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                                                                    EXHIBIT 3.4


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                        AGREEMENT OF LIMITED PARTNERSHIP

                                       OF

                             TEXAS PETROCHEMICALS LP




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                        AGREEMENT OF LIMITED PARTNERSHIP
                                       OF
                            TEXAS PETROCHEMICALS LP

                               TABLE OF CONTENTS

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                                                                                                          Page
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<S>          <C>                                                                                          <C>
                                                   ARTICLE I
                                                  DEFINITIONS
    1.01     CERTAIN DEFINITIONS.............................................................................1
    1.02     OTHER DEFINITIONS...............................................................................3
    1.03     CONSTRUCTION....................................................................................3

                                                  ARTICLE II
                                                 ORGANIZATION
    2.01     FORMATION.......................................................................................3
    2.02     NAME............................................................................................3
    2.03     REGISTERED OFFICE; REGISTERED AGENT; OTHER OFFICES..............................................3
    2.04     PURPOSES........................................................................................3
    2.05     CERTIFICATE, FOREIGN QUALIFICATION..............................................................4
    2.06     TERM............................................................................................4

                                                 ARTICLE III
                                            PARTNERSHIP INTERESTS
    3.01     INITIAL PARTNERS................................................................................4
    3.02     REPRESENTATIONS AND WARRANTIES..................................................................4
    3.03     GENERAL PROHIBITION.............................................................................4
    3.04     TRANSFER BY GENERAL PARTNER.....................................................................5
    3.05     TRANSFER BY LIMITED PARTNER.....................................................................5
    3.06     SECURITIES LAW COMPLIANCE.......................................................................5
    3.07     SUBSTITUTED PARTNERS............................................................................5
    3.08     ADDITIONAL PARTNERS.............................................................................5

                                                  ARTICLE IV
                                            CAPITAL CONTRIBUTIONS
    4.01     INITIAL CONTRIBUTIONS...........................................................................6
    4.02     SUBSEQUENT CONTRIBUTIONS........................................................................6
    4.03     ADVANCES BY PARTNERS............................................................................6

                                                  ARTICLE V
                                        ALLOCATIONS AND DISTRIBUTIONS
    5.01     ALLOCATIONS.....................................................................................6
    5.02     DISTRIBUTIONS...................................................................................6
    5.03     NO CAPITAL ACCOUNTS.............................................................................6
    5.04     WITHHOLDING: OTHER TAX PAYMENTS.................................................................6

                                                 ARTICLE VI
                                          MANAGEMENT AND OPERATION
    6.01     MANAGEMENT OF PARTNERSHIP AFFAIRS...............................................................7
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<TABLE>
<S>          <C>                                                                                           <C>
    6.02     RELIANCE ON AUTHORITY...........................................................................7
    6.03     OFFICERS AND OTHER AGENTS.......................................................................7
    6.04     COMPENSATION TO GENERAL PARTNER.................................................................9
    6.05     EXPENSES IN CONNECTION WITH ORGANIZATION OF THE PARTNERSHIP.....................................9
    6.06     REIMBURSEMENT OF EXPENSES.......................................................................9
    6.07     NATURE OF RELATIONSHIP..........................................................................9
    6.08     INDEMNIFICATION................................................................................10
    6.09     POWER OF ATTORNEY..............................................................................10
    6.10     OTHER ACTIVITIES...............................................................................10

                                              ARTICLE VII
                                           RIGHTS OF PARTNERS
    7.01     INFORMATION....................................................................................10
    7.02     LIMITATIONS....................................................................................10
    7.03     MEETINGS.......................................................................................10
    7.04     LIMITED LIABILITY..............................................................................10

                                              ARTICLE VIII
                                                 TAXES
    8.01     TAX RETURNS....................................................................................11
    8.02     TAX ELECTIONS..................................................................................11

                                               ARTICLE IX
                               BOOKS, RECORDS, REPORTS, AND BANK ACCOUNTS
    9.01     MAINTENANCE OF BOOKS...........................................................................11
    9.02     ACCOUNTS.......................................................................................11

                                               ARTICLE X
                                   WITHDRAWAL, REMOVAL, BANKRUPTCY, ETC.
    10.01    VOLUNTARY WITHDRAWAL...........................................................................12
    10.02    CONSEQUENCE OF WRONGFUL WITHDRAWAL.............................................................12
    10.03    CONVERSION OF INTEREST.........................................................................12
    10.04    REMOVAL OF THE GENERAL PARTNER.................................................................12
    10.05    NEW GENERAL PARTNER............................................................................12

                                               ARTICLE XI
                                              DISSOLUTION
    11.01    DISSOLUTION....................................................................................13
    11.02    CONTINUATION...................................................................................13
    11.03    EFFECT OF DISSOLUTION..........................................................................13

                                             ARTICLE XII
                           ALLOCATIONS AND DISTRIBUTIONS ON LIQUIDATION
    12.01    LIQUIDATION AND TERMINATION....................................................................14
    12.02    CANCELLATION OF CERTIFICATE....................................................................15


                                              ARTICLE XIII
                                           GENERAL PROVISIONS
    13.01    AMENDMENT OR MODIFICATION......................................................................15
    13.02    NOTICES........................................................................................15
    13.03    FAILURE TO PURSUE REMEDIES.....................................................................15
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<S>          <C>                                                                                           <C>
    13.04    SECTION HEADINGS...............................................................................15
    13.05    SEVERABILITY...................................................................................15
    13.06    GOVERNING LAW..................................................................................15
    13.07    CUMULATIVE REMEDIES............................................................................16
    13.08    COUNTERPARTS...................................................................................16
    13.09    SUCCESSORS AND ASSIGNS.........................................................................16
    13.10    SECTIONS, EXHIBITS, ETC........................................................................16
    13.11    FURTHER ASSURANCES.............................................................................16
    13.12    WAIVER OF CERTAIN RIGHTS.......................................................................16
    13.13    ATTORNEYS' FEES................................................................................16
    13.14    ENTIRE AGREEMENT...............................................................................16
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                        AGREEMENT OF LIMITED PARTNERSHIP
                                       OF
                             TEXAS PETROCHEMICALS LP

         This AGREEMENT OF LIMITED PARTNERSHIP (the "Agreement") of Texas
Petrochemicals LP is made and entered into as of the Effective Time (as defined
below) by and among the Partners (as defined below).

                                   WITNESSETH

         WHEREAS, this Partnership (as defined below) is created as part of a
plan of conversion and reorganization (the "Conversion") adopted by the Board of
Directors of Texas Petrochemicals Corporation, a Texas corporation (the
"Company"), and approved by all of the shareholders of the Company pursuant to
Article 5.17 of the Texas Business Corporation Act; and

         WHEREAS, all proper elections and filings will be made to classify this
Partnership as an association for federal tax purposes pursuant to Treasury
Regulation Section 301.7701-3(a) (and thus a corporation under Treasury
Regulation Section 301.7701-2(b)(2)) effective as of the Effective Time.

         NOW, THEREFORE, in consideration of the mutual covenants contained
herein and other good and valuable consideration, the receipt and sufficiency of
which are hereby acknowledged, and intending to be legally bound hereby, the
parties hereto do hereby agree as follows:

                                    ARTICLE I
                                   DEFINITIONS

         I.1 CERTAIN DEFINITIONS. As used in this Agreement, the following terms
have the following meanings:

         "Act" means the Texas Revised Limited Partnership Act, as amended from
time to time, and any successor law or laws.

         "Affiliate" means, with respect to any Person, any other Person
controlling, controlled by, or under common control with that first Person. As
used in this definition, the term "control " means (a) with respect to any
corporation or other entity having voting shares or the equivalent and elected
directors, managers, or Persons performing similar functions, the ownership or
power to vote more than 50% of shares or the equivalent having the power to vote
in the election of directors, managers, or Persons performing similar functions,
and (b) with respect to any other entity, the ability to direct its business and
affairs.

         "Agreement" means this Agreement of Limited Partnership of Texas
Petrochemicals LP as it may be amended in accordance with the provisions below.


<PAGE>   6


         "Articles of Conversion" means the Articles of Conversion of the
Company and the Partnership filed with the Secretary of State of the State of
Texas.

         "Capital Contribution" means any contribution by a Partner to the
capital of the Partnership.

         "Certificate" means the certificate of limited partnership of the
Partnership filed with the Secretary of State of the State of Texas along with
the Articles of Conversion pursuant to the Act and pursuant to Articles 5.17 and
5.18 of the Texas Business Corporation Act, as such certificate may be amended
or restated from time to time.

         "Code" means the Internal Revenue Code of 1986 and any successor
statute, as amended from time to time.

         "Company" shall have the meaning set forth in the recitals to this
Agreement.

         "Conversion" shall have the meaning set forth in the recitals to this
Agreement.

         "Effective Time" means 11:59 a.m., Houston, Texas time, on June 30,
2000.

         "General Interest Rate" means a rate per annum equal to the lesser of
(a) a varying rate per annum that is equal to the interest rate publicly quoted
by Chase Bank of Texas, National Association from time to time as its prime
commercial or similar reference interest rate, with adjustments in that varying
rate to be made on the same date as any change in that rate, and (b) the maximum
rate permitted by applicable law.

         "General Partner" means TPC Holding Corp., a Delaware corporation, or
any other Person subsequently admitted to the Partnership as a general partner
as provided in this Agreement, but does not include any Person who has ceased to
be a general partner in the Partnership.

         "Limited Partner" means any Person executing this Agreement as of the
date of this Agreement as a limited partner or subsequently admitted to the
Partnership as a limited partner as provided in this Agreement, but does not
include any Person who has ceased to be a limited partner.

         "Partner" means any General Partner or Limited Partner.

         "Partnership" has the meaning given that term in Section 2.01.

         "Partnership Assets" means all real and personal property owned by the
Partnership and any improvements thereto, and shall include both tangible and
intangible property.

         "Partnership Interest" means the interest of a Partner in the
Partnership, including, without limitation, rights to consent or to approve, or
rights to distributions (liquidating or otherwise), allocations, Sharing Ratios,
and information.


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         "Person" has the meaning given that term in Section 1.02(12) of the
Act.

         "Sharing Ratio" means, with respect to any Partner, a fraction
(expressed as a percentage), set forth by each Partner's name on Exhibit A
hereto, as the same may be amended from time to time.

         "Transfer" means a sale, assignment, transfer, exchange, mortgage,
pledge, grant of a security interest, or other disposition or encumbrance, or an
agreement to accomplish any of the foregoing.

         "Treasury Regulations" or "Tres. Reg" means the Income Tax Regulations
(including proposed and temporary) promulgated under the Code, as such
regulations may be amended from time to time (including corresponding provisions
of succeeding regulations).

         I.2 OTHER DEFINITIONS. Other terms defined in this Agreement have the
meanings so ascribed to them herein.

         I.3 CONSTRUCTION. Whenever the context requires, the gender of all
words used in this Agreement includes the masculine, feminine, and neuter.
Unless the context requires otherwise, all references to Articles and Sections
refer to articles and sections of this Agreement, and references to Exhibits are
to Exhibits attached to this Agreement, each of which is made a part of this
Agreement for all purposes.

                                   ARTICLE II
                                  ORGANIZATION

         II.1 FORMATION. The Persons executing this Agreement form a limited
partnership (the "Partnership ") as of the Effective Time pursuant to the Act
and Articles 5.17 through 5.19 of the Texas Business Corporation Act, upon the
terms and conditions set forth herein.

         II.2 NAME. The name of the Partnership is "Texas Petrochemicals LP,"
and all Partnership business must be conducted in that name or such other names
that comply with applicable law as the General Partner may select from time to
time.

         II.3 REGISTERED OFFICE; REGISTERED AGENT; OTHER OFFICES. The registered
office of the Partnership in the State of Texas shall be at such place as the
General Partner may designate from time to time. The registered agent for
service of process on the Partnership in the State of Texas or any other
jurisdiction shall be such Person or Persons as the General Partner may
designate from time to time. The Partnership may have such other offices as the
General Partner may designate from time to time.

         II.4 PURPOSES. The purposes of the Partnership are to engage in any
lawful business, act or other activity for which limited partnerships may be
organized under the Act and to engage in any other business or activity that now
or in the future may be necessary, incidental, proper, advisable,


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or convenient to accomplish the foregoing purposes (including, without
limitation, obtaining appropriate financing) and that is not forbidden by the
law of the jurisdiction in which the Partnership engages in that business.

         II.5 CERTIFICATE, FOREIGN QUALIFICATION. Pursuant to the Conversion,
the General Partner has executed and caused to be filed with the Secretary of
State of the State of Texas a Certificate containing information required by
Section 2.01 of the Act and such other information as the General Partner deemed
appropriate. Prior to the Partnership's conducting business in any jurisdiction
other than Texas, the General Partner shall cause the Partnership to comply, to
the extent those matters are reasonably within the control of the General
Partner, with all requirements necessary to qualify the Partnership as a foreign
limited partnership (or a partnership in which the Limited Partners have limited
liability) in that jurisdiction. At the request of the General Partner, each
Partner shall execute, acknowledge, swear to, and deliver all certificates and
other instruments conforming with this Agreement that are necessary or
appropriate to form, qualify, continue, and terminate the Partnership as a
limited partnership under the law of the State of Texas and to qualify,
continue, and terminate the Partnership as a foreign limited partnership (or a
partnership in which the Limited Partners have limited liability) in all other
jurisdictions in which the Partnership may conduct business, and to this end the
General Partner may use the power of attorney described in Section 6.09.

         II.6 TERM. The Partnership shall commence at the Effective Time and
shall continue in existence until its business and affairs are wound up
following dissolution, or such earlier time as this Agreement may specify.

                                   ARTICLE III
                              PARTNERSHIP INTERESTS

         III.1 INITIAL PARTNERS. The initial General Partner and Limited Partner
of the Partnership are the Persons executing this Agreement as of the date of
this Agreement as General Partner and Limited Partner, respectively, as set
forth on the signature pages hereof, each of which is admitted to the
Partnership as a general partner or a limited partner, as the case may be,
effective with the commencement of the Partnership.

         III.2 REPRESENTATIONS AND WARRANTIES. Each Partner represents and
warrants to the Partnership and each other Partner that (a) that Partner has
full power and authority to enter into this Agreement and to perform its
obligations under this Agreement, (b) that Partner has duly executed and
delivered this Agreement, and (c) that Partner's authorization, execution,
delivery, and performance of this Agreement do not conflict with any other
agreement or arrangement to which that Partner is a party or by which it is
bound.

         III.3 GENERAL PROHIBITION. Neither a Partner nor any assignee of a
Partner shall make or suffer any Transfer of all or any part of its Partnership
Interest, whether now owned or hereafter acquired, except in accordance with the
terms of this Agreement and any purported Transfer not made in compliance with
this Agreement shall be void and of no force and effect.


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         III.4 TRANSFER BY GENERAL PARTNER. The General Partner may not make or
suffer any Transfer of all or any part of its Partnership Interest, whether now
owned or hereafter acquired, without the prior written consent of the Limited
Partner.

         III.5 TRANSFER BY LIMITED PARTNER. No Limited Partner shall make or
suffer any Transfer of all or any part of its Partnership Interest, whether now
owned or hereafter acquired, without the prior written consent of the General
Partner.

         III.6 SECURITIES LAW COMPLIANCE. The Partnership Interests have not
been registered under the Securities Act of 1933, as amended, or the state
securities laws of Texas or any other state. Without such registration, no
Limited Partner may effect or suffer a Transfer of all or any part of its
Partnership Interest without delivery to the General Partner of an opinion of
counsel satisfactory to the General Partner that such registration is not
required for such transfer and/or submission to the General Partner of such
other evidence as may be reasonably satisfactory to the General Partner to the
effect that any transfer will not be in violation of the Securities Act of 1933,
as amended, applicable state securities laws, or any rule or regulation
promulgated thereunder. All costs incurred by the Partnership in connection with
any Transfer or admission of a Person to the Partnership shall be borne and paid
by the Partner effecting such Transfer and any Person admitted to the
Partnership in connection therewith within ten (10) days after the receipt by
such Partner and Person of the Partnership's invoice for the amount due.

         III.7 SUBSTITUTED PARTNERS. Unless otherwise provided in this
Agreement, an assignee of a Partner may become a substituted partner only with
the consent of the General Partner and compliance with any other requirements of
the Act (other than any that require a different consent of Partners).

         III.8 ADDITIONAL PARTNERS. Additional Persons may be admitted to the
Partnership as a General Partner or Limited Partners and additional interests in
the Partnership created and issued to those Persons and to existing Partners at
the direction of the General Partner on such terms and conditions as the General
Partner may determine at the time of admission. Such admission or issuance shall
specify the Sharing Ratio applicable to new interests in the Partnership and may
provide for the creation of different classes or groups of Limited Partners or
General Partners and having different rights, powers, and duties. The creation
of any new class or group shall be reflected in an amendment hereto indicating
such different rights, powers, and duties, and such amendment need be executed
only by the General Partner. Any such admission must also comply with the
provisions of Section 3.06 and shall not be effective until such new Partner has
executed and delivered to the General Partner a document including such new
Partner's notice address, its agreement to be bound by this Agreement, and an
agreement to perform and discharge timely all of its obligations and liabilities
hereunder. Additionally, such new Partner shall be liable for all costs incurred
by the Partnership in connection with the admission of such new Partner to the
Partnership and shall pay such costs within ten (10) days after its receipt of
the Partnership's invoice therefor.


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                                   ARTICLE IV
                              CAPITAL CONTRIBUTIONS

         IV.1 INITIAL CONTRIBUTIONS. All initial Capital Contributions were made
prior to the Conversion.

         IV.2 SUBSEQUENT CONTRIBUTIONS. No Partner shall be required to make any
Capital Contributions to the Partnership.

         IV.3 ADVANCES BY PARTNERS. If the Partnership does not have sufficient
cash to pay its obligations, the General Partner, or any other Partner(s) that
may agree to do so with the approval of the General Partner, may advance all or
part of the needed funds to or on behalf of the Partnership. Payment by the
General Partner on account of liability as a matter of law for Partnership
obligations is deemed to be an advance under this Section 4.03. An advance
described in this Section 4.03 constitutes a loan from the Partner to the
Partnership, bears interest at the General Interest Rate from the date of the
advance until the date of payment, and is not a Capital Contribution.

                                    ARTICLE V
                          ALLOCATIONS AND DISTRIBUTIONS

         V.1 ALLOCATIONS. All items of income, gain, loss, deduction, and credit
of the Partnership shall be allocated among the Partners in accordance with
their Sharing Ratios.

         V.2 DISTRIBUTIONS. (a) From time to time (but at least once each
calendar year), prior to the commencement of winding up under Section 11.02, the
General Partner shall determine in its reasonable judgment to what extent (if
any) the Partnership's cash on hand exceeds its current and anticipated needs,
including, without limitation, for operating expenses, debt service, and a
reasonable contingency reserve. If such an excess exists, the General Partner
shall cause the Partnership to distribute to the Partners in accordance with
their Sharing Ratios, an amount in cash equal to that excess.

                  (b) From time to time the General Partner also may cause
property of the Partnership other than cash to be distributed to the Partners,
which distribution must be made in accordance with their Sharing Ratios and may
be made subject to existing liabilities and obligations.

         V.3 NO CAPITAL ACCOUNTS. The Partnership will not be taxed as a
partnership pursuant to Subchapter K of the Code as a result of its election to
be taxed as an association for federal income tax purposes.

         V.4 WITHHOLDING: OTHER TAX PAYMENTS. The General Partner is authorized
to withhold from any Partner any portion of any distribution until they receive
such certifications as it deems legally sufficient in its sole judgment to
relieve the Partnership and the General Partner from potential liability for
payment of such Partner's tax under the Code. If and to the extent the
Partnership shall be required or authorized to withhold or pay any taxes on
behalf of a Partner, such Partner shall be deemed for all purposes of this
Agreement to have received a payment from the Partnership as of the time such
withholding or tax is required to be paid, which payment shall be


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deemed to be a distribution with respect to such Partner's Partnership Interest
to the extent that the Partner is then entitled to receive a distribution.

                                   ARTICLE VI
                            MANAGEMENT AND OPERATION

         VI.1 MANAGEMENT OF PARTNERSHIP AFFAIRS. Except as is otherwise provided
for in this Agreement or by non-waivable provisions of applicable law, the
General Partner shall have full, complete, and exclusive authority to manage and
control the business, affairs, and properties of the Partnership, to make all
decisions regarding the same, and to perform any and all other acts or
activities customary or incident to the management of the Partnership's
business. Except as is otherwise provided for in this Agreement or the Act, the
Limited Partner shall not participate in the control of the business affairs of
the Partnership, transact any business on behalf of the Partnership, or have any
power or authority to bind or obligate the Partnership.

         VI.2 RELIANCE ON AUTHORITY. In its dealings with the Partnership, a
third party may rely on the authority of the General Partner to bind the
Partnership without reviewing the provisions of this Agreement or confirming
compliance with the provisions of this Agreement.

         VI.3 OFFICERS AND OTHER AGENTS.

                  (a) Appointment and Tenure.

                           (i) Subject to the provisions hereof, the General
                  Partner may from time to time designate officers of the
                  Partnership to carry out the day-to-day business of the
                  Partnership.

                           (ii) The officers of the Partnership shall be
                  comprised of one or more individuals designated from time to
                  time by the General Partner. No officer need be a resident of
                  the State of Texas. Each officer shall hold his offices for
                  such terms and shall have such authority and exercise such
                  powers and perform such duties as shall be determined from
                  time to time by the General Partner. Any number of offices may
                  be held by the same individual. The salaries or other
                  compensation, if any, of the officers and agents of the
                  Partnership shall be fixed from time to time by the General
                  Partner.

                           (iii) The officers of the Partnership may consist of
                  a president/chief executive officer, a secretary and a
                  treasurer. The General Partner may also designate one or more
                  vice presidents, assistant secretaries, and assistant
                  treasurers. The General Partner may designate such other
                  officers and assistant officers and agents as the General
                  Partner shall deem necessary. To the extent it deems
                  desirable, the General Partner may, when taking any action,
                  deem itself to be acting as a single member "board of
                  directors" of the Partnership. Such a "board of directors"
                  shall include only the corporation then serving as the General
                  Partner, and shall not include


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<PAGE>   12


                  any officer, director, employee or agent of the General
                  Partner individually. The General Partner shall not be deemed
                  to be acting as a "board of directors" with respect to any
                  action unless it expressly determines with respect to a
                  specific action that it is so acting.

                  (b) Removal. Any officer may be removed as such at any time by
the General Partner, either with or without cause, in the discretion of the
General Partner, provided that such removal shall be without prejudice to the
contract rights, if any, of the Person so removed. Designation of an officer
shall not of itself create contract rights.

                  (c) Duties of Officers.

                           (i) President/Chief Executive Officer. The
                  president/chief executive officer, if one is designated, shall
                  be the chief executive officer of the Partnership, shall have
                  general and active management of the day-to-day business and
                  affairs of the Partnership as authorized from time to time by
                  the General Partner and shall be authorized and directed to
                  implement all orders, resolutions and business plans adopted
                  by the General Partner.

                           (ii) Vice Presidents. The vice presidents, if any are
                  designated, in the order of their seniority, unless otherwise
                  determined by the General Partner shall, in the absence or
                  disability of the president/chief executive officer, perform
                  the duties and have the authority and exercise the powers of
                  the president/chief executive officer. They shall perform such
                  other duties and have such other authority and powers as the
                  General Partner may from time to time prescribe. The General
                  Partner may designate one or more of the vice presidents as
                  executive vice presidents, senior vice presidents or other
                  types of vice presidents.

                           (iii) Secretary; Assistant Secretaries. The
                  secretary, if one is designated, shall perform such duties and
                  have such powers as the General Partner may from time to time
                  prescribe. The assistant secretaries, if any are designated,
                  in the order of their seniority, unless otherwise determined
                  by the General Partner, shall, in the absence or disability of
                  the secretary, perform the duties and exercise the powers of
                  the secretary. They shall perform such other duties and have
                  such other powers as the General Partner may from time to time
                  prescribe.

                           (iv) Treasurer; Assistant Treasurers. The treasurer,
                  if one is designated, shall have custody of the Partnership's
                  funds and securities and shall keep full and accurate accounts
                  and records of receipts, disbursements and other transactions
                  in books belonging to the Partnership, and shall deposit all
                  moneys and other valuable effects in the name and to the
                  credit of the Partnership in such depositories as may be
                  designated from time to time by the General Partner. The
                  treasurer shall disburse the funds of the Partnership as may
                  be ordered by the General Partner, taking proper vouchers for
                  such disbursements, and shall render the president/chief
                  executive officer and the Partners, when so directed, an
                  account of all his transactions as


                                      -8-
<PAGE>   13


                  treasurer and of the financial condition of the Partnership.
                  The treasurer shall perform such other duties and have such
                  other powers as the General Partner may from time to time
                  prescribe. If required by the General Partner, the treasurer
                  shall give the Partnership a bond of such type, character and
                  amount as the General Partner may require. The assistant
                  treasurers, if any are designated, in the order of their
                  seniority, unless otherwise determined by the General Partner,
                  shall, in the absence or disability of the treasurer, perform
                  the duties and exercise the powers of the treasurer. They
                  shall perform such other duties and have such other powers as
                  the General Partner may from time to time prescribe. If
                  required by the General Partner, the assistant treasurers
                  shall give the Partnership a bond of such type, character and
                  amount as the General Partner may require.

         VI.4 COMPENSATION TO GENERAL PARTNER. Except as expressly provided in
this Article VI, the General Partner shall receive no compensation from the
Partnership for services rendered in its capacity as General Partner of the
Partnership.

         VI.5 EXPENSES IN CONNECTION WITH ORGANIZATION OF THE PARTNERSHIP. The
Partnership shall be responsible for all out-of-pocket fees, costs and expenses
actually incurred by the General Partner and its Affiliates in connection with:
(a) the organization of the Partnership; (b) the qualification of the
Partnership to do business in any state in which the General Partner determines
that such qualification is advisable; (c) the legal (including tax advice) and
accounting fees and disbursements of the Partnership; and (d) other
out-of-pocket expenses of a similar nature incurred by the General Partner or
its Affiliates in connection with such activities.

         VI.6 REIMBURSEMENT OF EXPENSES. The General Partner shall be entitled
to reimbursement by the Partnership from time-to-time for all out-of-pocket
expenses which are incurred by the General Partner in connection with the
business and affairs of the Partnership including, but not limited to any
organizational fees, legal, accounting, printing, appraisal and similar
reasonable general and administrative overhead expenses incurred by the General
Partner (including, but not limited to, expenses for the compensation of the
management and any employees of the General Partner).

         VI.7 NATURE OF RELATIONSHIP. Except as is otherwise provided in this
Agreement, the General Partner shall perform its duties with respect to the
Partnership in good faith and in the best interests of the Partnership and shall
devote such time and effort to the Partnership business and operations as is
reasonably necessary to manage the affairs of the Partnership prudently. The
General Partner is liable for acts, errors, or omissions in performing its
duties with respect to the Partnership only if such performance is conducted in
bad faith or with gross negligence. THE GENERAL PARTNER IS NOT LIABLE FOR ACTS,
ERRORS, OR OMISSIONS IN PERFORMING ITS DUTIES IN ANY CAPACITY WITH RESPECT TO
THE PARTNERSHIP FOR ANY OTHER REASON, INCLUDING THE GENERAL PARTNER'S SOLE,
PARTIAL, OR CONCURRENT NEGLIGENCE.


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<PAGE>   14


         VI.8 INDEMNIFICATION. To the fullest extent permitted by law, and
subject to the procedures in Article 11 of the Act, on request by the Person
indemnified the Partnership shall indemnify each General Partner, acting in any
capacity, and its Affiliates and their respective officers, directors, partners,
employees, and agents, and the officers of the Partnership, and hold them
harmless from and against all losses, costs, liabilities, damages, and expenses
(including, without limitation, fees and disbursements of counsel) any of them
may incur as a General Partner in the Partnership or in performing the
obligations of the General Partner with respect to the Partnership, SPECIFICALLY
INCLUDING THE INDEMNIFIED PERSON'S SOLE, PARTIAL, OR CONCURRENT NEGLIGENCE, but
excluding any such items incurred as a result of something for which the General
Partner is liable under Section 6.07, and on request by the Person indemnified
the Partnership shall advance expenses associated with the defense of any
related action.

         VI.9 POWER OF ATTORNEY. Each Partner hereby appoints the General
Partner as such Partner's true and lawful attorney-in-fact for the purpose of
executing, swearing to, acknowledging, and delivering all certificates,
documents, and other instruments as may be necessary, appropriate, or advisable
in the judgment of the General Partner in furtherance of the business of the
Partnership or complying with applicable law, including, without limitation,
filings of the type described in Section 2.05. Such power shall be irrevocable
and is coupled with an interest. Upon request by the General Partner, any
Partner shall confirm its grant of such power of attorney or any use thereof by
the General Partner or shall execute, swear to, acknowledge, and deliver any
such certificate, document, or other instrument.

         VI.10 OTHER ACTIVITIES. Neither this Agreement nor the relationship
created hereby shall preclude or limit, in any respect, the right of the
Partners to engage, directly or indirectly, through participation, investment,
or otherwise, in any opportunity or business of any type, including those that
may be the same as or similar to the Partnership or its business, those that
compete with the Partnership, and those in which the Partnership has invested.
The Partners shall not have any obligation to offer to the Partnership or any
other Partner the right to participate in any such activity. Neither the
Partnership nor any Partner shall have any right, by virtue of this Agreement or
the relationship created by this Agreement, with respect to any such activity.

                                   ARTICLE VII
                               RIGHTS OF PARTNERS

         VII.1 INFORMATION. In addition to the other rights specifically set
forth herein, each Partner shall have access to all information to which such
Partner is entitled to have access pursuant to Section 1.07 of the Act under the
circumstances and subject to the conditions therein stated.

         VII.2 LIMITATIONS. No Limited Partner shall have the authority or power
in its capacity as such to act for or on behalf of the Partnership or any other
Partner, to do any act that would be binding on the Partnership or any other
Partner, or to incur any expenditures on behalf of or with respect to the
Partnership.


                                      -10-
<PAGE>   15


         VII.3 MEETINGS. From time to time, the General Partner, on thirty (30)
days prior notice to each Partner, may call a meeting of the Partnership and
apprise the Partners generally of the business and affairs of the Partnership
since the latest meeting. The notice of each such meeting of the Partnership
shall specify the location and time of the meeting and state the business to be
transacted at the meeting. The Partners may make recommendations to or otherwise
advise and consult with the General Partner regarding the business and affairs
of the Partnership, but nothing in this sentence shall be construed to authorize
the Limited Partners to engage in any action prohibited by Section 7.02.

         VII.4 LIMITED LIABILITY. No Limited Partner shall be liable for the
losses, debts, liabilities, contracts, or other obligations of the Partnership
except to the extent required by law.

                                  ARTICLE VIII
                                      TAXES

         VIII.1 TAX RETURNS. The General Partner shall cause to be prepared and
filed all necessary federal and state income tax returns for the Partnership.
Each Partner shall furnish to the General Partner all pertinent information in
its possession relating to Partnership operations that is necessary to enable
such income tax returns to be prepared and filed.

         VIII.2 TAX ELECTIONS. The following elections shall be made on the
appropriate returns of the Partnership:

                  (a) to adopt as the Partnership's fiscal year the period from
July 1 of each year through the next succeeding June 30;

                  (b) to adopt the accrual method of accounting;

                  (c) to elect to be taxed as an association for federal tax
purposes pursuant to Treasury Regulation Section 301.7701-3(a) (and, thus, a
corporation under Treasury Regulation Section 301.7701-2(b)(2)) effective as of
the date the Partnership's existence commences; and

                  (d) any other election the General Partner may deem
appropriate and in the best interests of the Partners.

                                   ARTICLE IX
                   BOOKS, RECORDS, REPORTS, AND BANK ACCOUNTS

         IX.1 MAINTENANCE OF BOOKS. The books of account for the Partnership
shall be maintained on an accrual basis in accordance with the terms of this
Agreement. The accounting year of the Partnership shall be the fiscal year in
accordance with Section 8.02(a).

         IX.2 ACCOUNTS. The General Partner shall establish and maintain one or
more separate bank and investment accounts and arrangements for Partnership
funds in the Partnership name with


                                      -11-
<PAGE>   16


financial institutions and firms that the General Partner determine. The General
Partner may not commingle the Partnership's funds with the funds of any Partner.

                                    ARTICLE X
                      WITHDRAWAL, REMOVAL, BANKRUPTCY, ETC.

         X.1 VOLUNTARY WITHDRAWAL. The General Partner does not have the right
to withdraw from the Partnership as a general partner. The General Partner
agrees that it will not voluntarily withdraw from the Partnership as a general
partner within the meaning of Section 6.02(a) of the Act, and any such voluntary
withdrawal shall be a violation of this Agreement. If the General Partner
voluntarily withdraws from the Partnership in violation of this covenant, the
withdrawal will not be effective until the 90th day following notice of the
withdrawal to all other Partners or such later date as the notice may specify.

         X.2 CONSEQUENCE OF WRONGFUL WITHDRAWAL. If a General Partner wrongfully
withdraws from the Partnership, including but not limited to in violation of
Section 10.01, the Partnership may (i) recover damages from the withdrawing
General Partner, including, without limitation, the reasonable cost of obtaining
replacement of the services that the General Partner is obligated to perform,
(ii) pursue any other remedies available under applicable law, and/or (iii)
effect the recovery of damages by offsetting those damages against the amount
otherwise distributable to that General Partner.

         X.3 CONVERSION OF INTEREST. Simultaneously with an event of withdrawal
with respect to the General Partner (as defined under Section 4.02(a) of the
Act), the former General Partner's Partnership Interest as a General Partner
shall be automatically converted into that of a Limited Partner having a right
to receive distributions from the Partnership and an obligation to make Capital
Contributions to the Partnership equal to the right and obligation of the former
General Partner as a General Partner immediately prior to its ceasing to be a
General Partner and the former General Partner shall be automatically admitted
to the Partnership as a new Limited Partner in respect of such Partnership
Interest. Following an event of withdrawal with respect to the General Partner,
the remaining Partners shall, by unanimous vote, select a new General Partner in
accordance with Section 10.05 hereof. The new General Partner shall be admitted
to the Partnership as a General Partner effective immediately prior to the
existing General Partner ceasing to be a General Partner.

         X.4 REMOVAL OF THE GENERAL PARTNER. The General Partner may be removed
from the Partnership by a unanimous vote of all of the Limited Partners.

         X.5 NEW GENERAL PARTNER. Any action for removal is conditioned on a new
General Partner, selected by the unanimous vote of all of the Limited Partners,
being admitted to the Partnership immediately prior to the effective date of
such removal. In connection with such admission, the new General Partner shall
(i) make or agree to make such Capital Contributions as all of the Limited
Partners specify in exchange for a Partnership Interest entitling it to
distributions as required by all of the Limited Partners and (ii) execute a
written instrument pursuant to which it agrees to be bound by this Agreement,
specifies its address for notice, and make such


                                      -12-
<PAGE>   17


representations, warranties, and covenants as the Limited Partners specify. The
new General Partner so selected shall be admitted to the Partnership as a
General Partner on such terms, and the removal of the old General Partner is
effective only immediately subsequent to that admission.

                                   ARTICLE XI
                                   DISSOLUTION

         XI.1 DISSOLUTION. The Partnership shall dissolve and commence winding
up upon the first to occur of any of the following unless the business of the
Partnership is continued under Section 11.02:

                  (a) an election to dissolve the Partnership by all of the
Partners;

                  (b) an election to dissolve the Partnership by the General
Partner;

                  (c) an event of withdrawal of the General Partner under
Section 4.02 of the Act; or

                  (d) the entry of a decree of judicial dissolution under
Section 8.02 of the Act.

The death, insanity, disability, bankruptcy, dissolution, or other event
occurring with respect to any Limited Partner shall not dissolve the
Partnership.

         XI.2 CONTINUATION. If an event described in Section 11.01(c) hereof
occurs, the Partnership will not be dissolved and the business of the
Partnership may be continued and no winding up shall be required if (a) there
remains at least one General Partner and the remaining General Partner(s)
continue to carry on the business of the Partnership, which such General
Partner(s) are expressly permitted to do, or (b) within ninety (90) days after
the occurrence, all remaining Partners agree in writing to continue the business
of the Partnership and, to the extent that they desire or if there are no
remaining General Partners, agree to the appointment, effective as of the date
of the event described in Section 11.01(c) hereof, of one or more new General
Partners.

         XI.3 EFFECT OF DISSOLUTION. The dissolution shall be effective on the
day on which the event giving rise to the dissolution occurs, but the
Partnership shall not terminate until the assets have been distributed in
accordance with Article XII.


                                      -13-
<PAGE>   18


                                   ARTICLE XII
                  ALLOCATIONS AND DISTRIBUTIONS ON LIQUIDATION

         XII.1 LIQUIDATION AND TERMINATION. Upon dissolution of the Partnership,
unless it is reconstituted and continued as provided in Section 11.02, the
General Partner shall act as liquidator or may appoint one or more other Persons
as liquidator; provided, however, that if the Partnership shall be dissolved on
account of an event of the type described in Section 4.02 of the Act with
respect to the General Partner, the liquidator shall, to the extent permitted by
the Act, be one or more Persons selected in writing by the Limited Partners. The
liquidator shall proceed diligently to wind up the affairs of the Partnership
and make final distributions as provided herein. The costs of liquidation shall
be borne as a Partnership expense. Until final distribution, the liquidator
shall continue to operate the Partnership Assets with all of the power and
authority of the General Partner. The steps to be accomplished by the liquidator
are as follows:

                  (a) As promptly as possible after dissolution and again after
final liquidation, the liquidator shall cause a proper accounting to be made by
a recognized firm of certified public accountants of the Partnership's assets,
liabilities, and operations through the last day of the calendar month in which
the dissolution shall occur or the final liquidation shall be completed, as
applicable;

                  (b) The liquidator shall pay all of the debts and liabilities
of the Partnership (including, without limitation, all expenses incurred in
liquidation) or otherwise make adequate provision therefor (including, without
limitation, the establishment of a cash escrow fund for contingent liabilities
in such amount and for such term as the liquidator may reasonably determine);
and

                  (c) All remaining Partnership Assets shall be distributed to
the Partners as follows:

                           (i) the liquidator may sell any or all Partnership
                  Assets, and any resulting gain or loss from each sale shall be
                  computed and allocated to the Partners in accordance with
                  Article V; and

                           (ii) with respect to all Partnership Assets that have
                  not been sold, the fair market value of such property shall be
                  determined and such Partnership Assets shall be distributed in
                  accordance with the Sharing Ratios.

All distributions in kind to the Partners shall be made subject to the liability
of each distributee for costs, expenses, and liabilities theretofore incurred or
for which the Partnership shall have committed prior to the date of termination
and such costs, expenses, and liabilities shall be allocated to such distributee
pursuant to this Section 12.01. Subject to the provisions of Section 12.02, the
distribution of cash and/or property to a Partner in accordance with the
provisions of this Section 12.01 shall constitute a complete return to the
Partner of its Capital Contributions and a complete distribution to the Partner
of its interest in the Partnership and all the Partnership Assets and shall
constitute a compromise to which all Partners have consented within the meaning
of Section 5.02(d) of the Act.


                                      -14-
<PAGE>   19


To the extent that a Partner shall return funds to the Partnership, it shall
have no claim against any other Partner for the same.

         XII.2 CANCELLATION OF CERTIFICATE. Upon completion of the distribution
of Partnership Assets as provided herein, the Partnership shall be terminated,
and the General Partner (or, if there shall be no General Partner, the Limited
Partners) shall cause the cancellation of the Certificate of Limited Partnership
and any other filings made pursuant to Section 2.05 and shall take such other
actions as may be necessary to terminate the Partnership.

                                  ARTICLE XIII
                               GENERAL PROVISIONS

         XIII.1 AMENDMENT OR MODIFICATION. This Agreement may be amended or
modified from time to time only by a written instrument executed by the General
Partner.

         XIII.2 NOTICES. All notices required or permitted to be given pursuant
to this Agreement shall be in writing and shall be personally delivered, or
mailed, first class postage prepaid, or delivered by a nationally recognized
courier service, charges prepaid, if to the Partnership to the address of the
Partnership's registered office (as reflected on the records of the Secretary of
State of the State of Texas) and if to a Partner, to the appropriate address set
forth in Exhibit A of this Agreement. Any such notice, when sent in accordance
with the provisions of the preceding sentence, shall be deemed to have been
given and received (a) on the day personally delivered, (b) on the third day
following the date mailed, or (c) twenty-four hours after shipment by such
courier service. A Partner may change its address by giving notice in writing to
all other Partners in the manner set forth in this Section 13.02, stating the
new address.

         XIII.3 FAILURE TO PURSUE REMEDIES. The failure of any party to seek
redress for violation, or to insist upon the strict performance, of any
provision of this Agreement shall not prevent a subsequent act, which would have
originally constituted a violation, from having the effect of an original
violation.

         XIII.4 SECTION HEADINGS. The headings in this Agreement are inserted
for convenience and identification only and are in no way intended to describe,
interpret, define, or limit the scope, extent, or intent of this Agreement or
any provision hereof.

         XIII.5 SEVERABILITY. Every provision of this Agreement is intended to
be severable. If any term or provision hereof is illegal or invalid for any
reason whatsoever, such illegality or invalidity shall not affect the validity
of the remainder of this Agreement and the illegal or invalid provision shall be
enforced to the maximum extent possible to still be legal and valid.

         XIII.6 GOVERNING LAW. This Agreement, and the application or
interpretation thereof, shall be governed exclusively by its terms and by the
laws of the State of Texas.


                                      -15-
<PAGE>   20


         XIII.7 CUMULATIVE REMEDIES. The rights and remedies provided by this
Agreement are cumulative and the use of any one right or remedy by any party
shall not preclude or constitute a waiver of its right to use any or all other
remedies. Such rights and remedies are given in addition to any other rights the
Partners may have by law, statute, ordinance, or otherwise.

         XIII.8 COUNTERPARTS. This Agreement may be executed in any number of
counterparts with the same effect as if the Partners had all signed the same
document. All counterparts shall be construed together and shall constitute one
instrument.

         XIII.9 SUCCESSORS AND ASSIGNS. Each and every covenant, term,
provision, and agreement herein contained shall be binding upon each of the
Partners and their respective heirs, legal representatives, successors, and
assigns and shall inure to the benefit of each of the Partners. Unless and until
properly admitted as a Partner, no assignee shall have any rights of a Partner
beyond those provided by the Act to assignees or otherwise as expressly provided
herein to assignees.

         XIII.10 SECTIONS, EXHIBITS, ETC. Each reference to a "Section" herein
is, unless specifically indicated otherwise, a reference to a section of this
Agreement. Each reference to an "Exhibit" herein is, unless specifically
indicated otherwise, a reference to an exhibit attached hereto, all of which are
made a part hereof for all purposes.

         XIII.11 FURTHER ASSURANCES. In connection with this Agreement and the
transactions contemplated by it, each Partner shall execute and deliver any
additional documents and instruments and perform any additional acts that may be
necessary or appropriate to effectuate and perform the provisions of this
Agreement and those transactions.

         XIII.12 WAIVER OF CERTAIN RIGHTS. Each Partner irrevocably waives any
right it may have to maintain an action for dissolution of the Partnership
(other than pursuant to Article XI) or for partition of the property of the
Partnership.

         XIII.13 ATTORNEYS' FEES. If the Partnership or any Partner brings any
legal action to enforce or interpret the provisions of this Agreement, the
prevailing party shall be entitled to reasonable attorneys' fees, costs, and
expenses, in addition to any other relief to which such party may be entitled.

         XIII.14 ENTIRE AGREEMENT. This Agreement sets forth the entire
agreement among the parties hereto with respect to the subject matter hereof and
supersedes all prior arrangements and understandings, if any, related hereto.

             [The remainder of this page intentionally left blank.]


                                      -16-
<PAGE>   21


         IN WITNESS WHEREOF, the Partners have executed this Agreement to be
effective as of the Effective Time.

GENERAL PARTNER:

TPC Holding Corp.

By: /s/ Carl Stutts
   -------------------------------------
Name: Carl Stutts
     -----------------------------------
Title: Executive Vice President
      ----------------------------------

LIMITED PARTNER:

Petrochemical Partnership Holdings, Inc.

By: /s/ Brian Bourque
   -------------------------------------
Name: Brian Bourque
     -----------------------------------
Title: Vice President
      ----------------------------------


                                      -17-
<PAGE>   22


                                    EXHIBIT A

<TABLE>
<CAPTION>
NAME AND ADDRESS OF PARTNER                        SHARING RATIO
---------------------------                        -------------

<S>                                               <C>
GENERAL PARTNER:

TPC Holding Corp.                                        1%
Three Riverway, Suite 1500
Houston, Texas 77056

LIMITED PARTNER:

Petrochemical Partnership Holdings, Inc.                99%
Three Riverway, Suite 1500
Houston, Texas 77056
</TABLE>