Page 247 - Fundamentals of Reservoir Engineering

OILWELL TESTING 185

7.2 (i.e. k = 240 mD, A = 35 acres, S = 4.5).

+
π
0.0189(3500 − p ) = 2 t DA + ½ In t DA + 8.632 − ½ p D(MBH) (t ) 4.5 (7.46)
wf
DA
in which
.000264 kt .000264 240 t (hrs)
×
×
t DA = =
-6
φµ cA .18 1 15 10 × 35 43560
×
×
××
t DA = 0.0154 t
For convenience, equ. (7.46) can be reduced to
0.0189 (3500 p ) = α − ½ p D(MBH) (t ) (7.47)
−
DA
wf
in which
α = 2t DA + ½ ln t DA + 13.132
π

and has the same value for all three geometries shown in fig. 7.16. Values of p wf in
equ. (7.47) can therefore be calculated by reading values of p D(MBH) (t DA) from the
appropriate MBH plots contained in figs. 7.11-15. The values of ½ p D(MBH) (t DA) and p wf
for all three geometries are listed in table 7.4 for the first 50 hours of the drawdown
test. Plots of ∆p wf, which is the difference between the calculated and observed bottom
hole flowing pressure, versus the flowing time, are shown in fig. 7.17. These plots tend
to confirm that the geological interpretation, fig. 7.16(b), is appropriate. For the other
two rectangular geometries the late transient flow period is not modelled correctly. For
comparison the plot has also been made for the case of a well draining from the centre
of circular bounded area, which is the simple case normally considered in the literature.
As can be seen, the value of ∆p wf after 50 hours, when semi-steady state conditions
prevail, is 44 psi for this latter case.