Page 246 - Reservoir Formation Damage

226 Reservoir Formation Damage

/—Constant-Flow-Rate Tests

Assuming that <|) and a essentially remained constant with time during
their experiments, Gruesbeck and Collins simplified Eq. 10-119 for a
constant injection rate as:

= 0 (10-179)

and designed special experiments to verify their model as described in
the following.

Case 1 — Particle Deposition and Mobilization in Nonplugging Pathways.
First they considered a case where particle mobilization does not occur,
and the particle deposition rate is proportional to the particle concentration
of the suspension according to

(10-180)

Then, Eqs. 10-179 and 180 can be solved subject to the conditions

e = e 0 , 0 < j c < L , r = 0 (10-181)

and

a = a !n, * = 0, ? > 0 (10-182)

to obtain the following analytic solutions:

|k/«) (10-183)

e = e 0 +(3ar (10-184)

An application of Eq. 10-183 over the length of the porous media yields:

(10-185)

Gruesbeck and Collins (1982) injected a low concentration of a suspen-
sion of CaCO 3 particles into a column of clean, unconsolidated sand pack.
Under these conditions, they assumed that removal of deposited particles
was negligible. They measured the concentration of particles in the