Page 325 - Reservoir Formation Damage

Cake Filtration: Mechanism, Parameters and Modeling 305

The local cake porosity at the slurry side of the cake can be expressed
in terms of the cake-thickness-average porosity. For linear filtration Civan
(1998b) differentiated Eq. 12-145 to obtain:

(12-150)

For radial filtration, Eq. 12-148 yields (Civan, 1999b):

2
r ,-r?
(12-151)
2r dr
Similar to Tiller and Crump (1985), the cake-thickness-average drag force,
p s, created by the flow of the suspension of fine particles through the
filter cake is determined using

P S=Pc~P (12-152)

in which p c is the pressure of the slurry applying at the progressing filter
cake surface and p is the cake-thickness-average pressure of the sus-
pension of fine particles flowing through the cake. For linear filtration,
and p can be related by differentiating Eq. 12-146 and then sub-
p c
stituting Eq. 12-150 to obtain (Civan, 1998b):

--r / \
p<b-(x w-x c) = p (12-153)

For computational convenience, Eq. 12-153 can be reformulated in a form
of an ordinary differential equation as (Civan, 1999b):

-1 dx 1
dp_ =
(12-154)
dt x - x d t dt
Differentiating Eq. 12-149 and then substituting Eq. 12-151 for radial flow,
Eqs. 12-153 and 12-154 are replaced, respectively, by (Civan, 1998b):

(12-155)