24-Pet-A3 Fundamental Reservoir Engineering · December 2018
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
17-Pet-A3 — Fundamental Reservoir Engineering · National Exams, December 2018 · 3 hours, closed book, approved Casio/Sharp 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: Craft, B.C. & Hawkins, M.F., Applied Petroleum Reservoir Engineering, 3rd ed. (material balance, well testing, relative permeability, Darcy flow); Ahmed, T., Reservoir Engineering Handbook, 5th ed. (material balance, transient well testing, gas PVT, decline-curve analysis); Lyons, W.C. (ed.), Standard Handbook of Petroleum and Natural Gas Engineering, 3rd ed.; McCain, W.D., The Properties of Petroleum Fluids, 3rd ed. (PVT properties, Z-factor correlations).
Given. Free water level (FWL, where $P_c=0$) at depth 6000 ft; $\rho_w=65$, $\rho_o=50\ \text{lb}_{\text{mass}}/\text{ft}^3$; $P_c$ vs. $S_w$ curve (reproduced below) that flattens to a nonzero asymptote $P_c\approx18$ psi as $S_w\to1$ and rises steeply to $P_c\approx70$ psi near $S_w\approx0.25$.
Find. (a) depth of the water-oil contact (WOC); (b) thickness of the transition zone.
Approach. The FWL is defined by $P_c=0$, but the curve's OWN data show $S_w$ does not reach 100% until $P_c$ reaches its flattened asymptote ($\approx18$ psi, not 0) — so the WOC sits above the FWL by the height equivalent to that residual capillary pressure. The top of the transition zone is where $S_w$ first reaches its practical irreducible value, read off the steep part of the curve. Convert each $P_c$ gap to a height with the formula sheet's $h=144P_c/(\rho_w-\rho_o)$.
Fig. 1: capillary-pressure curve with the WOC (100% $S_w$, $P_c\approx18$ psi) and the top of the transition zone (practical $S_{wirr}\approx0.25$, $P_c\approx70$ psi) marked.
Height from FWL up to the WOC. The curve flattens to $P_c\approx18$ psi as $S_w\to1$ rather than dropping to zero, so 100% water saturation is reached at $P_c=18$ psi, not at the FWL. $h=\dfrac{144P_c}{\rho_w-\rho_o}=\dfrac{144(18)}{65-50}$, so $\boxed{h_{\text{FWL}\to\text{WOC}}=172.8\ \text{ft}}$.
(a) Depth of the water-oil contact. The WOC sits above (shallower than) the FWL by that height: $\text{depth}_{\text{WOC}}=6000-172.8$, so $\boxed{\text{depth}_{\text{WOC}}=5827.2\ \text{ft}}$.
(b) Transition-zone thickness. The transition zone spans from the WOC ($P_c\approx18$ psi) up to the depth where $S_w$ first reaches its practical irreducible value ($S_w\approx0.25$, where the curve turns steeply vertical, $P_c\approx70$ psi). $h_{\text{trans}}=\dfrac{144(P_{c,\text{top}}-P_{c,\text{WOC}})}{\rho_w-\rho_o}=\dfrac{144(70-18)}{15}$, so $\boxed{h_{\text{trans}}=499.2\ \text{ft}}$.
Check: the top-of-transition-zone reading ($S_w\approx0.25$, $P_c\approx70$ psi) is taken from the point where the printed curve turns near-vertical; a chart reading is inherently approximate.
