Exhibit 5.1

June 2, 2021

CSI Compressco LP

CSI Compressco Finance Inc.

24955 Interstate 45 North

The Woodlands, TX 77380

Re:    CSI Compressco LP — Registration Statement on Form S-3

Ladies and Gentlemen:

We have acted as counsel for CSI Compressco LP, a Delaware limited partnership (the “Partnership”), and CSI Compressco Finance Inc., a Delaware corporation (“Compressco Finance”), as well as CSI Compressco Sub, Inc., a Delaware corporation, CSI Compressco Operating LLC, a Delaware limited liability company, CSI Compressco Field Services International LLC, a Delaware limited liability company, CSI Compressco International LLC, a Delaware limited liability company, CSI Compressco Holdings LLC, a Delaware limited liability company, CSI Compressco Leasing LLC, a Delaware limited liability company, CSI Compression Holdings, LLC, a Delaware limited liability company, and Rotary Compressor Systems, Inc., a Delaware corporation (collectively, the “Guarantors”), in connection with the preparation of a registration statement on Form S-3 (the “Registration Statement”) filed with the Securities and Exchange Commission (the “Commission”) by the Partnership and Compressco Finance under the Securities Act of 1933, as amended (the “Securities Act”), with respect to the offer and sale from time to time at an aggregate initial offering price not to exceed $100,000,000, pursuant to Rule 415 under the Securities Act, by:

(1)the Partnership of common units representing limited partner interests in the Partnership (the “Common Units”);

(2)the Partnership of preferred units representing limited partner interests in the Partnership (the “Preferred Units”)

(3)the Partnership of debt securities, which may be co-issued by Compressco Finance, in one or more series, consisting of notes, debentures or other evidences of indebtedness (the “Debt Securities”);

(4)the Guarantors of guarantees of payments on the Debt Securities by the Guarantors (the “Guarantees”); and

(5)the Partnership of other securities of the Partnership (the “Other Securities”).

The Common Units, Preferred Units, Debt Securities, Guarantees and Other Securities are collectively referred to herein as the “Securities.” We have also participated in the preparation of the Prospectus (the “Prospectus”) contained in the Registration Statement to which this opinion is an exhibit. The Securities will be offered in amounts, at prices and on terms to be determined in light of market conditions at the time of sale and to be set forth in supplements (each, a “Prospectus Supplement”) to the Prospectus. Capitalized terms not defined herein shall have the meanings ascribed to them in the Prospectus.

Vinson & Elkins LLP Attorneys at Law Austin Dallas Dubai Houston London Los Angeles New York Richmond Riyadh San Francisco Tokyo Washington 1001 Fannin Street, Suite 2500
Houston, TX 77002-6760 Tel +1.713.758.2222 Fax +1.713.758.2346 velaw.com

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In rendering the opinions set forth below, we have examined and relied upon  the Registration Statement, including the Prospectus,  the form of Senior Indenture (the “Senior Indenture”) filed as an exhibit to the Registration Statement,  the form of Subordinated Indenture (the “Subordinated Indenture” and, together with the Senior Indenture, the “Indentures”) filed as an exhibit to the Registration Statement,  the Second Amended and Restated Agreement of Limited Partnership of the Partnership, including any amendments thereto (the “Partnership Agreement”),  the Certificate of Limited Partnership of the Partnership filed with the Secretary of State of the State of Delaware,  the certificates of incorporation, bylaws, limited liability company agreements and other formation documents and agreements, as applicable, of Compressco Finance and the Guarantors,  resolutions of CSI Compressco GP LLC, a Delaware limited liability company and the general partner of the Partnership (the “General Partner”), of Compressco Finance and of the Guarantors and  such other documents as we have deemed necessary or appropriate for purposes of this opinion. In addition, we have reviewed certain certificates of officers of the General Partner and of public officials, and we have relied on such certificates with respect to certain factual matters that we have not independently established.

In connection with this opinion, we have assumed that:

(1)all information contained in all documents reviewed by us is true and correct;

(2)all signatures on all documents examined by us are genuine;

(3)each person signing documents we examined has the legal authority and capacity to do so;

(4)all documents submitted to us as originals are authentic and complete and all documents submitted to us as copies conform to the originals of those documents;

(5)each certificate from governmental officials reviewed by us is accurate, complete and authentic, and all official public records are accurate and complete;

(6)the Registration Statement, and any amendments thereto (including post-effective amendments), will have become effective and comply with all applicable laws;

(7)a Prospectus Supplement will have been prepared and filed with the Commission describing the Securities offered thereby and will comply with all applicable laws;

(8)all Securities will be issued and sold in compliance with applicable federal and state securities laws and in the manner stated in the Registration Statement and the applicable Prospectus Supplement;

(9)an indenture, and any supplemental indenture relating to a particular series of Debt Securities, will be duly authorized, executed and delivered by the parties thereto in substantially the form reviewed by us;

(10)any Securities issuable upon conversion, exchange or exercise of any Security being offered will be duly authorized, created and, if appropriate, reserved for issuance upon such conversion, exchange or exercise;

(11)a definitive purchase, underwriting or similar agreement with respect to any Securities offered will have been duly authorized and validly executed and delivered by the Partnership and Compressco Finance, as applicable, and the other parties thereto; and

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(12)the form and terms of any Debt Securities and Guarantees, the issuance, sale and delivery thereof by the Partnership, Compressco Finance and the Guarantors, as applicable, and their incurrence and performance of their obligations thereunder or in respect thereof in accordance with the terms thereof, will be in full compliance with, and will not violate, the formation documents and agreements, as applicable, of the Partnership, Compressco Finance and the Guarantors, as applicable, or any applicable law, rule, regulation, order, judgment, decree, award or agreement binding upon any of them, or to which the issuance, sale and delivery of such Securities, or the incurrence and performance of such obligations, may be subject, or violate any applicable public policy, or be subject to any defense in law or equity.

Based upon and subject to the foregoing, we are of the opinion that:

(1)With respect to the Common Units, when  the Partnership has taken all necessary action to duly authorize and approve the issuance of such Common Units and the limited partner interests represented thereby, the terms of the offering thereof and related matters and  the Common Units have been issued and delivered in accordance with the terms of the applicable definitive purchase, underwriting or similar agreement approved by the Partnership upon payment of the consideration thereof or provided for therein, then the Common Units will be validly issued, fully paid (to the extent required under the Partnership Agreement) and nonassessable (except as such nonassessability may be affected by Section 17-607 or 17-804 of the Delaware Revised Uniform Limited Partnership Act (“DRULPA”) and as described in the Prospectus Supplement and the Prospectus).

(2)With respect to the Preferred Units, when  the Partnership has taken all necessary action to duly authorize and approve the issuance and terms of such Preferred Units and the limited partner interests represented thereby, the terms of the offering thereof and related matters, including the adoption of a resolution establishing or designating the Preferred Units and fixing and determining the preferences, limitations and relative rights thereof, and  the Preferred Units have been issued and delivered in accordance with the terms of the applicable definitive purchase, underwriting or similar agreement approved by the Partnership upon payment of the consideration thereof or provided for therein, then the Preferred Units will be validly issued, fully paid (to the extent required under the Partnership Agreement) and nonassessable (except as such nonassessability may be affected by Section 17-607 or 17-804 of the Delaware Revised Uniform Limited Partnership Act (“DRULPA”) and as described in the Prospectus Supplement and the Prospectus)

(3)With respect to the Debt Securities and the Guarantees, when  the applicable Indenture has been duly qualified under the Trust Indenture Act of 1939, as amended;  the terms of the Debt Securities and, if applicable, the Guarantees and of their issuance and sale have been duly established in conformity with the indenture so as not to violate any applicable law or result in a default under or breach of any agreement or instrument binding upon the Partnership, Compressco Finance or the Guarantors, as applicable, and so as to comply with any requirements or restrictions imposed by any court or governmental body having jurisdiction over the Partnership, Compressco Finance and the Guarantors;  the Partnership, Compressco Finance and the Guarantors, as applicable, have taken all necessary action to duly authorize and approve the issuance and terms of such Debt Securities and Guarantees, the terms of the offering thereof and related matters; and  such Debt Securities and Guarantees have been duly authorized, executed, authenticated, issued and delivered in accordance with the provisions of the applicable Indenture and the applicable definitive purchase, underwriting or similar agreement approved by the Partnership, Compressco Finance and the Guarantors, as applicable, upon payment of the consideration thereof or provided for therein, such Debt Securities and, if applicable, the Guarantees will be legally issued and will constitute valid and legally binding obligations of the Partnership, Compressco Finance and the Guarantors, respectively, enforceable against the Partnership, Compressco Finance and the Guarantors, as applicable, in accordance with their terms, except as such enforcement may be subject to any applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance or other law relating to or affecting creditors’ rights and remedies generally or by general

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principles of equity (regardless of whether such principles are considered in a proceeding in equity or at law) and public policy, applicable law relating to fiduciary duties and indemnification and an implied covenant of good faith and fair dealing.

(4)With respect to the Other Securities, when  the Partnership has taken all necessary action to duly authorize and approve the issuance of such Other Securities and any limited partner interests represented thereby, the terms of the offering thereof and related matters and  the Other Securities have been issued and delivered in accordance with the terms of the applicable definitive purchase, underwriting or similar agreement approved by the Partnership upon payment of the consideration thereof or provided for therein, then the Other Securities will be validly issued, fully paid (to the extent required under the Partnership Agreement) and nonassessable (except as such nonassessability may be affected by Section 17-607 or 17-804 of the DRULPA and as described in the Prospectus Supplement and the Prospectus).

The opinions expressed herein are qualified in the following respects:

(1)We have assumed, without independent verification, that the certificates for the Common Units will conform to the specimens thereof examined by us and will have been duly countersigned by a transfer agent and duly registered by a registrar of the Common Units.

(2)We express no opinions concerning  the validity or enforceability of any provisions contained in the Indentures that purport to waive or not give effect to rights to notices, defenses, subrogation or other rights or benefits that cannot be effectively waived under applicable law or  the enforceability of indemnification provisions to the extent they purport to relate to liabilities resulting from or based upon negligence or any violation of federal or state securities or blue sky laws.

(3)The foregoing opinion is limited in all respects to the DRULPA, the Delaware Limited Liability Company Act, the Delaware General Corporation Law and the Constitution of the State of Delaware, as interpreted by the courts of the State of Delaware, the laws of the State of New York and the federal laws of the United States of America and we are expressing no opinion as to the effect of the laws of any other jurisdiction, domestic or foreign.

(4)We express no opinion as to any matters other than as expressly set forth above, and no opinion on any other matter may be inferred or implied herefrom.

The opinions expressed herein are given as of the date hereof, and we undertake no, and hereby disclaim any, obligation to advise you of any change in any matter set forth herein.

We hereby consent to the references to our firm under the caption “Legal Matters” in the Prospectus and to the filing of this opinion as an exhibit to the Registration Statement. By giving such consent, we do not admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission issued thereunder.

Very truly yours,

/s/ Vinson & Elkins L.L.P.