Undersaturated Oil Material Balance — Cumulative Production to Bubble Point: 24-Pet-A3 Fundamental Reservoir Engineering, December 2015, Q6

Question 6: Undersaturated Oil Material Balance — Cumulative Production to Bubble Point (20 marks)

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.

Given. $N=10$ MMSTB (initial pressure 3000 psia); $\phi=0.165$; $c_f=2.5\times10^{-6}$ psi$^{-1}$; $c_w=2.91\times10^{-6}$ psi$^{-1}$; $T=150$°F; $B_o$/$R_s$ table above.

Find. The cumulative oil production $N_p$ when reservoir pressure drops to the bubble point pressure.

Check: $\phi$, $c_f$ and $c_w$ are given but the connate water saturation $S_{wi}$ needed to evaluate the rock/connate-water expansion term $(c_wS_{wi}+c_f)/(1-S_{wi})$ is not provided; since actual measured $B_o(p)$ data spans the full undersaturated interval, the tank-type balance below (which uses that $B_o$ data directly) already captures the oil-phase expansion empirically and does not need this correction term.

Approach. Identify the bubble point pressure from where $R_s$ first departs from its initial (constant, single-phase) value; above $p_b$ with no free gas and no water influx, the reservoir voidage from production is filled purely by oil expansion, $N B_{oi}=(N-N_p)B_o$.

Locate the bubble point. $R_s$ is unchanged (650 $\to$ 650 SCF/STB) from 3000 to 2500 psia — still undersaturated, no free gas — then drops to 618 SCF/STB at 2300 psia, so gas has begun evolving somewhere between 2500 and 2300 psia. $B_o$ also peaks at 2500 psia (1.325, higher than both neighbours), consistent with oil expansion up to $p_b$ followed by shrinkage as gas comes out of solution below it. $\boxed{p_b=2500\ \text{psia}}$.
Undersaturated tank balance. With $B_{oi}=1.315$ (at 3000 psia) and $B_o=1.325$ (at $p_b=2500$ psia): $N_p=N\left(1-\dfrac{B_{oi}}{B_o}\right)=N\dfrac{B_o-B_{oi}}{B_o}=10{,}000{,}000\times\dfrac{1.325-1.315}{1.325}=\boxed{75{,}472\ \text{STB}}$.

Quantity	Value
Bubble point pressure, $p_b$	2500 psia
Cumulative oil production to $p_b$, $N_p$	75,472 STB (0.75% of $N$)

Concept & Theory

Topic: Undersaturated (single-phase) oil material balance.

Key relations: Above $p_b$: $N_pB_o=N(B_o-B_{oi})+NB_{oi}\dfrac{c_wS_{wi}+c_f}{1-S_{wi}}\Delta p$; the oil-expansion term $N(B_o-B_{oi})$ usually dominates the (typically small) rock/connate-water term.

Why this works: $B_o$ measured directly from PVT data already reflects the true oil compressibility over the interval, so using the measured $B_o(p)$ values is more accurate than substituting a correlation-based oil compressibility; only the (here unevaluable, and comparatively minor) rock/water term is left out.

Common pitfall: Applying the two-phase (below-$p_b$) balance — which needs $R_s$, $B_g$ and $B_t$ — to a pressure step that is still above $p_b$, where $R_s$ has not yet changed and no free gas exists.

Source: Ahmed, Reservoir Engineering Handbook, 5th ed., Ch. 4 (undersaturated-reservoir material balance); Craft & Hawkins, Applied Petroleum Reservoir Engineering, 3rd ed., Ch. 3.

Question 6 of 7: Undersaturated Oil Material Balance — Cumulative Production to Bubble Point

Question 6: Undersaturated Oil Material Balance — Cumulative Production to Bubble Point (20 marks)