24-Pet-A3 Fundamental Reservoir Engineering · December 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
98-Pet-A3 — Fundamental Reservoir Engineering · National Exams, December 2017 · 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: Craft, B.C. & Hawkins, M.F., Applied Petroleum Reservoir Engineering, 3rd ed. (material balance, well testing, relative permeability, Buckley-Leverett displacement, flow regimes); Ahmed, T., Reservoir Engineering Handbook, 5th ed. (material balance, transient well testing, immiscible displacement, rock/fluid properties); 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).
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.
For a water-wet rock, water preferentially coats the grain surfaces as a film and occupies the smallest pores and pore corners, while oil (the non-wetting phase) is pushed toward the centre of the larger pores and throats — the main interconnected flow conduits of the rock. This asymmetric pore occupancy is what gives the two curves in Fig. 5 their very different shapes.
Effect of the non-wetting phase on $k_{rw}$. Because oil invades the LARGEST pore throats first as soon as any oil saturation is present, even a small oil saturation blocks a disproportionate share of the rock's major flow paths for water. $k_{rw}$ therefore starts at exactly zero at $S_{wc}$ and rises only slowly at first — the curve is concave-up, climbing steeply only once $S_w$ is well above $S_{wc}$ and water has reconnected enough of the pore network to flow efficiently again.
Effect of the wetting phase on $k_{ro}$. Water, by contrast, first occupies the smallest pores and thin grain-surface films — locations that contribute little to bulk flow in any case — so a modest initial water saturation removes relatively little of oil's flow capacity, and $k_{ro}$ falls off comparatively gently just below $1-S_{or}$. But as $S_w$ continues to rise toward $1-S_{or}$, oil is increasingly pinched into disconnected, isolated globules (snapped off at pore throats) and $k_{ro}$ falls steeply to zero. The key asymmetry is therefore: a given saturation of the NON-wetting phase reduces the wetting phase's permeability more severely (at low saturations) than an equal saturation of the wetting phase reduces the non-wetting phase's permeability, because the non-wetting phase preferentially occupies the pore system's major conduits while the wetting phase occupies pore space that was contributing little to flow anyway.
Imbibition vs. drainage. Drainage is the process by which the NON-wetting phase displaces the wetting phase — e.g. oil migrating into an originally water-saturated trap, with $S_w$ falling from 1 toward $S_{wc}$ as oil invades progressively smaller pore throats as capillary pressure rises. Imbibition is the reverse: the WETTING phase re-invades and displaces the non-wetting phase — e.g. a waterflood, with $S_w$ rising from $S_{wc}$ toward $1-S_{or}$. Because water re-enters along the smallest throats and film paths first, oil retreating ahead of it becomes disconnected and trapped as isolated globules (snap-off) in the larger pores it can no longer efficiently vacate, which is why $S_{or}$ after imbibition is never zero. This asymmetry between the two processes is called capillary/relative-permeability hysteresis, and it is why laboratory curves and correlations are always reported as either a drainage curve or an imbibition curve — never one universal curve for both.
