Page 323 - Reservoir Formation Damage

Cake Filtration: Mechanism, Parameters and Modeling 303

T = 0, and the second term on the right side of Eq. 12-134 drops out,
leading to an expression similar to Corapcioglu and Abboud (1990) and
Tien et al. (1997).
is the minimum slurry shear-stress necessary for detachment of
i cr
particles from the progressing cake surface. Following Ravi et al. (1992),
the critical shear stress necessary for detachment of the deposited particles
from the progressing cake surface can be estimated according to Potanin
and Uriev (1991) by Eq. 12-6. However, the actual critical stress can be
substantially different than predicted by Eq. 12-6, because the ideal theory
neglects the effects of the other factors, including aging (Ravi et al.,
1992), surface roughness, and particle stickiness (Civan, 1996) on the
particle detachment. Therefore, Ravi et al. (1992) recommend that the
critical shear stress be determined experimentally. U(i s-i cr) is the
Heaviside unit step function. It is equal to zero when i s < i cr and one
for T^t cr . kj and k° are the rate coefficients for the total (fine plus
large) particles deposition and detachment at the progressing cake surface.
and are the rate coefficients for the fine_ particles deposition and
k° 2 k° 2
detachment at the progressing cake surface. k d and k e are the cake-
thickness-average rate coefficients for the deposition and mobilization of
the fine particles within the filter cake matrix.

Porosity and Permeability Relationships

Incorporating the effects of fine particles deposition according to
Arshad (1991) and cake compaction according to Tien et al. (1997), Civan
(1998a) estimates the cake-thickness-average porosity by the following
constitutive equation:

° (12-142)

Considering the fine particles deposition and cake compaction, Civan
(1998a) estimates the cake-thickness-average permeability by the Tien et
al. (1997) constitutive equation:

(12-143)

In Eqs. 12-142 and 143, <j)° and k° c represent the fine particles-free and
non-compacted cake porosity and permeability; respectively, a, n, p a,
P, a^a 2, and 8 are the empirically determined parameters.