Exhibit 5.1

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

September 18, 2020

Schlumberger Finance Canada Ltd.

Schlumberger N.V. (Schlumberger Limited)

c/o Schlumberger N.V. (Schlumberger Limited)

5599 San Felipe, 17^th Floor

Houston, Texas 77056

Ladies and Gentlemen:

We have acted as counsel to Schlumberger Finance Canada Ltd., a corporation incorporated under the laws of the Province of Alberta, Canada (the “Company”) and Schlumberger N.V. (Schlumberger Limited), a Curaçao company (the “Guarantor”) in connection with the preparation and filing with the Securities and Exchange Commission (the “Commission”) of a Registration Statement on Form S-3, file no. 333-248675 (the “Registration Statement”), under the Securities Act of 1933, as amended (the “Securities Act”), the prospectus included therein, the prospectus supplement, dated September 9, 2020, filed with the Commission on September 10, 2020 pursuant to Rule 424(b) of the Securities Act (the “Prospectus Supplement”), and the offering by the Company pursuant thereto of $500,000,000 aggregate principal amount of the Company’s 1.400% Senior Notes due 2025 (the “Notes”).

The Notes have been issued pursuant to the Indenture, dated September 18, 2020 (the “Base Indenture”), among the Company, the Guarantor and The Bank of New York Mellon (the “Trustee”), as modified and supplemented by the First Supplemental Indenture, dated September 18, 2020, relating to the Notes (the “Supplemental Indenture” and together with the Base Indenture, the “Indenture”) between the Company, the Guarantor and the Trustee, and are guaranteed pursuant to the terms of the Indenture by the Guarantor (the “Guarantee”).

In arriving at the opinion 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 Base Indenture, the Supplemental Indenture, the Notes, the Guarantee and such other documents, corporate records, certificates of officers of the Company and the Guarantor 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, without independent

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investigation, 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, the Guarantor and others.

We are not admitted or qualified to practice law in Canada or Curaçao. Therefore, we have relied upon the opinions of Bennett Jones LLP and STvB Advocaten (Europe) N.V., filed as exhibits to the Guarantor’s Current Report on Form 8-K filed with the Commission on September 18, 2020, with respect to matters governed by the laws of Canada and Curaçao.

Based upon the foregoing, and subject to the assumptions, exceptions, qualifications and limitations set forth herein, we are of the opinion that the Notes are legal, valid and binding obligations of the Company, enforceable against the Company in accordance with their respective terms, and the Guarantee of the Notes is a legal, valid and binding obligations of the Guarantor obligated thereon, enforceable against the Guarantor in accordance with its terms.

The opinion expressed above is subject to the following additional 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 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 the Indenture, the Guarantee or the certificate evidencing the global Notes (collectively, the “Specified Note Documents”) 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

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matter of law; (iii) any waiver (whether or not stated as such) contained in the Specified Note Documents 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 Specified Note 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.

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 Supplement. 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