The bottomhole temperature of a hydrocarbon gas reservoir is 140°F. What will be the amount of water expansion, per unit volume, that will occur when the pressure is decreased from 4000 psi to 3270 psi. (Given, estimated compressibility of water at 4000 psi is 2.8 × 10–6 psi–1).
2.04 × 10–3
Water compressibility \(c_w\) is the fractional change in volume per unit change in pressure, \(c_w = -\dfrac{1}{V}\dfrac{\Delta V}{\Delta P}\). When reservoir pressure falls, the connate water expands, and the expansion per unit volume is simply the compressibility multiplied by the pressure drop.
Step 1 — Pressure drop: \(\Delta P = 4000 - 3270 = 730\ \text{psi}\).
Step 2 — Expansion per unit volume: \(\dfrac{\Delta V}{V} = c_w \Delta P = (2.8 \times 10^{-6})(730)\).
Step 3 — \(\dfrac{\Delta V}{V} = 2.044 \times 10^{-3}\) (reservoir barrels of expansion per reservoir barrel of water). The bottomhole temperature of 140°F only fixes the compressibility value that was supplied.
The values 4.02, 3.02 and 2.02 are about a thousand times too large; a fractional volume change of order unity would mean the water doubled its volume, which is impossible for a nearly incompressible liquid over a 730 psi drop.
2.04 × 10–3 option is correct.
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