Page 390 - Fundamentals of Reservoir Engineering

NATURAL WATER INFLUX 325

For the first time step p a n-1 = p i, the initial reservoir and aquifer pressure.

The constant terms in equs. (9.28) and (9.29) can be evaluated (in field units), for the
correct aquifer size, i.e. r eD = 5, as follows:

W ei = cWp
i i
= cfπ ( e 2 r 2 o ) h p / 5.615 rb
φ
r −
i
6
6
−
×
×
7 10 × .3889 π (2116 85) 10 × 100 .25 2740
−
×
×
×
=
5.615
W ei = 211.9 MMrb
For a finite radial aquifer
3
−
7.08 10 fkh
×
J =
r 3
µ ln e −
r o 4 (9.30)
3
−
7.08 10 × .3889 200 100
×
×
×
= = 116.5b / d/psi
.55(In5 .75)
−
Therefore, Jp i/W ei = 116.5×2740/211.9×10 6
-3
= 1.506×10 /day
Since the ∆t in equ. (9.28) is in days, then for time steps of one year
3
−
∆
− Jp t / W − 1.506 10 × 365 = 0.4229
×
1e i ei = −
1e
−
Equ. (9.28) can therefore be reduced to
211.9 10 6
×
∆ W = ( p − p ) × 0.4229
n e 2740 a n 1 n
−
∆ W = 32705 ( p − p ) rb
n e a n 1 n
−