<SEC-DOCUMENT>0001628280-26-017153.txt : 20260312
<SEC-HEADER>0001628280-26-017153.hdr.sgml : 20260312
<ACCEPTANCE-DATETIME>20260312140823
ACCESSION NUMBER:		0001628280-26-017153
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20260310
FILED AS OF DATE:		20260312
DATE AS OF CHANGE:		20260312

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			Tameron David
		CENTRAL INDEX KEY:			0001954214
		ORGANIZATION NAME:           	

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-42282
		FILM NUMBER:		26747006

	MAIL ADDRESS:	
		STREET 1:		BKV CORPORATION
		STREET 2:		1200 17TH STREET, SUITE 2100
		CITY:			DENVER
		STATE:			CO
		ZIP:			80202

ISSUER:		

	COMPANY DATA:	
		COMPANY CONFORMED NAME:			BKV Corp
		CENTRAL INDEX KEY:			0001838406
		STANDARD INDUSTRIAL CLASSIFICATION:	CRUDE PETROLEUM & NATURAL GAS [1311]
		ORGANIZATION NAME:           	01 Energy & Transportation
		EIN:				850886382
		STATE OF INCORPORATION:			DE
		FISCAL YEAR END:			1231

	BUSINESS ADDRESS:	
		STREET 1:		1200 17TH ST., STE 2100
		CITY:			DENVER
		STATE:			CO
		ZIP:			80202
		BUSINESS PHONE:		(720) 375-9680

	MAIL ADDRESS:	
		STREET 1:		1200 17TH ST., STE 2100
		CITY:			DENVER
		STATE:			CO
		ZIP:			80202
</SEC-HEADER>
<DOCUMENT>
<TYPE>4
<SEQUENCE>1
<FILENAME>wk-form4_1773338900.xml
<DESCRIPTION>FORM 4
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0508</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2026-03-10</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001838406</issuerCik>
        <issuerName>BKV Corp</issuerName>
        <issuerTradingSymbol>BKV</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001954214</rptOwnerCik>
            <rptOwnerName>Tameron David</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1200 17TH STREET, SUITE 2100</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>DENVER</rptOwnerCity>
            <rptOwnerState>CO</rptOwnerState>
            <rptOwnerZipCode>80202</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Financial Officer</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2026-03-10</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>30407</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>69225</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>300</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By  Son</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>300</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Son</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Represents restricted stock units granted to the reporting person under the BKV Corporation 2024 Equity and Incentive Compensation Plan that vest in three equal annual installments beginning on March 10, 2027. Each restricted stock unit represents a contingent right to receive one share of common stock, par value $0.01 per share.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Kathleen Lenox, attorney-in-fact</signatureName>
        <signatureDate>2026-03-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
