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.
(a) Infinite-acting. Outer boundary condition: $\boxed{p\to p_i\ \text{as}\ r\to\infty}$ — equivalently $\partial p/\partial r\to0$ far from the well. This holds whenever the radius of investigation has not yet reached any real physical boundary; the reservoir "looks" infinite to the well because the transient simply hasn't found its edge yet. The pressure profile rises from a large drawdown at $r_w$ and asymptotically approaches $p_i$ at large $r$; as time goes on the point at which the curve rejoins $p_i$ keeps pushing outward (the radius of investigation grows as $\sqrt{t}$), but the profile near the well keeps the same log-shape.
(b) Pseudo-steady-state. Outer boundary condition: $\boxed{\left.\partial p/\partial r\right|_{r_e}=0}$ — no flow crosses a closed/sealed outer boundary (a fault block or a fully bounded reservoir with no aquifer support). Once the transient has fully felt this boundary, the SHAPE of the $p(r)$ profile becomes fixed (flattening to zero slope exactly at $r_e$), and from then on the entire curve simply translates downward at a uniform rate in time ($\partial p/\partial t$ the same at every $r$) as the fixed fluid-in-place depletes.
(c) Steady-state. Outer boundary condition: $\boxed{p(r_e)=p_e=\text{constant}}$ — an active aquifer or gas cap (or pattern water injection) continuously resupplies the boundary and holds its pressure fixed. The profile rises smoothly and monotonically from $p_{wf}$ at $r_w$ to the fixed $p_e$ at $r_e$, and — unlike the other two cases — this shape is time-invariant: the same curve persists indefinitely once steady state is established, since energy lost to production is exactly replaced at the boundary.
