Page 84 - Fundamentals of Reservoir Engineering

SOME BASIC CONCEPTS IN RESERVOIR ENGINEERING 23

the derivative of which, with respect to pressure, is

∂ V =− ZnRT 1 − 1 ∂ Z

∂ p p p Z ∂ p

and substituting these two expressions in the isothermal compressibility definition,
equ. (1.11), gives

1 ∂ V 1 1 ∂ Z
c =− = − (1.31)
g
V ∂ p p Z ∂ p
In fig. 1.9, a plot of the gas compressibility defined by equ. (1.31) is compared to the
approximate expression.

1
c = (1.32)
g
p
for the 0.85 gravity gas whose isothermal Z−factor is plotted in fig. 1.8 at 200°F. As can
be seen, the approximation, equ. (1.32), is valid in the intermediate pressure range
between 2000−2750 psia where ∂Z/∂p is small but is less acceptable at very high or
low pressures.

EXERCISE 1.1 GAS PRESSURE GRADIENT IN THE RESERVOIR

1) Calculate the density of the gas, at standard conditions, whose composition is
listed in table 1.1.
2) what is the gas pressure gradient in the reservoir at 2000 psia and 180° F
(Z = 0.865).

EXERCISE 1.1 SOLUTION

1) The molecular weight of the gas can be calculated as

M = nM = 19.91
i
i
i
and therefore, using equ. (1.28) the gravity is