Page 229 - Reservoir Formation Damage
P. 229
Single-Phase Formation Damage by Fines Migration and Clay Swelling 209
(10-135)
In Eqs. 10-133- through 135, <|) is the instantaneous porosity, p w and
are the densities of water and particles, u is the volumetric flux of
p p
the flowing suspension of particles, e w , e p , and e* represent the volume
fraction of porous media containing the absorbed water, particles deposited
from the flowing suspension, and the indigeneous particles in the pore
space, respectively, and o w and G p denote the volume fractions of the
water and particles, respectively, in the flowing suspension. Thus,
(10-136)
According to Eq. 10-135 the density of the flowing suspension is given
as a volumetric weighted sum of the densities of the water and par-
ticles by:
(10-137)
For simplification purposes, assume constant densities for the water and
particles. However, note that the density of suspension is not a constant,
because it is variable by the particle and water volume fractions based
on Eq. 10-137. Therefore, Eqs. 10-134 and 135 can be expressed,
respectively, as:
fit = 0 (10-138)
(10-139)
Considering the rapid flow of suspension as the flow passages narrow
during the formation damage, the Forchheimer equation is used as the
momentum balance equation:
(10-140)
where \j/ is the flow potential defined as:
