Page 281 - Fundamentals of Reservoir Engineering

OILWELL TESTING 218

does not necessarily mean that flow should be under semi-steady state conditions at
this final rate. The condition is usually satisfied since the reliable analysis of a multi-
rate test, as already noted, requires that the total test duration should be brief so that
transient analysis can be applied.

As a demonstration of the effectiveness of this analysis technique, a test has been
simulated in a well for which the following data are applicable
Area drained 650 acres

h = 50ft

geometry r e ≈3000 ft r w = .3 ft

B o = 1.2 rb/stb
-6
k = 20 mD c = 15 × 10 / psi
φ =.23 µ =1 cp

p i = 3500 psia S = 2.0

Prior to the test the well had been producing for one year at 1000 stb/d and for a
second year at 400 stb at which time a multi-rate test was conducted as detailed in
table 7.15. The bottom hole flowing pressure prior to the test was p wf N = 2085 psi.

Rate Cumulative time Flowing
stb/d hrs pressure
psia

600 4 1815
800 8 1533
1000 12 1244
1200 16 950
TABLE 7.15

For the above conditions the relationship between dimensionless and real time is
-5
t DA = 5.41 × 10 t (hours) and therefore, after the total test period of 16 hours
-4
t DA = 8.65 × 10 . This means that transient analysis can be safely applied to the test
since, for a well at the centre of a circle, transient conditions prevail until t DA ≈ 0.1.

The test data in table 7.15 are analysed using the plotting technique of equ. (7.76), with
the p D functions evaluated as

4t 4A
p D () = 1 2 ln D = 1 2 t DA + 1 2 ln (7.23)
t
D
γ r γ w 2
The analysis is detailed in table 7.16, and the resulting plot shown as fig. 7.30.