Page 264 - Reservoir Formation Damage

244 Reservoir Formation Damage

Note that the saturations add up to one:

S W+S N=1 (11-16)

Therefore, adding Eqs. 11-14 and 11-15 yields the following equation:

N ndwk rW
+ • K
V-N dx
(11-17)
dPcNW vS w
+
a* dS w dx dt

where the total volumetric loss of particles from the two-phase system
is given by:

(11-18)
q = q w+q N
Eqs. 11-14 and 17 can be solved simultaneously to determine the wetting
phase pressure and saturation, p w and S w.
A second and more convenient approach facilitates the fractional
flow formulation. This is especially suitable for incompressible systems
described by the equation of continuity given by Eq. 11-3. Civan's (1996)
formulation based on Richardson's (1961) formulation can be modified
as the following to include the loss terms and inertia flow affect in the
saturation equation:

(11-19)

for which the capillary and gravity dispersion coefficients are given,
respectively, by:

k
d
_ V rN P,cNW
(11-20)
dS