Page 325 - Fundamentals of Reservoir Engineering

REAL GAS FLOW: GAS WELL TESTING 260

was found to correlate almost exactly with the equivalent function for liquid flow for all
values of the flowing time. This is to be expected since the, µc product is not present in
equ. (8.38) as a result of the use of pseudo pressures, rather than pressures, in its
formulation. The correlations between m D and p D functions were only checked for a well
producing at the centre of a circular shaped reservoir, equs. (8.35) and (8.38) are
generalized expressions which include the dependence of m D on geometry and well
asymmetry.

In practice, one is interested in applying the constant terminal rate solution
(m D function) to the analysis of well tests and several examples of such usage are
provided in the following sections of this chapter. All the examples considered are for

initial well tests and, for this condition, the evaluation of the m D function using the (µc) i
product can be expected to be quite reliable, particularly if the test duration is not
excessively long and the pressure drawdowns imposed are not too large. Problems
arise, however, when analysing routine pressure surveys throughout the producing
lifetime of the reservoir. For instance, if a pressure test is conducted in a well several
years after the start of production, at what pressure should the µc product be
evaluated? This question will be dealt with in sec. 8.11 using the method presented by
10
Kazemi , which describes how the average reservoir pressure can be obtained from a
pressure analysis using a µc product which must be iteratively determined. Once the
average reservoir pressure is known, however, the inflow equation (8.38) can be used
with confidence to calculate the long term deliverability of wells.

8.9 GENERAL THEORY OF GAS WELL TESTING

Gas well tests can be interpreted using the following equations

kh ( mp m n Q m t t ) Q S′ (8.39)
=
i
1422T () − (p wf n ) ) ∆ j D ( D n − D j 1 + n n
−
j1
=
in which

m D ( D − t D ) = m D () = 2 t π ′ DA + 1 2 ln 4t′ D − 1 2 m DMBH ( DA )
t
t′
t′
D
n
j 1
−
γ ( )
∆ Q = Q − Q j 1 (8.40)
j
j
−
and
S′ = S DQ n
+
n
For convenience, equ. (8.39) is frequently expressed in the form
kh ( () m p 2 n Q m t t ) Q S (8.41)
(
=
−
i
1422T mp − wf n ) FQ n ) ∆ j D ( D n − D j 1 + n
−
j1
=
in which F is the non-Darcy flow coefficient, equ. (8.27).
These equations are analogous to equs. (7.31) and (7.42) which were used for oilwell
test analysis. Equation (8.39) results from the application of the principle of
superposition in time, as described in Chapter 7, sec. 5. In the summation of the