<SEC-DOCUMENT>0001628280-25-052689.txt : 20251117
<SEC-HEADER>0001628280-25-052689.hdr.sgml : 20251117
<ACCEPTANCE-DATETIME>20251117172116
ACCESSION NUMBER:		0001628280-25-052689
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20251117
FILED AS OF DATE:		20251117
DATE AS OF CHANGE:		20251117

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			Kalnin Christopher P
		CENTRAL INDEX KEY:			0001953932
		ORGANIZATION NAME:           	

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-42282
		FILM NUMBER:		251492057

	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_1763418073.xml
<DESCRIPTION>FORM 4
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0508</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2025-11-17</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001953932</rptOwnerCik>
            <rptOwnerName>Kalnin Christopher P</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>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Executive Officer</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>1</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2025-11-17</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>78281</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>28.0369</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1248580</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>875754</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Spouse</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The reported transaction was effected pursuant to a Rule 10b5-1 trading plan adopted by the reporting person on March 14, 2025.</footnote>
        <footnote id="F2">The price reported in Column 4 is a weighted average sale price. These shares were sold in multiple transactions at prices ranging from $28.00 to $28.28, inclusive. The reporting person undertakes to provide to the Issuer, any security holder of the Issuer, or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within the range set forth in this footnote.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Kathleen Lenox, attorney-in-fact</signatureName>
        <signatureDate>2025-11-17</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
