AMENDMENT NO. 2 TO THE PATINA OIL & GAS CORPORATION 1996 STOCK PLAN FOR NON-EMPLOYEE DIRECTORS

Exhibit 10.2

AMENDMENT NO. 2 TO THE

PATINA OIL & GAS CORPORATION

1996 STOCK PLAN FOR NON-EMPLOYEE DIRECTORS

THIS AMENDMENT NO. 2 (this “Amendment”) to the Patina Oil & Gas Corporation 1996 Stock Plan for Non-Employee Directors (the “Plan”), is hereby adopted as of May 3, 2005 by Patina Oil & Gas Corporation (the “Company”), pursuant to authority granted to it in Section 6 of the Plan.

WHEREAS, Section 1.8 of the Agreement and Plan of Merger (the “Merger Agreement”), dated as of December 15, 2004, by and among Noble Energy, Inc. (“Parent”), the Company and Noble Energy Production, Inc. (“Purchaser”), as amended, provides that at the Effective Time (as defined in the Merger Agreement) of the merger of the Company with and into Purchaser (the “Merger”), each Company Option (as defined in the Merger Agreement) that is outstanding and unexercised immediately prior to the Effective Time shall cease to represent a right to acquire shares of Company Common Stock (as defined in the Merger Agreement) and shall be converted automatically into options to purchase shares of Parent Common Stock (as defined in the Merger Agreement), subject to the other terms and conditions set forth in the Merger Agreement;

WHEREAS, Section 6 of the Plan provides that the Company may make certain adjustments to Stock Options in the event of certain corporate transactions, including a merger involving the Company in which the Company is not the surviving corporation; and

WHEREAS, on December 15, 2004, the Board of Directors resolved that the Plan and each Stock Option issued thereunder was to be modified to provide that, at the Effective Time, each Stock Option that is outstanding and unexercised immediately prior to the Effective Time shall cease to represent a right to acquire shares of Company capital stock and shall be converted automatically into options to purchase shares of Parent common stock which shall have the other terms and conditions set forth in the Merger Agreement, and that each of the Chief Executive Officer, the President and the Executive Vice President and Chief Financial Officer was authorized, empowered and directed in the name and on behalf of the Company to prepare, deliver, execute and adopt such amendments as are appropriate or necessary to effectuate the foregoing.

NOW, THEREFORE, the Plan is hereby amended as follows:

1. Amendment Relating to Treatment of Stock Options in the Merger. There is hereby added a new Section 6A to the Plan, which provides:

“SECTION 6A. EFFECT OF THE MERGER.

Notwithstanding any provision of the Plan to the contrary, each Stock Option that is outstanding and unexercised immediately prior to the Effective Time (as defined in the Agreement and Plan of Merger (the “Merger Agreement”), dated as of December 15, 2004, by and among Noble Energy, Inc. (“Parent”), the Company and Noble Energy Production, Inc.)

shall cease to represent a right to acquire shares of Common Stock and shall be converted automatically into options to purchase shares of Parent Common Stock (as defined in the Merger Agreement), and Parent shall assume each such Stock Option (hereinafter, “Assumed Option”) subject to the terms of the Plan and the agreement evidencing the grant hereunder of such Assumed Option (other than the provisions hereof providing for termination of such Assumed Option at the Effective Time); provided, however, that (i) the number of shares of Parent Common Stock purchasable upon exercise of such Assumed Option shall be equal to the number of shares of Common Stock that were purchasable under such Stock Option immediately prior to the Effective Time multiplied by the Exchange Ratio (as defined in the Merger Agreement) and rounded down to the nearest whole share and (ii) the per share exercise price under such Assumed Option shall be adjusted by dividing the per share exercise price under such Stock Option by the Exchange Ratio, and rounding up to the nearest whole cent.”

2. Capitalized Terms; Choice of Law. Capitalized terms used but not defined herein (or in the Merger Agreement) are used as defined in the Plan. This Amendment will be governed by and construed in accordance with the laws of the State of Delaware.

3. Effectiveness. This Amendment shall be effective as of the Effective Time of the Merger, provided, however, that in the event the Merger is not consummated and the Merger Agreement is terminated in accordance with its terms, this Amendment shall be null and void ab initio and of no further force or effect.

* * * * *

IN WITNESS WHEREOF, this Amendment has been executed as of the date first written above.