<SEC-DOCUMENT>0001628280-25-000211.txt : 20250103
<SEC-HEADER>0001628280-25-000211.hdr.sgml : 20250103
<ACCEPTANCE-DATETIME>20250103140008
ACCESSION NUMBER:		0001628280-25-000211
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20250102
FILED AS OF DATE:		20250103
DATE AS OF CHANGE:		20250103

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:		25505200

	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
		IRS NUMBER:				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_1735930801.xml
<DESCRIPTION>FORM 4
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0508</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2025-01-02</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>VP, Strategic Finance and IR</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2025-01-02</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1278</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>23.78</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>19790</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>300</value>
                    <footnoteId id="F2"/>
                </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>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By  Son</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Represents shares of common stock, par value $0.01 per share (&quot;Common Stock&quot;), withheld to satisfy tax withholding obligations upon the vesting of restricted stock units previously reported on Form 4. This net settlement was approved by the board of directors of the Issuer pursuant to Rule 16b-3 under the Securities Exchange Act of 1934, as amended.</footnote>
        <footnote id="F2">Represents shares of Common Stock purchased by the reporting person's son through the reserved share program conducted in connection with the Issuer's initial public offering.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Kathleen Lenox, attorney-in-fact</signatureName>
        <signatureDate>2025-01-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
