Page 266 - Reservoir Formation Damage

246 Reservoir Formation Damage

and

MS w
(11-26)
1 + (M-1)S W

Consequently, Eq. 11-19 can be simplified significantly by substituting
Eqs. 11-25 and 11-26. In addition, the non-Darcy effect can be neglected
by substituting

AU=1.0 ; J = W,N (11-27)

The end-point relative permeabilities and fluid densities may be replaced
by average values as:

k° k° ]f°
_£_ ~ rW ~!^rN_ ~ _ rW , rN
~ ~ (11-28)

_ Pw+P/v
~ n
— n )
-
P -Ptv =\ N — (11-29)
As a result of substituting Eqs. 11-27 and 11-28, Eq. 11-5 can be
simplified as (Civan, 1996):

t • n\
3~ sme) = -^ (11-30)
a
dx dx dt

Determination of Species Concentrations
in Various Phases

Once the phase saturations are determined, then the species con-
centrations can be determined by solving the following equation obtained
by combining Eqs. 11-1 and 11-3:

(11-31)
J = W, N, I, wS, nS, iS and j = w, n, wp, np, ip