<PAGE>

                                                                     EXHIBIT 3.1

                                SECOND AMENDMENT
                                       TO
                          AMENDED AND RESTATED LIMITED
                           LIABILITY COMPANY AGREEMENT
                       OF DUKE ENERGY FIELD SERVICES, LLC

      This Second Amendment to Amended and Restated Limited Liability Company
Agreement of Duke Energy Field Services, LLC (this "Amendment"), dated as of
July 29, 2004, is entered into by and between Phillips Gas Company, a Delaware
corporation ("PGC") and Duke Energy Field Services Corporation, a Delaware
Corporation ("DEFS Holding").

      WHEREAS, reference is made to that certain Amended and Restated Limited
Liability Company Agreement of Duke Energy Field Services, LLC by and between
PGC and DEFS Holding dated as of March 31, 2000, as amended by that certain
First Amendment to Amended and Restated Limited Liability Company Agreement of
Duke Energy Field Services, LLC, by and among PGC, DEFS Holding, Phillips Gas
Investment Company and Duke Energy Field Services Investment Corp. (the "LLC
Agreement") (capitalized terms used but not defined herein shall have the
meaning given thereto in the LLC Agreement); and

      WHEREAS, the parties desire to amend the LLC Agreement as set forth
herein.

      NOW, THEREFORE, for and in consideration of the mutual benefits to be
derived from this Amendment, and intending to be legally bound hereby, the
parties hereto hereby agree as follows:

      1.    LLC AGREEMENT AMENDMENT. The LLC Agreement is hereby amended by
            deleting the first sentence of Section 5.1 thereof and replacing it
            with the following in its place and stead:

            "For the period from the date hereof until the consummation of the
            IPO, (a) DEFS Holding shall own and hold all of Duke's Company
            Interests and (b) PGC shall own and hold all of Phillips' Company
            Interests and shall have no other assets or liabilities."

      2.    ACKNOWLEDGEMENT. Except as amended hereby, the LLC Agreement shall
            remain in full force and effect as previously executed, and the
            Members hereby ratify the LLC Agreement as amended hereby.

      3.    COUNTERPARTS. This Amendment may be executed in one or more
            counterparts, all of which shall be considered one and the same
            agreement, and shall become effective when one or more counterparts
            have been signed by each of the parties hereto and delivered
            (including by facsimile) to the other parties.

                                       1
<PAGE>

      IN WITNESS WHEREOF, each of the undersigned, intending to be legally
bound, has caused this Amendment to be duly executed and delivered on the date
first set forth above.

                                         PHILLIPS GAS COMPANY
                                         By:   /s/ John E. Lowe
                                               --------------------------------
                                         Name: John E. Lowe
                                         Title:President & CEO

                                         DUKE ENERGY FIELD SERVICES CORPORATION
                                         By:    /s/ W. H. Easter III
                                                -------------------------------
                                         Name:  W. H. Easter III
                                         Title: Chairman of the Board, President
                                                and CEO

                                       2