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24-Pet-B1 Natural Gas Engineering · Undated paper

Question 10 of 10: ESSP for Ideal and Nonideal Shale Membranes

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

National Examinations, 17-Pet-B1, Well Logging and Formation Evaluation — May 2019, 3 hours, closed book (Sharp or Casio approved calculators permitted), 10 questions, all marked. Every question on this paper is Well Logging & Formation Evaluation content, solved to the paper as printed. Every datum here was read from the paper: the Question 9 SP track prints "SSP −80 mV" and "PSP 47 mV", its gamma-ray track prints 28, 92 and 44 API against Zones B, C and A, and the attachments supply the gas-sand chart and SP departure chart used in Questions 7 and 10.

Reference texts: Bassiouni, Theory, Measurement, and Interpretation of Well Logs (SPE Textbook Series Vol. 4); Asquith & Krygowski, Basic Well Log Analysis, 2nd ed. (AAPG); Ellis & Singer, Well Logging for Earth Scientists, 2nd ed.; Schlumberger, Log Interpretation Charts / Log Interpretation Principles and Applications.

Question 10: ESSP for Ideal and Nonideal Shale Membranes (10 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given.

QuantityValue
Formation temperature, T200°F
Mud-filtrate resistivity (at F.T.), Rmf0.5 Ω·m
Formation-water resistivity (at F.T.), Rw0.1 Ω·m
Shale resistivity (nonideal case, at F.T.), Rsh2 Ω·m

Find. ESSP for (a) a perfect (ideal) shale membrane, and (b) a nonideal membrane with the given Rsh.

Approach. (a) Apply the attachment's ESSP formula directly, using K=61.3+0.133T. (b) An imperfect (leaky) shale membrane no longer follows the simple K·log(Rmf/Rw) law; the reduced SP is read from the departure-curve chart of Rmf/Rw vs. ESP parameterized by (Rsh/Rmf)@F.T.

  1. Temperature coefficient K. $$K=61.3+0.133T=61.3+0.133(200)=61.3+26.6=\boxed{87.9}$$
  2. (a) Ideal (perfect) membrane — direct formula. $$E_{SSP}=-K\log_{10}\!\left(\frac{R_{mf}}{R_w}\right)=-87.9\log_{10}\!\left(\frac{0.5}{0.1}\right)=-87.9\log_{10}(5)=-87.9(0.699)=\boxed{-61.4\text{ mV}}$$
  3. (b) Nonideal membrane — chart parameters. $$\frac{R_{mf}}{R_w}=\frac{0.5}{0.1}=5.0\qquad \left(\frac{R_{sh}}{R_{mf}}\right)_{@F.T.}=\frac{2.0}{0.5}=4.0$$
  4. (b) Read ESSP off the departure-curve chart. Entering the exam's own chart (the attachment page's Rmf/Rw vs. ESP departure curves, parameterized by (Rsh/Rmf)@F.T.) at Rmf/Rw=5.0 on the curve labelled 4: $$E_{SSP,\text{nonideal}}\approx\boxed{-27\text{ mV}}$$ — a much smaller deflection than the ideal −61.4 mV, because a shale resistivity only 4× the mud filtrate is a comparatively "leaky" (nonideal) cationic membrane that develops only a fraction of the ideal electrochemical EMF.
CaseESSP
(a) Perfect (ideal) shale membrane−61.4 mV
(b) Nonideal membrane, Rsh/Rmf=4≈ −27 mV
Check: part (b)'s value is read from the exam's own hand-drawn departure-curve chart (Rsh/Rmf family of curves vs. ESP, Rmf/Rw axis), by following the (Rsh/Rmf) = 4 curve against the printed gridlines (ESP every 20 mV, logarithmic Rmf/Rw axis): the curve reaches Rmf/Rw = 5.0 at about −27 mV. Treat it as a chart reading of roughly ±5 mV. The qualitative point — a shale only 4× more resistive than the mud filtrate develops well under half of the ideal SSP — is the intended lesson and is insensitive to that tolerance.
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