Page 279 - Fundamentals of Reservoir Engineering

OILWELL TESTING 216

5
multi-rate test in a gas well presented in the original Odeh-Jones paper for a well
positioned at the centre of a circular shaped area of radius 3000 ft (A ≈ 650 acres) and
-5
for which the permeability is 19.2 mD. In the example t DA = 9.2×10 , and for the
geometry considered, transient analysis can be applied for a total of 1086 hours. It is in
cases where reservoirs are not continuous and homogeneous over large areas but
splintered into separate reservoir blocks on account of faulting that errors can occur in
assuming the infinite reservoir case is applicable in the test analysis.

One further, complication arises in connection with this type of analysis, and that is,
that in order to apply the correct technique, using the general p D function, equ. (7.42),
requires a knowledge of the permeability in order to calculate t D or t DA. In buildup
analysis this presents no problem since k can be readily calculated from the slope of
the linear section of the buildup plot. In multi-rate testing, however, this can prove more
difficult. Sometimes it is possible to separately analyse the initial flow period by plotting
p wf versus log t and applying the transient analysis technique described in exercise 7.2.
Unfortunately, in high permeability reservoirs this is very difficult to apply in practice,
since the pressure fall-off is initially very rapid. Under these circumstances it may be
necessary, and indeed is always advisable, to conduct a buildup at the end of the flow
test which tends to defeat one of the main purposes of the multi-rate test, namely, to
avoid well closure.

It is commonly believed that multi-rate flow tests can only be analysed if the initial
equilibrium pressure within the drainage volume is known. This is an unnecessary
restriction which has tended to limit the application of this technique to initial well tests
for which p i can be readily determined. The following analysis shows that, with minor
modifications to the method presented so far, the multi-rate test can be analysed with
only a knowledge of the bottom hole pressure and surface production rate prior to the
survey.

Suppose that a well with the variable rate history shown in fig. 7.29 is to be tested by
flowing it at a series of different rates.

th
Prior to the test the well is produced at a constant rate q N during the N and final flow
period before the multi-rate test commences at time t N. Then, for any value of the total
time t n during the test, when the current rate is q n, the bottom hole flowing pressure p wf n
can be calculated as

kh n
t
7.08 10 − 3 ( i p wf ) = ∆ q p D ( D − t D ) + q S
×
p −
j
n
−
µ B o n j1 n j 1
=
in which p i is the initial pressure at t = 0 and the summation includes all the variable
rate history up to and including the test itself. This equation can be subdivided as