Exhibit 5.1

Gibson, Dunn & Crutcher LLP   200 Part Avenue New York, NY 10166-0193 Tel 212.351.4000 www.gibsondunn.com

August 14, 2023

Schlumberger N.V. (Schlumberger Limited)

5599 San Felipe

Houston, Texas 77056

Re: Schlumberger N.V. (Schlumberger Limited)

Registration Statement on Form S-3

Ladies and Gentlemen:

We have acted as counsel to Schlumberger N.V. (Schlumberger Limited), a Curaçao company (the “Company”), in connection with the preparation and filing with the Securities and Exchange Commission (the “Commission”) of a Registration Statement on Form S-3 (the “Registration Statement”) under the Securities Act of 1933, as amended (the “Securities Act”), relating to the registration under the Securities Act and the proposed issuance and sale from time to time pursuant to Rule 415 under the Securities Act, together or separately and in one or more series (if applicable) of:

(i)    the Company’s debt securities, which may either be senior debt securities (the “Senior Debt Securities”) or subordinated debt securities (the “Subordinated Debt Securities” and, collectively with the Senior Debt Securities, the “Debt Securities”);

(ii)    guarantees of debt securities (the “Guarantees”); and

(iii)    shares of the Company’s common stock, par value $0.01 per share (the “Common Stock”).

The Debt Securities, Guarantees and Common Stock are collectively referred to herein as the “Securities.” Any Senior Debt Securities are to be issued under an indenture to be entered into between the Company and a financial institution to be named at the time such indenture is executed (the “Trust Company”), as indenture trustee (the “Senior Base Indenture”). Any Subordinated Debt Securities are to be issued under an indenture to be entered into between the Company and Trust Company, as indenture trustee (the “Subordinated Base Indenture” and, together with the Senior Base Indenture, the “Base Indentures”).

Abu Dhabi • Beijing • Brussels • Century City • Dallas • Denver • Dubai • Frankfurt • Hong Kong • Houston • London • Los Angeles

Munich • New York • Orange County • Palo Alto • Paris • San Francisco • Singapore • Washington, D.C.

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In arriving at the opinions expressed below, we have examined originals, or copies certified or otherwise identified to our satisfaction as being true and complete copies of the originals, of the form of Senior Base Indenture filed as Exhibit 4.2 to the Registration Statement, the form of Subordinated Base Indenture filed as Exhibit 4.3 to the Registration Statement, and such other documents, corporate records, certificates of officers of the Company and of public officials and other instruments as we have deemed necessary or advisable to enable us to render these opinions. In our examination, we have assumed the genuineness of all signatures, the legal capacity and competency of all natural persons, the authenticity of all documents submitted to us as originals and the conformity to original documents of all documents submitted to us as copies. As to any facts material to these opinions, we have relied to the extent we deemed appropriate and without independent investigation upon statements and representations of officers and other representatives of the Company and others.

We are not admitted or qualified to practice law in Curaçao. Therefore, we have relied upon the opinion of STvB Advocaten (Europe) N.V., filed as an exhibit to the Registration Statement, with respect to matters governed by the laws of Curaçao.

We have assumed without independent investigation that:

(i)    at the time any Securities are sold pursuant to the Registration Statement (the “Relevant Time”), the Registration Statement and any supplements and amendments thereto (including post-effective amendments) will be effective and will comply with all applicable laws;

(ii)    at the Relevant Time, a prospectus supplement will have been prepared and filed with the Commission describing the Securities offered thereby and all related documentation and will comply with all applicable laws;

(iii)    all Securities will be issued and sold in the manner stated in the Registration Statement and the applicable prospectus supplement;

(iv)    at the Relevant Time, all corporate or other action required to be taken by the Company to duly authorize each proposed issuance of Securities and any related documentation (including the execution (in the case of certificated Securities), delivery and performance of the Securities and any related documentation referred to in paragraphs 1 and 2 below) shall have been duly completed and shall remain in full force and effect;

(v)    in the case of Debt Securities and Guarantees, at the Relevant Time, the relevant trustee shall have been qualified under the Trust Indenture Act of 1939, as amended (the “TIA”), a Statement of Eligibility of the Trustee on Form T-1 shall have been properly filed with the Commission and the relevant Base Indenture shall have been duly executed and delivered by the Company and all other parties thereto and duly qualified under the TIA; and

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(vi)    at the Relevant Time, a definitive purchase, underwriting or similar agreement and any other necessary agreement with respect to any Securities offered or issued will have been duly authorized by all necessary corporate or other action of the Company and duly executed and delivered by the Company and the other parties thereto.

Based on the foregoing and in reliance thereon, and subject to the assumptions, exceptions, qualifications and limitations set forth herein, we are of the opinion that:

1. With respect to any Debt Securities, when:

a. the relevant Base Indenture has been duly executed and delivered by the Company and the relevant trustee,

b. the terms and conditions of such Debt Securities have been duly established by supplemental indenture or officer’s certificate in accordance with the terms and conditions of the relevant Base Indenture,

c. any such supplemental indenture has been duly executed and delivered by the Company and the relevant trustee (together with the relevant Base Indenture, the relevant “Indenture”), and

d. such Debt Securities have been executed (in the case of certificated Debt Securities), delivered and authenticated in accordance with the terms of the relevant Indenture and issued and sold for the consideration set forth in the applicable definitive purchase, underwriting or similar agreement, such Debt Securities will be legal, valid and binding obligations of the Company, enforceable against the Company in accordance with their respective terms.

2. With respect to any Guarantees, when:

a. a guarantee agreement relating to such Guarantees (“Guarantee Agreement”) has been duly executed and delivered by the Company and each other party thereto,

b. the terms and conditions of such Guarantees have been duly established in accordance with the terms and conditions of the Guarantee Agreement, and

c. such Guarantees have been duly executed and delivered in accordance with the terms of the applicable Guarantee Agreement and issued and sold for the consideration set forth in the applicable definitive purchase, underwriting or

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similar agreement, such Guarantees will be legal, valid and binding obligations of the Company, enforceable against the Company in accordance with their respective terms.

The opinions expressed above are subject to the following exceptions, qualifications, limitations and assumptions:

A.    We render no opinion herein as to matters involving the laws of any jurisdiction other than the State of New York and the United States of America. This opinion is limited to the effect of the current state of the laws of the State of New York and the United States of America and the facts as they currently exist. We assume no obligation to revise or supplement this opinion in the event of future changes in such laws or the interpretations thereof or such facts.

B.    The opinions above with respect to the Indentures, the Debt Securities and the Guarantees (collectively, the “Documents”) are each subject to (i) the effect of any bankruptcy, insolvency, reorganization, moratorium, arrangement or similar laws affecting the rights and remedies of creditors’ generally, including without limitation the effect of statutory or other laws regarding fraudulent transfers or preferential transfers, and (ii) general principles of equity, including without limitation concepts of materiality, reasonableness, good faith and fair dealing and the possible unavailability of specific performance, injunctive relief or other equitable remedies regardless of whether enforceability is considered in a proceeding in equity or at law.

C.    We express no opinion regarding the effectiveness of (i) any waiver of stay, extension or usury laws or of unknown future rights; (ii) any waiver (whether or not stated as such) under any Indenture or any other Document of, or any consent thereunder relating to, unknown future rights or the rights of any party thereto existing, or duties owing to it, as a matter of law; (iii) any waiver (whether or not stated as such) contained in any Indenture or any other Document of rights of any party, or duties owing to it, that is broadly or vaguely stated or does not describe the right or duty purportedly waived with reasonable specificity; (iv) provisions relating to indemnification, exculpation or contribution, to the extent such provisions may be held unenforceable as contrary to public policy or federal or state securities laws or due to the negligence or willful misconduct of the indemnified party; (v) any purported fraudulent transfer “savings” clause; (vi) any provision in any Document waiving the right to object to venue in any court; (vii) any agreement to submit to the jurisdiction of any Federal court; (viii) any waiver of the right to jury trial; or (ix) any provision to the effect that every right or remedy is cumulative and may be exercised in addition to any other right or remedy or that the election of some particular remedy does not preclude recourse to one or more others.

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D.    To the extent relevant to our opinions in paragraph 2, we have assumed that the debt underlying any Guarantee is a legal, valid and binding obligation of the issuer thereof, enforceable against such issuer in accordance with its terms.

You have informed us that you intend to issue Securities from time to time on a delayed or continuous basis, and we understand that prior to issuing any Securities pursuant to the Registration Statement (i) you will advise us in writing of the terms thereof, and (ii) you will afford us an opportunity to (x) review the operative documents pursuant to which such Securities are to be issued or sold (including the applicable offering documents), and (y) file such supplement or amendment to this opinion (if any) as we may reasonably consider necessary or appropriate.

We consent to the filing of this opinion as an exhibit to the Registration Statement, and we further consent to the use of our name under the caption “Validity of the Securities” in the Registration Statement and the prospectus that forms a part thereof. In giving these consents, we do not thereby 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 promulgated thereunder.

Very truly yours,

/s/ Gibson, Dunn & Crutcher LLP