Page 275 - Introduction to Petroleum Engineering

262 PRODUCTION PERFORMANCE
A gas reservoir does not include an original oil phase, so N = 0 and N = 0. Substituting
p
N = 0 and N = 0 into Equation 13.20 gives
p
B B BS B B GB
GB gc gi G gi wig tw twi g gi cp
gi f
B gi 1 S wig B twi 1 S wig (13.21)
GB GB W W WB
pc gc i g e i p w

We simplify Equation 13.21 further by recognizing that water compressibility and
formation compressibility are relatively small compared to gas compressibility.
Neglecting water and formation compressibility terms gives

GB B G B G B W W W B (13.22)
g gi p g i g e i p w
The subscript c denoting gas cap has been dropped since there is no oil in the
reservoir.

13.5.1 Depletion Drive gas Reservoir
An important but relatively simple application of gas reservoir material balance is
the analysis of production from a gas reservoir containing only gas and irreducible
water. If we produce the gas reservoir without injection, the water influx, injection,
and production terms are zero, formation compressibility is negligible, and there is
no gas injection. The resulting material balance equation for the depletion drive gas
reservoir is

GB B G B (13.23)
g gi p g
where G is original free gas in place and G is cumulative free gas produced.
p
Substituting the real gas law into gas FVF and rearranging gives
/
pZ
G p 1 t G (13.24)
/
pZ i
where p is reservoir pressure and Z is the real gas compressibility factor. Subscript t
indicates that p/Z should be calculated at time t corresponding to G and subscript
p
i indicates that p/Z should be calculated at initial conditions. We can write Equation
13.24 in the form

p p p 1
G p (13.25)
Z t Z i Z i G
Equation 13.25 is a linear equation for (p/Z) when plotted versus G . The original gas
t
p
in place G is the value of G when (p/Z) is zero.
p t