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Exhibit 4.1

Execution Version

SECOND SUPPLEMENTAL INDENTURE

SECOND SUPPLEMENTAL INDENTURE (this “Supplemental Indenture”), dated as

of April 15, 2026, among BKV Marketing, LLC, a Delaware limited liability company

(“Guaranteeing Subsidiary”), a subsidiary of BKV Upstream Midstream, LLC, a Delaware

limited liability company (the “Issuer”), the Issuer, the other Guarantors party hereto, and U.S.

Bank Trust Company, National Association, as trustee under the Indenture referred to below (the

“Trustee”).

W I T N E S S E T H

WHEREAS, the Issuer has heretofore executed and delivered to the Trustee an indenture

dated as of September 26, 2025 (as supplemented by the First Supplemental Indenture dated as

of September 29, 2025, the “Indenture”), providing for the issuance of 7.500% Senior Notes due

2030 (collectively, the “Notes”);

WHEREAS, the Indenture provides that under certain circumstances the Guaranteeing

Subsidiary shall execute and deliver to the Trustee a supplemental indenture pursuant to which

the Guaranteeing Subsidiary shall unconditionally Guarantee all of the Issuer’s Obligations under

the Notes and the Indenture on the terms and conditions set forth herein (the “Note Guarantee”);

and

WHEREAS, pursuant to Section 9.01 of the Indenture, the Trustee is authorized to

execute and deliver this Supplemental Indenture.

NOW, THEREFORE, in consideration of the foregoing and for other good and valuable

consideration, the receipt of which is hereby acknowledged, the Guaranteeing Subsidiary and the

Trustee mutually covenant and agree for the equal and ratable benefit of the Holders of the Notes

as follows:

1.CAPITALIZED TERMS.  Capitalized terms used herein without definition shall

have the meanings assigned to them in the Indenture.

2.AGREEMENT TO GUARANTEE.  The Guaranteeing Subsidiary hereby agrees

to provide an unconditional Guarantee on the terms and subject to the conditions set forth in the

Note Guarantee and in the Indenture, including but not limited to Article 10 thereof.

3.NEW YORK LAW TO GOVERN. THE LAW OF THE STATE OF NEW

YORK SHALL GOVERN AND BE USED TO CONSTRUE THIS SUPPLEMENTAL

INDENTURE.

4.COUNTERPARTS. The parties may sign any number of copies of this

Supplemental Indenture.  Each signed copy shall be an original, but all of them together

represent the same agreement.  The exchange of copies of this Supplemental Indenture and of

signature pages by facsimile or PDF transmission shall constitute effective execution and

delivery of this Supplemental Indenture as to the parties hereto and may be used in lieu of the

original Supplemental Indenture for all purposes.  Signatures of the parties hereto transmitted by

facsimile or PDF shall be deemed to be their original signatures for all purposes.

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5.EFFECT OF HEADINGS. The Section headings herein are for convenience only

and shall not affect the construction hereof.

6.THE TRUSTEE.  The Trustee shall not be responsible in any manner whatsoever

for or in respect of the validity or sufficiency of this Supplemental Indenture or for or in respect

of the recitals contained herein, all of which recitals are made solely by the Guaranteeing

Subsidiary and the Issuer.

[Signatures on following page]

[Signature Page to Second Supplemental Indenture]

IN WITNESS WHEREOF, the parties hereto have caused this Supplemental Indenture to

be duly executed and attested, all as of the date first above written.

Dated: April 15, 2026

GUARANTEEING SUBSIDIARY	BKV MARKETING, LLC By:  /s/ Eric Jacobsen Name:  Eric Jacobsen Title:    President, Upstream
ISSUER	BKV UPSTREAM MIDSTREAM, LLC By:  /s/ Eric Jacobsen Name:  Eric Jacobsen Title:    President, Upstream
OTHER GUARANTORS	BKV CORPORATION By:  /s/ Eric Jacobsen Name:  Eric Jacobsen Title:    President, Upstream BKV BARNETT, LLC BKV CHELSEA, LLC BKV MIDSTREAM, LLC BKV NORTH TEXAS, LLC BKV OPERATING, LLC KALNIN VENTURES LLC BEDROCK PRODUCTION, LLC BEDROCK DEVELOPMENT PARTNERS, LLC BEP ABS I HOLDINGS, LLC BEDROCK ABS I, LLC
	By:  /s/ Eric Jacobsen Name:  Eric Jacobsen Title:    President, Upstream

[Signature Page to Second Supplemental Indenture]

TRUSTEE	U.S. BANK TRUST COMPANY, NATIONAL ASSOCIATION, as Trustee
	By:  /s/ Bradley E. Scarbrough Name:  Bradley E. Scarbrough Title:    Vice President