Page 91 - Introduction to Petroleum Engineering

PERMEABILITY 75
The units for Equation 4.15 are as follows:

Term Description Units

q o Flow rate STB/D
k Permeability Millidarcies (md)
h Thickness ft
p e Pressure at external boundary psi
p w Pressure in well (inside boundary) psi
μ o Viscosity Centipoise
B o Formation volume factor RB/STB
r w Well radius (inside boundary) ft
r Radius of external boundary ft
e

Switching from linear flow in Equation 4.12 to radial flow produced the constant
0.00708, which equals 2π × 0 001127. When pressure at the external boundary is
.
greater than well pressure, the flow rate is positive, corresponding to a producing well.
When p is greater than p , the flow rate is negative, corresponding to an injection well.
e
w
The external radius r is frequently called the drainage radius of the well. The flow rate
e
in Equation 4.15 is less sensitive to an error in the estimate of r than a similar error in a
e
parameter like permeability because the radial flow calculation depends on the logarithm
of r . It is therefore possible to tolerate larger errors in r than other flow parameters and
e
e
still obtain a reasonable value for radial flow rate. Usually, the drainage radius is equated
to the radius of a circle that has the same area as that based on well spacing. For example,
if there is one well centered on an area of 40 acres, the total area drained by that well in
=
×
2
.
6
square feet is (40acres )(43560ft /acre ) 17410 ft and the drainage radius is
2
×
π
2
r = (.17410 6 ft / ) / 12 = 745 ft. This estimate assumes that the well is centered in the
e
40‐acre area. Methods for noncentered wells are beyond the scope of this text.
4.2.4 Radial Flow of gases
Darcy’s law for radial flow of gases is complicated by changes in gas viscosity and gas
formation volume factor with pressure. To manage these complications, a new property
was developed called real gas pseudopressure, m(p). The details of real gas pseudopres-
sure are beyond the scope of this text, but in short, m(p) is a pressure‐weighted average of
gas viscosity and gas compressibility factor z, which is defined for real gases as follows:
pV
z = (4.16)
nRT
The compressibility factor z indicates departure from ideal gas behavior. For an ideal
gas, z equals unity. For real gases, z can be as low as about 0.3 and as high as 1.6. As
a result, Darcy’s law for radial flow of gases is as follows:
kh
q = 0 703   mp ( ) − ( )  (4.17)
mp
.
r r )
w
s
e
ln
T ( e / w
r