Page 251 - Fundamentals of Reservoir Engineering

OILWELL TESTING 188

In addition, the Earlougher paper describes a relatively simple method for generating
MBH functions for rectangular geometries other than those included in figs. 7.11-15
and for boundary conditions other than the no-flow condition which is assumed for the
MBH plots. MBH functions for a constant outer boundary pressure and for cases in
between pressure maintenance and volumetric depletion, corresponding to partial
11
water drive, can therefore be simulated. Ramey et al have also described the
simulation of well test analysis under water drive conditions. However, while the theory
exists to describe variable pressure conditions at the drainage boundary, the engineer
is still faced with the perennial problem of trying to determine exactly what outer
boundary condition he is trying to simulate.

To use the combination of equ. (7.31) and (7.42) to describe any form of oilwell test
appears at first sight to offer a simplified generalization of former analysis techniques,
yet, as will be shown in the remainder of this chapter and in Chapter 8, the approach
introduces certain difficulties. Providing the test is run under transient flow conditions
then the p D function, equ. (7.42), can be described by the simplified form

4t
p (t ) ½ ln D (7.23)
=
D
D
γ
in which there is no dependence upon the magnitude or shape of the drainage
boundary nor upon the degree of asymmetry of the well with respect to the boundary.
Therefore, if well tests are analysed using equ. (7.23) in conjunction with equ. (7.31),
the results of the test will only yield values of the permeability, k, (which is implicit in the
definition of t D) and the mechanical skin factor, S. As soon as the test extends for a
sufficient period of time so that either late transient or semi-steady state conditions
prevail then the effect of the boundary of the drainage area begins to influence the
constant terminal rate solution and the full p D function, equ. (7.42), must be used in the
test analysis. In this case the interpretation can become a great deal more complex
because new variables, namely, the area drained, shape and well asymmetry, are
introduced which are frequently additional unknowns. Exercise 7.5 illustrated how a
single rate drawdown test can be analysed to solve for these latter three parameters
using p D functions expressed by equ. (7.42), thus gaining additional information from
the test.

Largely due to the fact that test analysis becomes more complicated when tests are
run under conditions other than that of purely transient flow, the literature is permeated
with transient analysis techniques. This mathematical simplification does indeed
produce convenient analysis procedures but can, in some cases, lead to severe errors
in determining even the basic parameters k and S from a well test, particularly in the
case of multi-rate flow testing as will be illustrated in sec. 7.8. Fortunately, the pressure
buildup test, if it can be applied, leads to the unambiguous determination of k and S
and therefore this method will be described in considerable detail in sec. 7.7.