Page 358 - Fundamentals of Reservoir Engineering

REAL GAS FLOW: GAS WELL TESTING 293

where t DA = 0.000264kt /φµcA (field units), and β D(MBH)(t DA) is the ordinate of the MBH
charts, corresponding to the value of t DA, and includes allowance for the geometry of
the drainage area and the degree of well asymmetry with respect to the boundary.

Well test analysis techniques presented in the literature invariably require the
superposition of transient constant terminal rate solutions of equ. (8.67) which, in
comparison with equ. (8.70), have the form

4t′
β D (t D − t D ) = β D (t ) ′ = 1 2 ln D (8.71)
D
j 1
n
−
γ
Superposition of such solutions, however, automatically assumes the infinite boundary
condition and is therefore only appropriate for tests of short duration, whereas
superposition of the total solution, equ. (8.70), is theoretically correct for any value of
the flowing time and for any boundary condition.

Examples in this and the previous chapter (exercises 7.8 and 8.2), have shown that the
ad-hoc assumption of transient flow can be particularly dangerous in the interpretation
of multi-rate flow tests. Furthermore, conventional multi-rate test analysis techniques
do not permit the attempted matching of the drainage boundary, even using the correct
β D function, equ. (8.70), in the superposed test analysis equation, (8.69), as illustrated
in exercise 7.8. Multi-rate tests should only be planned when the engineer is quite
confident that transient conditions apply for the duration of the entire test, which is
difficult to ascertain in advance of the test itself.

In this author's opinion, the safest and most useful type of test, for any fluid system, is
the pressure buildup. Definition of a linear trend, for small values of the closed in time
on a Horner buildup plot, can lead to the unambiguous determination of the effective
permeability and the skin factor. Use of this early linear trend, in fact, imposes
transience on the buildup analysis. In addition, the test can be interpreted to determine
the average pressure within the drainage boundary of the well and also to gain some
impression of the shape, area and well position within the boundary, as illustrated in
exercise 7.7.

It must be admitted that the use of equ. (8.70) instead of equ. (8.71), in the basic well
test equation, (8.69), only serves to complicate well test analysis. Nevertheless, in
using the correct solution one is simply recognising the basic fact that second order
differential equations require the specification of both initial and boundary conditions to
obtain meaningful solutions.

As illustrated in the various exercises, it is not difficult to evaluate equ. (8.70) for use in
test analysis. These days when engineers have access to computers or, at least,
sophisticated electronic desk calculators, the evaluation is much less tedious than in
the past.

For instance, a perfectly general program for evaluating pressure buildup tests, for any
fluid, could be structured as shown in fig. 8.18.