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

December 23, 2025

BKV Corporation

1200 17^th Street, Suite 2100

Denver, Colorado 80202

Ladies and Gentlemen:

We have acted as counsel to BKV Corporation, a Delaware corporation (the “Company”), with respect to certain legal matters in connection with the preparation of the Registration Statement on Form S-3 (the “Registration Statement”) to be filed by the Company on or about the date hereof with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), registering the offer and resale, from time to time pursuant to Rule 415 under the Act, by the selling stockholder identified therein (the “Selling Stockholder”), of up to 5,233,957 shares of the Company’s common stock, par value $0.01 per share (the “Securities”), pursuant to and in accordance with the registration rights agreement, dated as of September 29, 2025, by and between the Company and the Selling Stockholder (the “Registration Rights Agreement”). The Registration Statement includes a base prospectus (the “Base Prospectus”) that provides it will be supplemented in the future, if required, by one or more prospectus supplements (each, a “Prospectus Supplement”). At your request, this opinion is being furnished to you for filing as Exhibit 5.1 to the Registration Statement.

In our capacity as your counsel in the connection referred to above and as a basis for the opinions herein after expressed, we have examined originals, or copies certified or otherwise identified, of (i) the Company’s Second Amended and Restated Certificate of Incorporation and Second Amended and Restated Bylaws, each as amended to date (together, the “Charter Documents”), (ii) corporate records of the Company, (iii) the Registration Statement, including the Base Prospectus contained therein relating to the Securities, (iv) the Registration Rights Agreement, (v) certificates of governmental and public officials and of officers and other representatives of the Company and (vi) statutes and such other records, certificates, documents and instruments as we have deemed necessary or advisable as a basis for giving the opinions set forth below.

In giving such opinions below, we have relied, to the extent we deemed proper, without independent investigation or verification, upon the truth and accuracy of the representations and warranties in the documents reviewed by us and the 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.

In making our examination, we have assumed, without independent investigation or verification, the legal capacity and competency of all natural persons, that each document submitted to us for review is accurate and complete, each such document that is an original is authentic, each such document that is a copy conforms to an authentic original and all signatures on each such document are genuine.

In connection with this opinion, we also have assumed that:

(i)             the Registration Statement and any amendments thereto (including post-effective amendments) will have become effective and comply with all applicable laws under the Act and such effectiveness shall not have been terminated or rescinded;

(ii)            a Prospectus Supplement, if required, will have been prepared and filed with the Commission describing the Securities offered thereby;

(iii)           all Securities will be offered and sold in compliance with applicable federal and state securities laws and in the manner stated in the Registration Statement (including post-effective amendments thereto) and the appropriate Prospectus Supplement; and

(v)            a definitive purchase agreement, underwriting agreement or similar agreement with respect to any Securities offered (each, a “Purchase Agreement”), if applicable, will have been duly authorized and validly executed and delivered by the Company, the Selling Stockholder and the other parties thereto, as applicable.

On the basis of the foregoing, and subject to the assumptions, limitations, qualifications and exceptions set forth herein, we are of the opinion that the Securities proposed to be sold by the Selling Stockholder have been duly authorized and validly issued and are fully paid and nonassessable.

The opinions set forth above are limited in all respects to the General Corporation Law of the State of Delaware as in effect on the date hereof, and we express no opinion as to the law of any other jurisdiction.

We hereby consent to the filing of this opinion of counsel with the Commission as Exhibit 5.1 to the Registration Statement. We also consent to the reference to our Firm under the heading “Legal Matters” in the Base Prospectus forming a part of the Registration Statement. In giving such consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission thereunder.