Page 210 - Reservoir Formation Damage

Single-Phase Formation Damage by Fines Migration and Clay Swelling 191

The rate of particle retention on the pore surface is assumed proportional
to the particle mass concentrations in the flowing phase according to:

(10-33)
r r=(dm p/dt) r=k rp pf
The rate of entrainment of the surface deposited particles by the flowing
phase is assumed proportional to the mass of particles available on the
pore surface according to:

(10-34)
k em p
Then, the net rate of deposition is given as the difference between the
retention and entrainment rates as:

dm p/dt = k rp pf-k em p (10-35)

subject to the initial condition given by:

0 (10-36)

Diagnostic Equations for Typical Cases
Wojtanowicz et al. (1987, 1988) have analyzed and developed diagnostic
equations for two special cases of practical importance:

1 . Deposition of the externally introduced particles during the injection
of a suspension of particles
2. Mobilization and subsequent deposition of the indigeneous particles
of porous medium during the injection of a particle free solution

Deposition of Externally Introduced Particles

Three distinct permeability damage mechanisms are analyzed for a
given injection fluid rate and particle concentration. As depicted in
Figure 10-4, particles are retained mainly in the thin core section near
the inlet face. In this region the concentration of the flowing phase is
-
assumed the same as the injected fluid (i.e., p p/ ( P p f ) . ).
Gradual pore reduction by surface deposition occurs when the particles
of the injected suspension are smaller than the pore constrictions. Assume
that the surface deposition is the dominant mechanism compared to the
entrainment, that is, k r»k e.