Question 9 of 10: Shale Volume from SP and Gamma Ray, Zone A

Question 9: Shale Volume from SP and Gamma Ray, Zone A (20 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.

Find. V_sh of Zone A from (a) the SP ratio and (c) the gamma-ray index, plus (e) a recommended value.

Approach. Both logs carry the numbers already: the IES section prints bracketed SP deflections labelled SSP −80 mV (Zone B) and PSP 47 mV (Zone A), and the FDC gamma-ray track carries three hand-written values — 28, 92 and 44 — each printed at its own position on the 0–120 API track, against Zone B (clean), Zone C (shale) and Zone A respectively. Nothing needs to be traced by eye: the annotations ARE the intended readings, and each one can be checked against its track scale.

(a) Shale content from the SP curve

1. SP-ratio method. With PSP_A the pseudo-static SP of Zone A measured from the shale base line, and SSP_B the full static SP of the adjacent clean, thick Zone B: $$V_{sh}=1-\frac{PSP_A}{SSP_B}=1-\frac{-47}{-80}=1-0.5875=\boxed{41.3\%}$$
2. Independent check on the 47 mV annotation. Measured against the SP track’s own scale on the printed log, the SSP bracket at Zone B is 108.5 units long and the PSP bracket at Zone A is 62.0 units long, so PSP = 80 × 62.0/108.5 = 45.7 mV — confirming the printed annotation to within 1.5 mV and giving V_sh = 42.9% on the measured ratio instead of 41.3% on the printed one.

(b) Assumptions implied by the SP-ratio method

• Zone B is a fully clean (V_sh≈0), thick sand whose SSP is the TRUE maximum SP achievable at this R_mf/R_w contrast — i.e., the reduction of PSP below SSP is caused ENTIRELY by shale, not by bed thinness or hydrocarbon effect.
• R_mf/R_w (hence the ideal SSP) is the SAME in Zone A as in Zone B — no significant change in formation-water salinity or temperature between the two intervals.
• SP reduction is LINEARLY proportional to shale volume (PSP/SSP = 1−V_sh), i.e., dispersed/laminated shale acts as a simple linear short circuit on the membrane potential.
• The bed is thick enough, and invasion shallow enough, that the SP curve reaches its full deflection (no bed-thickness or invasion suppression additional to the shale effect).
• The shale base line is correctly picked and does not drift across the interval, since both deflections are measured from it.

(c) Shale content from the gamma ray curve

3. Shale index. The clean and shale references are the log’s own annotated readings, Zone B at 28 API and Zone C at 92 API — NOT the 0 and 120 API ends of the printed track: $$I_{sh}=\frac{\gamma_{log,A}-\gamma_c}{\gamma_{sh}-\gamma_c}=\frac{44-28}{92-28}=\frac{16}{64}=\boxed{0.25}$$
4. Stieber transform (Tertiary, unconsolidated Gulf-Coast sand). $$V_{sh}=\frac{I_{sh}}{3-2I_{sh}}=\frac{0.25}{3-0.50}=\frac{0.25}{2.50}=\boxed{10.0\%}$$ (For comparison, the Larionov older-rock form also printed on the attachment, $V_{sh}=0.33(2^{2I_{sh}}-1)$, would give 13.7% — the same order, and both far below the SP answer.)

(d) Assumptions implied by the gamma-ray method

• All the excess (above clean-line) gamma radiation in Zone A comes from SHALE/CLAY minerals, not from an accessory radioactive mineral (feldspar, mica, glauconite, or a uranium-rich streak) carrying no clay.
• The clean line (28 API, Zone B) and shale line (92 API, Zone C) are representative, single-valued references applicable at Zone A — i.e., clay type and clean-sand mineralogy do not vary through the interval.
• The Stieber (younger, unconsolidated Tertiary) I_sh–V_sh transform is the appropriate non-linear correction for this Gulf-Coast setting, rather than the older-rock Larionov form.
• Borehole/tool environmental corrections (hole size, mud weight, source-detector spacing) have already been applied, so γ_log,A is a true formation reading.

(e) Comparison and recommended V_sh

The two methods disagree by a factor of four: 41% from SP against 10% from gamma ray. The gap is systematic, not a data error, and it is the SP value that is suspect. The SP-ratio method assumes a PURELY LINEAR reduction of SP with shale, but a pseudo-static SP is also suppressed by bed thickness, by invasion, and by hydrocarbon in the zone — every one of which biases it toward OVER-estimating V_sh, and Zone A is exactly the sort of moderately thin, invaded sand where all three act at once. The gamma-ray route, by contrast, uses the log’s own annotated clean and shale references, and after the Stieber correction for young, unconsolidated Gulf-Coast sediment it returns a shale index of only 0.25 — a reading much closer to the clean line (28 API) than to the shale line (92 API), which is what the raw 44 API plainly shows. Recommended value: V_sh ≈ 10% (the GR-Stieber value), i.e. Zone A is a good, only slightly shaly sand; the SP-derived 41% should be carried only as a pessimistic upper bound.