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. Nothing here has to be digitised by eye: both logs carry the readings the question needs as printed annotations. The IES log's SP track is annotated at two depths, and the FDC log's gamma-ray track (0–120 API) carries three annotated API values.

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 deflection from the shale base line (PSP) against the full static deflection read in the adjacent clean sand (SSP). (c) Convert Zone A's gamma ray into a shale index against the printed clean and shale lines, then apply the Stieber transform appropriate to an unconsolidated Gulf-Coast Tertiary sand. (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 and SSP_B the full static SP of the adjacent clean, thick Zone B (both read from the same drawn shale base line): $$V_{sh}=1-\frac{PSP_A}{SSP_B}=1-\frac{-47}{-80}=1-0.5875=\boxed{41.3\%}$$

(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., every volt by which Zone A falls short of it is caused by shale and by nothing else.
• 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 over the ~200 ft between them.
• SP reduction is LINEARLY proportional to shale volume (PSP/SSP = 1 − V_sh), i.e. dispersed or laminated shale acts as a simple linear short circuit on the membrane potential.
• The bed is thick relative to the SP's vertical resolution and invasion is shallow, so the curve reaches its full deflection: no bed-thickness or invasion suppression on top of the shale effect.
• The shale base line is correctly picked and does not drift across the interval being compared.

(c) Shale content from the gamma ray curve

2. Shale index, from the three values printed on the gamma-ray track. $$I_{sh}=\frac{\gamma_{log,A}-\gamma_c}{\gamma_{sh}-\gamma_c}=\frac{44-28}{92-28}=\frac{16}{64}=0.250$$
3. Stieber transform (young, unconsolidated Tertiary Gulf-Coast sand). $$V_{sh}=\frac{I_{sh}}{3-2I_{sh}}=\frac{0.250}{3-0.500}=\frac{0.250}{2.500}=\boxed{10.0\%}$$ (For comparison, the linear index would give 25% and the Larionov Tertiary form 7.5%; the non-linear transforms agree with each other and both sit far below the SP value.)

(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 clay content.
• The clean line (28 API) and shale line (92 API) are each constant, single-valued references applicable at Zone A's depth — i.e. the clay type and the clean-sand mineralogy do not change through the interval.
• The Stieber (young, unconsolidated) I_sh–V_sh transform is the correct non-linear correction for this Gulf-Coast Miocene setting, rather than the linear index or the older-rock Larionov form.
• Borehole and tool environmental corrections (hole size, mud weight, source–detector spacing) have already been applied, so 44 API is a true formation reading — the caliper on the same log confirms Zone A is close to gauge.

(e) Comparison and recommended V_sh

The two methods disagree by a factor of four: 41.3% from the SP and 10.0% from the gamma ray. The disagreement is not a reading error — every input is a printed annotation — and it is systematic in a well-understood direction, because the SP-ratio method credits ALL of the SP suppression to shale. Three effects suppress SP in Zone A that have nothing to do with clay content:

• Hydrocarbon. Zone A is the high-resistivity interval on the companion IES induction curve. Hydrocarbon in the flushed and invaded zones reduces the ionic path available to the membrane current and cuts the SP deflection, sometimes by tens of millivolts, with no change in V_sh at all.
• Bed thickness and invasion. Zone A is thinner than the thick Zone B used as the SSP reference, so part of the shortfall is simple bed-thickness suppression.
• The linearity assumption itself. PSP/SSP = 1 − V_sh is the crudest possible shale model; the gamma-ray route at least applies a transform calibrated to this basin's rock.

The gamma ray, by contrast, responds to mineralogy alone and is anchored here on two clean/shale reference readings picked on the SAME track and printed on the log. It is the more reliable of the two in this setting. Recommended value: V_sh ≈ 10% (the GR-Stieber value) — Zone A is a clean-to-slightly-shaly sand. The SP-derived 41.3% should be retained only as a pessimistic upper bound, and its excess over the gamma-ray value is itself a qualitative hydrocarbon indicator, consistent with the resistivity response and with Zone A plotting as a gas sand on the Question 8 crossplot.