POWER OF ATTORNEY

      KNOW ALL BY THESE PRESENTS, that each of the undersigned hereby makes,
constitutes and appoints Eric D. Marsh, Wayne B. Stoltenberg and Jonathan C.
Curth, signing singly, the undersigned's true and lawful attorneys-in-fact, with
full power and authority as hereinafter described on behalf of and in the name,
place and stead of the undersigned to:

      (i)   execute for and on behalf of the undersigned, in the undersigned's
            capacity as a director, director nominee, officer or beneficial
            owner of shares of common stock (the "Shares") of Vine Energy Inc.,
            a Delaware corporation (the "Company"), any Schedule 13D or Schedule
            13G, and any amendments, supplements or exhibits thereto (including
            any joint filing agreements) required to be filed by the undersigned
            under Section 13 of the Securities Exchange Act of 1934, as amended,
            and the rules and regulations promulgated thereunder (the "Exchange
            Act"), and any Forms 3, 4, and 5 and any amendments, supplements or
            exhibits thereto required to be filed by the undersigned under
            Section 16(a) of the Exchange Act;

      (ii)  do and perform any and all acts for and on behalf of the
            undersigned which may be necessary or desirable to complete and
            execute any such Schedule 13D, Schedule 13G, Form 3, 4, or 5 and
            timely file such forms with the United States Securities and
            Exchange Commission and any stock exchange on which the Shares are
            then listed; and

      (iii) take any other action of any type whatsoever in connection with
            the foregoing which, in the opinion of such attorneys-in-fact, may
            be of benefit to, in the best interest of, or legally required by,
            the undersigned, it being understood that the documents executed by
            such attorneys-in-fact on behalf of the undersigned pursuant to this
            Power of Attorney shall be in such form and shall contain such terms
            and conditions as such attorneys-in-fact may approve in such
            attorneys-in-fact's discretion.

      The undersigned hereby grants to such attorneys-in-fact full power and
authority to do and perform any and every act and thing whatsoever requisite,
necessary, or proper to be done in the exercise of any of the rights and powers
herein granted, as fully to all intents and purposes as the undersigned might or
could do if personally present, with full power of substitution or revocation,
hereby ratifying and confirming all that such attorneys-in-fact's substitute or
substitutes, shall lawfully do or cause to be done by virtue of this Power of
Attorney and the rights and powers herein granted. The undersigned acknowledges
that the foregoing attorneys-in-fact, in serving in such capacity at the request
of the undersigned, are not assuming, nor is the Company assuming, any of the
undersigned's responsibilities to comply with Section 13 and Section 16 of the
Exchange Act.

      This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file reports or schedules under Section 13
or Section 16 of the Exchange Act with respect to the undersigned's holdings of
and transactions in securities issued by the Company, unless earlier revoked by
the undersigned in a signed writing delivered to the foregoing
attorneys-in-fact.

                                   * * * * *

      IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to
be executed as of this 17th day of March, 2021.


                                        /s/ Jonathan C. Curth
                                        -----------------------------------
                                        Jonathan C. Curth