Exhibit 5.1

2001 ROSS AVENUE DALLAS, TEXAS 75201-2980   TEL +1 214.953.6500 FAX +1 214.953.6503 BakerBotts.com

AUSTIN BRUSSELS DALLAS DUBAI HOUSTON LONDON

NEW YORK PALO ALTO RIYADH SAN FRANCISCO SINGAPORE WASHINGTON

March 12, 2026

BKV Corporation

1200 17th Street, Suite 2100

Denver, Colorado 80202

Ladies and Gentlemen:

We have acted as counsel for BKV Corporation, a Delaware corporation (the “Company”), in connection with the proposed offer and sale in an underwritten public offering (the “Offering”) of an aggregate of 11,145,902 shares of the Company’s Common Stock, par value $0.01 per share (the “Common Stock”), which includes (i) 7,003,813 shares of Common Stock (the “Primary Shares”) to be issued and sold by the Company, including 1,453,813 shares of Common Stock issued and sold by the Company upon the exercise by the underwriter of an option to purchase additional shares of Common Stock and (ii) 4,142,089 shares of Common Stock (the “Secondary Shares”) to be offered and sold by Bedrock Energy Partners, LLC, as the selling stockholder (the “selling stockholder”), pursuant to that certain Underwriting Agreement, dated March 10, 2026 (the “Underwriting Agreement”), by and among the Company, the selling stockholder and RBC Capital Markets, LLC.

We refer to (i) the registration statement on Form S-3ASR (Registration Statement No. 333-292408) with respect to the Secondary Shares being sold by the selling stockholder in the Offering, which registration statement was filed by the Company with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), on December 23, 2025 (the “Secondary Registration Statement”), including the related prospectus dated December 23, 2025 (the “Secondary Prospectus”), and (ii) the registration statement on Form S-3 (Registration Statement No. 333-290676) with respect to the Primary Shares being sold by the Company in the Offering, which registration statement was filed by the Company with the Commission under the Securities Act on October 1, 2025 and became effective on December 1, 2025 (the “Shelf Registration Statement” and, together with the Secondary Registration Statement, the “Registration Statements”), including the related prospectus dated December 1, 2025 (the “Shelf Prospectus” and, together with the Secondary Prospectus, the “Base Prospectuses”). The final prospectus supplement dated March 10, 2026 (the “Prospectus Supplement”), which together with the accompanying Base Prospectuses (collectively, the “Prospectus”), has been filed by the Company with the Commission pursuant to Rule 424(b) and Rule 429 promulgated under the Securities Act.

In our capacity as your counsel in the connection referred to above and as a basis for the opinion hereinafter expressed, we have examined (i) the Underwriting Agreement, (ii) the Second Amended and Restated Certificate of Incorporation of the Company, (iii) the Second Amended and Restated Bylaws of the Company, (iv) records of proceedings of the Company’s Board of Directors, including committees thereof, (v) originals, or copies certified or otherwise identified, of certificates of public officials and of representatives of the Company, (vi) the Registration Statements and the Prospectus and (vii) statutes and other instruments and documents as we have deemed necessary or advisable for the purpose of rendering the opinion hereinafter expressed.

In addition, in giving the opinion hereinafter expressed, we have relied, to the extent we deemed proper, without independent investigation, upon certificates, statements and other representations of officers and other representatives of the Company and of governmental and public officials with respect to the accuracy and completeness of the material factual matters contained therein or covered thereby, and we have assumed, without independent investigation, that the signatures on all documents examined by us are genuine, that all documents submitted to us as originals are accurate and complete, that all documents submitted to us as copies are true and correct copies of the originals thereof, that such original copies are authentic and complete and that all information submitted to us was accurate and complete.

Based upon and subject to the foregoing, we are of the opinion that (i) the Primary Shares, when issued and delivered in the Offering on behalf of the Company in accordance with the terms of the Underwriting Agreement upon payment of the consideration therefor provided for therein, will be duly authorized, validly issued, fully paid and nonassessable, and (ii) the Secondary Shares are duly authorized, validly issued, fully paid and nonassessable.

The opinion set forth above is limited in all respects to matters of the General Corporation Law of the State of Delaware, and applicable reported judicial decisions, rules and regulations interpreting and implementing those laws, in each case, as in effect on the date hereof. We express no opinion as to the effect of the laws of any other jurisdiction.

At your request, this opinion is being furnished to you for filing as an exhibit to the Company’s Current Report on Form 8-K filed on the date hereof.  We hereby consent to the statements with respect to us under the heading “Legal Matters” in the Prospectus and to the filing of this opinion as an exhibit to the Company’s Current Report on Form 8-K filed on the date hereof. In giving this consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission thereunder.