<PAGE>

                                                                   EXHIBIT 10.12

                    FOURTH AMENDMENT TO SECOND AMENDED AND
                   RESTATED LIMITED PARTNERSHIP AGREEMENT OF
                          ARGOSY ENERGY INTERNATIONAL

     THIS FOURTH AMENDMENT TO THE SECOND AMENDED AND RESTATED AGREEMENT OF
LIMITED PARTNERSHIP OF ARGOSY ENERGY INTERNATIONAL (this "Amendment") is made as
                                                          ---------
of 8:00 a.m., June 1, 2000, by and among the partners (collectively the
"Partners") of Argosy Energy International, a Utah limited partnership (the
 --------
"Partnership").
 -----------

                                   RECITALS

     WHEREAS, Argosy Energy Incorporated, a Delaware Corporation ("Argosy
                                                                   ------
Energy"), Parkside Investments, a Utah corporation ("Parkside"), P-5, Ltd., a
------                                               --------
Utah limited partnership ("P-5"), Go Deo, Inc., a Utah corporation ("Go Deo"),
                           ---                                       ------
Dale E. Armstrong ("Armstrong"), William Gaskin ("Gaskin"), Richard Shane
                    ---------                     ------
McKnight ("McKnight") and Garnet Resource Corporation, a Delaware corporation
           --------
("Garnet") entered into that certain Second Amended and Restated Limited
  ------
Partnership Agreement of Argosy Energy International dated January 11, 1991, as
amended by the Amendment to the Second Amended and Restated Limited Partnership
Agreement of Argosy Energy International dated January 13, 1994, the Second
Amendment to the Second Amended and Restated Limited Partnership Agreement of
Argosy Energy International dated July 1, 1994, and the Third Amendment to the
Second Amended and Restated Limited Partnership Agreement of Argosy Energy
International dated May 31, 2000 (as amended, the "Original Partnership
                                                   --------------------
Agreement");
---------

     WHEREAS, on March 16, 1995, Garnet acquired though multiple conveyances all
of the limited partnership interests in and to the Partnership previously owned
by Parkside, P-5 and Go Geo;

     WHEREAS, on February 12, 1996, Gaskin assigned all of his limited
partnership interests in and to the Partnership to Argosy Energy, Garnet,
Armstrong and McKnight;

     WHEREAS, effective January 1, 1999, Neo Energy, Inc. ("Neo") acquired by
                                                            ---
contribution of property to the Partnership a 49.9054% limited partnership
interest in and to the Partnership, which resulted in a corresponding decrease
in the percentage interests of Garnet, Armstrong and McKnight;

     WHEREAS, pursuant to that certain Assignment and Assumption Agreement by
and between Neo and Crosby Capital, LLC, a Texas limited liability company
("Crosby LP") dated effective 7:00 a.m., June 1, 2000, Neo transferred a
  ---------
49.9054% limited partnership interest in the Partnership to Crosby LP ("Neo
                                                                        ---
Transfer");
--------
<PAGE>

         WHEREAS, pursuant to that certain Assignment and Assumption Agreement
by and between Argosy Energy and Crosby Acquisition, LLC, a Delaware limited
liability company ("Crosby GP"), dated effective 7:00 a.m., June 1, 2000, Argosy
                    ---------
Energy transferred a 44.6403% general partnership interest in the Partnership to
Crosby GP ("GP 1 Transfer");
            -------------

         WHEREAS, pursuant to that certain Assignment and Assumption Agreement
by and between Garnet and Crosby LP dated effective 7:00 a.m., June 1, 2000,
Garnet transferred a 5.0738% limited partnership interest in the Partnership to
Crosby LP ("Garnet Transfer");
            ---------------

         WHEREAS, pursuant to that certain Assignment and Assumption Agreement
by and between Crosby LP and Aviva Overseas, Inc., a Delaware corporation
("Aviva"), dated effective 7:30 a.m., June 1, 2000, Crosby LP transferred a
  -----
22.1196% limited partnership interest in the Partnership to Aviva ("Aviva
                                                                    -----
Transfer");
--------

         WHEREAS, the Partners desire to admit Crosby GP as an additional
General Partner, Crosby LP as an additional Limited Partner and Aviva as an
additional Limited Partner in the Partnership as of 8:00 a.m., June 1, 2000;

         WHEREAS, simultaneously with the execution of this Amendment, Crosby GP
desires to convert its 44.6403% general partnership interest in the Partnership
into a .4999% general partnership interest and a 44.1404% limited partnership
interest in the Partnership ("Conversion");
                              ----------

         WHEREAS, immediately after the execution of this Amendment, Crosby GP
desires to transfer the 44.1404% limited partnership interest in the Partnership
to Crosby LP pursuant to that certain Assignment and Assumption Agreement by and
between Crosby GP and Crosby LP dated effective 9:00 a.m., June 1, 2000 ("Crosby
                                                                          ------
Transfer");
--------

         WHEREAS, immediately after the admittance of Crosby GP as an additional
general partner, Argosy Energy desires to transfer its remaining .0001% general
partnership interest to Crosby GP pursuant to that certain Assignment and
Assumption Agreement by and between Argosy Energy and Crosby GP dated effective
9:00 a.m., June 1, 2000 ("GP 2 Transfer");
                          -------------

         WHEREAS, Garnet, Neo and Argosy Energy desire to withdraw as Partners
from the Partnership after all of the foregoing events as of 8:00 a.m., 8:00
a.m. and 9:00 a.m., June 1, 2000, respectively;

         WHEREAS, the undersigned Partners, which comprise the requisite percent
of Partners under the Original Partnership Agreement needed to approve the
foregoing transactions, desire to amend the Original Partnership Agreement to
reflect their approval of the (i) Neo Transfer, (ii) GP 1 Transfer, (iii)
Conversion, (iv) Crosby Transfer, (v) Garnet Transfer, (vi) GP 2 Transfer, (vii)
Aviva Transfer, (viii) admission of Crosby LP as a Limited Partner effective
8:00 a.m., June 1, 2000, (ix) admission of Crosby GP as an additional General
Partner effective 8:00 a.m., June 1, 2000, (x) admission of Aviva as a Limited
Partner effective 8:00 a.m., June 1, 2000, (xi) the withdrawal of Garnet and Neo
effective 8:00 a.m.,

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<PAGE>

June 1, 2000, and (xii) the withdrawal of Argosy Energy effective 9:00 a.m.,
June 1, 2000; and

         WHEREAS, this Amendment is being entered into, inter alia, to
effectuate certain terms agreed to by the parties under that certain Loan,
Settlement and Acquisition Agreement, dated effective May 31, 2000, by and among
Crosby LP, Aviva Petroleum Inc., Aviva America, Inc., Aviva Operating Co.,
Aviva, Neo, Garnet Argosy Energy and the Partnership.

                                   AGREEMENT

         NOW, THEREFORE, the Partners agree as follows:

         1. The Partners hereby approve the (i) Neo Transfer, (ii) GP 1
Transfer, (iii) GP 2 Transfer, (iv) Crosby Transfer, (v) Garnet Transfer and
(vi) Aviva Transfer.

         2. Crosby GP's general partnership interest is hereby converted into a
 .4999% general partnership interest and a 44.1404% limited partnership interest
effective as of 8:00 a.m. on June 1, 2000.

         3. Crosby GP is hereby admitted to the Partnership as a .4999%
additional General Partner effective as of 8:00 a.m. on June 1, 2000, and a
 .5000% General Partner effective as of 9:00 a.m. on June 1, 2000.

         4. Crosby LP is hereby admitted to the Partnership as an additional
Limited Partner, effective as of 8:00 a.m. on June 1, 2000.

         5. Aviva is hereby admitted to the Partnership as an additional Limited
Partner, effective as of 8:00 a.m. on June 1, 2000.

         6. The Partners hereby approve the withdrawal of Garnet and Neo
effective as of 8:00 a.m. on June 1, 2000.

         7. The Partners hereby approve the withdrawal of Argosy Energy
effective as of 9:00 a.m. on June 1, 2000.

         [THE REMAINDER OF THIS PAGE IS INTENTIONALLY LEFT BLANK]

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         8.    As of 9:00 a.m. on June 1, 2000, the following persons are
Partners of the Partnership, shall be referred to as indicated, and shall have
the percentage interests indicated:

                         Partners                        Percentage Interests
                         --------                        --------------------

General Partner:
---------------

         Crosby Acquisition, LLC                                 .5000%

Limited Partners:
----------------

         Crosby Capital, LLC                                   77.0000%

         Aviva Overseas, Inc.                                  22.1196%

         Dale E. Armstrong                                       .2901%

         Richard Shane McKnight                                  .0903%
                                                                 -----
                  Total                                            100%


         9.    The Partners hereby agree that, if elected by the Crosby GP in
its sole discretion, the Partnership shall make a Code Section 754 election with
respect to the transactions contemplated by this Amendment.

         10.   The Partners hereby agree that no distributions shall be made by
the Partnership to any Partner between 7:00 a.m. and 9:00 a.m. on June 1, 2000.

         11.   Section 7.1 of the Original Partnership Agreement is hereby
deleted in its entirety and replaced with the following Section 7.1, which shall
read as follows:

               Section 7.1    Allocations of Profits and Losses.

               After giving effect to the special allocations set forth in
         Section 7.2, for any taxable year of the Partnership ending after June
         1, 2000, all Net Profits or Net Losses for such year will be allocated
         to the Partners as follows:

               (a)  Net Profits.
                    -----------

                    (i)   Loss Chargeback. First, to the Partners, pro rata,
                          ---------------
               until the cumulative Net Profits allocated to each Partner under
               this Section 7.1(a)(i) equals the cumulative Net Loss allocated
               to such Partner under Section 7.1(b)(ii) for all prior periods;
               and

                    (ii)  Balance.  The balance, if any, to the Partners in
                          -------
               proportion to their respective Percentage Interests in the
               Partnership.

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<PAGE>

               (b)  Net Loss.
                    --------

                    (i)  Gain Chargeback.  First, to the Partners, pro rata,
                         ---------------
               until the cumulative Net Loss allocated to each Partner under
               this Section 7.1(b)(i) equals the cumulative Net Profits
               allocated to such Partner under Section 7.1(a)(ii) for all prior
               periods; and

                    (ii) Balance.  The balance, if any, to the Partners in
                         -------
               proportion to their respective Percentage Interests in the
               Partnership.

         12.   Exhibit B of the Original Partnership Agreement is hereby
superceded and replaced in its entirety with the attached Exhibit B.

         13.   In all other respects, the Original Partnership Agreement is
hereby ratified and confirmed.

         14.   Aviva, Crosby LP and Crosby GP hereby agree to be bound by the
terms of the Original Partnership Agreement, as amended by this Amendment, as of
the date of their admission as a Partner of the Partnership.

         15.   Terms not otherwise defined herein shall have the meaning set
forth in the Original Partnership Agreement.

         16.   In the event any one or more provisions contained in this
Amendment shall be held to be invalid, illegal or unenforceable in any respect,
such invalidity, illegality or unenforceability shall not affect the validity of
any other provision hereof and this Amendment shall be construed as if such
invalid, illegal or unenforceable provision had never been contained herein,
provided that the basic intent of this Amendment is not thereby impaired.

         17.   This Amendment may be executed in any number of counterparts each
of which shall be an original and all of which shall together constitute one and
the same Amendment.

         [THE REMAINDER OF THIS PAGE IS INTENTIONALLY LEFT BLANK]

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         IN WITNESS WHEREOF, the undersigned have executed this Amendment to be
effective with respect to each of them as of the date and time of their
admission to or withdrawal from the Partnership.

GENERAL PARTNER:
---------------

CROSBY ACQUISITION, LLC,
a Delaware limited liability company

         By:    CROSBY CAPITAL, LLC as Sole Member
         By:    /s/ Jay A. Chaffee
                ------------------
         Name:  Jay A. Chaffee
                --------------
         Title: President
                ---------

LIMITED PARTNERS:
----------------


CROSBY CAPITAL, LLC
a Texas limited liability company

         By:    /s/ Jay A. Chaffee
                ------------------
         Name:  Jay A. Chaffee
                --------------
         Title: President
                ---------

AVIVA OVERSEAS, INC.


         By:    /s/ R. Suttill
                --------------
         Name:  Ron Suttill
                -----------
         Title: President
                ---------

WITHDRAWING PARTNERS:
--------------------


ARGOSY ENERGY, INC.,
a Delaware corporation


         By:    /s/ R. Suttill
                --------------
         Name:  Ron Suttill
                -----------
         Title: President
                ---------

                                       6
<PAGE>

NEO ENERGY, INC.,
a Texas corporation


         By:    /s/ R. Suttill
                --------------
         Name:  Ron Suttill
                -----------
         Title: President
                ---------

GARNET RESOURCES, CORP.,
a Delaware corporation


         By:    /s/ R. Suttill
                --------------
         Name:  Ron Suttill
                -----------
         Title: President
                ---------

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