Page 95 - Fundamentals of Reservoir Engineering

SOME BASIC CONCEPTS IN RESERVOIR ENGINEERING 34

as much gas above as there is beneath, the pressures for use in the material
balance equation will always be evaluated at this depth.

To do this the water pressure at the gas−water contact must first be calculated as

p w = 0.441 × 9700 + 31 = 4309 psia = p g GWC

and the temperature as

9700
o
+
T = (1.258 × ) 80 + 460 = 662 R
100
for this 0.85 gravity gas the isothermal Z−factor plot at 200°F (660°R), fig. 1.8,
can be used to determine the Z−factor at the GWC, with negligible error. Thus

Z GWC = 0.888

p 35.37 × 4309
and E GWC = 35.37 = = 259.3
ZT 0.888 × 662

The pressure gradient in the gas, at the GWC, can now be calculated, as
described in exercise 1.1, as

dp ρ sc E 0.0763 0.85 259.3 0.117 psi/ ft
×
×
dD = 144 = 144 =
The gas pressure at the centroid is therefore

dp
p = p g − × ∆ D (1.45)
GWC
dD GWC

p = 4309 − 0.117 × (9700 − 9537) = 4290 psia

and the absolute temperature at the centroid is

9537 o
+
T = (1.258 × ) 80 + 460 = 660 R
100
One could improve on this estimate by re−evaluating the gas gradient at the
centroid, for p = 4290 psia and T = 660°R, and averaging this value with the
original value at the GWC to obtain a more reliable gas gradient to use in
'equ. (1.45). Gas gradients are generally so small, however, that this correction is
seldom necessary. The reader can verify that, in the present case, the correction
would only alter the centroid pressure by less than half of one psi.

For the centroid pressure and temperature of 4290 psia and 660°R, the GIIP can
be estimated as

GIIP = G = Vφ (1−S wc) E i (1.26)