Page 231 - Reservoir Formation Damage

Single-Phase Formation Damage by Fines Migration and Clay Swelling 211

fc w/dt = Bt-V 2 (10-149)

where t is the actual contact time of flowing water with the porous media
and B is an absorption rate constant.
The porosity change by clayey formation swelling is estimated by
(Civan and Knapp, 1987; Ohen and Civan, 1990, 1993):

(10-150)

where A, is the swelling coefficient determined by an appropriate empirical
correlation such as by those given by Seed et al. (1962) and Nayak and
Christensen (1970).
The volume balance of particles (indigeneous and/or external types)
of the flowing suspension deposited in porous media is given as the
difference of the deposition by the pore surface and pore throat deposition
processes and the re-entrainment rates by the colloidal and hydrodynamic
processes as (Civan, 1996, 1996):

2/3
= k d(a + w)o p(|> +
(10-151)
-c)-
-k re pr( e(c cr
where

k p=0 for t<t p (10-152)

= 0 for (10-153)
k r c>c r

k e=Q for T < i cr (10-154)

The initial condition is given by:

0 <
je < L
— W
—
P C „ =F C_ , \J ^ A ^: LJ , t t = 0 (10-155)
Let single and double primes denote the nonswelling and swelling
clays. The volume balances of the nonmobilized indigeneous nonswelling
and swelling clays remaining in porous media is given in terms of the
colloidal and hydrodynamic mobilization rates, respectively, by:

-c)-k (10-156)
= -* r'e' p T\' e(c' cr