Exhibit 5.1

[Letterhead of STvB Advocaten (Curaçao) N.V.]

Schlumberger N.V.

(Schlumberger Limited)

5599 San Felipe - 17th Floor

Houston, Texas 77056

U.S.A.

Curaçao, October 27, 2017

Ladies and Gentlemen,

We have acted as Curaçao legal counsel for Schlumberger N.V. (also referred to as Schlumberger Limited), a corporation with limited liability organized and existing under the laws of Curaçao (the “Company”), in connection with the registration under the Securities Act of 1933, as amended (the “Securities Act”) and the proposed issuance and sale from time to time pursuant to Rule 415 under the Securities Act of (i) the Company’s debt securities, which may either be senior debt securities or subordinated debt securities (together 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 “Shares”) that may be issued by the Company pursuant to applicable provisions of the Articles of Incorporation of the Company. We understand that a registration statement on Form S-3 relating to the Debt Securities, the Guarantees and the Shares (the “Registration Statement”) is being filed by the Company with the Securities and Exchange Commission under the Securities Act on October 27, 2017.

As Curaçao legal counsel for the Company we have examined and relied upon the following documents in original, photo static or facsimile form:

(a) a copy of the Registration Statement;

(b) a certified copy of the articles of incorporation of the Company (the “Articles of Incorporation”), as presently in effect;

(c) an extract obtained online on October 27, 2017 from the Curaçao Commercial Register, relating to the registration of the Company;

(d) a certified copy of the resolutions of the Board providing for the registration of the Securities.

In our examination of the documents referred to above and in expressing our opinion, we have assumed without independent verification of any kind:

(i) the genuineness of all signatures on all documents we have reviewed;

(ii) the authenticity of all such documents submitted to us as originals, and that each of the documents has been duly executed in the form, or substantially in the form submitted to us as execution copies; and

(iii) the conformity with originals of all documents submitted to us as copies.

In rendering the following, we are opining on the matters hereinafter referred to, only insofar as they are governed by the laws of Curaçao as currently in effect and as they are interpreted under presently published case law of Curaçao, including the Supreme Court of the Netherlands (Hoge Raad der Nederlanden).

Based upon and subject to the foregoing and subject to the qualifications set forth below and having due regard for such legal considerations as we deem relevant, we are of the opinion that:

(a) The Company has been duly incorporated under the laws of the former Netherlands Antilles, is currently validly existing under the laws of Curaçao and has all requisite corporate power and authority to own its properties, to conduct its business within the limits of its objects clause as set forth in article 2 of the Articles of Incorporation and to execute, deliver and perform its obligations under the Debt Securities and the Guarantees. The Company has been duly registered with the Curaçao Commercial Register under number 1674.

(b) With respect to the Shares, when (i) the Board has taken all necessary corporate action to approve the issuance of and the terms of the offering of such Shares and (ii) such Shares have been duly authorized and delivered in accordance with the applicable definitive purchase, underwriting or similar agreement for the consideration provided for therein, such Shares will be validly issued, fully paid and non-assessable.

(c) No personal liability will attach to the holders of the Shares under the laws of Curaçao by reason of their being stockholders of the Company.

(d) No consents, approvals, authorizations or other orders of Curaçao governmental authorities are legally required for the issuance of the Shares by the Company.

This opinion is strictly limited to the matters stated herein and may not read as extending by implication to any matters not specifically referred to herein, including tax matters.

We consent to the filing of this opinion as an exhibit to the Registration Statement. In giving such consent, we do not thereby concede 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 Securities and Exchange Commission promulgated thereunder.

Sincerely yours,

STvB Advocaten (Curaçao) N.V.

2