Page 453 - Petrophysics

LINEAR FLOW OF GAS 42 1

If one assumes the mean pressure p is equal to (p1 +p2)/2,
Equation 7.14a reduces to:

(PI
s = (E) - p2) (7.14b)
L
Equation 7.14b is the same as Equation 7.5, which gives the volumetric
flow rate of incompressible fluids. Therefore, the law for the linear flow
of ideal gas is the same as for a liquid, as long as the gas flow rate is
expressed as a function of the arithmetic pressure.
To include the effect of changes in the gas deviation factor, z, from
standard conditions of pressure, psc and temperature, p, to average
pressure, and temperature, T, let:

(7.15)

Combining Equations 7.14 and 7.15, and solving for qsc:

(7.16)

where qsc is in cm3/sec. Inasmuch as p = (PI + p2)/2, Equation 7.16
becomes:
qsc=(,>(A),(') kA PFP2 (7.17)
zscTsc

Converting from Darcy's units to practical field units and assuming
zsc = 1 at psc = 14.7 psia and T,, = GOOF or 520"R gives:

0.112kA
qsc = @P2) (7.18)
i!TpgL

where: qsc = volumetric flow rate at standard conditions, SCF/D.
k = permeability of the reservoir rock, mD.
pg = gas viscosity, CP
A = cross-sectional area, ft'.

T = mean temperature of the gas reservoir, OR
Z = mean gas deviation factor at T and p dimensionless.
L = length of the sand body, ft.
Ap2 = pf - p; psia2.