Capillary Pressure — Depth of 40% Water Saturation: 24-Pet-A3 Fundamental Reservoir Engineering, December 2015, Q7

Question 7: Capillary Pressure — Depth of 40% Water Saturation (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.

WOC depth	7000 ft
Capillary pressure at $S_w=40\%$, $P_c$	10 psi
Oil density, $\rho_o$	50 lbm/ft$^3$
Water density, $\rho_w$	62 lbm/ft$^3$

Find. (a) A schematic depth-vs-pressure plot; (b) the depth at which $S_w=40\%$.

Check: only a single capillary-pressure data point is given (not a full $P_c$–$S_w$ curve), so the reported WOC depth is treated as coincident with the free water level (i.e. $P_c=0$ there) — the standard simplifying assumption when the full lab transition-zone curve is not provided. A real transition-zone curve would generally place the true FWL slightly below the log-derived WOC.

Approach. Take the WOC/FWL depth as the datum where the oil- and water-pressure lines intersect ($P_c=0$), then convert the given $P_c$ to a height above that datum using the hydrostatic gradient difference between the two fluids.

Fig. 3 — Depth–pressure schematic: the oil and water hydrostatic lines cross at the FWL/WOC; the orange bracket marks the threshold (entry) capillary pressure separating them at $S_w=40\%$, 120 ft above the datum.

Height above the free water level. The gradient difference between the two fluids is $(\rho_w-\rho_o)/144=(62-50)/144=0.0833$ psi/ft, so $h=\dfrac{144\,P_c}{\rho_w-\rho_o}=\dfrac{144(10)}{62-50}=\boxed{120\ \text{ft}}$ above the FWL/WOC.
Depth of $S_w=40\%$. Since depth increases downward, a point above the WOC is shallower: $\boxed{D_{S_w=40\%}=7000-120=6880\ \text{ft}}$.

Quantity	Value
Height above FWL/WOC	120 ft
Depth of $S_w=40\%$	6880 ft

Concept & Theory

Topic: Capillary pressure and the oil/water transition zone.

Key relations: $P_c=p_o-p_w=\dfrac{(\rho_w-\rho_o)}{144}h$, where $h$ is height above the free water level (the datum where $P_c=0$); the threshold/entry pressure is the minimum $P_c$ needed for the non-wetting phase (oil) to first enter the largest pores at the top of the water leg.

Why this works: Above the FWL, oil and water pressures both still follow their own separate hydrostatic gradients, but oil's lower density gives it a shallower gradient than water's; their pressure difference at any height above the FWL is exactly the capillary pressure holding that height's saturation in place.

Common pitfall: Confusing the log-derived WOC (where the sonde first detects a shift to non-zero water saturation, typically at some finite $S_w<100\%$ or a resistivity cutoff) with the free water level (the $P_c=0$ datum, found only from a full lab capillary-pressure curve); the two coincide only when treated as a simplifying assumption, as here.

Source: Ahmed, Reservoir Engineering Handbook, 5th ed., Ch. 5 (capillary pressure and the transition zone); McCain, The Properties of Petroleum Fluids, 3rd ed. (capillary pressure laboratory measurement).

Question 7 of 7: Capillary Pressure — Depth of 40% Water Saturation

Question 7: Capillary Pressure — Depth of 40% Water Saturation (20 marks)