Page 340 - Fundamentals of Reservoir Engineering

REAL GAS FLOW: GAS WELL TESTING 275

that the high flow rates occur towards the end of the test. If the well had been tested
with a decreasing rate sequence, the degree of curvature would have been greater for
14
smaller values of the abscissa . The calculation of the left hand side of equ. (8.49) has
been repeated in table 8.6 for different values of F in an attempt to linearize the plot,
and from fig. 8.12 it can be seen that a value of F = .05 accomplishes this. For this
value, the plot has a slope of m = 491.5 and intercept 3993, from which the
permeability and skin factor can be calculated as

1637 T 1637 × 660
k = = = 44 mD
mh 491.5 × 50

intercept k

and S = 1.151 − log + 3.23 = 2.7
m ( ) c r 2
φµ i w
2) The Essis-Thomas analysis, which assumes transient flow conditions for the evaluation
of m D, equ. (8.32), will now be compared with the more general case in which m D is
calculated using equ. (8.40) for the 4:1 rectangular geometry. The general well test
equation (8.41) can be re-arranged as

m(p ) m(p wf n ) FQ 2 n 1422T n ∆ Q j 1422T
−
−
i
t
Q n = kh n m D ( D n − t D − j 1 ) + kh S (8.50)
j1 Q
=
in which m D is evaluated as
4A
′
m(t ) ′ = 2 π t′ + 1 2 ln t′ + 1 2 ln − 1 2 m D(MBH) (t ) (8.40)
DA
DA
DA
D
D
γ r w 2
or
′
m(t ) ′ = α − 1 2 m D(MBH) (t ) (8.51)
DA
D
D
Alternatively, adhering to the Essis-Thomas analysis expressed in terms of
dimensionless parameters
4t 4A
m (t ) ′ = 1 2 ln D = 1 2 ln t′ + 1 2 ln (8.32)
D
D
DA
γ r γ w 2
∆ Q j
A plot of the left hand side of equ. (8.50) versus m(t D − t D ) should be linear
D
Q n n j 1
−
with slope m = 1422 T/kh, and intercept = 1422 TS/kh, which will yield values of k and
S, respectively.
The first part of the analysis is to evaluate the m D functions, equs. (8.51) and (8.32), for
all values of the dimensionless time argument (t D n − t D j 1 ) required in the analysis.
−
These functions are listed in table 8.7, for k = 50 mD, the permeability value obtained
from the pressure buildup analysis, for which

.000264kt
t DA = = .0028 t
(c) A
φµ i