Question 11 of 11: SP- and GR-derived shale content, offshore Louisiana IES/FDC log
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
National Exams — December 2016. 98-Pet-B1, Well Logging and Formation Evaluation (every question is log-interpretation content, not gas-engineering material). 3-hour closed-book exam, 11 questions, all marked, calculators and attached graphs/formula sheet permitted.
Reference texts: Bassiouni, Theory, Measurement, and Interpretation of Well Logs (SPE Textbook Series Vol. 4); Asquith & Krygowski, Basic Well Log Analysis, 2nd ed.; Ellis & Singer, Well Logging for Earth Scientists, 2nd ed.; Schlumberger, Log Interpretation Charts.
Check: Q3, Q7, Q8, Q9(b), Q10 and Q11 are built on the paper's printed logs and attached charts. Values printed as annotations on the logs (Q11's SSP, PSP and GR labels) are used exactly as printed. Values read off a curve or a chart (Q9(b) and the Q8 chart check, Q10's track readings) are read from the printed figure and flagged inline with their precision. All arithmetic that follows is exact.
[Figure not reproduced: Source SP track and gamma-ray track with printed annotations. See the official exam paper or the cited reference text.]
Fig. Q11 — The printed SP track (page 14, left) and gamma-ray track (page 15, right, 0–120 API) for Zones B, C and A. Printed annotations: SSP −80 mV in Zone B and PSP 47 mV in Zone A on the SP track; 28 API in Zone B, 92 API in Zone C and 44 API in Zone A on the GR track.
Given (printed on the logs).
Quantity
Value
SSP, clean reference Zone B
−80 mV
PSP, Zone A (pseudo-static SP of the shaly bed)
−47 mV
GR, Zone B (clean line)
28 API
GR, Zone C (thick shale, shale line; the SP shale base line runs through it)
92 API
GR, Zone A
44 API
Bulk density (FDC), Zone C / Zone A
2.42 / 2.26 g/cm³
Find. $V_{sh}$ of Zone A by the SP-ratio method and by the GR method; the assumptions behind each; a recommended value.
(a) SP-ratio shale content. In a shaly bed, the SP deflection from the shale base line (the PSP) falls short of the full SSP of a clean bed. The simplest reading treats that shortfall as proportional to shale volume:
$$V_{sh,SP}=1-\frac{PSP_A}{SSP_B}=1-\frac{-47}{-80}=1-0.5875$$
$$\boxed{V_{sh,SP}\approx 0.413\ (41.3\%)}$$
(b) Assumptions for the SP method. (i) The PSP/SSP ratio falls linearly with shale volume, which is a simplification (the true response differs for laminated and dispersed shale). (ii) Zone A has the same $R_{mf}/R_w$ contrast, mud salinity and borehole conditions as the clean reference Zone B, so the SSP measured in B is a valid 0%-shale baseline for A. (iii) Nothing else suppresses the SP in Zone A: no hydrocarbons, and the bed is thick enough for the SP to reach its full deflection. (iv) The shale is distributed through the bed, not one thin unresolved streak. (v) The shale base line is correctly drawn through the thick shale.
(c) GR shale content. Clean line from Zone B (28 API), shale line from the thick shale of Zone C (92 API), Zone A reading 44 API:
$$I_{sh}=\frac{GR_A-GR_{clean}}{GR_{shale}-GR_{clean}}=\frac{44-28}{92-28}=\frac{16}{64}=0.25$$
This is a shallow, young, unconsolidated Gulf Coast Tertiary section, so apply the Stieber transform from the formula sheet:
$$V_{sh,GR}=\frac{I_{sh}}{3-2I_{sh}}=\frac{0.25}{3-0.50}=\frac{0.25}{2.50}$$
$$\boxed{V_{sh,GR}\approx 0.100\ (10.0\%)}$$
The linear index itself (25%) is the conservative upper bound.
(d) Assumptions for the GR method. (i) All of the gamma radiation above the clean line comes from clay, with no uranium from organics or phosphate (unlike the situation in Q10). (ii) The clay type, and so its radioactivity per unit volume, is the same in Zone A as in the Zone C shale. (iii) Zone B is genuinely clean and Zone C genuinely 100% shale. (iv) The log is corrected for hole size, mud weight and casing effects. (v) The Stieber transform suits this young, unconsolidated sediment. An older, consolidated section would call for the Larionov older-rock transform, and the linear index gives the upper bound.
(e) Compare and recommend. The two methods disagree by about 31 points: 41.3% from SP against 10.0% from GR-Stieber, or 25% even on the linear GR index. The gap is expected here rather than a sign of a bad reading. The SP ratio attributes every loss of SP deflection to shale, but the SP of Zone A is also reduced by anything else that lowers it: hydrocarbons, a bed too thin for the SP to develop fully, or a different water salinity from Zone B. The GR measures clay radioactivity directly and has none of those sensitivities. The density log supports a clean reading: Zone A's 2.26 g/cm³, against 2.42 g/cm³ in the Zone C shale, indicates a porous, relatively clean sand. Recommended value: $V_{sh}\approx10\%$ (GR with Stieber), with 25% as the upper bound if the more conservative linear index is preferred. The SP-derived 41% should not be used.
