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. (a) Ratio Zone A's own SP deflection from the shale base line (PSP) against the SSP read in a clean reference sand nearby (Zone B) — both values are printed on the SP track; (c) convert Zone A's printed GR reading to a shale index against the clean/shale lines and transform with the Stieber (Tertiary, unconsolidated Gulf-Coast) relation; (e) compare and recommend.

(a) Shale content from the SP curve

1. SP-ratio method. With PSP_A the pseudo-static SP measured in Zone A (from the shale base line) and SSP_B the full static SP in the adjacent clean, thick Zone B, both legible directly off this sitting's own log: $$V_{sh}=1-\frac{PSP_A}{SSP_B}=1-\frac{-47}{-80}=1-0.5875=\boxed{41.3\%}$$

(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., PSP reduction 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).

(c) Shale content from the gamma ray curve

2. Shale index. $$I_{sh}=\frac{\gamma_{log,A}-\gamma_c}{\gamma_{sh}-\gamma_c}=\frac{44-28}{92-28}=\frac{16}{64}=0.250$$
3. Stieber transform (Tertiary, unconsolidated Gulf-Coast sand; attachment formula). $$V_{sh}=\frac{I_{sh}}{3-2I_{sh}}=\frac{0.250}{3-0.500}=\frac{0.250}{2.500}=\boxed{10.0\%}$$ For comparison, the attachment's older-rock form $V_{sh}=0.33(2^{2I_{sh}}-1)$ gives 13.7%, and the linear index itself is 25%.

(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) with no shale content.
• The clean line (γ_c) and shale line (γ_sh) are each constant, single-valued reference readings applicable to Zone A — i.e., the clay TYPE and the 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 Miocene-age setting, rather than the older-rock (Larionov) form.
• Borehole/tool environmental corrections (hole size, mud weight, source-detector spacing) have already been applied so that γ_log,A is a true formation reading.

(e) Comparison and recommended V_sh

The SP-ratio method gives V_sh ≈ 41%; the gamma-ray method gives 10% (Stieber), with 25% as the upper bound from the linear index. The SP value is about 31 percentage points higher, and the gap is systematic rather than a reading error. The SP-ratio method attributes ALL of the reduction from SSP to PSP to shale, but other effects also suppress the SP in Zone A: hydrocarbon in the flushed zone raises R_xo, the zone is thinner than the thick, clean Zone B reference, and the linear PSP/SSP relation itself overstates shale. The gamma ray, by contrast, reads Zone A only 16 API above the clean line within a 64 API clean-to-shale range, which is a clean-looking sand. In a young, unconsolidated Gulf-Coast section that index converts to about 10% shale.

Recommended value: V_sh ≈ 10% (gamma ray, Stieber). Because the SP-ratio method is known to overestimate shale in hydrocarbon-bearing and thin beds, the SP result is best treated as an upper bound. If radioactive non-clay minerals were present the GR value would itself be high, which would push the true V_sh even lower, not toward the SP value.