Question 11 of 12: Recoverable Oil from ISF/Sonic and CNL/FDC Logs

Question 11: Recoverable Oil from ISF/Sonic and CNL/FDC Logs (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. R_w=0.05 Ω·m at formation temperature; ISF/sonic log (SP, IL/SFL resistivity, transit time, Fig. 11.26) and CNL/FDC log (caliper/GR, φ_CNL/φ_FDC, Fig. 11.27) over 6900–7000 ft; A=40 acres, F_R=35% (recovery factor), B_o=1.25 RB/STB, n=2 (saturation exponent, formula sheet).

Find. (a) Oil/water contact, if any. (b) Σφ_ih_i(S_o)_i over the productive interval. (c) Recoverable oil, N_R.

Approach. Put both figures on one depth scale from their printed 6900 ft and 7000 ft ticks; use the GR and the neutron–density separation to pick sand from shale, the deep induction to pick the resistive (hydrocarbon-bearing) part of the sand, and the two porosity curves (averaged, as the question instructs) for φ. Convert each pay zone's R_t to S_o via Humble + Archie, sum φh(S_o), and scale by the volumetric recoverable-oil formula from the attachment.

(a) Oil/water contact

Reading Figs. 11.26 and 11.27 together against the printed 6900 ft and 7000 ft depth ticks:

• Deep resistivity (IL). 0.7–1.0 Ω·m from the top of the logged interval (≈6850 ft) down to ≈6898 ft; rises sharply through 6900–6904 ft; holds 5–11 Ω·m from ≈6902 to ≈6932 ft, with one dip to ≈2 Ω·m at 6922–6927 ft; collapses to ≈1 Ω·m by 6934 ft and then stays between about 0.4 and 1.8 Ω·m all the way to the bottom of the log at ≈7040 ft.
• Gamma ray. ≈75 API above 6898 ft; 30–45 API over 6899–6932 ft (clean to slightly shaly sand, with a shalier streak reaching ≈50 API at 6922–6927 ft); back to ≈75 API by 6938 ft. Below that shale the GR settles at 45–60 API down to ≈6990 ft — shaly sand, never clean sand again.
• Porosity pair. φ_CNL and φ_FDC run within a few p.u. of each other across 6900–6932 ft and separate widely above and below it, the standard shale signature. The caliper is on gauge throughout the sand.

No oil/water contact can be picked on these logs. An OWC is a resistivity break at constant lithology and porosity; here the resistivity collapse at 6932–6934 ft coincides exactly with the GR rise to shale values and with the neutron–density curves separating, so the base of the hydrocarbon column is a lithologic (shale) boundary at ≈6932 ft, not a fluid contact. The sands below that shale do read wet (R_t ≈ 1 Ω·m, of the same order as their own R_o), but they are separate, shalier sand bodies beneath a shale break and therefore cannot define a contact for the sand above. Base of pay is taken at ≈6932 ft.

(b) Σφ_ih_i(S_o)_i

Net pay is the clean, resistive part of the 6902–6932 ft sand; the shalier, low-resistivity streak at 6922–6927 ft is excluded as non-pay. Porosity is the arithmetic mean of φ_CNL and φ_FDC, as the question instructs, and both curves read 29–33 p.u. throughout the pay, so a single φ = 0.31 is used for both intervals; R_t is the plateau deep-induction reading, ≈7 Ω·m in each.

1. Formation resistivity factor and S_o, via Humble's correlation and Archie (n=2), using R_w=0.05 Ω·m directly (already at formation temperature): $$F=\frac{0.62}{\phi^{2.15}},\qquad R_o=F R_w,\qquad S_w=\sqrt{\frac{R_o}{R_t}},\qquad S_o=1-S_w$$ With φ=0.31 in both zones: F=0.62/0.31^2.15=7.69; R_o=(7.69)(0.05)=0.385 Ω·m; S_w=√(0.385/7)=0.234; $\boxed{S_o=0.766}$ in each.
2. Sum φ_ih_i(S_o)_i over the two pay zones (the shaly streak and everything below the 6932 ft shale contribute zero net oil pay): $$\sum \phi_i h_i (S_o)_i = (0.31)(20)(0.766)+(0.31)(5)(0.766)=4.75+1.19=\boxed{5.94\ \text{ft}}$$

(c) Recoverable oil

3. Volumetric recoverable-oil formula (formula sheet), with F_R already a fractional recovery factor: $$N_R = 7758\,\frac{A\,F_R}{B_o}\sum h_i\phi_i(S_o)_i = 7758\times\frac{(40)(0.35)}{1.25}\times 5.94$$ $$N_R = 7758\times 11.2\times 5.94 = \boxed{516{,}000\ \text{STB}\approx 0.52\ \text{MMSTB}}$$