Page 321 - Reservoir Formation Damage

Cake Filtration: Mechanism, Parameters and Modeling 301

(12-131)
271 h V \'w

Y = -(p c -p e ) (12-132)

Although this approach leads to a reasonably good estimate, a more
rigorous approach should employ

2
r -r 'c 2
'w
(12-133)
2r,
The inertial flow coefficient is estimated by the Liu et al. (1995) cor-
relation given by Eq. 12-16.

Particle Deposition Rates
The rate of deposition of the particles of the slurry over the slurry side
cake surface is assumed proportional to the particle mass flux approaching
the filter cake. The rate of erosion of the particles from the slurry side
cake surface is assumed proportional to the tangential, excess shear stress
above the critical stress necessary for particle mobilization. Therefore, for
dynamic filtration involving cross flow, the net mass rate of all particles
(large plus small) deposition per unit area of the slurry side cake surface
is given by the difference between the deposition and erosion rates as
(Civan, 1996, 1998b):

(12-134)

where u t is the carrier fluid filtration flux normal to the cake surface
3
2
(cm / cm • s) and c pl is the slurry particle concentration expressed as the
particle mass per unit volume of the carrier fluid in the slurry.
For small particles retention over the slurry side of the cake, an
expression similar to Eq. 12-134 can be written as:

(12-135)

c
in which \ pii) slur denotes the mass of small particles per volume of
the carrier fluid in the slurry.