Exhibit 4.13

SECOND SUPPLEMENTAL INDENTURE

SECOND SUPPLEMENTAL INDENTURE (this “Second Supplemental Indenture”), dated as of the 4th day of December, 2014, among Kodiak Oil & Gas Corp., a Yukon corporation (the “Company”), Kodiak Oil & Gas (USA) Inc., a Colorado corporation (“Kodiak (USA)”), Kodiak Williston, LLC, a Delaware limited liability company (“Kodiak Williston” and, together with Kodiak (USA), the “Subsidiary Guarantors”), U.S. Bank National Association, as trustee (the “Trustee”), Computershare Trust Company of Canada, as Canadian Trustee (the “Canadian Trustee”), Whiting US Holding Company, a Delaware corporation (the “Co-Issuer”), and Whiting Oil and Gas Corporation, a Delaware corporation (the “Affiliate Guarantor”), under the Indenture referred to below.

W I T N E S S E T H

WHEREAS, the Company, Kodiak (USA), the Trustee and the Canadian Trustee have heretofore executed and delivered an indenture (the “Original Base Indenture”), dated as of January 15, 2013, providing for the issuance by the Company of up to $350,000,000 aggregate principal amount of the Company’s 5  ¹⁄₂% Senior Notes due 2021 (the “Notes”), as supplemented by that certain Supplemental Indenture, dated as of July 30, 2013, among the Company, KOG Finance, LLC, a Delaware limited liability company (“KOG Finance”), Kodiak Williston, the Trustee and the Canadian Trustee (the “2013 Supplemental Indenture”), that certain Supplemental Indenture, dated as of October 3, 2014, among the Company, KOG Oil & Gas ULC, a British Columbia unlimited liability company (“KOG ULC”), the Trustee and the Canadian Trustee (the “2014 Supplemental Indenture”), and that certain First Supplemental Indenture, dated as of October 17, 2014, among the Company, the Subsidiary Guarantors, KOG Finance, KOG ULC, the Trustee, the Canadian Trustee and Whiting Petroleum Corporation, a Delaware corporation (the “Parent Guarantor”) (the “First Supplemental Indenture”; the Original Base Indenture as supplemented by the 2013 Supplemental Indenture, the 2014 Supplemental Indenture and the First Supplemental Indenture, the “Base Indenture”; and such Base Indenture, together with this Second Supplemental Indenture, the “Indenture”);

WHEREAS, pursuant to the Arrangement Agreement (the “Arrangement Agreement”) dated as of July 13, 2014 among the Parent Guarantor, 1007695 B.C. Ltd. (“Whiting Canadian Sub”), and the Company, Whiting Canadian Sub will, subject to the satisfaction of the conditions stated therein, acquire all of the outstanding common shares of the Company, and Whiting Canadian Sub and the Company will amalgamate, with the Company surviving as a wholly-owned subsidiary of the Parent Guarantor (the “Arrangement”);

WHEREAS, in connection with the consummation of the Arrangement and effective upon completion of the Arrangement, the Affiliate Guarantor desires to issue an unconditional and irrevocable guarantee of the prompt payment, when due, of any amount owed to the Holders of the Notes under the Indenture and any other amounts due pursuant to the Indenture as contemplated by Section 2 of this Second Supplemental Indenture;

WHEREAS, Section 9.01(a)(vii) of the Base Indenture authorizes the Company, the Subsidiary Guarantors, the Trustee and the Canadian Trustee, without the consent of the Holders, to add the Affiliate Guarantor as a guarantor as contemplated by Section 2 of this

Second Supplemental Indenture, as Section 9.01(a)(vii) of the Base Indenture authorizes any change to any provision of the Base Indenture that would provide any additional rights or benefits to the Holders or that does not adversely affect the rights or interests of any such Holder;

WHEREAS, following the completion of the Arrangement, the Company will convert into a British Columbia unlimited liability company (the “Conversion”), and Section 5.01(a) of the Base Indenture requires the addition of a corporate co-issuer of the Notes in connection with the Conversion;

WHEREAS, effective simultaneously with the Conversion, the Company desires to add the Co-Issuer, and the Co-Issuer desires to be added, as a “co-issuer” of the Notes pursuant to and in accordance with Section 5.01(a) of the Base Indenture and as contemplated by Section 3 of this Second Supplemental Indenture;

WHEREAS, Section 9.01(a)(xiv) of the Base Indenture authorizes the Company, the Subsidiary Guarantors, the Trustee and the Canadian Trustee, without the consent of the Holders, to amend or supplement the Base Indenture to add the Co-Issuer as a corporate co-issuer as contemplated by Section 3 of this Second Supplemental Indenture;

WHEREAS, the Company has delivered to the Trustee and the Canadian Trustee simultaneously with the execution and delivery of this Second Supplemental Indenture the documents relating to this Second Supplemental Indenture contemplated by Sections 9.01, 11.04 and 11.05 of the Base Indenture;

WHEREAS, pursuant to Section 9.01 of the Base Indenture, the Company, the Subsidiary Guarantors, the Co-Issuer, the Affiliate Guarantor, the Trustee and the Canadian Trustee are authorized to execute and deliver this Second Supplemental Indenture; and

WHEREAS, KOG Finance has dissolved and KOG ULC was liquidated prior to the date hereof in compliance with the Indenture.

NOW THEREFORE, in consideration of the foregoing and for other good and valuable consideration, the receipt of which is hereby acknowledged, the Company, the Subsidiary Guarantors, the Co-Issuer, the Affiliate Guarantor, the Trustee and the Canadian Trustee mutually covenant and agree for the equal and ratable benefit of the Holders of the Notes as follows:

1. Capitalized Terms. Capitalized definitional terms used herein without definition shall have the meanings assigned to them in the Indenture.

2. Addition of Affiliate Guarantee. Effective contemporaneously with the completion of the Arrangement, the Affiliate Guarantor hereby guarantees the payment obligations of the Company under the Notes and the Indenture on the terms set forth as Appendix A hereto, on a joint and several basis with the Subsidiary Guarantors and the Parent Guarantor in accordance with the terms of their respective Guarantees. The guarantee contemplated hereby is the “Affiliate Guarantee.”

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3. Conversion. Effective simultaneously with the consummation of the Conversion:

4. Effectiveness; Amendments Becoming Operative. This Second Supplemental Indenture shall be effective upon its execution and delivery by the parties hereto. The amendments set forth in Section 2 hereof will not become operative and the Affiliate Guarantee will not be issued until the completion of the Arrangement. The amendments set forth in Section 3 hereof will not become operative and the addition of the Co-Issuer as a co-issuer of the Notes will not become effective until the consummation of the Conversion. Notwithstanding any provision of this Second Supplemental Indenture to the contrary, this Second Supplemental Indenture (other than this Section 4) shall automatically terminate and have no further force and effect if the Arrangement Agreement (other than any terms thereof that expressly survive termination) terminates prior to completion of the Arrangement.

5. No Liability of Directors, Officers, Employees, Incorporators, Members and Stockholders. No director, officer, employee, incorporator, member, manager, partner or stockholder of the Company (other than the Co-Issuer as provided herein and as a member of the Company), the Co-Issuer, any Subsidiary Guarantor or the Affiliate Guarantor, as such, shall have any liability for any obligations of the Company, the Co-Issuer, any Subsidiary Guarantor or the Affiliate Guarantor under the Notes, any Subsidiary Guarantee, the Affiliate Guarantee,

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the Indenture or this Second Supplemental Indenture, or for any claim based on, in respect of, or by reason of, such obligations or their creation. Each Holder by accepting the benefits of this Second Supplemental Indenture waives and releases all such liability. The waiver and release are part of the consideration for the issuance of the Affiliate Guarantee.

6. Ratification of Indenture; Second Supplemental Indenture Part of Indenture. Except as expressly amended hereby, the Base Indenture is in all respects ratified and confirmed and all the terms, conditions and provisions thereof shall remain in full force and effect. This Second Supplemental Indenture shall form a part of the Indenture for all purposes, and every Holder heretofore or hereafter authenticated and delivered shall be bound hereby.

7. Governing Law. This Second Supplemental Indenture shall be governed by, and construed in accordance with, the laws of the State of New York. Notwithstanding the preceding sentence, the exercise, performance or discharge by the Canadian Trustee of any of its rights, powers, duties or responsibilities hereunder shall be construed in accordance with the laws of the Province of British Columbia and the federal laws of Canada applicable thereto.

8. Duplicate Originals; Counterparts. The parties may sign any number of copies of this Second Supplemental Indenture. Each signed copy shall be an original, but all of them together represent the same agreement. The exchange of copies of this Second Supplemental Indenture and of signature pages by facsimile or PDF transmission shall constitute effective execution and delivery of this Second Supplemental Indenture as to the parties hereto and may be used in lieu of the original Second Supplemental Indenture for all purposes. Signatures of the parties hereto transmitted by facsimile or PDF shall be deemed to be their original signatures for all purposes.

9. Effect of Headings. The Section headings in this Second Supplemental Indenture have been inserted for convenience of reference only, are not to be considered a part of this Second Supplemental Indenture and in no way modify or restrict any of the terms and provisions of this Second Supplemental Indenture.

10. The Trustee and the Canadian Trustee. Neither the Trustee nor the Canadian Trustee shall be responsible in any manner whatsoever for or in respect of (i) the validity or sufficiency of this Second Supplemental Indenture, (ii) the recitals contained herein, all of which recitals are made solely by the Company, the Subsidiary Guarantors, the Co-Issuer and the Affiliate Guarantor, (iii) the due execution hereof by the Company, the Subsidiary Guarantors, the Co-Issuer and the Affiliate Guarantor, or (iv) the consequences of any amendment herein provided for, and the Trustee and the Canadian Trustee make no representation with respect to any such matters.

11. Enforceability. Each of the Company, the Subsidiary Guarantors, the Co-Issuer and the Affiliate Guarantor hereby represents and warrants that this Second Supplemental Indenture is the legal, valid and binding obligation of each of them, enforceable against each of them in accordance with its terms, subject to bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium and similar laws of general applicability relating to or affecting creditors’ rights and to general principles of equity (regardless of whether enforcement is considered in a proceeding in equity or at law).

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IN WITNESS WHEREOF, the parties hereto have caused this Second Supplemental Indenture to be duly executed and delivered, all as of the date first above written.

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Appendix A

AFFILIATE GUARANTEE

1. Guarantee. With respect to the 5  ¹⁄₂% Senior Notes due 2021 (the “Notes”) issued by Kodiak Oil & Gas Corp. (“Kodiak”) pursuant to an Indenture, dated as of January 15, 2013, as amended (as heretofore or hereafter amended and supplemented, the “Indenture”), by and among Kodiak, as issuer, Kodiak Oil & Gas (USA), Inc. and Kodiak Williston, LLC, as subsidiary guarantors, Whiting Petroleum Corporation, as parent guarantor, U.S. Bank National Association, as trustee (the “Trustee”), and Computershare Trust Company of Canada, as Canadian trustee (the “Canadian Trustee”), Whiting Oil and Gas Corporation, a Delaware corporation (the “Affiliate Guarantor”), unconditionally and irrevocably guarantees the prompt payment, when due, of any amount owed to the holders of the Notes under the Notes and the Indenture and any other amounts due pursuant to the Indenture (the “Obligations”).

2. Nature of Guarantee. The Affiliate Guarantor’s obligations hereunder shall not be affected by any circumstance relating to the Obligations that might otherwise constitute a legal or equitable discharge of or defense to the Affiliate Guarantor. The Affiliate Guarantor agrees that the Trustee, the Canadian Trustee or the holders of the Notes may resort to the Affiliate Guarantor for payment of any of the Obligations whether or not the Trustee, the Canadian Trustee, or the holders of the Notes shall have first proceeded against Kodiak or any other obligor principally or secondarily obligated with respect to the Obligations. The Trustee, the Canadian Trustee or the holders of the Notes shall not be obligated to file any claim relating to the Obligations in the event that Kodiak becomes subject to a bankruptcy, reorganization or similar proceeding, and the failure of the Trustee, the Canadian Trustee or the holders of the Notes to so file shall not affect the Affiliate Guarantor’s obligations hereunder. In the event that any payment to the Trustee, the Canadian Trustee or the holders of the Notes in respect of the Obligations is rescinded or must otherwise be returned for any reason whatsoever, the Affiliate Guarantor shall remain liable hereunder with respect to such Obligations as if such payment had not been made.

3. Changes in Obligations, and Agreements Relating thereto; Waiver of Certain Notices. The Affiliate Guarantor agrees that the Trustee, the Canadian Trustee or the holders of the Notes may at any time and from time to time, either before or after the maturity thereof, without notice to or further consent of the Affiliate Guarantor, extend the time of payment of, or renew all or any part of the Obligations, and may also make any agreement with Kodiak for the extension, renewal, payment, compromise, discharge or release thereof, in whole or in part, or for any modification of the terms thereof or of any agreement between the Trustee, the Canadian Trustee or the holders of the Notes and Kodiak, without in any way impairing or affecting this Guarantee. The Affiliate Guarantor waives notice of the acceptance of this Guarantee and of the Obligations, presentment, demand for payment, notice of dishonor and protest.

4. Expenses. The Affiliate Guarantor agrees to pay on demand all reasonable fees and out-of-pocket expenses (including the reasonable fees and expenses of one firm of counsel representing the Trustee, the Canadian Trustee or the holders of the Notes) in any way relating to the enforcement or protection of the rights of the Trustee, the Canadian Trustee or the holders of the Notes hereunder, provided that the Affiliate Guarantor shall not be liable for any expenses of the Trustee, the Canadian Trustee or the holders of the Notes if no payment under this Guarantee is due.

5. Subrogation. Upon payment of the Obligations to the Trustee, the Canadian Trustee or the holders of the Notes in full, the Affiliate Guarantor shall be subrogated to the rights of the Trustee, the Canadian Trustee or the holders of the Notes against Kodiak with respect to the Obligations, and the Trustee, the Canadian Trustee or the holders of the Notes agree to take at the Affiliate Guarantor’s expense such steps as the Affiliate Guarantor may reasonably request to implement such subrogation.

6. No Waiver; Cumulative Rights. No failure on the part of the Trustee, the Canadian Trustee or the holders of the Notes to exercise, and no delay in exercising, any right, remedy or power hereunder shall operate as a waiver thereof, nor shall any single or partial exercise by the Trustee, the Canadian Trustee or the holders of the Notes of any right, remedy or power hereunder preclude any other or further exercise of any right, remedy or power. Each and every right, remedy and power hereby granted to the Trustee, the Canadian Trustee and the holders of the Notes or allowed it or them by law or in equity or other agreement shall be cumulative and not exclusive of any other, and may be exercised by the Trustee, the Canadian Trustee or the holders of the Notes at any time or from time to time.

7. Assignment. Nothing contained in this Guarantee shall prevent any consolidation or merger of Affiliate Guarantor with or into any other Person (whether or not affiliated with the Affiliate Guarantor), or successive consolidations or mergers in which Affiliate Guarantor or its successor shall be a party or parties, or shall prevent any conveyance or transfer of the properties and assets of Affiliate Guarantor as an entirety or substantially as an entirety to any other Person (whether or not affiliated with Affiliate Guarantor) lawfully entitled to acquire the same; provided, however, that upon any such consolidation, merger, conveyance or transfer, the due and punctual performance and observance of all of the covenants and conditions of the Guarantee to be performed by Affiliate Guarantor, shall be expressly assumed, in form reasonably satisfactory to the Trustee and the Canadian Trustee, executed and delivered to the Trustee and the Canadian Trustee by the person (if other than the Affiliate Guarantor) formed by such consolidation, or into which Affiliate Guarantor shall have been merged, or by the Person which shall have acquired such properties and assets.

8. Notices. All notices to or demands on the Affiliate Guarantor shall be deemed effective when received, shall be in writing and shall be delivered by hand or by registered mail (or similar type mail), or by facsimile transmission promptly confirmed by registered mail (or similar type mail), addressed to the Affiliate Guarantor at:

Whiting Oil and Gas Corporation

1700 Broadway, Suite 2300

Denver, Colorado 80290

(303) 837-1661

Attention: Corporate Secretary

or to such other address or fax number as the Affiliate Guarantor shall have notified the Trustee and the Canadian Trustee in a written notice delivered to the Trustee and the Canadian Trustee at the address or facsimile number specified in the Indenture.

9. Continuing Guarantee. This Guarantee shall remain in full force and effect and shall be binding on the Affiliate Guarantor, its successors and assigns until all of the Obligations have been satisfied in full. Notwithstanding the foregoing or any other provision hereof to the contrary, in the event that the Affiliate Guarantor ceases to be an Affiliate (as defined in the Indenture) of Kodiak as the result of any transaction or series of transactions that complies with the Indenture, then the Affiliate Guarantor shall be released from this Guarantee upon the consummation thereof without the necessity of any further action by any party.

10. Representations and Warranties. The Affiliate Guarantor represents and warrants that: (i) this Guarantee has been duly executed and delivered by the Affiliate Guarantor and constitutes a valid and legally binding obligation of the Affiliate Guarantor enforceable in accordance with its terms, except as such enforceability may be limited by bankruptcy, insolvency, reorganization, moratorium or similar laws affecting creditors’ rights generally and subject to general principles of equity, (ii) no consent or approval of any Person, entity or governmental or regulatory authority, or of any securities exchange or self-regulatory organization, was or is necessary in connection with this Guarantee (other than any consents and approvals that have been obtained and are in effect) and (iii) the execution and delivery of this Guarantee by the Affiliate Guarantor and the performance by the Affiliate Guarantor of its obligations hereunder do not violate or conflict with any law applicable to it, any provision of its constitutive documents, any order or judgment of any court or other agency of government applicable to it or any of its assets or any contractual provision binding on or affecting it or any of its assets, in any manner that could reasonably be expected to impair its ability to perform its obligations hereunder.

11. Governing Law. This Guarantee shall be governed by and construed in accordance with the laws of the State of New York.