Volumetric Check and Water Influx by p/Z Gas Material Balance: 24-Pet-A3 Fundamental Reservoir Engineering, Undated paper, Q5

Question 5: Volumetric Check and Water Influx by p/Z Gas Material Balance (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.

Quantity	Value
Bulk reservoir volume, $V_b$	5,000 ac-ft
Porosity, $\phi$	0.18
Temperature, $T$	200°F (660°R)
Initial pressure, $p_i$ / $z_i$	5,000 psia / 0.95
Pressure / $z$ at second point	3,000 psia / 0.90
Estimated initial gas-in-place, $G$	7.5 MMM SCF ($7.5\times10^9$)
Estimated initial water saturation, $S_{wi}$	0.32
Cumulative gas produced, $G_p$ (at 3,000 psia)	3.52 MMM SCF ($3.52\times10^9$)
Water production	none ($W_p=0$)

Find. (1) Average water saturation at 3,000 psia; (2) the fraction of $G_p$ that is attributable to water influx rather than gas expansion.

Approach. Total reservoir pore volume ($V_b\phi$) is fixed; the gas-filled fraction of it shrinks both from pressure depletion (via $B_g$) and from water influx. Compute the gas-filled pore volume at 3,000 psia directly from $(G-G_p)B_g$, subtract from the fixed total pore volume to get the water volume and hence $S_w$; then use the gas MBE with water influx to isolate how much of $G_p$ is "extra" production caused by the shrinking gas space rather than pure gas expansion.

Gas formation volume factors. $B_g=0.02829\,zT/p$ ft³/SCF: $B_{gi}=0.02829(0.95)(660)/5{,}000=0.003548$ ft³/SCF; $B_g(3{,}000)=0.02829(0.90)(660)/3{,}000=0.005603$ ft³/SCF.
Total pore volume and water saturation at 3,000 psia. $V_b=5{,}000\ \text{ac-ft}\times43{,}560\ \text{ft}^3/\text{ac-ft}=2.178\times10^8$ ft³; total pore volume $=V_b\phi=0.18(2.178\times10^8)=3.9204\times10^7$ ft³ (constant — no rock/water compressibility given). Gas-filled volume at 3,000 psia: $(G-G_p)B_g=(7.5-3.52)\times10^9(0.005603)=2.230\times10^7$ ft³. Water volume there $=3.9204\times10^7-2.230\times10^7=1.690\times10^7$ ft³, so $\boxed{S_w(3{,}000\ \text{psia})=1.690\times10^7/3.9204\times10^7=0.431\approx43.1\%}$.
Water influx from the gas MBE. $G(B_g-B_{gi})+W_e=G_pB_g+W_pB_w\ \Rightarrow\ W_e=GB_{gi}-(G-G_p)B_g=7.5\times10^9(0.003548)-2.230\times10^7=2.661\times10^7-2.230\times10^7$, so $W_e=4.31\times10^6$ ft³.
Gas production attributable to water influx. Without any influx, the same pressure drop would require producing only $G_p'=G-\dfrac{GB_{gi}}{B_g(3{,}000)}=7.5\times10^9-\dfrac{2.661\times10^7}{0.005603}=2.751\times10^9$ SCF. The extra apparent production is $G_p-G_p'=W_e/B_g(3{,}000)=4.31\times10^6/0.005603$, so $\boxed{\Delta G_{p,\text{influx}}\approx0.77\ \text{MMM SCF},\ \text{about }21.9\%\text{ of the }3.52\ \text{MMM SCF total}}$.

Quantity	Value
(1) Average $S_w$ at 3,000 psia	0.431 (43.1%)
Water influx, $W_e$	$4.31\times10^6$ ft³
(2) Gas production from water influx	$\approx0.77$ MMM SCF ($\approx$21.9% of $G_p$)

Check: the given $z$-factor at 750 psia (0.95) is not needed for this two-point calculation (pressure only drops to 3,000 psia in the question asked) and is treated as reference data for a further depletion stage not required here.

Topic: $p/Z$ material balance for a gas reservoir with partial water-drive support, and back-calculating average reservoir water saturation from the shrinking gas-filled pore volume.

Key relations: $B_g=0.02829\,zT/p$; $G(B_g-B_{gi})+W_e=G_pB_g+W_pB_w$; total pore volume $=V_b\phi=$ (gas volume) + (water volume) when rock/water compressibility is negligible.

Why this works: in a purely volumetric gas reservoir the entire initial gas-filled pore space stays gas-filled and pressure alone tracks depletion via $p/Z$; once an aquifer connects, water physically invades and shrinks that space, so for the SAME pressure drop more gas must have been withdrawn than pure expansion would predict — the difference between the two predicted $G_p$ values isolates exactly how much of the observed production is "real" (expansion-driven) versus an artifact of losing reservoir volume to encroaching water.

Common pitfall: assuming a volumetric (no water influx) $p/Z$ straight line applies when an aquifer is present, which understates initial gas-in-place if fitted naively to pressure/production data without checking for encroachment; and forgetting that with $W_p=0$ all of $W_e$ stays in the reservoir, so it is recoverable directly from the pore-volume balance without needing a separate aquifer model.

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

Question 5 of 7: Volumetric Check and Water Influx by p/Z Gas Material Balance

Question 5: Volumetric Check and Water Influx by p/Z Gas Material Balance (20 marks)