Document:

<PAGE>   1
                                                                   EXHIBIT 10.12

                        [APPROPRIATE COMPANY LETTERHEAD]
         [PENNZOIL-QUAKER STATE COMPANY BENEFITS ACCELERATION AGREEMENT]

                                     (DATE)

PERSONAL & CONFIDENTIAL

(NAME)
(ADDRESS)

Dear (NAME):

                  You have previously been or may be designated a participant in
the Pennzoil-Quaker State Company Supplemental Life Insurance Plan (the
"Supplemental Life Insurance Plan"), a Company medical benefits plan and any
current and future stock option plans of the Company. In addition, you are
eligible to participate in the Pennzoil-Quaker State Company Savings and
Investment Plan (the "Savings and Investment Plan"). Your designation as a
participant or an eligible participant and participation in these plans has been
and is intended by the Company as additional compensation. The Company intends
that you not be unfairly deprived of the opportunity to fulfill service and age
prerequisites to entitlement to receipt of benefits in the described plans
because of or in connection with a change in control of the Company.

                  Accordingly, in consideration of your agreement to remain in
continued employment with the Company or its subsidiaries as (POSITION), or in
such other executive capacity as may be determined from time to time by the
Board of Directors of the Company and your agreement to devote your normal
working time to the business interests and activities of the Company and to
perform the duties and responsibilities assigned to you by the Board of

                                       1
<PAGE>   2

Directors to the best of your ability and with reasonable diligence, in the
event of a change in control of the Company, you will be entitled to the cash
payments described in Section I below. In addition, in the event that your
employment is terminated upon or within six months following the Effective Date
of such change in control, you will be entitled to the continued life insurance,
medical benefits and cash payments described in Section II below.

                 For purposes of this Agreement, a change in control shall
conclusively be deemed to have occurred (i) if the Board of Directors of the
Company determines by resolution that a change in control which has the
reasonable likelihood of depriving key employees of benefits they otherwise
would have earned, by depriving key employees of the opportunity to fulfill
applicable service and age prerequisites to benefits or otherwise, has occurred,
or (ii) upon the occurrence of an event specified for such purposes as a change
in control which has the reasonable likelihood of depriving key employees of
benefits they otherwise would have earned, by depriving key employees of the
opportunity to fulfill applicable service and age prerequisites to benefits or
otherwise, by resolution of the Board of Directors adopted not more than 60 days
prior to the occurrence of such event. The Effective Date of a change in control
shall be (a), in the case of such a change in control determined as specified in
clause (i) of the preceding sentence, the date (not more than 30 days prior to
the date on which the Board of Directors makes the determination) the Board of
Directors determines as the date on which the change in control has occurred, or
(b), in the case of such a change in control determined as specified in clause
(ii) of the preceding sentence, the date of occurrence of the event specified by
the Board of Directors as constituting such change in control.

                  I. In the event that a change in control as defined in this
Agreement occurs, you will receive from the Company forthwith cash payments
equal to the amount determined by

                                       2

<PAGE>   3

adding, for each share of Common Stock of the Company as to which a nonqualified
Option granted you under any stock option plan of the Company is not exercisable
on the Effective Date, the excess of the Value (as hereinafter defined) of such
Common Stock over the option price of such share; provided, however, that to the
extent any such Option has become exercisable and been exercised before the
amount described in this subparagraph is paid to you, you shall not receive any
payment under this Section I in lieu of such Option.

                  II. In the event that your employment with the Company is
terminated, whether voluntarily or involuntarily for any reason other than
death, upon or within six months following the Effective Date:

                  1. You will receive from the Company forthwith a cash payment
equal to the sum of the cash and the Value (as hereinafter defined) of the
Common Stock of the Company credited to your accounts maintained pursuant to the
Savings and Investment Plan that are not vested on the date of your termination
of employment.

                  2. Both the life insurance coverage provided you under the
Supplemental Life Insurance Plan in effect on the Effective Date and the medical
benefits coverage provided you, your spouse and dependents under the Company's
medical benefits plan in which you are participating as of the Effective Date
(as in effect on the Effective Date) shall be continued for one year after your
termination date.

                  For purposes of this Agreement, the Value of a share of Common
Stock of the Company shall mean the amount determined to be the fair value per
share thereof by the Board of Directors of the Company in the resolution or
resolutions adopted by it determining that a change in control has occurred or
will occur upon the occurrence of an event specified as a change in control, or,
in the absence of any such determination of fair value by the Board of

                                       3
<PAGE>   4

Directors, the average of the closing prices per share of the Common Stock on
the New York Stock Exchange Composite Tape during the ten trading days
immediately prior to the Effective Date. In the event the Board of Directors
determines the fair value, the amount so determined shall be not less than the
ten-day average price computed in accordance with the preceding sentence and not
in excess of an amount (assuming that such amount is in excess of such ten-day
average) equal to the highest consideration paid for the Common Stock in any
offer to the holders thereof made as a part or in connection with the
transaction or transactions resulting in the change in control.

                  If you find that this Agreement accurately describes the
agreement between Pennzoil-Quaker State Company and you concerning certain of
your employee benefits, please sign two copies of this Agreement and return one
to the Company, whereupon this letter shall constitute a binding agreement
between Pennzoil-Quaker State Company and you.

                This letter Agreement shall be effective as of (EFFECTIVE_DATE).

                                              Very truly yours,

                                              PENNZOIL-QUAKER STATE COMPANY

                                              By:
                                                 -------------------------------
                                                      James W. Shaddix
                                                      General Counsel

Accepted and Agreed to this
       day of
------       --------------

                                       4<PAGE>   1
                                                                   EXHIBIT 10.13

                   [PENNZOIL-QUAKER STATE COMPANY LETTERHEAD]

                                                                     May 4, 2000

Mr. James L. Pate
Chairman and CEO
Pennzoil-Quaker State Company
P. O. Box 2967
Houston, Texas  77252-2967

Dear Jim:

                  We propose the following Agreement to be effective as of May
4, 2000, for the three years commencing January 1, 2001, which is the day after
the termination of your employment with Pennzoil-Quaker State Company.

                  In consideration of the mutual promises and understanding
contained in this Agreement, you and Pennzoil-Quaker State Company agree as
follows:

         1.       The term of this Agreement shall be three years from January
                  1, 2001.

         2.       Office and secretarial support will be furnished in Houston in
                  accordance with the policy attached hereto as Exhibit A.

         3.       During the term of this Agreement, you will not, without the
                  prior written consent of Pennzoil-Quaker State Company, engage
                  directly or indirectly in any business or endeavor
                  (financially as an individual, investor or lenders or as an
                  employee, director, officer, partner, independent contractor,
                  consultant or owner or in any other capacity calling for the
                  rendition of personal services or acts of management,
                  operation or control) which is in competition or inconsistent
                  with, or adverse to or opposed to, the interests of
                  Pennzoil-Quaker State Company. You should contact the Chief
                  Executive Officer of Pennzoil-Quaker State Company to request
                  such written consent prior to determining it is appropriate to
                  engage in any particular business or endeavor. Notwithstanding
                  the above, you are not prohibited from investing or trading on
                  your own behalf in publicly traded securities of other
                  companies.

<PAGE>   2

Mr. James L. Pate                          -2-                       May 4, 2000

         4.       During the term of this Agreement, Pennzoil-Quaker State
                  Company will pay you a total of $2,100,000 on a payment
                  schedule as follows: payment will be made in equal monthly
                  amounts of $58,333.33 (except that the last payment shall be
                  $58,333.45) on the first day of the month, commencing January
                  1, 2001, and continuing each month thereafter with the last
                  payment payable on the first day of December, 2003. In
                  addition, Pennzoil-Quaker State Company will reimburse you for
                  all reasonable and necessary travel expenses incurred in
                  performing services for Pennzoil-Quaker State Company in
                  accordance with the policy set forth in Exhibit A. In the
                  event of your death or disability after December 31, 2000, any
                  amount unpaid under the terms hereof shall be paid to your
                  spouse, if living, or to your estate, on the same terms as
                  provided hereunder for payment, or, in the sole discretion of
                  the Board of Directors of Pennzoil-Quaker State Company, at
                  such earlier date as determined by the Board of Directors of
                  Pennzoil-Quaker State Company.

         5.       Neither you, nor your spouse or other beneficiaries shall have
                  the right to assign any part of your or their rights under
                  this Agreement. This Agreement contains the entire
                  understanding between Pennzoil-Quaker State Company and you
                  regarding this matter and supersedes any prior agreement
                  between the parties.

         6.       This Agreement may not be changed or otherwise amended except
                  by mutual consent evidenced in writing and executed by both
                  parties to this Agreement.

         7.       This Agreement is governed by the laws of the State of Texas.

                                                   Very truly yours,

                                                   /s/ JAMES J. POSTL
                                                   -----------------------------
                                                   James J. Postl
                                                   President
                                                   Pennzoil-Quaker State Company

Accepted and agreed to as of the 4th day of May, 2000.

/s/ JAMES L. PATE
-------------------------
James L. Pate

<PAGE>   3

                                                                       EXHIBIT A

                              SUPPORT AND EXPENSES

                  The following are policies with respect to support and
expenses of Mr. Pate during the three-year period commencing January 1, 2001:

         1.       Company cars and aircraft may be utilized, with any personal
                  use of aircraft subject to IRS imputed income requirements.

         2.       Expenses incurred by Mr. Pate in furtherance of the Company's
                  business shall be reimbursed in accordance with customary
                  Company practices and procedures regarding expense
                  reimbursements.

                  The following are existing Company policies with respect to
retired chief executive officers and will continue throughout Mr. Pate's
retirement:

         1.       Office space, furniture and equipment appropriate to the
                  status of a retired chairman of the board of a publicly-held
                  company will be provided.

         2.       Company will employ an executive assistant, acceptable to Mr.
                  Pate, who will be an employee of the Company with full
                  participation in the Company's employee benefit plans,
                  programs and practices. The executive assistant will report to
                  Mr. Pate and the duties and compensation of that assistant
                  will be determined by Mr. Pate (within the parameters of
                  overall Company guidelines and policy).

         3.       Mr. Pate and his executive assistant will be provided with
                  parking spaces acceptable to Mr. Pate.

         4.       Full reimbursement for cost of private ground transportation
                  service used in lieu of a Company chauffeured car.

Source: [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00021-of-00352.parquet"}, [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00021-of-00352.parquet"}]]