Page 328 - Fundamentals of Reservoir Engineering

REAL GAS FLOW: GAS WELL TESTING 263

The most popular current method of analysing such a test is to use the semi-steady
state inflow equation, (8.38), which, including both skin factor components and
assuming that for an initial test p = p i, becomes

1422QT 4A
() mp
mp − ( wf ) = 1 2 ln + S + FQ 2 (8.43)
i
kh γ C r 2
Aw
which can be further simplified as

mp i (p wf ) = BQ FQ 2 (8.44)
() m−
+
where B is the Darcy coefficient and F the non-Darcy coefficient of the inflow equation.
The purpose of testing is then to determine B and F and to use these values for
predicting the future deliverability of the well, for which p i is replaced by the current
average pressure p. The method of analysis is simply to plot

mp i ( wf n )
() m p−
Q n versus Q n (8.45)

in which the Q n are the surface production rates and p wf the values of the bottom hole
flowing pressure recorded at the end of each separate flow period. The plot should be
linear with slope F and intercept B, when Q n = 0; an example of such a plot is shown as
fig. 8.9.

This method of analysis is simple and the results obtained in terms of B and F are
considered more reliable parameters for estimating well deliverabilities than the
C and n determined using equ. (8.42).

Nevertheless, the application of the stabilized well inflow equation (8.43), to analyse a
well test is mathematically incorrect and the results obtained from such an analysis can
only be considered as an approximation, although, as will be demonstrated in
exercise 8.1, a perfectly acceptable approximation in many cases. The fault lies in
analysing the test data using an inflow equation rather than the superposed constant
terminal rate solutions, equ. (8.39). It may well be that each flow period in the test is
sufficiently long so that semi-steady state conditions prevail but that does not mean
that, for instance, the wellbore pressure response during the third flow period is
unaffected by what happened during the first and second periods, as implied by the
use of equ. (8.43) in the analysis.

The rigorously correct technique is to use equ. (8.39) in which the m D functions,
equ. (8.40), are evaluated for semi-steady state flow as

4A
m D ( DA ) = 1 2 ln + 2 π t′ DA (8.33)
t′
γ Cr 2
Aw
The test analysis equation is then