Page 212 - Reservoir Formation Damage

Single-Phase Formation Damage by Fines Migration and Clay Swelling 193

Mobilization and Subsequent Deposition of Indigeneous Particles

This case deals with the injection of a clear (particle free) solution into
a porous media. A core is visualized as having two sections designated
as the inlet and outlet sides. The particles of the porous media entrained
by the flowing phase in the inlet part are recaptured and deposited at the
outlet side of the core.
Near the inlet port, the mobilization and entrainment of particles by
the flowing phase is assumed to be the dominant mechanism compared
to the particles retention (i.e., k e » k r}. Thus, dropping the particle reten-
tion term, Eqs. 10-35 and 36 yield the following solution for the mass
of particles remaining on the pore surface

= m po exp(-£ e?) (10-45)
m p
Substituting Eq. 10-45 and (p p/). =0, Eq. 10-32 yields the following
expression for the particle concentration of the flowing phase passing
from the inlet to the outlet side of the core as

•k et) (10-46)

Depending on the particle concentration and size of the flowing phase
entering the core, the outlet side diagnostic equations for three permeability
damage mechanisms mentioned previously are derived next.

Gradual Pore Reduction by Surface Deposition and Sweeping

Assume that the mass of the indigeneous or previously deposited
particles on the pore surface is m*. Then, the area occupied by these
particles is given by Eq. 10-29 as

(10-47)

and the area open for flow is given by Eq. 10-28 as

(10-48)

Af g denotes the open flow area when all the deposits are removed.
If simultaneous, gradual pore surface deposition and sweeping are
occurring near the outlet region, then both the entrainment and retention
terms are considered equally important. Thus, substituting Eq. 10-46,
Eq. 10-35 yields the following ordinary differential equation: