Constellation Energy Partners LLC 2009 OmnibusIncentive Compensation Plan Grant Agreement Relating to Restricted Units Executives

Exhibit 10.31

Constellation Energy Partners LLC

2009 Omnibus Incentive Compensation Plan

Grant Agreement Relating to

Restricted Units – Executives

Grantee: [—]

Grant Date: [—]

1. Grant of Restricted Units.

(a) Grant. Constellation Energy Partners LLC, a Delaware limited liability company (the “Company”), hereby grants to you [—] Restricted Units (the “Restricted Units” and each, a “Restricted Unit”) under the Constellation Energy Partners LLC 2009 Omnibus Incentive Compensation Plan (the “Plan”) on the terms and conditions set forth herein and in the Plan, which is attached hereto as Appendix A and incorporated herein by reference as a part of this agreement (the “Grant Agreement”).

(b) No Certificates. The Restricted Units shall be evidenced in book-entry form in the name of Grantee.

(c) General. Except where explicitly noted herein, in the event of any conflict between the terms of the Plan and the remaining terms of this Grant Agreement, the Plan shall control. Capitalized terms used in this Grant Agreement but not defined herein shall have the meanings ascribed to such terms in the Plan, unless the context requires otherwise.

2. Vesting and Distributions.

(a) Vesting of Restricted Units. Except as otherwise provided in Section 2(b), each tranche of Restricted Units identified below (a “Tranche”) shall fully vest in Grantee and the restrictions set forth in this Section 2(a), Section 2(b), Section 2(c) and Section 2(d) shall lapse according to the following schedule of vesting dates:

Grantee shall receive cash UDRs on the Restricted Units during the vesting period at the time distributions are made to holders of common units of the Company.

(b) Forfeiture.

(i) Subject to Section 2(b)(ii), all Restricted Units that are then unvested, shall become forfeited, null and void on the date on which Grantee’s employment by the Company or its Affiliates is terminated.

(ii) Employment Agreement. Notwithstanding Section 2(b)(i) and anything to the contrary herein or in the Plan, if Grantee’s Employment Agreement (defined below) provides for a treatment of the Restricted Units that differs from Section 2(b)(i), the terms of Grantee’s Employment Agreement shall control upon the termination of Grantee’s employment by the Company or its Affiliates. “Employment Agreement” means that certain Employment Agreement, dated as of May 1, 2009, entered into by and between the Company and Grantee, as such agreement may be amended from time to time.

(iii) Committee Discretion. The Committee may, in its discretion, waive in whole or in part any forfeiture pursuant to this Section 2(b).

(c) Transfer Restrictions. None of the Restricted Units may be assigned, alienated, pledged, attached, sold or otherwise transferred or encumbered by Grantee and any such purported assignment, alienation, pledge, attachment, sale, transfer or encumbrance shall be void and unenforceable against the Company or any of its Affiliates; provided, however, that the Restricted Units may be transferred by Grantee without consideration to immediate family members or related family trusts, family limited partnerships or similar entities.

(d) Ownership Rights. Subject to the vesting restrictions provided in Section 2(a) and the risk of forfeiture pursuant to Section 2(b), Grantee shall have full ownership rights in respect of the Restricted Units, including the right to vote along with the other common unitholders.

3. Withholding of Tax.

(a) General. The Company or any Affiliate is authorized to withhold from any payment due or transfer made pursuant to this Grant Agreement, or from any compensation or other amount owing to Grantee, the amount (in cash, Units, other securities, Units that would otherwise be issued pursuant to this Grant Agreement or other property) of any applicable taxes payable at the minimum statutory rate in respect of this Grant Agreement, the vesting or any payment or transfer under the Grant Agreement and to take such other action as may be necessary in the opinion of the Company to satisfy its withholding obligations for the payment of such taxes, and in this regard, such withholding obligation may be satisfied by Grantee timely remitting (in cash, check or wire transfer) to the Company or the Internal Revenue Service, at the Company’s election, the amount of any such applicable taxes (as determined by the Company).

(b) Net Units. Unless Grantee satisfies the tax withholding obligation set forth above by timely remitting such amounts to the Company or the Internal Revenue Service (at the Company’s election) by cash, check or wire transfer, all Units to be issued pursuant to this Grant Agreement shall be net of tax withholding, such that the tax withholding obligation of

Grantee in respect of this Grant Agreement and such Units is satisfied through the retention by the Company of a number of Units equal to Grantee’s aggregate tax withholding obligation divided by the per-unit Fair Market Value for the date immediately prior to the date of such issuance of Units.

(c) Section 83(b) Election. As a condition to receiving his or her award of Restricted Units, Grantee agrees to waive his or her right to make an election under Section 83(b) of the Code with regard to the Restricted Units.

4. Limitations on Transfer. All rights under this Grant Agreement shall belong to Grantee alone and may not be transferred, assigned, pledged or hypothecated by Grantee in any way (whether by operation of law or otherwise), other than by will or the laws of descent and distribution and shall not be subject to execution, attachment or similar process. Upon any attempt by Grantee to transfer, assign, pledge, hypothecate or otherwise dispose of such rights contrary to the provisions in this Grant Agreement or the Plan, or upon the levy of any attachment or similar process upon such rights, such rights shall immediately become null and void.

5. Binding Effect. This Grant Agreement shall be binding upon and inure to the benefit of any successor or successors of the Company and upon any person lawfully claiming under Grantee.

6. Entire Agreement and Amendment. This Grant Agreement constitutes the entire agreement of the parties with regard to the subject matter hereof, and contains all the covenants, promises, representations, warranties and agreements between the parties with respect to the Restricted Units. Without limiting the scope of the preceding sentence, all prior understandings and agreements, if any, among the parties hereto relating to the subject matter hereof are hereby made null and void and of no further force and effect.

7. Notices. Any notices given in connection with this Grant Agreement shall, if issued to Grantee, be delivered to Grantee’s current address on file with the Company, or if issued to the Company, be delivered to the Company’s principal offices.

8. Execution of Receipts and Releases. Payment of cash or issuance or transfer of Units or other property to Grantee, or to Grantee’s legal representatives, heirs, legatees or distributees, in accordance with the provisions hereof, shall, to the extent thereof, be in full satisfaction of all claims of such persons hereunder. The Company may require Grantee or Grantee’s legal representatives, heirs, legatees or distributees, as a condition precedent to such payment or issuance, to execute a release and receipt therefor in such form as the Company shall reasonably determine.

9. Reorganization of the Company. The existence of this Grant Agreement shall not affect in any way the right or power of any of the Company and its Affiliates or their respective unitholders, stockholders or other equity holders to make or authorize (a) any or all adjustments, recapitalizations, reorganizations or other changes in the respective capital structures or businesses of any of the Company and its Affiliates; (b) any merger or consolidation of any of the Company and its Affiliates; (c) any issue of bonds, debentures, preferred or prior preference

units or securities ahead of or affecting the Restricted Units or the rights thereof; (d) the dissolution or liquidation of any of the Company and its Affiliates, or any sale or transfer of all or any part of their respective assets or businesses; or (e) or any other limited liability company or corporate act or proceeding, as applicable, whether of a similar character or otherwise.

10. Recapitalization Events. In the event that the Committee determines that any distribution (whether in the form of cash, common units, other securities or other property), recapitalization, split, reverse split, reorganization, merger, consolidation, split-up, spin-off, combination, repurchase, or exchange of Units or other securities of the Company, issuance of warrants or other rights to purchase Units or other securities of the Company, or other similar transaction or event affects the Units such that an adjustment is determined by the Committee to be appropriate in order to prevent dilution or enlargement of the benefits or potential benefits intended to be made available under this Grant Agreement, then the Committee shall, in such manner as it may deem equitable, adjust the number and type of Units (or other securities or property) subject to the Grant Agreement hereunder or, if deemed appropriate by the Committee, make provision for a cash payment to Grantee; provided, however, that the number of Units subject to the Grant Agreement shall always be a whole number.

11. Certain Restrictions. By executing this Grant Agreement, Grantee acknowledges that he or she has received a copy of the Plan and agrees that Grantee will enter into such written representations, warranties and agreements and execute such documents as the Company may reasonably request in order to comply with the securities laws or any other applicable laws, rules or regulations or with this document or the terms of the Plan.

12. Amendment and Termination. No amendment or termination of this Grant Agreement that adversely affects the rights of the Grantee shall be made by the Company at any time without the prior written consent of Grantee.

13. Governing Law. This grant shall be governed by, and construed in accordance with, the laws of the State of Delaware, without regard to conflicts of laws principles thereof.

[Signature page follows]

IN WITNESS WHEREOF, the parties hereto have executed this Award Agreement to be effective as of [—].

APPENDIX A

CONSTELLATION ENERGY PARTNERS LLC

2009 OMNIBUS INCENTIVE COMPENSATION PLAN