Page 323 - Principles of Applied Reservoir Simulation 2E

308 Principles of Applied Reservoir Simulation

and POT is the pot aquifer coefficient. The minus sign preceding the bracketed
n
term indicates water is entering the block when P > P n + l .

Steady-State Aquifer
The steady-state aquifer model is based on Schilthuis's assumption that
the water influx rate q wss is proportional to the pressure difference between the
aquifer and the hydrocarbon reservoir. It is further assumed that the aquifer is
sufficiently large that it experiences no net pressure change throughout the
producing life of the reservoir. With these assumptions, WINB4D computes
steady-state aquifer influx into a specified gridblock as

= -[SSAQ (/>° - P w + 1 )]; SSAQ * 0 (29.2)
q wss
+l
where P" is the gridblock pressure at the future time level n + 1 ; P° is the initial
gridblock pressure; and SSAQ is the proportionality constant. The minus sign
preceding the bracketed term indicates water is entering the block when we have
n +
the inequality p°>p \

Carter-Tracy Aquifer
The Carter-Tracy [ 1 960] modification of the Hurst- van Everdingen [ 1 949]
unsteady-state aquifer influx calculation is available in WINB4D. The Carter-
Tracy aquifer influx rate q wa for a specified gridblock is

*Wr = -M - B(P n+l - P")] (29.3)

where P",P" +l are gridblock pressures at time levels n and n + 1, respectively,
The coefficients A and B are given by

P(p° />")-
-
A = K t (29.4)
DENOM
with
= K t H (29 5)
' DENOM l J

+l +l
DENOM = P" D - t£p' t£ (29.6)