Page 389 - Fundamentals of Reservoir Engineering

NATURAL WATER INFLUX 324

and, when dealing with very large, finite aquifers, it is initially still necessary to apply
the unsteady state influx theory of Hurst and van Everdingen for the first few time
steps. The following example will illustrate the speed and accuracy in using the method
of Fetkovitch in comparison to that of Hurst and van Everdingen. In addition, it will
demonstrate how the two methods can be combined when dealing with a large aquifer,
r eD = 10, in which, for the first few years, the influx occurs under transient flow
conditions.

EXERCISE 9.3 WATER INFLUX CALCULATIONS USING THE METHOD OF
FETKOVITCH

Recalculate the cumulative water influx as a function of time, using all the reservoir and
aquifer data presented in exercise 9.2, but applying the method of Fetkovitch. Perform
the calculations for both r eD = 5 and 10.

EXERCISE 9.3 SOLUTION

Using the method of Fetkovitch the following two equations are required

n1
−
∆ W j e

p = p 1− j1 (9.29)
=
n1
a − i W
ei

and
W − Jp t / W
∆
−
∆ W = p i ei (p a n1 − p )(1 e i n ei ) (9.28)
n
e
n
−
th
where p a n-1 is the average pressure in the aquifer at the end of the (n - 1) time
interval
th
and p n is the average reservoir-aquifer boundary pressure during the n time
interval.

Since in this present application a history match is being sought for available reservoir
pressures, that is, values of p which are listed in column 3 of table 9.2 in the previous
n
exercise, the manner of solving the above equations, to explicitly calculate the
cumulative water influx, is as follows
th
- having obtained ∆W e 1for the n - 1 time step
n-1
n1
−
then W e = ∆ W
n-1 j e
j1
=
- using equ. (9.29), evaluate p a n1
−
- insert p a n1 in equ. (9.28) and solve for ∆W e n
−