SECURITY AGREEMENT (PLEDGE)

Exhibit 10.22.5.10

SECURITY AGREEMENT (PLEDGE)

This SECURITY AGREEMENT (PLEDGE) (as amended, supplemented, restated or otherwise modified from time to time, this “Security Agreement”) is made and entered into effective as of the              day of                 , 2010, by PRIMEENERGY CORPORATION, a Delaware corporation, the address for which, for purposes hereof, is One Landmark Square, Stamford Connecticut 06901, Attn: Beverly A. Cummings (“Debtor”), in favor of COMPASS BANK, an Alabama banking association and successor in interest to Guaranty Bank, FSB, federal savings bank, in its capacity as agent under the Second Amended and Restated Credit Agreement referred to below, the address for which for purposes hereof is 24 Greenway Plaza, Suite 1400A, Houston, Texas 770456, Attn: Kathleen J. Bowen (in such capacity, together with its successors and assigns in such capacity, “Secured Party”), for the benefit of the lenders party to such Second Amended and Restated Credit Agreement from time to time (the “Lenders”) and, under certain circumstances, certain additional parties.

W I T N E S S E T H:

WHEREAS, pursuant to a Second Amended and Restated Credit Agreement dated of even date herewith by and among Debtor, certain other parties, as guarantors, the Lenders and Secured Party (as amended, supplemented, restated or otherwise modified from time to time, the “Credit Agreement”), Debtor is obligated for the full and prompt payment when due of the principal of, premium, if any, and interest on the promissory notes and loans made pursuant to the Credit Agreement; and

WHEREAS, pursuant to the Credit Agreement, and as a condition to the obligations of the Lenders to make or maintain loans or participate in letters of credit issued thereunder and the obligation of Secured Party to issue such letters of credit, Debtor has agreed and is required to execute and deliver this Security Agreement;

NOW, THEREFORE, (i) in order to comply with the terms and conditions of the Credit Agreement (ii) for and in consideration of the premises and the agreements herein contained and (iii) for other good and valuable consideration, the receipt and sufficiency of all of which being hereby acknowledged, Debtor hereby agrees with Secured Party as follows:

A. DEFINITIONS.

1. Terms Defined Above. As used in this Security Agreement (Pledge), each of the terms “Credit Agreement,” “Debtor,” “Lenders,” “Secured Party” and “Security Agreement” shall have the meaning indicated above for such term.

2. Terms Defined in Credit Agreement. Capitalized terms used and not defined herein shall have the respective meanings assigned to such terms in the Credit Agreement.

3. Additional Defined Terms. The following terms, as used in this Security Agreement (Pledge), shall have the respective meanings indicated below, unless the context otherwise requires:

“Collateral” shall mean all of Debtor’s right, title and interest in and to (a) the Shares, including, without limitation, (i) the Distributions, (ii) allocation of loss, gain, deduction, credit or similar items, (iii) property or rights issued in connection with, or as a result of a conversion of, or substituted or exchanged for, interests in the Companies, and (iv) all papers, documents, chattel paper, instruments and general intangibles relating to or evidencing all or any part of the Collateral described in clauses (i) through (iii) above, including, without limitation, certificates evidencing the Shares, (b) all proceeds, income, fees, moneys, salaries or other distributions made with respect to the Shares and (c) any and all proceeds of or from any of the above.

“Companies” shall mean, collectively, PrimeEnergy Management, Prime Operating, Eastern Oil Well Service, Southwest Oilfield Construction and EOWS Midland.

“Distributions” shall mean (i) all of Debtor’s rights to receive and payments of proceeds, income, dividends, distributions, returns or repayments of capital or loans, profits, and other sums, whether payable in cash or otherwise, attributable to the Shares, and (ii) all other payments or any other sums of any nature payable to Debtor or paid to Debtor by or on behalf of the Companies.

“Secured Creditors” shall mean Secured Party, the Lenders and any other Lender Hedge Counterparties.

“Secured Obligations” shall mean the Obligations.

“Shares” shall mean (i) any and all shares of the common stock, par value $                , of PrimeEnergy Management now or hereafter owned by Debtor, including without limitation, those certain              shares of the common stock, par value $            , of PrimeEnergy Management evidenced by Certificate No.              registered in the name of Debtor on the books of PrimeEnergy Management; (ii) any and all shares of the common stock, no par value $            , of Prime Operating now or hereafter owned by Debtor, including without limitation, those certain              shares of the common stock, par value $            , of Prime Operating evidenced by Certificate No.              registered in the name of Debtor on the books of Prime Operating; (iii) any and all shares of the common stock, par value $            , of Eastern Oil Well Service now or hereafter owned by Debtor, including, without limitation, those certain              shares of the common stock, par value $            , of Eastern Oil Well Service evidenced by Certificate No.              registered in the name of Debtor on the books of Eastern Oil Well Service; (iv) and all shares of the common stock, par value $            , of Southwest Oilfield Construction now or hereafter owned by Debtor, including, without limitation, those certain              shares of the common stock of Southwest Oilfield Construction evidenced by Certificate No.              registered in the name of Debtor on the books of Southwest Oilfield Construction; and (v) and all shares of the common stock, par value $            , of EOWS Midland now or hereafter owned by Debtor, including, without limitation, those certain              shares of the common stock of EOWS Midland evidenced by Certificate No.              registered in the name of Debtor on the books of EOWS Midland.

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B. PLEDGE. Debtor has pledged, and by these presents does pledge, unto Secured Party, and its successors and assigns, for the benefit of the Secured Creditors, and Debtor hereby grants to Secured Party, and its successors and assigns, for the benefit of the Secured Creditors, a security interest in and to, the Collateral, to the fullest extent the Collateral may be assigned pursuant to applicable law.

C. OBLIGATIONS SECURED. The rights granted pursuant to Article B above are granted to Secured Party, for the benefit of the Secured Creditors, to secure the payment and performance of the Secured Obligations.

D. WARRANTIES AND REPRESENTATIONS BY DEBTOR. Debtor warrants and represents to Secured Party, for the benefit of the Secured Creditors, as follows:

1. Collateral. Subject in each case to Permitted Liens, Debtor has good title to the Collateral and has full power and authority to assign the Collateral, and no other Person has any right, title or interest therein, nor are there any enforceable provisions in any indenture, contract, agreement or other document controlling (directly or indirectly) Debtor or to which Debtor is a party or is bound which affect the Collateral, directly or indirectly, which prohibit the execution and delivery of this Security Agreement or the performance of its terms. Except for the security interest of Secured Party herein and other Permitted Liens, Debtor is the owner of all the Collateral, free from any Liens or other right, title or interest of any other Person.

2. Prior Financing Statements. Other than with respect to any Permitted Liens, there is no presently effective financing statement (or other evidence of a Lien) now on file in any public office covering any of the Collateral in which Debtor is named as debtor or assignor, and no presently effective security interest has attached or been perfected in the Collateral or any part thereof.

3. Jurisdiction of Organization. The jurisdiction of organization of Debtor is as set forth in the preamble hereof.

E. AGREEMENTS OF DEBTOR. Debtor covenants and agrees with Secured Party, for the benefit of the Secured Creditors, as follows:

1. Filings of Financing Statements. Debtor shall not, so long as any Secured Obligation remains outstanding or there exists any commitment on the part of the Lenders to make or maintain loans or participate in letters of credit pursuant to the Credit Agreement or on the part of Secured Party to issue letters of credit pursuant to the Credit Agreement, execute or authorize the filing of, and there will not be on file in any public office, any financing statement or statements (or other evidence of any Lien) covering the Collateral or any interest therein, except any financing statement filed or to be filed in respect of and for the security interest to Secured Party granted or provided for in this Security Agreement or any other security agreement or security agreements by and between Debtor and Secured Party or with respect to any Permitted Liens.

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2. Notice of Change. Debtor shall promptly notify Secured Party of any change in the jurisdiction of organization of Debtor.

3. Defense of Claims. Debtor shall defend the Collateral against all claims and demands of all Persons at any time claiming the same or any interest therein adverse to Secured Party, other than holders of Permitted Liens.

4. Payover. After the occurrence and during the continuation of an Event of Default, Debtor shall make payment of any Collateral which is due and owing to Debtor directly to Secured Party until the termination of this Security Agreement.

5. Power of Attorney. Subject to the further provisions of this Section 5, Debtor hereby irrevocably appoints Secured Party, for the benefit of the Secured Creditors, as Debtor’s true and lawful agent and attorney-in-fact, with full power of substitution, in the name of Secured Party or in the name of Debtor, for the sole use and benefit of Secured Party and the other Secured Creditors, but at the cost and expense of Debtor, to exercise all or any of the following powers and rights with respect to the Collateral (without any obligation on the part of Secured Party to exercise any of the following powers and rights): (a) to demand, receive, collect, sue and give acquittance for, settle, compromise, compound, prosecute or defend any action or proceeding with respect to the Collateral; (b) to endorse, collect, deposit and receipt for any checks, drafts or other means of payment thereof received from any source and constituting a portion of the Collateral; (c) to receive, collect and demand payment of all the Collateral due and payable to Debtor with respect to the Shares and to apply the Collateral against the Secured Obligations in accordance with the Collateral Agency Agreement; (d) to make payments thereon directly to Secured Party; and (e) to exercise, enforce, enjoy, carry out, receive and/or perform any and all rights, powers, duties, benefits, obligations and remedies of Debtor with respect to and arising under the Collateral; provided, however, the exercise by Secured Party of or failure of Secured Party to exercise any such authority shall in no manner affect the liability of Debtor hereunder or as to the Secured Obligations, and Secured Party shall be under no obligation or duty to exercise any of the powers hereby conferred upon it and shall be without liability for any act or failure to act in connection with the collection of, or the preservation of any rights under, any of the Collateral; and provided, further, Secured Party shall exercise such powers only upon the occurrence and during the continuation of an Event of Default. The agency and authority hereby granted and created constitute an agency coupled with an interest and are irrevocable. Secured Party shall not be bound to take any steps necessary to preserve rights in any of the Collateral against any Person.

6. Delivery to Secured Party. If any Collateral is received by Debtor after the occurrence of an Event of Default, Debtor shall deliver to Secured Party all such Collateral on the day received, with any checks being endorsed by Debtor in favor of Secured Party. Debtor shall not commingle any such Collateral with any other funds, proceeds or monies of Debtor and shall keep such proceeds separate and apart from any other funds, proceeds or monies of Debtor and shall hold any such Collateral in trust for Secured Party until same shall be paid over to Secured Party as agreed to herein.

7. Financing Statement Filings. Debtor authorizes Secured Party to file, without notice to Debtor and with all appropriate jurisdictions, any and all financing statements under the Uniform Commercial Code as Secured Party deems necessary or desirable, without need of further

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authorization from Debtor, describing the Collateral. Debtor will pay the cost of filing such financing statements, or the cost of filing or recording this Security Agreement, in all public offices where Secured Party deems such filing or recording to be necessary or desirable.

8. Transfer or Pledge of Collateral. Debtor shall not sell, assign, transfer, encumber, pledge, hypothecate or otherwise dispose of any interest in the Collateral.

9. Jurisdiction of Organization. Debtor shall not change its jurisdiction of organization without complying with the provisions of Section 2 of this Article E.

10. Expenses of Secured Party. Debtor shall pay to Secured Party all reasonable expenses and expenditures, including, without limitation, reasonable attorneys’ fees and expenses, incurred or paid by Secured Party in exercising or protecting its interests, rights and remedies under this Security Agreement, subject to any limitations on certain of such expenses or expenditures set forth in any of the Loan Documents. The amount of all such expenses and expenditures shall be due and payable by Debtor to Secured Party on demand and shall bear interest at the Default Rate.

11. Payments to Protect Collateral. Debtor shall pay, prior to delinquency, all taxes, charges, Liens (other than Permitted Liens) and assessments, if any, against the Collateral, except any of the foregoing being contested in good faith and as to which adequate reserve in accordance with GAAP has been established. Upon Debtor’s failure to make such payments, Secured Party shall have the right, but not the obligation, to pay the same and shall be the sole judge of the legality or validity thereof and the amount necessary to discharge the same. Any such payment made by Secured Party shall then and thereupon be and become a part of the Secured Obligations and shall be payable by Debtor to Secured Party upon demand, with interest from the date advanced by Secured Party at the Default Rate.

12. Further Assurances. Debtor shall make, procure, execute and deliver all acts, things, writings and assurances as Secured Party may at any time reasonably request, to protect, assure or enforce its interests, rights and remedies pursuant to this Security Agreement.

F. RIGHTS AND REMEDIES OF SECURED PARTY.

1. Remedies. Upon the occurrence and during the continuation of an Event of Default:

(a) Secured Party shall have the rights and remedies provided in the UCC or the Uniform Commercial Code in force in any other applicable jurisdiction; and

(b) in addition to, substitution for, modification of or conjunction with the rights and remedies provided in clause (a) immediately above and in any of the Loan Documents, Secured Party may, subject to any applicable law:

(i) in its discretion, sell, assign, transfer and deliver the whole of the Collateral or any part thereof, or any additions thereto, or substitutes therefor, as a whole or in parcels, in such order as Secured Party may elect, at public or private sale,

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through brokers or otherwise, with such notice or advertisement as may be required by the UCC or other applicable Uniform Commercial Code;

(ii) bid and become purchaser at any public sale of the Collateral or any part thereof;

(iii) apply the net proceeds of disposition of all or any part of the Collateral available for application on the Secured Obligations in accordance with the Credit Agreement, and Debtor shall remain liable for any deficiency;

(iv) demand, collect, and receive all or any part of the Collateral thereafter due and payable to Debtor; and/or

(v) transfer to itself or to its nominee all or any part of the Collateral, and receive the monies, interest, income or benefits attributable or accruing to the Collateral, and hold the same as security for the Secured Obligations, whether or not then due, in accordance with the Credit Agreement.

Secured Party shall be entitled to immediate possession of all books and records evidencing any Collateral and it or its representatives shall have the authority to enter upon any premises upon which any of the same, or any Collateral, may be situated and remove the same therefrom without liability. The proceeds of any distribution after default available to satisfy the Secured Obligations shall be applied to the Secured Obligations in accordance with the Credit Agreement.

Debtor specifically understands and agrees that any sale by Secured Party of all or part of the Collateral pursuant to the terms of this Security Agreement may be effected by Secured Party at times and in manners which could result in the proceeds of such sale being significantly and materially less than might have been received if such sale had occurred at different times or in different manners, and Debtor hereby releases Secured Party and its officers and representatives from and against any and all obligations and liabilities arising out of or related to the timing or manner of any such sale.

2. Sufficiency of Recitals. All recitals in any instrument of assignment or any other instrument executed by Secured Party incident to the sale, transfer, assignment or other disposition or utilization of the Collateral or any part thereof hereunder shall be full proof of the matters stated therein and no other proof shall be requisite to establish full legal propriety of the sale or other action taken by Secured Party or of any fact, condition or thing incident thereto and all prerequisites of such sale or other action shall be presumed conclusively to have been performed or to have occurred.

3. Subrogation. Notwithstanding a foreclosure sale, transfer, assignment or other disposition of or upon any of the Collateral hereunder or exercise of any other remedy by Secured Party in connection with an Event of Default, Debtor shall thereby not be subrogated to any rights of Secured Party or any other Secured Creditor against the Collateral or any other security for the Secured Obligations, nor shall Debtor be deemed to be the owner of any interest in any of the

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Secured Obligations, nor shall Debtor exercise any rights or remedies with respect to the Collateral or any other security for the Secured Obligations until all Secured Obligations have been indefeasibly paid and fully performed and discharged.

4. Waivers. Debtor waives demand, notice, protest and all demands and notices of any action taken by Secured Party under this Security Agreement, except as is specifically elsewhere provided herein and except as to notices which are required (and which may not be waived under the provisions of the UCC or other applicable Uniform Commercial Code), and any indulgence by Secured Party, substitution for, exchange of, or release of the Collateral is hereby assented to and consented to by Debtor.

5. Negation of Liability. Secured Party shall not be responsible in any way for any depreciation or diminution in the value or price of the Collateral and shall not have any duty or responsibility whatsoever to enforce collection of the Collateral by legal proceedings or otherwise, the sole duty of Secured Party being to receive collections, remittances and payments on the Collateral if and when tendered to Secured Party, and at Secured Party’s option to apply the amount or amounts so received, after deduction of any collection costs incurred, as payment upon the Secured Obligations in accordance with the Credit Agreement.

G. GENERAL.

1. Security Agreement. The rights of Secured Party hereunder or the Secured Obligations may be assigned at any time and from time to time, whether in whole or in part, and in such case the assignee shall be entitled to all of the rights, privileges and remedies granted in this Security Agreement to Secured Party or for the benefit thereof and Debtor will assert no claims or defenses it may have against Secured Party or any other Secured Creditor against the assignee, except those granted in this Security Agreement.

2. Waiver. No delay of Secured Party in exercising any power or right shall operate as a waiver thereof; nor shall any single or partial exercise of any power or right preclude other or further exercise thereof or the exercise of any other power or right. No waiver by Secured Party of any right hereunder or of any default by Debtor shall be binding upon Secured Party unless in writing, and no failure by Secured Party to exercise any power or right hereunder or waiver of any default by Debtor shall operate as a waiver of any other or further exercise of such right or power or of any further default. The exercise or beginning of the exercise by Secured Party of any one or more of such rights, powers or remedies shall not preclude the simultaneous or later exercise by Secured Party of any or all other such rights, powers or remedies. No indulgence by Secured Party, or waiver of compliance with any provision hereof, shall be construed as a waiver of the right of Secured Party to subsequently require strict performance hereof by Debtor.

3. Release of Lien. Upon the indefeasible payment and performance in full of the Secured Obligations, the termination of the commitments of the Lenders to make or maintain loans or participate in letters of credit pursuant to the Credit Agreement and the commitment of Secured Party to issue letters of credit pursuant to the Credit Agreement, Secured Party shall promptly, at Debtor’s expense, execute and deliver release instruments and documents and take all further action that Debtor may reasonably request in order to release Secured Party’s security interest in the Collateral.

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4. Remedies Cumulative. Each right, power and remedy of Secured Party as provided for herein or in any other Loan Document, or which shall now or hereafter exist at law or in equity or by statute or otherwise, shall be cumulative and concurrent and shall be in addition to every other such right, power or remedy and the exercise of any one or more of the remedies provided for herein shall not be construed as a waiver of any of the other remedies of Secured Party.

5. Parties in Interest. The terms “Secured Party” and “Debtor” as used in this instrument include the respective heirs, executors, administrators, successors, representatives, trustees and permitted assigns of such parties.

6. Reasonable Notice. Notice mailed to Debtor’s address as set forth in the preamble of this Security Agreement, or to Debtor’s most recent changed address on file with Secured Party, at least ten days prior to the related action, or if the UCC or other applicable Uniform Commercial Code specifies a longer period, such longer period prior to the related action, shall be deemed reasonable.

7. Governing Law and Amendments. THIS SECURITY AGREEMENT AND THE SECURITY INTEREST GRANTED HEREBY IS GRANTED IN, AND SHALL BE GOVERNED BY THE LAWS OF THE STATE OF TEXAS AND THE LAWS OF THE UNITED STATES OF AMERICA APPLICABLE TO TRANSACTIONS WITHIN THE STATE OF TEXAS, INCLUDING, WITHOUT LIMITATION, MATTERS OF CONSTRUCTION, VALIDITY, ENFORCEMENT AND PERFORMANCE, and this Security Agreement may not be modified, altered or amended except in writing duly signed by an authorized officer of Secured Party and by Debtor. Except as the context may otherwise require, any term used herein and defined in either Article 1 or Article 9 of the UCC or other applicable Uniform Commercial Code shall have the meaning given therein.

8. Notices. All notices, demands, requests and other communications required or permitted hereunder shall be in writing and may be personally served or sent by mail, and if given by personal service, it shall be deemed to have been given upon receipt, and if sent by mail, it shall be deemed to have been given upon its deposit in the mail, postage prepaid, registered or certified, return receipt requested, addressed to Debtor or Secured Party, as the case may be. For purposes hereof, the addresses of the parties to this Security Agreement shall be as set forth in the preamble hereof. Each of Debtor and Secured Party shall have the right to change its address by designating a new address in a written notice to the other as herein required.

9. Invalidity of Certain Provisions. In the event any one or more of the provisions contained in this Security Agreement shall, for any reason, be held to be invalid, illegal or unenforceable in any respect, such invalidity, illegality or unenforceability shall not affect any other provision of this Security Agreement.

10. Counterparts. This Security Agreement may be executed by the parties hereto in any number of separate counterparts, each of which shall be deemed an original, but all of which shall constitute one and the same instrument. In this regard, each of the parties hereto acknowledges that a counterpart of this Security Agreement containing a set of counterpart execution pages reflecting the execution of each party hereto shall be sufficient to reflect the execution of this Security Agreement by each party hereto and shall constitute one instrument.

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11. Benefits of Credit Agreement. In connection with its execution and acting hereunder, Secured Party is entitled to all rights, privileges, protections, immunities, benefits and indemnities provided to it as agent under the Credit Agreement.

12. Conflict with Credit Agreement. In the event of a conflict between any provision of this Security Agreement and a provision in the Credit Agreement, the provision of the Credit Agreement shall control; provided, however, the inclusion in this Security Agreement of a provision with respect to which there is no corresponding provision in the Credit Agreement shall not constitute a conflict with any provision of the Credit Agreement.

IN WITNESS WHEREOF, Debtor Secured Party and have executed this Security Agreement (Pledge) as of the date first above written.

(Signatures continue on following page)

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