Page 396 - Fundamentals of Reservoir Engineering

NATURAL WATER INFLUX 331

1
− Insert this initial estimate of p n , which is admittedly too small, in the water influx
1
equation thus calculating a new value of W e , which will now be too large.
n
1
1
− Rework the material balance with this new value of W, giving p which must
n e n
now be too large.
3
2
3
2
− Iterate finding (W ,p ), (W ,p ) . . . etc. until the difference between
n e n n e n
k
successive values of p n is less than some tolerance level, at which point the
procedure is repeated for the next time step.
b) Fetkovitch
The iterative solution technique can again be applied but in this case the equations
used are (9.28) and (9.29).

Aquifer material balance

W e
p = p 1− n-1
i
n1
a − W
ei
Water influx

∆
i
n
∆ W k = W ei p − 1 p + p k )) (1 e − Jp t / W ei )
−
n e p i ( a n1 2 ( n 1 n
−
−
n1
−
W e k = ∆ W + ∆ W e k
j e
n
j1 n
=
Reservoir material balance
k
p k p G W E
i
n e
n p
i
= 1− 1 −
Z n Z i G G

A flow chart showing the sequence of steps is included as fig. 9.20. An example
illustrating this technique is presented in Fetkovitch's paper. 2