Page 480 - Petrophysics

448 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

The steady- or pseudosteady-state solutions of this diffusivity equation
can be obtained using essentially the same mathematical procedure as
that used to solve Equation 7.54 for the flow of incompressible fluids.
Thus, Equation 7.77 is equivalent to:

wm(p) - m(pw)l
qsc = (7.93)
1,422T[ln (0.472re/rw) + 0.25f + s)]

where: qsc = gas flow rate at T,, = GOOF and psc = 14.7 psia, MSCF/D.
k = permeability, mD.
h = thickness of formation, ft.
T = absolute reservoir temperature, OR
re = drainage radius, ft.
r, = wellbore radius, ft.
f = drainage boundary index, dimensionless.
s = total skin factor, dimensionless.
m(pw), m(p) = real gas pseudo-pressure at the well pressure and the
average reservoir pressure, respectively, psi2/cP.

The real gas pseudopressure terms at any pressure, m(p), can be obtained
from published tables or by numerical integration (trapezoidal rule)
[26, 281. p also can be converted to m(p) by plotting the group 2p/pgz
vs. p on a Cartesian graph. This group is calculated for several values of
p using experimental values of pg and z. The area under the curve from
any convenient reference pressure, generally zero, to p is the value of
m(p) corresponding to p.
The m(p) approach is theoretically a better method than p and p2
approaches because it is valid for all pressure ranges, especially during
the unsteady-state flow regime when pg and z may vary considerably.
Inasmuch as only the radial flows of gas during the steady and pseudo-
steady states are considered, all the gas-flow equations in the remainder
of this chapter will be expressed in terms of the pressure-squared
approach, and ps and z will be assumed to remain constant at the average
reservoir pressure. Several approaches are available in the literature for
deriving radial gasflow equations during the steady-state flow regime
[27-291. By treating natural gas as a highly compressible fluid, radial flow
equations may be developed by combining Darcy’s law (assuming laminar
flow):

(7.94)