<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2026 Workiva-->
<!--r:019ed0cf-4dfe-7a1a-ad83-ed9e4f8f29ce,g:70944c00-49f1-42f6-8f4f-d3c5fba551a7-->
<link:linkbase xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedPeriodStartLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedPeriodStartLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/netLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/net-2009-12-16.xsd#netLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedNetLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedNetLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedTerseLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedPeriodEndLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedPeriodEndLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedLabel"/>
  <link:roleRef roleURI="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedTotalLabel"/>
  <link:labelLink xlink:role="http://www.xbrl.org/2003/role/link" xlink:type="extended">
    <link:label id="lab_ecd_TradingArrByIndTable_terseLabel_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual</link:label>
    <link:label id="lab_ecd_TradingArrByIndTable_label_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrByIndTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TradingArrByIndTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TradingArrByIndTable" xlink:to="lab_ecd_TradingArrByIndTable" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_ContractualObligationToBePaidAfterYearFour_019ed0cf-533b-739a-9b86-06010b873942_totalLabel_en-US" xlink:label="lab_bkv_ContractualObligationToBePaidAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_bkv_ContractualObligationToBePaidAfterYearFour_label_en-US" xlink:label="lab_bkv_ContractualObligationToBePaidAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contractual Obligation, to be Paid, after Year Four</link:label>
    <link:label id="lab_bkv_ContractualObligationToBePaidAfterYearFour_documentation_en-US" xlink:label="lab_bkv_ContractualObligationToBePaidAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Contractual Obligation, to be Paid, after Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_ContractualObligationToBePaidAfterYearFour" xlink:href="bkv-20260630.xsd#bkv_ContractualObligationToBePaidAfterYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_ContractualObligationToBePaidAfterYearFour" xlink:to="lab_bkv_ContractualObligationToBePaidAfterYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TradingArrAxis_terseLabel_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangement:</link:label>
    <link:label id="lab_ecd_TradingArrAxis_label_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TradingArrAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TradingArrAxis" xlink:to="lab_ecd_TradingArrAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MaximumMember_019ed0cf-533b-7d25-89d8-b5e8c10ebb93_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum</link:label>
    <link:label id="lab_srt_MaximumMember_label_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maximum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MaximumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MaximumMember" xlink:to="lab_srt_MaximumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnDerivativesAndCommodityContracts_019ed0cf-533b-7ebe-bb12-a41e81d67966_terseLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnDerivativesAndCommodityContracts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total unrealized gains (losses) on derivatives, net</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnDerivativesAndCommodityContracts_label_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnDerivativesAndCommodityContracts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) on Derivatives and Commodity Contracts</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrealizedGainLossOnDerivativesAndCommodityContracts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnrealizedGainLossOnDerivativesAndCommodityContracts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrealizedGainLossOnDerivativesAndCommodityContracts" xlink:to="lab_us-gaap_UnrealizedGainLossOnDerivativesAndCommodityContracts" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_Security12bTitle_019ed0cf-533c-71f9-9db2-78f83b68c579_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:label id="lab_dei_Security12bTitle_label_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_Security12bTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_Security12bTitle" xlink:to="lab_dei_Security12bTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventMember_019ed0cf-53cf-7390-adbc-d982a7f0e1b3_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event</link:label>
    <link:label id="lab_us-gaap_SubsequentEventMember_label_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventMember" xlink:to="lab_us-gaap_SubsequentEventMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_Ms.LindsayLarrickMember_label_en-US" xlink:label="lab_bkv_Ms.LindsayLarrickMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ms. Lindsay Larrick [Member]</link:label>
    <link:label id="lab_bkv_Ms.LindsayLarrickMember_documentation_en-US" xlink:label="lab_bkv_Ms.LindsayLarrickMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Ms. Lindsay Larrick</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_Ms.LindsayLarrickMember" xlink:href="bkv-20260630.xsd#bkv_Ms.LindsayLarrickMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_Ms.LindsayLarrickMember" xlink:to="lab_bkv_Ms.LindsayLarrickMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation, Amount</link:label>
    <link:label id="lab_ecd_AdjToCompAmt_label_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAmt" xlink:to="lab_ecd_AdjToCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_InterestPayableAfterYearFour_019ed0cf-53ce-7d62-bc5a-bd0ee5ac7cfa_terseLabel_en-US" xlink:label="lab_bkv_InterestPayableAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_bkv_InterestPayableAfterYearFour_label_en-US" xlink:label="lab_bkv_InterestPayableAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable, After Year Four</link:label>
    <link:label id="lab_bkv_InterestPayableAfterYearFour_documentation_en-US" xlink:label="lab_bkv_InterestPayableAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Payable, After Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_InterestPayableAfterYearFour" xlink:href="bkv-20260630.xsd#bkv_InterestPayableAfterYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_InterestPayableAfterYearFour" xlink:to="lab_bkv_InterestPayableAfterYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract_019ed0cf-533b-7a79-898c-f94dbdb0b28c_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial liabilities</link:label>
    <link:label id="lab_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Liabilities Fair Value Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract" xlink:to="lab_us-gaap_FinancialLiabilitiesFairValueDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingAbstract_label_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingAbstract" xlink:to="lab_us-gaap_SegmentReportingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_OPISPropaneMontBelvieuNonTETMember_019ed0cf-533b-7091-87c3-f3d44b6400b5_terseLabel_en-US" xlink:label="lab_bkv_OPISPropaneMontBelvieuNonTETMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">OPIS Propane Mont Belvieu Non-TET</link:label>
    <link:label id="lab_bkv_OPISPropaneMontBelvieuNonTETMember_label_en-US" xlink:label="lab_bkv_OPISPropaneMontBelvieuNonTETMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">OPIS Propane Mont Belvieu Non-TET [Member]</link:label>
    <link:label id="lab_bkv_OPISPropaneMontBelvieuNonTETMember_documentation_en-US" xlink:label="lab_bkv_OPISPropaneMontBelvieuNonTETMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">OPIS Propane Mont Belvieu Non-TET</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_OPISPropaneMontBelvieuNonTETMember" xlink:href="bkv-20260630.xsd#bkv_OPISPropaneMontBelvieuNonTETMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_OPISPropaneMontBelvieuNonTETMember" xlink:to="lab_bkv_OPISPropaneMontBelvieuNonTETMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent_019ed0cf-53ce-73a7-b08f-7cf8940f0f6e_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued payroll</link:label>
    <link:label id="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Employee-related Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeRelatedLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:to="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour_019ed0cf-533c-7d4d-b99d-d80540138cf8_terseLabel_en-US" xlink:label="lab_bkv_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_bkv_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour_label_en-US" xlink:label="lab_bkv_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, After Year Four</link:label>
    <link:label id="lab_bkv_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour_documentation_en-US" xlink:label="lab_bkv_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, After Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:href="bkv-20260630.xsd#bkv_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:to="lab_bkv_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_NetAssetsAttributableToMajorityShareholder_019fd7ce-c9b6-798d-8859-0814f2573d29_terseLabel_en-US" xlink:label="lab_bkv_NetAssetsAttributableToMajorityShareholder" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net assets attributable to Banpu</link:label>
    <link:label id="lab_bkv_NetAssetsAttributableToMajorityShareholder_label_en-US" xlink:label="lab_bkv_NetAssetsAttributableToMajorityShareholder" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Assets Attributable To Majority Shareholder</link:label>
    <link:label id="lab_bkv_NetAssetsAttributableToMajorityShareholder_documentation_en-US" xlink:label="lab_bkv_NetAssetsAttributableToMajorityShareholder" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Assets Attributable To Majority Shareholder</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_NetAssetsAttributableToMajorityShareholder" xlink:href="bkv-20260630.xsd#bkv_NetAssetsAttributableToMajorityShareholder"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_NetAssetsAttributableToMajorityShareholder" xlink:to="lab_bkv_NetAssetsAttributableToMajorityShareholder" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFloorPrice_019ed0cf-53ce-7747-92a4-1a0b0732580a_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFloorPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative, floor price (in USD per unit)</link:label>
    <link:label id="lab_us-gaap_DerivativeFloorPrice_label_en-US" xlink:label="lab_us-gaap_DerivativeFloorPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Floor Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFloorPrice" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeFloorPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFloorPrice" xlink:to="lab_us-gaap_DerivativeFloorPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingencyAccrualAtCarryingValue_019ed0cf-533b-7a70-a64a-f6b851215f81_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other contingent liabilities</link:label>
    <link:label id="lab_us-gaap_LossContingencyAccrualAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency Accrual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LossContingencyAccrualAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:to="lab_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityExTransitionPeriod_019ed0cf-533b-724e-a622-e98877d95995_terseLabel_en-US" xlink:label="lab_dei_EntityExTransitionPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Ex Transition Period</link:label>
    <link:label id="lab_dei_EntityExTransitionPeriod_label_en-US" xlink:label="lab_dei_EntityExTransitionPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Ex Transition Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityExTransitionPeriod" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityExTransitionPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityExTransitionPeriod" xlink:to="lab_dei_EntityExTransitionPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SupplyCommitmentAxis_019fa907-a2c6-732e-90af-e8f0e104e23c_terseLabel_en-US" xlink:label="lab_us-gaap_SupplyCommitmentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SupplyCommitmentAxis [Axis]</link:label>
    <link:label id="lab_us-gaap_SupplyCommitmentAxis_label_en-US" xlink:label="lab_us-gaap_SupplyCommitmentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Supply Commitment [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplyCommitmentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SupplyCommitmentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SupplyCommitmentAxis" xlink:to="lab_us-gaap_SupplyCommitmentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_PerformanceBasedRestrictedStockUnitsMember_019ed0cf-533b-77f7-bc56-e3ecb61018f3_terseLabel_en-US" xlink:label="lab_bkv_PerformanceBasedRestrictedStockUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PRSUs</link:label>
    <link:label id="lab_bkv_PerformanceBasedRestrictedStockUnitsMember_label_en-US" xlink:label="lab_bkv_PerformanceBasedRestrictedStockUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Performance-Based Restricted Stock Units [Member]</link:label>
    <link:label id="lab_bkv_PerformanceBasedRestrictedStockUnitsMember_documentation_en-US" xlink:label="lab_bkv_PerformanceBasedRestrictedStockUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Performance-Based Restricted Stock Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_PerformanceBasedRestrictedStockUnitsMember" xlink:href="bkv-20260630.xsd#bkv_PerformanceBasedRestrictedStockUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_PerformanceBasedRestrictedStockUnitsMember" xlink:to="lab_bkv_PerformanceBasedRestrictedStockUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_019ed0cf-533b-7d21-8360-516837caaaf7_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeInstrumentRiskAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:to="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems_019ed0cf-5275-741d-93ec-59ba159a6777_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsidiary of Limited Liability Company or Limited Partnership [Line Items]</link:label>
    <link:label id="lab_us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems_label_en-US" xlink:label="lab_us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary of Limited Liability Company or Limited Partnership [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems" xlink:to="lab_us-gaap_SubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidatedEntitiesAxis_019ed0cf-533c-7174-8add-cf9d5d853fda_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
    <link:label id="lab_srt_ConsolidatedEntitiesAxis_label_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidatedEntitiesAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidatedEntitiesAxis" xlink:to="lab_srt_ConsolidatedEntitiesAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_A2027CallOptionMember_019ed0cf-53ce-79aa-a54e-1c7be151afd3_terseLabel_en-US" xlink:label="lab_bkv_A2027CallOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027 Call Option</link:label>
    <link:label id="lab_bkv_A2027CallOptionMember_label_en-US" xlink:label="lab_bkv_A2027CallOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2027 Call Option [Member]</link:label>
    <link:label id="lab_bkv_A2027CallOptionMember_documentation_en-US" xlink:label="lab_bkv_A2027CallOptionMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2027 Call Option</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_A2027CallOptionMember" xlink:href="bkv-20260630.xsd#bkv_A2027CallOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_A2027CallOptionMember" xlink:to="lab_bkv_A2027CallOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_019ed0cf-533c-7e63-92cf-a55ea2c75edf_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCommonStockSharesOutstanding" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCommonStockSharesOutstanding" xlink:to="lab_dei_EntityCommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherDepreciationAndAmortization_019ed0cf-533b-7912-b074-501b956cd960_terseLabel_en-US" xlink:label="lab_us-gaap_OtherDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation</link:label>
    <link:label id="lab_us-gaap_OtherDepreciationAndAmortization_label_en-US" xlink:label="lab_us-gaap_OtherDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Depreciation and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherDepreciationAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherDepreciationAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherDepreciationAndAmortization" xlink:to="lab_us-gaap_OtherDepreciationAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidatedEntitiesDomain_019ed0cf-533b-788f-b9dd-e44ec2bf0b17_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntitiesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Domain]</link:label>
    <link:label id="lab_srt_ConsolidatedEntitiesDomain_label_en-US" xlink:label="lab_srt_ConsolidatedEntitiesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidatedEntitiesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidatedEntitiesDomain" xlink:to="lab_srt_ConsolidatedEntitiesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToMinorityShareholders_019fc8ba-a3a8-7b68-979b-2a585dfa9cbc_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToMinorityShareholders" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Acquisition of additional interest in BKV-BPP Power</link:label>
    <link:label id="lab_us-gaap_PaymentsToMinorityShareholders_label_en-US" xlink:label="lab_us-gaap_PaymentsToMinorityShareholders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Noncontrolling Interests</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToMinorityShareholders" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToMinorityShareholders"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToMinorityShareholders" xlink:to="lab_us-gaap_PaymentsToMinorityShareholders" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativePremiumPaid_019ed0cf-533c-7e00-936a-96d1dfc69525_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DerivativePremiumPaid" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Derivative, premium paid</link:label>
    <link:label id="lab_us-gaap_DerivativePremiumPaid_label_en-US" xlink:label="lab_us-gaap_DerivativePremiumPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Premium Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativePremiumPaid" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativePremiumPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativePremiumPaid" xlink:to="lab_us-gaap_DerivativePremiumPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCommitmentDueInFourthYear_019ed0cf-533c-7921-8d00-31ab6bd973e7_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitmentDueInFourthYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_OtherCommitmentDueInFourthYear_label_en-US" xlink:label="lab_us-gaap_OtherCommitmentDueInFourthYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitment, to be Paid, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitmentDueInFourthYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherCommitmentDueInFourthYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCommitmentDueInFourthYear" xlink:to="lab_us-gaap_OtherCommitmentDueInFourthYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock_019ed0cf-53ce-78f9-9317-b87982c4f473_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Cash and Cash Equivalents</link:label>
    <link:label id="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Cash and Cash Equivalents [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationSettlements_019f7fc9-6fc5-795c-9fda-a900c52ebf96_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationSettlements" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Settlements</link:label>
    <link:label id="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationSettlements_label_en-US" xlink:label="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationSettlements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis, Unobservable Inputs Reconciliation, Settlements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationSettlements" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationSettlements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationSettlements" xlink:to="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationSettlements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_019ed0cf-533b-72b4-b0c2-7ea41f90f45e_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock par value (in USD per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProvedOilAndGasPropertySuccessfulEffortMethod_019ed0cf-53ce-7696-8d14-64652d5cda00_terseLabel_en-US" xlink:label="lab_us-gaap_ProvedOilAndGasPropertySuccessfulEffortMethod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Developed properties</link:label>
    <link:label id="lab_us-gaap_ProvedOilAndGasPropertySuccessfulEffortMethod_label_en-US" xlink:label="lab_us-gaap_ProvedOilAndGasPropertySuccessfulEffortMethod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Oil and Gas, Successful Efforts Method, Property and Equipment, Proved Property, before Accumulated Depreciation, Depletion, Amortization, and Impairment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProvedOilAndGasPropertySuccessfulEffortMethod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProvedOilAndGasPropertySuccessfulEffortMethod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProvedOilAndGasPropertySuccessfulEffortMethod" xlink:to="lab_us-gaap_ProvedOilAndGasPropertySuccessfulEffortMethod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetAcquisitionAxis_019ed0cf-533b-74d6-808d-67f46f6c087c_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Axis]</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionAxis_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetAcquisitionAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionAxis" xlink:to="lab_us-gaap_AssetAcquisitionAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_019ed0cf-533b-7173-8697-878254eef71e_periodStartLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Unvested RSUs, beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_019ed0cf-533b-7948-8a4c-548bf71d6ef1_periodEndLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Unvested RSUs, ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_OilAndGasMidstreamAssetsDepreciationDepletionAmortizationAndAccretion_019ed0cf-53ce-742c-98df-4546330856eb_terseLabel_en-US" xlink:label="lab_bkv_OilAndGasMidstreamAssetsDepreciationDepletionAmortizationAndAccretion" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Midstream assets, depreciation, depletion, amortization, and accretion</link:label>
    <link:label id="lab_bkv_OilAndGasMidstreamAssetsDepreciationDepletionAmortizationAndAccretion_label_en-US" xlink:label="lab_bkv_OilAndGasMidstreamAssetsDepreciationDepletionAmortizationAndAccretion" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Oil and Gas, Midstream Assets, Depreciation, Depletion, Amortization, and Accretion</link:label>
    <link:label id="lab_bkv_OilAndGasMidstreamAssetsDepreciationDepletionAmortizationAndAccretion_documentation_en-US" xlink:label="lab_bkv_OilAndGasMidstreamAssetsDepreciationDepletionAmortizationAndAccretion" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Oil and Gas, Midstream Assets, Depreciation, Depletion, Amortization, and Accretion</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_OilAndGasMidstreamAssetsDepreciationDepletionAmortizationAndAccretion" xlink:href="bkv-20260630.xsd#bkv_OilAndGasMidstreamAssetsDepreciationDepletionAmortizationAndAccretion"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_OilAndGasMidstreamAssetsDepreciationDepletionAmortizationAndAccretion" xlink:to="lab_bkv_OilAndGasMidstreamAssetsDepreciationDepletionAmortizationAndAccretion" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingAggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingAggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingAggtErrCompAmt" xlink:to="lab_ecd_OutstandingAggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetRetirementObligation_019ed0cf-53ce-740c-b25d-164dafef2110_periodStartLabel_en-US" xlink:label="lab_us-gaap_AssetRetirementObligation" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Balance, beginning of period</link:label>
    <link:label id="lab_us-gaap_AssetRetirementObligation_019ed0cf-53ce-7f48-8d22-210f16ac41a5_periodEndLabel_en-US" xlink:label="lab_us-gaap_AssetRetirementObligation" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Balance, end of period</link:label>
    <link:label id="lab_us-gaap_AssetRetirementObligation_label_en-US" xlink:label="lab_us-gaap_AssetRetirementObligation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Retirement Obligation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetRetirementObligation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetRetirementObligation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetRetirementObligation" xlink:to="lab_us-gaap_AssetRetirementObligation" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_GatheringAndTransportationCosts_019ed0cf-53ce-7449-b9b8-37cc293fc3c6_terseLabel_en-US" xlink:label="lab_bkv_GatheringAndTransportationCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gathering and transportation</link:label>
    <link:label id="lab_bkv_GatheringAndTransportationCosts_label_en-US" xlink:label="lab_bkv_GatheringAndTransportationCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gathering and Transportation Costs</link:label>
    <link:label id="lab_bkv_GatheringAndTransportationCosts_documentation_en-US" xlink:label="lab_bkv_GatheringAndTransportationCosts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gathering and Transportation Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_GatheringAndTransportationCosts" xlink:href="bkv-20260630.xsd#bkv_GatheringAndTransportationCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_GatheringAndTransportationCosts" xlink:to="lab_bkv_GatheringAndTransportationCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInEquityPercentage_019ed0cf-533c-7539-88d2-7a8c041a7f36_terseLabel_en-US" xlink:label="lab_bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInEquityPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business combination, consideration transferred, equity interest, percentage</link:label>
    <link:label id="lab_bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInEquityPercentage_label_en-US" xlink:label="lab_bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInEquityPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Liabilities Paid In Equity, Percentage</link:label>
    <link:label id="lab_bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInEquityPercentage_documentation_en-US" xlink:label="lab_bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInEquityPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Liabilities Paid In Equity, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInEquityPercentage" xlink:href="bkv-20260630.xsd#bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInEquityPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInEquityPercentage" xlink:to="lab_bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInEquityPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_019ed0cf-53ce-73ce-b894-71bae709ece1_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of reportable segments</link:label>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Reportable Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfReportableSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NumberOfReportableSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfReportableSegments" xlink:to="lab_us-gaap_NumberOfReportableSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesCurrent_019ed0cf-533b-7abd-9f12-ca5b4224f577_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total current liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesCurrent" xlink:to="lab_us-gaap_LiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TaxesExcludingIncomeAndExciseTaxes_019ed0cf-53ce-7fcf-914c-b4892899d893_terseLabel_en-US" xlink:label="lab_us-gaap_TaxesExcludingIncomeAndExciseTaxes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Taxes other than income</link:label>
    <link:label id="lab_us-gaap_TaxesExcludingIncomeAndExciseTaxes_label_en-US" xlink:label="lab_us-gaap_TaxesExcludingIncomeAndExciseTaxes" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Taxes, Miscellaneous</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TaxesExcludingIncomeAndExciseTaxes" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TaxesExcludingIncomeAndExciseTaxes"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TaxesExcludingIncomeAndExciseTaxes" xlink:to="lab_us-gaap_TaxesExcludingIncomeAndExciseTaxes" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_019ed0cf-53ce-7f7c-b603-b531f5983247_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Instruments</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Instruments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDerivativeInstrumentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:to="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilitiesCurrent_019ed0cf-533b-7ef8-909f-a55087c72d67_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commodity derivative liabilities, current</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilitiesCurrent" xlink:to="lab_us-gaap_DerivativeLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamAssetsAccumulatedDepreciationDepletionAmortizationAndImpairment_019ed0cf-533b-7ae3-ae3d-d31d6ec79482_terseLabel_en-US" xlink:label="lab_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamAssetsAccumulatedDepreciationDepletionAmortizationAndImpairment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Midstream assets, accumulated depreciation, depletion, amortization, and impairment</link:label>
    <link:label id="lab_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamAssetsAccumulatedDepreciationDepletionAmortizationAndImpairment_label_en-US" xlink:label="lab_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamAssetsAccumulatedDepreciationDepletionAmortizationAndImpairment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Oil and Gas, Successful Efforts Method, Property and Equipment, Midstream Assets, Accumulated Depreciation, Depletion, Amortization, and Impairment</link:label>
    <link:label id="lab_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamAssetsAccumulatedDepreciationDepletionAmortizationAndImpairment_documentation_en-US" xlink:label="lab_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamAssetsAccumulatedDepreciationDepletionAmortizationAndImpairment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Oil and Gas, Successful Efforts Method, Property and Equipment, Midstream Assets, Accumulated Depreciation, Depletion, Amortization, and Impairment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamAssetsAccumulatedDepreciationDepletionAmortizationAndImpairment" xlink:href="bkv-20260630.xsd#bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamAssetsAccumulatedDepreciationDepletionAmortizationAndImpairment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamAssetsAccumulatedDepreciationDepletionAmortizationAndImpairment" xlink:to="lab_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamAssetsAccumulatedDepreciationDepletionAmortizationAndImpairment" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_019ed0cf-533b-7a87-9f9c-872b0183b9a9_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeNet_019ed0cf-533b-7e97-ad23-b184e468e763_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative, fair value, net</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeNet_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Fair Value, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFairValueOfDerivativeNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeFairValueOfDerivativeNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFairValueOfDerivativeNet" xlink:to="lab_us-gaap_DerivativeFairValueOfDerivativeNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_019ed0cf-533b-752c-9d55-b7e59c764b28_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Granted (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019ed0cf-53ce-7974-9cc2-b8400af7707d_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfFinancialPositionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:to="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeerGroupTotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:to="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital_019ed0cf-533c-7890-aa1b-036d6c758109_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Return of capital</link:label>
    <link:label id="lab_us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital_label_en-US" xlink:label="lab_us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Equity Method Investment, Distribution, Return of Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital" xlink:to="lab_us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd_019ed0cf-53ce-7d7e-b4a0-7886129cbbf8_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effective interest rate</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Interest Rate at Period End</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd" xlink:to="lab_us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromStockPlans_019ed0cf-533b-7db9-9168-504ada3cf05e_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromStockPlans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock issued from employee purchase plan</link:label>
    <link:label id="lab_us-gaap_ProceedsFromStockPlans_label_en-US" xlink:label="lab_us-gaap_ProceedsFromStockPlans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Stock Plans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromStockPlans" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromStockPlans"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromStockPlans" xlink:to="lab_us-gaap_ProceedsFromStockPlans" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_019ed0cf-5275-747d-943d-ab4fa2421a1e_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Significant Other Observable Inputs (Level 2)</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel2Member" xlink:to="lab_us-gaap_FairValueInputsLevel2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TotalShareholderRtnVsPeerGroupTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:to="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_BanpuPublicCompanyLimitedBanpuMember_019fc961-135b-74a8-9113-4349c0a08756_terseLabel_en-US" xlink:label="lab_bkv_BanpuPublicCompanyLimitedBanpuMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Banpu</link:label>
    <link:label id="lab_bkv_BanpuPublicCompanyLimitedBanpuMember_label_en-US" xlink:label="lab_bkv_BanpuPublicCompanyLimitedBanpuMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banpu Public Company Limited (Banpu) [Member]</link:label>
    <link:label id="lab_bkv_BanpuPublicCompanyLimitedBanpuMember_documentation_en-US" xlink:label="lab_bkv_BanpuPublicCompanyLimitedBanpuMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Banpu Public Company Limited (Banpu)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_BanpuPublicCompanyLimitedBanpuMember" xlink:href="bkv-20260630.xsd#bkv_BanpuPublicCompanyLimitedBanpuMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_BanpuPublicCompanyLimitedBanpuMember" xlink:to="lab_bkv_BanpuPublicCompanyLimitedBanpuMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonRule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:to="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTextBlock_019ed0cf-53ce-75e5-bae7-ca29c1b9be4f_terseLabel_en-US" xlink:label="lab_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting, Reconciliation of Asset by Segment to Consolidated</link:label>
    <link:label id="lab_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTextBlock_label_en-US" xlink:label="lab_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Reconciliation of Asset by Segment to Consolidated [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTextBlock" xlink:to="lab_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OilAndGasPropertySuccessfulEffortMethodNet_019ed0cf-53ce-7959-8340-aaa866fe013d_totalLabel_en-US" xlink:label="lab_us-gaap_OilAndGasPropertySuccessfulEffortMethodNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total natural gas properties, net</link:label>
    <link:label id="lab_us-gaap_OilAndGasPropertySuccessfulEffortMethodNet_label_en-US" xlink:label="lab_us-gaap_OilAndGasPropertySuccessfulEffortMethodNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Oil and Gas, Successful Efforts Method, Property and Equipment, after Accumulated Depreciation, Depletion, Amortization, and Impairment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OilAndGasPropertySuccessfulEffortMethodNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OilAndGasPropertySuccessfulEffortMethodNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OilAndGasPropertySuccessfulEffortMethodNet" xlink:to="lab_us-gaap_OilAndGasPropertySuccessfulEffortMethodNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_019ed0cf-533b-7d9a-9444-3754189544be_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeAxis" xlink:to="lab_us-gaap_SubsequentEventTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_019ed0cf-533c-7d08-8aa7-b5a8c5eaf64b_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskByTypeAxis" xlink:to="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTable_019ed0cf-53ce-7ca4-9ec2-cb412b3d2998_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTable_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTable" xlink:to="lab_us-gaap_DebtInstrumentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_JointVentureFormationCommittedContributionByNonControllingInterest_019ed0cf-53ce-7f17-829e-63f9f1768048_terseLabel_en-US" xlink:label="lab_bkv_JointVentureFormationCommittedContributionByNonControllingInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contribution by non-controlling interest in joint venture</link:label>
    <link:label id="lab_bkv_JointVentureFormationCommittedContributionByNonControllingInterest_label_en-US" xlink:label="lab_bkv_JointVentureFormationCommittedContributionByNonControllingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Joint Venture Formation, Committed Contribution By Non-Controlling Interest</link:label>
    <link:label id="lab_bkv_JointVentureFormationCommittedContributionByNonControllingInterest_documentation_en-US" xlink:label="lab_bkv_JointVentureFormationCommittedContributionByNonControllingInterest" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Joint Venture Formation, Committed Contribution By Non-Controlling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_JointVentureFormationCommittedContributionByNonControllingInterest" xlink:href="bkv-20260630.xsd#bkv_JointVentureFormationCommittedContributionByNonControllingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_JointVentureFormationCommittedContributionByNonControllingInterest" xlink:to="lab_bkv_JointVentureFormationCommittedContributionByNonControllingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_AssetAcquisitionDepositForAcquisition_019ed0cf-53ce-755c-827d-cd633efe92f8_terseLabel_en-US" xlink:label="lab_bkv_AssetAcquisitionDepositForAcquisition" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deposit for acquisition</link:label>
    <link:label id="lab_bkv_AssetAcquisitionDepositForAcquisition_label_en-US" xlink:label="lab_bkv_AssetAcquisitionDepositForAcquisition" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Deposit For Acquisition</link:label>
    <link:label id="lab_bkv_AssetAcquisitionDepositForAcquisition_documentation_en-US" xlink:label="lab_bkv_AssetAcquisitionDepositForAcquisition" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Deposit For Acquisition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_AssetAcquisitionDepositForAcquisition" xlink:href="bkv-20260630.xsd#bkv_AssetAcquisitionDepositForAcquisition"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_AssetAcquisitionDepositForAcquisition" xlink:to="lab_bkv_AssetAcquisitionDepositForAcquisition" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_019ed0cf-533c-7c95-8337-047ddd6355fd_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:to="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_ManufacturingReservationAgreementMember_019ed0cf-533c-75b9-8420-5cd456e9d33e_terseLabel_en-US" xlink:label="lab_bkv_ManufacturingReservationAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Manufacturing reservation agreement</link:label>
    <link:label id="lab_bkv_ManufacturingReservationAgreementMember_label_en-US" xlink:label="lab_bkv_ManufacturingReservationAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Manufacturing Reservation Agreement [Member]</link:label>
    <link:label id="lab_bkv_ManufacturingReservationAgreementMember_documentation_en-US" xlink:label="lab_bkv_ManufacturingReservationAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Manufacturing Reservation Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_ManufacturingReservationAgreementMember" xlink:href="bkv-20260630.xsd#bkv_ManufacturingReservationAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_ManufacturingReservationAgreementMember" xlink:to="lab_bkv_ManufacturingReservationAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_EarningsPerShareAttributableToMajorityStockholdersDiluted_019fd7d8-446c-7495-9e39-4dfce247eddd_terseLabel_en-US" xlink:label="lab_bkv_EarningsPerShareAttributableToMajorityStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted (in USD per share)</link:label>
    <link:label id="lab_bkv_EarningsPerShareAttributableToMajorityStockholdersDiluted_label_en-US" xlink:label="lab_bkv_EarningsPerShareAttributableToMajorityStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Attributable to Majority Stockholders, Diluted</link:label>
    <link:label id="lab_bkv_EarningsPerShareAttributableToMajorityStockholdersDiluted_documentation_en-US" xlink:label="lab_bkv_EarningsPerShareAttributableToMajorityStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Attributable to Majority Stockholders, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_EarningsPerShareAttributableToMajorityStockholdersDiluted" xlink:href="bkv-20260630.xsd#bkv_EarningsPerShareAttributableToMajorityStockholdersDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_EarningsPerShareAttributableToMajorityStockholdersDiluted" xlink:to="lab_bkv_EarningsPerShareAttributableToMajorityStockholdersDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UseOfEstimates_019ed0cf-5275-701e-8cac-9257053fcaa6_terseLabel_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Significant Judgments and Accounting Estimates</link:label>
    <link:label id="lab_us-gaap_UseOfEstimates_label_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Use of Estimates, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UseOfEstimates" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UseOfEstimates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UseOfEstimates" xlink:to="lab_us-gaap_UseOfEstimates" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ImpairmentOfLongLivedAssetsToBeDisposedOf_019ed0cf-53ce-7c61-aab5-057ddafd09d5_terseLabel_en-US" xlink:label="lab_us-gaap_ImpairmentOfLongLivedAssetsToBeDisposedOf" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Impairment of asset held for sale</link:label>
    <link:label id="lab_us-gaap_ImpairmentOfLongLivedAssetsToBeDisposedOf_label_en-US" xlink:label="lab_us-gaap_ImpairmentOfLongLivedAssetsToBeDisposedOf" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impairment of Long-Lived Assets to be Disposed of</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ImpairmentOfLongLivedAssetsToBeDisposedOf" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ImpairmentOfLongLivedAssetsToBeDisposedOf"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ImpairmentOfLongLivedAssetsToBeDisposedOf" xlink:to="lab_us-gaap_ImpairmentOfLongLivedAssetsToBeDisposedOf" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_019ed0cf-53ce-7126-8a6b-77c8da4222ea_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfLinesOfCredit_019ed0cf-533c-7f83-af29-db570104517d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfLinesOfCredit" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payments on Temple Term Loan Facility</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfLinesOfCredit_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Lines of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfLinesOfCredit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentsOfLinesOfCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfLinesOfCredit" xlink:to="lab_us-gaap_RepaymentsOfLinesOfCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_MarketingMember_019ed0cf-53ce-72be-8a42-f671eaf16838_terseLabel_en-US" xlink:label="lab_bkv_MarketingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Marketing revenues</link:label>
    <link:label id="lab_bkv_MarketingMember_label_en-US" xlink:label="lab_bkv_MarketingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketing [Member]</link:label>
    <link:label id="lab_bkv_MarketingMember_documentation_en-US" xlink:label="lab_bkv_MarketingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Marketing</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_MarketingMember" xlink:href="bkv-20260630.xsd#bkv_MarketingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_MarketingMember" xlink:to="lab_bkv_MarketingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_019ed0cf-53ce-772c-b4d0-b4211f0e90b8_terseLabel_en-US" xlink:label="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-cash investing and financing activities:</link:label>
    <link:label id="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Flow, Noncash Investing and Financing Activities Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:to="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentPeriodEndDate_019ed0cf-53ce-7938-964c-76cbaebd7d80_terseLabel_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:label id="lab_dei_DocumentPeriodEndDate_label_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentPeriodEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentPeriodEndDate" xlink:to="lab_dei_DocumentPeriodEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_OPISIsoButaneMontBelvieuNonTETMember_019ed0cf-533b-7804-9448-e3e892e0ecd5_terseLabel_en-US" xlink:label="lab_bkv_OPISIsoButaneMontBelvieuNonTETMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">OPIS IsoButane Mont Belvieu Non-TET</link:label>
    <link:label id="lab_bkv_OPISIsoButaneMontBelvieuNonTETMember_label_en-US" xlink:label="lab_bkv_OPISIsoButaneMontBelvieuNonTETMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">OPIS IsoButane Mont Belvieu Non-TET [Member]</link:label>
    <link:label id="lab_bkv_OPISIsoButaneMontBelvieuNonTETMember_documentation_en-US" xlink:label="lab_bkv_OPISIsoButaneMontBelvieuNonTETMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">OPIS IsoButane Mont Belvieu Non-TET</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_OPISIsoButaneMontBelvieuNonTETMember" xlink:href="bkv-20260630.xsd#bkv_OPISIsoButaneMontBelvieuNonTETMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_OPISIsoButaneMontBelvieuNonTETMember" xlink:to="lab_bkv_OPISIsoButaneMontBelvieuNonTETMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnSaleOfProperties_019ed0cf-533c-7c08-b30d-73fab40160bf_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfProperties" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain (loss) on sale of properties</link:label>
    <link:label id="lab_us-gaap_GainLossOnSaleOfProperties_label_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfProperties" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Sale of Properties</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnSaleOfProperties" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainLossOnSaleOfProperties"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnSaleOfProperties" xlink:to="lab_us-gaap_GainLossOnSaleOfProperties" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_019ed0cf-533b-78e0-9f15-eb9e347863f0_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, face amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_019ed0cf-533b-78b4-8686-0473915552a7_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Principal amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Face Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFaceAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentFaceAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFaceAmount" xlink:to="lab_us-gaap_DebtInstrumentFaceAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_019ed0cf-533b-7339-86b7-ce5454eb4416_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommodityMember_019ed0cf-533b-7321-96e2-3a311f4a495c_terseLabel_en-US" xlink:label="lab_us-gaap_CommodityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commodity</link:label>
    <link:label id="lab_us-gaap_CommodityMember_label_en-US" xlink:label="lab_us-gaap_CommodityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commodity [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommodityMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommodityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommodityMember" xlink:to="lab_us-gaap_CommodityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockCommonValue_019ed0cf-53ce-78ae-a1c8-475a24bfea37_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonValue" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Treasury stock, shares at cost; 214 shares as of June 30, 2026 and December 31, 2025</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonValue_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TreasuryStockCommonValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockCommonValue" xlink:to="lab_us-gaap_TreasuryStockCommonValue" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_OtherRevenueMember_019ed0cf-533b-74b1-840c-1405e02e4d46_terseLabel_en-US" xlink:label="lab_bkv_OtherRevenueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_bkv_OtherRevenueMember_label_en-US" xlink:label="lab_bkv_OtherRevenueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Revenue [Member]</link:label>
    <link:label id="lab_bkv_OtherRevenueMember_documentation_en-US" xlink:label="lab_bkv_OtherRevenueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_OtherRevenueMember" xlink:href="bkv-20260630.xsd#bkv_OtherRevenueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_OtherRevenueMember" xlink:to="lab_bkv_OtherRevenueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromMinorityShareholders_019ed0cf-533b-7bb9-ac85-e8fbfbbeb0f5_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromMinorityShareholders" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contributions from noncontrolling interest</link:label>
    <link:label id="lab_us-gaap_ProceedsFromMinorityShareholders_label_en-US" xlink:label="lab_us-gaap_ProceedsFromMinorityShareholders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Noncontrolling Interests</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromMinorityShareholders" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromMinorityShareholders"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromMinorityShareholders" xlink:to="lab_us-gaap_ProceedsFromMinorityShareholders" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis_019ed0cf-5275-763a-8b45-32a6646a8d24_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Nonconsolidated Investee [Axis]</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Nonconsolidated Investee [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis" xlink:to="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_OtherReceivableMember_019ed0cf-533b-7430-a8da-05658a455061_terseLabel_en-US" xlink:label="lab_bkv_OtherReceivableMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Receivable</link:label>
    <link:label id="lab_bkv_OtherReceivableMember_label_en-US" xlink:label="lab_bkv_OtherReceivableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Receivable [Member]</link:label>
    <link:label id="lab_bkv_OtherReceivableMember_documentation_en-US" xlink:label="lab_bkv_OtherReceivableMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_OtherReceivableMember" xlink:href="bkv-20260630.xsd#bkv_OtherReceivableMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_OtherReceivableMember" xlink:to="lab_bkv_OtherReceivableMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_BKVBPPCottonCoveLLCMember_019ed0cf-53ce-7feb-b385-18a6b2fb21e6_terseLabel_en-US" xlink:label="lab_bkv_BKVBPPCottonCoveLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">BKV-BPP Cotton Cove</link:label>
    <link:label id="lab_bkv_BKVBPPCottonCoveLLCMember_label_en-US" xlink:label="lab_bkv_BKVBPPCottonCoveLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">BKV-BPP Cotton Cove, LLC [Member]</link:label>
    <link:label id="lab_bkv_BKVBPPCottonCoveLLCMember_documentation_en-US" xlink:label="lab_bkv_BKVBPPCottonCoveLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">BKV-BPP Cotton Cove, LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_BKVBPPCottonCoveLLCMember" xlink:href="bkv-20260630.xsd#bkv_BKVBPPCottonCoveLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_BKVBPPCottonCoveLLCMember" xlink:to="lab_bkv_BKVBPPCottonCoveLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityShellCompany_019ed0cf-53ce-783d-a6b2-a594dbfaa9d9_terseLabel_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:label id="lab_dei_EntityShellCompany_label_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityShellCompany" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityShellCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityShellCompany" xlink:to="lab_dei_EntityShellCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidationItemsDomain_019ed0cf-533c-701f-8eb1-b4fb2dceb8c0_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation Items [Domain]</link:label>
    <link:label id="lab_srt_ConsolidationItemsDomain_label_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation Items [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidationItemsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidationItemsDomain" xlink:to="lab_srt_ConsolidationItemsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_019ed0cf-53ce-7939-83bb-09d07cc51abb_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareTextBlock" xlink:to="lab_us-gaap_EarningsPerShareTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_019ed0cf-53ce-7fc0-9a19-15ea01c65e80_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income per common share attributable to BKV:</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareAbstract" xlink:to="lab_us-gaap_EarningsPerShareAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_019ed0cf-533c-72b7-94cc-985c44745e89_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalPeriodFocus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentFiscalPeriodFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalPeriodFocus" xlink:to="lab_dei_DocumentFiscalPeriodFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_BanpuNorthAmericaCorporationBNACMember_019ed0cf-533b-7470-92c3-8524f8af74e2_terseLabel_en-US" xlink:label="lab_bkv_BanpuNorthAmericaCorporationBNACMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">BNAC</link:label>
    <link:label id="lab_bkv_BanpuNorthAmericaCorporationBNACMember_label_en-US" xlink:label="lab_bkv_BanpuNorthAmericaCorporationBNACMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banpu North America Corporation (BNAC) [Member]</link:label>
    <link:label id="lab_bkv_BanpuNorthAmericaCorporationBNACMember_documentation_en-US" xlink:label="lab_bkv_BanpuNorthAmericaCorporationBNACMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Banpu North America Corporation (BNAC)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_BanpuNorthAmericaCorporationBNACMember" xlink:href="bkv-20260630.xsd#bkv_BanpuNorthAmericaCorporationBNACMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_BanpuNorthAmericaCorporationBNACMember" xlink:to="lab_bkv_BanpuNorthAmericaCorporationBNACMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote</link:label>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_label_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeerGroupIssuersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:to="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Liabilities_019ed0cf-53ce-7a7e-936b-c8257dea9c95_totalLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_label_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Liabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Liabilities" xlink:to="lab_us-gaap_Liabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_TradingSymbol_019ed0cf-533b-7fc7-9c8f-f4578f229418_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:label id="lab_dei_TradingSymbol_label_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_TradingSymbol"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_TradingSymbol" xlink:to="lab_dei_TradingSymbol" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_019ed0cf-53cf-7bdd-9f40-42f97055df9c_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Capital expenditures</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Property, Plant, and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:to="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_InterestPayableYearThree_019ed0cf-53ce-7ce6-a000-14ca61903ec3_terseLabel_en-US" xlink:label="lab_bkv_InterestPayableYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_bkv_InterestPayableYearThree_label_en-US" xlink:label="lab_bkv_InterestPayableYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable, Year Three</link:label>
    <link:label id="lab_bkv_InterestPayableYearThree_documentation_en-US" xlink:label="lab_bkv_InterestPayableYearThree" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Payable, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_InterestPayableYearThree" xlink:href="bkv-20260630.xsd#bkv_InterestPayableYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_InterestPayableYearThree" xlink:to="lab_bkv_InterestPayableYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedIncomeTaxesCurrent_019ed0cf-53ce-7883-8054-f31ef02dfe0c_verboseLabel_en-US" xlink:label="lab_us-gaap_AccruedIncomeTaxesCurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Income taxes payable to related party</link:label>
    <link:label id="lab_us-gaap_AccruedIncomeTaxesCurrent_label_en-US" xlink:label="lab_us-gaap_AccruedIncomeTaxesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Income Taxes, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedIncomeTaxesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccruedIncomeTaxesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedIncomeTaxesCurrent" xlink:to="lab_us-gaap_AccruedIncomeTaxesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLongTermDebtCurrent_019ed0cf-53ce-7da2-8f37-ae72767abf49_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLongTermDebtCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current portion of long-term debt, net</link:label>
    <link:label id="lab_us-gaap_OtherLongTermDebtCurrent_label_en-US" xlink:label="lab_us-gaap_OtherLongTermDebtCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Long-Term Debt, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLongTermDebtCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherLongTermDebtCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLongTermDebtCurrent" xlink:to="lab_us-gaap_OtherLongTermDebtCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureName_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureName_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CoSelectedMeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureName" xlink:to="lab_ecd_CoSelectedMeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_019ed0cf-533b-7e60-b411-9c60df891697_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_label_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockNameOfTransactionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock_019ed0cf-533c-7b10-89ec-b349735de3e7_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restrictions on Cash and Cash Equivalents</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restrictions on Cash and Cash Equivalents [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:to="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:to="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasicLineItems_019ed0cf-533c-7a4c-a60c-cec173af43c4_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasicLineItems_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasicLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareBasicLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasicLineItems" xlink:to="lab_us-gaap_EarningsPerShareBasicLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityDomain_019ed0cf-53ce-7673-86f7-cbb926c1e42a_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityDomain_label_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CreditFacilityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityDomain" xlink:to="lab_us-gaap_CreditFacilityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_019ed0cf-533c-784c-951d-142426e5c0e4_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from operating activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersBasic_019fd7da-687c-7a32-8448-8dd37422bb76_terseLabel_en-US" xlink:label="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic (in shares)</link:label>
    <link:label id="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersBasic_label_en-US" xlink:label="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Attributable to Majority Stockholders, Basic</link:label>
    <link:label id="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersBasic_documentation_en-US" xlink:label="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Attributable to Majority Stockholders, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersBasic" xlink:href="bkv-20260630.xsd#bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersBasic" xlink:to="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote</link:label>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_label_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EquityValuationAssumptionDifferenceFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:to="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeNonmonetaryNotionalAmountVolume_019ed0cf-533b-71a0-bf90-3d0fc8506b7c_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeNonmonetaryNotionalAmountVolume" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gallons</link:label>
    <link:label id="lab_us-gaap_DerivativeNonmonetaryNotionalAmountVolume_label_en-US" xlink:label="lab_us-gaap_DerivativeNonmonetaryNotionalAmountVolume" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Nonmonetary Notional Amount, Volume</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeNonmonetaryNotionalAmountVolume" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeNonmonetaryNotionalAmountVolume"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeNonmonetaryNotionalAmountVolume" xlink:to="lab_us-gaap_DerivativeNonmonetaryNotionalAmountVolume" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentOther_019ed0cf-533b-74fa-bcfb-43b1e54119f3_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentOther_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment, Other, before Accumulated Depreciation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentOther" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentOther"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentOther" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentOther" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019ed0cf-53ce-7b61-8ff1-59d0a9612e50_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:to="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsReceivableRelatedParties_019ed0cf-533b-77bf-99a9-78b99039eb57_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsReceivableRelatedParties" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable, related party</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsReceivableRelatedParties_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsReceivableRelatedParties" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accounts Receivable, Related Parties</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsReceivableRelatedParties" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccountsReceivableRelatedParties"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccountsReceivableRelatedParties" xlink:to="lab_us-gaap_IncreaseDecreaseInAccountsReceivableRelatedParties" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity_019ed0cf-53ce-798b-be42-ac4b97c9be02_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Borrowing base amount</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Current Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy_019ed0cf-533b-78aa-8645-8a123a0d6a95_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Cash</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, Restricted Cash and Cash Equivalents, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:to="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_PayableToAffiliatesSubsidiariesAssociatesAndJointVenturesCurrent_019ed0cf-53ce-7eed-b4df-7b70e449adf7_terseLabel_en-US" xlink:label="lab_bkv_PayableToAffiliatesSubsidiariesAssociatesAndJointVenturesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payable to BPPUS for the BKV-BPP Power Joint Venture Transaction</link:label>
    <link:label id="lab_bkv_PayableToAffiliatesSubsidiariesAssociatesAndJointVenturesCurrent_label_en-US" xlink:label="lab_bkv_PayableToAffiliatesSubsidiariesAssociatesAndJointVenturesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payable To Affiliates, Subsidiaries, Associates, And Joint Ventures, Current</link:label>
    <link:label id="lab_bkv_PayableToAffiliatesSubsidiariesAssociatesAndJointVenturesCurrent_documentation_en-US" xlink:label="lab_bkv_PayableToAffiliatesSubsidiariesAssociatesAndJointVenturesCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payable To Affiliates, Subsidiaries, Associates, And Joint Ventures, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_PayableToAffiliatesSubsidiariesAssociatesAndJointVenturesCurrent" xlink:href="bkv-20260630.xsd#bkv_PayableToAffiliatesSubsidiariesAssociatesAndJointVenturesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_PayableToAffiliatesSubsidiariesAssociatesAndJointVenturesCurrent" xlink:to="lab_bkv_PayableToAffiliatesSubsidiariesAssociatesAndJointVenturesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet_019ed0cf-53ce-773e-ae72-6f8272806492_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other changes in operating assets and liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Assets and Liabilities, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined</link:label>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_label_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgPredtrmndFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgPredtrmndFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgPredtrmndFlag" xlink:to="lab_ecd_AwardTmgPredtrmndFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote</link:label>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToPeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToPeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToPeoCompFnTextBlock" xlink:to="lab_ecd_AdjToPeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_019ed0cf-53ce-70cb-ac8e-eab921105260_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity-based compensation</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:to="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations_019ed0cf-53ce-7d68-93d7-a0884fe1f7ca_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effective income tax rate (percent)</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EffectiveIncomeTaxRateContinuingOperations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_InterestPayableYearOne_019ed0cf-5275-78c9-ba8e-b470e465c48c_terseLabel_en-US" xlink:label="lab_bkv_InterestPayableYearOne" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_bkv_InterestPayableYearOne_label_en-US" xlink:label="lab_bkv_InterestPayableYearOne" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable, Year One</link:label>
    <link:label id="lab_bkv_InterestPayableYearOne_documentation_en-US" xlink:label="lab_bkv_InterestPayableYearOne" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Payable, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_InterestPayableYearOne" xlink:href="bkv-20260630.xsd#bkv_InterestPayableYearOne"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_InterestPayableYearOne" xlink:to="lab_bkv_InterestPayableYearOne" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_CommodityDerivativeSettlementsPayableCurrent_019ed0cf-533b-7774-8f4a-1689588679ed_terseLabel_en-US" xlink:label="lab_bkv_CommodityDerivativeSettlementsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commodity derivative settlements payable</link:label>
    <link:label id="lab_bkv_CommodityDerivativeSettlementsPayableCurrent_label_en-US" xlink:label="lab_bkv_CommodityDerivativeSettlementsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commodity Derivative Settlements Payable, Current</link:label>
    <link:label id="lab_bkv_CommodityDerivativeSettlementsPayableCurrent_documentation_en-US" xlink:label="lab_bkv_CommodityDerivativeSettlementsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Commodity Derivative Settlements Payable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_CommodityDerivativeSettlementsPayableCurrent" xlink:href="bkv-20260630.xsd#bkv_CommodityDerivativeSettlementsPayableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_CommodityDerivativeSettlementsPayableCurrent" xlink:to="lab_bkv_CommodityDerivativeSettlementsPayableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetRetirementObligationLiabilitiesIncurred_019ed0cf-533c-7b00-96b7-a0931ae30e6a_terseLabel_en-US" xlink:label="lab_us-gaap_AssetRetirementObligationLiabilitiesIncurred" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities incurred</link:label>
    <link:label id="lab_us-gaap_AssetRetirementObligationLiabilitiesIncurred_label_en-US" xlink:label="lab_us-gaap_AssetRetirementObligationLiabilitiesIncurred" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Retirement Obligation, Liabilities Incurred</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetRetirementObligationLiabilitiesIncurred" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetRetirementObligationLiabilitiesIncurred"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetRetirementObligationLiabilitiesIncurred" xlink:to="lab_us-gaap_AssetRetirementObligationLiabilitiesIncurred" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements_019ed0cf-53ce-7374-853b-3c648dd661dc_terseLabel_en-US" xlink:label="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Add: dilutive effect of RSUs (in shares)</link:label>
    <link:label id="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements_label_en-US" xlink:label="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Incremental Common Shares Attributable to Dilutive Effect of Share-Based Payment Arrangements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:to="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_NetIncomeLossAvailableToCommonStockholders_019fd7eb-6327-7c6d-b421-3307768ee054_verboseLabel_en-US" xlink:label="lab_bkv_NetIncomeLossAvailableToCommonStockholders" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net income attributable to common shareholders</link:label>
    <link:label id="lab_bkv_NetIncomeLossAvailableToCommonStockholders_label_en-US" xlink:label="lab_bkv_NetIncomeLossAvailableToCommonStockholders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available To Common Stockholders</link:label>
    <link:label id="lab_bkv_NetIncomeLossAvailableToCommonStockholders_documentation_en-US" xlink:label="lab_bkv_NetIncomeLossAvailableToCommonStockholders" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available To Common Stockholders</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_NetIncomeLossAvailableToCommonStockholders" xlink:href="bkv-20260630.xsd#bkv_NetIncomeLossAvailableToCommonStockholders"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_NetIncomeLossAvailableToCommonStockholders" xlink:to="lab_bkv_NetIncomeLossAvailableToCommonStockholders" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtFairValue_019ed0cf-533b-76a8-b458-3ab5ed039bd9_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term debt, fair value</link:label>
    <link:label id="lab_us-gaap_LongTermDebtFairValue_label_en-US" xlink:label="lab_us-gaap_LongTermDebtFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtFairValue" xlink:to="lab_us-gaap_LongTermDebtFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_FixedPricePowerPurchaseMember_019ed0cf-533b-726b-9665-62d6319cb645_terseLabel_en-US" xlink:label="lab_bkv_FixedPricePowerPurchaseMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Power forwards - purchases</link:label>
    <link:label id="lab_bkv_FixedPricePowerPurchaseMember_label_en-US" xlink:label="lab_bkv_FixedPricePowerPurchaseMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Price Power Purchase [Member]</link:label>
    <link:label id="lab_bkv_FixedPricePowerPurchaseMember_documentation_en-US" xlink:label="lab_bkv_FixedPricePowerPurchaseMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Price Power Purchase</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_FixedPricePowerPurchaseMember" xlink:href="bkv-20260630.xsd#bkv_FixedPricePowerPurchaseMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_FixedPricePowerPurchaseMember" xlink:to="lab_bkv_FixedPricePowerPurchaseMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PlanNameDomain_019ed0cf-5275-7bdb-8cbe-e20949909def_terseLabel_en-US" xlink:label="lab_us-gaap_PlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Plan Name [Domain]</link:label>
    <link:label id="lab_us-gaap_PlanNameDomain_label_en-US" xlink:label="lab_us-gaap_PlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Plan Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PlanNameDomain" xlink:to="lab_us-gaap_PlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_019ed0cf-533b-7b31-87ce-f9f432a32451_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities [Axis]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:to="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareholdersEquityAndShareBasedPaymentsTextBlock_019ed0cf-533b-707e-9bff-462bd606a5b6_terseLabel_en-US" xlink:label="lab_us-gaap_ShareholdersEquityAndShareBasedPaymentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stockholders' Equity</link:label>
    <link:label id="lab_us-gaap_ShareholdersEquityAndShareBasedPaymentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ShareholdersEquityAndShareBasedPaymentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shareholders' Equity and Share-Based Payments [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareholdersEquityAndShareBasedPaymentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareholdersEquityAndShareBasedPaymentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareholdersEquityAndShareBasedPaymentsTextBlock" xlink:to="lab_us-gaap_ShareholdersEquityAndShareBasedPaymentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskTypeDomain_019ed0cf-533b-72e3-b2ae-34b144f64b08_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Domain]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskTypeDomain_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskTypeDomain" xlink:to="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_BusinessCombinationConsiderationTransferredPercent_019ed0cf-53ce-7f21-a629-982957a774a8_terseLabel_en-US" xlink:label="lab_bkv_BusinessCombinationConsiderationTransferredPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage of purchase price</link:label>
    <link:label id="lab_bkv_BusinessCombinationConsiderationTransferredPercent_label_en-US" xlink:label="lab_bkv_BusinessCombinationConsiderationTransferredPercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Percent</link:label>
    <link:label id="lab_bkv_BusinessCombinationConsiderationTransferredPercent_documentation_en-US" xlink:label="lab_bkv_BusinessCombinationConsiderationTransferredPercent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_BusinessCombinationConsiderationTransferredPercent" xlink:href="bkv-20260630.xsd#bkv_BusinessCombinationConsiderationTransferredPercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_BusinessCombinationConsiderationTransferredPercent" xlink:to="lab_bkv_BusinessCombinationConsiderationTransferredPercent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresAbstract" xlink:to="lab_us-gaap_FairValueDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_019ed0cf-53ce-7772-8c02-60bd3bb2b187_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentNameDomain" xlink:to="lab_us-gaap_DebtInstrumentNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DepositsAssetsNoncurrent_019ed0cf-53ce-7486-8331-e3fe4d78874b_terseLabel_en-US" xlink:label="lab_us-gaap_DepositsAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deposits</link:label>
    <link:label id="lab_us-gaap_DepositsAssetsNoncurrent_label_en-US" xlink:label="lab_us-gaap_DepositsAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deposits Assets, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepositsAssetsNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DepositsAssetsNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DepositsAssetsNoncurrent" xlink:to="lab_us-gaap_DepositsAssetsNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrExpirationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expiration Date</link:label>
    <link:label id="lab_ecd_TrdArrExpirationDate_label_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Expiration Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrExpirationDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrExpirationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrExpirationDate" xlink:to="lab_ecd_TrdArrExpirationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect_019ed0cf-53cf-72ea-a85b-a9a1d1fc7a63_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net increase (decrease) in cash, cash equivalents, and restricted cash</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Excluding Exchange Rate Effect, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_019ed0cf-533b-7872-8258-d025c65f21ed_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_EarningsPerShareAttributableToCommonStockholdersBasic_019fd7d7-3c2e-79dd-b3ea-4e2a9020907f_terseLabel_en-US" xlink:label="lab_bkv_EarningsPerShareAttributableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic (in USD per share)</link:label>
    <link:label id="lab_bkv_EarningsPerShareAttributableToCommonStockholdersBasic_label_en-US" xlink:label="lab_bkv_EarningsPerShareAttributableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Attributable to Common Stockholders, Basic</link:label>
    <link:label id="lab_bkv_EarningsPerShareAttributableToCommonStockholdersBasic_documentation_en-US" xlink:label="lab_bkv_EarningsPerShareAttributableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Attributable to Common Stockholders, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_EarningsPerShareAttributableToCommonStockholdersBasic" xlink:href="bkv-20260630.xsd#bkv_EarningsPerShareAttributableToCommonStockholdersBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_EarningsPerShareAttributableToCommonStockholdersBasic" xlink:to="lab_bkv_EarningsPerShareAttributableToCommonStockholdersBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_019ed0cf-533b-79ad-8866-7c61545611f3_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_019ed0cf-533b-757a-ac67-fba77ec6a54e_periodStartLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_019ed0cf-533b-7d06-aceb-4938314d57ac_periodEndLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BuildingMember_019ed0cf-533b-750b-aa94-5ddcbaee1559_terseLabel_en-US" xlink:label="lab_us-gaap_BuildingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Buildings</link:label>
    <link:label id="lab_us-gaap_BuildingMember_label_en-US" xlink:label="lab_us-gaap_BuildingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Building [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BuildingMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BuildingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BuildingMember" xlink:to="lab_us-gaap_BuildingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NonrelatedPartyMember_019ed0cf-533b-72b9-8a55-e1ca34eacea1_terseLabel_en-US" xlink:label="lab_us-gaap_NonrelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nonrelated Party</link:label>
    <link:label id="lab_us-gaap_NonrelatedPartyMember_label_en-US" xlink:label="lab_us-gaap_NonrelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonrelated Party [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonrelatedPartyMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonrelatedPartyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonrelatedPartyMember" xlink:to="lab_us-gaap_NonrelatedPartyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_A2027PutOptionsMember_019ed0cf-5275-7bb3-a5e1-817527ed94d2_terseLabel_en-US" xlink:label="lab_bkv_A2027PutOptionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027 Put Options</link:label>
    <link:label id="lab_bkv_A2027PutOptionsMember_label_en-US" xlink:label="lab_bkv_A2027PutOptionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2027 Put Options [Member]</link:label>
    <link:label id="lab_bkv_A2027PutOptionsMember_documentation_en-US" xlink:label="lab_bkv_A2027PutOptionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2027 Put Options</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_A2027PutOptionsMember" xlink:href="bkv-20260630.xsd#bkv_A2027PutOptionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_A2027PutOptionsMember" xlink:to="lab_bkv_A2027PutOptionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtPnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:to="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeTable_019ed0cf-533b-751c-8e8d-f19b730ed4dd_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative [Table]</link:label>
    <link:label id="lab_us-gaap_DerivativeTable_label_en-US" xlink:label="lab_us-gaap_DerivativeTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeTable" xlink:to="lab_us-gaap_DerivativeTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherIncomeAndExpensesAbstract_019ed0cf-53ce-7b43-8011-eff904bcd585_terseLabel_en-US" xlink:label="lab_us-gaap_OtherIncomeAndExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income (expense)</link:label>
    <link:label id="lab_us-gaap_OtherIncomeAndExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_OtherIncomeAndExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Income and Expenses [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherIncomeAndExpensesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherIncomeAndExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherIncomeAndExpensesAbstract" xlink:to="lab_us-gaap_OtherIncomeAndExpensesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_019ed0cf-533b-7009-abd7-f20aba63633a_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from issuance of common stock, net of underwriting discounts and commissions</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromIssuanceOfCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_PurchasedPowerDerivativesMember_019ed0cf-533b-72ff-be8d-a5237b7a3305_terseLabel_en-US" xlink:label="lab_bkv_PurchasedPowerDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchased Power Derivatives</link:label>
    <link:label id="lab_bkv_PurchasedPowerDerivativesMember_label_en-US" xlink:label="lab_bkv_PurchasedPowerDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Purchased Power Derivatives [Member]</link:label>
    <link:label id="lab_bkv_PurchasedPowerDerivativesMember_documentation_en-US" xlink:label="lab_bkv_PurchasedPowerDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Purchased Power Derivatives</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_PurchasedPowerDerivativesMember" xlink:href="bkv-20260630.xsd#bkv_PurchasedPowerDerivativesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_PurchasedPowerDerivativesMember" xlink:to="lab_bkv_PurchasedPowerDerivativesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInCashPercentage_019ed0cf-533b-792c-b0de-5e40d729b3c1_terseLabel_en-US" xlink:label="lab_bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInCashPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business combination, consideration transferred, cash, percentage</link:label>
    <link:label id="lab_bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInCashPercentage_label_en-US" xlink:label="lab_bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInCashPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Liabilities Paid In Cash, Percentage</link:label>
    <link:label id="lab_bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInCashPercentage_documentation_en-US" xlink:label="lab_bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInCashPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Liabilities Paid In Cash, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInCashPercentage" xlink:href="bkv-20260630.xsd#bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInCashPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInCashPercentage" xlink:to="lab_bkv_BusinessCombinationConsiderationTransferredLiabilitiesPaidInCashPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_019ed0cf-5275-759d-8221-1ce63ab695e7_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from investing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_ContractualObligationPaymentOfReservationFees_019ed0cf-53ce-73a7-810e-ba86d0e98e1d_terseLabel_en-US" xlink:label="lab_bkv_ContractualObligationPaymentOfReservationFees" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reservation fees</link:label>
    <link:label id="lab_bkv_ContractualObligationPaymentOfReservationFees_label_en-US" xlink:label="lab_bkv_ContractualObligationPaymentOfReservationFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contractual Obligation, Payment Of Reservation Fees</link:label>
    <link:label id="lab_bkv_ContractualObligationPaymentOfReservationFees_documentation_en-US" xlink:label="lab_bkv_ContractualObligationPaymentOfReservationFees" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Contractual Obligation, Payment Of Reservation Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_ContractualObligationPaymentOfReservationFees" xlink:href="bkv-20260630.xsd#bkv_ContractualObligationPaymentOfReservationFees"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_ContractualObligationPaymentOfReservationFees" xlink:to="lab_bkv_ContractualObligationPaymentOfReservationFees" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_EarningsPerShareAttributableToMajorityStockholdersBasic_019fd7d7-e3cf-7ab3-86be-8328dc6bfab9_terseLabel_en-US" xlink:label="lab_bkv_EarningsPerShareAttributableToMajorityStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic (in USD per share)</link:label>
    <link:label id="lab_bkv_EarningsPerShareAttributableToMajorityStockholdersBasic_label_en-US" xlink:label="lab_bkv_EarningsPerShareAttributableToMajorityStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Attributable to Majority Stockholders, Basic</link:label>
    <link:label id="lab_bkv_EarningsPerShareAttributableToMajorityStockholdersBasic_documentation_en-US" xlink:label="lab_bkv_EarningsPerShareAttributableToMajorityStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Attributable to Majority Stockholders, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_EarningsPerShareAttributableToMajorityStockholdersBasic" xlink:href="bkv-20260630.xsd#bkv_EarningsPerShareAttributableToMajorityStockholdersBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_EarningsPerShareAttributableToMajorityStockholdersBasic" xlink:to="lab_bkv_EarningsPerShareAttributableToMajorityStockholdersBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_019ed0cf-53ce-751b-becf-ab1a30239471_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecognized compensation expense</link:label>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:to="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetsAbstract_019ed0cf-533b-70f9-99e6-964fcead08a9_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Asset [Abstract]</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetsAbstract_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetsAbstract" xlink:to="lab_us-gaap_DerivativeAssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentDomain_019ed0cf-533b-7967-ba70-1351449282d5_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:label id="lab_us-gaap_SegmentDomain_label_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentDomain" xlink:to="lab_us-gaap_SegmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_CSquaredSolutionsInc.Member_019ed0cf-53ce-70f9-b806-fdfb5c36de32_terseLabel_en-US" xlink:label="lab_bkv_CSquaredSolutionsInc.Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class B Members</link:label>
    <link:label id="lab_bkv_CSquaredSolutionsInc.Member_label_en-US" xlink:label="lab_bkv_CSquaredSolutionsInc.Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">C Squared Solutions, Inc. [Member]</link:label>
    <link:label id="lab_bkv_CSquaredSolutionsInc.Member_documentation_en-US" xlink:label="lab_bkv_CSquaredSolutionsInc.Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">C Squared Solutions, Inc.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_CSquaredSolutionsInc.Member" xlink:href="bkv-20260630.xsd#bkv_CSquaredSolutionsInc.Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_CSquaredSolutionsInc.Member" xlink:to="lab_bkv_CSquaredSolutionsInc.Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_019ed0cf-533b-7d4b-97f3-3d9c44d13e1e_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureTextBlock" xlink:to="lab_us-gaap_DebtDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_A2029SwapMember_019ed0cf-53ce-70d0-b739-0975d0bb8526_terseLabel_en-US" xlink:label="lab_bkv_A2029SwapMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029 Swap</link:label>
    <link:label id="lab_bkv_A2029SwapMember_label_en-US" xlink:label="lab_bkv_A2029SwapMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2029 Swap [Member]</link:label>
    <link:label id="lab_bkv_A2029SwapMember_documentation_en-US" xlink:label="lab_bkv_A2029SwapMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2029 Swap</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_A2029SwapMember" xlink:href="bkv-20260630.xsd#bkv_A2029SwapMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_A2029SwapMember" xlink:to="lab_bkv_A2029SwapMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractualObligation_019ed0cf-533b-72fe-8ff9-5d624bfc578f_verboseLabel_en-US" xlink:label="lab_us-gaap_ContractualObligation" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Contractual obligation</link:label>
    <link:label id="lab_us-gaap_ContractualObligation_019ed0cf-533b-74c7-94ff-6d349afd13b9_totalLabel_en-US" xlink:label="lab_us-gaap_ContractualObligation" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_ContractualObligation_label_en-US" xlink:label="lab_us-gaap_ContractualObligation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contractual Obligation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractualObligation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractualObligation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractualObligation" xlink:to="lab_us-gaap_ContractualObligation" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ContractualObligationFiscalYearMaturityScheduleTableTextBlock_019ed0cf-533b-718f-a2c6-325508af2c54_terseLabel_en-US" xlink:label="lab_srt_ContractualObligationFiscalYearMaturityScheduleTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of the Company's commitments, excluding contingent consideration</link:label>
    <link:label id="lab_srt_ContractualObligationFiscalYearMaturityScheduleTableTextBlock_label_en-US" xlink:label="lab_srt_ContractualObligationFiscalYearMaturityScheduleTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contractual Obligation, Fiscal Year Maturity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ContractualObligationFiscalYearMaturityScheduleTableTextBlock" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ContractualObligationFiscalYearMaturityScheduleTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ContractualObligationFiscalYearMaturityScheduleTableTextBlock" xlink:to="lab_srt_ContractualObligationFiscalYearMaturityScheduleTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_019ed0cf-533b-7d1a-94a2-f84d74d637b4_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt issuance costs, net</link:label>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_label_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredFinanceCostsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredFinanceCostsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredFinanceCostsNet" xlink:to="lab_us-gaap_DeferredFinanceCostsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OilReservesMember_019ed0cf-533c-78b2-9bf0-9d5f93f207e5_terseLabel_en-US" xlink:label="lab_srt_OilReservesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Oil</link:label>
    <link:label id="lab_srt_OilReservesMember_label_en-US" xlink:label="lab_srt_OilReservesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crude Oil, Condensate, and Natural Gas Liquids (NGL) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OilReservesMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_OilReservesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_OilReservesMember" xlink:to="lab_srt_OilReservesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_019ed0cf-533b-756b-ab19-cb12b808f3c4_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:to="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_label_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoActuallyPaidCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoActuallyPaidCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoActuallyPaidCompAmt" xlink:to="lab_ecd_PeoActuallyPaidCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_InterestPayableToBePaidFiscalYearMaturityAbstract_019ed0cf-53ce-72a3-8f44-f5e4653317f9_terseLabel_en-US" xlink:label="lab_bkv_InterestPayableToBePaidFiscalYearMaturityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest payable</link:label>
    <link:label id="lab_bkv_InterestPayableToBePaidFiscalYearMaturityAbstract_label_en-US" xlink:label="lab_bkv_InterestPayableToBePaidFiscalYearMaturityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable, to be Paid, Fiscal Year Maturity [Abstract]</link:label>
    <link:label id="lab_bkv_InterestPayableToBePaidFiscalYearMaturityAbstract_documentation_en-US" xlink:label="lab_bkv_InterestPayableToBePaidFiscalYearMaturityAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Payable, to be Paid, Fiscal Year Maturity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_InterestPayableToBePaidFiscalYearMaturityAbstract" xlink:href="bkv-20260630.xsd#bkv_InterestPayableToBePaidFiscalYearMaturityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_InterestPayableToBePaidFiscalYearMaturityAbstract" xlink:to="lab_bkv_InterestPayableToBePaidFiscalYearMaturityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuredDebtMember_019ed0cf-53ce-717e-9594-30362012734d_terseLabel_en-US" xlink:label="lab_us-gaap_SecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Secured Debt</link:label>
    <link:label id="lab_us-gaap_SecuredDebtMember_label_en-US" xlink:label="lab_us-gaap_SecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Secured Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuredDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SecuredDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuredDebtMember" xlink:to="lab_us-gaap_SecuredDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Asset Acquisition, Transaction between Entities under Common Control, and Joint Venture Formation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationAndAssetAcquisitionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:to="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CostsAndExpenses_019ed0cf-53ce-7bc0-8e0a-c1909ae435fb_totalLabel_en-US" xlink:label="lab_us-gaap_CostsAndExpenses" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total operating expenses</link:label>
    <link:label id="lab_us-gaap_CostsAndExpenses_label_en-US" xlink:label="lab_us-gaap_CostsAndExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Costs and Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostsAndExpenses" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CostsAndExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CostsAndExpenses" xlink:to="lab_us-gaap_CostsAndExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_019ed0cf-53cf-722a-96da-0d210b86a54b_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stated rate (percent)</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Stated Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:to="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_019ed0cf-533b-7613-b741-c48fef5fe7a3_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total stockholders' equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_019ed0cf-533b-7d4f-8759-5948475f8409_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">BKV&#8217;s interest in BKV-BPP Power</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCommitmentDueInSecondYear_019ed0cf-53ce-7d9b-8dac-b0be8a3355c8_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitmentDueInSecondYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_OtherCommitmentDueInSecondYear_label_en-US" xlink:label="lab_us-gaap_OtherCommitmentDueInSecondYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitment, to be Paid, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitmentDueInSecondYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherCommitmentDueInSecondYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCommitmentDueInSecondYear" xlink:to="lab_us-gaap_OtherCommitmentDueInSecondYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsAbstract_019ed0cf-533b-72d2-bcc5-018f997fde17_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsAbstract" xlink:to="lab_us-gaap_AssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_019ed0cf-5275-7ef9-b2ad-5e477c43189e_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consideration transferred, equity interest, (in shares)</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Equity Interest, Share Issued, Number of Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:to="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_019ed0cf-533b-7686-b941-ee9c6d170eb7_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:to="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingPoliciesProcLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTradingPoliciesProcLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:to="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock_019ed0cf-53ce-7578-9296-86dcc3a15b6e_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts Payable and Accrued Liabilities</link:label>
    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable and Accrued Liabilities Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock" xlink:to="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefit_019ed0cf-53ce-79fc-8850-94ca6136a144_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred income tax expense (benefit)</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredIncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_ClassAUnitsMember_019ed0cf-533b-7d1e-bf3c-de43022cef1b_terseLabel_en-US" xlink:label="lab_bkv_ClassAUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class A Units</link:label>
    <link:label id="lab_bkv_ClassAUnitsMember_label_en-US" xlink:label="lab_bkv_ClassAUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class A Units [Member]</link:label>
    <link:label id="lab_bkv_ClassAUnitsMember_documentation_en-US" xlink:label="lab_bkv_ClassAUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class A Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_ClassAUnitsMember" xlink:href="bkv-20260630.xsd#bkv_ClassAUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_ClassAUnitsMember" xlink:to="lab_bkv_ClassAUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfOperatingSegments_019ed0cf-5275-7f89-a64d-cab711eb9c70_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of operating segments</link:label>
    <link:label id="lab_us-gaap_NumberOfOperatingSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Operating Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfOperatingSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NumberOfOperatingSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfOperatingSegments" xlink:to="lab_us-gaap_NumberOfOperatingSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCentralIndexKey_019ed0cf-533c-78a2-bedb-75dd56bdb01f_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Central Index Key</link:label>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCentralIndexKey"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCentralIndexKey" xlink:to="lab_dei_EntityCentralIndexKey" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityAbstract_019ed0cf-533c-77b4-8628-a70a720f2f8b_terseLabel_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stockholders' equity</link:label>
    <link:label id="lab_us-gaap_EquityAbstract_label_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityAbstract" xlink:to="lab_us-gaap_EquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year</link:label>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_label_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:to="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_019ed0cf-53ce-725c-9ff8-cb70ff5a32bc_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OwnershipAxis_019ed0cf-53ce-79eb-b164-475572daf0d8_terseLabel_en-US" xlink:label="lab_srt_OwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Axis]</link:label>
    <link:label id="lab_srt_OwnershipAxis_label_en-US" xlink:label="lab_srt_OwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_OwnershipAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_OwnershipAxis" xlink:to="lab_srt_OwnershipAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_019ed0cf-53ce-76d5-a6e3-325a4e50c9e6_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_019ed0cf-533b-720f-9957-ee61398e56dd_terseLabel_en-US" xlink:label="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Name [Axis]</link:label>
    <link:label id="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_label_en-US" xlink:label="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:to="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_019ed0cf-53cf-7415-a7b1-a740681c0194_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit spread adjustment</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Basis Spread on Variable Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentBasisSpreadOnVariableRate1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:to="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_BKVBPPPowerLLCMember_019ed0cf-5275-7d3d-8add-3507d16a08ed_terseLabel_en-US" xlink:label="lab_bkv_BKVBPPPowerLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">BKV-BPP Power, LLC</link:label>
    <link:label id="lab_bkv_BKVBPPPowerLLCMember_019ed0cf-5275-724a-a620-838db7482777_verboseLabel_en-US" xlink:label="lab_bkv_BKVBPPPowerLLCMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">BKV-BPP Power</link:label>
    <link:label id="lab_bkv_BKVBPPPowerLLCMember_label_en-US" xlink:label="lab_bkv_BKVBPPPowerLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">BKV-BPP Power, LLC [Member]</link:label>
    <link:label id="lab_bkv_BKVBPPPowerLLCMember_documentation_en-US" xlink:label="lab_bkv_BKVBPPPowerLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">BKV-BPP Power, LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_BKVBPPPowerLLCMember" xlink:href="bkv-20260630.xsd#bkv_BKVBPPPowerLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_BKVBPPPowerLLCMember" xlink:to="lab_bkv_BKVBPPPowerLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllIndividualsMember_terseLabel_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Individuals</link:label>
    <link:label id="lab_ecd_AllIndividualsMember_label_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Individuals [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllIndividualsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllIndividualsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllIndividualsMember" xlink:to="lab_ecd_AllIndividualsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_019ed0cf-5275-799b-a7be-32d91b00cc21_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average period (in years)</link:label>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:to="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementLineItems_019ed0cf-533b-7469-840f-fc3dc6f05f1a_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:label id="lab_us-gaap_StatementLineItems_label_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementLineItems" xlink:to="lab_us-gaap_StatementLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Assets_019ed0cf-533b-75aa-85e5-e4ba80313340_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Assets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Assets" xlink:to="lab_us-gaap_Assets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract_019ed0cf-53ce-760b-9181-23f58971290b_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease payments</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Fiscal Year Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xlink:to="lab_us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeNonmonetaryNotionalAmountEnergyMeasure_019ed0cf-5275-73d4-8ad9-aada992b9f75_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeNonmonetaryNotionalAmountEnergyMeasure" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Quantity</link:label>
    <link:label id="lab_us-gaap_DerivativeNonmonetaryNotionalAmountEnergyMeasure_019ed0cf-5275-7a33-9ed2-e83adb24ecb8_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeNonmonetaryNotionalAmountEnergyMeasure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MMBtu</link:label>
    <link:label id="lab_us-gaap_DerivativeNonmonetaryNotionalAmountEnergyMeasure_label_en-US" xlink:label="lab_us-gaap_DerivativeNonmonetaryNotionalAmountEnergyMeasure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Nonmonetary Notional Amount, Energy Measure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeNonmonetaryNotionalAmountEnergyMeasure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeNonmonetaryNotionalAmountEnergyMeasure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeNonmonetaryNotionalAmountEnergyMeasure" xlink:to="lab_us-gaap_DerivativeNonmonetaryNotionalAmountEnergyMeasure" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_LongTermDebtPrincipalAmount_019ed0cf-53ce-7a7e-946c-8cc23b2b76be_totalLabel_en-US" xlink:label="lab_bkv_LongTermDebtPrincipalAmount" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total debt, net</link:label>
    <link:label id="lab_bkv_LongTermDebtPrincipalAmount_label_en-US" xlink:label="lab_bkv_LongTermDebtPrincipalAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Principal Amount</link:label>
    <link:label id="lab_bkv_LongTermDebtPrincipalAmount_documentation_en-US" xlink:label="lab_bkv_LongTermDebtPrincipalAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Principal Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_LongTermDebtPrincipalAmount" xlink:href="bkv-20260630.xsd#bkv_LongTermDebtPrincipalAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_LongTermDebtPrincipalAmount" xlink:to="lab_bkv_LongTermDebtPrincipalAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_BedrockAcquisitionMember_019ed0cf-533b-77cd-bddc-5a7160ffc977_terseLabel_en-US" xlink:label="lab_bkv_BedrockAcquisitionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Bedrock Acquisition</link:label>
    <link:label id="lab_bkv_BedrockAcquisitionMember_label_en-US" xlink:label="lab_bkv_BedrockAcquisitionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Bedrock Acquisition [Member]</link:label>
    <link:label id="lab_bkv_BedrockAcquisitionMember_documentation_en-US" xlink:label="lab_bkv_BedrockAcquisitionMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Bedrock Acquisition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_BedrockAcquisitionMember" xlink:href="bkv-20260630.xsd#bkv_BedrockAcquisitionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_BedrockAcquisitionMember" xlink:to="lab_bkv_BedrockAcquisitionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain_019ed0cf-53ce-73f4-b15e-3ba6d6e822ef_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Nonconsolidated Investee [Domain]</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Nonconsolidated Investee [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xlink:to="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingSegmentsMember_019ed0cf-53ce-7836-a59e-37d54bbda21d_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Segments</link:label>
    <link:label id="lab_us-gaap_OperatingSegmentsMember_label_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Segments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingSegmentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingSegmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingSegmentsMember" xlink:to="lab_us-gaap_OperatingSegmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_LineOfCreditFacilityCovenantTermsMaximumNetLeverageRatio_019ed0cf-533b-7141-9d2f-832cd7255b30_terseLabel_en-US" xlink:label="lab_bkv_LineOfCreditFacilityCovenantTermsMaximumNetLeverageRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum net leverage ratio</link:label>
    <link:label id="lab_bkv_LineOfCreditFacilityCovenantTermsMaximumNetLeverageRatio_label_en-US" xlink:label="lab_bkv_LineOfCreditFacilityCovenantTermsMaximumNetLeverageRatio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Covenant Terms, Maximum Net Leverage Ratio</link:label>
    <link:label id="lab_bkv_LineOfCreditFacilityCovenantTermsMaximumNetLeverageRatio_documentation_en-US" xlink:label="lab_bkv_LineOfCreditFacilityCovenantTermsMaximumNetLeverageRatio" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Covenant Terms, Maximum Net Leverage Ratio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_LineOfCreditFacilityCovenantTermsMaximumNetLeverageRatio" xlink:href="bkv-20260630.xsd#bkv_LineOfCreditFacilityCovenantTermsMaximumNetLeverageRatio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_LineOfCreditFacilityCovenantTermsMaximumNetLeverageRatio" xlink:to="lab_bkv_LineOfCreditFacilityCovenantTermsMaximumNetLeverageRatio" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseNonoperating_019ed0cf-5275-7fbf-934e-fd1666e90676_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseNonoperating" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseNonoperating_019fc97a-c6d4-7b85-8fe0-419968edf43a_negatedLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseNonoperating" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Interest expense, net</link:label>
    <link:label id="lab_us-gaap_InterestExpenseNonoperating_label_en-US" xlink:label="lab_us-gaap_InterestExpenseNonoperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Nonoperating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseNonoperating" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpenseNonoperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseNonoperating" xlink:to="lab_us-gaap_InterestExpenseNonoperating" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_BedrockMember_019ed0cf-533c-7e04-9b3f-be7bdea0bc8c_terseLabel_en-US" xlink:label="lab_bkv_BedrockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Bedrock</link:label>
    <link:label id="lab_bkv_BedrockMember_label_en-US" xlink:label="lab_bkv_BedrockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Bedrock [Member]</link:label>
    <link:label id="lab_bkv_BedrockMember_documentation_en-US" xlink:label="lab_bkv_BedrockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Bedrock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_BedrockMember" xlink:href="bkv-20260630.xsd#bkv_BedrockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_BedrockMember" xlink:to="lab_bkv_BedrockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractualObligationFutureMinimumPaymentsDueRemainderOfFiscalYear_019ed0cf-533c-7d36-96ec-72886938e455_totalLabel_en-US" xlink:label="lab_us-gaap_ContractualObligationFutureMinimumPaymentsDueRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_ContractualObligationFutureMinimumPaymentsDueRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_ContractualObligationFutureMinimumPaymentsDueRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contractual Obligation, to be Paid, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractualObligationFutureMinimumPaymentsDueRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractualObligationFutureMinimumPaymentsDueRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractualObligationFutureMinimumPaymentsDueRemainderOfFiscalYear" xlink:to="lab_us-gaap_ContractualObligationFutureMinimumPaymentsDueRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_PowerRevenuesMember_019ed0cf-533b-78fa-85b3-3ad2834edc78_terseLabel_en-US" xlink:label="lab_bkv_PowerRevenuesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Power revenues</link:label>
    <link:label id="lab_bkv_PowerRevenuesMember_label_en-US" xlink:label="lab_bkv_PowerRevenuesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Power Revenues [Member]</link:label>
    <link:label id="lab_bkv_PowerRevenuesMember_documentation_en-US" xlink:label="lab_bkv_PowerRevenuesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Power Revenues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_PowerRevenuesMember" xlink:href="bkv-20260630.xsd#bkv_PowerRevenuesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_PowerRevenuesMember" xlink:to="lab_bkv_PowerRevenuesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommodityContractAssetCurrent_019ed0cf-533b-786e-99e6-c268593a12f4_terseLabel_en-US" xlink:label="lab_us-gaap_CommodityContractAssetCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commodity derivative assets, current</link:label>
    <link:label id="lab_us-gaap_CommodityContractAssetCurrent_label_en-US" xlink:label="lab_us-gaap_CommodityContractAssetCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commodity Contract Asset, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommodityContractAssetCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommodityContractAssetCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommodityContractAssetCurrent" xlink:to="lab_us-gaap_CommodityContractAssetCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoMember_terseLabel_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO</link:label>
    <link:label id="lab_ecd_PeoMember_label_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoMember" xlink:to="lab_ecd_PeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_019ed0cf-533b-7339-aeee-4f25bb30c607_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesNoncurrent_019ed0cf-533b-7889-b961-86557f6b8f0e_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other noncurrent liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesNoncurrent_019ef5b6-7ce3-7773-8e53-58e5a3ef0653_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesNoncurrent_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherLiabilitiesNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesNoncurrent" xlink:to="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_JointVentureFormationInitialAccountingIncompleteAdjustmentToProvisionalAmountAsset_019fceef-a019-720d-a0fb-8359e0c9ccab_terseLabel_en-US" xlink:label="lab_us-gaap_JointVentureFormationInitialAccountingIncompleteAdjustmentToProvisionalAmountAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets contributed during the period</link:label>
    <link:label id="lab_us-gaap_JointVentureFormationInitialAccountingIncompleteAdjustmentToProvisionalAmountAsset_label_en-US" xlink:label="lab_us-gaap_JointVentureFormationInitialAccountingIncompleteAdjustmentToProvisionalAmountAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Joint Venture Formation, Initial Accounting Incomplete, Adjustment to Provisional Amount, Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_JointVentureFormationInitialAccountingIncompleteAdjustmentToProvisionalAmountAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_JointVentureFormationInitialAccountingIncompleteAdjustmentToProvisionalAmountAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_JointVentureFormationInitialAccountingIncompleteAdjustmentToProvisionalAmountAsset" xlink:to="lab_us-gaap_JointVentureFormationInitialAccountingIncompleteAdjustmentToProvisionalAmountAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Goodwill_019ed0cf-533b-7e12-87c0-e743ff9e59e6_terseLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_Goodwill_label_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Goodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Goodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Goodwill" xlink:to="lab_us-gaap_Goodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_TemporaryEquityDistributionPayable_019ed0cf-533b-7aaf-bb5f-d1bc11d38657_terseLabel_en-US" xlink:label="lab_bkv_TemporaryEquityDistributionPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distributions payable to noncontrolling interest</link:label>
    <link:label id="lab_bkv_TemporaryEquityDistributionPayable_label_en-US" xlink:label="lab_bkv_TemporaryEquityDistributionPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Distribution Payable</link:label>
    <link:label id="lab_bkv_TemporaryEquityDistributionPayable_documentation_en-US" xlink:label="lab_bkv_TemporaryEquityDistributionPayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Distribution Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_TemporaryEquityDistributionPayable" xlink:href="bkv-20260630.xsd#bkv_TemporaryEquityDistributionPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_TemporaryEquityDistributionPayable" xlink:to="lab_bkv_TemporaryEquityDistributionPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsMember_019ed0cf-533b-77f5-b89f-29920821e720_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retained Earnings</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsMember_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsMember" xlink:to="lab_us-gaap_RetainedEarningsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_019ed0cf-53ce-72c3-87b9-86e04fa6a785_terseLabel_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Temple Revolving Facility</link:label>
    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_label_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revolving Credit Facility [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevolvingCreditFacilityMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevolvingCreditFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevolvingCreditFacilityMember" xlink:to="lab_us-gaap_RevolvingCreditFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember_019ed0cf-5275-7ba5-9ed0-e9b81966a4a2_terseLabel_en-US" xlink:label="lab_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Computer software</link:label>
    <link:label id="lab_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember_label_en-US" xlink:label="lab_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Software, In-Development, Internally Developed, and Purchased [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SoftwareAndSoftwareDevelopmentCostsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember" xlink:to="lab_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock_019ed0cf-533b-7408-b409-670d9029fc5c_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:to="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_019ed0cf-53ce-7f8b-81e7-c4b4ab142d13_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019ed0cf-53ce-7b1f-a4f3-d3eeb2778b19_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019ed0cf-53ce-79ab-9c07-e6cd3d727dac_periodStartLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019ed0cf-53ce-726e-add1-0430bca671b4_periodEndLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019ed0cf-53ce-7023-96a2-9608c466c8b4_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Shares of BKV Corporation's common stock (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesOutstanding" xlink:to="lab_us-gaap_CommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgDiscLineItems_label_en-US" xlink:label="lab_ecd_AwardTmgDiscLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Disclosures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgDiscLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgDiscLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgDiscLineItems" xlink:to="lab_ecd_AwardTmgDiscLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_019ed0cf-53ce-791d-adf4-b56a855d56b1_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted (in USD per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareDiluted" xlink:to="lab_us-gaap_EarningsPerShareDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OwnershipDomain_019ed0cf-533b-7902-8425-031c295ec1eb_terseLabel_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:label id="lab_srt_OwnershipDomain_label_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_OwnershipDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_OwnershipDomain" xlink:to="lab_srt_OwnershipDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCommitmentFiscalYearMaturityAbstract_019ed0cf-5275-7409-a866-66e82a83886c_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitmentFiscalYearMaturityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Commitments</link:label>
    <link:label id="lab_us-gaap_OtherCommitmentFiscalYearMaturityAbstract_label_en-US" xlink:label="lab_us-gaap_OtherCommitmentFiscalYearMaturityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitment, Fiscal Year Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitmentFiscalYearMaturityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherCommitmentFiscalYearMaturityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCommitmentFiscalYearMaturityAbstract" xlink:to="lab_us-gaap_OtherCommitmentFiscalYearMaturityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffsettingAssetsTableTextBlock_019ed0cf-53ce-7c65-a5b8-7d32c7eae980_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Offsetting Assets</link:label>
    <link:label id="lab_us-gaap_OffsettingAssetsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_OffsettingAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Assets [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingAssetsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OffsettingAssetsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingAssetsTableTextBlock" xlink:to="lab_us-gaap_OffsettingAssetsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_NaturalGasReservesMember_019ed0cf-53ce-77ca-b443-8f4cbaa253a7_terseLabel_en-US" xlink:label="lab_srt_NaturalGasReservesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Natural gas</link:label>
    <link:label id="lab_srt_NaturalGasReservesMember_label_en-US" xlink:label="lab_srt_NaturalGasReservesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Natural Gas [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_NaturalGasReservesMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_NaturalGasReservesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_NaturalGasReservesMember" xlink:to="lab_srt_NaturalGasReservesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentProvedPropertyAccumulatedDepreciationDepletionAmortizationAndImpairment_019ed0cf-53ce-74cd-9b9d-f7f28904a0fd_terseLabel_en-US" xlink:label="lab_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentProvedPropertyAccumulatedDepreciationDepletionAmortizationAndImpairment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated depreciation, depletion, amortization, and impairment</link:label>
    <link:label id="lab_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentProvedPropertyAccumulatedDepreciationDepletionAmortizationAndImpairment_label_en-US" xlink:label="lab_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentProvedPropertyAccumulatedDepreciationDepletionAmortizationAndImpairment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Oil and Gas, Successful Efforts Method, Property and Equipment, Proved Property, Accumulated Depreciation, Depletion, Amortization, and Impairment</link:label>
    <link:label id="lab_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentProvedPropertyAccumulatedDepreciationDepletionAmortizationAndImpairment_documentation_en-US" xlink:label="lab_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentProvedPropertyAccumulatedDepreciationDepletionAmortizationAndImpairment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Oil and Gas, Successful Efforts Method, Property and Equipment, Proved Property, Accumulated Depreciation, Depletion, Amortization, and Impairment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentProvedPropertyAccumulatedDepreciationDepletionAmortizationAndImpairment" xlink:href="bkv-20260630.xsd#bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentProvedPropertyAccumulatedDepreciationDepletionAmortizationAndImpairment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentProvedPropertyAccumulatedDepreciationDepletionAmortizationAndImpairment" xlink:to="lab_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentProvedPropertyAccumulatedDepreciationDepletionAmortizationAndImpairment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_label_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:to="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_019ed0cf-53ce-7710-a192-ddbd04a21b54_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenues</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer, Excluding Assessed Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_019ed0cf-533c-7488-8fea-e6aab32c6540_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remaining borrowing capacity</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Remaining Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_A2027CollarsMember_019ed0cf-53ce-795b-a8c2-dfa5369a885a_terseLabel_en-US" xlink:label="lab_bkv_A2027CollarsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027 Collars</link:label>
    <link:label id="lab_bkv_A2027CollarsMember_label_en-US" xlink:label="lab_bkv_A2027CollarsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2027 Collars [Member]</link:label>
    <link:label id="lab_bkv_A2027CollarsMember_documentation_en-US" xlink:label="lab_bkv_A2027CollarsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2027 Collars</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_A2027CollarsMember" xlink:href="bkv-20260630.xsd#bkv_A2027CollarsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_A2027CollarsMember" xlink:to="lab_bkv_A2027CollarsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_TimeBasedRestrictedStockUnitsMember_019ed0cf-533b-7fc1-bdf7-9b22e2882871_terseLabel_en-US" xlink:label="lab_bkv_TimeBasedRestrictedStockUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">TRSUs</link:label>
    <link:label id="lab_bkv_TimeBasedRestrictedStockUnitsMember_label_en-US" xlink:label="lab_bkv_TimeBasedRestrictedStockUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Time-Based Restricted Stock Units [Member]</link:label>
    <link:label id="lab_bkv_TimeBasedRestrictedStockUnitsMember_documentation_en-US" xlink:label="lab_bkv_TimeBasedRestrictedStockUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Time-Based Restricted Stock Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_TimeBasedRestrictedStockUnitsMember" xlink:href="bkv-20260630.xsd#bkv_TimeBasedRestrictedStockUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_TimeBasedRestrictedStockUnitsMember" xlink:to="lab_bkv_TimeBasedRestrictedStockUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:to="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_DevonBarnettAcquisitionMember_019ed0cf-533b-76f1-9c85-b70ce4cf6185_terseLabel_en-US" xlink:label="lab_bkv_DevonBarnettAcquisitionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Devon Barnett Acquisition</link:label>
    <link:label id="lab_bkv_DevonBarnettAcquisitionMember_label_en-US" xlink:label="lab_bkv_DevonBarnettAcquisitionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Devon Barnett Acquisition [Member]</link:label>
    <link:label id="lab_bkv_DevonBarnettAcquisitionMember_documentation_en-US" xlink:label="lab_bkv_DevonBarnettAcquisitionMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Devon Barnett Acquisition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_DevonBarnettAcquisitionMember" xlink:href="bkv-20260630.xsd#bkv_DevonBarnettAcquisitionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_DevonBarnettAcquisitionMember" xlink:to="lab_bkv_DevonBarnettAcquisitionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConstructionInProgressMember_019ed0cf-5275-700a-b397-e6b71078cedd_terseLabel_en-US" xlink:label="lab_us-gaap_ConstructionInProgressMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Construction in process</link:label>
    <link:label id="lab_us-gaap_ConstructionInProgressMember_label_en-US" xlink:label="lab_us-gaap_ConstructionInProgressMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Construction in Progress [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConstructionInProgressMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConstructionInProgressMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConstructionInProgressMember" xlink:to="lab_us-gaap_ConstructionInProgressMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable_019ed0cf-533c-7b4e-90cf-edacf66c1ec8_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Method Investment [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:to="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_019ed0cf-533b-7e9b-b4ad-d02e96874fcb_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_label_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsidiarySaleOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:to="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeGainLossOnDerivativeNet_019ed0cf-53ce-7da5-ab1f-ee3699580e83_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Derivative gains, net</link:label>
    <link:label id="lab_us-gaap_DerivativeGainLossOnDerivativeNet_label_en-US" xlink:label="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Gain (Loss) on Derivative, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeGainLossOnDerivativeNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:to="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_019ed0cf-53ce-7bcb-8553-08ed69fed5ac_totalLabel_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income from operations</link:label>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_019ed0cf-53ce-7a40-bbc6-c57b811d74d1_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income (loss) from operations</link:label>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_019ed0cf-53ce-710b-a608-959c9f162098_verboseLabel_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total segment operating income</link:label>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_label_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Income (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingIncomeLoss" xlink:to="lab_us-gaap_OperatingIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAverageFloorPrice_019ed0cf-5275-769c-a742-4d58812c5f4c_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAverageFloorPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average floor price (in USD per unit)</link:label>
    <link:label id="lab_us-gaap_DerivativeAverageFloorPrice_label_en-US" xlink:label="lab_us-gaap_DerivativeAverageFloorPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Average Floor Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAverageFloorPrice" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAverageFloorPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAverageFloorPrice" xlink:to="lab_us-gaap_DerivativeAverageFloorPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Rule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:to="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_NaturalGasBasisSwapDerivativeMember_019ed0cf-533b-7d30-8052-44ffc72d3c2c_terseLabel_en-US" xlink:label="lab_bkv_NaturalGasBasisSwapDerivativeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Natural gas basis swaps</link:label>
    <link:label id="lab_bkv_NaturalGasBasisSwapDerivativeMember_label_en-US" xlink:label="lab_bkv_NaturalGasBasisSwapDerivativeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Natural Gas Basis Swap Derivative [Member]</link:label>
    <link:label id="lab_bkv_NaturalGasBasisSwapDerivativeMember_documentation_en-US" xlink:label="lab_bkv_NaturalGasBasisSwapDerivativeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Natural Gas Basis Swap Derivative</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_NaturalGasBasisSwapDerivativeMember" xlink:href="bkv-20260630.xsd#bkv_NaturalGasBasisSwapDerivativeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_NaturalGasBasisSwapDerivativeMember" xlink:to="lab_bkv_NaturalGasBasisSwapDerivativeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_019ed0cf-533b-7f37-8dd4-51258d8aed37_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, issued (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesIssued" xlink:to="lab_us-gaap_CommonStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_TemporaryEquityInvestmentOnCapital_019ed0cf-53ce-7e9b-a64b-6282c39c6aa1_terseLabel_en-US" xlink:label="lab_bkv_TemporaryEquityInvestmentOnCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Temporary equity, investment on capital</link:label>
    <link:label id="lab_bkv_TemporaryEquityInvestmentOnCapital_label_en-US" xlink:label="lab_bkv_TemporaryEquityInvestmentOnCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Investment On Capital</link:label>
    <link:label id="lab_bkv_TemporaryEquityInvestmentOnCapital_documentation_en-US" xlink:label="lab_bkv_TemporaryEquityInvestmentOnCapital" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Investment On Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_TemporaryEquityInvestmentOnCapital" xlink:href="bkv-20260630.xsd#bkv_TemporaryEquityInvestmentOnCapital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_TemporaryEquityInvestmentOnCapital" xlink:to="lab_bkv_TemporaryEquityInvestmentOnCapital" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RestatementAdjustmentMember_019ed0cf-533b-77dc-bba3-02299e578f5e_terseLabel_en-US" xlink:label="lab_srt_RestatementAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustments</link:label>
    <link:label id="lab_srt_RestatementAdjustmentMember_label_en-US" xlink:label="lab_srt_RestatementAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revision of Prior Period, Adjustment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RestatementAdjustmentMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RestatementAdjustmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RestatementAdjustmentMember" xlink:to="lab_srt_RestatementAdjustmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsReceivable_019ed0cf-533b-7b41-bd65-ef2d3a0f5015_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable, net</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsReceivable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accounts Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccountsReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:to="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductsAndServicesDomain_019ed0cf-53ce-772c-a770-d6b39e04f96f_terseLabel_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:label id="lab_srt_ProductsAndServicesDomain_label_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductsAndServicesDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductsAndServicesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductsAndServicesDomain" xlink:to="lab_srt_ProductsAndServicesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_NaturalGasCommitmentsMember_019ed0cf-533b-7448-831a-0006bcfd63b8_terseLabel_en-US" xlink:label="lab_bkv_NaturalGasCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Natural Gas, Commitments</link:label>
    <link:label id="lab_bkv_NaturalGasCommitmentsMember_label_en-US" xlink:label="lab_bkv_NaturalGasCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Natural Gas, Commitments [Member]</link:label>
    <link:label id="lab_bkv_NaturalGasCommitmentsMember_documentation_en-US" xlink:label="lab_bkv_NaturalGasCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Natural Gas, Commitments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_NaturalGasCommitmentsMember" xlink:href="bkv-20260630.xsd#bkv_NaturalGasCommitmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_NaturalGasCommitmentsMember" xlink:to="lab_bkv_NaturalGasCommitmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTable_019ed0cf-53ce-7c37-a8a8-164cc3ddcca3_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Table]</link:label>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTable_label_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisaggregationOfRevenueTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisaggregationOfRevenueTable" xlink:to="lab_us-gaap_DisaggregationOfRevenueTable" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_ChangeInExpendituresIncurredButNotYetPaid_019ed0cf-533b-7bd7-93b4-4aba2b8f0b77_terseLabel_en-US" xlink:label="lab_bkv_ChangeInExpendituresIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (decrease) in accrued capital expenditures</link:label>
    <link:label id="lab_bkv_ChangeInExpendituresIncurredButNotYetPaid_label_en-US" xlink:label="lab_bkv_ChangeInExpendituresIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change In Expenditures Incurred But Not Yet Paid</link:label>
    <link:label id="lab_bkv_ChangeInExpendituresIncurredButNotYetPaid_documentation_en-US" xlink:label="lab_bkv_ChangeInExpendituresIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Change In Expenditures Incurred But Not Yet Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_ChangeInExpendituresIncurredButNotYetPaid" xlink:href="bkv-20260630.xsd#bkv_ChangeInExpendituresIncurredButNotYetPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_ChangeInExpendituresIncurredButNotYetPaid" xlink:to="lab_bkv_ChangeInExpendituresIncurredButNotYetPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet_019ed0cf-533c-7689-80c4-110407a74398_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax liability, net</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Liabilities, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredIncomeTaxLiabilitiesNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:to="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsOtherMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrantIncrease_019ed0cf-533b-74e0-8487-f0505ca66fd8_terseLabel_en-US" xlink:label="lab_bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrantIncrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of shares available for grant, increase (in shares)</link:label>
    <link:label id="lab_bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrantIncrease_label_en-US" xlink:label="lab_bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrantIncrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement By Share-Based Payment Award, Number Of Shares Available For Grant, Increase</link:label>
    <link:label id="lab_bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrantIncrease_documentation_en-US" xlink:label="lab_bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrantIncrease" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement By Share-Based Payment Award, Number Of Shares Available For Grant, Increase</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrantIncrease" xlink:href="bkv-20260630.xsd#bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrantIncrease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrantIncrease" xlink:to="lab_bkv_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrantIncrease" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_019ed0cf-53ce-7e1b-9289-ba49f08ed95d_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrTerminationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Termination Date</link:label>
    <link:label id="lab_ecd_TrdArrTerminationDate_label_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Termination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrTerminationDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrTerminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrTerminationDate" xlink:to="lab_ecd_TrdArrTerminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCommitmentsAxis_019ed0cf-533b-76af-a1c8-77bb104080ab_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitmentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Commitments [Axis]</link:label>
    <link:label id="lab_us-gaap_OtherCommitmentsAxis_label_en-US" xlink:label="lab_us-gaap_OtherCommitmentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitments [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitmentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherCommitmentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCommitmentsAxis" xlink:to="lab_us-gaap_OtherCommitmentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_AccretionToRedemptionValue_019ed0cf-533c-7f7a-bfcc-1ff4f1338eed_terseLabel_en-US" xlink:label="lab_bkv_AccretionToRedemptionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accretion of Class B Units to redemption value</link:label>
    <link:label id="lab_bkv_AccretionToRedemptionValue_label_en-US" xlink:label="lab_bkv_AccretionToRedemptionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accretion To Redemption Value</link:label>
    <link:label id="lab_bkv_AccretionToRedemptionValue_documentation_en-US" xlink:label="lab_bkv_AccretionToRedemptionValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accretion To Redemption Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_AccretionToRedemptionValue" xlink:href="bkv-20260630.xsd#bkv_AccretionToRedemptionValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_AccretionToRedemptionValue" xlink:to="lab_bkv_AccretionToRedemptionValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedStockValueSharesIssuedNetOfTaxWithholdings_019ed0cf-533b-79fa-850c-f22ace9b68d4_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockValueSharesIssuedNetOfTaxWithholdings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock issued upon vesting of restricted stock units, net of shares withheld for income taxes</link:label>
    <link:label id="lab_us-gaap_RestrictedStockValueSharesIssuedNetOfTaxWithholdings_label_en-US" xlink:label="lab_us-gaap_RestrictedStockValueSharesIssuedNetOfTaxWithholdings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock, Value, Shares Issued Net of Tax Withholdings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedStockValueSharesIssuedNetOfTaxWithholdings" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestrictedStockValueSharesIssuedNetOfTaxWithholdings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedStockValueSharesIssuedNetOfTaxWithholdings" xlink:to="lab_us-gaap_RestrictedStockValueSharesIssuedNetOfTaxWithholdings" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesCurrent_019ed0cf-533c-79c8-b773-571b13001717_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other current liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesCurrent" xlink:to="lab_us-gaap_OtherLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardGrantDateFairValue_terseLabel_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value as of Grant Date</link:label>
    <link:label id="lab_ecd_AwardGrantDateFairValue_label_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardGrantDateFairValue" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardGrantDateFairValue" xlink:to="lab_ecd_AwardGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTable_019ed0cf-533c-7419-adff-b8fedb6010ed_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic, by Common Class, Including Two-Class Method [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic, by Common Class, Including Two-Class Method [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTable" xlink:to="lab_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward_019ed0cf-5275-7ca4-875c-cb4449779858_verboseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Mezzanine Equity</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Temporary Equity [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInTemporaryEquityRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:to="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SupplyCommitmentArrangementMember_019fa907-e5d6-7b0b-bbc2-2553debe2314_terseLabel_en-US" xlink:label="lab_us-gaap_SupplyCommitmentArrangementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supply Commitment Arrangement [Domain]</link:label>
    <link:label id="lab_us-gaap_SupplyCommitmentArrangementMember_label_en-US" xlink:label="lab_us-gaap_SupplyCommitmentArrangementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Supply Commitment Arrangement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplyCommitmentArrangementMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SupplyCommitmentArrangementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SupplyCommitmentArrangementMember" xlink:to="lab_us-gaap_SupplyCommitmentArrangementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure, Table</link:label>
    <link:label id="lab_ecd_PvpTableTextBlock_label_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PvpTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTableTextBlock" xlink:to="lab_ecd_PvpTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrDuration_terseLabel_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arrangement Duration</link:label>
    <link:label id="lab_ecd_TrdArrDuration_label_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Duration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrDuration" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrDuration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrDuration" xlink:to="lab_ecd_TrdArrDuration" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_InterestPayableRemainderOfFiscalYear_019ed0cf-53ce-779a-ba25-dad76b063c3d_terseLabel_en-US" xlink:label="lab_bkv_InterestPayableRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_bkv_InterestPayableRemainderOfFiscalYear_label_en-US" xlink:label="lab_bkv_InterestPayableRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable, Remainder of Fiscal Year</link:label>
    <link:label id="lab_bkv_InterestPayableRemainderOfFiscalYear_documentation_en-US" xlink:label="lab_bkv_InterestPayableRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Payable, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_InterestPayableRemainderOfFiscalYear" xlink:href="bkv-20260630.xsd#bkv_InterestPayableRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_InterestPayableRemainderOfFiscalYear" xlink:to="lab_bkv_InterestPayableRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_RBLCreditAgreementMember_019ed0cf-533b-7676-b5e9-fa4acf5c85b6_terseLabel_en-US" xlink:label="lab_bkv_RBLCreditAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">RBL Credit Agreement</link:label>
    <link:label id="lab_bkv_RBLCreditAgreementMember_label_en-US" xlink:label="lab_bkv_RBLCreditAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">RBL Credit Agreement [Member]</link:label>
    <link:label id="lab_bkv_RBLCreditAgreementMember_documentation_en-US" xlink:label="lab_bkv_RBLCreditAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">RBL Credit Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_RBLCreditAgreementMember" xlink:href="bkv-20260630.xsd#bkv_RBLCreditAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_RBLCreditAgreementMember" xlink:to="lab_bkv_RBLCreditAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidationItemsAxis_019ed0cf-5275-71fb-8646-bd5c32954245_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation Items [Axis]</link:label>
    <link:label id="lab_srt_ConsolidationItemsAxis_label_en-US" xlink:label="lab_srt_ConsolidationItemsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation Items [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidationItemsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidationItemsAxis" xlink:to="lab_srt_ConsolidationItemsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressPostalZipCode_019ed0cf-533b-748d-a333-fe514db1b6d1_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:label id="lab_dei_EntityAddressPostalZipCode_label_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressPostalZipCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressPostalZipCode" xlink:to="lab_dei_EntityAddressPostalZipCode" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_019ed0cf-53ce-7cce-a27e-0735d24996f4_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityRegistrantName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityRegistrantName" xlink:to="lab_dei_EntityRegistrantName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationBasisOfPresentationBusinessDescriptionAndAccountingPoliciesTextBlock_019ed0cf-53ce-7783-a74a-195391dbdf0e_terseLabel_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationBasisOfPresentationBusinessDescriptionAndAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business and Basis of Presentation</link:label>
    <link:label id="lab_us-gaap_OrganizationConsolidationBasisOfPresentationBusinessDescriptionAndAccountingPoliciesTextBlock_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationBasisOfPresentationBusinessDescriptionAndAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation, Basis of Presentation, Business Description and Accounting Policies [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationBasisOfPresentationBusinessDescriptionAndAccountingPoliciesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OrganizationConsolidationBasisOfPresentationBusinessDescriptionAndAccountingPoliciesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrganizationConsolidationBasisOfPresentationBusinessDescriptionAndAccountingPoliciesTextBlock" xlink:to="lab_us-gaap_OrganizationConsolidationBasisOfPresentationBusinessDescriptionAndAccountingPoliciesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireOtherProductiveAssets_019ed0cf-533b-7502-8b8a-de995182f4fe_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireOtherProductiveAssets" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Asset acquisition</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireOtherProductiveAssets_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireOtherProductiveAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Other Productive Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireOtherProductiveAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireOtherProductiveAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireOtherProductiveAssets" xlink:to="lab_us-gaap_PaymentsToAcquireOtherProductiveAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:to="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Revenues_019ed0cf-5275-7406-8f18-20a9ba9e327d_verboseLabel_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Revenues and other income</link:label>
    <link:label id="lab_us-gaap_Revenues_019ed0cf-5275-7c13-a99b-ceba27701e3f_terseLabel_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenues</link:label>
    <link:label id="lab_us-gaap_Revenues_label_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Revenues" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Revenues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Revenues" xlink:to="lab_us-gaap_Revenues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAverageCapPrice_019ed0cf-533b-7e4e-bd03-497acefe8624_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAverageCapPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average price ceiling (in USD per unit)</link:label>
    <link:label id="lab_us-gaap_DerivativeAverageCapPrice_label_en-US" xlink:label="lab_us-gaap_DerivativeAverageCapPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Average Cap Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAverageCapPrice" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAverageCapPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAverageCapPrice" xlink:to="lab_us-gaap_DerivativeAverageCapPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities_019ed0cf-533b-793c-9823-90bebdc56684_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable and accrued liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accounts Payable and Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent_019ed0cf-533b-7af1-9d2e-ced552ff7416_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Temporary equity, carrying amount, attributable to parent</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Carrying Amount, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TemporaryEquityCarryingAmountAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:to="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_019ed0cf-53ce-703b-a3bf-042198437605_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractualObligationDueInThirdYear_019ed0cf-53ce-7e35-b467-cbde87c99913_totalLabel_en-US" xlink:label="lab_us-gaap_ContractualObligationDueInThirdYear" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_ContractualObligationDueInThirdYear_label_en-US" xlink:label="lab_us-gaap_ContractualObligationDueInThirdYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contractual Obligation, to be Paid, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractualObligationDueInThirdYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractualObligationDueInThirdYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractualObligationDueInThirdYear" xlink:to="lab_us-gaap_ContractualObligationDueInThirdYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019ed0cf-533b-741c-90d2-e25f2857d9cd_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Award Types</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_019ed0cf-533b-7de2-b9b7-7391ba4d6f0d_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_TransportationCommitmentsMember_019ed0cf-53ce-7240-95fb-ec48884b0b67_terseLabel_en-US" xlink:label="lab_bkv_TransportationCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transportation commitments</link:label>
    <link:label id="lab_bkv_TransportationCommitmentsMember_label_en-US" xlink:label="lab_bkv_TransportationCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transportation Commitments [Member]</link:label>
    <link:label id="lab_bkv_TransportationCommitmentsMember_documentation_en-US" xlink:label="lab_bkv_TransportationCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Transportation Commitments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_TransportationCommitmentsMember" xlink:href="bkv-20260630.xsd#bkv_TransportationCommitmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_TransportationCommitmentsMember" xlink:to="lab_bkv_TransportationCommitmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueOptionQuantitativeDisclosuresTable_019ed0cf-533b-7ca4-ba52-32b9d0fdbbdb_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOptionQuantitativeDisclosuresTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Option, Disclosures [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueOptionQuantitativeDisclosuresTable_label_en-US" xlink:label="lab_us-gaap_FairValueOptionQuantitativeDisclosuresTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Option, Disclosures [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueOptionQuantitativeDisclosuresTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueOptionQuantitativeDisclosuresTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueOptionQuantitativeDisclosuresTable" xlink:to="lab_us-gaap_FairValueOptionQuantitativeDisclosuresTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_019ed0cf-533b-7951-b37e-0339e810e388_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurements</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosuresTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:to="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_019ed0cf-533b-7c6c-aa5c-c867293d1108_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Significant Unobservable Inputs (Level 3)</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 3 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel3Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel3Member" xlink:to="lab_us-gaap_FairValueInputsLevel3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_019ed0cf-53ce-7ec7-800b-633d462f263b_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage owned by noncontrolling members</link:label>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_label_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary, Ownership Percentage, Noncontrolling Owner</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:to="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StatementGeographicalAxis_019ed0cf-53ce-7ef9-af1a-9257f1b3d8ee_terseLabel_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:label id="lab_srt_StatementGeographicalAxis_label_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementGeographicalAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_StatementGeographicalAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StatementGeographicalAxis" xlink:to="lab_srt_StatementGeographicalAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCash_019ed0cf-533b-71a2-b416-3aa37a0b5edb_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted cash</link:label>
    <link:label id="lab_us-gaap_RestrictedCash_label_en-US" xlink:label="lab_us-gaap_RestrictedCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCash" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestrictedCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCash" xlink:to="lab_us-gaap_RestrictedCash" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LegalEntityAxis_019ed0cf-5275-7ba3-a363-cac9a51a893e_terseLabel_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:label id="lab_dei_LegalEntityAxis_label_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LegalEntityAxis" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LegalEntityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LegalEntityAxis" xlink:to="lab_dei_LegalEntityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019ed0cf-53ce-741f-ae46-e2d5dac76ddf_terseLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash, cash equivalents, and restricted cash, beginning of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019ed0cf-53ce-77b2-b03a-4eb0810bc4d9_verboseLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash, cash equivalents, and restricted cash, end of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019ed0cf-53ce-7bc4-97a7-0845f0bc8d81_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Cash, cash equivalents, and restricted cash</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonNeosMember_terseLabel_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-NEOs</link:label>
    <link:label id="lab_ecd_NonNeosMember_label_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-NEOs [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonNeosMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonNeosMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonNeosMember" xlink:to="lab_ecd_NonNeosMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage_019ed0cf-53ce-7fab-a900-ce8243da2361_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity method investment, ownership percentage</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Ownership Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestmentOwnershipPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:to="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesGross_019ed0cf-53cf-74ae-a4c9-7224b009b086_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payments to acquire businesses, gross</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesGross_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Businesses, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireBusinessesGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireBusinessesGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireBusinessesGross" xlink:to="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OilAndGasPropertySuccessfulEffortMethodAccumulatedDepreciationDepletionAndAmortization_019ed0cf-53ce-7095-8697-e962ee96e7ea_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OilAndGasPropertySuccessfulEffortMethodAccumulatedDepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accumulated depreciation, depletion, and amortization</link:label>
    <link:label id="lab_us-gaap_OilAndGasPropertySuccessfulEffortMethodAccumulatedDepreciationDepletionAndAmortization_label_en-US" xlink:label="lab_us-gaap_OilAndGasPropertySuccessfulEffortMethodAccumulatedDepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Oil and Gas, Successful Efforts Method, Property and Equipment, Accumulated Depreciation, Depletion, and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OilAndGasPropertySuccessfulEffortMethodAccumulatedDepreciationDepletionAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OilAndGasPropertySuccessfulEffortMethodAccumulatedDepreciationDepletionAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OilAndGasPropertySuccessfulEffortMethodAccumulatedDepreciationDepletionAndAmortization" xlink:to="lab_us-gaap_OilAndGasPropertySuccessfulEffortMethodAccumulatedDepreciationDepletionAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_NameOfMajorCustomerDomain_019ed0cf-53ce-7856-9076-77f3779c2724_terseLabel_en-US" xlink:label="lab_srt_NameOfMajorCustomerDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer [Domain]</link:label>
    <link:label id="lab_srt_NameOfMajorCustomerDomain_label_en-US" xlink:label="lab_srt_NameOfMajorCustomerDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_NameOfMajorCustomerDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_NameOfMajorCustomerDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_NameOfMajorCustomerDomain" xlink:to="lab_srt_NameOfMajorCustomerDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_EquityMethodInvesteeNameDomain_019ed0cf-533c-77b5-b646-aa49e4cb2b78_terseLabel_en-US" xlink:label="lab_srt_EquityMethodInvesteeNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Name [Domain]</link:label>
    <link:label id="lab_srt_EquityMethodInvesteeNameDomain_label_en-US" xlink:label="lab_srt_EquityMethodInvesteeNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_EquityMethodInvesteeNameDomain" xlink:to="lab_srt_EquityMethodInvesteeNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_019ed0cf-53ce-7158-8a73-c3c39dfe7252_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_019ed0cf-533b-7741-8add-5229e2508179_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeDomain" xlink:to="lab_us-gaap_LongtermDebtTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityCurrent_019ed0cf-53ce-77fa-9195-7b78db301cf9_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenues payable</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityCurrent_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Liability, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractWithCustomerLiabilityCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:to="lab_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_SeniorUnsecuredNotesDue2030Member_019ed0cf-53ce-74c6-ba45-336f3ab53b26_terseLabel_en-US" xlink:label="lab_bkv_SeniorUnsecuredNotesDue2030Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030 Senior Notes (7.50%)</link:label>
    <link:label id="lab_bkv_SeniorUnsecuredNotesDue2030Member_label_en-US" xlink:label="lab_bkv_SeniorUnsecuredNotesDue2030Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Senior Unsecured Notes Due 2030 [Member]</link:label>
    <link:label id="lab_bkv_SeniorUnsecuredNotesDue2030Member_documentation_en-US" xlink:label="lab_bkv_SeniorUnsecuredNotesDue2030Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Senior Unsecured Notes Due 2030</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_SeniorUnsecuredNotesDue2030Member" xlink:href="bkv-20260630.xsd#bkv_SeniorUnsecuredNotesDue2030Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_SeniorUnsecuredNotesDue2030Member" xlink:to="lab_bkv_SeniorUnsecuredNotesDue2030Member" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_OPISNaturalGasolineMontBelvieuNonTETMember_019ed0cf-533c-7671-b188-03db3a254226_terseLabel_en-US" xlink:label="lab_bkv_OPISNaturalGasolineMontBelvieuNonTETMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">OPIS Natural Gasoline Mont Belvieu Non-TET</link:label>
    <link:label id="lab_bkv_OPISNaturalGasolineMontBelvieuNonTETMember_label_en-US" xlink:label="lab_bkv_OPISNaturalGasolineMontBelvieuNonTETMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">OPIS Natural Gasoline Mont Belvieu Non-TET [Member]</link:label>
    <link:label id="lab_bkv_OPISNaturalGasolineMontBelvieuNonTETMember_documentation_en-US" xlink:label="lab_bkv_OPISNaturalGasolineMontBelvieuNonTETMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">OPIS Natural Gasoline Mont Belvieu Non-TET</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_OPISNaturalGasolineMontBelvieuNonTETMember" xlink:href="bkv-20260630.xsd#bkv_OPISNaturalGasolineMontBelvieuNonTETMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_OPISNaturalGasolineMontBelvieuNonTETMember" xlink:to="lab_bkv_OPISNaturalGasolineMontBelvieuNonTETMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_019ed0cf-53ce-79fe-bce1-b1425ce151ef_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeAxis" xlink:to="lab_srt_RangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTable_019ed0cf-53ce-79a9-95fc-999d111286a4_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTable_label_en-US" xlink:label="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:to="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock_019ed0cf-53ce-74ad-9fa2-1def2ab9e52a_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Derivative Instrument Gain (Loss)</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:to="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AwardTypeAxis_019ed0cf-533b-75df-a128-7627957b5e1e_terseLabel_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type</link:label>
    <link:label id="lab_us-gaap_AwardTypeAxis_label_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AwardTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AwardTypeAxis" xlink:to="lab_us-gaap_AwardTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_JointVentureFormationFairValueOfJointVenture_019ed0cf-53ce-7792-9245-55be4c96dc1f_terseLabel_en-US" xlink:label="lab_us-gaap_JointVentureFormationFairValueOfJointVenture" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Joint venture formation, fair value of joint venture</link:label>
    <link:label id="lab_us-gaap_JointVentureFormationFairValueOfJointVenture_label_en-US" xlink:label="lab_us-gaap_JointVentureFormationFairValueOfJointVenture" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Joint Venture Formation, Fair Value of Joint Venture</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_JointVentureFormationFairValueOfJointVenture" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_JointVentureFormationFairValueOfJointVenture"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_JointVentureFormationFairValueOfJointVenture" xlink:to="lab_us-gaap_JointVentureFormationFairValueOfJointVenture" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote</link:label>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_label_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NamedExecutiveOfficersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:to="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_019ed0cf-53ce-7b89-b1fa-c1af733edec2_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retained earnings</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:to="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_LineOfCreditFacilityCovenantTermsMinimumCurrentRatio_019ed0cf-5275-7c26-b310-4a53c15c4760_terseLabel_en-US" xlink:label="lab_bkv_LineOfCreditFacilityCovenantTermsMinimumCurrentRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum current ratio</link:label>
    <link:label id="lab_bkv_LineOfCreditFacilityCovenantTermsMinimumCurrentRatio_label_en-US" xlink:label="lab_bkv_LineOfCreditFacilityCovenantTermsMinimumCurrentRatio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Covenant Terms, Minimum Current Ratio</link:label>
    <link:label id="lab_bkv_LineOfCreditFacilityCovenantTermsMinimumCurrentRatio_documentation_en-US" xlink:label="lab_bkv_LineOfCreditFacilityCovenantTermsMinimumCurrentRatio" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Covenant Terms, Minimum Current Ratio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_LineOfCreditFacilityCovenantTermsMinimumCurrentRatio" xlink:href="bkv-20260630.xsd#bkv_LineOfCreditFacilityCovenantTermsMinimumCurrentRatio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_LineOfCreditFacilityCovenantTermsMinimumCurrentRatio" xlink:to="lab_bkv_LineOfCreditFacilityCovenantTermsMinimumCurrentRatio" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductOrServiceAxis_019ed0cf-533c-7e9d-ad68-fe9f52e8aa18_terseLabel_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:label id="lab_srt_ProductOrServiceAxis_label_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductOrServiceAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductOrServiceAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductOrServiceAxis" xlink:to="lab_srt_ProductOrServiceAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_CounterpartyTwoMember_019ed0cf-53cf-7be0-9c07-3c7f79b71300_terseLabel_en-US" xlink:label="lab_bkv_CounterpartyTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Counterparty Two</link:label>
    <link:label id="lab_bkv_CounterpartyTwoMember_label_en-US" xlink:label="lab_bkv_CounterpartyTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Counterparty Two [Member]</link:label>
    <link:label id="lab_bkv_CounterpartyTwoMember_documentation_en-US" xlink:label="lab_bkv_CounterpartyTwoMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Counterparty Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_CounterpartyTwoMember" xlink:href="bkv-20260630.xsd#bkv_CounterpartyTwoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_CounterpartyTwoMember" xlink:to="lab_bkv_CounterpartyTwoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentOtherNet_019ed0cf-53ce-7687-b1dc-0f2cd52eb8ef_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentOtherNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other property, plant, and equipment, net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentOtherNet_019ed0cf-53ce-7329-a3af-d9d9b921eb72_totalLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentOtherNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Other property, plant, and equipment, net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentOtherNet_019ed0cf-53ce-7023-b3ce-69c1cc545de4_verboseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentOtherNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other property, plant, and equipment, net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentOtherNet_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentOtherNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment, Other, after Accumulated Depreciation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentOtherNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentOtherNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentOtherNet" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentOtherNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockMember_019ed0cf-533b-75fe-849f-a79fcff5fc46_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_label_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockMember" xlink:to="lab_us-gaap_CommonStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfSecuredDebt_019ed0cf-53ce-79f3-8691-7272c6c7183b_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfSecuredDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds under RBL Credit Agreement</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfSecuredDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfSecuredDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Secured Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfSecuredDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromIssuanceOfSecuredDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfSecuredDebt" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfSecuredDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskByBenchmarkAxis_019ed0cf-53ce-774a-aa16-f017fe82d375_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Axis]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskByBenchmarkAxis_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskByBenchmarkAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:to="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_019ed0cf-533b-7101-bb71-601eddcbd524_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_label_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeContractTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeContractTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeContractTypeDomain" xlink:to="lab_us-gaap_DerivativeContractTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_OtherCommitmentVolumeRequired_019ed0cf-533c-79e0-9b66-601e53ff4580_terseLabel_en-US" xlink:label="lab_bkv_OtherCommitmentVolumeRequired" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Volume required under commitment</link:label>
    <link:label id="lab_bkv_OtherCommitmentVolumeRequired_label_en-US" xlink:label="lab_bkv_OtherCommitmentVolumeRequired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitment, Volume Required</link:label>
    <link:label id="lab_bkv_OtherCommitmentVolumeRequired_documentation_en-US" xlink:label="lab_bkv_OtherCommitmentVolumeRequired" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Commitment, Volume Required</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_OtherCommitmentVolumeRequired" xlink:href="bkv-20260630.xsd#bkv_OtherCommitmentVolumeRequired"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_OtherCommitmentVolumeRequired" xlink:to="lab_bkv_OtherCommitmentVolumeRequired" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_019ed0cf-53ce-724d-93d3-eadeff5173c4_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities, mezzanine equity, and equity</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee Stock Option</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOptionMember" xlink:to="lab_us-gaap_EmployeeStockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetRetirementObligationCurrent_019ed0cf-533c-728d-8b31-868b92b2c498_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AssetRetirementObligationCurrent" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less current portion</link:label>
    <link:label id="lab_us-gaap_AssetRetirementObligationCurrent_label_en-US" xlink:label="lab_us-gaap_AssetRetirementObligationCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Retirement Obligation, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetRetirementObligationCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetRetirementObligationCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetRetirementObligationCurrent" xlink:to="lab_us-gaap_AssetRetirementObligationCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_JointVentureOwnershipPercentageOfNoncontrollingInterest_019ed0cf-5275-720d-bc9d-3b2b7e88a0de_terseLabel_en-US" xlink:label="lab_bkv_JointVentureOwnershipPercentageOfNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage of noncontrolling interest (percent)</link:label>
    <link:label id="lab_bkv_JointVentureOwnershipPercentageOfNoncontrollingInterest_label_en-US" xlink:label="lab_bkv_JointVentureOwnershipPercentageOfNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Joint Venture, Ownership Percentage of Noncontrolling Interest</link:label>
    <link:label id="lab_bkv_JointVentureOwnershipPercentageOfNoncontrollingInterest_documentation_en-US" xlink:label="lab_bkv_JointVentureOwnershipPercentageOfNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Joint Venture, Ownership Percentage of Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_JointVentureOwnershipPercentageOfNoncontrollingInterest" xlink:href="bkv-20260630.xsd#bkv_JointVentureOwnershipPercentageOfNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_JointVentureOwnershipPercentageOfNoncontrollingInterest" xlink:to="lab_bkv_JointVentureOwnershipPercentageOfNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterest_019ed0cf-5275-746c-b62c-9a3bdcbb2bd9_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling interest</link:label>
    <link:label id="lab_us-gaap_MinorityInterest_019fd765-4edb-7f88-b148-29933b49a9e4_verboseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling interest in BKV-BPP Power</link:label>
    <link:label id="lab_us-gaap_MinorityInterest_label_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterest" xlink:to="lab_us-gaap_MinorityInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_019ed0cf-53ce-7fea-82e8-1db398f640f5_terseLabel_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:to="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_SoftwareLicensingCommitmentMember_019fb3f6-9d83-766f-9a23-ff777c4147be_terseLabel_en-US" xlink:label="lab_bkv_SoftwareLicensingCommitmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Software Licensing, Commitment</link:label>
    <link:label id="lab_bkv_SoftwareLicensingCommitmentMember_label_en-US" xlink:label="lab_bkv_SoftwareLicensingCommitmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Software Licensing, Commitment [Member]</link:label>
    <link:label id="lab_bkv_SoftwareLicensingCommitmentMember_documentation_en-US" xlink:label="lab_bkv_SoftwareLicensingCommitmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Software Licensing, Commitment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_SoftwareLicensingCommitmentMember" xlink:href="bkv-20260630.xsd#bkv_SoftwareLicensingCommitmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_SoftwareLicensingCommitmentMember" xlink:to="lab_bkv_SoftwareLicensingCommitmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure</link:label>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_label_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Additional402vDisclosureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Additional402vDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Additional402vDisclosureTextBlock" xlink:to="lab_ecd_Additional402vDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyDomain_019ed0cf-53ce-7efd-98df-be2cfb553fce_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyDomain" xlink:to="lab_us-gaap_RelatedPartyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TabularListTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tabular List, Table</link:label>
    <link:label id="lab_ecd_TabularListTableTextBlock_label_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tabular List [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TabularListTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TabularListTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TabularListTableTextBlock" xlink:to="lab_ecd_TabularListTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_019ed0cf-53ce-736f-8236-6458c806e9da_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional paid-in capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid in Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapital" xlink:to="lab_us-gaap_AdditionalPaidInCapital" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetRetirementObligationAccretionExpense_019ed0cf-5275-76c4-8841-c409265c92a1_terseLabel_en-US" xlink:label="lab_us-gaap_AssetRetirementObligationAccretionExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accretion of discount</link:label>
    <link:label id="lab_us-gaap_AssetRetirementObligationAccretionExpense_label_en-US" xlink:label="lab_us-gaap_AssetRetirementObligationAccretionExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Retirement Obligation, Accretion Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetRetirementObligationAccretionExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetRetirementObligationAccretionExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetRetirementObligationAccretionExpense" xlink:to="lab_us-gaap_AssetRetirementObligationAccretionExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_OPISPurityEthaneMontBelvieuMember_019ed0cf-533b-731e-9a57-b31b6942e4d1_terseLabel_en-US" xlink:label="lab_bkv_OPISPurityEthaneMontBelvieuMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">OPIS Purity Ethane Mont Belvieu</link:label>
    <link:label id="lab_bkv_OPISPurityEthaneMontBelvieuMember_label_en-US" xlink:label="lab_bkv_OPISPurityEthaneMontBelvieuMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">OPIS Purity Ethane Mont Belvieu [Member]</link:label>
    <link:label id="lab_bkv_OPISPurityEthaneMontBelvieuMember_documentation_en-US" xlink:label="lab_bkv_OPISPurityEthaneMontBelvieuMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">OPIS Purity Ethane Mont Belvieu</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_OPISPurityEthaneMontBelvieuMember" xlink:href="bkv-20260630.xsd#bkv_OPISPurityEthaneMontBelvieuMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_OPISPurityEthaneMontBelvieuMember" xlink:to="lab_bkv_OPISPurityEthaneMontBelvieuMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetRetirementObligationRollForwardAnalysisRollForward_019ed0cf-533b-7ecb-b24f-2a11b7b2dce8_terseLabel_en-US" xlink:label="lab_us-gaap_AssetRetirementObligationRollForwardAnalysisRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Retirement Obligation, Roll Forward Analysis [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_AssetRetirementObligationRollForwardAnalysisRollForward_label_en-US" xlink:label="lab_us-gaap_AssetRetirementObligationRollForwardAnalysisRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Retirement Obligation, Roll Forward Analysis [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetRetirementObligationRollForwardAnalysisRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetRetirementObligationRollForwardAnalysisRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetRetirementObligationRollForwardAnalysisRollForward" xlink:to="lab_us-gaap_AssetRetirementObligationRollForwardAnalysisRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:to="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_terseLabel_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_label_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:to="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UtilitiesOperatingExpenseMaintenanceOperationsAndOtherCostsAndExpenses_019ed0cf-53ce-731d-a8ca-11ca6d9a3cd8_terseLabel_en-US" xlink:label="lab_us-gaap_UtilitiesOperatingExpenseMaintenanceOperationsAndOtherCostsAndExpenses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Power operating and maintenance</link:label>
    <link:label id="lab_us-gaap_UtilitiesOperatingExpenseMaintenanceOperationsAndOtherCostsAndExpenses_label_en-US" xlink:label="lab_us-gaap_UtilitiesOperatingExpenseMaintenanceOperationsAndOtherCostsAndExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Utilities Operating Expense, Maintenance, Operations, and Other Costs and Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UtilitiesOperatingExpenseMaintenanceOperationsAndOtherCostsAndExpenses" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UtilitiesOperatingExpenseMaintenanceOperationsAndOtherCostsAndExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UtilitiesOperatingExpenseMaintenanceOperationsAndOtherCostsAndExpenses" xlink:to="lab_us-gaap_UtilitiesOperatingExpenseMaintenanceOperationsAndOtherCostsAndExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_019ed0cf-5275-7ae7-97ba-7a0ac73c06de_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Lived Asset, Class [Domain]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Asset, Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_019ed0cf-53ce-7368-adc1-96e0302795de_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfPropertyPlantAndEquipmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:to="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfBuildings_019ed0cf-53ce-7df1-b592-e81131a417b9_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfBuildings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale of buildings</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfBuildings_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfBuildings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale of Buildings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleOfBuildings" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromSaleOfBuildings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleOfBuildings" xlink:to="lab_us-gaap_ProceedsFromSaleOfBuildings" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAxis_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation:</link:label>
    <link:label id="lab_ecd_AdjToCompAxis_label_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToCompAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAxis" xlink:to="lab_ecd_AdjToCompAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireMachineryAndEquipment_019ed0cf-53ce-7202-ad4a-7792994cfac5_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireMachineryAndEquipment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payments to acquire machinery and equipment</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireMachineryAndEquipment_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireMachineryAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Machinery and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireMachineryAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireMachineryAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireMachineryAndEquipment" xlink:to="lab_us-gaap_PaymentsToAcquireMachineryAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_NetAssetsAttributableToCommonShareholders_019fd764-49d8-72b2-a709-d095c3cee487_terseLabel_en-US" xlink:label="lab_bkv_NetAssetsAttributableToCommonShareholders" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net assets attributable to common shareholders</link:label>
    <link:label id="lab_bkv_NetAssetsAttributableToCommonShareholders_label_en-US" xlink:label="lab_bkv_NetAssetsAttributableToCommonShareholders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Assets Attributable To Common Shareholders</link:label>
    <link:label id="lab_bkv_NetAssetsAttributableToCommonShareholders_documentation_en-US" xlink:label="lab_bkv_NetAssetsAttributableToCommonShareholders" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Assets Attributable To Common Shareholders</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_NetAssetsAttributableToCommonShareholders" xlink:href="bkv-20260630.xsd#bkv_NetAssetsAttributableToCommonShareholders"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_NetAssetsAttributableToCommonShareholders" xlink:to="lab_bkv_NetAssetsAttributableToCommonShareholders" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember_019ed0cf-533b-7217-a915-72a7422aedb8_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Financial Instruments, Liabilities</link:label>
    <link:label id="lab_us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember_label_en-US" xlink:label="lab_us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Financial Instruments, Liabilities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember" xlink:to="lab_us-gaap_DerivativeFinancialInstrumentsLiabilitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Rule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:to="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_AggtErrCompAmt_label_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompAmt" xlink:to="lab_ecd_AggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPaidNet_019ed0cf-53ce-720e-8911-277905d55124_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest</link:label>
    <link:label id="lab_us-gaap_InterestPaidNet_label_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Paid, Excluding Capitalized Interest, Operating Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPaidNet" xlink:to="lab_us-gaap_InterestPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractualObligationDueInNextTwelveMonths_019ed0cf-533b-7c15-af8d-f562685b8f0c_totalLabel_en-US" xlink:label="lab_us-gaap_ContractualObligationDueInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_ContractualObligationDueInNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_ContractualObligationDueInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contractual Obligation, to be Paid, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractualObligationDueInNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractualObligationDueInNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractualObligationDueInNextTwelveMonths" xlink:to="lab_us-gaap_ContractualObligationDueInNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherGeneralExpense_019ed0cf-53ce-79f5-84eb-2cc01e09df86_terseLabel_en-US" xlink:label="lab_us-gaap_OtherGeneralExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other operating expenses</link:label>
    <link:label id="lab_us-gaap_OtherGeneralExpense_019ed0cf-53ce-79fc-a13d-8d0554d9a5de_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherGeneralExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Corporate and Other other operating expenses</link:label>
    <link:label id="lab_us-gaap_OtherGeneralExpense_label_en-US" xlink:label="lab_us-gaap_OtherGeneralExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other General Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherGeneralExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherGeneralExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherGeneralExpense" xlink:to="lab_us-gaap_OtherGeneralExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityAxis_019ed0cf-533b-7426-87c2-f5ba97b09e13_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityAxis_label_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CreditFacilityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityAxis" xlink:to="lab_us-gaap_CreditFacilityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_BusinessCombinationEquityConsiderationLockUpPeriod_019ed0cf-533c-7908-ab43-143a46a199cd_terseLabel_en-US" xlink:label="lab_bkv_BusinessCombinationEquityConsiderationLockUpPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity consideration lock-up period</link:label>
    <link:label id="lab_bkv_BusinessCombinationEquityConsiderationLockUpPeriod_label_en-US" xlink:label="lab_bkv_BusinessCombinationEquityConsiderationLockUpPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Equity Consideration Lock-Up Period</link:label>
    <link:label id="lab_bkv_BusinessCombinationEquityConsiderationLockUpPeriod_documentation_en-US" xlink:label="lab_bkv_BusinessCombinationEquityConsiderationLockUpPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Equity Consideration Lock-Up Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_BusinessCombinationEquityConsiderationLockUpPeriod" xlink:href="bkv-20260630.xsd#bkv_BusinessCombinationEquityConsiderationLockUpPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_BusinessCombinationEquityConsiderationLockUpPeriod" xlink:to="lab_bkv_BusinessCombinationEquityConsiderationLockUpPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_PowerJVTermLoanFacilityMember_019ed0cf-53ce-7792-8966-9e702c904232_terseLabel_en-US" xlink:label="lab_bkv_PowerJVTermLoanFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">BKV-BPP Power commitment agreements</link:label>
    <link:label id="lab_bkv_PowerJVTermLoanFacilityMember_label_en-US" xlink:label="lab_bkv_PowerJVTermLoanFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Power JV Term Loan Facility [Member]</link:label>
    <link:label id="lab_bkv_PowerJVTermLoanFacilityMember_documentation_en-US" xlink:label="lab_bkv_PowerJVTermLoanFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Power JV Term Loan Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_PowerJVTermLoanFacilityMember" xlink:href="bkv-20260630.xsd#bkv_PowerJVTermLoanFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_PowerJVTermLoanFacilityMember" xlink:to="lab_bkv_PowerJVTermLoanFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureName_terseLabel_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_MeasureName_label_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureName" xlink:to="lab_ecd_MeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PayVsPerformanceDisclosureLineItems_label_en-US" xlink:label="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PayVsPerformanceDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:to="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_019ed0cf-533c-75d3-a28a-6e0307416c30_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_BusinessCombinationAggregateConsideration_019ed0cf-533c-7c4b-866a-946806e9662c_terseLabel_en-US" xlink:label="lab_bkv_BusinessCombinationAggregateConsideration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business combination, aggregate consideration</link:label>
    <link:label id="lab_bkv_BusinessCombinationAggregateConsideration_label_en-US" xlink:label="lab_bkv_BusinessCombinationAggregateConsideration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Aggregate Consideration</link:label>
    <link:label id="lab_bkv_BusinessCombinationAggregateConsideration_documentation_en-US" xlink:label="lab_bkv_BusinessCombinationAggregateConsideration" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Aggregate Consideration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_BusinessCombinationAggregateConsideration" xlink:href="bkv-20260630.xsd#bkv_BusinessCombinationAggregateConsideration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_BusinessCombinationAggregateConsideration" xlink:to="lab_bkv_BusinessCombinationAggregateConsideration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_019ed0cf-533b-7824-b1aa-ee223b61e7f8_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentLineItems" xlink:to="lab_us-gaap_DebtInstrumentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_019ed0cf-5275-7127-b5b1-18ef9aa578de_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional Paid-In Capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid-in Capital [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapitalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:to="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtByCurrentAndNoncurrentAbstract_019ed0cf-5275-75a8-8478-0f1a7d0da066_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtByCurrentAndNoncurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carrying Value</link:label>
    <link:label id="lab_us-gaap_LongTermDebtByCurrentAndNoncurrentAbstract_label_en-US" xlink:label="lab_us-gaap_LongTermDebtByCurrentAndNoncurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, by Current and Noncurrent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtByCurrentAndNoncurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtByCurrentAndNoncurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtByCurrentAndNoncurrentAbstract" xlink:to="lab_us-gaap_LongTermDebtByCurrentAndNoncurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_NaturalGasTranscoLeidyBasisMember_019ed0cf-53ce-7caa-8305-cf1155973179_terseLabel_en-US" xlink:label="lab_bkv_NaturalGasTranscoLeidyBasisMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transco Leidy Basis</link:label>
    <link:label id="lab_bkv_NaturalGasTranscoLeidyBasisMember_label_en-US" xlink:label="lab_bkv_NaturalGasTranscoLeidyBasisMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Natural Gas, Transco Leidy Basis [Member]</link:label>
    <link:label id="lab_bkv_NaturalGasTranscoLeidyBasisMember_documentation_en-US" xlink:label="lab_bkv_NaturalGasTranscoLeidyBasisMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Natural Gas, Transco Leidy Basis</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_NaturalGasTranscoLeidyBasisMember" xlink:href="bkv-20260630.xsd#bkv_NaturalGasTranscoLeidyBasisMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_NaturalGasTranscoLeidyBasisMember" xlink:to="lab_bkv_NaturalGasTranscoLeidyBasisMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_TempleILoanAgreementsMember_019ed0cf-533b-76cf-b953-9cc351c75877_terseLabel_en-US" xlink:label="lab_bkv_TempleILoanAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Temple I Loan Agreements</link:label>
    <link:label id="lab_bkv_TempleILoanAgreementsMember_label_en-US" xlink:label="lab_bkv_TempleILoanAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temple I Loan Agreements [Member]</link:label>
    <link:label id="lab_bkv_TempleILoanAgreementsMember_documentation_en-US" xlink:label="lab_bkv_TempleILoanAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temple I Loan Agreements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_TempleILoanAgreementsMember" xlink:href="bkv-20260630.xsd#bkv_TempleILoanAgreementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_TempleILoanAgreementsMember" xlink:to="lab_bkv_TempleILoanAgreementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_JointVentureAccruedReceivablesAllowanceForCreditLoss_019ed0cf-53ce-7077-852d-942e4be983d9_terseLabel_en-US" xlink:label="lab_bkv_JointVentureAccruedReceivablesAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Section 45Q accrued receivables</link:label>
    <link:label id="lab_bkv_JointVentureAccruedReceivablesAllowanceForCreditLoss_label_en-US" xlink:label="lab_bkv_JointVentureAccruedReceivablesAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Joint Venture, Accrued Receivables, Allowance For Credit Loss</link:label>
    <link:label id="lab_bkv_JointVentureAccruedReceivablesAllowanceForCreditLoss_documentation_en-US" xlink:label="lab_bkv_JointVentureAccruedReceivablesAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Joint Venture, Accrued Receivables, Allowance For Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_JointVentureAccruedReceivablesAllowanceForCreditLoss" xlink:href="bkv-20260630.xsd#bkv_JointVentureAccruedReceivablesAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_JointVentureAccruedReceivablesAllowanceForCreditLoss" xlink:to="lab_bkv_JointVentureAccruedReceivablesAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndName_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_TrdArrIndName_label_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndName" xlink:to="lab_ecd_TrdArrIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_019ed0cf-53ce-713b-b62b-7237048a697b_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_PurchaserThreeMember_019ed0cf-533b-7de1-b691-58fe68ca0784_terseLabel_en-US" xlink:label="lab_bkv_PurchaserThreeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchaser Three</link:label>
    <link:label id="lab_bkv_PurchaserThreeMember_label_en-US" xlink:label="lab_bkv_PurchaserThreeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Purchaser Three [Member]</link:label>
    <link:label id="lab_bkv_PurchaserThreeMember_documentation_en-US" xlink:label="lab_bkv_PurchaserThreeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Purchaser Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_PurchaserThreeMember" xlink:href="bkv-20260630.xsd#bkv_PurchaserThreeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_PurchaserThreeMember" xlink:to="lab_bkv_PurchaserThreeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CoSelectedMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureAmt" xlink:to="lab_ecd_CoSelectedMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_LongTermDebtPrincipalValueExcludingCurrentMaturities_019ed0cf-53ce-734f-b42c-fb09dbff2666_terseLabel_en-US" xlink:label="lab_bkv_LongTermDebtPrincipalValueExcludingCurrentMaturities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total long-term debt, net</link:label>
    <link:label id="lab_bkv_LongTermDebtPrincipalValueExcludingCurrentMaturities_label_en-US" xlink:label="lab_bkv_LongTermDebtPrincipalValueExcludingCurrentMaturities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Principal Value, Excluding Current Maturities</link:label>
    <link:label id="lab_bkv_LongTermDebtPrincipalValueExcludingCurrentMaturities_documentation_en-US" xlink:label="lab_bkv_LongTermDebtPrincipalValueExcludingCurrentMaturities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Principal Value, Excluding Current Maturities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_LongTermDebtPrincipalValueExcludingCurrentMaturities" xlink:href="bkv-20260630.xsd#bkv_LongTermDebtPrincipalValueExcludingCurrentMaturities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_LongTermDebtPrincipalValueExcludingCurrentMaturities" xlink:to="lab_bkv_LongTermDebtPrincipalValueExcludingCurrentMaturities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTextBlock_019ed0cf-53ce-71c4-a54f-f7bdf7b507d6_terseLabel_en-US" xlink:label="lab_us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting, Reconciliation of Profit (Loss) by Segment to Consolidated</link:label>
    <link:label id="lab_us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTextBlock_label_en-US" xlink:label="lab_us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Reconciliation of Profit (Loss) by Segment to Consolidated [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTextBlock" xlink:to="lab_us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DepreciationDepletionAndAmortization_019ed0cf-53ce-7b2f-bb3a-8036b37a710d_terseLabel_en-US" xlink:label="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation, depletion, amortization, and accretion</link:label>
    <link:label id="lab_us-gaap_DepreciationDepletionAndAmortization_label_en-US" xlink:label="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation, Depletion and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationDepletionAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DepreciationDepletionAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DepreciationDepletionAndAmortization" xlink:to="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_EquipmentSupplyContractTwoMember_019fa909-5d22-7c91-82c0-00e4e5eb8414_terseLabel_en-US" xlink:label="lab_bkv_EquipmentSupplyContractTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract Two</link:label>
    <link:label id="lab_bkv_EquipmentSupplyContractTwoMember_label_en-US" xlink:label="lab_bkv_EquipmentSupplyContractTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equipment Supply Contract Two [Member]</link:label>
    <link:label id="lab_bkv_EquipmentSupplyContractTwoMember_documentation_en-US" xlink:label="lab_bkv_EquipmentSupplyContractTwoMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equipment Supply Contract Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_EquipmentSupplyContractTwoMember" xlink:href="bkv-20260630.xsd#bkv_EquipmentSupplyContractTwoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_EquipmentSupplyContractTwoMember" xlink:to="lab_bkv_EquipmentSupplyContractTwoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_019ed0cf-53ce-7478-9fac-53ddc7c3697f_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common stock under equity incentive plans, net (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Issued, Shares, Share-Based Payment Arrangement, after Forfeiture</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability_019ed0cf-53cf-76cc-b0b3-c6314d202b13_terseLabel_en-US" xlink:label="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease liabilities arising from obtaining right-of-use assets</link:label>
    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability_label_en-US" xlink:label="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Right-of-Use Asset Obtained in Exchange for Finance Lease Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:to="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoMember_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO</link:label>
    <link:label id="lab_ecd_NonPeoNeoMember_label_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoMember" xlink:to="lab_ecd_NonPeoNeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CustomerConcentrationRiskMember_019ed0cf-533b-77fc-9f1d-a69b31a6074f_terseLabel_en-US" xlink:label="lab_us-gaap_CustomerConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer Concentration Risk</link:label>
    <link:label id="lab_us-gaap_CustomerConcentrationRiskMember_label_en-US" xlink:label="lab_us-gaap_CustomerConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer Concentration Risk [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CustomerConcentrationRiskMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CustomerConcentrationRiskMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CustomerConcentrationRiskMember" xlink:to="lab_us-gaap_CustomerConcentrationRiskMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest_019ed0cf-53ce-79a6-b043-af4c43e35873_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss)</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss), Including Portion Attributable to Nonredeemable Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest" xlink:to="lab_us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_DerivativeWeightedAverageBasisDifferential_019ed0cf-5275-77a0-bcfe-8c4cd42e1228_terseLabel_en-US" xlink:label="lab_bkv_DerivativeWeightedAverageBasisDifferential" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average basis differential (in USD per unit)</link:label>
    <link:label id="lab_bkv_DerivativeWeightedAverageBasisDifferential_label_en-US" xlink:label="lab_bkv_DerivativeWeightedAverageBasisDifferential" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Weighted Average Basis Differential</link:label>
    <link:label id="lab_bkv_DerivativeWeightedAverageBasisDifferential_documentation_en-US" xlink:label="lab_bkv_DerivativeWeightedAverageBasisDifferential" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative, Weighted Average Basis Differential</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_DerivativeWeightedAverageBasisDifferential" xlink:href="bkv-20260630.xsd#bkv_DerivativeWeightedAverageBasisDifferential"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_DerivativeWeightedAverageBasisDifferential" xlink:to="lab_bkv_DerivativeWeightedAverageBasisDifferential" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Method</link:label>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMethodTextBlock" xlink:to="lab_ecd_AwardTmgMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:to="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_NaturalGasHSCBasisMember_019ed0cf-53ce-7c9f-ac77-e5df05adcf3b_terseLabel_en-US" xlink:label="lab_bkv_NaturalGasHSCBasisMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">HSC Basis</link:label>
    <link:label id="lab_bkv_NaturalGasHSCBasisMember_label_en-US" xlink:label="lab_bkv_NaturalGasHSCBasisMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Natural Gas, HSC Basis [Member]</link:label>
    <link:label id="lab_bkv_NaturalGasHSCBasisMember_documentation_en-US" xlink:label="lab_bkv_NaturalGasHSCBasisMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Natural Gas, HSC Basis</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_NaturalGasHSCBasisMember" xlink:href="bkv-20260630.xsd#bkv_NaturalGasHSCBasisMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_NaturalGasHSCBasisMember" xlink:to="lab_bkv_NaturalGasHSCBasisMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetRetirementObligationRevisionOfEstimate_019ed0cf-533b-7110-8668-1fcee0ddcac6_terseLabel_en-US" xlink:label="lab_us-gaap_AssetRetirementObligationRevisionOfEstimate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revision of asset retirement obligations</link:label>
    <link:label id="lab_us-gaap_AssetRetirementObligationRevisionOfEstimate_019ef544-2ca1-7aac-8c90-c05ce792ff3f_verboseLabel_en-US" xlink:label="lab_us-gaap_AssetRetirementObligationRevisionOfEstimate" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Revisions of estimates</link:label>
    <link:label id="lab_us-gaap_AssetRetirementObligationRevisionOfEstimate_label_en-US" xlink:label="lab_us-gaap_AssetRetirementObligationRevisionOfEstimate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Retirement Obligation, Revision of Estimate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetRetirementObligationRevisionOfEstimate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetRetirementObligationRevisionOfEstimate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetRetirementObligationRevisionOfEstimate" xlink:to="lab_us-gaap_AssetRetirementObligationRevisionOfEstimate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLoss_019ed0cf-533b-7417-8315-fd4447d5811b_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income attributable to BKV</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_019ed0cf-533b-7b17-b1f4-6484818fc6c4_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss) attributable to BKV</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_019ed0cf-533b-764b-8e67-e030b50b256a_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income attributable to BKV</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLoss" xlink:to="lab_us-gaap_NetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_ParentalGuaranteeCommitmentsMember_019fb3f8-a854-7e2a-b35a-13852df7a390_terseLabel_en-US" xlink:label="lab_bkv_ParentalGuaranteeCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Parental Guarantee, Commitments</link:label>
    <link:label id="lab_bkv_ParentalGuaranteeCommitmentsMember_label_en-US" xlink:label="lab_bkv_ParentalGuaranteeCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Parental Guarantee, Commitments [Member]</link:label>
    <link:label id="lab_bkv_ParentalGuaranteeCommitmentsMember_documentation_en-US" xlink:label="lab_bkv_ParentalGuaranteeCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Parental Guarantee, Commitments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_ParentalGuaranteeCommitmentsMember" xlink:href="bkv-20260630.xsd#bkv_ParentalGuaranteeCommitmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_ParentalGuaranteeCommitmentsMember" xlink:to="lab_bkv_ParentalGuaranteeCommitmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_019ed0cf-533b-712e-8034-393eb2e7bf67_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeAxis" xlink:to="lab_us-gaap_LongtermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis</link:label>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_label_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompAnalysisTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ErrCompAnalysisTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompAnalysisTextBlock" xlink:to="lab_ecd_ErrCompAnalysisTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionLocationBalanceAxis_019ed0cf-53ce-7ac3-a73c-054e68025522_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionLocationBalanceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Location, Statement of Financial Position, Balance [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionLocationBalanceAxis_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionLocationBalanceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Location, Statement of Financial Position, Balance [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfFinancialPositionLocationBalanceAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfFinancialPositionLocationBalanceAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfFinancialPositionLocationBalanceAxis" xlink:to="lab_us-gaap_StatementOfFinancialPositionLocationBalanceAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDateAxis_terseLabel_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date:</link:label>
    <link:label id="lab_ecd_RestatementDateAxis_label_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDateAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDateAxis" xlink:to="lab_ecd_RestatementDateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_ReferencePriceAxis_019ed0cf-53ce-7c12-b0d7-3e1c5b724476_terseLabel_en-US" xlink:label="lab_bkv_ReferencePriceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reference Price [Axis]</link:label>
    <link:label id="lab_bkv_ReferencePriceAxis_label_en-US" xlink:label="lab_bkv_ReferencePriceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reference Price [Axis]</link:label>
    <link:label id="lab_bkv_ReferencePriceAxis_documentation_en-US" xlink:label="lab_bkv_ReferencePriceAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reference Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_ReferencePriceAxis" xlink:href="bkv-20260630.xsd#bkv_ReferencePriceAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_ReferencePriceAxis" xlink:to="lab_bkv_ReferencePriceAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromNotesPayable_019ed0cf-533b-7240-bf03-a3c56ab9f5dc_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromNotesPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from Promissory Note</link:label>
    <link:label id="lab_us-gaap_ProceedsFromNotesPayable_label_en-US" xlink:label="lab_us-gaap_ProceedsFromNotesPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Notes Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromNotesPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromNotesPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromNotesPayable" xlink:to="lab_us-gaap_ProceedsFromNotesPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTableTextBlock_019ed0cf-53ce-702b-bb79-99bbb56748ec_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis, Unobservable Input Reconciliation</link:label>
    <link:label id="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTableTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis, Unobservable Input Reconciliation [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTableTextBlock" xlink:to="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamPropertyBeforeAccumulatedDepreciationDepletionAmortizationAndImpairment_019ed0cf-53ce-7681-848e-fb5fd0f1bdc1_terseLabel_en-US" xlink:label="lab_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamPropertyBeforeAccumulatedDepreciationDepletionAmortizationAndImpairment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Midstream assets</link:label>
    <link:label id="lab_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamPropertyBeforeAccumulatedDepreciationDepletionAmortizationAndImpairment_label_en-US" xlink:label="lab_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamPropertyBeforeAccumulatedDepreciationDepletionAmortizationAndImpairment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Oil and Gas, Successful Efforts Method, Property and Equipment, Midstream Property, before Accumulated Depreciation, Depletion, Amortization, and Impairment</link:label>
    <link:label id="lab_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamPropertyBeforeAccumulatedDepreciationDepletionAmortizationAndImpairment_documentation_en-US" xlink:label="lab_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamPropertyBeforeAccumulatedDepreciationDepletionAmortizationAndImpairment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Oil and Gas, Successful Efforts Method, Property and Equipment, Midstream Property, before Accumulated Depreciation, Depletion, Amortization, and Impairment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamPropertyBeforeAccumulatedDepreciationDepletionAmortizationAndImpairment" xlink:href="bkv-20260630.xsd#bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamPropertyBeforeAccumulatedDepreciationDepletionAmortizationAndImpairment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamPropertyBeforeAccumulatedDepreciationDepletionAmortizationAndImpairment" xlink:to="lab_bkv_OilAndGasSuccessfulEffortsMethodPropertyAndEquipmentMidstreamPropertyBeforeAccumulatedDepreciationDepletionAmortizationAndImpairment" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_BKVUpstreamMidstreamLLCMember_019ed0cf-533b-7cb5-909f-8912bd3aa865_terseLabel_en-US" xlink:label="lab_bkv_BKVUpstreamMidstreamLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">BKV Upstream Midstream, LLC</link:label>
    <link:label id="lab_bkv_BKVUpstreamMidstreamLLCMember_019ef5c9-3395-723f-8d82-55fcab49c6d7_verboseLabel_en-US" xlink:label="lab_bkv_BKVUpstreamMidstreamLLCMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Upstream/Midstream</link:label>
    <link:label id="lab_bkv_BKVUpstreamMidstreamLLCMember_label_en-US" xlink:label="lab_bkv_BKVUpstreamMidstreamLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">BKV Upstream Midstream, LLC [Member]</link:label>
    <link:label id="lab_bkv_BKVUpstreamMidstreamLLCMember_documentation_en-US" xlink:label="lab_bkv_BKVUpstreamMidstreamLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">BKV Upstream Midstream, LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_BKVUpstreamMidstreamLLCMember" xlink:href="bkv-20260630.xsd#bkv_BKVUpstreamMidstreamLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_BKVUpstreamMidstreamLLCMember" xlink:to="lab_bkv_BKVUpstreamMidstreamLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenuesAbstract_019ed0cf-53ce-7fb3-838d-0c9a723913c5_terseLabel_en-US" xlink:label="lab_us-gaap_RevenuesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenues and other operating income</link:label>
    <link:label id="lab_us-gaap_RevenuesAbstract_label_en-US" xlink:label="lab_us-gaap_RevenuesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenuesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenuesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenuesAbstract" xlink:to="lab_us-gaap_RevenuesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_EquipmentSupplyContractMember_019ed0cf-5275-7300-ac38-3a267949871f_terseLabel_en-US" xlink:label="lab_bkv_EquipmentSupplyContractMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equipment supply contract</link:label>
    <link:label id="lab_bkv_EquipmentSupplyContractMember_label_en-US" xlink:label="lab_bkv_EquipmentSupplyContractMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equipment Supply Contract [Member]</link:label>
    <link:label id="lab_bkv_EquipmentSupplyContractMember_documentation_en-US" xlink:label="lab_bkv_EquipmentSupplyContractMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equipment Supply Contract</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_EquipmentSupplyContractMember" xlink:href="bkv-20260630.xsd#bkv_EquipmentSupplyContractMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_EquipmentSupplyContractMember" xlink:to="lab_bkv_EquipmentSupplyContractMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityAbstract_019ed0cf-533b-720f-b10d-07121d822ad6_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mezzanine equity</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityAbstract_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TemporaryEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityAbstract" xlink:to="lab_us-gaap_TemporaryEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnBnftsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:to="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_PromissoryNoteMember_019ed0cf-533b-752f-9a11-e35ee8bc76a5_terseLabel_en-US" xlink:label="lab_bkv_PromissoryNoteMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Promissory Note</link:label>
    <link:label id="lab_bkv_PromissoryNoteMember_label_en-US" xlink:label="lab_bkv_PromissoryNoteMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Promissory Note [Member]</link:label>
    <link:label id="lab_bkv_PromissoryNoteMember_documentation_en-US" xlink:label="lab_bkv_PromissoryNoteMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Promissory Note</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_PromissoryNoteMember" xlink:href="bkv-20260630.xsd#bkv_PromissoryNoteMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_PromissoryNoteMember" xlink:to="lab_bkv_PromissoryNoteMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract_019ed0cf-533b-7fed-8c47-ad6f830a520f_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average number of common shares outstanding:</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract" xlink:to="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetAcquisitionTable_019ed0cf-533b-74f2-8d17-89e41b851b78_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Table]</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionTable_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetAcquisitionTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionTable" xlink:to="lab_us-gaap_AssetAcquisitionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeMember_019ed0cf-5275-710e-b042-499dd0758ddd_terseLabel_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:label id="lab_srt_RangeMember_label_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeMember" xlink:to="lab_srt_RangeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalYearFocus_019ed0cf-5275-7aef-bea9-9897f8bbab5f_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalYearFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalYearFocus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentFiscalYearFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalYearFocus" xlink:to="lab_dei_DocumentFiscalYearFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset_019ed0cf-533b-724a-875e-cd69d93374aa_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Offset Adjustments</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, Asset Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilityFairValueGrossAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:to="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts_019ed0cf-53ce-77db-968c-b14afdb8b641_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquisition-related cost, expense</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Acquisition-Related Cost, Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationAcquisitionRelatedCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:to="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward_019ed0cf-533c-7f74-b54d-42c7f9b8cd3c_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Number of Shares [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MajorCustomersAxis_019ed0cf-53ce-715b-ae83-91d63217b2e9_terseLabel_en-US" xlink:label="lab_srt_MajorCustomersAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer [Axis]</link:label>
    <link:label id="lab_srt_MajorCustomersAxis_label_en-US" xlink:label="lab_srt_MajorCustomersAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MajorCustomersAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MajorCustomersAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MajorCustomersAxis" xlink:to="lab_srt_MajorCustomersAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockValue_019ed0cf-533b-7f6c-8397-ab0e1848eb39_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, $0.01 par value; 500,000 authorized shares; 109,417 and 96,872 shares issued and outstanding as of June 30, 2026 and December 31, 2025, respectively</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_label_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockValue" xlink:to="lab_us-gaap_CommonStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_019ed0cf-533b-7d57-9b56-11898319270c_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_019ed0cf-5275-7add-8692-99bfbc2ecf41_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net share settlements, equity-based compensation</link:label>
    <link:label id="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment, Tax Withholding, Share-Based Payment Arrangement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:to="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock_019ed0cf-533c-7eda-8aec-1f9ce4856d5b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDebtInstrumentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:to="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_NaturalGasNGPLTXOKMember_019ed0cf-53ce-711f-aa1a-29d5fdf35f12_terseLabel_en-US" xlink:label="lab_bkv_NaturalGasNGPLTXOKMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">NGPL TXOK Basis</link:label>
    <link:label id="lab_bkv_NaturalGasNGPLTXOKMember_label_en-US" xlink:label="lab_bkv_NaturalGasNGPLTXOKMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Natural Gas, NGPL TXOK [Member]</link:label>
    <link:label id="lab_bkv_NaturalGasNGPLTXOKMember_documentation_en-US" xlink:label="lab_bkv_NaturalGasNGPLTXOKMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Natural Gas, NGPL TXOK</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_NaturalGasNGPLTXOKMember" xlink:href="bkv-20260630.xsd#bkv_NaturalGasNGPLTXOKMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_NaturalGasNGPLTXOKMember" xlink:to="lab_bkv_NaturalGasNGPLTXOKMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OilAndGasPropertyFullCostMethodNetAbstract_019ed0cf-533c-78f2-adde-581e937bb175_terseLabel_en-US" xlink:label="lab_us-gaap_OilAndGasPropertyFullCostMethodNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Natural gas properties and equipment</link:label>
    <link:label id="lab_us-gaap_OilAndGasPropertyFullCostMethodNetAbstract_label_en-US" xlink:label="lab_us-gaap_OilAndGasPropertyFullCostMethodNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Oil and Gas, Full Cost Method, Property and Equipment, after Accumulated Depletion [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OilAndGasPropertyFullCostMethodNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OilAndGasPropertyFullCostMethodNetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OilAndGasPropertyFullCostMethodNetAbstract" xlink:to="lab_us-gaap_OilAndGasPropertyFullCostMethodNetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditMember_019ed0cf-53ce-7160-8bed-62bdd0defe7f_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of Credit</link:label>
    <link:label id="lab_us-gaap_LineOfCreditMember_label_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditMember" xlink:to="lab_us-gaap_LineOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDeterminationDate_terseLabel_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:label id="lab_ecd_RestatementDeterminationDate_label_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDeterminationDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDeterminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDeterminationDate" xlink:to="lab_ecd_RestatementDeterminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivable_019ed0cf-53ce-78fe-bc78-3818f2f8d9f7_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Allowance for credit losses</link:label>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivable_label_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:to="lab_us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AmendmentFlag_019ed0cf-53ce-77bc-9799-26e06301e7e8_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:label id="lab_dei_AmendmentFlag_label_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_AmendmentFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AmendmentFlag" xlink:to="lab_dei_AmendmentFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesCurrentAbstract_019ed0cf-533c-7170-81fa-2385a4f97a2b_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesCurrentAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Current [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesCurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesCurrentAbstract" xlink:to="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_DerivativeAveragePricePerUnit_019ed0cf-53ce-7b96-a825-ebf669b5343a_terseLabel_en-US" xlink:label="lab_bkv_DerivativeAveragePricePerUnit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average price (in USD per unit)</link:label>
    <link:label id="lab_bkv_DerivativeAveragePricePerUnit_label_en-US" xlink:label="lab_bkv_DerivativeAveragePricePerUnit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Average Price Per Unit</link:label>
    <link:label id="lab_bkv_DerivativeAveragePricePerUnit_documentation_en-US" xlink:label="lab_bkv_DerivativeAveragePricePerUnit" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative, Average Price Per Unit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_DerivativeAveragePricePerUnit" xlink:href="bkv-20260630.xsd#bkv_DerivativeAveragePricePerUnit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_DerivativeAveragePricePerUnit" xlink:to="lab_bkv_DerivativeAveragePricePerUnit" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersDiluted_019fd7da-d0d1-742f-a355-3fe04024e608_terseLabel_en-US" xlink:label="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted (in shares)</link:label>
    <link:label id="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersDiluted_label_en-US" xlink:label="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Attributable to Majority Stockholders, Diluted</link:label>
    <link:label id="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersDiluted_documentation_en-US" xlink:label="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Attributable to Majority Stockholders, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersDiluted" xlink:href="bkv-20260630.xsd#bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersDiluted" xlink:to="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToMajorityStockholdersDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_ContractPriceToBePaidContractTerminationBeforeManufacturingPercentage_019ed0cf-53ce-7ff5-beab-f318cc9edfd0_terseLabel_en-US" xlink:label="lab_bkv_ContractPriceToBePaidContractTerminationBeforeManufacturingPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract price to be paid, contract termination, before manufacturing percentage</link:label>
    <link:label id="lab_bkv_ContractPriceToBePaidContractTerminationBeforeManufacturingPercentage_label_en-US" xlink:label="lab_bkv_ContractPriceToBePaidContractTerminationBeforeManufacturingPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract Price To Be Paid, Contract Termination, Before Manufacturing, Percentage</link:label>
    <link:label id="lab_bkv_ContractPriceToBePaidContractTerminationBeforeManufacturingPercentage_documentation_en-US" xlink:label="lab_bkv_ContractPriceToBePaidContractTerminationBeforeManufacturingPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Contract Price To Be Paid, Contract Termination, Before Manufacturing, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_ContractPriceToBePaidContractTerminationBeforeManufacturingPercentage" xlink:href="bkv-20260630.xsd#bkv_ContractPriceToBePaidContractTerminationBeforeManufacturingPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_ContractPriceToBePaidContractTerminationBeforeManufacturingPercentage" xlink:to="lab_bkv_ContractPriceToBePaidContractTerminationBeforeManufacturingPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_NaturalGasTranscoSt85Z4BasisMember_019ed0cf-53ce-7609-97ab-24c10a536e99_terseLabel_en-US" xlink:label="lab_bkv_NaturalGasTranscoSt85Z4BasisMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transco St 85 (Z4) Basis</link:label>
    <link:label id="lab_bkv_NaturalGasTranscoSt85Z4BasisMember_label_en-US" xlink:label="lab_bkv_NaturalGasTranscoSt85Z4BasisMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Natural Gas, Transco St 85 (Z4) Basis [Member]</link:label>
    <link:label id="lab_bkv_NaturalGasTranscoSt85Z4BasisMember_documentation_en-US" xlink:label="lab_bkv_NaturalGasTranscoSt85Z4BasisMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Natural Gas, Transco St 85 (Z4) Basis</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_NaturalGasTranscoSt85Z4BasisMember" xlink:href="bkv-20260630.xsd#bkv_NaturalGasTranscoSt85Z4BasisMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_NaturalGasTranscoSt85Z4BasisMember" xlink:to="lab_bkv_NaturalGasTranscoSt85Z4BasisMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueAcquisitions_019ed0cf-533b-7b3f-9653-0f62742b638d_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueAcquisitions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common stock to BPPUS</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueAcquisitions_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueAcquisitions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Acquisitions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueAcquisitions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueAcquisitions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueAcquisitions" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueAcquisitions" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote</link:label>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToNonPeoNeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:to="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetRetirementObligationLiabilitiesSettled_019ed0cf-533b-7247-8ad2-0f8a4b252e10_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AssetRetirementObligationLiabilitiesSettled" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Liabilities settled</link:label>
    <link:label id="lab_us-gaap_AssetRetirementObligationLiabilitiesSettled_label_en-US" xlink:label="lab_us-gaap_AssetRetirementObligationLiabilitiesSettled" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Retirement Obligation, Liabilities Settled</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetRetirementObligationLiabilitiesSettled" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetRetirementObligationLiabilitiesSettled"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetRetirementObligationLiabilitiesSettled" xlink:to="lab_us-gaap_AssetRetirementObligationLiabilitiesSettled" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAbstract_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_019ed0cf-533b-71c9-81f9-21635ee2ed97_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:label id="lab_dei_EntityAddressStateOrProvince_label_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressStateOrProvince"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressStateOrProvince" xlink:to="lab_dei_EntityAddressStateOrProvince" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoTotalCompAmt_label_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoTotalCompAmt" xlink:to="lab_ecd_PeoTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_019ed0cf-533b-7c0e-88fd-125ac783006a_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial assets</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsFairValueDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsFairValueDisclosureAbstract" xlink:to="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_BanpuPowerUSCorporationBPPUSMember_019ed0cf-53ce-7831-8404-3cdccc4d4584_terseLabel_en-US" xlink:label="lab_bkv_BanpuPowerUSCorporationBPPUSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">BPPUS</link:label>
    <link:label id="lab_bkv_BanpuPowerUSCorporationBPPUSMember_label_en-US" xlink:label="lab_bkv_BanpuPowerUSCorporationBPPUSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banpu Power US Corporation ("BPPUS") [Member]</link:label>
    <link:label id="lab_bkv_BanpuPowerUSCorporationBPPUSMember_documentation_en-US" xlink:label="lab_bkv_BanpuPowerUSCorporationBPPUSMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Banpu Power US Corporation ("BPPUS")</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_BanpuPowerUSCorporationBPPUSMember" xlink:href="bkv-20260630.xsd#bkv_BanpuPowerUSCorporationBPPUSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_BanpuPowerUSCorporationBPPUSMember" xlink:to="lab_bkv_BanpuPowerUSCorporationBPPUSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentExpenditureAdditionToLongLivedAssets_019ed0cf-53ce-7f22-bec1-ea63a6df0fa4_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentExpenditureAdditionToLongLivedAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital expenditures</link:label>
    <link:label id="lab_us-gaap_SegmentExpenditureAdditionToLongLivedAssets_label_en-US" xlink:label="lab_us-gaap_SegmentExpenditureAdditionToLongLivedAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Long-Lived Asset, Expenditure for Addition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentExpenditureAdditionToLongLivedAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentExpenditureAdditionToLongLivedAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentExpenditureAdditionToLongLivedAssets" xlink:to="lab_us-gaap_SegmentExpenditureAdditionToLongLivedAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_019ed0cf-53ce-77e1-89c3-820f66dd86ef_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_019ed0cf-53ce-7493-b28c-e4ab83b667c0_verboseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Basic weighted average common shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:to="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_LongTermDebtPrincipalValueCurrentMaturities_019ed0cf-53ce-7613-b2c4-66f302ebdf5d_negatedTerseLabel_en-US" xlink:label="lab_bkv_LongTermDebtPrincipalValueCurrentMaturities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: current portion of long-term debt</link:label>
    <link:label id="lab_bkv_LongTermDebtPrincipalValueCurrentMaturities_label_en-US" xlink:label="lab_bkv_LongTermDebtPrincipalValueCurrentMaturities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Principal Value, Current Maturities</link:label>
    <link:label id="lab_bkv_LongTermDebtPrincipalValueCurrentMaturities_documentation_en-US" xlink:label="lab_bkv_LongTermDebtPrincipalValueCurrentMaturities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Principal Value, Current Maturities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_LongTermDebtPrincipalValueCurrentMaturities" xlink:href="bkv-20260630.xsd#bkv_LongTermDebtPrincipalValueCurrentMaturities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_LongTermDebtPrincipalValueCurrentMaturities" xlink:to="lab_bkv_LongTermDebtPrincipalValueCurrentMaturities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_019ed0cf-53ce-79ca-afa3-c93a888f304e_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetAcquisitionConsiderationTransferred_019ed0cf-533c-7cd6-b63e-8f79a6cb578b_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset acquisition, consideration transferred</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionConsiderationTransferred_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Consideration Transferred</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetAcquisitionConsiderationTransferred"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:to="lab_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMnpiDiscTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:to="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_019ed0cf-53ce-7c01-be01-208f708884f0_terseLabel_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_label_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementClassOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementClassOfStockAxis" xlink:to="lab_us-gaap_StatementClassOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_019ed0cf-533c-756c-a142-3792c91dba9e_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Vested (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Vested in Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_019ed0cf-533b-79d9-b97e-9ded4f7839d7_terseLabel_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basis of Presentation of the Unaudited Condensed Consolidated Financial Statements</link:label>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Basis of Accounting, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BasisOfAccountingPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:to="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeNonmonetaryNotionalAmount_019ed0cf-5275-796e-88d1-a84d4ed3daae_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeNonmonetaryNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative, nonmonetary notional amount</link:label>
    <link:label id="lab_us-gaap_DerivativeNonmonetaryNotionalAmount_label_en-US" xlink:label="lab_us-gaap_DerivativeNonmonetaryNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Nonmonetary Notional Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeNonmonetaryNotionalAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeNonmonetaryNotionalAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeNonmonetaryNotionalAmount" xlink:to="lab_us-gaap_DerivativeNonmonetaryNotionalAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_019fd772-a789-744a-aac3-3bc376f430a9_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">BKV-BPP Power net income (loss) attributable to common shareholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_019ed0cf-533b-7ffe-b578-30c327b1f9ca_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income including accretion of Class B Units to redemption value</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableGross_019ed0cf-533c-706c-abd2-9e2566bd09c6_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableGross_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, before Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableGross" xlink:to="lab_us-gaap_AccountsReceivableGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerMember_019ed0cf-53ce-7276-b351-9cf8f20c6f68_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer Benchmark</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerMember_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer Benchmark [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromContractWithCustomerMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerMember" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReceivableTypeDomain_019ed0cf-53cf-7c4c-a193-507d23b7c98e_terseLabel_en-US" xlink:label="lab_us-gaap_ReceivableTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivable [Domain]</link:label>
    <link:label id="lab_us-gaap_ReceivableTypeDomain_label_en-US" xlink:label="lab_us-gaap_ReceivableTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivable [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivableTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReceivableTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReceivableTypeDomain" xlink:to="lab_us-gaap_ReceivableTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_019ed0cf-533b-707d-88bb-8d2b29b79279_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum credit commitment</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_019ed0cf-533b-7c06-92b4-8cab4be4ccb0_verboseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Maximum borrowing capacity</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtCurrent_019ed0cf-5275-739a-ac08-bff9060f5617_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total current portion of long-term debt, net</link:label>
    <link:label id="lab_us-gaap_LongTermDebtCurrent_label_en-US" xlink:label="lab_us-gaap_LongTermDebtCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Current Maturities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtCurrent" xlink:to="lab_us-gaap_LongTermDebtCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToCommonStockholdersDiluted_019fd7d9-f788-7526-8765-4216aa8da584_terseLabel_en-US" xlink:label="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted (in shares)</link:label>
    <link:label id="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToCommonStockholdersDiluted_label_en-US" xlink:label="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Attributable to Common Stockholders, Diluted</link:label>
    <link:label id="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToCommonStockholdersDiluted_documentation_en-US" xlink:label="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Attributable to Common Stockholders, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToCommonStockholdersDiluted" xlink:href="bkv-20260630.xsd#bkv_WeightedAverageNumberOfSharesOutstandingAttributableToCommonStockholdersDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToCommonStockholdersDiluted" xlink:to="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToCommonStockholdersDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_EquipmentSupplyContractOneMember_019fa909-28c3-7435-b4f3-29e9df4a374d_terseLabel_en-US" xlink:label="lab_bkv_EquipmentSupplyContractOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract One</link:label>
    <link:label id="lab_bkv_EquipmentSupplyContractOneMember_label_en-US" xlink:label="lab_bkv_EquipmentSupplyContractOneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equipment Supply Contract One [Member]</link:label>
    <link:label id="lab_bkv_EquipmentSupplyContractOneMember_documentation_en-US" xlink:label="lab_bkv_EquipmentSupplyContractOneMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equipment Supply Contract One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_EquipmentSupplyContractOneMember" xlink:href="bkv-20260630.xsd#bkv_EquipmentSupplyContractOneMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_EquipmentSupplyContractOneMember" xlink:to="lab_bkv_EquipmentSupplyContractOneMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_019ed0cf-53ce-79d4-a369-3df9ce7390ab_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounting Pronouncements Not Yet Adopted</link:label>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LandMember_019ed0cf-53ce-7c8d-801f-85905a1912dc_terseLabel_en-US" xlink:label="lab_us-gaap_LandMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Land</link:label>
    <link:label id="lab_us-gaap_LandMember_label_en-US" xlink:label="lab_us-gaap_LandMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Land [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LandMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LandMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LandMember" xlink:to="lab_us-gaap_LandMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncontrollingInterestMember_019ed0cf-53ce-7d24-9dbf-c4c0f7b7106e_terseLabel_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest</link:label>
    <link:label id="lab_us-gaap_NoncontrollingInterestMember_label_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncontrollingInterestMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NoncontrollingInterestMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncontrollingInterestMember" xlink:to="lab_us-gaap_NoncontrollingInterestMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_TempleTermLoanFacilityMember_019ed0cf-5275-7196-b9e2-49f1af8bd98f_terseLabel_en-US" xlink:label="lab_bkv_TempleTermLoanFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Temple Term Loan Facility</link:label>
    <link:label id="lab_bkv_TempleTermLoanFacilityMember_label_en-US" xlink:label="lab_bkv_TempleTermLoanFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temple Term Loan Facility [Member]</link:label>
    <link:label id="lab_bkv_TempleTermLoanFacilityMember_documentation_en-US" xlink:label="lab_bkv_TempleTermLoanFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temple Term Loan Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_TempleTermLoanFacilityMember" xlink:href="bkv-20260630.xsd#bkv_TempleTermLoanFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_TempleTermLoanFacilityMember" xlink:to="lab_bkv_TempleTermLoanFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetAcquisitionTextBlock_019ed0cf-533b-7dca-9edc-6dbb3740c012_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquisition</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionTextBlock_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetAcquisitionTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionTextBlock" xlink:to="lab_us-gaap_AssetAcquisitionTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebt_019ed0cf-53ce-7053-9d0f-913248a21e03_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total debt, net</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_019ed0cf-53ce-76db-8381-8cf649064b4d_totalLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Long-term debt, net</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_label_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebt" xlink:to="lab_us-gaap_LongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues_019ed0cf-533c-7bcb-9362-7fc78e1b6868_terseLabel_en-US" xlink:label="lab_bkv_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Temporary equity, stock issued during period, shares, new issues</link:label>
    <link:label id="lab_bkv_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues_label_en-US" xlink:label="lab_bkv_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Stock Issued During Period, Shares, New Issues</link:label>
    <link:label id="lab_bkv_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues_documentation_en-US" xlink:label="lab_bkv_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Stock Issued During Period, Shares, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues" xlink:href="bkv-20260630.xsd#bkv_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues" xlink:to="lab_bkv_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_019ed0cf-533b-7f2c-8439-53ee7e938931_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash used in investing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in Compensation Table</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in the Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:to="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_SecurityExchangeName_019ed0cf-533b-7136-aa6c-ab0e9cd052a1_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:label id="lab_dei_SecurityExchangeName_label_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_SecurityExchangeName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_SecurityExchangeName" xlink:to="lab_dei_SecurityExchangeName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_019ed0cf-53ce-73f3-878a-ae91be7a37cc_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ValuationTechniqueAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueAxis" xlink:to="lab_us-gaap_ValuationTechniqueAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPayableCurrent_019ed0cf-533b-747f-a7a7-4314a86d690e_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest payable</link:label>
    <link:label id="lab_us-gaap_InterestPayableCurrent_label_en-US" xlink:label="lab_us-gaap_InterestPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPayableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestPayableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPayableCurrent" xlink:to="lab_us-gaap_InterestPayableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTextBlock_019ed0cf-533b-74e4-972e-435b65e91a5b_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTextBlock_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_PA_019ed0cf-53ce-7f39-8ca0-5e72de07fcce_terseLabel_en-US" xlink:label="lab_stpr_PA" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pennsylvania</link:label>
    <link:label id="lab_stpr_PA_label_en-US" xlink:label="lab_stpr_PA" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PENNSYLVANIA</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_PA" xlink:href="https://xbrl.sec.gov/stpr/2026/stpr-2026.xsd#stpr_PA"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_PA" xlink:to="lab_stpr_PA" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryIndName" xlink:to="lab_ecd_OutstandingRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgHowMnpiCnsdrdTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:to="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_NaturalGasDerivativesMember_019ed0cf-53ce-737a-bb2a-90a19e6e6fd0_terseLabel_en-US" xlink:label="lab_bkv_NaturalGasDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Natural gas derivatives</link:label>
    <link:label id="lab_bkv_NaturalGasDerivativesMember_label_en-US" xlink:label="lab_bkv_NaturalGasDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Natural Gas Derivatives [Member]</link:label>
    <link:label id="lab_bkv_NaturalGasDerivativesMember_documentation_en-US" xlink:label="lab_bkv_NaturalGasDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Natural Gas Derivatives</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_NaturalGasDerivativesMember" xlink:href="bkv-20260630.xsd#bkv_NaturalGasDerivativesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_NaturalGasDerivativesMember" xlink:to="lab_bkv_NaturalGasDerivativesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_PaymentsForDepositOnPropertyPlantAndEquipment_019ed0cf-53ce-7089-a828-39dcf33d0145_negatedTerseLabel_en-US" xlink:label="lab_bkv_PaymentsForDepositOnPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Deposits on fixed asset purchases</link:label>
    <link:label id="lab_bkv_PaymentsForDepositOnPropertyPlantAndEquipment_label_en-US" xlink:label="lab_bkv_PaymentsForDepositOnPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments For Deposit On Property, Plant, And Equipment</link:label>
    <link:label id="lab_bkv_PaymentsForDepositOnPropertyPlantAndEquipment_documentation_en-US" xlink:label="lab_bkv_PaymentsForDepositOnPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments For Deposit On Property, Plant, And Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_PaymentsForDepositOnPropertyPlantAndEquipment" xlink:href="bkv-20260630.xsd#bkv_PaymentsForDepositOnPropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_PaymentsForDepositOnPropertyPlantAndEquipment" xlink:to="lab_bkv_PaymentsForDepositOnPropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_SegmentGeographicalDomain_019ed0cf-533b-7dff-a4ad-1fbabe42eba7_terseLabel_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographical [Domain]</link:label>
    <link:label id="lab_srt_SegmentGeographicalDomain_label_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_SegmentGeographicalDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_SegmentGeographicalDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_SegmentGeographicalDomain" xlink:to="lab_srt_SegmentGeographicalDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_A2027SwapMember_019ed0cf-53ce-7b07-a04a-7d5878bc2da3_terseLabel_en-US" xlink:label="lab_bkv_A2027SwapMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027 Swap</link:label>
    <link:label id="lab_bkv_A2027SwapMember_label_en-US" xlink:label="lab_bkv_A2027SwapMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2027 Swap [Member]</link:label>
    <link:label id="lab_bkv_A2027SwapMember_documentation_en-US" xlink:label="lab_bkv_A2027SwapMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2027 Swap</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_A2027SwapMember" xlink:href="bkv-20260630.xsd#bkv_A2027SwapMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_A2027SwapMember" xlink:to="lab_bkv_A2027SwapMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year</link:label>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_label_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:to="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnAdjsPrrSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:to="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UtilitiesOperatingExpensePurchasedPower_019ed0cf-5275-71f8-ad4a-8ef1461d4803_terseLabel_en-US" xlink:label="lab_us-gaap_UtilitiesOperatingExpensePurchasedPower" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchased power</link:label>
    <link:label id="lab_us-gaap_UtilitiesOperatingExpensePurchasedPower_label_en-US" xlink:label="lab_us-gaap_UtilitiesOperatingExpensePurchasedPower" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Utilities Operating Expense, Purchased Power</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UtilitiesOperatingExpensePurchasedPower" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UtilitiesOperatingExpensePurchasedPower"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UtilitiesOperatingExpensePurchasedPower" xlink:to="lab_us-gaap_UtilitiesOperatingExpensePurchasedPower" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_DerivativeNumberOfCounterparties_019ed0cf-533b-7f41-9a7d-b5ce79c5698c_terseLabel_en-US" xlink:label="lab_bkv_DerivativeNumberOfCounterparties" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of counterparties</link:label>
    <link:label id="lab_bkv_DerivativeNumberOfCounterparties_label_en-US" xlink:label="lab_bkv_DerivativeNumberOfCounterparties" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Number Of Counterparties</link:label>
    <link:label id="lab_bkv_DerivativeNumberOfCounterparties_documentation_en-US" xlink:label="lab_bkv_DerivativeNumberOfCounterparties" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative, Number Of Counterparties</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_DerivativeNumberOfCounterparties" xlink:href="bkv-20260630.xsd#bkv_DerivativeNumberOfCounterparties"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_DerivativeNumberOfCounterparties" xlink:to="lab_bkv_DerivativeNumberOfCounterparties" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnDerivatives_019ed0cf-53ce-7f0d-a5a4-9b06e7e30447_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnDerivatives" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Unrealized (gains) losses on derivatives, net</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnDerivatives_label_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnDerivatives" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) on Derivatives</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrealizedGainLossOnDerivatives" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnrealizedGainLossOnDerivatives"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrealizedGainLossOnDerivatives" xlink:to="lab_us-gaap_UnrealizedGainLossOnDerivatives" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByParent_019ed0cf-533b-755a-ab5e-91a3dba16c12_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage owned by parent</link:label>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByParent_label_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary, Ownership Percentage, Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterestOwnershipPercentageByParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:to="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_019ed0cf-5275-7cf4-8bf7-87fa19854096_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term debt, gross</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentCarryingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:to="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_AssetAcquisitionVotingEquityInterestAcquiredPercentage_019ed0cf-53ce-7f87-a22e-159aee28f8d1_terseLabel_en-US" xlink:label="lab_bkv_AssetAcquisitionVotingEquityInterestAcquiredPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Voting equity interest acquired, percentage</link:label>
    <link:label id="lab_bkv_AssetAcquisitionVotingEquityInterestAcquiredPercentage_label_en-US" xlink:label="lab_bkv_AssetAcquisitionVotingEquityInterestAcquiredPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Voting Equity Interest Acquired, Percentage</link:label>
    <link:label id="lab_bkv_AssetAcquisitionVotingEquityInterestAcquiredPercentage_documentation_en-US" xlink:label="lab_bkv_AssetAcquisitionVotingEquityInterestAcquiredPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Voting Equity Interest Acquired, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_AssetAcquisitionVotingEquityInterestAcquiredPercentage" xlink:href="bkv-20260630.xsd#bkv_AssetAcquisitionVotingEquityInterestAcquiredPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_AssetAcquisitionVotingEquityInterestAcquiredPercentage" xlink:to="lab_bkv_AssetAcquisitionVotingEquityInterestAcquiredPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingRecoveryCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryCompAmt" xlink:to="lab_ecd_OutstandingRecoveryCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_IndividualAxis_terseLabel_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Individual:</link:label>
    <link:label id="lab_ecd_IndividualAxis_label_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Individual [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_IndividualAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_IndividualAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_IndividualAxis" xlink:to="lab_ecd_IndividualAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_019ed0cf-53ce-7b0a-89ed-47f709e53e9e_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Voting equity interest acquired, percentage</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Voting Equity Interest Acquired, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:to="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019ed0cf-533b-72d7-b741-88c0ba16fbd5_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019ed0cf-533b-7570-bd0a-7b44f91637da_totalLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Diluted weighted average of common shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueLineItems_019ed0cf-533c-71d0-9e6d-12bde0c535a0_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Line Items]</link:label>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueLineItems_label_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisaggregationOfRevenueLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisaggregationOfRevenueLineItems" xlink:to="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_019ed0cf-533b-79b5-8352-0af3b4630b10_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_label_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityEmergingGrowthCompany" xlink:to="lab_dei_EntityEmergingGrowthCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_terseLabel_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change</link:label>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_label_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_UndrlygSecurityMktPriceChngPct"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:to="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_019ed0cf-53ce-7b9c-ab55-1f035c2c8cc4_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:to="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_LongTermDebtMaturityAfterYearFour_019ed0cf-53ce-7cc5-a6b4-b387af8419e7_terseLabel_en-US" xlink:label="lab_bkv_LongTermDebtMaturityAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_bkv_LongTermDebtMaturityAfterYearFour_label_en-US" xlink:label="lab_bkv_LongTermDebtMaturityAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, After Year Four</link:label>
    <link:label id="lab_bkv_LongTermDebtMaturityAfterYearFour_documentation_en-US" xlink:label="lab_bkv_LongTermDebtMaturityAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, After Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_LongTermDebtMaturityAfterYearFour" xlink:href="bkv-20260630.xsd#bkv_LongTermDebtMaturityAfterYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_LongTermDebtMaturityAfterYearFour" xlink:to="lab_bkv_LongTermDebtMaturityAfterYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_PhysicalPowerPurchasedMember_019ed0cf-53ce-7fe2-b92f-eacc0f56f264_terseLabel_en-US" xlink:label="lab_bkv_PhysicalPowerPurchasedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Physical power purchased</link:label>
    <link:label id="lab_bkv_PhysicalPowerPurchasedMember_label_en-US" xlink:label="lab_bkv_PhysicalPowerPurchasedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Physical Power Purchased [Member]</link:label>
    <link:label id="lab_bkv_PhysicalPowerPurchasedMember_documentation_en-US" xlink:label="lab_bkv_PhysicalPowerPurchasedMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Physical Power Purchased</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_PhysicalPowerPurchasedMember" xlink:href="bkv-20260630.xsd#bkv_PhysicalPowerPurchasedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_PhysicalPowerPurchasedMember" xlink:to="lab_bkv_PhysicalPowerPurchasedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeLiability_019ed0cf-53ce-7505-ba97-d23d711539ca_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Gross Amounts of Assets and Liabilities</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeLiability_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, before Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeFairValueOfDerivativeLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:to="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerAbstract_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromContractWithCustomerAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_PurchaserOneMember_019ed0cf-53ce-73a1-be5d-801e23a3f005_terseLabel_en-US" xlink:label="lab_bkv_PurchaserOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchaser One</link:label>
    <link:label id="lab_bkv_PurchaserOneMember_label_en-US" xlink:label="lab_bkv_PurchaserOneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Purchaser One [Member]</link:label>
    <link:label id="lab_bkv_PurchaserOneMember_documentation_en-US" xlink:label="lab_bkv_PurchaserOneMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Purchaser One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_PurchaserOneMember" xlink:href="bkv-20260630.xsd#bkv_PurchaserOneMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_PurchaserOneMember" xlink:to="lab_bkv_PurchaserOneMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_CarbonCaptureUtilizationAndSequestrationMember_019ed0cf-53ce-7182-835b-13c514347ead_terseLabel_en-US" xlink:label="lab_bkv_CarbonCaptureUtilizationAndSequestrationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carbon capture, utilization, and sequestration</link:label>
    <link:label id="lab_bkv_CarbonCaptureUtilizationAndSequestrationMember_label_en-US" xlink:label="lab_bkv_CarbonCaptureUtilizationAndSequestrationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Carbon Capture, Utilization, And Sequestration [Member]</link:label>
    <link:label id="lab_bkv_CarbonCaptureUtilizationAndSequestrationMember_documentation_en-US" xlink:label="lab_bkv_CarbonCaptureUtilizationAndSequestrationMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Carbon Capture, Utilization, And Sequestration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_CarbonCaptureUtilizationAndSequestrationMember" xlink:href="bkv-20260630.xsd#bkv_CarbonCaptureUtilizationAndSequestrationMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_CarbonCaptureUtilizationAndSequestrationMember" xlink:to="lab_bkv_CarbonCaptureUtilizationAndSequestrationMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCashCurrent_019ed0cf-533b-73ec-a85d-7d6d433ba78e_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted cash</link:label>
    <link:label id="lab_us-gaap_RestrictedCashCurrent_label_en-US" xlink:label="lab_us-gaap_RestrictedCashCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestrictedCashCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCashCurrent" xlink:to="lab_us-gaap_RestrictedCashCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockCommonMember_019ed0cf-533b-764d-90a6-ec72d9680f07_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonMember_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TreasuryStockCommonMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockCommonMember" xlink:to="lab_us-gaap_TreasuryStockCommonMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LettersOfCreditOutstandingAmount_019ed0cf-5275-788e-a7a4-885e67c18762_terseLabel_en-US" xlink:label="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding letters of credit</link:label>
    <link:label id="lab_us-gaap_LettersOfCreditOutstandingAmount_label_en-US" xlink:label="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Letters of Credit Outstanding, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LettersOfCreditOutstandingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LettersOfCreditOutstandingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LettersOfCreditOutstandingAmount" xlink:to="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement_019ed0cf-533b-7ea4-a44b-6744a6da4e03_totalLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Amounts of Assets and Liabilities</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, after Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement" xlink:to="lab_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:to="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_019ed0cf-533b-7837-904c-cea810d9b53d_totalLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_MeasurementInputPowerVolatilityMember_019ed0cf-53ce-7a59-ad04-956b0e512ec8_terseLabel_en-US" xlink:label="lab_bkv_MeasurementInputPowerVolatilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Power volatility (non-liquid hours)</link:label>
    <link:label id="lab_bkv_MeasurementInputPowerVolatilityMember_label_en-US" xlink:label="lab_bkv_MeasurementInputPowerVolatilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Power Volatility [Member]</link:label>
    <link:label id="lab_bkv_MeasurementInputPowerVolatilityMember_documentation_en-US" xlink:label="lab_bkv_MeasurementInputPowerVolatilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Power Volatility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_MeasurementInputPowerVolatilityMember" xlink:href="bkv-20260630.xsd#bkv_MeasurementInputPowerVolatilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_MeasurementInputPowerVolatilityMember" xlink:to="lab_bkv_MeasurementInputPowerVolatilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_PurchaserTwoMember_019ed0cf-533c-7f92-a523-2305219a6b7c_terseLabel_en-US" xlink:label="lab_bkv_PurchaserTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchaser Two</link:label>
    <link:label id="lab_bkv_PurchaserTwoMember_label_en-US" xlink:label="lab_bkv_PurchaserTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Purchaser Two [Member]</link:label>
    <link:label id="lab_bkv_PurchaserTwoMember_documentation_en-US" xlink:label="lab_bkv_PurchaserTwoMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Purchaser Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_PurchaserTwoMember" xlink:href="bkv-20260630.xsd#bkv_PurchaserTwoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_PurchaserTwoMember" xlink:to="lab_bkv_PurchaserTwoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssetsAndLiabilitiesNetAbstract_019ed0cf-533b-74ac-b93d-9583d3f4cf92_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssetsAndLiabilitiesNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in operating assets and liabilities:</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssetsAndLiabilitiesNetAbstract_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssetsAndLiabilitiesNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Assets and Liabilities, Net [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssetsAndLiabilitiesNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOtherOperatingAssetsAndLiabilitiesNetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssetsAndLiabilitiesNetAbstract" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssetsAndLiabilitiesNetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_InterestPayableYearFour_019ed0cf-533b-79f2-a2b5-236dbf5fb30d_terseLabel_en-US" xlink:label="lab_bkv_InterestPayableYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_bkv_InterestPayableYearFour_label_en-US" xlink:label="lab_bkv_InterestPayableYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable, Year Four</link:label>
    <link:label id="lab_bkv_InterestPayableYearFour_documentation_en-US" xlink:label="lab_bkv_InterestPayableYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Payable, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_InterestPayableYearFour" xlink:href="bkv-20260630.xsd#bkv_InterestPayableYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_InterestPayableYearFour" xlink:to="lab_bkv_InterestPayableYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_019ed0cf-533c-749d-b003-f2074fb780fb_periodStartLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Unvested RSUs, beginning balance (in USD per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_019ed0cf-533c-7064-a0ca-1fb677d0c5fc_periodEndLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Unvested RSUs, ending balance (in USD per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_terseLabel_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Executive Categories</link:label>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_label_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Executive Categories [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllExecutiveCategoriesMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllExecutiveCategoriesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllExecutiveCategoriesMember" xlink:to="lab_ecd_AllExecutiveCategoriesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueDomain_019ed0cf-53cf-7ba7-9263-64d7a87e2646_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Domain]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueDomain_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ValuationTechniqueDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueDomain" xlink:to="lab_us-gaap_ValuationTechniqueDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_A2024EquityAndIncentiveCompensationPlanMember_019ed0cf-533b-7309-a640-1e431289737a_terseLabel_en-US" xlink:label="lab_bkv_A2024EquityAndIncentiveCompensationPlanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2024 Equity and Incentive Compensation Plan</link:label>
    <link:label id="lab_bkv_A2024EquityAndIncentiveCompensationPlanMember_label_en-US" xlink:label="lab_bkv_A2024EquityAndIncentiveCompensationPlanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2024 Equity And Incentive Compensation Plan [Member]</link:label>
    <link:label id="lab_bkv_A2024EquityAndIncentiveCompensationPlanMember_documentation_en-US" xlink:label="lab_bkv_A2024EquityAndIncentiveCompensationPlanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2024 Equity And Incentive Compensation Plan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_A2024EquityAndIncentiveCompensationPlanMember" xlink:href="bkv-20260630.xsd#bkv_A2024EquityAndIncentiveCompensationPlanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_A2024EquityAndIncentiveCompensationPlanMember" xlink:to="lab_bkv_A2024EquityAndIncentiveCompensationPlanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAssetRetirementObligationsTableTextBlock_019ed0cf-5275-7433-9f7a-890e2d16f8fa_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAssetRetirementObligationsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Asset Retirement Obligations</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAssetRetirementObligationsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAssetRetirementObligationsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Asset Retirement Obligations [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAssetRetirementObligationsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAssetRetirementObligationsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAssetRetirementObligationsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfAssetRetirementObligationsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsSvcCstMember" xlink:to="lab_ecd_PnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityCommitmentFeeAmount_019ed0cf-533b-7e43-8d57-f2b9ff15f3b3_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityCommitmentFeeAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitment fee amount</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityCommitmentFeeAmount_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityCommitmentFeeAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Commitment Fee Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityCommitmentFeeAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityCommitmentFeeAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityCommitmentFeeAmount" xlink:to="lab_us-gaap_LineOfCreditFacilityCommitmentFeeAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipTable_019ed0cf-53ce-71e5-926e-fa3a19e731cb_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsidiary of LLC or LP [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary of LLC or LP [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfSubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipTable" xlink:to="lab_us-gaap_ScheduleOfSubsidiaryOfLimitedLiabilityCompanyOrLimitedPartnershipTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_019ed0cf-533b-7af7-b4b7-2682faa1fc0d_terseLabel_en-US" xlink:label="lab_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling interest</link:label>
    <link:label id="lab_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_019ed0cf-533b-7b55-9c42-f5926eb44d6c_periodStartLabel_en-US" xlink:label="lab_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance, Mezzanine Equity</link:label>
    <link:label id="lab_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_019ed0cf-533b-7bf7-b416-9ffe52ff6534_periodEndLabel_en-US" xlink:label="lab_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance, Mezzanine Equity</link:label>
    <link:label id="lab_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_label_en-US" xlink:label="lab_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Redeemable Noncontrolling Interest, Equity, Carrying Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount" xlink:to="lab_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetAcquisitionDomain_019ed0cf-5275-7a5d-8e55-506987e54c7d_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Domain]</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionDomain_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetAcquisitionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionDomain" xlink:to="lab_us-gaap_AssetAcquisitionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractualObligationDueInFourthYear_019ed0cf-5275-77db-abbb-7a562b551598_totalLabel_en-US" xlink:label="lab_us-gaap_ContractualObligationDueInFourthYear" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_ContractualObligationDueInFourthYear_label_en-US" xlink:label="lab_us-gaap_ContractualObligationDueInFourthYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contractual Obligation, to be Paid, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractualObligationDueInFourthYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractualObligationDueInFourthYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractualObligationDueInFourthYear" xlink:to="lab_us-gaap_ContractualObligationDueInFourthYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_019ed0cf-533b-70db-8e47-8871d82ebaa9_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Earnings Per Share, Basic and Diluted</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Earnings Per Share, Basic and Diluted [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureAbstract" xlink:to="lab_us-gaap_DebtDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_019ed0cf-533b-7c53-a1d9-e835e8bc6c1c_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reportable Segment</link:label>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:to="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MinimumMember_019ed0cf-53ce-7cec-b5f1-0297e0f2ce94_terseLabel_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum</link:label>
    <link:label id="lab_srt_MinimumMember_label_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Minimum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MinimumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MinimumMember" xlink:to="lab_srt_MinimumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_019ed0cf-533b-70dd-9046-41bdbcf8f41b_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAbstract" xlink:to="lab_us-gaap_LiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTableTextBlock_019ed0cf-5275-7acf-bf9e-874a8b8a26e2_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue</link:label>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTableTextBlock_label_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisaggregationOfRevenueTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:to="lab_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfIncomeLocationBalanceAxis_019ed0cf-533b-7fc8-9031-3fe7b8c84940_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Location, Statement of Income, Balance [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementOfIncomeLocationBalanceAxis_label_en-US" xlink:label="lab_us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Location, Statement of Income, Balance [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfIncomeLocationBalanceAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:to="lab_us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_ModificationOfLeaseContracts_019ed0cf-533b-78ff-b2b4-2b81fb2c0610_terseLabel_en-US" xlink:label="lab_bkv_ModificationOfLeaseContracts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Modification of lease contracts</link:label>
    <link:label id="lab_bkv_ModificationOfLeaseContracts_label_en-US" xlink:label="lab_bkv_ModificationOfLeaseContracts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Modification Of Lease Contracts</link:label>
    <link:label id="lab_bkv_ModificationOfLeaseContracts_documentation_en-US" xlink:label="lab_bkv_ModificationOfLeaseContracts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Modification Of Lease Contracts</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_ModificationOfLeaseContracts" xlink:href="bkv-20260630.xsd#bkv_ModificationOfLeaseContracts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_ModificationOfLeaseContracts" xlink:to="lab_bkv_ModificationOfLeaseContracts" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonRule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:to="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionLineItems_019ed0cf-533b-7673-a6e3-ecd35098b846_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Line Items]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionLineItems_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems" xlink:to="lab_us-gaap_BusinessAcquisitionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts_019fb3a3-5d5d-74a0-a583-70712d779c41_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Additional offering costs</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustments to Additional Paid in Capital, Stock Issued, Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts" xlink:to="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalStockIssuedIssuanceCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_NaturalGasLiquidsNGLDerivativesMember_019ed0cf-533b-74b0-9e20-aa6b54dc2420_terseLabel_en-US" xlink:label="lab_bkv_NaturalGasLiquidsNGLDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">NGL derivatives</link:label>
    <link:label id="lab_bkv_NaturalGasLiquidsNGLDerivativesMember_label_en-US" xlink:label="lab_bkv_NaturalGasLiquidsNGLDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Natural Gas Liquids (NGL) Derivatives [Member]</link:label>
    <link:label id="lab_bkv_NaturalGasLiquidsNGLDerivativesMember_documentation_en-US" xlink:label="lab_bkv_NaturalGasLiquidsNGLDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Natural Gas Liquids (NGL) Derivatives</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_NaturalGasLiquidsNGLDerivativesMember" xlink:href="bkv-20260630.xsd#bkv_NaturalGasLiquidsNGLDerivativesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_NaturalGasLiquidsNGLDerivativesMember" xlink:to="lab_bkv_NaturalGasLiquidsNGLDerivativesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_MeasurementInputCommodityPriceCorrelationMember_019ed0cf-5275-7460-851f-e25fc86f81e1_terseLabel_en-US" xlink:label="lab_bkv_MeasurementInputCommodityPriceCorrelationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Power and natural gas price correlation</link:label>
    <link:label id="lab_bkv_MeasurementInputCommodityPriceCorrelationMember_label_en-US" xlink:label="lab_bkv_MeasurementInputCommodityPriceCorrelationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Commodity Price Correlation [Member]</link:label>
    <link:label id="lab_bkv_MeasurementInputCommodityPriceCorrelationMember_documentation_en-US" xlink:label="lab_bkv_MeasurementInputCommodityPriceCorrelationMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Commodity Price Correlation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_MeasurementInputCommodityPriceCorrelationMember" xlink:href="bkv-20260630.xsd#bkv_MeasurementInputCommodityPriceCorrelationMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_MeasurementInputCommodityPriceCorrelationMember" xlink:to="lab_bkv_MeasurementInputCommodityPriceCorrelationMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_LeaseOperatingAndWorkover_019ed0cf-53ce-79be-83fe-c5cad4a96e65_terseLabel_en-US" xlink:label="lab_bkv_LeaseOperatingAndWorkover" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease operating and workover</link:label>
    <link:label id="lab_bkv_LeaseOperatingAndWorkover_label_en-US" xlink:label="lab_bkv_LeaseOperatingAndWorkover" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease Operating And Workover</link:label>
    <link:label id="lab_bkv_LeaseOperatingAndWorkover_documentation_en-US" xlink:label="lab_bkv_LeaseOperatingAndWorkover" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lease Operating And Workover</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_LeaseOperatingAndWorkover" xlink:href="bkv-20260630.xsd#bkv_LeaseOperatingAndWorkover"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_LeaseOperatingAndWorkover" xlink:to="lab_bkv_LeaseOperatingAndWorkover" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_019ed0cf-533b-7cb4-a500-afb794ab6732_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesAuthorized" xlink:to="lab_us-gaap_CommonStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_019ed0cf-533b-7613-b0d6-b11c63d35c8e_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">IPO shares (in shares)</link:label>
    <link:label id="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_label_en-US" xlink:label="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Number of Shares Issued in Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:to="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock_019ed0cf-53ce-7253-ba5a-665d3e7316e2_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Restricted Stock Unit Activity</link:label>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Restricted Stock Unit, Activity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardExrcPrice_terseLabel_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise Price</link:label>
    <link:label id="lab_ecd_AwardExrcPrice_label_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardExrcPrice" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardExrcPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardExrcPrice" xlink:to="lab_ecd_AwardExrcPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_019ed0cf-533b-740c-82cb-87250579b403_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Equity Method Investments [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Equity Method Investments [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:to="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_019ed0cf-533b-7a0c-857e-958c47fca173_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting [Line Items]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_label_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems" xlink:to="lab_us-gaap_SegmentReportingInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_NaturalGasLiquidsReservesMember_019ed0cf-53ce-71dc-b512-4762947024a7_terseLabel_en-US" xlink:label="lab_srt_NaturalGasLiquidsReservesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">NGLs</link:label>
    <link:label id="lab_srt_NaturalGasLiquidsReservesMember_label_en-US" xlink:label="lab_srt_NaturalGasLiquidsReservesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Natural Gas Liquids (NGL) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_NaturalGasLiquidsReservesMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_NaturalGasLiquidsReservesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_NaturalGasLiquidsReservesMember" xlink:to="lab_srt_NaturalGasLiquidsReservesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentQuarterlyReport_019ed0cf-533c-717c-8db2-a28ce69ac775_terseLabel_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:label id="lab_dei_DocumentQuarterlyReport_label_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentQuarterlyReport" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentQuarterlyReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentQuarterlyReport" xlink:to="lab_dei_DocumentQuarterlyReport" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_label_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:to="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_TX_019ed0cf-53ce-7ea9-b7f2-f907ce7ef74e_terseLabel_en-US" xlink:label="lab_stpr_TX" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Texas</link:label>
    <link:label id="lab_stpr_TX_label_en-US" xlink:label="lab_stpr_TX" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">TEXAS</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_TX" xlink:href="https://xbrl.sec.gov/stpr/2026/stpr-2026.xsd#stpr_TX"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_TX" xlink:to="lab_stpr_TX" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableNet_019ed0cf-533b-7032-8ee3-0db173e49c91_totalLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total accounts receivable, net</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableNet_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableNet" xlink:to="lab_us-gaap_AccountsReceivableNet" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_A2028SwapMember_019ed0cf-533b-78e1-85cd-0eef87c2a3f0_terseLabel_en-US" xlink:label="lab_bkv_A2028SwapMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028 Swap</link:label>
    <link:label id="lab_bkv_A2028SwapMember_label_en-US" xlink:label="lab_bkv_A2028SwapMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2028 Swap [Member]</link:label>
    <link:label id="lab_bkv_A2028SwapMember_documentation_en-US" xlink:label="lab_bkv_A2028SwapMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2028 Swap</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_A2028SwapMember" xlink:href="bkv-20260630.xsd#bkv_A2028SwapMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_A2028SwapMember" xlink:to="lab_bkv_A2028SwapMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_BKVBPPPowerCreditFacilityMember_019ed0cf-533b-7f1c-b17f-41f4cc255539_terseLabel_en-US" xlink:label="lab_bkv_BKVBPPPowerCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">BKV-BPP Power Credit Facility</link:label>
    <link:label id="lab_bkv_BKVBPPPowerCreditFacilityMember_label_en-US" xlink:label="lab_bkv_BKVBPPPowerCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">BKV-BPP Power Credit Facility [Member]</link:label>
    <link:label id="lab_bkv_BKVBPPPowerCreditFacilityMember_documentation_en-US" xlink:label="lab_bkv_BKVBPPPowerCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">BKV-BPP Power Credit Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_BKVBPPPowerCreditFacilityMember" xlink:href="bkv-20260630.xsd#bkv_BKVBPPPowerCreditFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_BKVBPPPowerCreditFacilityMember" xlink:to="lab_bkv_BKVBPPPowerCreditFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetLiabilityNetMeasurementInput_019ed0cf-53ce-7a30-aac3-16dc224bfb65_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetLiabilityNetMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Input</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetLiabilityNetMeasurementInput_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetLiabilityNetMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset (Liability) Net, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetLiabilityNetMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssetLiabilityNetMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetLiabilityNetMeasurementInput" xlink:to="lab_us-gaap_DerivativeAssetLiabilityNetMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_019ed0cf-533b-73a9-b481-b0fd8332ddce_totalLabel_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestPayableCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:to="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilitiesAbstract_019ed0cf-53ce-785d-8d00-506582049b91_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Liability [Abstract]</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilitiesAbstract" xlink:to="lab_us-gaap_DerivativeLiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCommitmentDueInThirdYear_019ed0cf-5275-7154-b910-e21c7a6bdf80_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitmentDueInThirdYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_OtherCommitmentDueInThirdYear_label_en-US" xlink:label="lab_us-gaap_OtherCommitmentDueInThirdYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitment, to be Paid, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitmentDueInThirdYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherCommitmentDueInThirdYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCommitmentDueInThirdYear" xlink:to="lab_us-gaap_OtherCommitmentDueInThirdYear" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Table</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestments_019ed0cf-533b-7c66-a928-44a9671320d3_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity method investments</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestments_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestments" xlink:to="lab_us-gaap_EquityMethodInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityComponentDomain_019ed0cf-533b-760f-a2b3-047c48c4b751_terseLabel_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:label id="lab_us-gaap_EquityComponentDomain_label_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityComponentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityComponentDomain" xlink:to="lab_us-gaap_EquityComponentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputTypeDomain_019ed0cf-5275-7f67-b37a-f30f33c60077_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Domain]</link:label>
    <link:label id="lab_us-gaap_MeasurementInputTypeDomain_label_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputTypeDomain" xlink:to="lab_us-gaap_MeasurementInputTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationGainLossIncludedInEarnings_019ed0cf-533b-7541-9469-0d85aadac4f8_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationGainLossIncludedInEarnings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total realized gains</link:label>
    <link:label id="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationGainLossIncludedInEarnings_label_en-US" xlink:label="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationGainLossIncludedInEarnings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis, Unobservable Inputs Reconciliation, Gain (Loss) Included in Earnings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationGainLossIncludedInEarnings" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationGainLossIncludedInEarnings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationGainLossIncludedInEarnings" xlink:to="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationGainLossIncludedInEarnings" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction_019ed0cf-53ce-749e-ad7d-bb1a17b30c8b_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate purchase price</link:label>
    <link:label id="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction_label_en-US" xlink:label="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Consideration Received on Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockConsiderationReceivedOnTransaction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:to="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrAdoptionDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adoption Date</link:label>
    <link:label id="lab_ecd_TrdArrAdoptionDate_label_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Adoption Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrAdoptionDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrAdoptionDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrAdoptionDate" xlink:to="lab_ecd_TrdArrAdoptionDate" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RepurchaseAgreementCounterpartyNameDomain_019ed0cf-53ce-7678-ae89-26ff2aaf6e88_terseLabel_en-US" xlink:label="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Counterparty Name [Domain]</link:label>
    <link:label id="lab_srt_RepurchaseAgreementCounterpartyNameDomain_label_en-US" xlink:label="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Counterparty Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RepurchaseAgreementCounterpartyNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:to="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndTitle_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title</link:label>
    <link:label id="lab_ecd_TrdArrIndTitle_label_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Title</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndTitle" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrIndTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndTitle" xlink:to="lab_ecd_TrdArrIndTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_terseLabel_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement does not require Recovery</link:label>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_label_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Does Not Require Recovery [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDoesNotRequireRecoveryTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:to="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_OtherCommitmentToBePaidAfterYearFour_019ed0cf-5275-7a0c-b538-8dbf30211a2b_terseLabel_en-US" xlink:label="lab_bkv_OtherCommitmentToBePaidAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_bkv_OtherCommitmentToBePaidAfterYearFour_label_en-US" xlink:label="lab_bkv_OtherCommitmentToBePaidAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitment, to be Paid, After Year Four</link:label>
    <link:label id="lab_bkv_OtherCommitmentToBePaidAfterYearFour_documentation_en-US" xlink:label="lab_bkv_OtherCommitmentToBePaidAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Commitment, to be Paid, After Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_OtherCommitmentToBePaidAfterYearFour" xlink:href="bkv-20260630.xsd#bkv_OtherCommitmentToBePaidAfterYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_OtherCommitmentToBePaidAfterYearFour" xlink:to="lab_bkv_OtherCommitmentToBePaidAfterYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTrdPoliciesProcAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:to="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_AssetAcquisitionPossiblePowerPurposesNet_019ed0cf-533b-7b88-b9f8-379cb0616e8e_terseLabel_en-US" xlink:label="lab_bkv_AssetAcquisitionPossiblePowerPurposesNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset acquisition, possible power purposes, net</link:label>
    <link:label id="lab_bkv_AssetAcquisitionPossiblePowerPurposesNet_label_en-US" xlink:label="lab_bkv_AssetAcquisitionPossiblePowerPurposesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Possible Power Purposes, Net</link:label>
    <link:label id="lab_bkv_AssetAcquisitionPossiblePowerPurposesNet_documentation_en-US" xlink:label="lab_bkv_AssetAcquisitionPossiblePowerPurposesNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Possible Power Purposes, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_AssetAcquisitionPossiblePowerPurposesNet" xlink:href="bkv-20260630.xsd#bkv_AssetAcquisitionPossiblePowerPurposesNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_AssetAcquisitionPossiblePowerPurposesNet" xlink:to="lab_bkv_AssetAcquisitionPossiblePowerPurposesNet" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_Mr.JavierHinojosaMember_label_en-US" xlink:label="lab_bkv_Mr.JavierHinojosaMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mr. Javier Hinojosa [Member]</link:label>
    <link:label id="lab_bkv_Mr.JavierHinojosaMember_documentation_en-US" xlink:label="lab_bkv_Mr.JavierHinojosaMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mr. Javier Hinojosa</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_Mr.JavierHinojosaMember" xlink:href="bkv-20260630.xsd#bkv_Mr.JavierHinojosaMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_Mr.JavierHinojosaMember" xlink:to="lab_bkv_Mr.JavierHinojosaMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfDebt_019ed0cf-533b-7f6c-bdc6-793583b3cd49_terseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repayments of debt</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentsOfDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfDebt" xlink:to="lab_us-gaap_RepaymentsOfDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionAcquireeDomain_019ed0cf-53ce-7de0-9b9e-301acdd9c786_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Domain]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionAcquireeDomain_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:to="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ResultsOfOperationsDepreciationDepletionAmortizationAndAccretion_019ed0cf-53ce-7daf-acd7-25c8dd2cc03a_terseLabel_en-US" xlink:label="lab_us-gaap_ResultsOfOperationsDepreciationDepletionAmortizationAndAccretion" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation, depletion, amortization, and accretion</link:label>
    <link:label id="lab_us-gaap_ResultsOfOperationsDepreciationDepletionAmortizationAndAccretion_019ed0cf-53ce-7601-8d2e-dfdf115de21d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ResultsOfOperationsDepreciationDepletionAmortizationAndAccretion" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Corporate and Other depreciation, depletion, amortization, and accretion</link:label>
    <link:label id="lab_us-gaap_ResultsOfOperationsDepreciationDepletionAmortizationAndAccretion_label_en-US" xlink:label="lab_us-gaap_ResultsOfOperationsDepreciationDepletionAmortizationAndAccretion" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Oil and Gas, Result of Operation, Depreciation, Depletion, Amortization, and Accretion</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ResultsOfOperationsDepreciationDepletionAmortizationAndAccretion" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ResultsOfOperationsDepreciationDepletionAmortizationAndAccretion"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ResultsOfOperationsDepreciationDepletionAmortizationAndAccretion" xlink:to="lab_us-gaap_ResultsOfOperationsDepreciationDepletionAmortizationAndAccretion" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_MerchantEnergySalesAndOtherMember_019ed0cf-53ce-7806-af78-9be18f1e0faf_terseLabel_en-US" xlink:label="lab_bkv_MerchantEnergySalesAndOtherMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Merchant energy sales and other</link:label>
    <link:label id="lab_bkv_MerchantEnergySalesAndOtherMember_label_en-US" xlink:label="lab_bkv_MerchantEnergySalesAndOtherMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Merchant Energy Sales And Other [Member]</link:label>
    <link:label id="lab_bkv_MerchantEnergySalesAndOtherMember_documentation_en-US" xlink:label="lab_bkv_MerchantEnergySalesAndOtherMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Merchant Energy Sales And Other</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_MerchantEnergySalesAndOtherMember" xlink:href="bkv-20260630.xsd#bkv_MerchantEnergySalesAndOtherMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_MerchantEnergySalesAndOtherMember" xlink:to="lab_bkv_MerchantEnergySalesAndOtherMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_019ed0cf-53ce-74cd-aa85-be40be48796b_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingenciesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsNetIncomeTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_WeightedAverageMember_019ed0cf-533b-7250-a510-667da8a8174a_terseLabel_en-US" xlink:label="lab_srt_WeightedAverageMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average</link:label>
    <link:label id="lab_srt_WeightedAverageMember_label_en-US" xlink:label="lab_srt_WeightedAverageMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_WeightedAverageMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_WeightedAverageMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_WeightedAverageMember" xlink:to="lab_srt_WeightedAverageMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NotesPayableCurrent_019ed0cf-5275-77a4-8587-491640e9fc8e_terseLabel_en-US" xlink:label="lab_us-gaap_NotesPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current portion of Temple I Loan Agreements</link:label>
    <link:label id="lab_us-gaap_NotesPayableCurrent_label_en-US" xlink:label="lab_us-gaap_NotesPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Payable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotesPayableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NotesPayableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NotesPayableCurrent" xlink:to="lab_us-gaap_NotesPayableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllAdjToCompMember_terseLabel_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation</link:label>
    <link:label id="lab_ecd_AllAdjToCompMember_label_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllAdjToCompMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllAdjToCompMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllAdjToCompMember" xlink:to="lab_ecd_AllAdjToCompMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CorporateNonSegmentMember_019ed0cf-5275-7aa5-a3db-4f97acdaaebd_terseLabel_en-US" xlink:label="lab_us-gaap_CorporateNonSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment reporting, reconciling item, corporate nonsegment</link:label>
    <link:label id="lab_us-gaap_CorporateNonSegmentMember_label_en-US" xlink:label="lab_us-gaap_CorporateNonSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Reconciling Item, Corporate Nonsegment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CorporateNonSegmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CorporateNonSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CorporateNonSegmentMember" xlink:to="lab_us-gaap_CorporateNonSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionAxis_019ed0cf-53ce-74fe-8726-26dd6250d5ba_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Axis]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionAxis_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionAxis" xlink:to="lab_us-gaap_BusinessAcquisitionAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_019ed0cf-53ce-7744-bb36-87ca6a73ce04_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_019ed0cf-53ce-7863-b36a-050f2b2e461b_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableMember_019ed0cf-533c-77a5-bd01-6df4462a0221_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts Receivable</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableMember_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableMember" xlink:to="lab_us-gaap_AccountsReceivableMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeStatementAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementAbstract" xlink:to="lab_us-gaap_IncomeStatementAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentTransitionReport_019ed0cf-5275-7d47-bfdf-2dcd32d84be8_terseLabel_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:label id="lab_dei_DocumentTransitionReport_label_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentTransitionReport" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentTransitionReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentTransitionReport" xlink:to="lab_dei_DocumentTransitionReport" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_InterestPayableYearTwo_019ed0cf-5275-7dd3-82c3-d026f0864b69_terseLabel_en-US" xlink:label="lab_bkv_InterestPayableYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_bkv_InterestPayableYearTwo_label_en-US" xlink:label="lab_bkv_InterestPayableYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable, Year Two</link:label>
    <link:label id="lab_bkv_InterestPayableYearTwo_documentation_en-US" xlink:label="lab_bkv_InterestPayableYearTwo" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Payable, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_InterestPayableYearTwo" xlink:href="bkv-20260630.xsd#bkv_InterestPayableYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_InterestPayableYearTwo" xlink:to="lab_bkv_InterestPayableYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueOptionQuantitativeDisclosuresLineItems_019ed0cf-53cf-7a9a-b340-774eb1bbe143_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOptionQuantitativeDisclosuresLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Option, Quantitative Disclosures [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueOptionQuantitativeDisclosuresLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueOptionQuantitativeDisclosuresLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Option, Quantitative Disclosures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueOptionQuantitativeDisclosuresLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueOptionQuantitativeDisclosuresLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueOptionQuantitativeDisclosuresLineItems" xlink:to="lab_us-gaap_FairValueOptionQuantitativeDisclosuresLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_019ed0cf-533c-7bff-b16e-1c3fcfd246a3_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating expenses</link:label>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpensesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingExpensesAbstract" xlink:to="lab_us-gaap_OperatingExpensesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_terseLabel_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs)</link:label>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_label_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockAppreciationRightsSARSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:to="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCommitmentsDomain_019ed0cf-533b-7eb0-946c-9f7ef74ead68_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitmentsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Commitments [Domain]</link:label>
    <link:label id="lab_us-gaap_OtherCommitmentsDomain_label_en-US" xlink:label="lab_us-gaap_OtherCommitmentsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitmentsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherCommitmentsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCommitmentsDomain" xlink:to="lab_us-gaap_OtherCommitmentsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_DerivativeLiabilitiesNonPerformanceRiskAdjustment_019ed0cf-533c-7df2-af99-aa36f716e43a_terseLabel_en-US" xlink:label="lab_bkv_DerivativeLiabilitiesNonPerformanceRiskAdjustment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commodity derivative liability</link:label>
    <link:label id="lab_bkv_DerivativeLiabilitiesNonPerformanceRiskAdjustment_label_en-US" xlink:label="lab_bkv_DerivativeLiabilitiesNonPerformanceRiskAdjustment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liabilities, Non-Performance Risk Adjustment</link:label>
    <link:label id="lab_bkv_DerivativeLiabilitiesNonPerformanceRiskAdjustment_documentation_en-US" xlink:label="lab_bkv_DerivativeLiabilitiesNonPerformanceRiskAdjustment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Liabilities, Non-Performance Risk Adjustment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_DerivativeLiabilitiesNonPerformanceRiskAdjustment" xlink:href="bkv-20260630.xsd#bkv_DerivativeLiabilitiesNonPerformanceRiskAdjustment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_DerivativeLiabilitiesNonPerformanceRiskAdjustment" xlink:to="lab_bkv_DerivativeLiabilitiesNonPerformanceRiskAdjustment" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CityAreaCode_019ed0cf-53cf-76c6-93ef-c2439623ac1a_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:label id="lab_dei_CityAreaCode_label_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CityAreaCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CityAreaCode" xlink:to="lab_dei_CityAreaCode" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MarketingExpense_019f71e7-6376-7b97-bd46-da1f89858b95_terseLabel_en-US" xlink:label="lab_us-gaap_MarketingExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Marketing expense</link:label>
    <link:label id="lab_us-gaap_MarketingExpense_label_en-US" xlink:label="lab_us-gaap_MarketingExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketing Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MarketingExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MarketingExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MarketingExpense" xlink:to="lab_us-gaap_MarketingExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_TemporaryEquityIncreaseDecreaseInDistributionPayable_019fb398-2c81-76e7-9566-6acee97ddbfa_terseLabel_en-US" xlink:label="lab_bkv_TemporaryEquityIncreaseDecreaseInDistributionPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distributions payable to noncontrolling interest</link:label>
    <link:label id="lab_bkv_TemporaryEquityIncreaseDecreaseInDistributionPayable_label_en-US" xlink:label="lab_bkv_TemporaryEquityIncreaseDecreaseInDistributionPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Increase (Decrease) in Distribution Payable</link:label>
    <link:label id="lab_bkv_TemporaryEquityIncreaseDecreaseInDistributionPayable_documentation_en-US" xlink:label="lab_bkv_TemporaryEquityIncreaseDecreaseInDistributionPayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Increase (Decrease) in Distribution Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_TemporaryEquityIncreaseDecreaseInDistributionPayable" xlink:href="bkv-20260630.xsd#bkv_TemporaryEquityIncreaseDecreaseInDistributionPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_TemporaryEquityIncreaseDecreaseInDistributionPayable" xlink:to="lab_bkv_TemporaryEquityIncreaseDecreaseInDistributionPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryIndName" xlink:to="lab_ecd_ForgoneRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description</link:label>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_label_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonGaapMeasureDescriptionTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:to="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward_019ed0cf-533c-7ee6-97b4-314a1cfb410d_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average Grant Date Fair Value</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Weighted Average Grant Date Fair Value [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityDomain_019ed0cf-533b-788c-9b5d-0c29a5bde6b8_terseLabel_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:label id="lab_dei_EntityDomain_label_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityDomain" xlink:to="lab_dei_EntityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_019ed0cf-53ce-7454-823e-11ce32457007_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common stock (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent_019ed0cf-533c-7c31-a3fd-ad47b629aa69_terseLabel_en-US" xlink:label="lab_us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Oil, gas, and power production and other taxes payable</link:label>
    <link:label id="lab_us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent_label_en-US" xlink:label="lab_us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrual for Taxes Other than Income Taxes, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent" xlink:to="lab_us-gaap_AccrualForTaxesOtherThanIncomeTaxesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CustomerContractsMember_019ed0cf-53ce-7267-8202-44c92d8be05b_terseLabel_en-US" xlink:label="lab_us-gaap_CustomerContractsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer Contracts</link:label>
    <link:label id="lab_us-gaap_CustomerContractsMember_label_en-US" xlink:label="lab_us-gaap_CustomerContractsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer Contracts [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CustomerContractsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CustomerContractsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CustomerContractsMember" xlink:to="lab_us-gaap_CustomerContractsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractualObligationDueInSecondYear_019ed0cf-53ce-7351-8ecf-a77b8e82647c_totalLabel_en-US" xlink:label="lab_us-gaap_ContractualObligationDueInSecondYear" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_ContractualObligationDueInSecondYear_label_en-US" xlink:label="lab_us-gaap_ContractualObligationDueInSecondYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contractual Obligation, to be Paid, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractualObligationDueInSecondYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractualObligationDueInSecondYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractualObligationDueInSecondYear" xlink:to="lab_us-gaap_ContractualObligationDueInSecondYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_019ed0cf-53ce-70ee-8319-2a3069b721de_terseLabel_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock-based compensation</link:label>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_label_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllocatedShareBasedCompensationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AllocatedShareBasedCompensationExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllocatedShareBasedCompensationExpense" xlink:to="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetFairValueGrossLiability_019ed0cf-53cf-7ab1-9cef-ce5c8298816b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Offset Adjustments</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetFairValueGrossLiability_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, Liability Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssetFairValueGrossLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:to="lab_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_BKVDCarbonProjectLLCMember_019ed0cf-53ce-7858-b2d2-4e2a76de3210_terseLabel_en-US" xlink:label="lab_bkv_BKVDCarbonProjectLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">BKV dCarbon Project, LLC</link:label>
    <link:label id="lab_bkv_BKVDCarbonProjectLLCMember_label_en-US" xlink:label="lab_bkv_BKVDCarbonProjectLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">BKV dCarbon Project, LLC [Member]</link:label>
    <link:label id="lab_bkv_BKVDCarbonProjectLLCMember_documentation_en-US" xlink:label="lab_bkv_BKVDCarbonProjectLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">BKV dCarbon Project, LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_BKVDCarbonProjectLLCMember" xlink:href="bkv-20260630.xsd#bkv_BKVDCarbonProjectLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_BKVDCarbonProjectLLCMember" xlink:to="lab_bkv_BKVDCarbonProjectLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SfpLocationActivityCapitalizationAxis_019fc8bd-dabe-7854-8d16-005b62e8401d_terseLabel_en-US" xlink:label="lab_us-gaap_SfpLocationActivityCapitalizationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Location, Statement of Financial Position, Activity, Capitalization [Axis]</link:label>
    <link:label id="lab_us-gaap_SfpLocationActivityCapitalizationAxis_label_en-US" xlink:label="lab_us-gaap_SfpLocationActivityCapitalizationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Location, Statement of Financial Position, Activity, Capitalization [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SfpLocationActivityCapitalizationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SfpLocationActivityCapitalizationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SfpLocationActivityCapitalizationAxis" xlink:to="lab_us-gaap_SfpLocationActivityCapitalizationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems_019ed0cf-533c-78ef-95a1-ffe3daf2b387_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_019ed0cf-533b-726e-a64e-d8f4c09e87ca_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Granted (in USD per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_019ed0cf-53ce-78ee-883b-e596e5e727fe_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeDomain" xlink:to="lab_us-gaap_SubsequentEventTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PayablesAndAccrualsAbstract_label_en-US" xlink:label="lab_us-gaap_PayablesAndAccrualsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payables and Accruals [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PayablesAndAccrualsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PayablesAndAccrualsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PayablesAndAccrualsAbstract" xlink:to="lab_us-gaap_PayablesAndAccrualsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RestatementDomain_019ed0cf-53ce-7246-aabd-44698792033d_terseLabel_en-US" xlink:label="lab_srt_RestatementDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revision of Prior Period [Domain]</link:label>
    <link:label id="lab_srt_RestatementDomain_label_en-US" xlink:label="lab_srt_RestatementDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revision of Prior Period [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RestatementDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RestatementDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RestatementDomain" xlink:to="lab_srt_RestatementDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue_019ed0cf-53ce-7a7d-b0b1-2f78226776a6_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forfeited (in USD per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Forfeitures, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_LineOfCreditFacilityAggregateElectedCommitment_019ed0cf-533b-7dba-bdc6-a4f88fbf2292_terseLabel_en-US" xlink:label="lab_bkv_LineOfCreditFacilityAggregateElectedCommitment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Elected commitment amount</link:label>
    <link:label id="lab_bkv_LineOfCreditFacilityAggregateElectedCommitment_label_en-US" xlink:label="lab_bkv_LineOfCreditFacilityAggregateElectedCommitment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line Of Credit Facility, Aggregate Elected Commitment</link:label>
    <link:label id="lab_bkv_LineOfCreditFacilityAggregateElectedCommitment_documentation_en-US" xlink:label="lab_bkv_LineOfCreditFacilityAggregateElectedCommitment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Line Of Credit Facility, Aggregate Elected Commitment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_LineOfCreditFacilityAggregateElectedCommitment" xlink:href="bkv-20260630.xsd#bkv_LineOfCreditFacilityAggregateElectedCommitment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_LineOfCreditFacilityAggregateElectedCommitment" xlink:to="lab_bkv_LineOfCreditFacilityAggregateElectedCommitment" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_TemporaryEquityEstimatedRedemptionValue_019ed0cf-533b-79e7-a557-6f7ff7316347_terseLabel_en-US" xlink:label="lab_bkv_TemporaryEquityEstimatedRedemptionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Temporary equity, estimated redemption value</link:label>
    <link:label id="lab_bkv_TemporaryEquityEstimatedRedemptionValue_label_en-US" xlink:label="lab_bkv_TemporaryEquityEstimatedRedemptionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Estimated Redemption Value</link:label>
    <link:label id="lab_bkv_TemporaryEquityEstimatedRedemptionValue_documentation_en-US" xlink:label="lab_bkv_TemporaryEquityEstimatedRedemptionValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Estimated Redemption Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_TemporaryEquityEstimatedRedemptionValue" xlink:href="bkv-20260630.xsd#bkv_TemporaryEquityEstimatedRedemptionValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_TemporaryEquityEstimatedRedemptionValue" xlink:to="lab_bkv_TemporaryEquityEstimatedRedemptionValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompRecoveryTable_terseLabel_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery</link:label>
    <link:label id="lab_ecd_ErrCompRecoveryTable_label_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompRecoveryTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ErrCompRecoveryTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompRecoveryTable" xlink:to="lab_ecd_ErrCompRecoveryTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock_019ed0cf-53ce-718a-b7e7-1ae7c7ae852a_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDebtIssuanceCosts_019ed0cf-533c-7846-8fcf-fb6dc701e050_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payment of debt issuance costs</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDebtIssuanceCosts_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Debt Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsOfDebtIssuanceCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:to="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationRollForward_019ed0cf-53ce-7c87-8082-eeacf07f5ebe_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis, Unobservable Input Reconciliation [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationRollForward_label_en-US" xlink:label="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis, Unobservable Input Reconciliation [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationRollForward" xlink:to="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputReconciliationRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCurrentReportingStatus_019ed0cf-533b-789b-a3e9-a963d0bc3b00_terseLabel_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:label id="lab_dei_EntityCurrentReportingStatus_label_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCurrentReportingStatus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCurrentReportingStatus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCurrentReportingStatus" xlink:to="lab_dei_EntityCurrentReportingStatus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_019ed0cf-5275-77f0-84c9-0d3b9923bb1c_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by financing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnAmt" xlink:to="lab_ecd_TotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_HeatRateCallOptionMember_019ed0cf-533c-7ce9-9d6e-a7dde774a1f6_terseLabel_en-US" xlink:label="lab_bkv_HeatRateCallOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Heat rate call option</link:label>
    <link:label id="lab_bkv_HeatRateCallOptionMember_label_en-US" xlink:label="lab_bkv_HeatRateCallOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Heat Rate Call Option [Member]</link:label>
    <link:label id="lab_bkv_HeatRateCallOptionMember_documentation_en-US" xlink:label="lab_bkv_HeatRateCallOptionMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Heat Rate Call Option</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_HeatRateCallOptionMember" xlink:href="bkv-20260630.xsd#bkv_HeatRateCallOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_HeatRateCallOptionMember" xlink:to="lab_bkv_HeatRateCallOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_ClassBUnitsMember_019ed0cf-533c-7e32-938f-887e627b8e86_terseLabel_en-US" xlink:label="lab_bkv_ClassBUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class B Units</link:label>
    <link:label id="lab_bkv_ClassBUnitsMember_label_en-US" xlink:label="lab_bkv_ClassBUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class B Units [Member]</link:label>
    <link:label id="lab_bkv_ClassBUnitsMember_documentation_en-US" xlink:label="lab_bkv_ClassBUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class B Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_ClassBUnitsMember" xlink:href="bkv-20260630.xsd#bkv_ClassBUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_ClassBUnitsMember" xlink:to="lab_bkv_ClassBUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_OilAndGasProvedPropertyDepreciationDepletionAmortizationAndAccretion_019ed0cf-533b-76a5-9a34-c4523f414373_terseLabel_en-US" xlink:label="lab_bkv_OilAndGasProvedPropertyDepreciationDepletionAmortizationAndAccretion" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation, depletion, amortization, and accretion</link:label>
    <link:label id="lab_bkv_OilAndGasProvedPropertyDepreciationDepletionAmortizationAndAccretion_label_en-US" xlink:label="lab_bkv_OilAndGasProvedPropertyDepreciationDepletionAmortizationAndAccretion" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Oil and Gas, Proved Property, Depreciation, Depletion, Amortization, and Accretion</link:label>
    <link:label id="lab_bkv_OilAndGasProvedPropertyDepreciationDepletionAmortizationAndAccretion_documentation_en-US" xlink:label="lab_bkv_OilAndGasProvedPropertyDepreciationDepletionAmortizationAndAccretion" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Oil and Gas, Proved Property, Depreciation, Depletion, Amortization, and Accretion</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_OilAndGasProvedPropertyDepreciationDepletionAmortizationAndAccretion" xlink:href="bkv-20260630.xsd#bkv_OilAndGasProvedPropertyDepreciationDepletionAmortizationAndAccretion"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_OilAndGasProvedPropertyDepreciationDepletionAmortizationAndAccretion" xlink:to="lab_bkv_OilAndGasProvedPropertyDepreciationDepletionAmortizationAndAccretion" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock_019ed0cf-53ce-71a4-b448-715f41d0c6c1_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination</link:label>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock" xlink:to="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPManagingMemberOrGeneralPartnerOwnershipInterest_019ed0cf-53ce-7032-aeb6-d2e17556b2cb_terseLabel_en-US" xlink:label="lab_us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPManagingMemberOrGeneralPartnerOwnershipInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership interest</link:label>
    <link:label id="lab_us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPManagingMemberOrGeneralPartnerOwnershipInterest_label_en-US" xlink:label="lab_us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPManagingMemberOrGeneralPartnerOwnershipInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Limited Liability Company (LLC) or Limited Partnership (LP), Managing Member or General Partner, Ownership Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPManagingMemberOrGeneralPartnerOwnershipInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPManagingMemberOrGeneralPartnerOwnershipInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPManagingMemberOrGeneralPartnerOwnershipInterest" xlink:to="lab_us-gaap_LimitedLiabilityCompanyLLCOrLimitedPartnershipLPManagingMemberOrGeneralPartnerOwnershipInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UtilitiesOperatingExpenseMaintenanceAndOperations_019ed0cf-53ce-70b6-8a8f-53a74faa0b01_terseLabel_en-US" xlink:label="lab_us-gaap_UtilitiesOperatingExpenseMaintenanceAndOperations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Power operating and maintenance</link:label>
    <link:label id="lab_us-gaap_UtilitiesOperatingExpenseMaintenanceAndOperations_label_en-US" xlink:label="lab_us-gaap_UtilitiesOperatingExpenseMaintenanceAndOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Utilities Operating Expense, Maintenance and Operations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UtilitiesOperatingExpenseMaintenanceAndOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UtilitiesOperatingExpenseMaintenanceAndOperations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UtilitiesOperatingExpenseMaintenanceAndOperations" xlink:to="lab_us-gaap_UtilitiesOperatingExpenseMaintenanceAndOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_019ed0cf-53ce-7d96-863d-27130953fdca_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustments to reconcile net income to net cash provided by operating activities:</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_019ed0cf-53ce-7cd5-a25f-b8e539827201_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_019ed0cf-53ce-7811-9a51-065e342b510b_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from financing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationGainLossIncludedInOtherComprehensiveIncomeLoss_019ed0cf-533b-766f-beeb-08364fdfcf8a_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total unrealized gains (losses)</link:label>
    <link:label id="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationGainLossIncludedInOtherComprehensiveIncomeLoss_label_en-US" xlink:label="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis, Unobservable Inputs Reconciliation, Gain (Loss) Included in Other Comprehensive Income (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationGainLossIncludedInOtherComprehensiveIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:to="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireInterestInJointVenture_019ed0cf-53ce-735d-bc97-d75f8b239167_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireInterestInJointVenture" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payments to acquire interest in joint venture</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireInterestInJointVenture_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireInterestInJointVenture" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Interest in Joint Venture</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireInterestInJointVenture" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireInterestInJointVenture"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireInterestInJointVenture" xlink:to="lab_us-gaap_PaymentsToAcquireInterestInJointVenture" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_A2027InstrumentMember_019fb3df-0db3-7c7a-a9ee-2557a2e50d69_terseLabel_en-US" xlink:label="lab_bkv_A2027InstrumentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_bkv_A2027InstrumentMember_label_en-US" xlink:label="lab_bkv_A2027InstrumentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2027 Instrument [Member]</link:label>
    <link:label id="lab_bkv_A2027InstrumentMember_documentation_en-US" xlink:label="lab_bkv_A2027InstrumentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2027 Instrument</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_A2027InstrumentMember" xlink:href="bkv-20260630.xsd#bkv_A2027InstrumentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_A2027InstrumentMember" xlink:to="lab_bkv_A2027InstrumentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract_019ed0cf-53ce-7191-9f05-a86b541cc7db_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income per common share attributable to BKV:</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssets_019ed0cf-53ce-7612-b2ed-a7bfd8f34033_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Asset</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_label_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssets" xlink:to="lab_us-gaap_DerivativeAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_terseLabel_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Securities</link:label>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_label_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Underlying Securities Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardUndrlygSecuritiesAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:to="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentOtherAccumulatedDepreciation_019ed0cf-53ce-7d02-8139-7605a026b1c1_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentOtherAccumulatedDepreciation" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accumulated depreciation</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentOtherAccumulatedDepreciation_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentOtherAccumulatedDepreciation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment, Other, Accumulated Depreciation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentOtherAccumulatedDepreciation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentOtherAccumulatedDepreciation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentOtherAccumulatedDepreciation" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentOtherAccumulatedDepreciation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerTextBlock_019ed0cf-533c-702c-ade2-e223cbd430f7_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue from Contracts with Customers</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerTextBlock_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromContractWithCustomerTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_019ed0cf-53ce-7195-8b3a-47cded82432a_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common stock</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable_019ed0cf-53ce-7439-9aa0-a9a3f4013dbf_terseLabel_en-US" xlink:label="lab_us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Values Derivatives, Balance Sheet Location, by Derivative Contract Type [Table]</link:label>
    <link:label id="lab_us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable_label_en-US" xlink:label="lab_us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Values Derivatives, Balance Sheet Location, by Derivative Contract Type [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable" xlink:to="lab_us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrepaidExpenseCurrent_019ed0cf-53ce-77b9-89e1-a08ea018d245_terseLabel_en-US" xlink:label="lab_us-gaap_PrepaidExpenseCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepaid expenses</link:label>
    <link:label id="lab_us-gaap_PrepaidExpenseCurrent_label_en-US" xlink:label="lab_us-gaap_PrepaidExpenseCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepaid Expense, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidExpenseCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrepaidExpenseCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrepaidExpenseCurrent" xlink:to="lab_us-gaap_PrepaidExpenseCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_EnergyRetailSalesMember_019ed0cf-533c-78a7-a931-9cf5f1d5ecc6_terseLabel_en-US" xlink:label="lab_bkv_EnergyRetailSalesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Energy retail sales</link:label>
    <link:label id="lab_bkv_EnergyRetailSalesMember_label_en-US" xlink:label="lab_bkv_EnergyRetailSalesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Energy Retail Sales [Member]</link:label>
    <link:label id="lab_bkv_EnergyRetailSalesMember_documentation_en-US" xlink:label="lab_bkv_EnergyRetailSalesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Energy Retail Sales</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_EnergyRetailSalesMember" xlink:href="bkv-20260630.xsd#bkv_EnergyRetailSalesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_EnergyRetailSalesMember" xlink:to="lab_bkv_EnergyRetailSalesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnprovedOilAndGasPropertySuccessfulEffortMethod_019ed0cf-533c-743a-809f-fedfa4d40264_terseLabel_en-US" xlink:label="lab_us-gaap_UnprovedOilAndGasPropertySuccessfulEffortMethod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Undeveloped properties</link:label>
    <link:label id="lab_us-gaap_UnprovedOilAndGasPropertySuccessfulEffortMethod_label_en-US" xlink:label="lab_us-gaap_UnprovedOilAndGasPropertySuccessfulEffortMethod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Oil and Gas, Successful Efforts Method, Property and Equipment, Unproved Property, before Accumulated Depreciation, Depletion, Amortization, and Impairment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnprovedOilAndGasPropertySuccessfulEffortMethod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnprovedOilAndGasPropertySuccessfulEffortMethod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnprovedOilAndGasPropertySuccessfulEffortMethod" xlink:to="lab_us-gaap_UnprovedOilAndGasPropertySuccessfulEffortMethod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesAcquisitions_019ed0cf-5275-7e73-b706-384a5c97ea51_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common stock to BPPUS (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesAcquisitions_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Acquisitions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesAcquisitions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_019ed0cf-533b-7374-a646-3c729ed73455_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other investing activities, net</link:label>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_label_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment for (Proceeds from) Other Investing Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsForProceedsFromOtherInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:to="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_019ed0cf-533c-72f0-9151-90981de4405e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:to="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_019ed0cf-533b-7976-83ef-a9756f0c133a_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares available for grant (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Available for Grant</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityNetIncome_019ed0cf-533b-7431-9518-ad506c2f61b5_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityNetIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityNetIncome_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityNetIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Net Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityNetIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TemporaryEquityNetIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityNetIncome" xlink:to="lab_us-gaap_TemporaryEquityNetIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeNumberOfInstrumentsHeld_019ed0cf-533b-7206-856a-3656ccc95147_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeNumberOfInstrumentsHeld" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of instruments held</link:label>
    <link:label id="lab_us-gaap_DerivativeNumberOfInstrumentsHeld_label_en-US" xlink:label="lab_us-gaap_DerivativeNumberOfInstrumentsHeld" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Number of Instruments Held</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeNumberOfInstrumentsHeld" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeNumberOfInstrumentsHeld"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeNumberOfInstrumentsHeld" xlink:to="lab_us-gaap_DerivativeNumberOfInstrumentsHeld" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_DebtInstrumentMinimumNetWorthRequirement_019ed0cf-53ce-7fa6-a5c1-d87429fced7c_terseLabel_en-US" xlink:label="lab_bkv_DebtInstrumentMinimumNetWorthRequirement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum net worth requirement</link:label>
    <link:label id="lab_bkv_DebtInstrumentMinimumNetWorthRequirement_label_en-US" xlink:label="lab_bkv_DebtInstrumentMinimumNetWorthRequirement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Minimum Net Worth Requirement</link:label>
    <link:label id="lab_bkv_DebtInstrumentMinimumNetWorthRequirement_documentation_en-US" xlink:label="lab_bkv_DebtInstrumentMinimumNetWorthRequirement" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Minimum Net Worth Requirement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_DebtInstrumentMinimumNetWorthRequirement" xlink:href="bkv-20260630.xsd#bkv_DebtInstrumentMinimumNetWorthRequirement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_DebtInstrumentMinimumNetWorthRequirement" xlink:to="lab_bkv_DebtInstrumentMinimumNetWorthRequirement" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationLiabilityCurrent_019ed0cf-53ce-7e2f-a483-6bb47952625a_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business combination, contingent consideration, liability, current</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationLiabilityCurrent_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Contingent Consideration, Liability, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationContingentConsiderationLiabilityCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationContingentConsiderationLiabilityCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationContingentConsiderationLiabilityCurrent" xlink:to="lab_us-gaap_BusinessCombinationContingentConsiderationLiabilityCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssetsCurrent_019ed0cf-53cf-782b-bfea-1eafd23d377e_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other current assets</link:label>
    <link:label id="lab_us-gaap_OtherAssetsCurrent_label_en-US" xlink:label="lab_us-gaap_OtherAssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAssetsCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetsCurrent" xlink:to="lab_us-gaap_OtherAssetsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingenciesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllTradingArrangementsMember_terseLabel_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Trading Arrangements</link:label>
    <link:label id="lab_ecd_AllTradingArrangementsMember_label_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Trading Arrangements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllTradingArrangementsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllTradingArrangementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllTradingArrangementsMember" xlink:to="lab_ecd_AllTradingArrangementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_IncreaseOfAssetRetirementObligations_019ed0cf-53ce-7052-99e8-3e46598b8a4c_terseLabel_en-US" xlink:label="lab_bkv_IncreaseOfAssetRetirementObligations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additions to asset retirement obligations</link:label>
    <link:label id="lab_bkv_IncreaseOfAssetRetirementObligations_label_en-US" xlink:label="lab_bkv_IncreaseOfAssetRetirementObligations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase Of Asset Retirement Obligations</link:label>
    <link:label id="lab_bkv_IncreaseOfAssetRetirementObligations_documentation_en-US" xlink:label="lab_bkv_IncreaseOfAssetRetirementObligations" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Increase Of Asset Retirement Obligations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_IncreaseOfAssetRetirementObligations" xlink:href="bkv-20260630.xsd#bkv_IncreaseOfAssetRetirementObligations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_IncreaseOfAssetRetirementObligations" xlink:to="lab_bkv_IncreaseOfAssetRetirementObligations" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_label_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OtherPerfMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OtherPerfMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OtherPerfMeasureAmt" xlink:to="lab_ecd_OtherPerfMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMnpiCnsdrdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:to="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_019ed0cf-53ce-7989-b5ad-ee9a894a8a95_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_label_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CurrentFiscalYearEndDate" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CurrentFiscalYearEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CurrentFiscalYearEndDate" xlink:to="lab_dei_CurrentFiscalYearEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCommitmentsFutureMinimumPaymentsRemainderOfFiscalYear_019ed0cf-533b-7f04-99d5-0bfccd7b3d34_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitmentsFutureMinimumPaymentsRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_OtherCommitmentsFutureMinimumPaymentsRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_OtherCommitmentsFutureMinimumPaymentsRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitment, to be Paid, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitmentsFutureMinimumPaymentsRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherCommitmentsFutureMinimumPaymentsRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCommitmentsFutureMinimumPaymentsRemainderOfFiscalYear" xlink:to="lab_us-gaap_OtherCommitmentsFutureMinimumPaymentsRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoAvgTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:to="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLineItems_019ed0cf-533b-797b-b1b0-09c7a589b9cc_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativeLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLineItems" xlink:to="lab_us-gaap_DerivativeLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues_019ed0cf-53ce-7b90-a131-9a1134ce1b88_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contributions from noncontrolling interest</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Stock Issued During Period, Value, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues" xlink:to="lab_us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year</link:label>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:to="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFileNumber_019ed0cf-533b-785e-87d0-2c7800371053_terseLabel_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:label id="lab_dei_EntityFileNumber_label_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFileNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFileNumber" xlink:to="lab_dei_EntityFileNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_019ed0cf-53ce-71ff-a619-47f58476c071_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common stock under equity incentive plans, net</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Issued, Value, Share-Based Payment Arrangement, after Forfeiture</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders_019ed0cf-53ce-7fb2-b3c0-255ab6dcb1d8_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Distribution declared to noncontrolling interest</link:label>
    <link:label id="lab_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders_label_en-US" xlink:label="lab_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest, Decrease from Distributions to Noncontrolling Interest Holders</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xlink:to="lab_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RecoveryOfErrCompDisclosureLineItems_label_en-US" xlink:label="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recovery of Erroneously Awarded Compensation Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RecoveryOfErrCompDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:to="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureAxis_terseLabel_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measure:</link:label>
    <link:label id="lab_ecd_MeasureAxis_label_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MeasureAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureAxis" xlink:to="lab_ecd_MeasureAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsDisclosureTextBlock_019ed0cf-533c-76ad-a3d0-697821faf59a_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments and Joint Ventures Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestmentsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:to="lab_us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock_019ed0cf-53ce-7418-8b22-20d2a74b6834_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Variable Interest Entities</link:label>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Variable Interest Entities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfVariableInterestEntitiesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:to="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_019ed0cf-53ce-7726-b3fc-fe8e3d95403d_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury stock, at cost (in shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_019ed0cf-53ce-79c1-906a-a0bdeef8f839_periodStartLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_019ed0cf-53ce-7338-8c9c-75555a9f00ad_periodEndLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonShares" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TreasuryStockCommonShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockCommonShares" xlink:to="lab_us-gaap_TreasuryStockCommonShares" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetRetirementObligationsNoncurrent_019ef4e2-5d86-7eca-901c-0b14301ad91e_verboseLabel_en-US" xlink:label="lab_us-gaap_AssetRetirementObligationsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Asset retirement obligations</link:label>
    <link:label id="lab_us-gaap_AssetRetirementObligationsNoncurrent_019ed0cf-533b-7e1f-92c6-b08d57a09019_terseLabel_en-US" xlink:label="lab_us-gaap_AssetRetirementObligationsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset retirement obligations, long-term</link:label>
    <link:label id="lab_us-gaap_AssetRetirementObligationsNoncurrent_label_en-US" xlink:label="lab_us-gaap_AssetRetirementObligationsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Retirement Obligations, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetRetirementObligationsNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetRetirementObligationsNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetRetirementObligationsNoncurrent" xlink:to="lab_us-gaap_AssetRetirementObligationsNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfOtherPropertyPlantAndEquipment_019ed0cf-53ce-7ecf-b02f-794db98eed0c_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfOtherPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale of other property, plant, and equipment</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfOtherPropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfOtherPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale of Other Property, Plant, and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleOfOtherPropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromSaleOfOtherPropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleOfOtherPropertyPlantAndEquipment" xlink:to="lab_us-gaap_ProceedsFromSaleOfOtherPropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_019ed0cf-533c-70f9-88e4-e05f6d386e84_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementEquityComponentsAxis" xlink:to="lab_us-gaap_StatementEquityComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyMember_019ed0cf-533b-7859-b6f8-edd692c16acb_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party</link:label>
    <link:label id="lab_us-gaap_RelatedPartyMember_label_en-US" xlink:label="lab_us-gaap_RelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyMember" xlink:to="lab_us-gaap_RelatedPartyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_019ed0cf-53ce-79c6-a79c-92966880e263_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income tax</link:label>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_label_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Paid, after Refund Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxesPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxesPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxesPaidNet" xlink:to="lab_us-gaap_IncomeTaxesPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_019ed0cf-53ce-79da-9c07-6309830cc23e_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_label_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInteractiveDataCurrent" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityInteractiveDataCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInteractiveDataCurrent" xlink:to="lab_dei_EntityInteractiveDataCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_019ed0cf-533b-70f0-90a3-f160d83b5a93_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: net income (loss) attributable to noncontrolling interest</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrent_019ed0cf-533c-7f8f-a96e-0ad4d8104f72_verboseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable and accrued liabilities</link:label>
    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrent_019ed0cf-533c-793d-88f5-6d36f452c982_totalLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable and Accrued Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsPayableAndAccruedLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrent" xlink:to="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitySmallBusiness_019ed0cf-533b-78ea-bc65-42b2a424bbda_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:label id="lab_dei_EntitySmallBusiness_label_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitySmallBusiness" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntitySmallBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitySmallBusiness" xlink:to="lab_dei_EntitySmallBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentLineItems_019ed0cf-533b-7a7d-b60a-4ee60fac4ca6_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Line Items]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentLineItems_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_terseLabel_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value</link:label>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_label_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MnpiDiscTimedForCompValFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:to="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement_019ed0cf-53ce-7aa0-8df6-efa20507a637_totalLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Amounts of Assets and Liabilities</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, after Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement" xlink:to="lab_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssetsNoncurrent_019ed0cf-5275-7b39-88ce-8908a21454a4_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other noncurrent assets</link:label>
    <link:label id="lab_us-gaap_OtherAssetsNoncurrent_019ed0cf-5275-76f9-9f05-6a4ddcbc3a97_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_OtherAssetsNoncurrent_label_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAssetsNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetsNoncurrent" xlink:to="lab_us-gaap_OtherAssetsNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentType_019ed0cf-533b-7fa3-b543-5fe35f6069f7_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:label id="lab_dei_DocumentType_label_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentType"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentType" xlink:to="lab_dei_DocumentType" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LocalPhoneNumber_019ed0cf-53ce-755f-bf07-6559c68b9103_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:label id="lab_dei_LocalPhoneNumber_label_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LocalPhoneNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LocalPhoneNumber" xlink:to="lab_dei_LocalPhoneNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentForContingentConsiderationLiabilityOperatingActivities_019ed0cf-533b-746d-be98-da7277f47c91_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentForContingentConsiderationLiabilityOperatingActivities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Settlement of contingent consideration</link:label>
    <link:label id="lab_us-gaap_PaymentForContingentConsiderationLiabilityOperatingActivities_label_en-US" xlink:label="lab_us-gaap_PaymentForContingentConsiderationLiabilityOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment for Contingent Consideration Liability, Operating Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentForContingentConsiderationLiabilityOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentForContingentConsiderationLiabilityOperatingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentForContingentConsiderationLiabilityOperatingActivities" xlink:to="lab_us-gaap_PaymentForContingentConsiderationLiabilityOperatingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019ed0cf-53ce-7bd8-98f6-e5fd8fe7f80e_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income before income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment_019ed0cf-533b-74f7-8ef6-7f9e6da07d23_negatedLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Accretion of Class B Units to redemption value</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Accretion to Redemption Value, Adjustment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment" xlink:to="lab_us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_019ed0cf-533c-7973-a619-49d953cdaa6a_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and contingencies (Note 11)</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingencies" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingencies"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingencies" xlink:to="lab_us-gaap_CommitmentsAndContingencies" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_EarningsPerShareAttributableToCommonStockholdersDiluted_019fd7d7-7e9a-7f02-a04c-eb0bec0b8a4e_terseLabel_en-US" xlink:label="lab_bkv_EarningsPerShareAttributableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted (in USD per share)</link:label>
    <link:label id="lab_bkv_EarningsPerShareAttributableToCommonStockholdersDiluted_label_en-US" xlink:label="lab_bkv_EarningsPerShareAttributableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Attributable to Common Stockholders, Diluted</link:label>
    <link:label id="lab_bkv_EarningsPerShareAttributableToCommonStockholdersDiluted_documentation_en-US" xlink:label="lab_bkv_EarningsPerShareAttributableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Attributable to Common Stockholders, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_EarningsPerShareAttributableToCommonStockholdersDiluted" xlink:href="bkv-20260630.xsd#bkv_EarningsPerShareAttributableToCommonStockholdersDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_EarningsPerShareAttributableToCommonStockholdersDiluted" xlink:to="lab_bkv_EarningsPerShareAttributableToCommonStockholdersDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_019ed0cf-533b-7fad-bd2e-86eeb45004e7_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:to="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote</link:label>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_label_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChangedPeerGroupFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:to="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_terseLabel_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Executive Category:</link:label>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_label_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Executive Category [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ExecutiveCategoryAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ExecutiveCategoryAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ExecutiveCategoryAxis" xlink:to="lab_ecd_ExecutiveCategoryAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_PaymentsForThePurchaseOfPutOptions_019ed0cf-533b-7c42-a07b-9418a6dd52c3_negatedLabel_en-US" xlink:label="lab_bkv_PaymentsForThePurchaseOfPutOptions" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Payments for the purchase of put options</link:label>
    <link:label id="lab_bkv_PaymentsForThePurchaseOfPutOptions_label_en-US" xlink:label="lab_bkv_PaymentsForThePurchaseOfPutOptions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments For The Purchase Of Put Options</link:label>
    <link:label id="lab_bkv_PaymentsForThePurchaseOfPutOptions_documentation_en-US" xlink:label="lab_bkv_PaymentsForThePurchaseOfPutOptions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments For The Purchase Of Put Options</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_PaymentsForThePurchaseOfPutOptions" xlink:href="bkv-20260630.xsd#bkv_PaymentsForThePurchaseOfPutOptions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_PaymentsForThePurchaseOfPutOptions" xlink:to="lab_bkv_PaymentsForThePurchaseOfPutOptions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis_019ed0cf-533c-7899-b954-ae86ab45f190_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivable Type [Axis]</link:label>
    <link:label id="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis_label_en-US" xlink:label="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivable Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:to="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_CounterpartyNameAxis_019ed0cf-533b-7a7d-9bd1-6360214bfa59_terseLabel_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Counterparty Name [Axis]</link:label>
    <link:label id="lab_srt_CounterpartyNameAxis_label_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Counterparty Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_CounterpartyNameAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_CounterpartyNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_CounterpartyNameAxis" xlink:to="lab_srt_CounterpartyNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_019ed0cf-533b-70c9-b9cd-5f3cf7e0f6f2_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities, mezzanine equity, and equity</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCommitmentsTable_019ed0cf-533b-7c7a-9012-e791e377af26_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitmentsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Commitments [Table]</link:label>
    <link:label id="lab_us-gaap_OtherCommitmentsTable_label_en-US" xlink:label="lab_us-gaap_OtherCommitmentsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitmentsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherCommitmentsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCommitmentsTable" xlink:to="lab_us-gaap_OtherCommitmentsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryNet_019ed0cf-533b-7a21-a2a3-53830883f7ec_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Inventory</link:label>
    <link:label id="lab_us-gaap_InventoryNet_label_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InventoryNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryNet" xlink:to="lab_us-gaap_InventoryNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoAvgCompActuallyPaidAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:to="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_019ed0cf-533b-7ba3-b578-3e68acd1f1b0_terseLabel_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental cash flow information:</link:label>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_label_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Supplemental Cash Flow Information [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SupplementalCashFlowInformationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:to="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoName_terseLabel_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:label id="lab_ecd_PeoName_label_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoName" xlink:to="lab_ecd_PeoName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquitySharesIssued_019ed0cf-53ce-7992-97e8-92c5072dc729_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Temporary equity issued (in units)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesIssued_label_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Shares Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquitySharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TemporaryEquitySharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquitySharesIssued" xlink:to="lab_us-gaap_TemporaryEquitySharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseholdImprovementsMember_019ed0cf-53cf-7086-b113-2e92a6c9cd55_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseholdImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leasehold improvements</link:label>
    <link:label id="lab_us-gaap_LeaseholdImprovementsMember_label_en-US" xlink:label="lab_us-gaap_LeaseholdImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leasehold Improvements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseholdImprovementsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LeaseholdImprovementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseholdImprovementsMember" xlink:to="lab_us-gaap_LeaseholdImprovementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_019ed0cf-53cf-78f3-a78a-0dd597d4d860_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Lived Asset, Class [Axis]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Asset, Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfSecuredDebt_019ed0cf-533c-78df-9563-07ce97c8fa5d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfSecuredDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payments on RBL Credit Agreement</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfSecuredDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfSecuredDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Secured Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfSecuredDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentsOfSecuredDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfSecuredDebt" xlink:to="lab_us-gaap_RepaymentsOfSecuredDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method</link:label>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_label_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_StkPrcOrTsrEstimationMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:to="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_BKVBPPPowerJointVentureMember_019fd7a8-1162-7256-a6db-facefeb6e3c1_terseLabel_en-US" xlink:label="lab_bkv_BKVBPPPowerJointVentureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">BKV-BPP Power</link:label>
    <link:label id="lab_bkv_BKVBPPPowerJointVentureMember_label_en-US" xlink:label="lab_bkv_BKVBPPPowerJointVentureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">BKV-BPP Power Joint Venture [Member]</link:label>
    <link:label id="lab_bkv_BKVBPPPowerJointVentureMember_documentation_en-US" xlink:label="lab_bkv_BKVBPPPowerJointVentureMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">BKV-BPP Power Joint Venture</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_BKVBPPPowerJointVentureMember" xlink:href="bkv-20260630.xsd#bkv_BKVBPPPowerJointVentureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_BKVBPPPowerJointVentureMember" xlink:to="lab_bkv_BKVBPPPowerJointVentureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_019ed0cf-53ce-793e-a9d8-685a41d71d18_terseLabel_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_label_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityTaxIdentificationNumber" xlink:to="lab_dei_EntityTaxIdentificationNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCommitmentsLineItems_019ed0cf-5275-7558-85f6-315b5f647ba4_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Commitments [Line Items]</link:label>
    <link:label id="lab_us-gaap_OtherCommitmentsLineItems_label_en-US" xlink:label="lab_us-gaap_OtherCommitmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitments [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitmentsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherCommitmentsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCommitmentsLineItems" xlink:to="lab_us-gaap_OtherCommitmentsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedStockSharesIssuedNetOfSharesForTaxWithholdings_019ed0cf-53ce-78e2-9812-56247a3c72bf_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockSharesIssuedNetOfSharesForTaxWithholdings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock issued upon vesting of RSUs, net of shares withheld for income taxes (in shares)</link:label>
    <link:label id="lab_us-gaap_RestrictedStockSharesIssuedNetOfSharesForTaxWithholdings_label_en-US" xlink:label="lab_us-gaap_RestrictedStockSharesIssuedNetOfSharesForTaxWithholdings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock, Shares Issued Net of Shares for Tax Withholdings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedStockSharesIssuedNetOfSharesForTaxWithholdings" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestrictedStockSharesIssuedNetOfSharesForTaxWithholdings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedStockSharesIssuedNetOfSharesForTaxWithholdings" xlink:to="lab_us-gaap_RestrictedStockSharesIssuedNetOfSharesForTaxWithholdings" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_TemporaryEquityPricePerShare_019ed0cf-533c-745b-adbb-068f0baf2a3a_terseLabel_en-US" xlink:label="lab_bkv_TemporaryEquityPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Temporary equity, price per share (in USD per unit)</link:label>
    <link:label id="lab_bkv_TemporaryEquityPricePerShare_label_en-US" xlink:label="lab_bkv_TemporaryEquityPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Price Per Share</link:label>
    <link:label id="lab_bkv_TemporaryEquityPricePerShare_documentation_en-US" xlink:label="lab_bkv_TemporaryEquityPricePerShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_TemporaryEquityPricePerShare" xlink:href="bkv-20260630.xsd#bkv_TemporaryEquityPricePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_TemporaryEquityPricePerShare" xlink:to="lab_bkv_TemporaryEquityPricePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAccruedLiabilitiesCurrent_019ed0cf-533b-753b-9122-f23d94588e29_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other accrued liabilities</link:label>
    <link:label id="lab_us-gaap_OtherAccruedLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Accrued Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAccruedLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:to="lab_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_019ed0cf-533b-7efa-8259-8fb34a80779c_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_label_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityIncorporationStateCountryCode" xlink:to="lab_dei_EntityIncorporationStateCountryCode" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined</link:label>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_label_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtErrCompNotYetDeterminedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:to="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_terseLabel_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement</link:label>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_label_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MtrlTermsOfTrdArrTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:to="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year</link:label>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:to="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_PowerDerivativesMember_019ed0cf-53ce-7b1b-a1ef-62edbc915ec4_terseLabel_en-US" xlink:label="lab_bkv_PowerDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Power derivatives</link:label>
    <link:label id="lab_bkv_PowerDerivativesMember_label_en-US" xlink:label="lab_bkv_PowerDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Power Derivatives [Member]</link:label>
    <link:label id="lab_bkv_PowerDerivativesMember_documentation_en-US" xlink:label="lab_bkv_PowerDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Power Derivatives</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_PowerDerivativesMember" xlink:href="bkv-20260630.xsd#bkv_PowerDerivativesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_PowerDerivativesMember" xlink:to="lab_bkv_PowerDerivativesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OilAndGasPropertiesTextBlock_019ed0cf-533c-7d76-8c85-bf43a5c28368_terseLabel_en-US" xlink:label="lab_us-gaap_OilAndGasPropertiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Natural Gas Properties &amp; Other Property and Equipment</link:label>
    <link:label id="lab_us-gaap_OilAndGasPropertiesTextBlock_label_en-US" xlink:label="lab_us-gaap_OilAndGasPropertiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Oil and Gas, Property and Equipment [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OilAndGasPropertiesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OilAndGasPropertiesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OilAndGasPropertiesTextBlock" xlink:to="lab_us-gaap_OilAndGasPropertiesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_SoftwareCommitmentsMember_019fb427-cf6b-7da2-b9e1-e773b72788e3_terseLabel_en-US" xlink:label="lab_bkv_SoftwareCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Software commitments</link:label>
    <link:label id="lab_bkv_SoftwareCommitmentsMember_label_en-US" xlink:label="lab_bkv_SoftwareCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Software Commitments [Member]</link:label>
    <link:label id="lab_bkv_SoftwareCommitmentsMember_documentation_en-US" xlink:label="lab_bkv_SoftwareCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Software Commitments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_SoftwareCommitmentsMember" xlink:href="bkv-20260630.xsd#bkv_SoftwareCommitmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_SoftwareCommitmentsMember" xlink:to="lab_bkv_SoftwareCommitmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_019ed0cf-53ce-7c63-81e7-edc166b37faf_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentAxis" xlink:to="lab_us-gaap_DebtInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensation_019ed0cf-533b-7624-aa46-6e05b1dadf4f_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity-based compensation expense</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Noncash Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensation" xlink:to="lab_us-gaap_ShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfOilAndGasPropertyAndEquipment_019ed0cf-53cf-7d1c-b91f-6389a66a0575_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfOilAndGasPropertyAndEquipment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sales of assets</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfOilAndGasPropertyAndEquipment_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfOilAndGasPropertyAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale of Oil and Gas Property and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleOfOilAndGasPropertyAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromSaleOfOilAndGasPropertyAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleOfOilAndGasPropertyAndEquipment" xlink:to="lab_us-gaap_ProceedsFromSaleOfOilAndGasPropertyAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockMember_019ed0cf-533b-78e2-a56a-5a0af41d841e_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee Stock</link:label>
    <link:label id="lab_us-gaap_EmployeeStockMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Employee Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockMember" xlink:to="lab_us-gaap_EmployeeStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_019ed0cf-53ce-700d-9caa-c6843e6cc123_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic (in USD per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasic" xlink:to="lab_us-gaap_EarningsPerShareBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputTypeAxis_019ed0cf-533b-7dd7-96f6-3ca13508d775_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Axis]</link:label>
    <link:label id="lab_us-gaap_MeasurementInputTypeAxis_label_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputTypeAxis" xlink:to="lab_us-gaap_MeasurementInputTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityAccretionToRedemptionValue_019ed0cf-5275-7c30-b8e5-f25d33282ed0_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityAccretionToRedemptionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accretion of Class B Units to redemption value</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityAccretionToRedemptionValue_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityAccretionToRedemptionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Accretion to Redemption Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityAccretionToRedemptionValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TemporaryEquityAccretionToRedemptionValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityAccretionToRedemptionValue" xlink:to="lab_us-gaap_TemporaryEquityAccretionToRedemptionValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsCurrent_019ed0cf-533c-7d78-9c44-837c24e9a912_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total current assets</link:label>
    <link:label id="lab_us-gaap_AssetsCurrent_label_en-US" xlink:label="lab_us-gaap_AssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsCurrent" xlink:to="lab_us-gaap_AssetsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingArrLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingArrLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Arrangements [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingArrLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTradingArrLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingArrLineItems" xlink:to="lab_ecd_InsiderTradingArrLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtNoncurrent_019ed0cf-53ce-7e85-b8e1-581a7e941bb0_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtNoncurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Long-term debt, net</link:label>
    <link:label id="lab_us-gaap_LongTermDebtNoncurrent_019ed0cf-53ce-7abb-9dcf-a07088aadd49_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total long-term debt, net</link:label>
    <link:label id="lab_us-gaap_LongTermDebtNoncurrent_label_en-US" xlink:label="lab_us-gaap_LongTermDebtNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Excluding Current Maturities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtNoncurrent" xlink:to="lab_us-gaap_LongTermDebtNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_A2026SwapMember_019ed0cf-533b-79be-92a6-eed152f7cc3b_terseLabel_en-US" xlink:label="lab_bkv_A2026SwapMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026 Swap</link:label>
    <link:label id="lab_bkv_A2026SwapMember_label_en-US" xlink:label="lab_bkv_A2026SwapMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2026 Swap [Member]</link:label>
    <link:label id="lab_bkv_A2026SwapMember_documentation_en-US" xlink:label="lab_bkv_A2026SwapMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2026 Swap</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_A2026SwapMember" xlink:href="bkv-20260630.xsd#bkv_A2026SwapMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_A2026SwapMember" xlink:to="lab_bkv_A2026SwapMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableNetCurrent_019ed0cf-53ce-7e6f-9875-d9ffcd54ea92_verboseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableNetCurrent_019ed0cf-53ce-7405-bfa9-fb02a98db1e9_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable, net</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableNetCurrent_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, after Allowance for Credit Loss, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableNetCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableNetCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableNetCurrent" xlink:to="lab_us-gaap_AccountsReceivableNetCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CoverAbstract_label_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CoverAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CoverAbstract" xlink:to="lab_dei_CoverAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription_019ed0cf-53ce-7a9e-acdd-a04fea2b36cc_terseLabel_en-US" xlink:label="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassification</link:label>
    <link:label id="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription_label_en-US" xlink:label="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification, Comparability Adjustment [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PriorPeriodReclassificationAdjustmentDescription"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:to="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_ContractPriceToBePaidContractTerminationAfterManufacturingBeginsPercentage_019ed0cf-533c-7a42-b0ce-f40d0462e179_terseLabel_en-US" xlink:label="lab_bkv_ContractPriceToBePaidContractTerminationAfterManufacturingBeginsPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract price to be paid, contract termination, after manufacturing begins, percentage</link:label>
    <link:label id="lab_bkv_ContractPriceToBePaidContractTerminationAfterManufacturingBeginsPercentage_label_en-US" xlink:label="lab_bkv_ContractPriceToBePaidContractTerminationAfterManufacturingBeginsPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract Price To Be Paid, Contract Termination, After Manufacturing Begins, Percentage</link:label>
    <link:label id="lab_bkv_ContractPriceToBePaidContractTerminationAfterManufacturingBeginsPercentage_documentation_en-US" xlink:label="lab_bkv_ContractPriceToBePaidContractTerminationAfterManufacturingBeginsPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Contract Price To Be Paid, Contract Termination, After Manufacturing Begins, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_ContractPriceToBePaidContractTerminationAfterManufacturingBeginsPercentage" xlink:href="bkv-20260630.xsd#bkv_ContractPriceToBePaidContractTerminationAfterManufacturingBeginsPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_ContractPriceToBePaidContractTerminationAfterManufacturingBeginsPercentage" xlink:to="lab_bkv_ContractPriceToBePaidContractTerminationAfterManufacturingBeginsPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable_019ed0cf-53ce-7ef7-aa4e-2e0a2257c1fd_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_DebtInstrumentCollateralHeldPercent_019ed0cf-53ce-75b3-8fa8-c1e47d8bc675_terseLabel_en-US" xlink:label="lab_bkv_DebtInstrumentCollateralHeldPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral held, percent</link:label>
    <link:label id="lab_bkv_DebtInstrumentCollateralHeldPercent_label_en-US" xlink:label="lab_bkv_DebtInstrumentCollateralHeldPercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Collateral Held, Percent</link:label>
    <link:label id="lab_bkv_DebtInstrumentCollateralHeldPercent_documentation_en-US" xlink:label="lab_bkv_DebtInstrumentCollateralHeldPercent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Collateral Held, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_DebtInstrumentCollateralHeldPercent" xlink:href="bkv-20260630.xsd#bkv_DebtInstrumentCollateralHeldPercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_DebtInstrumentCollateralHeldPercent" xlink:to="lab_bkv_DebtInstrumentCollateralHeldPercent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_019ed0cf-533b-755f-befc-4a42c34433b5_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration risk, percentage</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskPercentage1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskPercentage1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskPercentage1" xlink:to="lab_us-gaap_ConcentrationRiskPercentage1" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_BusinessCombinationThresholdConsecutiveTradingDays_019ed0cf-533b-7298-b506-1da93c8dcd89_terseLabel_en-US" xlink:label="lab_bkv_BusinessCombinationThresholdConsecutiveTradingDays" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business combination, threshold consecutive trading days</link:label>
    <link:label id="lab_bkv_BusinessCombinationThresholdConsecutiveTradingDays_label_en-US" xlink:label="lab_bkv_BusinessCombinationThresholdConsecutiveTradingDays" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Threshold Consecutive Trading Days</link:label>
    <link:label id="lab_bkv_BusinessCombinationThresholdConsecutiveTradingDays_documentation_en-US" xlink:label="lab_bkv_BusinessCombinationThresholdConsecutiveTradingDays" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Threshold Consecutive Trading Days</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_BusinessCombinationThresholdConsecutiveTradingDays" xlink:href="bkv-20260630.xsd#bkv_BusinessCombinationThresholdConsecutiveTradingDays"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_BusinessCombinationThresholdConsecutiveTradingDays" xlink:to="lab_bkv_BusinessCombinationThresholdConsecutiveTradingDays" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsMember" xlink:to="lab_ecd_EqtyAwrdsAdjsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetAcquisitionLineItems_019ed0cf-53ce-7848-ae18-77dc2383bcf0_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Line Items]</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionLineItems_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetAcquisitionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionLineItems" xlink:to="lab_us-gaap_AssetAcquisitionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilitiesNoncurrent_019ed0cf-533b-71fc-ac9b-6f3fc3bab8a9_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commodity derivative liabilities</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilitiesNoncurrent_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilitiesNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilitiesNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilitiesNoncurrent" xlink:to="lab_us-gaap_DerivativeLiabilitiesNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_BKVCIPJointVentureMember_019ed0cf-533b-7cc2-a64b-c3e2bce7aa30_terseLabel_en-US" xlink:label="lab_bkv_BKVCIPJointVentureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">BKV-CIP Joint Venture</link:label>
    <link:label id="lab_bkv_BKVCIPJointVentureMember_label_en-US" xlink:label="lab_bkv_BKVCIPJointVentureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">BKV-CIP Joint Venture [Member]</link:label>
    <link:label id="lab_bkv_BKVCIPJointVentureMember_documentation_en-US" xlink:label="lab_bkv_BKVCIPJointVentureMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">BKV-CIP Joint Venture</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_BKVCIPJointVentureMember" xlink:href="bkv-20260630.xsd#bkv_BKVCIPJointVentureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_BKVCIPJointVentureMember" xlink:to="lab_bkv_BKVCIPJointVentureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NotesPayableOtherPayablesMember_019ed0cf-533b-7411-99a7-42f3d6f22ce0_terseLabel_en-US" xlink:label="lab_us-gaap_NotesPayableOtherPayablesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notes Payable, Other Payables</link:label>
    <link:label id="lab_us-gaap_NotesPayableOtherPayablesMember_label_en-US" xlink:label="lab_us-gaap_NotesPayableOtherPayablesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Payable, Other Payables [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotesPayableOtherPayablesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NotesPayableOtherPayablesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NotesPayableOtherPayablesMember" xlink:to="lab_us-gaap_NotesPayableOtherPayablesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfSeniorLongTermDebt_019ed0cf-533b-788f-9ed1-1883778c3628_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfSeniorLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from issuance of senior long-term debt</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfSeniorLongTermDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfSeniorLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Senior Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfSeniorLongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromIssuanceOfSeniorLongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfSeniorLongTermDebt" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfSeniorLongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PlanNameAxis_019ed0cf-533b-7148-b3e2-ff48d15a8882_terseLabel_en-US" xlink:label="lab_us-gaap_PlanNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Plan Name [Axis]</link:label>
    <link:label id="lab_us-gaap_PlanNameAxis_label_en-US" xlink:label="lab_us-gaap_PlanNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Plan Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PlanNameAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PlanNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PlanNameAxis" xlink:to="lab_us-gaap_PlanNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_019ed0cf-533b-7c7d-aa81-492913d19566_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Accounts, Notes, Loans and Financing Receivable</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accounts, Notes, Loans and Financing Receivable [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:to="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfSeniorDebt_019ed0cf-533b-79d4-8eb6-ebf833f0bf80_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfSeniorDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payments on Temple I Loan Agreements</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfSeniorDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfSeniorDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Senior Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfSeniorDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentsOfSeniorDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfSeniorDebt" xlink:to="lab_us-gaap_RepaymentsOfSeniorDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNoncashIncomeTaxExpense_019ed0cf-53ce-75bb-b365-eab1c598ae36_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherNoncashIncomeTaxExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Corporate and Other taxes other than income</link:label>
    <link:label id="lab_us-gaap_OtherNoncashIncomeTaxExpense_label_en-US" xlink:label="lab_us-gaap_OtherNoncashIncomeTaxExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Noncash Income Tax Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNoncashIncomeTaxExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherNoncashIncomeTaxExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNoncashIncomeTaxExpense" xlink:to="lab_us-gaap_OtherNoncashIncomeTaxExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock_019ed0cf-533b-77cc-96e6-82dee963037b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Accounts Payable and Accrued Liabilities</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accounts Payable and Accrued Liabilities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod_019ed0cf-53ce-7116-8e39-832910dcd14a_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Forfeited (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Forfeited in Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_019ed0cf-533c-73c4-b348-ee8b3c9e1c62_terseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">General and administrative</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_019ed0cf-533c-7554-b7bb-cab10eba1fec_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Corporate and Other general and administrative</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General and Administrative Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GeneralAndAdministrativeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:to="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_KirkSpreadOptionModelMember_019ed0cf-533b-73db-8d8d-19319e74f2ef_terseLabel_en-US" xlink:label="lab_bkv_KirkSpreadOptionModelMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Kirk Spread Option Model</link:label>
    <link:label id="lab_bkv_KirkSpreadOptionModelMember_label_en-US" xlink:label="lab_bkv_KirkSpreadOptionModelMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Kirk Spread Option Model [Member]</link:label>
    <link:label id="lab_bkv_KirkSpreadOptionModelMember_documentation_en-US" xlink:label="lab_bkv_KirkSpreadOptionModelMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Kirk Spread Option Model</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_KirkSpreadOptionModelMember" xlink:href="bkv-20260630.xsd#bkv_KirkSpreadOptionModelMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_KirkSpreadOptionModelMember" xlink:to="lab_bkv_KirkSpreadOptionModelMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativesFairValueLineItems_019ed0cf-5275-77ab-a593-4887e4987ee0_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativesFairValueLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivatives, Fair Value [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativesFairValueLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativesFairValueLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivatives, Fair Value [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativesFairValueLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativesFairValueLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativesFairValueLineItems" xlink:to="lab_us-gaap_DerivativesFairValueLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_LineOfCreditFacilityCovenantTermsMinimumHedgedProjectedProductionFromProvedDevelopedReservesSubsequent24MonthsPercentage_019ed0cf-53ce-7e03-bba3-d2ceeab09325_terseLabel_en-US" xlink:label="lab_bkv_LineOfCreditFacilityCovenantTermsMinimumHedgedProjectedProductionFromProvedDevelopedReservesSubsequent24MonthsPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum hedged projected production from proved, developed reserves, subsequent 24 months, percentage</link:label>
    <link:label id="lab_bkv_LineOfCreditFacilityCovenantTermsMinimumHedgedProjectedProductionFromProvedDevelopedReservesSubsequent24MonthsPercentage_label_en-US" xlink:label="lab_bkv_LineOfCreditFacilityCovenantTermsMinimumHedgedProjectedProductionFromProvedDevelopedReservesSubsequent24MonthsPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line Of Credit Facility, Covenant Terms, Minimum Hedged Projected Production From Proved, Developed Reserves, Subsequent 24 Months, Percentage</link:label>
    <link:label id="lab_bkv_LineOfCreditFacilityCovenantTermsMinimumHedgedProjectedProductionFromProvedDevelopedReservesSubsequent24MonthsPercentage_documentation_en-US" xlink:label="lab_bkv_LineOfCreditFacilityCovenantTermsMinimumHedgedProjectedProductionFromProvedDevelopedReservesSubsequent24MonthsPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Line Of Credit Facility, Covenant Terms, Minimum Hedged Projected Production From Proved, Developed Reserves, Subsequent 24 Months, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_LineOfCreditFacilityCovenantTermsMinimumHedgedProjectedProductionFromProvedDevelopedReservesSubsequent24MonthsPercentage" xlink:href="bkv-20260630.xsd#bkv_LineOfCreditFacilityCovenantTermsMinimumHedgedProjectedProductionFromProvedDevelopedReservesSubsequent24MonthsPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_LineOfCreditFacilityCovenantTermsMinimumHedgedProjectedProductionFromProvedDevelopedReservesSubsequent24MonthsPercentage" xlink:to="lab_bkv_LineOfCreditFacilityCovenantTermsMinimumHedgedProjectedProductionFromProvedDevelopedReservesSubsequent24MonthsPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_OPISNormalButaneMontBelvieuNonTETMember_019ed0cf-53ce-7fb1-8f9a-86572f307be1_terseLabel_en-US" xlink:label="lab_bkv_OPISNormalButaneMontBelvieuNonTETMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">OPIS Normal Butane Mont Belvieu Non-TET</link:label>
    <link:label id="lab_bkv_OPISNormalButaneMontBelvieuNonTETMember_label_en-US" xlink:label="lab_bkv_OPISNormalButaneMontBelvieuNonTETMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">OPIS Normal Butane Mont Belvieu Non-TET [Member]</link:label>
    <link:label id="lab_bkv_OPISNormalButaneMontBelvieuNonTETMember_documentation_en-US" xlink:label="lab_bkv_OPISNormalButaneMontBelvieuNonTETMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">OPIS Normal Butane Mont Belvieu Non-TET</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_OPISNormalButaneMontBelvieuNonTETMember" xlink:href="bkv-20260630.xsd#bkv_OPISNormalButaneMontBelvieuNonTETMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_OPISNormalButaneMontBelvieuNonTETMember" xlink:to="lab_bkv_OPISNormalButaneMontBelvieuNonTETMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockDomain_019ed0cf-53ce-76d4-b811-1e184bf187a4_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockDomain" xlink:to="lab_us-gaap_ClassOfStockDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:to="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCommitment_019ed0cf-53ce-7844-b4bf-4add82b30e1e_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_OtherCommitment_019ed0cf-53ce-7f25-adb4-2f78d9b546f0_totalLabel_en-US" xlink:label="lab_us-gaap_OtherCommitment" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_OtherCommitment_label_en-US" xlink:label="lab_us-gaap_OtherCommitment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherCommitment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCommitment" xlink:to="lab_us-gaap_OtherCommitment" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_PlantFacilityMember_019ed0cf-53cf-7a66-863e-4ba6b9d80ea5_terseLabel_en-US" xlink:label="lab_bkv_PlantFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Plant facility</link:label>
    <link:label id="lab_bkv_PlantFacilityMember_label_en-US" xlink:label="lab_bkv_PlantFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Plant Facility [Member]</link:label>
    <link:label id="lab_bkv_PlantFacilityMember_documentation_en-US" xlink:label="lab_bkv_PlantFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Plant Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_PlantFacilityMember" xlink:href="bkv-20260630.xsd#bkv_PlantFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_PlantFacilityMember" xlink:to="lab_bkv_PlantFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_FixedPricePowerForwardMember_019ed0cf-53ce-7018-97b0-94de4c781eb1_terseLabel_en-US" xlink:label="lab_bkv_FixedPricePowerForwardMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Power forwards - sales</link:label>
    <link:label id="lab_bkv_FixedPricePowerForwardMember_label_en-US" xlink:label="lab_bkv_FixedPricePowerForwardMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Price Power Forward [Member]</link:label>
    <link:label id="lab_bkv_FixedPricePowerForwardMember_documentation_en-US" xlink:label="lab_bkv_FixedPricePowerForwardMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Price Power Forward</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_FixedPricePowerForwardMember" xlink:href="bkv-20260630.xsd#bkv_FixedPricePowerForwardMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_FixedPricePowerForwardMember" xlink:to="lab_bkv_FixedPricePowerForwardMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_terseLabel_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Available</link:label>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_label_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Securities Aggregate Available Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrSecuritiesAggAvailAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:to="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_019ed0cf-533b-7b27-9db3-473fb24f16c6_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:to="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableCurrent_019ed0cf-5275-7751-ae58-c83ace0a7550_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable</link:label>
    <link:label id="lab_us-gaap_AccountsPayableCurrent_label_en-US" xlink:label="lab_us-gaap_AccountsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsPayableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableCurrent" xlink:to="lab_us-gaap_AccountsPayableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNoncashIncomeExpense_019ed0cf-533b-7156-acde-c0f58ba4566a_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherNoncashIncomeExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other, net</link:label>
    <link:label id="lab_us-gaap_OtherNoncashIncomeExpense_label_en-US" xlink:label="lab_us-gaap_OtherNoncashIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Noncash Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNoncashIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherNoncashIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNoncashIncomeExpense" xlink:to="lab_us-gaap_OtherNoncashIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTable_terseLabel_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure</link:label>
    <link:label id="lab_ecd_PvpTable_label_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PvpTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTable" xlink:to="lab_ecd_PvpTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnSaleOfDerivatives_019ed0cf-53ce-7349-b7d7-743c18877f7b_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfDerivatives" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total realized gains on derivatives, net</link:label>
    <link:label id="lab_us-gaap_GainLossOnSaleOfDerivatives_label_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfDerivatives" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Sale of Derivatives</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnSaleOfDerivatives" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainLossOnSaleOfDerivatives"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnSaleOfDerivatives" xlink:to="lab_us-gaap_GainLossOnSaleOfDerivatives" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFilerCategory_019ed0cf-53ce-728c-be74-b12a37b4196b_terseLabel_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:label id="lab_dei_EntityFilerCategory_label_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFilerCategory" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFilerCategory"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFilerCategory" xlink:to="lab_dei_EntityFilerCategory" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_NetIncomeLossAvailableToMajorityStockholders_019fd7d2-2d82-7cc0-8465-9a466105326a_terseLabel_en-US" xlink:label="lab_bkv_NetIncomeLossAvailableToMajorityStockholders" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Majority Stockholders</link:label>
    <link:label id="lab_bkv_NetIncomeLossAvailableToMajorityStockholders_label_en-US" xlink:label="lab_bkv_NetIncomeLossAvailableToMajorityStockholders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Majority Stockholders</link:label>
    <link:label id="lab_bkv_NetIncomeLossAvailableToMajorityStockholders_documentation_en-US" xlink:label="lab_bkv_NetIncomeLossAvailableToMajorityStockholders" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Majority Stockholders</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_NetIncomeLossAvailableToMajorityStockholders" xlink:href="bkv-20260630.xsd#bkv_NetIncomeLossAvailableToMajorityStockholders"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_NetIncomeLossAvailableToMajorityStockholders" xlink:to="lab_bkv_NetIncomeLossAvailableToMajorityStockholders" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffsettingLiabilitiesTableTextBlock_019ed0cf-533b-7722-87ca-b8e66f78ce5a_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Offsetting Liabilities</link:label>
    <link:label id="lab_us-gaap_OffsettingLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Liabilities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OffsettingLiabilitiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:to="lab_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RestatementAxis_019ed0cf-533c-7d79-887f-e1205cd558cf_terseLabel_en-US" xlink:label="lab_srt_RestatementAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revision of Prior Period [Axis]</link:label>
    <link:label id="lab_srt_RestatementAxis_label_en-US" xlink:label="lab_srt_RestatementAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revision of Prior Period [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RestatementAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RestatementAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RestatementAxis" xlink:to="lab_srt_RestatementAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractualObligationFiscalYearMaturityAbstract_019ed0cf-533b-7fe1-bb42-8bfc612c7f24_terseLabel_en-US" xlink:label="lab_us-gaap_ContractualObligationFiscalYearMaturityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_ContractualObligationFiscalYearMaturityAbstract_label_en-US" xlink:label="lab_us-gaap_ContractualObligationFiscalYearMaturityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contractual Obligation, Fiscal Year Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractualObligationFiscalYearMaturityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractualObligationFiscalYearMaturityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractualObligationFiscalYearMaturityAbstract" xlink:to="lab_us-gaap_ContractualObligationFiscalYearMaturityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_RevenuesAndOtherOperatingIncome_019ed0cf-533b-7f53-bdae-b9404661c6f7_totalLabel_en-US" xlink:label="lab_bkv_RevenuesAndOtherOperatingIncome" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total revenues and other operating income</link:label>
    <link:label id="lab_bkv_RevenuesAndOtherOperatingIncome_019ed0cf-533b-75dc-8eef-4cf1cde0f773_terseLabel_en-US" xlink:label="lab_bkv_RevenuesAndOtherOperatingIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Corporate and Other revenues and other operating income</link:label>
    <link:label id="lab_bkv_RevenuesAndOtherOperatingIncome_label_en-US" xlink:label="lab_bkv_RevenuesAndOtherOperatingIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues and Other Operating Income</link:label>
    <link:label id="lab_bkv_RevenuesAndOtherOperatingIncome_documentation_en-US" xlink:label="lab_bkv_RevenuesAndOtherOperatingIncome" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Revenues and Other Operating Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_RevenuesAndOtherOperatingIncome" xlink:href="bkv-20260630.xsd#bkv_RevenuesAndOtherOperatingIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_RevenuesAndOtherOperatingIncome" xlink:to="lab_bkv_RevenuesAndOtherOperatingIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToCommonStockholdersBasic_019fd7d9-7e5e-7be2-a278-b326d3005925_terseLabel_en-US" xlink:label="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic (in shares)</link:label>
    <link:label id="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToCommonStockholdersBasic_label_en-US" xlink:label="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Attributable to Common Stockholders, Basic</link:label>
    <link:label id="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToCommonStockholdersBasic_documentation_en-US" xlink:label="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Attributable to Common Stockholders, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToCommonStockholdersBasic" xlink:href="bkv-20260630.xsd#bkv_WeightedAverageNumberOfSharesOutstandingAttributableToCommonStockholdersBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToCommonStockholdersBasic" xlink:to="lab_bkv_WeightedAverageNumberOfSharesOutstandingAttributableToCommonStockholdersBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtByMaturityAbstract_019ed0cf-53ce-7432-a0b2-eae2a083c7fc_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtByMaturityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt</link:label>
    <link:label id="lab_us-gaap_LongTermDebtByMaturityAbstract_label_en-US" xlink:label="lab_us-gaap_LongTermDebtByMaturityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Fiscal Year Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtByMaturityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtByMaturityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtByMaturityAbstract" xlink:to="lab_us-gaap_LongTermDebtByMaturityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskBenchmarkDomain_019ed0cf-53ce-73b4-ab27-92edef722973_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Domain]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskBenchmarkDomain_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskBenchmarkDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:to="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_ExpendituresPaidByParentCompanyOnBehalfOfTheJointVenture_019ed0cf-53ce-7dff-8757-4a758fc455af_terseLabel_en-US" xlink:label="lab_bkv_ExpendituresPaidByParentCompanyOnBehalfOfTheJointVenture" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expenditures paid by BKV dCarbon Ventures on behalf of BKV-BPP Cotton Cove</link:label>
    <link:label id="lab_bkv_ExpendituresPaidByParentCompanyOnBehalfOfTheJointVenture_label_en-US" xlink:label="lab_bkv_ExpendituresPaidByParentCompanyOnBehalfOfTheJointVenture" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Expenditures Paid By Parent Company On Behalf Of The Joint Venture</link:label>
    <link:label id="lab_bkv_ExpendituresPaidByParentCompanyOnBehalfOfTheJointVenture_documentation_en-US" xlink:label="lab_bkv_ExpendituresPaidByParentCompanyOnBehalfOfTheJointVenture" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Expenditures Paid By Parent Company On Behalf Of The Joint Venture</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_ExpendituresPaidByParentCompanyOnBehalfOfTheJointVenture" xlink:href="bkv-20260630.xsd#bkv_ExpendituresPaidByParentCompanyOnBehalfOfTheJointVenture"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_ExpendituresPaidByParentCompanyOnBehalfOfTheJointVenture" xlink:to="lab_bkv_ExpendituresPaidByParentCompanyOnBehalfOfTheJointVenture" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments and Joint Ventures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract" xlink:to="lab_us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCommitmentDueInNextTwelveMonths_019ed0cf-533b-7729-a374-2de861f96939_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitmentDueInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_OtherCommitmentDueInNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_OtherCommitmentDueInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitment, to be Paid, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitmentDueInNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherCommitmentDueInNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCommitmentDueInNextTwelveMonths" xlink:to="lab_us-gaap_OtherCommitmentDueInNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_Section45QTaxCreditsMember_019ed0cf-53ce-71f1-9b5e-1edda3a88d24_terseLabel_en-US" xlink:label="lab_bkv_Section45QTaxCreditsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Section 45Q tax credits</link:label>
    <link:label id="lab_bkv_Section45QTaxCreditsMember_label_en-US" xlink:label="lab_bkv_Section45QTaxCreditsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Section 45Q Tax Credits [Member]</link:label>
    <link:label id="lab_bkv_Section45QTaxCreditsMember_documentation_en-US" xlink:label="lab_bkv_Section45QTaxCreditsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Section 45Q Tax Credits</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_Section45QTaxCreditsMember" xlink:href="bkv-20260630.xsd#bkv_Section45QTaxCreditsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_Section45QTaxCreditsMember" xlink:to="lab_bkv_Section45QTaxCreditsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine2_019ed0cf-5275-7e58-8454-30ae3481c741_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine2" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line Two</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine2_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine2" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine2" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressAddressLine2"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine2" xlink:to="lab_dei_EntityAddressAddressLine2" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProfitLoss_019ed0cf-5275-7b2b-9f0d-c46f4b79a6c9_totalLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_019ed0cf-5275-75ee-91a1-35b5f2e37207_terseLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_019f1f1c-52aa-78c5-88c2-dba749518aac_verboseLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss)</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_label_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProfitLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProfitLoss" xlink:to="lab_us-gaap_ProfitLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionSharePrice_019ed0cf-533b-79ab-b981-229358ca0f61_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionSharePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">BKV common stock price (in USD per share)</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionSharePrice_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionSharePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionSharePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionSharePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionSharePrice" xlink:to="lab_us-gaap_BusinessAcquisitionSharePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_AdjustmentOfEquityBasedCompensationToRedemptionValue_019ed0cf-53ce-7dba-83b1-048f8d5a728a_terseLabel_en-US" xlink:label="lab_bkv_AdjustmentOfEquityBasedCompensationToRedemptionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accretion of Class B Units to redemption value</link:label>
    <link:label id="lab_bkv_AdjustmentOfEquityBasedCompensationToRedemptionValue_label_en-US" xlink:label="lab_bkv_AdjustmentOfEquityBasedCompensationToRedemptionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment Of Equity-Based Compensation To Redemption Value</link:label>
    <link:label id="lab_bkv_AdjustmentOfEquityBasedCompensationToRedemptionValue_documentation_en-US" xlink:label="lab_bkv_AdjustmentOfEquityBasedCompensationToRedemptionValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Adjustment Of Equity-Based Compensation To Redemption Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_AdjustmentOfEquityBasedCompensationToRedemptionValue" xlink:href="bkv-20260630.xsd#bkv_AdjustmentOfEquityBasedCompensationToRedemptionValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_AdjustmentOfEquityBasedCompensationToRedemptionValue" xlink:to="lab_bkv_AdjustmentOfEquityBasedCompensationToRedemptionValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsCurrentAbstract_019ed0cf-533b-72d7-93f2-5e86eb923c0b_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current assets</link:label>
    <link:label id="lab_us-gaap_AssetsCurrentAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Current [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsCurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsCurrentAbstract" xlink:to="lab_us-gaap_AssetsCurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_ReferencePriceDomain_019ed0cf-533b-76c5-9ece-02193d815f38_terseLabel_en-US" xlink:label="lab_bkv_ReferencePriceDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reference Price [Domain]</link:label>
    <link:label id="lab_bkv_ReferencePriceDomain_label_en-US" xlink:label="lab_bkv_ReferencePriceDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reference Price [Domain]</link:label>
    <link:label id="lab_bkv_ReferencePriceDomain_documentation_en-US" xlink:label="lab_bkv_ReferencePriceDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reference Price [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_ReferencePriceDomain" xlink:href="bkv-20260630.xsd#bkv_ReferencePriceDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_ReferencePriceDomain" xlink:to="lab_bkv_ReferencePriceDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilities_019ed0cf-53ce-711f-929d-2798bce8e03a_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Liability</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilities" xlink:to="lab_us-gaap_DerivativeLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeniorNotesMember_019ed0cf-533b-7345-a999-83b3f6eec2fd_terseLabel_en-US" xlink:label="lab_us-gaap_SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Senior Notes</link:label>
    <link:label id="lab_us-gaap_SeniorNotesMember_label_en-US" xlink:label="lab_us-gaap_SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Senior Notes [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeniorNotesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SeniorNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeniorNotesMember" xlink:to="lab_us-gaap_SeniorNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_WorkingCapitalSurplusNet_019ed0cf-533b-7504-8c50-fe0f6571e00a_terseLabel_en-US" xlink:label="lab_bkv_WorkingCapitalSurplusNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Working capital surplus, net</link:label>
    <link:label id="lab_bkv_WorkingCapitalSurplusNet_label_en-US" xlink:label="lab_bkv_WorkingCapitalSurplusNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Working Capital Surplus, Net</link:label>
    <link:label id="lab_bkv_WorkingCapitalSurplusNet_documentation_en-US" xlink:label="lab_bkv_WorkingCapitalSurplusNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Working Capital Surplus, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_WorkingCapitalSurplusNet" xlink:href="bkv-20260630.xsd#bkv_WorkingCapitalSurplusNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_WorkingCapitalSurplusNet" xlink:to="lab_bkv_WorkingCapitalSurplusNet" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine1_019ed0cf-533b-7c34-ad4c-95e99a4bc055_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine1_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressAddressLine1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine1" xlink:to="lab_dei_EntityAddressAddressLine1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue_019ed0cf-533c-7ce7-9ee5-df7e0de27d14_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vested (in USD per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Vested in Period, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_019ed0cf-533b-7e96-88d5-427cbc71927a_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Income tax benefit (expense)</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_TemporaryEquityLiquidationPreferencePercentage_019ed0cf-53ce-7332-81a2-4dcb7fdd57f4_terseLabel_en-US" xlink:label="lab_bkv_TemporaryEquityLiquidationPreferencePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Temporary equity, liquidation preference, percentage</link:label>
    <link:label id="lab_bkv_TemporaryEquityLiquidationPreferencePercentage_label_en-US" xlink:label="lab_bkv_TemporaryEquityLiquidationPreferencePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Liquidation Preference, Percentage</link:label>
    <link:label id="lab_bkv_TemporaryEquityLiquidationPreferencePercentage_documentation_en-US" xlink:label="lab_bkv_TemporaryEquityLiquidationPreferencePercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Liquidation Preference, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_TemporaryEquityLiquidationPreferencePercentage" xlink:href="bkv-20260630.xsd#bkv_TemporaryEquityLiquidationPreferencePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_TemporaryEquityLiquidationPreferencePercentage" xlink:to="lab_bkv_TemporaryEquityLiquidationPreferencePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsMember_019ed0cf-533b-7139-98d6-41e33842a8b3_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments</link:label>
    <link:label id="lab_us-gaap_CommitmentsMember_label_en-US" xlink:label="lab_us-gaap_CommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsMember" xlink:to="lab_us-gaap_CommitmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNonoperatingIncome_019ed0cf-533b-7749-ae4e-ca326087bda9_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncome_label_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Nonoperating Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNonoperatingIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherNonoperatingIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNonoperatingIncome" xlink:to="lab_us-gaap_OtherNonoperatingIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommodityContractAssetNoncurrent_019ed0cf-53ce-7352-8058-338832d3e0ce_terseLabel_en-US" xlink:label="lab_us-gaap_CommodityContractAssetNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commodity derivative assets</link:label>
    <link:label id="lab_us-gaap_CommodityContractAssetNoncurrent_label_en-US" xlink:label="lab_us-gaap_CommodityContractAssetNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commodity Contract Asset, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommodityContractAssetNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommodityContractAssetNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommodityContractAssetNoncurrent" xlink:to="lab_us-gaap_CommodityContractAssetNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_FurnitureFixturesEquipmentAndVehiclesMember_019ed0cf-533b-79a2-825f-0d6cd7bf9917_terseLabel_en-US" xlink:label="lab_bkv_FurnitureFixturesEquipmentAndVehiclesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Furniture, fixtures, equipment, and vehicles</link:label>
    <link:label id="lab_bkv_FurnitureFixturesEquipmentAndVehiclesMember_label_en-US" xlink:label="lab_bkv_FurnitureFixturesEquipmentAndVehiclesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Furniture, Fixtures, Equipment, and Vehicles [Member]</link:label>
    <link:label id="lab_bkv_FurnitureFixturesEquipmentAndVehiclesMember_documentation_en-US" xlink:label="lab_bkv_FurnitureFixturesEquipmentAndVehiclesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Furniture, Fixtures, Equipment, and Vehicles</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_FurnitureFixturesEquipmentAndVehiclesMember" xlink:href="bkv-20260630.xsd#bkv_FurnitureFixturesEquipmentAndVehiclesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_FurnitureFixturesEquipmentAndVehiclesMember" xlink:to="lab_bkv_FurnitureFixturesEquipmentAndVehiclesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_019ed0cf-53ce-734f-aa9c-bbec26d1daff_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principles of Consolidation</link:label>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConsolidationPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:to="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_019ed0cf-53ce-7031-8ad8-44c01a25f7df_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Primary Beneficiary</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Primary Beneficiary [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableInterestEntityPrimaryBeneficiaryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:to="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_BKVCorpMember_019ed0cf-53ce-7b75-b095-8a0333409822_terseLabel_en-US" xlink:label="lab_bkv_BKVCorpMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">BKV Corp</link:label>
    <link:label id="lab_bkv_BKVCorpMember_label_en-US" xlink:label="lab_bkv_BKVCorpMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">BKV Corp [Member]</link:label>
    <link:label id="lab_bkv_BKVCorpMember_documentation_en-US" xlink:label="lab_bkv_BKVCorpMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">BKV Corp</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_BKVCorpMember" xlink:href="bkv-20260630.xsd#bkv_BKVCorpMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_BKVCorpMember" xlink:to="lab_bkv_BKVCorpMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FuelCosts_019ed0cf-533c-7e62-b260-f621663fbd61_terseLabel_en-US" xlink:label="lab_us-gaap_FuelCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fuel commodity costs</link:label>
    <link:label id="lab_us-gaap_FuelCosts_label_en-US" xlink:label="lab_us-gaap_FuelCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fuel Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FuelCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FuelCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FuelCosts" xlink:to="lab_us-gaap_FuelCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_NaturalGasNGLAndOilMember_019ed0cf-533b-7ef8-a6fa-82e495c57a39_terseLabel_en-US" xlink:label="lab_bkv_NaturalGasNGLAndOilMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Natural gas, NGL, and oil sales</link:label>
    <link:label id="lab_bkv_NaturalGasNGLAndOilMember_label_en-US" xlink:label="lab_bkv_NaturalGasNGLAndOilMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Natural Gas, NGL, And Oil [Member]</link:label>
    <link:label id="lab_bkv_NaturalGasNGLAndOilMember_documentation_en-US" xlink:label="lab_bkv_NaturalGasNGLAndOilMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Natural Gas, NGL, And Oil</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_NaturalGasNGLAndOilMember" xlink:href="bkv-20260630.xsd#bkv_NaturalGasNGLAndOilMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_NaturalGasNGLAndOilMember" xlink:to="lab_bkv_NaturalGasNGLAndOilMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementTable_019ed0cf-53ce-7561-b2d1-a33a5bc71875_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementTable" xlink:to="lab_us-gaap_StatementTable" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_CorporateAndOtherMarketingExpense_019fc8b2-3cdd-73e4-987f-358195d3e82a_negatedTerseLabel_en-US" xlink:label="lab_bkv_CorporateAndOtherMarketingExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Corporate and Other marketing expense</link:label>
    <link:label id="lab_bkv_CorporateAndOtherMarketingExpense_label_en-US" xlink:label="lab_bkv_CorporateAndOtherMarketingExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Corporate And Other Marketing Expense</link:label>
    <link:label id="lab_bkv_CorporateAndOtherMarketingExpense_documentation_en-US" xlink:label="lab_bkv_CorporateAndOtherMarketingExpense" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Corporate And Other Marketing Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_CorporateAndOtherMarketingExpense" xlink:href="bkv-20260630.xsd#bkv_CorporateAndOtherMarketingExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_CorporateAndOtherMarketingExpense" xlink:to="lab_bkv_CorporateAndOtherMarketingExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_A2026InstrumentMember_019fb3de-d4f7-7897-a0af-a5c220866ab5_terseLabel_en-US" xlink:label="lab_bkv_A2026InstrumentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_bkv_A2026InstrumentMember_label_en-US" xlink:label="lab_bkv_A2026InstrumentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2026 Instrument [Member]</link:label>
    <link:label id="lab_bkv_A2026InstrumentMember_documentation_en-US" xlink:label="lab_bkv_A2026InstrumentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2026 Instrument</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_A2026InstrumentMember" xlink:href="bkv-20260630.xsd#bkv_A2026InstrumentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_A2026InstrumentMember" xlink:to="lab_bkv_A2026InstrumentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeInterest_019ed0cf-533b-7f63-ae7a-8ef1099dd3e3_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest income</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeInterest_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income, Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentIncomeInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIncomeInterest" xlink:to="lab_us-gaap_InvestmentIncomeInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAsset_019ed0cf-533b-73b1-9c8e-3524794b53c9_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Amounts of Assets and Liabilities</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAsset_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, before Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeFairValueOfDerivativeAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:to="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_bkv_SolarRevenueMember_019ed0cf-53ce-7d87-b3b3-32389994db02_terseLabel_en-US" xlink:label="lab_bkv_SolarRevenueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Solar revenue</link:label>
    <link:label id="lab_bkv_SolarRevenueMember_label_en-US" xlink:label="lab_bkv_SolarRevenueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Solar Revenue [Member]</link:label>
    <link:label id="lab_bkv_SolarRevenueMember_documentation_en-US" xlink:label="lab_bkv_SolarRevenueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Solar Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bkv_SolarRevenueMember" xlink:href="bkv-20260630.xsd#bkv_SolarRevenueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bkv_SolarRevenueMember" xlink:to="lab_bkv_SolarRevenueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentsAbstract_019ed0cf-533b-7186-ac89-f8616d80ef27_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principal Value</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentsAbstract_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instruments [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentsAbstract" xlink:to="lab_us-gaap_DebtInstrumentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisWithUnobservableInputs_019ed0cf-5275-7f2e-9f07-8e543c41f898_periodStartLabel_en-US" xlink:label="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisWithUnobservableInputs" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Balance, beginning of period</link:label>
    <link:label id="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisWithUnobservableInputs_019ed0cf-5275-7007-a79e-75c3699cddcb_periodEndLabel_en-US" xlink:label="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisWithUnobservableInputs" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Balance, end of period</link:label>
    <link:label id="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisWithUnobservableInputs_label_en-US" xlink:label="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisWithUnobservableInputs" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis with Unobservable Inputs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisWithUnobservableInputs" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisWithUnobservableInputs"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisWithUnobservableInputs" xlink:to="lab_us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisWithUnobservableInputs" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:to="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:type="arc" order="1"/>
  </link:labelLink>
</link:linkbase>
