Page 225 - Reservoir Formation Damage

Single-Phase Formation Damage by Fines Migration and Clay Swelling 205

and the mean pore diameter is given by:

(10-110)

where C is an empirical shape factor.
It can be shown that Eqs. 10-101 and 105 simplify to the deposition
rate equations given by Gruesbeck and Collins (1982):

(10-111)

(10-112)

where c 1? c 2, c 3,and c 4 are some empirically determined coefficients.
This requires that the effects of the permeability and porosity changes
be negligible, the fraction of the uncovered deposits be unity, the sus-
pension of particles be Newtonian, and the particle volume fractions of
the suspensions flowing through the plugging and nonplugging pathways
be the same, that is,

a p=a np=G (10-113)

The permeabilities of the plugging and nonplugging pathways are given
by the following empirical relationships (Civan, 1994):

= (10-114)
K p

and

Then, the average permeability of the porous medium is given by:

(10-116)
K = f pK p + f npK np

Note that Eq. 10-116 was derived independently by Civan (1992) and
Schechter (1992) and is different than the expression given by Gruesbeck
and Collins (1982).
The superficial flows in the plugging and nonplugging pathways are
given, respectively, by:

u p=uK p/K (10-117)