Page 218 - Reservoir Formation Damage

Single-Phase Formation Damage by Fines Migration and Clay Swelling 199

(10-77)
oc c =OforC s >C; c
is the salt concentration. is the critical salt concentration for
C s C sc
particle expulsion. <* h is the hydrodynamically induced release coefficient
given by (Gruesbeck and Collins, 1982):

(10-78)
c

is the critical shear stress required to mobilize particles on pore surface.
f c
The rate of capture of particles at pore throats is assumed proportional
to the flowing phase particle concentration:

(10-80)
r c=V tP pf
P, is the capture coefficient.
Let p pfc be the critical particle concentration above which bridging at
pore throats occur and particles cannot travel between pore bodies. If the
particle concentration is below p pfc , then no trapping at pore throats takes
place. Therefore,

7 = 1, P^Oforp^p^ (10-81)

7 = 0, P f *Ofor P / 7 / >p p / c (10-82)

The correlation between entrapment and permeability reduction is based
on the Hagen-Poiseuille flow assumption of flow through the pore throat

K/K 0=[l-Bm p/m* po] 2 (10-83)

where B is a characteristic constant and K 0 is the initial permeability.

Simplified Partial Differential Model

Cernansky and Siroky (1985) considered injection of a low particle
concentration suspension at a constant rate into porous media made of a
bed of filaments. Neglecting the diffusion of particles and the contribution
of the small amount of particles in the flowing suspension, they expressed
the total mass balance of particles similar to Gruesbeck and Collins'
(1982) simplified mass balance equation. Thus, for incompressible liquid