Page 289 - Reservoir Formation Damage

Cake Filtration: Mechanism, Parameters and Modeling 269

Then, Eq. 12-3 can be simplified to Civan's (1999a) equation as

-i rHE (12-9)

in which //(e^) = 0 when ^=0 (no cake) and //(e 5) = l when e 5 >0.
The function #(ej can be expressed in terms of the cake thickness, 5,
as //(S) = 0 when 8 = 0 and /f(8) = l when 8>0, because e^=0 when
5 = 0.
The filter cake thickness 8 is given by

5 = x,., - (12-10)

Note the slurry side filter surface position x w is fixed.
Substituting Eqs. 12-2, 4, 9 and 10, Eq. 12-1 can be written as (Civan,
1998a)

(12-11)

where

(12-12)

(12-13)

The initial condition for Eq. 12-11 is

8 = 0, t = 0 (12-14)

The rapid filtration flow of the carrier fluid through the cake and filter
can be expressed by Forchheimer's (1901) equation

(12 15)
a, jr-"- ' -

The inertial flow coefficient is given by the Liu et al. (1995)

4
p = 2.92 xlO t/($K) (12-16)