24-Pet-A2 Petroleum Reservoir Fluids · December 2016
Question 7 of 7: Black-Oil PVT — Bubble Point, Total FVF, Compressibility, Volume Change
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
98-Pet-A2 — Petroleum Reservoir Fluids · National Exams, December 2016 · 3 hours, closed book, non-communicating calculator only · first five questions 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. (Ch. 1–2, PVT properties, reservoir/well-stream classification, material balance); Lyons, W.C. (ed.), Standard Handbook of Petroleum and Natural Gas Engineering, 3rd ed. (Standing–Katz Z-factor correlation, gas properties); McCain, W.D., The Properties of Petroleum Fluids, 3rd ed. (phase behaviour, black-oil PVT laboratory data); Ahmed, T., Reservoir Engineering Handbook, 5th ed. (reservoir fluid classification, material balance, well-stream gravity); Danesh, A., PVT and Phase Behaviour of Petroleum Reservoir Fluids (equilibrium K-value flash calculations).
Question 7: Black-Oil PVT — Bubble Point, Total FVF, Compressibility, Volume Change (20 marks)
Check: the paper supplies this data only as two printed charts (solution GOR $R_s$ vs. $p$, and oil FVF $B_o$ vs. $p$; no data table). The values below were read from the two charts against their gridlines (300 psia by 200 SCF/STB, and 300 psia by 0.024 bbl/STB; about ±10 SCF/STB and ±0.005 bbl/STB) rather than from an exact table, so treat all Q7 numeric results as chart-reading estimates, consistent with the "estimate" language the exam itself uses for the analogous Question 3 diagram.
Given. $T=225\,{}^{\circ}\text{F}=684.67\,{}^{\circ}\text{R}$ (constant, laboratory/reservoir temperature); $Z=0.95$ at 1000 psia (given). Digitized from the $R_s$–$p$ and $B_o$–$p$ charts: $R_s$ rises roughly linearly from near zero at low pressure to a plateau of $\approx640$ SCF/STB by $\approx$2700 psia and stays flat to 4500 psia (the plateau marks the bubble point); correspondingly $B_o$ rises to a peak of $\approx1.41$ bbl/STB at the same $\approx$2700 psia, then decreases above it (ordinary liquid compression) to $\approx1.345$ bbl/STB by 4500 psia. Reading further points: $R_s(1000\text{ psia})\approx240$ SCF/STB, $B_o(1000\text{ psia})\approx1.20$ bbl/STB, $B_o(3000\text{ psia})\approx1.40$ bbl/STB. Formula sheet: $B_t=B_o+B_g(R_{sob}-R_{so})$; $c_o=-\dfrac{1}{B_{ob}}\left(\dfrac{dB_o}{dP}\right)_T$; $B_g=0.02827\,ZT/p$ (ft$^3$/SCF); 1 bbl $=5.6146$ ft$^3$.
Find. (a) $p_b$; (b) $B_t$ at 1000 psia; (c) $c_o$ above $p_b$; (d) change in oil volume, 4500→3000 psia.
Approach. Identify $p_b$ as the pressure where the rising $R_s$ curve flattens and the rising $B_o$ curve peaks (below $p_b$ free gas is present and both vary with pressure; above $p_b$ the oil is undersaturated, $R_s$ is pinned at $R_{sb}$, and $B_o$ falls with increasing pressure from ordinary liquid compression). Below $p_b$, add the liberated-gas volume via $B_g(R_{sob}-R_{so})$ (converted to bbl/SCF) to get $B_t$; above $p_b$, estimate compressibility from the slope of $B_o$ vs. $p$, and get the volume change directly from the two $B_o$ values since both endpoints of part (d) sit above $p_b$.
Part (a) — bubble point. The digitized $R_s$ curve rises steadily up to $\approx$2700 psia, where it plateaus at $R_{sb}\approx640$ SCF/STB and stays flat through 4500 psia — the classic saturated/undersaturated break (no more gas can go into solution once the oil is saturated). The $B_o$ curve peaks at the same pressure ($B_{ob}\approx1.41$ bbl/STB at $\approx$2700 psia) and falls above it, confirming the same break point from the other chart. So $\boxed{p_b\approx2700\ \text{psia}}$.
Part (b) — $B_t$ at 1000 psia. 1000 psia $<p_b$, so the oil is saturated: $R_s(1000)\approx240$ SCF/STB $<R_{sb}=640$ SCF/STB, and free gas is present. $B_g(1000)=0.02827\dfrac{ZT}{p}=0.02827\times\dfrac{(0.95)(684.67)}{1000}=0.02827\times0.6504=0.018388\ \text{ft}^3/\text{SCF}$, i.e. $0.018388/5.6146=0.003275\ \text{bbl/SCF}$. Then $B_t=B_o+B_g(R_{sob}-R_{so})=1.20+0.003275\times(640-240)=1.20+0.003275\times400=1.20+1.310$. So $\boxed{B_t(1000)\approx2.51\ \text{bbl/STB}}$.
Part (c) — compressibility above the bubble point. Using the two undersaturated chart points that bracket the whole above-$p_b$ range, $B_o(p_b)=B_{ob}=1.41$ bbl/STB at 2700 psia and $B_o(4500)\approx1.345$ bbl/STB: $\left(\dfrac{dB_o}{dP}\right)_T\approx\dfrac{1.345-1.41}{4500-2700}=\dfrac{-0.065}{1800}=-3.611\times10^{-5}\ \text{bbl/STB per psi}$. With the formula sheet's $1/B_{ob}$: $c_o=-\dfrac{1}{1.41}\times(-3.611\times10^{-5})$, giving $\boxed{c_o\approx2.56\times10^{-5}\ \text{psi}^{-1}}$ (about 26 microsips), a typical undersaturated black-oil value.
Part (d) — volume change, 4500 → 3000 psia. Both 4500 and 3000 psia lie above $p_b\,(\approx2700)$, so the oil stays single-phase (no free gas evolves) across this whole interval — only ordinary liquid expansion as pressure falls. Per stock-tank barrel, reservoir volume at 4500 psia is $B_o(4500)\approx1.345$ bbl and at 3000 psia is $B_o(3000)\approx1.40$ bbl. $\Delta V=B_o(3000)-B_o(4500)=1.40-1.345=\boxed{+0.055\ \text{bbl/STB (a 4.1\% increase)}}$ — the reservoir oil volume grows as pressure drops from 4500 to 3000 psia, exactly the undersaturated-liquid-expansion behaviour that the compressibility in part (c) quantifies.
