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                                                                   EXHIBIT 10.31

                           AMENDMENT TO LOAN AGREEMENT

         THIS AMENDMENT TO LOAN AGREEMENT ("Amendment") dated as of January 1,
2000 (the "Amendment Effective Date") is made and entered into by and among M-I
L.L.C. (the "Borrower"), a Delaware limited liability company, the banking
institutions (each, together with its successors and assigns, a "Bank" and
collectively, the "Banks") from time to time a party to the Loan Agreement (as
hereinafter defined), as amended by this Amendment, ABN AMRO BANK N.V. and DEN
NORSKE BANK AS, as Co-Agents (in such capacity, together with their successors
in such capacity, collectively called the "Co-Agents") and CHASE BANK OF TEXAS,
NATIONAL ASSOCIATION (formerly known as Texas Commerce Bank National
Association), a national banking association, as agent for the Banks (in such
capacity, together with its successors in such capacity, the "Agent").

RECITALS:

         WHEREAS, the Borrower, the Banks, the Co-Agents, and the Agent are
parties to a Loan Agreement dated as of April 4, 1996, as amended by instruments
dated April 8, 1997, December 23, 1997 and August 31, 1998 (the "Loan
Agreement"); and

         WHEREAS, the Borrower, the Banks, the Co-Agents, and the Agent have
agreed, on the terms and conditions herein set forth, that the Loan Agreement be
amended in certain respects;

         NOW, THEREFORE, IT IS AGREED:

         Section 1. Definitions. Terms used herein which are defined in the Loan
Agreement shall have the same meanings when used herein unless otherwise
provided herein.

         Section 2. Amendments to the Loan Agreement. On and after the Amendment
Effective Date, the Loan Agreement shall be amended as follows:

         (a) Clause (vii) of the definition of "Permitted Investments" set forth
in Section 1.1 of the Loan Agreement is hereby amended to read in its entirety
as follows:

                  (vii) loans or advances to Smith or Schlumberger, or
         Affiliates of Smith or Schlumberger, and other loans or advances in the
         usual and ordinary course of business to officers, directors and
         employees for expenses incidental to carrying on the business of the
         Borrower, any Subsidiary;

         (b) A new definition of "Schlumberger" is hereby added to Section 1.1
of the Loan Agreement, such new definition to read in its entirety as follows:

             Schlumberger means Schlumberger Limited, a Netherland Antilles
             corporation.
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         (c) Section 7.3(b) of the Loan Agreement is hereby amended to read in
its entirety as follows:

                   (b) Net Worth - Net Worth of not less than (1) for the period
             commencing on January 1, 2000 through and including March 31, 2000,
             $600,000,000 and (2) for each fiscal quarter thereafter, the
             minimum Net Worth required during the immediately preceding fiscal
             quarter plus 50% of the Net Income (if positive) of the Borrower
             for the immediately preceding fiscal quarter plus 100% of any
             increase in Net Worth during such fiscal quarter resulting from any
             merger, sale or issuance of equity.

         (d) A new Section 9.1(m) is hereby added to the Loan Agreement, such
new section to read in its entirety as follows:

                   (m) Default under Smith International Facility - a default or
             an event of default shall occur under the Smith International
             Facility (without amendment except as approved by the Majority
             Banks and regardless of whether the Smith International Facility
             shall have been paid in full or shall have terminated in accordance
             with its terms) or the Smith International Facility shall be
             refinanced or terminated; or any provision of the Smith
             International Facility shall be amended or modified--or any waiver
             of any provision of the Smith International Facility shall be
             obtained or granted--without the prior written consent of the
             Majority Banks.

         Section 3. Consent to Transfer of Equity Interest in Borrower. The
Banks hereby consent to the transfer to Schlumberger, Inc. of a forty percent
(40%) equity interest in and to Borrower.

         Section 4. Limitations. The amendments set forth herein are limited
precisely as written and shall not be deemed to (a) be a consent to, or waiver
or modification of, any other term or condition of the Loan Agreement or any of
the other Loan Documents, or (b) except as expressly set forth herein, prejudice
any right or rights which the Banks may now have or may have in the future under
or in connection with the Loan Agreement, the Loan Documents or any of the other
documents referred to therein. Except as expressly modified hereby or by express
written amendments thereof, the terms and provisions of the Loan Agreement, the
Notes, and any other Loan Documents or any other documents or instruments
executed in connection with any of the foregoing are and shall remain in full
force and effect. In the event of a conflict between this Amendment and any of
the foregoing documents, the terms of this Amendment shall be controlling.

         Section 5. Payment of Expenses. The Borrower agrees, whether or not the
transactions hereby contemplated shall be consummated, to reimburse and save the
Co-Agents, the Agent and the Bank(s) harmless from and against liability for the
payment of all reasonable substantiated out-of-pocket costs and expenses arising
in connection with the preparation, execution, delivery and enforcement of, or
the preservation of any rights under this Amendment, including, without
limitation, the reasonable fees and expenses of any local or other counsel for
the Agent, and all stamp taxes (including interest and penalties, if any),
recording taxes and fees, filing taxes and fees, and other similar charges which
may be payable in respect of, or in respect of any modification of,


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the Loan Agreement and the other Loan Documents. The provisions of this Section
shall survive the termination of the Loan Agreement and the repayment of the
Loans.

         Section 6. Governing Law. This Amendment and the rights and obligations
of the parties hereunder and under the Loan Agreement shall be construed in
accordance with and be governed by the laws of the State of Texas and the United
States of America.

         Section 7. Descriptive Headings, etc. The descriptive headings of the
several Sections of this Amendment are inserted for convenience only and shall
not be deemed to affect the meaning or construction of any of the provisions
hereof.

         Section 8. Entire Agreement. This Amendment and the documents referred
to herein represent the entire understanding of the parties hereto regarding the
subject matter hereof and supersede all prior and contemporaneous oral and
written agreements of the parties hereto with respect to the subject matter
hereof, including, without limitation, any commitment letters regarding the
transactions contemplated by this Amendment.

         Section 9. Counterparts. This Amendment may be executed in any number
of counterparts and by different parties on separate counterparts and all of
such counterparts shall together constitute one and the same instrument.
Complete sets of counterparts shall be lodged with the Borrower and the Agent.

         Section 10. Amended Definitions. As used in the Loan Agreement
(including all Exhibits thereto) and all other instruments and documents
executed in connection therewith, on and subsequent to the Amendment Effective
Date the term (i) "Agreement" shall mean the Loan Agreement as amended by this
Amendment, and (ii) references to any and all other Loan Documents shall mean
such documents as amended as contemplated hereby.


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         IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
duly executed and delivered by their respective duly authorized offices as of
the date first above written.


                                           M-I L.L.C.


                                           By: /s/ MARGARET DORMAN
                                              ----------------------------------
                                           Name:   MARGARET DORMAN
                                                --------------------------------
                                           Title:  Sr. V.P. & CFO
                                                 -------------------------------


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                                        CHASE BANK OF TEXAS, NATIONAL
                                         ASSOCIATION, as the Agent and as a Bank


                                        By:    /s/  MONA M. FOCH
                                           -------------------------------------
                                        Name:       MONA M. FOCH
                                              ----------------------------------
                                        Title:      MANAGING DIRECTOR
                                              ----------------------------------


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                                        THE CHASE MANHATTAN BANK


                                        By:   /s/ PETER M. LING
                                           -------------------------------------
                                        Name:     PETER M. LING
                                             -----------------------------------
                                        Title:    VICE PRESIDENT
                                              ----------------------------------


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                                        ABN AMRO BANK, N.V.,
                                        as Co-Agent and as a Bank


                                        By:    /s/ CHARLES W. RANDALL
                                           -------------------------------------
                                        Name:      CHARLES W. RANDALL
                                             -----------------------------------
                                        Title:     SENIOR VICE PRESIDENT
                                              ----------------------------------


                                        By:     /s/ BRANDI LIPPINCOTT
                                           -------------------------------------
                                        Name:       BRANDI LIPPINCOTT
                                             -----------------------------------
                                        Title:      ASSISTANT VICE PRESIDENT
                                              ----------------------------------


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                                        DEN NORSKE BANK AS,
                                        as Co-Agent and as a Bank


                                        By:   /s/ J. MORTEN KREUTZ
                                           -------------------------------------
                                        Name:     J. MORTEN KREUTZ
                                             -----------------------------------
                                        Title:    FIRST VICE PRESIDENT
                                              ----------------------------------



                                        By:   /s/ LASSE WAGENE
                                           -------------------------------------
                                        Name:     LASSE WAGENE
                                             -----------------------------------
                                        Title:    VICE PRESIDENT
                                              ----------------------------------


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                                        BANK OF AMERICA, N.A.


                                        By:  /s/ PAUL L. COLON
                                           -------------------------------------
                                        Name:    PAUL L. COLON
                                             -----------------------------------
                                        Title:   VICE PRESIDENT
                                              ----------------------------------


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                                        WELLS FARGO BANK (TEXAS), NATIONAL
                                        ASSOCIATION


                                        By:   /s/ FRANK W. SCHAGEMAN
                                           -------------------------------------
                                        Name:     FRANK W. SCHAGEMAN
                                             -----------------------------------
                                        Title:    VICE PRESIDENT
                                              ----------------------------------

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                                        UNION BANK OF CALIFORNIA N.A.


                                        By:    /s/ J. SCOTT JESSUP
                                           -------------------------------------
                                        Name:      J. SCOTT JESSUP
                                             -----------------------------------
                                        Title:     VICE PRESIDENT
                                              ----------------------------------


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                                        BANK OF NEW YORK


                                        By:   /s/ HELEN L. SARRO
                                           -------------------------------------
                                        Name:     HELEN L. SARRO
                                             -----------------------------------
                                        Title:    VICE PRESIDENT
                                              ----------------------------------


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                                        FIRST UNION NATIONAL BANK (successor
                                        to Corestates Bank, N.A.)


                                        By:  /s/ ROBERT R. WETTEROFF
                                           -------------------------------------
                                        Name:    ROBERT R. WETTEROFF
                                             -----------------------------------
                                        Title:   SENIOR VICE PRESIDENT
                                              ----------------------------------



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