Page 297 - Reservoir Formation Damage

Cake Filtration: Mechanism, Parameters and Modeling 277

«=-«- (12-53)
2nrh

Thus, substituting Eq. 12-53 into Eq. 12-52 results in

M- 9 ,
=
(12-54)
Integration of Eq. 12-54 for conditions prevailing prior to and during
filter cake formation leads to the following expressions, respectively
(Civan, 1999a)

(12-55)
r,., r.
2nhK f {r w

and

q\L
2nhK K

(12-56)
1 1
(2nh)

Thus, eliminating (/? c - p e) between Eqs. 12-55 and 56, substituting Eq.
12-46, and then solving for q, yields for Darcy flow ( f =P C = O :

(12-57a)

and for non-Darcy flow:

(12-57b)

in which

1 1
(12-58)
r w -8 r w