POWER OF ATTORNEY
                   FOR EXECUTING FORMS 3, FORMS 4, AND FORMS 5

The undersigned hereby constitutes and appoints Daniel J. Rice IV, Grayson T.
Lisenby, James W. Rogers and William E. Jordan, or any of them acting without
the other, with full power of substitution, as the undersigned's true and lawful
attorney-in-fact to:

        1.      execute for and on behalf of the undersigned any Form 3, Form 4,
                and Form 5 (including any amendments, corrections, supplements
                or other changes thereto) in accordance with Section 16(a) of
                the Securities Exchange Act of 1934, as amended (the "Exchange
                Act"), and the rules thereunder, but only to the extent each
                form relates to the undersigned's beneficial ownership of
                securities of Rice Midstream Partners LP or any of its
                subsidiaries;

        2.      do and perform any and all acts for and on behalf of the
                undersigned that may be necessary or desirable to complete and
                execute any Form 3, Form 4, or Form 5 (including any amendments,
                corrections, supplements or other changes thereto) and timely
                file the forms with the Securities and Exchange Commission and
                any stock exchange or quotation system, self-regulatory
                association or any other authority, and provide a copy as
                required by law or advisable to such persons as the
                attorney-in-fact deems appropriate; and

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

The undersigned hereby grants to the attorney-in-fact full power and authority
to do and perform all and every act 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 the attorney-in-fact shall lawfully do or cause to be done by virtue of
this Power of Attorney and the rights and powers granted herein. The undersigned
acknowledges that the attorneys-in-fact, in serving in such capacity at the
request of the undersigned, are not assuming (nor is Rice Midstream Partners LP
assuming) any of the undersigned's responsibilities to comply with Section 16 of
the Exchange Act.

The undersigned agrees that the attorney-in-fact may rely entirely on
information furnished orally or in writing by or at the direction of the
undersigned to the attorney-in-fact. The undersigned also agrees to indemnify
and hold harmless Rice Midstream Partners LP and the attorney-in-fact against
any losses, claims, damages or liabilities (or actions in these respects) that
arise out of or are based upon any untrue statements or omissions of necessary
facts in the information provided by or at the direction of the undersigned, or
upon the lack of timeliness in the delivery of information by or at the
direction of the undersigned, to the attorney-in fact for purposes of executing,
acknowledging, delivering or filing a Form 3, Form 4, or Form 5 (including any
amendments, corrections, supplements or other changes thereto) with respect to
the undersigned's holdings of and transactions in securities issued by Rice
Midstream Partners LP, and agrees to reimburse Rice Midstream Partners LP and
the attorney-in-fact on demand for any legal or other expenses reasonably
incurred in connection with investigating or defending against any such loss,
claim, damage, liability or action.

This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file Form 3, Form 4, and Form 5 (including
any amendments, corrections, supplements or other changes thereto) with respect
to the undersigned's holdings of and transactions in securities issued by Rice
Midstream Partners LP, unless earlier revoked by the undersigned in a signed
writing delivered to the attorney-in-fact. This Power of Attorney does not
revoke any other power of attorney that the undersigned has previously granted.

IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be
executed as of the date written below.

/s/ Stephanie C. Hildebrandt
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Signature

Stephanie C. Hildebrandt
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Type or Print Name

March 18, 2016
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Date