Page 65 - Principles of Applied Reservoir Simulation 2E

50 Principles of Applied Reservoir Simulation

(6.8)
P 0 = A 0x+B 0
where the constant coefficients {A e B s} are determined by applying the boundary
conditions. Substituting Eq. (6.5) in Eq. (6.7) gives

= (6.9)
B w P {
The remaining coefficients are found by simultaneously solving Eqs. (6.4), (6,7),
and (6.8) subject to Eqs. (6.3), (6.5), and (6.6). The resulting coefficients are
AP
= -~rz—-——— (6.10)
A w
ML + (1 - M}x f

(6.11)
A 0=MA W

B 0 = PI = (A w - A 0)x f = P, + (1- M)A wx f (6.12)

where M is the mobility ratio

M=-~- (6.13)
k
o
and the pressure difference is
(6.14)
AP=P,-P 2
The frontal velocity Vyis given by
dx v

where S or is residual oil saturation, S wc is connate water saturation, and v w is the
Darcy velocity:

V =
w ~ ~^w~A ~^w^w (6.16)
Substituting Eq. (6.16) into (6.15) gives

dt ~ n~ s - ? ^F i>rr . /, m~l (6.17)
A
- A/)*,]