24-Pet-A3 Fundamental Reservoir Engineering · December 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
98-Pet-A3 — Fundamental Reservoir Engineering · National Exams, December 2015 · 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. All seven questions are solved below for completeness.
Reference texts: Ahmed, T., Reservoir Engineering Handbook, 5th ed. (Darcy's law and relative permeability, transient well testing, p/Z and oil material balance, capillary pressure); Craft, B.C. & Hawkins, M.F., Applied Petroleum Reservoir Engineering, 3rd ed. (reservoir drive mechanisms, pseudo-steady-state inflow); Lyons, W.C. (ed.), Standard Handbook of Petroleum and Natural Gas Engineering, 3rd ed. (Standing–Katz Z-factor correlation, Dranchuk–Abu-Kassem fit); McCain, W.D., The Properties of Petroleum Fluids, 3rd ed. (capillary pressure and relative permeability laboratory data).
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) Original oil in place. The stock-tank oil originally in the reservoir before any production, $N=\dfrac{7758\,A\,h\,\phi\,(1-S_{wi})}{B_{oi}}$ STB, computed volumetrically from the areal extent $A$ (acres), net pay $h$ (ft), porosity $\phi$, connate water saturation $S_{wi}$ and initial oil formation volume factor $B_{oi}$.
b) Residual oil saturation. $S_{or}$ is the oil saturation left trapped and immobile in the pore space after a displacing phase (water or gas) has swept through as far as capillary and viscous forces allow; oil at $S_{or}$ cannot be recovered by that displacement mechanism alone.
c) Oil formation volume factor. $B_o=V_{\text{oil+gas in soln, reservoir}}/V_{\text{stock tank}}$, bbl/STB — the ratio of reservoir-condition oil volume (including dissolved gas) to the stock-tank volume of that same oil after surface separation; it captures both thermal expansion and shrinkage on releasing solution gas.
d) Water influx. $W_e$ is the volume of water that moves from an attached aquifer into the hydrocarbon reservoir as reservoir pressure declines from production, supplying pressure support and volumetrically replacing produced fluid in a water-drive reservoir.
e) Gas cap drive. A displacement mechanism in which an existing free gas cap expands as reservoir pressure falls under oil production, supplying pressure support and displacing oil down-structure toward the wells; its strength is set by the gas-cap-to-oil-zone size ratio $m$.
f) Pseudo-steady-state. The flow regime reached in a bounded (no-flow-boundary) reservoir once the transient pressure disturbance has reached every drainage boundary; thereafter the pressure at every point — including the boundary and the average reservoir pressure $\bar p$ — declines at the same constant rate, $\partial p/\partial t=\text{const}$, while the pressure profile shape stays fixed.
g) Skin factor. A dimensionless factor $s$ representing the extra (or reduced) pressure drop concentrated right at the wellbore from near-wellbore permeability alteration (formation damage, $s>0$; stimulation, $s<0$) beyond what the undamaged radial-flow solution predicts: $\Delta p_{\text{skin}}=\dfrac{141.2\,q\,\mu\,B}{kh}\,s$.
h) Fractional flow curve. A plot of the water cut $f_w=q_w/(q_w+q_o)$ against water saturation $S_w$, built from the relative-permeability ratio $k_{ro}/k_{rw}$ and the fluid viscosities/densities; it feeds the Buckley–Leverett/Welge construction used to predict frontal advance rate and breakthrough behaviour in a waterflood.
i) Effective permeability. The permeability of the rock to one phase (e.g. $k_o$, $k_w$) when more than one fluid phase occupies the pore space; always $\le$ the single-phase absolute permeability $k$ because the other phase(s) block part of the flow paths, and it is a function of saturation.
j) Breakthrough time. The elapsed time (or produced pore volumes) from the start of injection until the displacing fluid (e.g. water in a waterflood) first arrives at the producing well; after breakthrough the produced stream contains both phases and water cut rises.
