xlink:label="us-gaap_CommodityMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommodityMember" xlink:to="us-gaap_CommodityMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommodityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commodity [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommodityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commodity</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BalanceSheetLocationAxis" xlink:label="us-gaap_BalanceSheetLocationAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BalanceSheetLocationAxis" xlink:to="us-gaap_BalanceSheetLocationAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BalanceSheetLocationAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Statement of Financial Position Location, Balance [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BalanceSheetLocationAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Statement of Financial Position Location, Balance [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BalanceSheetLocationDomain" xlink:label="us-gaap_BalanceSheetLocationDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BalanceSheetLocationDomain" xlink:to="us-gaap_BalanceSheetLocationDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BalanceSheetLocationDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Statement of Financial Position Location, Balance [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BalanceSheetLocationDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Statement of Financial Position Location, Balance [Domain]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_CommodityContractAssetCurrentMember" xlink:label="bkv_CommodityContractAssetCurrentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_CommodityContractAssetCurrentMember" xlink:to="bkv_CommodityContractAssetCurrentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_CommodityContractAssetCurrentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commodity Contract Asset, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_CommodityContractAssetCurrentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commodity Contract Asset, Current [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_CommodityContractAssetCurrentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commodity derivative assets, current</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_CommodityContractAssetNoncurrentMember" xlink:label="bkv_CommodityContractAssetNoncurrentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_CommodityContractAssetNoncurrentMember" xlink:to="bkv_CommodityContractAssetNoncurrentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_CommodityContractAssetNoncurrentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commodity Contract Asset, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_CommodityContractAssetNoncurrentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commodity Contract Asset, Noncurrent [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_CommodityContractAssetNoncurrentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commodity derivative assets</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_CommodityContractLiabilityCurrentMember" xlink:label="bkv_CommodityContractLiabilityCurrentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_CommodityContractLiabilityCurrentMember" xlink:to="bkv_CommodityContractLiabilityCurrentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_CommodityContractLiabilityCurrentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commodity Contract Liability, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_CommodityContractLiabilityCurrentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commodity Contract Liability, Current [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_CommodityContractLiabilityCurrentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commodity derivative liabilities, current</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_CommodityContractLiabilityNoncurrentMember" xlink:label="bkv_CommodityContractLiabilityNoncurrentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_CommodityContractLiabilityNoncurrentMember" xlink:to="bkv_CommodityContractLiabilityNoncurrentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_CommodityContractLiabilityNoncurrentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commodity Contract Liability, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_CommodityContractLiabilityNoncurrentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commodity Contract Liability, Noncurrent [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_CommodityContractLiabilityNoncurrentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commodity derivative liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativesFairValueLineItems" xlink:label="us-gaap_DerivativesFairValueLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativesFairValueLineItems" xlink:to="us-gaap_DerivativesFairValueLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativesFairValueLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivatives, Fair Value [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativesFairValueLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivatives, Fair Value [Line Items]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAssetsAbstract" xlink:label="us-gaap_DerivativeAssetsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeAssetsAbstract" xlink:to="us-gaap_DerivativeAssetsAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeAssetsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Asset [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeAssetsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Asset [Abstract]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:label="us-gaap_DerivativeFairValueOfDerivativeAsset" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:to="us-gaap_DerivativeFairValueOfDerivativeAsset_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeFairValueOfDerivativeAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Asset, Subject to Master Netting Arrangement, before Offset</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeFairValueOfDerivativeAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gross Amounts of Assets and Liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAssetFairValueGrossLiability" xlink:label="us-gaap_DerivativeAssetFairValueGrossLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeAssetFairValueGrossLiability" xlink:to="us-gaap_DerivativeAssetFairValueGrossLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeAssetFairValueGrossLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Asset, Subject to Master Netting Arrangement, Liability Offset</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_DerivativeAssetFairValueGrossLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Offset Adjustments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement" xlink:label="us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement" xlink:to="us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Asset, Subject to Master Netting Arrangement, after Offset</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Amounts of Assets and Liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLiabilitiesAbstract" xlink:label="us-gaap_DerivativeLiabilitiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeLiabilitiesAbstract" xlink:to="us-gaap_DerivativeLiabilitiesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeLiabilitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Liability [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeLiabilitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Liability [Abstract]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:label="us-gaap_DerivativeFairValueOfDerivativeLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:to="us-gaap_DerivativeFairValueOfDerivativeLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeFairValueOfDerivativeLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Liability, Subject to Master Netting Arrangement, before Offset</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DerivativeFairValueOfDerivativeLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gross Amounts of Assets and Liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:label="us-gaap_DerivativeLiabilityFairValueGrossAsset" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:to="us-gaap_DerivativeLiabilityFairValueGrossAsset_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeLiabilityFairValueGrossAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Liability, Subject to Master Netting Arrangement, Asset Offset</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_DerivativeLiabilityFairValueGrossAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Offset Adjustments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement" xlink:label="us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement" xlink:to="us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Liability, Subject to Master Netting Arrangement, after Offset</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Amounts of Assets and Liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeTable" xlink:label="us-gaap_DerivativeTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeTable" xlink:to="us-gaap_DerivativeTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative [Table]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative [Table]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_PurchasedPowerDerivativesMember" xlink:label="bkv_PurchasedPowerDerivativesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_PurchasedPowerDerivativesMember" xlink:to="bkv_PurchasedPowerDerivativesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_PurchasedPowerDerivativesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchased Power Derivatives</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_PurchasedPowerDerivativesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchased Power Derivatives [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_PurchasedPowerDerivativesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchased Power Derivatives</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLineItems" xlink:label="us-gaap_DerivativeLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeLineItems" xlink:to="us-gaap_DerivativeLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative [Line Items]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnSaleOfDerivatives" xlink:label="us-gaap_GainLossOnSaleOfDerivatives" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GainLossOnSaleOfDerivatives" xlink:to="us-gaap_GainLossOnSaleOfDerivatives_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GainLossOnSaleOfDerivatives_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) on Sale of Derivatives</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GainLossOnSaleOfDerivatives_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total realized gains on derivatives, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrealizedGainLossOnDerivativesAndCommodityContracts" xlink:label="us-gaap_UnrealizedGainLossOnDerivativesAndCommodityContracts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_UnrealizedGainLossOnDerivativesAndCommodityContracts" xlink:to="us-gaap_UnrealizedGainLossOnDerivativesAndCommodityContracts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_UnrealizedGainLossOnDerivativesAndCommodityContracts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unrealized Gain (Loss) on Derivatives and Commodity Contracts</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_UnrealizedGainLossOnDerivativesAndCommodityContracts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total unrealized gains (losses) on derivatives, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_NaturalGasReservesMember" xlink:label="srt_NaturalGasReservesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_NaturalGasReservesMember" xlink:to="srt_NaturalGasReservesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_NaturalGasReservesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural Gas [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_NaturalGasReservesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural gas</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_FixedPricePowerForwardMember" xlink:label="bkv_FixedPricePowerForwardMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_FixedPricePowerForwardMember" xlink:to="bkv_FixedPricePowerForwardMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_FixedPricePowerForwardMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fixed Price Power Forward</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_FixedPricePowerForwardMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fixed Price Power Forward [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_FixedPricePowerForwardMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Power forwards - sales</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_HeatRateCallOptionMember" xlink:label="bkv_HeatRateCallOptionMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_HeatRateCallOptionMember" xlink:to="bkv_HeatRateCallOptionMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_HeatRateCallOptionMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Heat Rate Call Option</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_HeatRateCallOptionMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Heat Rate Call Option [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_HeatRateCallOptionMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Heat rate call option</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_FixedPricePowerPurchaseMember" xlink:label="bkv_FixedPricePowerPurchaseMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_FixedPricePowerPurchaseMember" xlink:to="bkv_FixedPricePowerPurchaseMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_FixedPricePowerPurchaseMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fixed Price Power Purchase</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_FixedPricePowerPurchaseMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fixed Price Power Purchase [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_FixedPricePowerPurchaseMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Power forwards - purchases</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_A2026InstrumentMember" xlink:label="bkv_A2026InstrumentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_A2026InstrumentMember" xlink:to="bkv_A2026InstrumentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_A2026InstrumentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026 Instrument</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_A2026InstrumentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">A2026 Instrument [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_A2026InstrumentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeNonmonetaryNotionalAmountEnergyMeasure" xlink:label="us-gaap_DerivativeNonmonetaryNotionalAmountEnergyMeasure" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeNonmonetaryNotionalAmountEnergyMeasure" xlink:to="us-gaap_DerivativeNonmonetaryNotionalAmountEnergyMeasure_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeNonmonetaryNotionalAmountEnergyMeasure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative, Nonmonetary Notional Amount, Energy Measure</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeNonmonetaryNotionalAmountEnergyMeasure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Quantity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DerivativeNonmonetaryNotionalAmountEnergyMeasure_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">MMBtu</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_DerivativeNonmonetaryNotionalAmountPowerForwardsPurchases" xlink:label="bkv_DerivativeNonmonetaryNotionalAmountPowerForwardsPurchases" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_DerivativeNonmonetaryNotionalAmountPowerForwardsPurchases" xlink:to="bkv_DerivativeNonmonetaryNotionalAmountPowerForwardsPurchases_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_DerivativeNonmonetaryNotionalAmountPowerForwardsPurchases_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Nominal power forwards-purchases used to calculate payments on a derivative instrument.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_DerivativeNonmonetaryNotionalAmountPowerForwardsPurchases_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative, Nonmonetary Notional Amount, Power forwards, purchases</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_DerivativeNonmonetaryNotionalAmountPowerForwardsPurchases_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Power forwards - purchases, quantity</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeFairValueOfDerivativeNet" xlink:label="us-gaap_DerivativeFairValueOfDerivativeNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeFairValueOfDerivativeNet" xlink:to="us-gaap_DerivativeFairValueOfDerivativeNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeFairValueOfDerivativeNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative, Fair Value, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeFairValueOfDerivativeNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative, fair value, net</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_A2026SwapMember" xlink:label="bkv_A2026SwapMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_A2026SwapMember" xlink:to="bkv_A2026SwapMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_A2026SwapMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026 Swap</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_A2026SwapMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026 Swap [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_A2026SwapMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026 Swap</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_A2027SwapMember" xlink:label="bkv_A2027SwapMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_A2027SwapMember" xlink:to="bkv_A2027SwapMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_A2027SwapMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027 Swap</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_A2027SwapMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027 Swap [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_A2027SwapMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027 Swap</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_A2027CollarsMember" xlink:label="bkv_A2027CollarsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_A2027CollarsMember" xlink:to="bkv_A2027CollarsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_A2027CollarsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027 Collars</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_A2027CollarsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027 Collars [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_A2027CollarsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027 Collars</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_A2027CallOptionMember" xlink:label="bkv_A2027CallOptionMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_A2027CallOptionMember" xlink:to="bkv_A2027CallOptionMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_A2027CallOptionMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027 Call Option</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_A2027CallOptionMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027 Call Option [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_A2027CallOptionMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027 Call Option</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_A2027PutOptionsMember" xlink:label="bkv_A2027PutOptionsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_A2027PutOptionsMember" xlink:to="bkv_A2027PutOptionsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_A2027PutOptionsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027 Put Options</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_A2027PutOptionsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027 Put Options [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_A2027PutOptionsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027 Put Options</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_A2028SwapMember" xlink:label="bkv_A2028SwapMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_A2028SwapMember" xlink:to="bkv_A2028SwapMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_A2028SwapMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2028 Swap</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_A2028SwapMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2028 Swap [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_A2028SwapMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2028 Swap</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ReferencePriceAxis" xlink:label="bkv_ReferencePriceAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ReferencePriceAxis" xlink:to="bkv_ReferencePriceAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ReferencePriceAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reference Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ReferencePriceAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reference Price [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ReferencePriceAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reference Price [Axis]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ReferencePriceDomain" xlink:label="bkv_ReferencePriceDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ReferencePriceDomain" xlink:to="bkv_ReferencePriceDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ReferencePriceDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reference Price [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ReferencePriceDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reference Price [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ReferencePriceDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reference Price [Domain]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_NaturalGasTranscoLeidyBasisMember" xlink:label="bkv_NaturalGasTranscoLeidyBasisMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_NaturalGasTranscoLeidyBasisMember" xlink:to="bkv_NaturalGasTranscoLeidyBasisMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_NaturalGasTranscoLeidyBasisMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural Gas, Transco Leidy Basis</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_NaturalGasTranscoLeidyBasisMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural Gas, Transco Leidy Basis [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_NaturalGasTranscoLeidyBasisMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Transco Leidy Basis</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_NaturalGasHSCBasisMember" xlink:label="bkv_NaturalGasHSCBasisMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_NaturalGasHSCBasisMember" xlink:to="bkv_NaturalGasHSCBasisMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_NaturalGasHSCBasisMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural Gas, HSC Basis</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_NaturalGasHSCBasisMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural Gas, HSC Basis [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_NaturalGasHSCBasisMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">HSC Basis</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_NaturalGasTranscoSt85Z4BasisMember" xlink:label="bkv_NaturalGasTranscoSt85Z4BasisMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_NaturalGasTranscoSt85Z4BasisMember" xlink:to="bkv_NaturalGasTranscoSt85Z4BasisMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_NaturalGasTranscoSt85Z4BasisMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural Gas, Transco St 85 (Z4) Basis</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_NaturalGasTranscoSt85Z4BasisMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural Gas, Transco St 85 (Z4) Basis [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_NaturalGasTranscoSt85Z4BasisMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Transco St 85 (Z4) Basis</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_NaturalGasNGPLTXOKMember" xlink:label="bkv_NaturalGasNGPLTXOKMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_NaturalGasNGPLTXOKMember" xlink:to="bkv_NaturalGasNGPLTXOKMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_NaturalGasNGPLTXOKMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural Gas, NGPL TXOK</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_NaturalGasNGPLTXOKMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural Gas, NGPL TXOK [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_NaturalGasNGPLTXOKMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">NGPL TXOK Basis</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_DerivativeAverageContractPrice" xlink:label="bkv_DerivativeAverageContractPrice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_DerivativeAverageContractPrice" xlink:to="bkv_DerivativeAverageContractPrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_DerivativeAverageContractPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative, Average Contract Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_DerivativeAverageContractPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative, Average Contract Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_DerivativeAverageContractPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted Average Price (in USD per unit)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAverageCapPrice" xlink:label="us-gaap_DerivativeAverageCapPrice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeAverageCapPrice" xlink:to="us-gaap_DerivativeAverageCapPrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeAverageCapPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative, Average Cap Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeAverageCapPrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted Average Price Ceiling (in USD per unit)</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_DerivativeWeightedAverageBasisDifferential" xlink:label="bkv_DerivativeWeightedAverageBasisDifferential" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_DerivativeWeightedAverageBasisDifferential" xlink:to="bkv_DerivativeWeightedAverageBasisDifferential_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_DerivativeWeightedAverageBasisDifferential_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative, Weighted Average Basis Differential</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_DerivativeWeightedAverageBasisDifferential_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative, Weighted Average Basis Differential</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_DerivativeWeightedAverageBasisDifferential_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted Average Basis Differential</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_OPISPurityEthaneMontBelvieuMember" xlink:label="bkv_OPISPurityEthaneMontBelvieuMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_OPISPurityEthaneMontBelvieuMember" xlink:to="bkv_OPISPurityEthaneMontBelvieuMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_OPISPurityEthaneMontBelvieuMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">OPIS Purity Ethane Mont Belvieu</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_OPISPurityEthaneMontBelvieuMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">OPIS Purity Ethane Mont Belvieu [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_OPISPurityEthaneMontBelvieuMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">OPIS Purity Ethane Mont Belvieu</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_OPISIsoButaneMontBelvieuNonTETMember" xlink:label="bkv_OPISIsoButaneMontBelvieuNonTETMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_OPISIsoButaneMontBelvieuNonTETMember" xlink:to="bkv_OPISIsoButaneMontBelvieuNonTETMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_OPISIsoButaneMontBelvieuNonTETMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">OPIS IsoButane Mont Belvieu Non-TET</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_OPISIsoButaneMontBelvieuNonTETMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">OPIS IsoButane Mont Belvieu Non-TET [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_OPISIsoButaneMontBelvieuNonTETMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">OPIS IsoButane Mont Belvieu Non-TET</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_OPISNormalButaneMontBelvieuNonTETMember" xlink:label="bkv_OPISNormalButaneMontBelvieuNonTETMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_OPISNormalButaneMontBelvieuNonTETMember" xlink:to="bkv_OPISNormalButaneMontBelvieuNonTETMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_OPISNormalButaneMontBelvieuNonTETMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">OPIS Normal Butane Mont Belvieu Non-TET</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_OPISNormalButaneMontBelvieuNonTETMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">OPIS Normal Butane Mont Belvieu Non-TET [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_OPISNormalButaneMontBelvieuNonTETMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">OPIS Normal Butane Mont Belvieu Non-TET</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_OPISPropaneMontBelvieuNonTETMember" xlink:label="bkv_OPISPropaneMontBelvieuNonTETMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_OPISPropaneMontBelvieuNonTETMember" xlink:to="bkv_OPISPropaneMontBelvieuNonTETMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_OPISPropaneMontBelvieuNonTETMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">OPIS Propane Mont Belvieu Non-TET</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_OPISPropaneMontBelvieuNonTETMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">OPIS Propane Mont Belvieu Non-TET [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_OPISPropaneMontBelvieuNonTETMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">OPIS Propane Mont Belvieu Non-TET</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_OPISNaturalGasolineMontBelvieuNonTETMember" xlink:label="bkv_OPISNaturalGasolineMontBelvieuNonTETMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_OPISNaturalGasolineMontBelvieuNonTETMember" xlink:to="bkv_OPISNaturalGasolineMontBelvieuNonTETMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_OPISNaturalGasolineMontBelvieuNonTETMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">OPIS Natural Gasoline Mont Belvieu Non-TET</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_OPISNaturalGasolineMontBelvieuNonTETMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">OPIS Natural Gasoline Mont Belvieu Non-TET [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_OPISNaturalGasolineMontBelvieuNonTETMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">OPIS Natural Gasoline Mont Belvieu Non-TET</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeNonmonetaryNotionalAmountVolume" xlink:label="us-gaap_DerivativeNonmonetaryNotionalAmountVolume" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeNonmonetaryNotionalAmountVolume" xlink:to="us-gaap_DerivativeNonmonetaryNotionalAmountVolume_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeNonmonetaryNotionalAmountVolume_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative, Nonmonetary Notional Amount, Volume</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeNonmonetaryNotionalAmountVolume_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gallons</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetRetirementObligationAccretionExpense" xlink:label="us-gaap_AssetRetirementObligationAccretionExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetRetirementObligationAccretionExpense" xlink:to="us-gaap_AssetRetirementObligationAccretionExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetRetirementObligationAccretionExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Retirement Obligation, Accretion Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetRetirementObligationAccretionExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accretion of discount</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetRetirementObligationRollForwardAnalysisRollForward" xlink:label="us-gaap_AssetRetirementObligationRollForwardAnalysisRollForward" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetRetirementObligationRollForwardAnalysisRollForward" xlink:to="us-gaap_AssetRetirementObligationRollForwardAnalysisRollForward_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetRetirementObligationRollForwardAnalysisRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Retirement Obligation, Roll Forward Analysis [Roll Forward]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetRetirementObligationRollForwardAnalysisRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset retirement obligations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetRetirementObligation" xlink:label="us-gaap_AssetRetirementObligation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetRetirementObligation" xlink:to="us-gaap_AssetRetirementObligation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetRetirementObligation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Retirement Obligation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_AssetRetirementObligation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Balance, as of December 31,</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_AssetRetirementObligation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Balance, as of January 1,</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_AssetRetirementObligationAdditionsThroughAcquisitions" xlink:label="bkv_AssetRetirementObligationAdditionsThroughAcquisitions" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_AssetRetirementObligationAdditionsThroughAcquisitions" xlink:to="bkv_AssetRetirementObligationAdditionsThroughAcquisitions_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_AssetRetirementObligationAdditionsThroughAcquisitions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Retirement Obligation, Additions Through Acquisitions</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AssetRetirementObligationAdditionsThroughAcquisitions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Retirement Obligation, Additions Through Acquisitions</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_AssetRetirementObligationAdditionsThroughAcquisitions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additions through acquisitions (1)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetRetirementObligationLiabilitiesSettled" xlink:label="us-gaap_AssetRetirementObligationLiabilitiesSettled" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetRetirementObligationLiabilitiesSettled" xlink:to="us-gaap_AssetRetirementObligationLiabilitiesSettled_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetRetirementObligationLiabilitiesSettled_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Retirement Obligation, Liabilities Settled</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_AssetRetirementObligationLiabilitiesSettled_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities settled</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_AssetRetirementObligationLiabilitiesAssociatedWithPropertySold" xlink:label="bkv_AssetRetirementObligationLiabilitiesAssociatedWithPropertySold" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_AssetRetirementObligationLiabilitiesAssociatedWithPropertySold" xlink:to="bkv_AssetRetirementObligationLiabilitiesAssociatedWithPropertySold_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_AssetRetirementObligationLiabilitiesAssociatedWithPropertySold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Retirement Obligation, Liabilities Associated With Property Sold</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AssetRetirementObligationLiabilitiesAssociatedWithPropertySold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Retirement Obligation, Liabilities Associated With Property Sold</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="bkv_AssetRetirementObligationLiabilitiesAssociatedWithPropertySold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities associated with property sold</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetRetirementObligationCurrent" xlink:label="us-gaap_AssetRetirementObligationCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetRetirementObligationCurrent" xlink:to="us-gaap_AssetRetirementObligationCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetRetirementObligationCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Retirement Obligation, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_AssetRetirementObligationCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less current portion</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party Transaction [Table]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party Transaction [Table]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TempleGenerationILLCMember" xlink:label="bkv_TempleGenerationILLCMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_TempleGenerationILLCMember" xlink:to="bkv_TempleGenerationILLCMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TempleGenerationILLCMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temple Generation I LLC</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_TempleGenerationILLCMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temple Generation I LLC [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_TempleGenerationILLCMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temple Generation I LLC</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionAxis" xlink:label="us-gaap_RelatedPartyTransactionAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionAxis" xlink:to="us-gaap_RelatedPartyTransactionAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party Transaction [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RelatedPartyTransactionAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party Transaction [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionDomain" xlink:label="us-gaap_RelatedPartyTransactionDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionDomain" xlink:to="us-gaap_RelatedPartyTransactionDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party Transaction [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RelatedPartyTransactionDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party Transaction [Domain]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_SharedGeneralAndAdministrativeExpensesMember" xlink:label="bkv_SharedGeneralAndAdministrativeExpensesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_SharedGeneralAndAdministrativeExpensesMember" xlink:to="bkv_SharedGeneralAndAdministrativeExpensesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_SharedGeneralAndAdministrativeExpensesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shared General And Administrative Expenses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_SharedGeneralAndAdministrativeExpensesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shared General And Administrative Expenses [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_SharedGeneralAndAdministrativeExpensesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shared General And Administrative Expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionLineItems" xlink:label="us-gaap_RelatedPartyTransactionLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_RelatedPartyTransactionLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party Transaction [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RelatedPartyTransactionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party Transaction [Line Items]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseDebt" xlink:label="us-gaap_InterestExpenseDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestExpenseDebt" xlink:to="us-gaap_InterestExpenseDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InterestExpenseDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Expense, Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InterestExpenseDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest expense</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisaggregationOfRevenueTable" xlink:label="us-gaap_DisaggregationOfRevenueTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisaggregationOfRevenueTable" xlink:to="us-gaap_DisaggregationOfRevenueTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisaggregationOfRevenueTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disaggregation of Revenue [Table]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisaggregationOfRevenueTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disaggregation of Revenue [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_NaturalGasLiquidsReservesMember" xlink:label="srt_NaturalGasLiquidsReservesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_NaturalGasLiquidsReservesMember" xlink:to="srt_NaturalGasLiquidsReservesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_NaturalGasLiquidsReservesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural Gas Liquids (NGL) [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_NaturalGasLiquidsReservesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">NGLs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OilReservesMember" xlink:label="srt_OilReservesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_OilReservesMember" xlink:to="srt_OilReservesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_OilReservesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Crude Oil, Condensate, and Natural Gas Liquids (NGL) [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_OilReservesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_MerchantEnergySalesAndOtherMember" xlink:label="bkv_MerchantEnergySalesAndOtherMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_MerchantEnergySalesAndOtherMember" xlink:to="bkv_MerchantEnergySalesAndOtherMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_MerchantEnergySalesAndOtherMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">represents information pertaining to merchant energy sales and other</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_MerchantEnergySalesAndOtherMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Merchant Energy Sales And Other [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_MerchantEnergySalesAndOtherMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Merchant energy sales and other</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_EnergyRetailSalesMember" xlink:label="bkv_EnergyRetailSalesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_EnergyRetailSalesMember" xlink:to="bkv_EnergyRetailSalesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_EnergyRetailSalesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to energy retail sales.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_EnergyRetailSalesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Energy Retail Sales [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_EnergyRetailSalesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Energy retail sales</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_SolarRevenueMember" xlink:label="bkv_SolarRevenueMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_SolarRevenueMember" xlink:to="bkv_SolarRevenueMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_SolarRevenueMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to solar revenue.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_SolarRevenueMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Solar Revenue [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_SolarRevenueMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Solar revenue</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_PhysicalPowerPurchasedMember" xlink:label="bkv_PhysicalPowerPurchasedMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_PhysicalPowerPurchasedMember" xlink:to="bkv_PhysicalPowerPurchasedMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_PhysicalPowerPurchasedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to physical power purchased.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_PhysicalPowerPurchasedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Physical Power Purchased [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_PhysicalPowerPurchasedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Physical power purchased</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/stpr/2025/stpr-2025.xsd#stpr_PA" xlink:label="stpr_PA" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="stpr_PA" xlink:to="stpr_PA_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="stpr_PA_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">PENNSYLVANIA</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="stpr_PA_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Pennsylvania</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/stpr/2025/stpr-2025.xsd#stpr_TX" xlink:label="stpr_TX" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="stpr_TX" xlink:to="stpr_TX_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="stpr_TX_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">TEXAS</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="stpr_TX_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Texas</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisaggregationOfRevenueLineItems" xlink:label="us-gaap_DisaggregationOfRevenueLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisaggregationOfRevenueLineItems" xlink:to="us-gaap_DisaggregationOfRevenueLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisaggregationOfRevenueLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disaggregation of Revenue [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisaggregationOfRevenueLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disaggregation of Revenue [Line Items]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:to="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue from Contract with Customer, Excluding Assessed Tax</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenues</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:label="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:to="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts and Financing Receivables [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:label="us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:to="us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Receivable Type [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReceivableTypeDomain" xlink:label="us-gaap_ReceivableTypeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ReceivableTypeDomain" xlink:to="us-gaap_ReceivableTypeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ReceivableTypeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Receivable [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CustomerContractsMember" xlink:label="us-gaap_CustomerContractsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CustomerContractsMember" xlink:to="us-gaap_CustomerContractsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CustomerContractsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer Contracts [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CustomerContractsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contracts with customers</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember" xlink:label="us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember" xlink:to="us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative Financial Instruments, Liabilities [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Derivative instruments</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_OtherReceivableMember" xlink:label="bkv_OtherReceivableMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_OtherReceivableMember" xlink:to="bkv_OtherReceivableMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_OtherReceivableMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to other receivable.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_OtherReceivableMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Receivable [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_OtherReceivableMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">other</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:label="us-gaap_AccountsNotesAndLoansReceivableLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:to="us-gaap_AccountsNotesAndLoansReceivableLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsNotesAndLoansReceivableLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts, Notes, Loans and Financing Receivable [Line Items]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsReceivableGross" xlink:label="us-gaap_AccountsReceivableGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableGross" xlink:to="us-gaap_AccountsReceivableGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsReceivableGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, before Allowance for Credit Loss</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccountsReceivableGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts receivable, Gross</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:to="us-gaap_AllowanceForDoubtfulAccountsReceivable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, Allowance for Credit Loss</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Allowance for credit losses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsReceivableNet" xlink:label="us-gaap_AccountsReceivableNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableNet" xlink:to="us-gaap_AccountsReceivableNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsReceivableNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, after Allowance for Credit Loss</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_AccountsReceivableNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total accounts receivable, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsPayableCurrent" xlink:label="us-gaap_AccountsPayableCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsPayableCurrent" xlink:to="us-gaap_AccountsPayableCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Payable, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractWithCustomerLiabilityCurrent" xlink:label="us-gaap_ContractWithCustomerLiabilityCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ContractWithCustomerLiabilityCurrent" xlink:to="us-gaap_ContractWithCustomerLiabilityCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ContractWithCustomerLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract with Customer, Liability, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ContractWithCustomerLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenues payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:to="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Employee-related Liabilities, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued payroll</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SettlementLiabilitiesCurrent" xlink:label="us-gaap_SettlementLiabilitiesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SettlementLiabilitiesCurrent" xlink:to="us-gaap_SettlementLiabilitiesCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SettlementLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Settlement Liabilities, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SettlementLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commodity derivative settlements payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAccruedLiabilitiesCurrent" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherAccruedLiabilitiesCurrent" xlink:to="us-gaap_OtherAccruedLiabilitiesCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Accrued Liabilities, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other accrued liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:to="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PlanNameAxis" xlink:label="us-gaap_PlanNameAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PlanNameAxis" xlink:to="us-gaap_PlanNameAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PlanNameAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Plan Name [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PlanNameAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Plan Name [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PlanNameDomain" xlink:label="us-gaap_PlanNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PlanNameDomain" xlink:to="us-gaap_PlanNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PlanNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Plan Name [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PlanNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Plan Name [Domain]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_A2024EquityAndIncentiveCompensationPlanMember" xlink:label="bkv_A2024EquityAndIncentiveCompensationPlanMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_A2024EquityAndIncentiveCompensationPlanMember" xlink:to="bkv_A2024EquityAndIncentiveCompensationPlanMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_A2024EquityAndIncentiveCompensationPlanMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2024 Equity And Incentive Compensation Plan</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_A2024EquityAndIncentiveCompensationPlanMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2024 Equity And Incentive Compensation Plan [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_A2024EquityAndIncentiveCompensationPlanMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2024 Equity and Incentive Compensation Plan</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AwardTypeAxis" xlink:label="us-gaap_AwardTypeAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AwardTypeAxis" xlink:to="us-gaap_AwardTypeAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AwardTypeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Award Type [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AwardTypeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Award Type</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Award Type [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">All Award Types</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_PerformanceBasedRestrictedStockUnitsMember" xlink:label="bkv_PerformanceBasedRestrictedStockUnitsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_PerformanceBasedRestrictedStockUnitsMember" xlink:to="bkv_PerformanceBasedRestrictedStockUnitsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_PerformanceBasedRestrictedStockUnitsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Performance-Based Restricted Stock Units</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_PerformanceBasedRestrictedStockUnitsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Performance-Based Restricted Stock Units [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_PerformanceBasedRestrictedStockUnitsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">PRSUs</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_PerformanceBasedRestrictedStockUnitsAnnualizedTotalShareholderReturnMember" xlink:label="bkv_PerformanceBasedRestrictedStockUnitsAnnualizedTotalShareholderReturnMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_PerformanceBasedRestrictedStockUnitsAnnualizedTotalShareholderReturnMember" xlink:to="bkv_PerformanceBasedRestrictedStockUnitsAnnualizedTotalShareholderReturnMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_PerformanceBasedRestrictedStockUnitsAnnualizedTotalShareholderReturnMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Performance-Based Restricted Stock Units, Annualized Total Shareholder Return</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_PerformanceBasedRestrictedStockUnitsAnnualizedTotalShareholderReturnMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Performance-Based Restricted Stock Units, Annualized Total Shareholder Return [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_PerformanceBasedRestrictedStockUnitsAnnualizedTotalShareholderReturnMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">aTSR</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_PerformanceBasedRestrictedStockUnitsRelativeTotalShareholderReturnMember" xlink:label="bkv_PerformanceBasedRestrictedStockUnitsRelativeTotalShareholderReturnMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_PerformanceBasedRestrictedStockUnitsRelativeTotalShareholderReturnMember" xlink:to="bkv_PerformanceBasedRestrictedStockUnitsRelativeTotalShareholderReturnMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_PerformanceBasedRestrictedStockUnitsRelativeTotalShareholderReturnMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Performance-Based Restricted Stock Units, Relative Total Shareholder Return</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_PerformanceBasedRestrictedStockUnitsRelativeTotalShareholderReturnMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Performance-Based Restricted Stock Units, Relative Total Shareholder Return [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_PerformanceBasedRestrictedStockUnitsRelativeTotalShareholderReturnMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">rTSR</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_PerformanceBasedRestrictedStockUnitsROCEComponentMember" xlink:label="bkv_PerformanceBasedRestrictedStockUnitsROCEComponentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_PerformanceBasedRestrictedStockUnitsROCEComponentMember" xlink:to="bkv_PerformanceBasedRestrictedStockUnitsROCEComponentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_PerformanceBasedRestrictedStockUnitsROCEComponentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Performance-Based Restricted Stock Units, ROCE Component</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_PerformanceBasedRestrictedStockUnitsROCEComponentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Performance-Based Restricted Stock Units, ROCE Component [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_PerformanceBasedRestrictedStockUnitsROCEComponentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ROCE component of the Performance-Based Restricted Stock Units</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TimeBasedRestrictedStockUnitsMember" xlink:label="bkv_TimeBasedRestrictedStockUnitsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_TimeBasedRestrictedStockUnitsMember" xlink:to="bkv_TimeBasedRestrictedStockUnitsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TimeBasedRestrictedStockUnitsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Time-Based Restricted Stock Units</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_TimeBasedRestrictedStockUnitsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Time-Based Restricted Stock Units [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_TimeBasedRestrictedStockUnitsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">TRSUs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AwardDateAxis" xlink:label="us-gaap_AwardDateAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AwardDateAxis" xlink:to="us-gaap_AwardDateAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AwardDateAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Award Date [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AwardDateAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Award Date [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AwardDateDomain" xlink:label="us-gaap_AwardDateDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AwardDateDomain" xlink:to="us-gaap_AwardDateDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AwardDateDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Award Date [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AwardDateDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Award Date [Domain]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_GrantsIn2024Member" xlink:label="bkv_GrantsIn2024Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_GrantsIn2024Member" xlink:to="bkv_GrantsIn2024Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_GrantsIn2024Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Grants In 2024</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_GrantsIn2024Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Grants In 2024 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_GrantsIn2024Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Grants In 2024</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_GrantsIn2025Member" xlink:label="bkv_GrantsIn2025Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_GrantsIn2025Member" xlink:to="bkv_GrantsIn2025Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_GrantsIn2025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Grants In 2025</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_GrantsIn2025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Grants In 2025 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_GrantsIn2025Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Grants In 2025</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrantIncrease" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrantIncrease" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrantIncrease" xlink:to="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrantIncrease_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrantIncrease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement By Share-Based Payment Award, Number Of Shares Available For Grant, Increase</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrantIncrease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement By Share-Based Payment Award, Number Of Shares Available For Grant, Increase</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrantIncrease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase to shares available for grant (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:label="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:to="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Capital Shares Reserved for Future Issuance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares received from capital contribution (in shares)</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardCommonStockAvailableReductionConversionBasis" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardCommonStockAvailableReductionConversionBasis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardCommonStockAvailableReductionConversionBasis" xlink:to="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardCommonStockAvailableReductionConversionBasis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardCommonStockAvailableReductionConversionBasis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Common Stock Available Reduction, Conversion Basis</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardCommonStockAvailableReductionConversionBasis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Common Stock Available Reduction, Conversion Basis</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardCommonStockAvailableReductionConversionBasis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-based compensation arrangement by share-based payment award, common stock available reduction, conversion basis</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Available for Grant</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares available for grant (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Granted (in shares)</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardWeightedAverageCommonStock" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardWeightedAverageCommonStock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardWeightedAverageCommonStock" xlink:to="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardWeightedAverageCommonStock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardWeightedAverageCommonStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Weighted Average Common Stock</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardWeightedAverageCommonStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Weighted Average Common Stock</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardWeightedAverageCommonStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted average common stock percentage</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardTargetPerformanceEstimatedPercentageBelowTarget" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardTargetPerformanceEstimatedPercentageBelowTarget" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardTargetPerformanceEstimatedPercentageBelowTarget" xlink:to="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardTargetPerformanceEstimatedPercentageBelowTarget_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardTargetPerformanceEstimatedPercentageBelowTarget_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement By Share-Based Payment Award, Target Performance, Estimated Percentage Below Target</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardTargetPerformanceEstimatedPercentageBelowTarget_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement By Share-Based Payment Award, Target Performance, Estimated Percentage Below Target</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardTargetPerformanceEstimatedPercentageBelowTarget_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Estimated percentage below target</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Number of Shares [Roll Forward]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Number</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unvested RSUs, ending balance (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unvested RSUs, beginning balance (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Vested in Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vested (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Forfeited (in shares)</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Weighted Average Grant Date Fair Value [Abstract]</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Weighted Average Grant Date Fair Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unvested RSUs, ending balance (in USD per share)</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumOfferingPeriod" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumOfferingPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumOfferingPeriod" xlink:to="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumOfferingPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumOfferingPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Maximum Offering Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumOfferingPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Maximum Offering Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumOfferingPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum offering period</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ShareBasedCompensationArrangementNumberOfOfferingPeriods" xlink:label="bkv_ShareBasedCompensationArrangementNumberOfOfferingPeriods" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ShareBasedCompensationArrangementNumberOfOfferingPeriods" xlink:to="bkv_ShareBasedCompensationArrangementNumberOfOfferingPeriods_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ShareBasedCompensationArrangementNumberOfOfferingPeriods_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share Based Compensation Arrangement, Number Of Offering Periods</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ShareBasedCompensationArrangementNumberOfOfferingPeriods_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share Based Compensation Arrangement, Number Of Offering Periods</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ShareBasedCompensationArrangementNumberOfOfferingPeriods_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of offering periods</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_A2021EquityAndIncentiveCompensationPlanMember" xlink:label="bkv_A2021EquityAndIncentiveCompensationPlanMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_A2021EquityAndIncentiveCompensationPlanMember" xlink:to="bkv_A2021EquityAndIncentiveCompensationPlanMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_A2021EquityAndIncentiveCompensationPlanMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2021 Equity and Incentive Compensation Plan</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_A2021EquityAndIncentiveCompensationPlanMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2021 Equity and Incentive Compensation Plan [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_A2021EquityAndIncentiveCompensationPlanMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2021 Equity and Incentive Compensation Plan</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardThresholdAxis" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardThresholdAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardThresholdAxis" xlink:to="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardThresholdAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardThresholdAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-based Payment Award, Threshold</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardThresholdAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-based Payment Award, Threshold [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardThresholdAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-based Payment Award, Threshold [Axis]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardThresholdDomain" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardThresholdDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardThresholdDomain" xlink:to="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardThresholdDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardThresholdDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-based Payment Award, Threshold [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardThresholdDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-based Payment Award, Threshold [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardThresholdDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-based Payment Award, Threshold [Domain]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TotalShareholderReturnMember" xlink:label="bkv_TotalShareholderReturnMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_TotalShareholderReturnMember" xlink:to="bkv_TotalShareholderReturnMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TotalShareholderReturnMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total Shareholder Return</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_TotalShareholderReturnMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total Shareholder Return [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_TotalShareholderReturnMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">TSR</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ROCEMember" xlink:label="bkv_ROCEMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ROCEMember" xlink:to="bkv_ROCEMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ROCEMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ROCE</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ROCEMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ROCE [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ROCEMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ROCE</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardPeriodFollowingInception" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardPeriodFollowingInception" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardPeriodFollowingInception" xlink:to="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardPeriodFollowingInception_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardPeriodFollowingInception_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Period Following Inception</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardPeriodFollowingInception_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Period Following Inception</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardPeriodFollowingInception_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period following inception</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardThreshold" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardThreshold" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardThreshold" xlink:to="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardThreshold_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardThreshold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Threshold</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardThreshold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Threshold</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardThreshold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-based compensation arrangement by share-based payment award, threshold</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodFairValuePerShare" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodFairValuePerShare" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodFairValuePerShare" xlink:to="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodFairValuePerShare_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodFairValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Vested in Period, Fair Value Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodFairValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Vested in Period, Fair Value Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodFairValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total fair value of the shares vested (in USD per share)</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_PerformanceBasedRestrictedStockUnitsAnnualAndRelativeTotalShareholderReturnMember" xlink:label="bkv_PerformanceBasedRestrictedStockUnitsAnnualAndRelativeTotalShareholderReturnMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_PerformanceBasedRestrictedStockUnitsAnnualAndRelativeTotalShareholderReturnMember" xlink:to="bkv_PerformanceBasedRestrictedStockUnitsAnnualAndRelativeTotalShareholderReturnMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_PerformanceBasedRestrictedStockUnitsAnnualAndRelativeTotalShareholderReturnMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Performance-Based Restricted Stock Units, Annual And Relative Total Shareholder Return</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_PerformanceBasedRestrictedStockUnitsAnnualAndRelativeTotalShareholderReturnMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Performance-Based Restricted Stock Units, Annual And Relative Total Shareholder Return [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_PerformanceBasedRestrictedStockUnitsAnnualAndRelativeTotalShareholderReturnMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Performance-Based Restricted Stock Units, Annual And Relative Total Shareholder Return</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Volatility Rate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Volatility rate</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Risk Free Interest Rate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Risk free interest rate</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1" xlink:to="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Term</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfCapitalUnitsTable" xlink:label="us-gaap_ScheduleOfCapitalUnitsTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfCapitalUnitsTable" xlink:to="us-gaap_ScheduleOfCapitalUnitsTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfCapitalUnitsTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity, Capital Unit or Share [Table]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfCapitalUnitsTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity, Capital Unit or Share [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalUnitLineItems" xlink:label="us-gaap_CapitalUnitLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CapitalUnitLineItems" xlink:to="us-gaap_CapitalUnitLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CapitalUnitLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capital Unit [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CapitalUnitLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capital Unit [Line Items]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityNoteStockSplitConversionRatio1" xlink:label="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1" xlink:to="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockholders' Equity Note, Stock Split, Conversion Ratio</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock split, conversion ratio</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_SaleOfStockConsiderationReceivedOnTransactionGross" xlink:label="bkv_SaleOfStockConsiderationReceivedOnTransactionGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_SaleOfStockConsiderationReceivedOnTransactionGross" xlink:to="bkv_SaleOfStockConsiderationReceivedOnTransactionGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_SaleOfStockConsiderationReceivedOnTransactionGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Stock, Consideration Received on Transaction, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_SaleOfStockConsiderationReceivedOnTransactionGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Stock, Consideration Received on Transaction, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_SaleOfStockConsiderationReceivedOnTransactionGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gross proceeds</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_AssetAcquisitionConsiderationEquityValueThreshold" xlink:label="bkv_AssetAcquisitionConsiderationEquityValueThreshold" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_AssetAcquisitionConsiderationEquityValueThreshold" xlink:to="bkv_AssetAcquisitionConsiderationEquityValueThreshold_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_AssetAcquisitionConsiderationEquityValueThreshold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Consideration, Equity Value Threshold</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AssetAcquisitionConsiderationEquityValueThreshold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition, Consideration, Equity Value Threshold</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_AssetAcquisitionConsiderationEquityValueThreshold_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset acquisition, consideration, equity value threshold</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_SharePriceWeightedAverageOverConsecutiveTradingDays" xlink:label="bkv_SharePriceWeightedAverageOverConsecutiveTradingDays" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_SharePriceWeightedAverageOverConsecutiveTradingDays" xlink:to="bkv_SharePriceWeightedAverageOverConsecutiveTradingDays_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_SharePriceWeightedAverageOverConsecutiveTradingDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share Price, Weighted Average Over Consecutive Trading Days</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_SharePriceWeightedAverageOverConsecutiveTradingDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share Price, Weighted Average Over Consecutive Trading Days</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_SharePriceWeightedAverageOverConsecutiveTradingDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share price, weighted average over consecutive trading days (in USD per share)</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_AssetAcquisitionConvertibleThresholdConsecutiveTradingDays" xlink:label="bkv_AssetAcquisitionConvertibleThresholdConsecutiveTradingDays" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_AssetAcquisitionConvertibleThresholdConsecutiveTradingDays" xlink:to="bkv_AssetAcquisitionConvertibleThresholdConsecutiveTradingDays_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_AssetAcquisitionConvertibleThresholdConsecutiveTradingDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition , Convertible, Threshold Consecutive Trading Days</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AssetAcquisitionConvertibleThresholdConsecutiveTradingDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset Acquisition , Convertible, Threshold Consecutive Trading Days</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_AssetAcquisitionConvertibleThresholdConsecutiveTradingDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset acquisition, convertible, threshold consecutive trading days</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_EquityInvestmentsCapitalCall" xlink:label="bkv_EquityInvestmentsCapitalCall" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_EquityInvestmentsCapitalCall" xlink:to="bkv_EquityInvestmentsCapitalCall_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_EquityInvestmentsCapitalCall_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Investments, Capital Call</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_EquityInvestmentsCapitalCall_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Investments, Capital Call</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_EquityInvestmentsCapitalCall_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capital call</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_EquityInvestmentsContributedCapitalShares" xlink:label="bkv_EquityInvestmentsContributedCapitalShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_EquityInvestmentsContributedCapitalShares" xlink:to="bkv_EquityInvestmentsContributedCapitalShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_EquityInvestmentsContributedCapitalShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Investments, Contributed Capital, Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_EquityInvestmentsContributedCapitalShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Investments, Contributed Capital, Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_EquityInvestmentsContributedCapitalShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contributed capital (in shares)</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_EquityInvestmentsContributedCapitalPlaceInDebtReserveAccount" xlink:label="bkv_EquityInvestmentsContributedCapitalPlaceInDebtReserveAccount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_EquityInvestmentsContributedCapitalPlaceInDebtReserveAccount" xlink:to="bkv_EquityInvestmentsContributedCapitalPlaceInDebtReserveAccount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_EquityInvestmentsContributedCapitalPlaceInDebtReserveAccount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Investments, Contributed Capital Place In Debt Reserve Account</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_EquityInvestmentsContributedCapitalPlaceInDebtReserveAccount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Investments, Contributed Capital Place In Debt Reserve Account</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_EquityInvestmentsContributedCapitalPlaceInDebtReserveAccount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contributed capital</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityByClassOfStockTable" xlink:label="us-gaap_TemporaryEquityByClassOfStockTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityByClassOfStockTable" xlink:to="us-gaap_TemporaryEquityByClassOfStockTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TemporaryEquityByClassOfStockTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, by Class of Stock [Table]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TemporaryEquityByClassOfStockTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, by Class of Stock [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementClassOfStockAxis" xlink:to="us-gaap_StatementClassOfStockAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementClassOfStockAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class of Stock [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StatementClassOfStockAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class of Stock [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="us-gaap_ClassOfStockDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ClassOfStockDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class of Stock [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ClassOfStockDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class of Stock [Domain]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ManagementSharesMember" xlink:label="bkv_ManagementSharesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ManagementSharesMember" xlink:to="bkv_ManagementSharesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ManagementSharesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Management Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ManagementSharesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Management Shares [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ManagementSharesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Management Shares</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_NonControllingManagementShareholdersMember" xlink:label="bkv_NonControllingManagementShareholdersMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_NonControllingManagementShareholdersMember" xlink:to="bkv_NonControllingManagementShareholdersMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_NonControllingManagementShareholdersMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-controlling Management Shareholders</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_NonControllingManagementShareholdersMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-controlling Management Shareholders [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_NonControllingManagementShareholdersMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-controlling Management Shareholders</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityLineItems" xlink:label="us-gaap_TemporaryEquityLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityLineItems" xlink:to="us-gaap_TemporaryEquityLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TemporaryEquityLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TemporaryEquityLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity [Line Items]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues" xlink:label="bkv_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues" xlink:to="bkv_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Stock Issued During Period, Shares, New Issues</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Stock Issued During Period, Shares, New Issues</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Mezzanine equity, issued (in shares)</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TemporaryEquityStockIssuedDuringThePeriodAcquisitions" xlink:label="bkv_TemporaryEquityStockIssuedDuringThePeriodAcquisitions" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_TemporaryEquityStockIssuedDuringThePeriodAcquisitions" xlink:to="bkv_TemporaryEquityStockIssuedDuringThePeriodAcquisitions_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TemporaryEquityStockIssuedDuringThePeriodAcquisitions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Stock Issued During The Period, Acquisitions</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_TemporaryEquityStockIssuedDuringThePeriodAcquisitions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Stock Issued During The Period, Acquisitions</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_TemporaryEquityStockIssuedDuringThePeriodAcquisitions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Mezzanine equity, acquisitions (in shares)</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TemporaryEquityPutAndCallFeatureRepurchasePrice" xlink:label="bkv_TemporaryEquityPutAndCallFeatureRepurchasePrice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_TemporaryEquityPutAndCallFeatureRepurchasePrice" xlink:to="bkv_TemporaryEquityPutAndCallFeatureRepurchasePrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TemporaryEquityPutAndCallFeatureRepurchasePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Put And Call Feature, Repurchase Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_TemporaryEquityPutAndCallFeatureRepurchasePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Put And Call Feature, Repurchase Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_TemporaryEquityPutAndCallFeatureRepurchasePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Mezzanine equity, repurchase price (in USD per share)</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TemporaryEquityMinorityOwnershipPuttableSharesToRedemptionValueRedemptionPeriod" xlink:label="bkv_TemporaryEquityMinorityOwnershipPuttableSharesToRedemptionValueRedemptionPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_TemporaryEquityMinorityOwnershipPuttableSharesToRedemptionValueRedemptionPeriod" xlink:to="bkv_TemporaryEquityMinorityOwnershipPuttableSharesToRedemptionValueRedemptionPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TemporaryEquityMinorityOwnershipPuttableSharesToRedemptionValueRedemptionPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Minority Ownership Puttable Shares to Redemption Value, Redemption Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_TemporaryEquityMinorityOwnershipPuttableSharesToRedemptionValueRedemptionPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Minority Ownership Puttable Shares to Redemption Value, Redemption Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_TemporaryEquityMinorityOwnershipPuttableSharesToRedemptionValueRedemptionPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption period for puttable shares</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfStockByClassTable" xlink:label="us-gaap_ScheduleOfStockByClassTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfStockByClassTable" xlink:to="us-gaap_ScheduleOfStockByClassTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfStockByClassTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock, Class of Stock [Table]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfStockByClassTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock, Class of Stock [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfStockLineItems" xlink:label="us-gaap_ClassOfStockLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ClassOfStockLineItems" xlink:to="us-gaap_ClassOfStockLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ClassOfStockLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class of Stock [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ClassOfStockLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class of Stock [Line Items]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockRedeemedOrCalledDuringPeriodShares" xlink:label="us-gaap_StockRedeemedOrCalledDuringPeriodShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockRedeemedOrCalledDuringPeriodShares" xlink:to="us-gaap_StockRedeemedOrCalledDuringPeriodShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockRedeemedOrCalledDuringPeriodShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Redeemed or Called During Period, Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockRedeemedOrCalledDuringPeriodShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock redeemed during period (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VestingAxis" xlink:label="us-gaap_VestingAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_VestingAxis" xlink:to="us-gaap_VestingAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_VestingAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vesting [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_VestingAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vesting [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VestingDomain" xlink:label="us-gaap_VestingDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_VestingDomain" xlink:to="us-gaap_VestingDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_VestingDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vesting [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_VestingDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Vesting [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationAwardTrancheOneMember" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheOneMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationAwardTrancheOneMember" xlink:to="us-gaap_ShareBasedCompensationAwardTrancheOneMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Payment Arrangement, Tranche One [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Payment Arrangement, Tranche One</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationAwardTrancheTwoMember" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheTwoMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationAwardTrancheTwoMember" xlink:to="us-gaap_ShareBasedCompensationAwardTrancheTwoMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Payment Arrangement, Tranche Two [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Payment Arrangement, Tranche Two</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardVestingTermsHoldingPeriod" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardVestingTermsHoldingPeriod" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardVestingTermsHoldingPeriod" xlink:to="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardVestingTermsHoldingPeriod_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardVestingTermsHoldingPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Vesting Terms, Holding Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardVestingTermsHoldingPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Compensation Arrangement by Share-Based Payment Award, Vesting Terms, Holding Period</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardVestingTermsHoldingPeriod_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Holding period</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TemporaryEquitySharesIssuedInSettlementOfVestedAwardsOutstanding" xlink:label="bkv_TemporaryEquitySharesIssuedInSettlementOfVestedAwardsOutstanding" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_TemporaryEquitySharesIssuedInSettlementOfVestedAwardsOutstanding" xlink:to="bkv_TemporaryEquitySharesIssuedInSettlementOfVestedAwardsOutstanding_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TemporaryEquitySharesIssuedInSettlementOfVestedAwardsOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Shares, Issued In Settlement Of Vested Awards Outstanding</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_TemporaryEquitySharesIssuedInSettlementOfVestedAwardsOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Shares, Issued In Settlement Of Vested Awards Outstanding</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_TemporaryEquitySharesIssuedInSettlementOfVestedAwardsOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares of common stock in settlement of vested incentive awards outstanding (in shares)</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TemporaryEquityRedemptionValue" xlink:label="bkv_TemporaryEquityRedemptionValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_TemporaryEquityRedemptionValue" xlink:to="bkv_TemporaryEquityRedemptionValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TemporaryEquityRedemptionValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Redemption Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_TemporaryEquityRedemptionValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Redemption Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_TemporaryEquityRedemptionValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary equity, redemption value</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TreasuryStockSharesAcquired" xlink:label="us-gaap_TreasuryStockSharesAcquired" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TreasuryStockSharesAcquired" xlink:to="us-gaap_TreasuryStockSharesAcquired_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TreasuryStockSharesAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Treasury Stock, Shares, Acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TreasuryStockSharesAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Treasury stock, acquired (in shares)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TreasuryStockAcquiredAverageCostPerShare" xlink:label="us-gaap_TreasuryStockAcquiredAverageCostPerShare" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TreasuryStockAcquiredAverageCostPerShare" xlink:to="us-gaap_TreasuryStockAcquiredAverageCostPerShare_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TreasuryStockAcquiredAverageCostPerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares Acquired, Average Cost Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TreasuryStockAcquiredAverageCostPerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares acquired, average cost per share</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:label="us-gaap_PaymentsForRepurchaseOfCommonStock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:to="us-gaap_PaymentsForRepurchaseOfCommonStock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsForRepurchaseOfCommonStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments for Repurchase of Common Stock</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PaymentsForRepurchaseOfCommonStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments for repurchase of common stock</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:to="us-gaap_ScheduleOfEquityMethodInvestmentsTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment [Table]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment [Table]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_BKVDCarbonProjectLLCMember" xlink:label="bkv_BKVDCarbonProjectLLCMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_BKVDCarbonProjectLLCMember" xlink:to="bkv_BKVDCarbonProjectLLCMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_BKVDCarbonProjectLLCMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV dCarbon Project, LLC</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_BKVDCarbonProjectLLCMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV dCarbon Project, LLC [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_BKVDCarbonProjectLLCMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV dCarbon Project, LLC</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ClassAUnitsMember" xlink:label="bkv_ClassAUnitsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ClassAUnitsMember" xlink:to="bkv_ClassAUnitsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ClassAUnitsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class A Units</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ClassAUnitsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class A Units [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ClassAUnitsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class A Units</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ClassBUnitsMember" xlink:label="bkv_ClassBUnitsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ClassBUnitsMember" xlink:to="bkv_ClassBUnitsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ClassBUnitsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class B Units</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ClassBUnitsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class B Units [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ClassBUnitsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class B Units</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_CSquaredSolutionsInc.Member" xlink:label="bkv_CSquaredSolutionsInc.Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_CSquaredSolutionsInc.Member" xlink:to="bkv_CSquaredSolutionsInc.Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_CSquaredSolutionsInc.Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">C Squared Solutions, Inc.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_CSquaredSolutionsInc.Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">C Squared Solutions, Inc. [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_CSquaredSolutionsInc.Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class B Members</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:to="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Equity Method Investments [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Equity Method Investments [Line Items]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_JointVentureFormationFairValueOfJointVenture" xlink:label="us-gaap_JointVentureFormationFairValueOfJointVenture" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_JointVentureFormationFairValueOfJointVenture" xlink:to="us-gaap_JointVentureFormationFairValueOfJointVenture_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_JointVentureFormationFairValueOfJointVenture_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Joint Venture Formation, Fair Value of Joint Venture</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_JointVentureFormationFairValueOfJointVenture_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Joint venture formation, fair value of joint venture</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_JointVentureAccruedReceivablesAllowanceForCreditLoss" xlink:label="bkv_JointVentureAccruedReceivablesAllowanceForCreditLoss" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_JointVentureAccruedReceivablesAllowanceForCreditLoss" xlink:to="bkv_JointVentureAccruedReceivablesAllowanceForCreditLoss_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_JointVentureAccruedReceivablesAllowanceForCreditLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Joint Venture, Accrued Receivables, Allowance For Credit Loss</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_JointVentureAccruedReceivablesAllowanceForCreditLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Joint Venture, Accrued Receivables, Allowance For Credit Loss</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_JointVentureAccruedReceivablesAllowanceForCreditLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Section 45Q accrued receivables</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquitySharesIssued" xlink:label="us-gaap_TemporaryEquitySharesIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquitySharesIssued" xlink:to="us-gaap_TemporaryEquitySharesIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TemporaryEquitySharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Shares Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TemporaryEquitySharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary equity issued (in units)</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TemporaryEquityPricePerShare" xlink:label="bkv_TemporaryEquityPricePerShare" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_TemporaryEquityPricePerShare" xlink:to="bkv_TemporaryEquityPricePerShare_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TemporaryEquityPricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Price Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_TemporaryEquityPricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Price Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_TemporaryEquityPricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary equity, price per share (in USD per unit)</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_JointVentureFormationCommittedContributionByNonControllingInterest" xlink:label="bkv_JointVentureFormationCommittedContributionByNonControllingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_JointVentureFormationCommittedContributionByNonControllingInterest" xlink:to="bkv_JointVentureFormationCommittedContributionByNonControllingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_JointVentureFormationCommittedContributionByNonControllingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Joint Venture Formation, Committed Contribution By Non-Controlling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_JointVentureFormationCommittedContributionByNonControllingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Joint Venture Formation, Committed Contribution By Non-Controlling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_JointVentureFormationCommittedContributionByNonControllingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contribution by non-controlling interest in joint venture</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ProceedsFromJointVentureDistribution" xlink:label="bkv_ProceedsFromJointVentureDistribution" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ProceedsFromJointVentureDistribution" xlink:to="bkv_ProceedsFromJointVentureDistribution_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ProceedsFromJointVentureDistribution_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Joint Venture, Distribution</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ProceedsFromJointVentureDistribution_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Joint Venture, Distribution</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ProceedsFromJointVentureDistribution_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from joint venture, distribution</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TemporaryEquityLiquidationPreferencePercentage" xlink:label="bkv_TemporaryEquityLiquidationPreferencePercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_TemporaryEquityLiquidationPreferencePercentage" xlink:to="bkv_TemporaryEquityLiquidationPreferencePercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TemporaryEquityLiquidationPreferencePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Liquidation Preference, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_TemporaryEquityLiquidationPreferencePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Liquidation Preference, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_TemporaryEquityLiquidationPreferencePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary equity, liquidation preference, percentage</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_BKVBPPCottonCoveLLCMember" xlink:label="bkv_BKVBPPCottonCoveLLCMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_BKVBPPCottonCoveLLCMember" xlink:to="bkv_BKVBPPCottonCoveLLCMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_BKVBPPCottonCoveLLCMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV-BPP Cotton Cove, LLC</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_BKVBPPCottonCoveLLCMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV-BPP Cotton Cove, LLC [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_BKVBPPCottonCoveLLCMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV-BPP Cotton Cove, LLC</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bkv_BKVBPPCottonCoveLLCMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV-BPP Cotton Cove</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireInterestInJointVenture" xlink:label="us-gaap_PaymentsToAcquireInterestInJointVenture" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToAcquireInterestInJointVenture" xlink:to="us-gaap_PaymentsToAcquireInterestInJointVenture_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsToAcquireInterestInJointVenture_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to Acquire Interest in Joint Venture</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PaymentsToAcquireInterestInJointVenture_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash acquired in consolidation of BKV-BPP Cotton Cove</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ExpendituresPaidByParentCompanyOnBehalfOfTheJointVenture" xlink:label="bkv_ExpendituresPaidByParentCompanyOnBehalfOfTheJointVenture" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ExpendituresPaidByParentCompanyOnBehalfOfTheJointVenture" xlink:to="bkv_ExpendituresPaidByParentCompanyOnBehalfOfTheJointVenture_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ExpendituresPaidByParentCompanyOnBehalfOfTheJointVenture_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Expenditures Paid By Parent Company On Behalf Of The Joint Venture</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ExpendituresPaidByParentCompanyOnBehalfOfTheJointVenture_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Expenditures Paid By Parent Company On Behalf Of The Joint Venture</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ExpendituresPaidByParentCompanyOnBehalfOfTheJointVenture_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Expenditures paid by BKV dCarbon Ventures on behalf of BKV-BPP Cotton Cove</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital" xlink:label="us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital" xlink:to="us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Equity Method Investment, Distribution, Return of Capital</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Return of capital</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestments" xlink:label="us-gaap_EquityMethodInvestments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestments" xlink:to="us-gaap_EquityMethodInvestments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_EquityMethodInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity method investments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPManagingMemberOrGeneralPartnerOwnershipInterest" xlink:label="us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPManagingMemberOrGeneralPartnerOwnershipInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPManagingMemberOrGeneralPartnerOwnershipInterest" xlink:to="us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPManagingMemberOrGeneralPartnerOwnershipInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPManagingMemberOrGeneralPartnerOwnershipInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Limited Liability Company (LLC) or Limited Partnership (LP), Managing Member or General Partner, Ownership Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPManagingMemberOrGeneralPartnerOwnershipInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ownership interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidatedEntitiesAxis" xlink:label="srt_ConsolidatedEntitiesAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ConsolidatedEntitiesAxis" xlink:to="srt_ConsolidatedEntitiesAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ConsolidatedEntitiesAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consolidated Entities [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ConsolidatedEntitiesAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consolidated Entities [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidatedEntitiesDomain" xlink:label="srt_ConsolidatedEntitiesDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ConsolidatedEntitiesDomain" xlink:to="srt_ConsolidatedEntitiesDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ConsolidatedEntitiesDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consolidated Entities [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ConsolidatedEntitiesDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consolidated Entities [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:label="us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:to="us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Variable Interest Entity, Primary Beneficiary [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Variable Interest Entity, Primary Beneficiary</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_AccountsReceivableAfterAllowanceForCreditLossNet" xlink:label="bkv_AccountsReceivableAfterAllowanceForCreditLossNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_AccountsReceivableAfterAllowanceForCreditLossNet" xlink:to="bkv_AccountsReceivableAfterAllowanceForCreditLossNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_AccountsReceivableAfterAllowanceForCreditLossNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, after Allowance for Credit Loss, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AccountsReceivableAfterAllowanceForCreditLossNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, after Allowance for Credit Loss, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_AccountsReceivableAfterAllowanceForCreditLossNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Account receivable, net</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_BkvCipJointVentureMember" xlink:label="bkv_BkvCipJointVentureMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_BkvCipJointVentureMember" xlink:to="bkv_BkvCipJointVentureMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_BkvCipJointVentureMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV-CIP Joint Venture</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_BkvCipJointVentureMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV-CIP Joint Venture [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_BkvCipJointVentureMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV-CIP Joint Venture</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedCash" xlink:label="us-gaap_RestrictedCash" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RestrictedCash" xlink:to="us-gaap_RestrictedCash_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RestrictedCash_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Restricted Cash</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RestrictedCash_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Restricted cash</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAbstract" xlink:label="us-gaap_LiabilitiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesAbstract" xlink:to="us-gaap_LiabilitiesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LiabilitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_BusinessCombinationPercentOfIndebtednessUsedInCalculatingConsideration" xlink:label="bkv_BusinessCombinationPercentOfIndebtednessUsedInCalculatingConsideration" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_BusinessCombinationPercentOfIndebtednessUsedInCalculatingConsideration" xlink:to="bkv_BusinessCombinationPercentOfIndebtednessUsedInCalculatingConsideration_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_BusinessCombinationPercentOfIndebtednessUsedInCalculatingConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Joint Venture, Ownership Percentage of Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_BusinessCombinationPercentOfIndebtednessUsedInCalculatingConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination Percent Of Indebtedness Used In Calculating Consideration</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_BusinessCombinationPercentOfIndebtednessUsedInCalculatingConsideration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of noncontrolling interest</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TemporaryEquityInvestmentOnCapital" xlink:label="bkv_TemporaryEquityInvestmentOnCapital" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_TemporaryEquityInvestmentOnCapital" xlink:to="bkv_TemporaryEquityInvestmentOnCapital_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TemporaryEquityInvestmentOnCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Investment On Capital</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_TemporaryEquityInvestmentOnCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Investment On Capital</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_TemporaryEquityInvestmentOnCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary equity, investment on capital</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TemporaryEquityEstimatedRedemptionValue" xlink:label="bkv_TemporaryEquityEstimatedRedemptionValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_TemporaryEquityEstimatedRedemptionValue" xlink:to="bkv_TemporaryEquityEstimatedRedemptionValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TemporaryEquityEstimatedRedemptionValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity, Estimated Redemption Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_TemporaryEquityEstimatedRedemptionValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary Equity Estimated Redemption Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_TemporaryEquityEstimatedRedemptionValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Temporary equity, estimated redemption value</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskTable" xlink:label="us-gaap_ConcentrationRiskTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskTable" xlink:to="us-gaap_ConcentrationRiskTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConcentrationRiskTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk [Table]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConcentrationRiskTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MajorCustomersAxis" xlink:label="srt_MajorCustomersAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_MajorCustomersAxis" xlink:to="srt_MajorCustomersAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_MajorCustomersAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_MajorCustomersAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_NameOfMajorCustomerDomain" xlink:label="srt_NameOfMajorCustomerDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_NameOfMajorCustomerDomain" xlink:to="srt_NameOfMajorCustomerDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_NameOfMajorCustomerDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_NameOfMajorCustomerDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer [Domain]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_PurchaserOneMember" xlink:label="bkv_PurchaserOneMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_PurchaserOneMember" xlink:to="bkv_PurchaserOneMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_PurchaserOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchaser One</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_PurchaserOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchaser One [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_PurchaserOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchaser One</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_PurchaserTwoMember" xlink:label="bkv_PurchaserTwoMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_PurchaserTwoMember" xlink:to="bkv_PurchaserTwoMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_PurchaserTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchaser Two</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_PurchaserTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchaser Two [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_PurchaserTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchaser Two</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_PurchaserThreeMember" xlink:label="bkv_PurchaserThreeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_PurchaserThreeMember" xlink:to="bkv_PurchaserThreeMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_PurchaserThreeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchaser Three</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_PurchaserThreeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchaser Three [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_PurchaserThreeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchaser Three</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_PurchaserFourMember" xlink:label="bkv_PurchaserFourMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_PurchaserFourMember" xlink:to="bkv_PurchaserFourMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_PurchaserFourMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchaser Four</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_PurchaserFourMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchaser Four [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bkv_PurchaserFourMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchaser Four</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:label="us-gaap_ConcentrationRiskByBenchmarkAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:to="us-gaap_ConcentrationRiskByBenchmarkAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConcentrationRiskByBenchmarkAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk Benchmark [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConcentrationRiskByBenchmarkAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk Benchmark [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskBenchmarkDomain" xlink:label="us-gaap_ConcentrationRiskBenchmarkDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskBenchmarkDomain" xlink:to="us-gaap_ConcentrationRiskBenchmarkDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConcentrationRiskBenchmarkDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk Benchmark [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConcentrationRiskBenchmarkDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk Benchmark [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsReceivableMember" xlink:label="us-gaap_AccountsReceivableMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableMember" xlink:to="us-gaap_AccountsReceivableMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsReceivableMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccountsReceivableMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueFromContractWithCustomerMember" xlink:label="us-gaap_RevenueFromContractWithCustomerMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevenueFromContractWithCustomerMember" xlink:to="us-gaap_RevenueFromContractWithCustomerMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RevenueFromContractWithCustomerMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue from Contract with Customer Benchmark [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RevenueFromContractWithCustomerMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue from Contract with Customer Benchmark</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskByTypeAxis" xlink:label="us-gaap_ConcentrationRiskByTypeAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskByTypeAxis" xlink:to="us-gaap_ConcentrationRiskByTypeAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConcentrationRiskByTypeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk Type [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConcentrationRiskByTypeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk Type [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskTypeDomain" xlink:label="us-gaap_ConcentrationRiskTypeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskTypeDomain" xlink:to="us-gaap_ConcentrationRiskTypeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConcentrationRiskTypeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk Type [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConcentrationRiskTypeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk Type [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CustomerConcentrationRiskMember" xlink:label="us-gaap_CustomerConcentrationRiskMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CustomerConcentrationRiskMember" xlink:to="us-gaap_CustomerConcentrationRiskMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CustomerConcentrationRiskMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer Concentration Risk [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CustomerConcentrationRiskMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer Concentration Risk</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskLineItems" xlink:label="us-gaap_ConcentrationRiskLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskLineItems" xlink:to="us-gaap_ConcentrationRiskLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConcentrationRiskLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConcentrationRiskLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk [Line Items]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskPercentage1" xlink:label="us-gaap_ConcentrationRiskPercentage1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskPercentage1" xlink:to="us-gaap_ConcentrationRiskPercentage1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConcentrationRiskPercentage1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConcentrationRiskPercentage1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration risk, percentage</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherCommitmentsTable" xlink:label="us-gaap_OtherCommitmentsTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherCommitmentsTable" xlink:to="us-gaap_OtherCommitmentsTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherCommitmentsTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Commitments [Table]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherCommitmentsTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Commitments [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherCommitmentsAxis" xlink:label="us-gaap_OtherCommitmentsAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherCommitmentsAxis" xlink:to="us-gaap_OtherCommitmentsAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherCommitmentsAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Commitments [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherCommitmentsAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Commitments [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherCommitmentsDomain" xlink:label="us-gaap_OtherCommitmentsDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherCommitmentsDomain" xlink:to="us-gaap_OtherCommitmentsDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherCommitmentsDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Commitments [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherCommitmentsDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Commitments [Domain]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_NaturalGasCommitmentsMember" xlink:label="bkv_NaturalGasCommitmentsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_NaturalGasCommitmentsMember" xlink:to="bkv_NaturalGasCommitmentsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_NaturalGasCommitmentsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural Gas, Commitments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_NaturalGasCommitmentsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural Gas, Commitments [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_NaturalGasCommitmentsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural Gas, Commitments</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_BusinessCombinationContingentConsiderationThresholdAxis" xlink:label="bkv_BusinessCombinationContingentConsiderationThresholdAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_BusinessCombinationContingentConsiderationThresholdAxis" xlink:to="bkv_BusinessCombinationContingentConsiderationThresholdAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_BusinessCombinationContingentConsiderationThresholdAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Contingent Consideration, Threshold</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_BusinessCombinationContingentConsiderationThresholdAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Contingent Consideration, Threshold [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_BusinessCombinationContingentConsiderationThresholdAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Contingent Consideration, Threshold [Axis]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_BusinessCombinationContingentConsiderationThresholdDomain" xlink:label="bkv_BusinessCombinationContingentConsiderationThresholdDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_BusinessCombinationContingentConsiderationThresholdDomain" xlink:to="bkv_BusinessCombinationContingentConsiderationThresholdDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_BusinessCombinationContingentConsiderationThresholdDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Contingent Consideration, Threshold [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_BusinessCombinationContingentConsiderationThresholdDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Contingent Consideration, Threshold [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_BusinessCombinationContingentConsiderationThresholdDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Contingent Consideration, Threshold [Domain]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_Threshold1Member" xlink:label="bkv_Threshold1Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_Threshold1Member" xlink:to="bkv_Threshold1Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_Threshold1Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold 1</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_Threshold1Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold 1 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_Threshold1Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold 1</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_Threshold2Member" xlink:label="bkv_Threshold2Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_Threshold2Member" xlink:to="bkv_Threshold2Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_Threshold2Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold 2</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_Threshold2Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold 2 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_Threshold2Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold 2</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_Threshold3Member" xlink:label="bkv_Threshold3Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_Threshold3Member" xlink:to="bkv_Threshold3Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_Threshold3Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold 3</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_Threshold3Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold 3 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_Threshold3Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold 3</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_Threshold4Member" xlink:label="bkv_Threshold4Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_Threshold4Member" xlink:to="bkv_Threshold4Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_Threshold4Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold 4</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_Threshold4Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold 4 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_Threshold4Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold 4</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_WTIIndexMember" xlink:label="bkv_WTIIndexMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_WTIIndexMember" xlink:to="bkv_WTIIndexMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_WTIIndexMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">WTI Index</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_WTIIndexMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">WTI Index [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_WTIIndexMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">WTI Index</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_NEPAAcquisitionMember" xlink:label="bkv_NEPAAcquisitionMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_NEPAAcquisitionMember" xlink:to="bkv_NEPAAcquisitionMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_NEPAAcquisitionMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">NEPA Acquisition</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_NEPAAcquisitionMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">NEPA Acquisition [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_NEPAAcquisitionMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">NEPA Acquisition</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ExxonBarnettAcquisitionMember" xlink:label="bkv_ExxonBarnettAcquisitionMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ExxonBarnettAcquisitionMember" xlink:to="bkv_ExxonBarnettAcquisitionMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ExxonBarnettAcquisitionMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Exxon Barnett Acquisition</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ExxonBarnettAcquisitionMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Exxon Barnett Acquisition [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ExxonBarnettAcquisitionMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Exxon Barnett Acquisition</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherCommitmentsLineItems" xlink:label="us-gaap_OtherCommitmentsLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherCommitmentsLineItems" xlink:to="us-gaap_OtherCommitmentsLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherCommitmentsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Commitments [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherCommitmentsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Commitments [Line Items]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LossContingencyAccrualAtCarryingValue" xlink:label="us-gaap_LossContingencyAccrualAtCarryingValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LossContingencyAccrualAtCarryingValue" xlink:to="us-gaap_LossContingencyAccrualAtCarryingValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LossContingencyAccrualAtCarryingValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss Contingency Accrual</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LossContingencyAccrualAtCarryingValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other contingent liabilities</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_BusinessCombinationContingentConsiderationPayout" xlink:label="bkv_BusinessCombinationContingentConsiderationPayout" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_BusinessCombinationContingentConsiderationPayout" xlink:to="bkv_BusinessCombinationContingentConsiderationPayout_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_BusinessCombinationContingentConsiderationPayout_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Contingent Consideration, Payout</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_BusinessCombinationContingentConsiderationPayout_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Contingent Consideration, Payout</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_BusinessCombinationContingentConsiderationPayout_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payout</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_BusinessCombinationContingentConsiderationEarnoutAmount" xlink:label="bkv_BusinessCombinationContingentConsiderationEarnoutAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_BusinessCombinationContingentConsiderationEarnoutAmount" xlink:to="bkv_BusinessCombinationContingentConsiderationEarnoutAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_BusinessCombinationContingentConsiderationEarnoutAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Contingent Consideration, Earnout Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_BusinessCombinationContingentConsiderationEarnoutAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Contingent Consideration, Earnout Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_BusinessCombinationContingentConsiderationEarnoutAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_OtherCommitmentVolumeRequired" xlink:label="bkv_OtherCommitmentVolumeRequired" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_OtherCommitmentVolumeRequired" xlink:to="bkv_OtherCommitmentVolumeRequired_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_OtherCommitmentVolumeRequired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Commitment, Volume Required</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_OtherCommitmentVolumeRequired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Commitment, Volume Required</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_OtherCommitmentVolumeRequired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Volume required under commitment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherCommitment" xlink:label="us-gaap_OtherCommitment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherCommitment" xlink:to="us-gaap_OtherCommitment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherCommitment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Commitment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_OtherCommitment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_OtherCommitment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other commitment</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TransportationAgreementContractualTerm" xlink:label="bkv_TransportationAgreementContractualTerm" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_TransportationAgreementContractualTerm" xlink:to="bkv_TransportationAgreementContractualTerm_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TransportationAgreementContractualTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The contractual term of the transportation agreement.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_TransportationAgreementContractualTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Transportation Agreement, Contractual Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_TransportationAgreementContractualTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Term of transportation agreement</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_AccruedImbalancePenaltiesCurrent" xlink:label="bkv_AccruedImbalancePenaltiesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_AccruedImbalancePenaltiesCurrent" xlink:to="bkv_AccruedImbalancePenaltiesCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_AccruedImbalancePenaltiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of payables for imbalance penalties, classified as current.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_AccruedImbalancePenaltiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued Imbalance Penalties, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_AccruedImbalancePenaltiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Imbalance penalties</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_ImbalancePenaltyExpenses" xlink:label="bkv_ImbalancePenaltyExpenses" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_ImbalancePenaltyExpenses" xlink:to="bkv_ImbalancePenaltyExpenses_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_ImbalancePenaltyExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of expenses incurred for imbalance penalties.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_ImbalancePenaltyExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Imbalance Penalty Expenses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_ImbalancePenaltyExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Imbalance penalties expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommitmentsMember" xlink:label="us-gaap_CommitmentsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommitmentsMember" xlink:to="us-gaap_CommitmentsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommitmentsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commitments [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommitmentsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commitments</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_PowerJvTermLoanFacilityMember" xlink:label="bkv_PowerJvTermLoanFacilityMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_PowerJvTermLoanFacilityMember" xlink:to="bkv_PowerJvTermLoanFacilityMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_PowerJvTermLoanFacilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Power JV Term Loan Facility</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_PowerJvTermLoanFacilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Power JV Term Loan Facility [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_PowerJvTermLoanFacilityMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Power JV Term Loan Facility</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_TransportationCommitmentsMember" xlink:label="bkv_TransportationCommitmentsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_TransportationCommitmentsMember" xlink:to="bkv_TransportationCommitmentsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_TransportationCommitmentsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Transportation Commitments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_TransportationCommitmentsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Transportation Commitments [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_TransportationCommitmentsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Transportation commitments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtByMaturityAbstract" xlink:label="us-gaap_LongTermDebtByMaturityAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtByMaturityAbstract" xlink:to="us-gaap_LongTermDebtByMaturityAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebtByMaturityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Fiscal Year Maturity [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermDebtByMaturityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:to="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Maturity, Year One</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:to="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Maturity, Year Two</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:to="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Maturity, Year Three</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2028</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:to="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Maturity, Year Four</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2029</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:to="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Maturity, Year Five</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2030</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:to="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Debt, Maturity, after Year Five</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Thereafter</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_InterestPayableToBePaidFiscalYearMaturityAbstract" xlink:label="bkv_InterestPayableToBePaidFiscalYearMaturityAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_InterestPayableToBePaidFiscalYearMaturityAbstract" xlink:to="bkv_InterestPayableToBePaidFiscalYearMaturityAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_InterestPayableToBePaidFiscalYearMaturityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Payable, to be Paid, Fiscal Year Maturity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_InterestPayableToBePaidFiscalYearMaturityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Payable, to be Paid, Fiscal Year Maturity [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_InterestPayableToBePaidFiscalYearMaturityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest payable</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_InterestPayableYearOne" xlink:label="bkv_InterestPayableYearOne" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_InterestPayableYearOne" xlink:to="bkv_InterestPayableYearOne_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_InterestPayableYearOne_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Payable, Year One</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_InterestPayableYearOne_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Payable, Year One</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_InterestPayableYearOne_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_InterestPayableYearTwo" xlink:label="bkv_InterestPayableYearTwo" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_InterestPayableYearTwo" xlink:to="bkv_InterestPayableYearTwo_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_InterestPayableYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Payable, Year Two</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_InterestPayableYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Payable, Year Two</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_InterestPayableYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_InterestPayableYearThree" xlink:label="bkv_InterestPayableYearThree" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_InterestPayableYearThree" xlink:to="bkv_InterestPayableYearThree_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_InterestPayableYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Payable, Year Three</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_InterestPayableYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Payable, Year Three</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_InterestPayableYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2028</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_InterestPayableYearFour" xlink:label="bkv_InterestPayableYearFour" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_InterestPayableYearFour" xlink:to="bkv_InterestPayableYearFour_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_InterestPayableYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Payable, Year Four</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_InterestPayableYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Payable, Year Four</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_InterestPayableYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2029</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_InterestPayableYearFive" xlink:label="bkv_InterestPayableYearFive" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_InterestPayableYearFive" xlink:to="bkv_InterestPayableYearFive_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_InterestPayableYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Payable, Year Five</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_InterestPayableYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Payable, Year Five</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_InterestPayableYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2030</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_InterestPayableAfterYearFive" xlink:label="bkv_InterestPayableAfterYearFive" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_InterestPayableAfterYearFive" xlink:to="bkv_InterestPayableAfterYearFive_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_InterestPayableAfterYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Payable, After Year Five</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_InterestPayableAfterYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Payable, After Year Five</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_InterestPayableAfterYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Thereafter</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestPayableCurrentAndNoncurrent" xlink:label="us-gaap_InterestPayableCurrentAndNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestPayableCurrentAndNoncurrent" xlink:to="us-gaap_InterestPayableCurrentAndNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InterestPayableCurrentAndNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_InterestPayableCurrentAndNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xlink:label="us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xlink:to="us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, to be Paid, Fiscal Year Maturity [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating lease payments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, to be Paid, Year One</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, to be Paid, Year Two</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, to be Paid, Year Three</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2028</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, to be Paid, Year Four</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2029</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, to be Paid, Year Five</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2030</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, to be Paid, after Year Five</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Thereafter</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, to be Paid</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherCommitmentFiscalYearMaturityAbstract" xlink:label="us-gaap_OtherCommitmentFiscalYearMaturityAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherCommitmentFiscalYearMaturityAbstract" xlink:to="us-gaap_OtherCommitmentFiscalYearMaturityAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherCommitmentFiscalYearMaturityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Commitment, Fiscal Year Maturity [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherCommitmentFiscalYearMaturityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Natural gas transportation commitments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherCommitmentDueInNextTwelveMonths" xlink:label="us-gaap_OtherCommitmentDueInNextTwelveMonths" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherCommitmentDueInNextTwelveMonths" xlink:to="us-gaap_OtherCommitmentDueInNextTwelveMonths_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherCommitmentDueInNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Commitment, to be Paid, Year One</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherCommitmentDueInNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherCommitmentDueInSecondYear" xlink:label="us-gaap_OtherCommitmentDueInSecondYear" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherCommitmentDueInSecondYear" xlink:to="us-gaap_OtherCommitmentDueInSecondYear_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherCommitmentDueInSecondYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Commitment, to be Paid, Year Two</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherCommitmentDueInSecondYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherCommitmentDueInThirdYear" xlink:label="us-gaap_OtherCommitmentDueInThirdYear" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherCommitmentDueInThirdYear" xlink:to="us-gaap_OtherCommitmentDueInThirdYear_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherCommitmentDueInThirdYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Commitment, to be Paid, Year Three</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherCommitmentDueInThirdYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2028</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherCommitmentDueInFourthYear" xlink:label="us-gaap_OtherCommitmentDueInFourthYear" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherCommitmentDueInFourthYear" xlink:to="us-gaap_OtherCommitmentDueInFourthYear_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherCommitmentDueInFourthYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Commitment, to be Paid, Year Four</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherCommitmentDueInFourthYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2029</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherCommitmentDueInFifthYear" xlink:label="us-gaap_OtherCommitmentDueInFifthYear" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherCommitmentDueInFifthYear" xlink:to="us-gaap_OtherCommitmentDueInFifthYear_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherCommitmentDueInFifthYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Commitment, to be Paid, Year Five</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherCommitmentDueInFifthYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2030</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherCommitmentDueAfterFifthYear" xlink:label="us-gaap_OtherCommitmentDueAfterFifthYear" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherCommitmentDueAfterFifthYear" xlink:to="us-gaap_OtherCommitmentDueAfterFifthYear_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherCommitmentDueAfterFifthYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Commitment, to be Paid, after Year Five</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherCommitmentDueAfterFifthYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Thereafter</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractualObligationFiscalYearMaturityAbstract" xlink:label="us-gaap_ContractualObligationFiscalYearMaturityAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ContractualObligationFiscalYearMaturityAbstract" xlink:to="us-gaap_ContractualObligationFiscalYearMaturityAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ContractualObligationFiscalYearMaturityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contractual Obligation, Fiscal Year Maturity [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ContractualObligationFiscalYearMaturityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractualObligationDueInNextTwelveMonths" xlink:label="us-gaap_ContractualObligationDueInNextTwelveMonths" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ContractualObligationDueInNextTwelveMonths" xlink:to="us-gaap_ContractualObligationDueInNextTwelveMonths_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ContractualObligationDueInNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contractual Obligation, to be Paid, Year One</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_ContractualObligationDueInNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractualObligationDueInSecondYear" xlink:label="us-gaap_ContractualObligationDueInSecondYear" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ContractualObligationDueInSecondYear" xlink:to="us-gaap_ContractualObligationDueInSecondYear_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ContractualObligationDueInSecondYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contractual Obligation, to be Paid, Year Two</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_ContractualObligationDueInSecondYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractualObligationDueInThirdYear" xlink:label="us-gaap_ContractualObligationDueInThirdYear" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ContractualObligationDueInThirdYear" xlink:to="us-gaap_ContractualObligationDueInThirdYear_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ContractualObligationDueInThirdYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contractual Obligation, to be Paid, Year Three</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_ContractualObligationDueInThirdYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2028</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractualObligationDueInFourthYear" xlink:label="us-gaap_ContractualObligationDueInFourthYear" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_IncomeTaxReconciliationTaxCreditsInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment tax credit</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsAbstract" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Tax credits</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsInvestment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment tax credit</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_EffectiveIncomeTaxRateReconciliationMarginalWellCredit" xlink:label="bkv_EffectiveIncomeTaxRateReconciliationMarginalWellCredit" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_EffectiveIncomeTaxRateReconciliationMarginalWellCredit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective Income Tax Rate Reconciliation, Marginal Well Credit,</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="bkv_EffectiveIncomeTaxRateReconciliationMarginalWellCredit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Marginal well credit</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseAbstract" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Nontaxable or nondeductible items</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_EffectiveIncomeTaxRateReconciliationSection162mLimitationPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective Income Tax Rate Reconciliation, Section 162(m) Limitation, Percent</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationShareBasedCompensationExcessTaxBenefitPercent" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationShareBasedCompensationExcessTaxBenefitPercent" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationShareBasedCompensationExcessTaxBenefitPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Excess tax benefits from vesting of restricted shares</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationTaxExemptIncome_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Section 45Q tax credits</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOther" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOther" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingSegmentsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Segments [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingSegmentsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Segments</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CorporateNonSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segment Reporting, Reconciling Item, Corporate Nonsegment [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CorporateNonSegmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segment reporting, reconciling item, corporate nonsegment</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementBusinessSegmentsAxis" xlink:to="us-gaap_StatementBusinessSegmentsAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementBusinessSegmentsAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segments [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StatementBusinessSegmentsAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segments [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain" xlink:label="us-gaap_SegmentDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentDomain" xlink:to="us-gaap_SegmentDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SegmentDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segments [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SegmentDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segments [Domain]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_BKVUpstreamMidstreamLLCMember" xlink:label="bkv_BKVUpstreamMidstreamLLCMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_BKVUpstreamMidstreamLLCMember" xlink:to="bkv_BKVUpstreamMidstreamLLCMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_BKVUpstreamMidstreamLLCMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV Upstream Midstream, LLC</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_BKVUpstreamMidstreamLLCMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV Upstream Midstream, LLC [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_BKVUpstreamMidstreamLLCMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">BKV Upstream Midstream, LLC</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CostsAndExpenses" xlink:to="us-gaap_CostsAndExpenses_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CostsAndExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Costs and Expenses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_CostsAndExpenses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total operating expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentExpenditureAdditionToLongLivedAssets" xlink:label="us-gaap_SegmentExpenditureAdditionToLongLivedAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SegmentExpenditureAdditionToLongLivedAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segment, Expenditure, Addition to Long-Lived Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SegmentExpenditureAdditionToLongLivedAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capital expenditures</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherNoncashIncomeTaxExpense" xlink:label="us-gaap_OtherNoncashIncomeTaxExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherNoncashIncomeTaxExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Noncash Income Tax Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherNoncashIncomeTaxExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Corporate and Other taxes other than income</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTable" xlink:label="us-gaap_SubsequentEventTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventTable" xlink:to="us-gaap_SubsequentEventTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent Event [Table]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SubsequentEventTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent Event [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventLineItems" xlink:label="us-gaap_SubsequentEventLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventLineItems" xlink:to="us-gaap_SubsequentEventLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent Event [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SubsequentEventLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent Event [Line Items]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:label="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Voting equity interest acquired, percentage</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_BusinessCombinationConvertibleThresholdTradingDays" xlink:label="bkv_BusinessCombinationConvertibleThresholdTradingDays" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_BusinessCombinationConvertibleThresholdTradingDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Convertible, Threshold Trading Days</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_BusinessCombinationConvertibleThresholdTradingDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Convertible, Threshold Trading Days</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_BusinessCombinationConvertibleThresholdTradingDays_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business combination, convertible, threshold trading days</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationConsiderationTransferred1" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationConsiderationTransferred1" xlink:to="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Consideration Transferred</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consideration transferred</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalizedCostsProvedProperties" xlink:label="us-gaap_CapitalizedCostsProvedProperties" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CapitalizedCostsProvedProperties" xlink:to="us-gaap_CapitalizedCostsProvedProperties_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CapitalizedCostsProvedProperties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Capitalized Cost, before Accumulated Depreciation, Depletion, Amortization, and Valuation Allowance, Proved Property</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CapitalizedCostsProvedProperties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Developed properties</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalizedCostsUnprovedProperties" xlink:label="us-gaap_CapitalizedCostsUnprovedProperties" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CapitalizedCostsUnprovedProperties" xlink:to="us-gaap_CapitalizedCostsUnprovedProperties_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CapitalizedCostsUnprovedProperties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Capitalized Cost, before Accumulated Depreciation, Depletion, Amortization, and Valuation Allowance, Unproved Property</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CapitalizedCostsUnprovedProperties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Undeveloped properties</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_CapitalizedCostsOilAndGasProducingActivitiesGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total capitalized costs</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_CapitalizedCostsAccumulatedDepreciationDepletionAmortizationAndValuationAllowanceForRelatingToOilAndGasProducingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less: accumulated depreciation, depletion, and amortization</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CapitalizedCostsOilAndGasProducingActivitiesNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Capitalized Cost, after Accumulated Depreciation, Depletion, Amortization, and Valuation Allowance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_CapitalizedCostsOilAndGasProducingActivitiesNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total natural gas properties, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalizedCostsRelatingToOilAndGasProducingActivitiesByGeographicAreaTable" xlink:label="us-gaap_CapitalizedCostsRelatingToOilAndGasProducingActivitiesByGeographicAreaTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CapitalizedCostsRelatingToOilAndGasProducingActivitiesByGeographicAreaTable" xlink:to="us-gaap_CapitalizedCostsRelatingToOilAndGasProducingActivitiesByGeographicAreaTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CapitalizedCostsRelatingToOilAndGasProducingActivitiesByGeographicAreaTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Capitalized Cost [Table]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CapitalizedCostsRelatingToOilAndGasProducingActivitiesByGeographicAreaTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Capitalized Cost [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalizedCostsRelatingToOilAndGasProducingActivitiesByGeographicAreaLineItems" xlink:label="us-gaap_CapitalizedCostsRelatingToOilAndGasProducingActivitiesByGeographicAreaLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CapitalizedCostsRelatingToOilAndGasProducingActivitiesByGeographicAreaLineItems" xlink:to="us-gaap_CapitalizedCostsRelatingToOilAndGasProducingActivitiesByGeographicAreaLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CapitalizedCostsRelatingToOilAndGasProducingActivitiesByGeographicAreaLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Capitalized Cost [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CapitalizedCostsRelatingToOilAndGasProducingActivitiesByGeographicAreaLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Capitalized Cost [Line Items]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CostsIncurredAcquisitionOfUnprovedOilAndGasProperties" xlink:label="us-gaap_CostsIncurredAcquisitionOfUnprovedOilAndGasProperties" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CostsIncurredAcquisitionOfUnprovedOilAndGasProperties" xlink:to="us-gaap_CostsIncurredAcquisitionOfUnprovedOilAndGasProperties_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CostsIncurredAcquisitionOfUnprovedOilAndGasProperties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Cost Incurred, Unproved Reserve, Property Acquisition Cost</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CostsIncurredAcquisitionOfUnprovedOilAndGasProperties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Undeveloped property acquisition costs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CostsIncurredAcquisitionOfOilAndGasPropertiesWithProvedReserves" xlink:label="us-gaap_CostsIncurredAcquisitionOfOilAndGasPropertiesWithProvedReserves" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CostsIncurredAcquisitionOfOilAndGasPropertiesWithProvedReserves" xlink:to="us-gaap_CostsIncurredAcquisitionOfOilAndGasPropertiesWithProvedReserves_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CostsIncurredAcquisitionOfOilAndGasPropertiesWithProvedReserves_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Cost Incurred, Proved Reserve, Property Acquisition Cost</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CostsIncurredAcquisitionOfOilAndGasPropertiesWithProvedReserves_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquisitions</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CostsIncurredDevelopmentCosts" xlink:label="us-gaap_CostsIncurredDevelopmentCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CostsIncurredDevelopmentCosts" xlink:to="us-gaap_CostsIncurredDevelopmentCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CostsIncurredDevelopmentCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Cost Incurred, Development Cost</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CostsIncurredDevelopmentCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Development costs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CostsIncurredAcquisitionOfOilAndGasProperties" xlink:label="us-gaap_CostsIncurredAcquisitionOfOilAndGasProperties" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CostsIncurredAcquisitionOfOilAndGasProperties" xlink:to="us-gaap_CostsIncurredAcquisitionOfOilAndGasProperties_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CostsIncurredAcquisitionOfOilAndGasProperties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Cost Incurred, Property Acquisition Cost</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_CostsIncurredAcquisitionOfOilAndGasProperties_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total cost incurred</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CostsIncurredAssetRetirementObligationIncurred" xlink:label="us-gaap_CostsIncurredAssetRetirementObligationIncurred" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CostsIncurredAssetRetirementObligationIncurred" xlink:to="us-gaap_CostsIncurredAssetRetirementObligationIncurred_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CostsIncurredAssetRetirementObligationIncurred_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Cost Incurred, Asset Retirement Obligation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CostsIncurredAssetRetirementObligationIncurred_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset retirement obligations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CostsIncurredOilAndGasPropertyAcquisitionExplorationAndDevelopmentActivities" xlink:label="us-gaap_CostsIncurredOilAndGasPropertyAcquisitionExplorationAndDevelopmentActivities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CostsIncurredOilAndGasPropertyAcquisitionExplorationAndDevelopmentActivities" xlink:to="us-gaap_CostsIncurredOilAndGasPropertyAcquisitionExplorationAndDevelopmentActivities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CostsIncurredOilAndGasPropertyAcquisitionExplorationAndDevelopmentActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Cost Incurred, Property Acquisition, Exploration, and Development Costs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_CostsIncurredOilAndGasPropertyAcquisitionExplorationAndDevelopmentActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total costs incurred including asset retirement obligations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProvedDevelopedAndUndevelopedOilAndGasReserveQuantitiesTable" xlink:label="srt_ProvedDevelopedAndUndevelopedOilAndGasReserveQuantitiesTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProvedDevelopedAndUndevelopedOilAndGasReserveQuantitiesTable" xlink:to="srt_ProvedDevelopedAndUndevelopedOilAndGasReserveQuantitiesTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProvedDevelopedAndUndevelopedOilAndGasReserveQuantitiesTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Reserve, Quantity [Table]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ProvedDevelopedAndUndevelopedOilAndGasReserveQuantitiesTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Reserve, Quantity [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ReserveQuantitiesByTypeOfReserveAxis" xlink:label="srt_ReserveQuantitiesByTypeOfReserveAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ReserveQuantitiesByTypeOfReserveAxis" xlink:to="srt_ReserveQuantitiesByTypeOfReserveAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ReserveQuantitiesByTypeOfReserveAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Petroleum Reserves [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ReserveQuantitiesByTypeOfReserveAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Petroleum Reserves [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_TypeOfReserveDomain" xlink:label="srt_TypeOfReserveDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_TypeOfReserveDomain" xlink:to="srt_TypeOfReserveDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_TypeOfReserveDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Type of Reserve [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_TypeOfReserveDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Type of Reserve [Domain]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_DevelopedReservesMember" xlink:label="bkv_DevelopedReservesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_DevelopedReservesMember" xlink:to="bkv_DevelopedReservesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_DevelopedReservesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Developed Reserves</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_DevelopedReservesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Developed Reserves [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_DevelopedReservesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Developed Reserves</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_UndevelopedReservesMember" xlink:label="bkv_UndevelopedReservesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_UndevelopedReservesMember" xlink:to="bkv_UndevelopedReservesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_UndevelopedReservesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Undeveloped Reserves</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_UndevelopedReservesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Undeveloped Reserves [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_UndevelopedReservesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Undeveloped Reserves</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ReserveQuantitiesLineItems" xlink:label="srt_ReserveQuantitiesLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ReserveQuantitiesLineItems" xlink:to="srt_ReserveQuantitiesLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ReserveQuantitiesLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Reserve, Quantity [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ReserveQuantitiesLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Reserve, Quantity [Line Items]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_IncreaseDecreaseInProvedDevelopedAndUndevelopedReservesRollForward" xlink:label="srt_IncreaseDecreaseInProvedDevelopedAndUndevelopedReservesRollForward" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_IncreaseDecreaseInProvedDevelopedAndUndevelopedReservesRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Reserve, Quantity, Volume [Roll Forward]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProvedDevelopedAndUndevelopedReservesNet" xlink:label="srt_ProvedDevelopedAndUndevelopedReservesNet" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="srt_ProvedDevelopedAndUndevelopedReservesNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending balance, volume</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="srt_ProvedDevelopedAndUndevelopedReservesNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning balance, volume</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProvedDevelopedAndUndevelopedReservesRevisionsOfPreviousEstimatesIncreaseDecrease" xlink:label="srt_ProvedDevelopedAndUndevelopedReservesRevisionsOfPreviousEstimatesIncreaseDecrease" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProvedDevelopedAndUndevelopedReservesRevisionsOfPreviousEstimatesIncreaseDecrease" xlink:to="srt_ProvedDevelopedAndUndevelopedReservesRevisionsOfPreviousEstimatesIncreaseDecrease_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProvedDevelopedAndUndevelopedReservesRevisionsOfPreviousEstimatesIncreaseDecrease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Reserve, Quantity, Volume, Revision of Previous Estimate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ProvedDevelopedAndUndevelopedReservesRevisionsOfPreviousEstimatesIncreaseDecrease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revision of previous estimates</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProvedDevelopedAndUndevelopedReservesExtensionsDiscoveriesAndAdditions" xlink:label="srt_ProvedDevelopedAndUndevelopedReservesExtensionsDiscoveriesAndAdditions" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProvedDevelopedAndUndevelopedReservesExtensionsDiscoveriesAndAdditions" xlink:to="srt_ProvedDevelopedAndUndevelopedReservesExtensionsDiscoveriesAndAdditions_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProvedDevelopedAndUndevelopedReservesExtensionsDiscoveriesAndAdditions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Reserve, Quantity, Volume, Addition from Extension and Discovery</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ProvedDevelopedAndUndevelopedReservesExtensionsDiscoveriesAndAdditions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Extensions and discoveries</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProvedDevelopedAndUndevelopedReservesImprovedRecovery" xlink:label="srt_ProvedDevelopedAndUndevelopedReservesImprovedRecovery" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProvedDevelopedAndUndevelopedReservesImprovedRecovery" xlink:to="srt_ProvedDevelopedAndUndevelopedReservesImprovedRecovery_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProvedDevelopedAndUndevelopedReservesImprovedRecovery_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Reserve, Quantity, Volume, Improved Recovery</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ProvedDevelopedAndUndevelopedReservesImprovedRecovery_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Improved recoveries</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProvedDevelopedAndUndevelopedReservesSalesOfMineralsInPlace" xlink:label="srt_ProvedDevelopedAndUndevelopedReservesSalesOfMineralsInPlace" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProvedDevelopedAndUndevelopedReservesSalesOfMineralsInPlace" xlink:to="srt_ProvedDevelopedAndUndevelopedReservesSalesOfMineralsInPlace_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProvedDevelopedAndUndevelopedReservesSalesOfMineralsInPlace_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Reserve, Quantity, Volume, Sale of Mineral in Place</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="srt_ProvedDevelopedAndUndevelopedReservesSalesOfMineralsInPlace_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net sales of minerals in place</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProvedDevelopedAndUndevelopedReservesPurchasesOfMineralsInPlace" xlink:label="srt_ProvedDevelopedAndUndevelopedReservesPurchasesOfMineralsInPlace" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProvedDevelopedAndUndevelopedReservesPurchasesOfMineralsInPlace" xlink:to="srt_ProvedDevelopedAndUndevelopedReservesPurchasesOfMineralsInPlace_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProvedDevelopedAndUndevelopedReservesPurchasesOfMineralsInPlace_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Reserve, Quantity, Volume, Purchase of Mineral in Place</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ProvedDevelopedAndUndevelopedReservesPurchasesOfMineralsInPlace_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchases of minerals in place</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProvedDevelopedAndUndevelopedReservesProduction" xlink:label="srt_ProvedDevelopedAndUndevelopedReservesProduction" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProvedDevelopedAndUndevelopedReservesProduction" xlink:to="srt_ProvedDevelopedAndUndevelopedReservesProduction_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProvedDevelopedAndUndevelopedReservesProduction_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Reserve, Quantity, Volume, Production</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="srt_ProvedDevelopedAndUndevelopedReservesProduction_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Production</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProvedDevelopedReservesVolume" xlink:label="srt_ProvedDevelopedReservesVolume" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProvedDevelopedReservesVolume" xlink:to="srt_ProvedDevelopedReservesVolume_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProvedDevelopedReservesVolume_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Developed Reserve, Quantity, Volume</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ProvedDevelopedReservesVolume_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proved developed reserves (volume)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProvedUndevelopedReserveVolume" xlink:label="srt_ProvedUndevelopedReserveVolume" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProvedUndevelopedReserveVolume" xlink:to="srt_ProvedUndevelopedReserveVolume_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProvedUndevelopedReserveVolume_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Undeveloped Reserve, Quantity, Volume</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ProvedUndevelopedReserveVolume_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proved undeveloped reserve (volume)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProvedDevelopedAndUndevelopedReserveEnergyRollForward" xlink:label="srt_ProvedDevelopedAndUndevelopedReserveEnergyRollForward" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProvedDevelopedAndUndevelopedReserveEnergyRollForward" xlink:to="srt_ProvedDevelopedAndUndevelopedReserveEnergyRollForward_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProvedDevelopedAndUndevelopedReserveEnergyRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Reserve, Quantity, Energy [Roll Forward]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ProvedDevelopedAndUndevelopedReserveEnergyRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Reserve, Quantity, Energy [Roll Forward]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProvedDevelopedAndUndevelopedReserveNetEnergy" xlink:label="srt_ProvedDevelopedAndUndevelopedReserveNetEnergy" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProvedDevelopedAndUndevelopedReserveNetEnergy" xlink:to="srt_ProvedDevelopedAndUndevelopedReserveNetEnergy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProvedDevelopedAndUndevelopedReserveNetEnergy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Reserve, Quantity, Energy</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="srt_ProvedDevelopedAndUndevelopedReserveNetEnergy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending balance, energy</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="srt_ProvedDevelopedAndUndevelopedReserveNetEnergy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning balance, energy</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProvedDevelopedAndUndevelopedReserveRevisionOfPreviousEstimateEnergy" xlink:label="srt_ProvedDevelopedAndUndevelopedReserveRevisionOfPreviousEstimateEnergy" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProvedDevelopedAndUndevelopedReserveRevisionOfPreviousEstimateEnergy" xlink:to="srt_ProvedDevelopedAndUndevelopedReserveRevisionOfPreviousEstimateEnergy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProvedDevelopedAndUndevelopedReserveRevisionOfPreviousEstimateEnergy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Reserve, Quantity, Energy, Revision of Previous Estimate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ProvedDevelopedAndUndevelopedReserveRevisionOfPreviousEstimateEnergy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revision of previous estimates</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="srt_ProvedDevelopedAndUndevelopedReserveRevisionOfPreviousEstimateEnergy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revision of estimates</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProvedDevelopedAndUndevelopedReserveExtensionAndDiscoveryEnergy" xlink:label="srt_ProvedDevelopedAndUndevelopedReserveExtensionAndDiscoveryEnergy" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProvedDevelopedAndUndevelopedReserveExtensionAndDiscoveryEnergy" xlink:to="srt_ProvedDevelopedAndUndevelopedReserveExtensionAndDiscoveryEnergy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProvedDevelopedAndUndevelopedReserveExtensionAndDiscoveryEnergy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Reserve, Quantity, Energy, Addition from Extension and Discovery</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ProvedDevelopedAndUndevelopedReserveExtensionAndDiscoveryEnergy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Extensions and discoveries</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProvedDevelopedAndUndevelopedReserveImprovedRecoveryEnergy" xlink:label="srt_ProvedDevelopedAndUndevelopedReserveImprovedRecoveryEnergy" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProvedDevelopedAndUndevelopedReserveImprovedRecoveryEnergy" xlink:to="srt_ProvedDevelopedAndUndevelopedReserveImprovedRecoveryEnergy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProvedDevelopedAndUndevelopedReserveImprovedRecoveryEnergy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Reserve, Quantity, Energy, Improved Recovery</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ProvedDevelopedAndUndevelopedReserveImprovedRecoveryEnergy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Improved recoveries</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProvedDevelopedAndUndevelopedReservesSaleOfMineralInPlaceEnergy" xlink:label="srt_ProvedDevelopedAndUndevelopedReservesSaleOfMineralInPlaceEnergy" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProvedDevelopedAndUndevelopedReservesSaleOfMineralInPlaceEnergy" xlink:to="srt_ProvedDevelopedAndUndevelopedReservesSaleOfMineralInPlaceEnergy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProvedDevelopedAndUndevelopedReservesSaleOfMineralInPlaceEnergy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Reserve, Quantity, Energy, Sale of Mineral in Place</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="srt_ProvedDevelopedAndUndevelopedReservesSaleOfMineralInPlaceEnergy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net sales of minerals in place</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProvedDevelopedAndUndevelopedReservePurchaseOfMineralInPlaceEnergy" xlink:label="srt_ProvedDevelopedAndUndevelopedReservePurchaseOfMineralInPlaceEnergy" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProvedDevelopedAndUndevelopedReservePurchaseOfMineralInPlaceEnergy" xlink:to="srt_ProvedDevelopedAndUndevelopedReservePurchaseOfMineralInPlaceEnergy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProvedDevelopedAndUndevelopedReservePurchaseOfMineralInPlaceEnergy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Reserve, Quantity, Energy, Purchase of Mineral in Place</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ProvedDevelopedAndUndevelopedReservePurchaseOfMineralInPlaceEnergy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net purchases of minerals in place</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProvedDevelopedAndUndevelopedReserveProductionEnergy" xlink:label="srt_ProvedDevelopedAndUndevelopedReserveProductionEnergy" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProvedDevelopedAndUndevelopedReserveProductionEnergy" xlink:to="srt_ProvedDevelopedAndUndevelopedReserveProductionEnergy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProvedDevelopedAndUndevelopedReserveProductionEnergy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Reserve, Quantity, Energy, Production</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="srt_ProvedDevelopedAndUndevelopedReserveProductionEnergy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Production</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="srt_ProvedDevelopedAndUndevelopedReserveProductionEnergy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Production</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProvedUndevelopedReserveBOE1" xlink:label="srt_ProvedUndevelopedReserveBOE1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProvedUndevelopedReserveBOE1" xlink:to="srt_ProvedUndevelopedReserveBOE1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProvedUndevelopedReserveBOE1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Undeveloped Reserve, Quantity, Energy</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ProvedUndevelopedReserveBOE1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proved undeveloped reserve (energy)</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_OilAndGasProvedReserveQuantityEnergyUndevelopedReservesConvertedToDeveloped" xlink:label="bkv_OilAndGasProvedReserveQuantityEnergyUndevelopedReservesConvertedToDeveloped" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_OilAndGasProvedReserveQuantityEnergyUndevelopedReservesConvertedToDeveloped" xlink:to="bkv_OilAndGasProvedReserveQuantityEnergyUndevelopedReservesConvertedToDeveloped_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_OilAndGasProvedReserveQuantityEnergyUndevelopedReservesConvertedToDeveloped_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Reserve, Quantity, Energy, Undeveloped Reserves Converted To Developed</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_OilAndGasProvedReserveQuantityEnergyUndevelopedReservesConvertedToDeveloped_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Reserve, Quantity, Energy, Undeveloped Reserves Converted To Developed</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_OilAndGasProvedReserveQuantityEnergyUndevelopedReservesConvertedToDeveloped_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Undeveloped reserves converted to developed</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_UndevelopedReservesSpecificLocationsMember" xlink:label="bkv_UndevelopedReservesSpecificLocationsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_UndevelopedReservesSpecificLocationsMember" xlink:to="bkv_UndevelopedReservesSpecificLocationsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_UndevelopedReservesSpecificLocationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Undeveloped Reserves, Specific Locations</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_UndevelopedReservesSpecificLocationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Undeveloped Reserves, Specific Locations [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_UndevelopedReservesSpecificLocationsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Undeveloped Reserves, Specific Locations</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_OilAndGasRevisionDescriptionAxis" xlink:label="bkv_OilAndGasRevisionDescriptionAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_OilAndGasRevisionDescriptionAxis" xlink:to="bkv_OilAndGasRevisionDescriptionAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_OilAndGasRevisionDescriptionAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil And Gas, Revision, Description</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_OilAndGasRevisionDescriptionAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil And Gas, Revision, Description [Axis]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_OilAndGasRevisionDescriptionAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil And Gas, Revision, Description [Axis]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_OilAndGasRevisionDescriptionDomain" xlink:label="bkv_OilAndGasRevisionDescriptionDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_OilAndGasRevisionDescriptionDomain" xlink:to="bkv_OilAndGasRevisionDescriptionDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_OilAndGasRevisionDescriptionDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil And Gas, Revision, Description [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_OilAndGasRevisionDescriptionDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil And Gas, Revision, Description [Domain]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_OilAndGasRevisionDescriptionDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil And Gas, Revision, Description [Domain]</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_LowerAveragePricingMember" xlink:label="bkv_LowerAveragePricingMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_LowerAveragePricingMember" xlink:to="bkv_LowerAveragePricingMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_LowerAveragePricingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lower Average Pricing</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_LowerAveragePricingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lower Average Pricing [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_LowerAveragePricingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lower Average Pricing</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_LowerCapitalSpendMember" xlink:label="bkv_LowerCapitalSpendMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_LowerCapitalSpendMember" xlink:to="bkv_LowerCapitalSpendMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_LowerCapitalSpendMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lower Capital Spend</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_LowerCapitalSpendMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lower Capital Spend [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_LowerCapitalSpendMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lower Capital Spend</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_NEPAMember" xlink:label="bkv_NEPAMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_NEPAMember" xlink:to="bkv_NEPAMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_NEPAMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">NEPA</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_NEPAMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">NEPA [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_NEPAMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">NEPA</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProvedDevelopedAndUndevelopedReserveNetEnergyPeriodIncreaseDecrease" xlink:label="srt_ProvedDevelopedAndUndevelopedReserveNetEnergyPeriodIncreaseDecrease" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProvedDevelopedAndUndevelopedReserveNetEnergyPeriodIncreaseDecrease" xlink:to="srt_ProvedDevelopedAndUndevelopedReserveNetEnergyPeriodIncreaseDecrease_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProvedDevelopedAndUndevelopedReserveNetEnergyPeriodIncreaseDecrease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Proved Reserve, Quantity, Energy, Period Increase (Decrease)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ProvedDevelopedAndUndevelopedReserveNetEnergyPeriodIncreaseDecrease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (decrease) in proved reserves</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_OilAndGasDevelopmentOfLocations.Gross" xlink:label="bkv_OilAndGasDevelopmentOfLocations.Gross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_OilAndGasDevelopmentOfLocations.Gross" xlink:to="bkv_OilAndGasDevelopmentOfLocations.Gross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_OilAndGasDevelopmentOfLocations.Gross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Development of Locations. Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_OilAndGasDevelopmentOfLocations.Gross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Development of Locations. Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_OilAndGasDevelopmentOfLocations.Gross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and gas, development of locations. gross</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_OilAndGasDevelopmentOfLocations.Net" xlink:label="bkv_OilAndGasDevelopmentOfLocations.Net" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_OilAndGasDevelopmentOfLocations.Net" xlink:to="bkv_OilAndGasDevelopmentOfLocations.Net_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_OilAndGasDevelopmentOfLocations.Net_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Development of Locations. Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_OilAndGasDevelopmentOfLocations.Net_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Development of Locations. Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_OilAndGasDevelopmentOfLocations.Net_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, development of locations. net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_GasAndOilAreaUndevelopedGross" xlink:label="srt_GasAndOilAreaUndevelopedGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_GasAndOilAreaUndevelopedGross" xlink:to="srt_GasAndOilAreaUndevelopedGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_GasAndOilAreaUndevelopedGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Undeveloped Acreage, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_GasAndOilAreaUndevelopedGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and gas, undeveloped acreage, gross</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_GasAndOilAreaUndevelopedNet" xlink:label="srt_GasAndOilAreaUndevelopedNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_GasAndOilAreaUndevelopedNet" xlink:to="srt_GasAndOilAreaUndevelopedNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_GasAndOilAreaUndevelopedNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Undeveloped Acreage, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_GasAndOilAreaUndevelopedNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and gas, undeveloped acreage, net</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_GasProductiveWellNumberOfWellsGross" xlink:label="bkv_GasProductiveWellNumberOfWellsGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_GasProductiveWellNumberOfWellsGross" xlink:to="bkv_GasProductiveWellNumberOfWellsGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_GasProductiveWellNumberOfWellsGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gas, Productive Well, Number of Wells, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_GasProductiveWellNumberOfWellsGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gas, Productive Well, Number of Wells, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_GasProductiveWellNumberOfWellsGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gas, productive well, number of wells, gross</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_GasProductiveWellNumberOfWellsNet" xlink:label="bkv_GasProductiveWellNumberOfWellsNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_GasProductiveWellNumberOfWellsNet" xlink:to="bkv_GasProductiveWellNumberOfWellsNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_GasProductiveWellNumberOfWellsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gas, Productive Well, Number of Wells, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_GasProductiveWellNumberOfWellsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gas, Productive Well, Number of Wells, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_GasProductiveWellNumberOfWellsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gas, productive well, number of wells, net</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_OilAndGasProductiveWellNumberOfWellsCompletedGross" xlink:label="bkv_OilAndGasProductiveWellNumberOfWellsCompletedGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_OilAndGasProductiveWellNumberOfWellsCompletedGross" xlink:to="bkv_OilAndGasProductiveWellNumberOfWellsCompletedGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_OilAndGasProductiveWellNumberOfWellsCompletedGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil And Gas, Productive Well, Number of Wells Completed, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_OilAndGasProductiveWellNumberOfWellsCompletedGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil And Gas, Productive Well, Number of Wells Completed, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_OilAndGasProductiveWellNumberOfWellsCompletedGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of wells completed, gross</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_OilAndGasProductiveWellNumberOfWellsCompletedNet" xlink:label="bkv_OilAndGasProductiveWellNumberOfWellsCompletedNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_OilAndGasProductiveWellNumberOfWellsCompletedNet" xlink:to="bkv_OilAndGasProductiveWellNumberOfWellsCompletedNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_OilAndGasProductiveWellNumberOfWellsCompletedNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil And Gas, Productive Well, Number of Wells Completed, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_OilAndGasProductiveWellNumberOfWellsCompletedNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil And Gas, Productive Well, Number of Wells Completed, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_OilAndGasProductiveWellNumberOfWellsCompletedNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of wells completed, net</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_OilAndGasNumberOfLocationsSaleOfMineralsInPlaceGross" xlink:label="bkv_OilAndGasNumberOfLocationsSaleOfMineralsInPlaceGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_OilAndGasNumberOfLocationsSaleOfMineralsInPlaceGross" xlink:to="bkv_OilAndGasNumberOfLocationsSaleOfMineralsInPlaceGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_OilAndGasNumberOfLocationsSaleOfMineralsInPlaceGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil And Gas, Number Of Locations, Sale Of Minerals In Place, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_OilAndGasNumberOfLocationsSaleOfMineralsInPlaceGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil And Gas, Number Of Locations, Sale Of Minerals In Place, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_OilAndGasNumberOfLocationsSaleOfMineralsInPlaceGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of locations, divested, gross</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_OilAndGasNumberOfLocationsSaleOfMineralsInPlaceNet" xlink:label="bkv_OilAndGasNumberOfLocationsSaleOfMineralsInPlaceNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_OilAndGasNumberOfLocationsSaleOfMineralsInPlaceNet" xlink:to="bkv_OilAndGasNumberOfLocationsSaleOfMineralsInPlaceNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_OilAndGasNumberOfLocationsSaleOfMineralsInPlaceNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil And Gas, Number Of Locations, Sale Of Minerals In Place, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_OilAndGasNumberOfLocationsSaleOfMineralsInPlaceNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil And Gas, Number Of Locations, Sale Of Minerals In Place, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_OilAndGasNumberOfLocationsSaleOfMineralsInPlaceNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of locations, divested, net</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_OilAndGasUndevelopedLocationNet" xlink:label="bkv_OilAndGasUndevelopedLocationNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_OilAndGasUndevelopedLocationNet" xlink:to="bkv_OilAndGasUndevelopedLocationNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_OilAndGasUndevelopedLocationNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Undeveloped Location, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_OilAndGasUndevelopedLocationNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Undeveloped Location, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_OilAndGasUndevelopedLocationNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and gas, undeveloped location, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesCashInflows" xlink:label="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesCashInflows" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesCashInflows_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Future cash inflows</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesProductionCosts" xlink:label="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesProductionCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesProductionCosts" xlink:to="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesProductionCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesProductionCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Standardized Measure, Discounted Future Net Cash Flow, Production Cost</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesProductionCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Future production costs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesDevelopmentCosts" xlink:label="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesDevelopmentCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesDevelopmentCosts" xlink:to="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesDevelopmentCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesDevelopmentCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Standardized Measure, Discounted Future Net Cash Flow, Development Cost</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesDevelopmentCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Future development costs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesIncomeTaxExpense" xlink:label="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesIncomeTaxExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesIncomeTaxExpense" xlink:to="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesIncomeTaxExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesIncomeTaxExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Standardized Measure, Discounted Future Net Cash Flow, Income Tax Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesIncomeTaxExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Future income tax expense</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesNetCashFlows" xlink:label="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesNetCashFlows" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesNetCashFlows" xlink:to="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesNetCashFlows_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesNetCashFlows_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Standardized Measure, Discounted Future Net Cash Flow, Future Net Cash Flow, before Discount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesNetCashFlows_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Future net cash flows</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesTenPercentAnnualDiscountForEstimatedTimingOfCashFlows" xlink:label="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesTenPercentAnnualDiscountForEstimatedTimingOfCashFlows" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesTenPercentAnnualDiscountForEstimatedTimingOfCashFlows" xlink:to="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesTenPercentAnnualDiscountForEstimatedTimingOfCashFlows_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesTenPercentAnnualDiscountForEstimatedTimingOfCashFlows_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Standardized Measure, Discounted Future Net Cash Flow, Discount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="srt_FutureNetCashFlowsRelatingToProvedOilAndGasReservesTenPercentAnnualDiscountForEstimatedTimingOfCashFlows_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">10% annual discount for estimated timing of cash flows</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardizedMeasureOfDiscountedFutureNetCashFlowsRelatingToProvedOilAndGasReserves" xlink:label="srt_StandardizedMeasureOfDiscountedFutureNetCashFlowsRelatingToProvedOilAndGasReserves" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_StandardizedMeasureOfDiscountedFutureNetCashFlowsRelatingToProvedOilAndGasReserves" xlink:to="srt_StandardizedMeasureOfDiscountedFutureNetCashFlowsRelatingToProvedOilAndGasReserves_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_StandardizedMeasureOfDiscountedFutureNetCashFlowsRelatingToProvedOilAndGasReserves_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Standardized Measure, Discounted Future Net Cash Flow, Future Net Cash Flow, after Discount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="srt_StandardizedMeasureOfDiscountedFutureNetCashFlowsRelatingToProvedOilAndGasReserves_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending balance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="srt_StandardizedMeasureOfDiscountedFutureNetCashFlowsRelatingToProvedOilAndGasReserves_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning balance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="srt_StandardizedMeasureOfDiscountedFutureNetCashFlowsRelatingToProvedOilAndGasReserves_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Standardized measure of discounted future net cash flows related to proved reserves</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_IncreaseDecreaseInStandardizedMeasureOfDiscountedFutureNetCashFlowRelatingToProvedOilAndGasReservesRollForward" xlink:label="srt_IncreaseDecreaseInStandardizedMeasureOfDiscountedFutureNetCashFlowRelatingToProvedOilAndGasReservesRollForward" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_IncreaseDecreaseInStandardizedMeasureOfDiscountedFutureNetCashFlowRelatingToProvedOilAndGasReservesRollForward" xlink:to="srt_IncreaseDecreaseInStandardizedMeasureOfDiscountedFutureNetCashFlowRelatingToProvedOilAndGasReservesRollForward_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_IncreaseDecreaseInStandardizedMeasureOfDiscountedFutureNetCashFlowRelatingToProvedOilAndGasReservesRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Standardized Measure, Discounted Future Net Cash Flow [Roll Forward]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_IncreaseDecreaseInStandardizedMeasureOfDiscountedFutureNetCashFlowRelatingToProvedOilAndGasReservesRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Standardized Measure, Discounted Future Net Cash Flow [Roll Forward]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_NetIncreaseDecreaseInSalesAndTransferPricesAndProductionCosts" xlink:label="srt_NetIncreaseDecreaseInSalesAndTransferPricesAndProductionCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_NetIncreaseDecreaseInSalesAndTransferPricesAndProductionCosts" xlink:to="srt_NetIncreaseDecreaseInSalesAndTransferPricesAndProductionCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_NetIncreaseDecreaseInSalesAndTransferPricesAndProductionCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Standardized Measure, Discounted Future Net Cash Flow, Sale and Transfer Prices and Production Cost, Increase (Decrease)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_NetIncreaseDecreaseInSalesAndTransferPricesAndProductionCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net change in sales and transfer prices and in production (lifting) costs related to future production</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_IncreaseDecreaseInEstimatedFutureDevelopmentCosts" xlink:label="srt_IncreaseDecreaseInEstimatedFutureDevelopmentCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_IncreaseDecreaseInEstimatedFutureDevelopmentCosts" xlink:to="srt_IncreaseDecreaseInEstimatedFutureDevelopmentCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_IncreaseDecreaseInEstimatedFutureDevelopmentCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Standardized Measure, Discounted Future Net Cash Flow, Estimated Future Development Cost, Increase (Decrease)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_IncreaseDecreaseInEstimatedFutureDevelopmentCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Changes in estimated future development costs</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_SalesAndTransfersOfOilAndGasProducedNetOfProductionCosts" xlink:label="srt_SalesAndTransfersOfOilAndGasProducedNetOfProductionCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_SalesAndTransfersOfOilAndGasProducedNetOfProductionCosts" xlink:to="srt_SalesAndTransfersOfOilAndGasProducedNetOfProductionCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_SalesAndTransfersOfOilAndGasProducedNetOfProductionCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Standardized Measure, Discounted Future Net Cash Flow, Sale and Transfer of Oil and Gas Produced</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="srt_SalesAndTransfersOfOilAndGasProducedNetOfProductionCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sales and transfers of natural gas, NGLs, and oil produced during the period</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ExtensionsDiscoveriesAdditionsAndImprovedRecoveryLessRelatedCosts" xlink:label="srt_ExtensionsDiscoveriesAdditionsAndImprovedRecoveryLessRelatedCosts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ExtensionsDiscoveriesAdditionsAndImprovedRecoveryLessRelatedCosts" xlink:to="srt_ExtensionsDiscoveriesAdditionsAndImprovedRecoveryLessRelatedCosts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ExtensionsDiscoveriesAdditionsAndImprovedRecoveryLessRelatedCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Standardized Measure, Discounted Future Net Cash Flow, Extension, Discovery, and Improved Recovery</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ExtensionsDiscoveriesAdditionsAndImprovedRecoveryLessRelatedCosts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net change due to extensions, discoveries, and improved recoveries</label>
    <loc xlink:type="locator" xlink:href="bkv-20251231.xsd#bkv_OilAndGasStandardizedMeasureDiscountedFutureNetCashFlowPurchaseSalesOfMineralInPlace" xlink:label="bkv_OilAndGasStandardizedMeasureDiscountedFutureNetCashFlowPurchaseSalesOfMineralInPlace" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bkv_OilAndGasStandardizedMeasureDiscountedFutureNetCashFlowPurchaseSalesOfMineralInPlace" xlink:to="bkv_OilAndGasStandardizedMeasureDiscountedFutureNetCashFlowPurchaseSalesOfMineralInPlace_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bkv_OilAndGasStandardizedMeasureDiscountedFutureNetCashFlowPurchaseSalesOfMineralInPlace_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Standardized Measure, Discounted Future Net Cash Flow, Purchase (Sales) of Mineral in Place</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bkv_OilAndGasStandardizedMeasureDiscountedFutureNetCashFlowPurchaseSalesOfMineralInPlace_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Standardized Measure, Discounted Future Net Cash Flow, Purchase (Sales) of Mineral in Place</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bkv_OilAndGasStandardizedMeasureDiscountedFutureNetCashFlowPurchaseSalesOfMineralInPlace_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net change due to purchases (sales) of minerals in place</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RevisionsOfPreviousQuantityEstimates" xlink:label="srt_RevisionsOfPreviousQuantityEstimates" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RevisionsOfPreviousQuantityEstimates" xlink:to="srt_RevisionsOfPreviousQuantityEstimates_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RevisionsOfPreviousQuantityEstimates_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Standardized Measure, Discounted Future Net Cash Flow, Revision of Previous Quantity Estimate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_RevisionsOfPreviousQuantityEstimates_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net change due to revisions in quantity estimates</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_PreviouslyEstimatedDevelopmentCostsIncurred" xlink:label="srt_PreviouslyEstimatedDevelopmentCostsIncurred" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_PreviouslyEstimatedDevelopmentCostsIncurred" xlink:to="srt_PreviouslyEstimatedDevelopmentCostsIncurred_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_PreviouslyEstimatedDevelopmentCostsIncurred_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Standardized Measure, Discounted Future Net Cash Flow, Previously Estimated Development Cost Incurred</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_PreviouslyEstimatedDevelopmentCostsIncurred_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Previously estimated development costs incurred during the period</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_IncreaseDecreaseInFutureIncomeTaxExpenseEstimatesOnFutureCashFlowsRelatedToProvedOilAndGasReserves" xlink:label="srt_IncreaseDecreaseInFutureIncomeTaxExpenseEstimatesOnFutureCashFlowsRelatedToProvedOilAndGasReserves" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_IncreaseDecreaseInFutureIncomeTaxExpenseEstimatesOnFutureCashFlowsRelatedToProvedOilAndGasReserves_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Oil and Gas, Standardized Measure, Discounted Future Net Cash Flow, Future Income Tax Expense (Benefit)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_IncreaseDecreaseInFutureIncomeTaxExpenseEstimatesOnFutureCashFlowsRelatedToProvedOilAndGasReserves_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net change in future income taxes</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardizedMeasureOfDiscountedFutureNetCashFlowRelatingToProvedOilAndGasReservesAccretionOfDiscount" xlink:label="srt_StandardizedMeasureOfDiscountedFutureNetCashFlowRelatingToProvedOilAndGasReservesAccretionOfDiscount" xmlns="http://www.xbrl.org/2003/linkbase" />
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