24-Pet-A3 Fundamental Reservoir Engineering · May 2016
Question 5 of 7: Capillary Pressure — Water-Oil Contact and Transition-Zone Thickness
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
98-Pet-A3 — Fundamental Reservoir Engineering · National Exams, May 2016 · 3 hours, closed book, non-communicating calculator only · five (5) questions constitute a complete exam paper (the first five as they appear in the answer book are marked), all questions equal value, all parts of a multipart question equal weight.
Reference texts: Ahmed, T., Reservoir Engineering Handbook, 5th ed. (Darcy's law, transient well testing and image wells, p/Z and oil material balance, capillary pressure/relative permeability); Craft, B.C. & Hawkins, M.F., Applied Petroleum Reservoir Engineering, 3rd ed. (steady-state radial flow, reservoir drive mechanisms); Lyons, W.C. (ed.), Standard Handbook of Petroleum and Natural Gas Engineering, 3rd ed.; McCain, W.D., The Properties of Petroleum Fluids, 3rd ed. (capillary pressure and relative permeability laboratory data).
$P_c\approx58$ psi at $S_w=0.30$ (top of near-vertical rise)
Capillary curve, $S_w\to1$ asymptote
$P_c\approx14$ psi
Find. (a) Depth of the water-oil contact (WOC); (b) thickness of the transition zone.
Fig. 2 — Capillary pressure vs. water saturation. The curve rises sharply from $S_w=0.30$ (entry pressure, top of the oil zone) and flattens toward $\approx14$ psi as $S_w\to1$ (practical 100%-water level, the WOC) — it never reaches $P_c=0$, which defines the deeper FWL.
Approach. Convert capillary pressure to height above the FWL via the buoyancy relation $h=144P_c/(\rho_w-\rho_o)$. The WOC is the depth at which the curve's own data first read $S_w\approx1$ (its low-$P_c$ asymptote, not $P_c=0$); the top of the transition zone is the depth at which $S_w$ first reaches its irreducible value (the curve's near-vertical entry/threshold point). The transition-zone thickness is the height difference between those two levels.
Height-pressure conversion factor. $h=\dfrac{144P_c}{\rho_w-\rho_o}=\dfrac{144P_c}{65-50}=9.6\,P_c$ ft above the FWL.
WOC (practical 100%-water level). The curve flattens to $P_c\approx14$ psi as $S_w\to1$, so $h_{\text{WOC}}=9.6(14)=134.4$ ft above the FWL: $\boxed{\text{WOC}=6000-134.4=5865.6\ \text{ft}}$.
Top of the transition zone (irreducible water saturation reached). The curve's near-vertical rise begins at the entry pressure $P_c\approx58$ psi ($S_w=0.30$, effectively the irreducible saturation for this rock): $h_{\text{top}}=9.6(58)=556.8$ ft above the FWL, at a depth of $6000-556.8=5443.2$ ft.
Transition-zone thickness. The zone spans from the WOC down to where irreducible saturation is reached: $\boxed{\Delta h=h_{\text{top}}-h_{\text{WOC}}=556.8-134.4=422.4\ \text{ft}}$ (equivalently $9.6\times(58-14)$).
Quantity
Value
Height/pressure factor, $144/(\rho_w-\rho_o)$
9.6 ft/psi
(a) WOC depth
5865.6 ft
Top-of-transition-zone depth
5443.2 ft
(b) Transition-zone thickness
422.4 ft
Check: the source supplies the capillary-pressure curve graphically with axes 0–1 ($S_w$) and 0–70 psi ($P_c$); the entry pressure ($\approx58$ psi at $S_w=0.30$, top of the near-vertical rise) and the high-$S_w$ asymptote ($\approx14$ psi) were read directly off the printed chart, the only two features the curve's own shape calls out numerically.
