Page 485 - Petrophysics

TURBULENT FLOW OF GAS 453

For gases, Katz et al. expressed Equation 7.108 in terms of the mass
flow rate, q,, because the mass flow rate is a constant when the
cross-sectional area, A, is constant, permitting integration of Forchheimer
equation [35]. Let

where p is the density of the fluid and q is the volumetric flow rate.
If the equation of state for real gases (Equation 7.96) is substituted in
Equation 7.109, the mass flow rate is:

qm = ($)vA (7.110)

Solving for v and substituting in Equation 7.108 gives:
----[,+P(F)] 2 (7.11 1)
ZRT Pgqm
dp
-
dL
pM
If the variables are separated and integration is carried out over the length
of the porous body, such as a core of length L and where the inlet and
outlet pressures are p1 and p2, respectively, one obtains:

(7.112)

The gas deviation factor Z is kept outside the integrand because it is
assumed to remain constant at the average pressure p , which is equal to
(p1 + p2)/2. The integration gives:

(7.113)

In practical oillield units, Equation 7.1 13 can be written as follows:

(7.114)

where yg is the specific gas gravity.
Cornell used Equation 7.113 to evaluate the permeability, k, and
non-Darcy factor, P for a large number of core samples from a variety of
rocks by dividing the left-hand side of Equation 7.1 13 by qm and plotting