SECOND AMENDMENT TO THE LIMITED PARTNERSHIP AGREEMENT OF

Exhibit 10.22(b)

SECOND AMENDMENT

TO THE

LIMITED PARTNERSHIP AGREEMENT

OF

LYONDELL-CITGO REFINING LP

This Second Amendment (this “Second Amendment”) to the Limited Partnership Agreement of LYONDELL-CITGO REFINING LP, a Delaware limited partnership (the “Partnership”), is made as of July 31, 2006 by and among CITGO REFINING INVESTMENT COMPANY, an Oklahoma corporation (“CITGO LP”), CITGO GULF COAST REFINING, INC., a Delaware corporation (“CITGO GP”), LYONDELL REFINING PARTNERS LP, a Delaware limited partnership (“Lyondell LP”), and LYONDELL REFINING COMPANY LP, a Delaware limited partnership (“Lyondell GP” and, together with CITGO LP, CITGO GP and Lyondell LP, the “LCR Partners”).

RECITALS

WHEREAS, in accordance with Section 12.4 of the Limited Partnership Agreement of the Partnership dated December 31, 1998, as amended (the “LP Agreement”), the Representatives have approved this Amendment;

WHEREAS, the LCR Partners being all of the Partners of the Partnership desire to amend the Agreement.

NOW, THEREFORE, the LP Agreement is hereby amended as follows:

Section 1. Defined Terms. Capitalized terms used and not otherwise defined herein shall have the meanings given such terms in the LP Agreement.

Section 2. Effectiveness of Partnership Agreement. Except as amended by this Second Amendment, all terms and conditions of the LP Agreement shall remain in full force and effect among the Partners.

Section 3. Amendment. Section 3.8(C) of the LP Agreement shall be amended to read as follows in its entirety:

(C) [Reserved];

Section 4. Amendment. Section 12.4 of the LP Agreement shall be amended to read as follows in its entirety:

Section 5. Governing Law. This Second Amendment will be governed by and construed in accordance with the laws of the State of Delaware.

Section 6. Severability. In the event that any provision of this Second Amendment shall finally be determined to be unlawful, such provision shall, so long as the economic and legal substance of the transactions contemplated hereby is not affected in any materially adverse manner as to any Partner, be deemed severed from this Second Amendment and every other provision of this Second Amendment shall remain in full force and effect.

Section 7. Counterparts. This Second Amendment may be executed in multiple counterparts by different parties hereto in separate counterparts, each of which when executed shall be deemed to be an original but all of which taken together shall constitute one and the same agreement.

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IN WITNESS WHEREOF, all of the Partners of the Partnership have executed this Second Amendment, effective as of the date first listed above.