Page 499 - Petrophysics

TURBULENT FLOW OF GAS 467

Then, separating the variables and integrating between rw and re, where
the pressures are pw and Pe, respectively:

(7.134)

or:

2 = Qiln? + 42 (k - i)
PZ - Pw
2 r2

Substituting Q1 and 42, and assuming rw << re yields:

(7.135)

If Equation 7.135 is expressed in field units and qm is set equal to
qsc PscM/T,,R, one finds:

2 2 1,422pgzTln (re/r2) 3.161 x 10-12zTygP
Pe -Pw = 4sc + GC (7.136)
kh rwh2
where q,, is expressed in MSCF/D. After some algebraic manipulation,
Equation 7.136 can be written as:

(7.137)

If D is the non-Darcy flow coefficient:

D=( 2.22 x 10-15yg)Pk
(7.138)
CLgrwh
Equation 7.137 becomes:

(7.139)

or, in a more familiar form:

qsc = (7.140)
1 ,422pgZT
Equation 7.140 is similar to Equation 7.103 for the bounded reservoir
case, Le., f= 1 and no skin damage. Again, if the pressure at the outer