Page 383 - Fundamentals of Reservoir Engineering

NATURAL WATER INFLUX 318

T W e = U n1 p W D (T D - t D ) W e
−
(years) ∆ j j (MMrb)
j0
=
1 6446 (120×4.88) 3.775
2 6446 (120×7.46 + 225×4.88) 12.848

3 6446 (120×9.10 + 225×7.46 + 196×4.88) 24.024
4 6446 (120×10.09 + 225×9.10 + 196×7.46 + 170×4.88) 35.775
5 6446 (120×10.83 + 225×10.09 + 196×9.10 + 170×7.46 47.276
+ 146×4.88)
6 6446 (120×11.27 + 225×10.83 + 196×10.09 + 170×9.10 58.035
+ 146×7.46 + 123×4.88)
7 6446 (120×11.52 + 225×11.27 + 196×10.83 + 170×10.09 67.778
+ 146×9.10 + 123×7.46 + 105×4.88)
8 6446 (120×11.69 + 225×11.52 + 196×11.27 + 170×10.83 76.259
+ 146×10.09 + 123×9.10 + 105×7.46 + 84×4.88)

9 6446 (120×11.81 + 225×11.69 + 196×11.52 + 170×11.27 83.398
+ 146×10.83 + 123×10.09 + 105×9.10 + 84×7.46
+ 64×4.88)

10 6446 (120×11.89 + 225×11.81 + 196×11.69 + 170×11.52 89.225
+ 146×11.27 + 123×10.83 + 105×10.09 + 84×9.10
+ 64×7.46 + 47×4.88)
TABLE 9.7

The corresponding values of W e/E o, required for the material balance calculations, are
listed in table 9.6 and plotted in fig. 9.15. As can be seen, in this case, all the points lie
on the straight line of unit slope which intercepts the ordinate at N p = 312 MMstb, thus
confirming that r eD = 5 is the correct value of the ratio of the aquifer/reservoir radius.

Also apparent from this plot is the fact that after the third year there occurs a reversal in
the trend of plotted points with both W e/ E o and F/E o decreasing with time. Havlena and
4,5
Odeh have pointed out that this reversal is to be expected for a finite acting aquifer
but nevertheless all points, for the correct value of r eD, must lie on the linear trend. For
the incorrect aquifer model (r eD = 10), however, the calculated values of W e/E o
continually increase as F/E o decrease, as illustrated in fig. 9.15.