Page 247 - Reservoir Formation Damage

Single-Phase Formation Damage by Fines Migration and Clay Swelling 227

effluent. Applying Eq. 10-185 with their data given in Figure 10-22,
Gruesbeck and Collins determined the same |3 value on the average for
different flow rates. Therefore, they concluded that the rate law postulated
by Eq. 10-180 is valid.
Second, Gruesbeck and Collins neglected the deposition rate and
considered that the mobilization phenomena is dominant. Thus, integrating
Eq. 10-179 over the length of the porous media and applying the mean
value theorem yields:

(10-186)
a* I LJ dt L
'avg

where G in = 0 for injection of a particle free solution.
In order to test the validity of Eq. 10-186, Gruesbeck and Collins
prepared a sand pack by mixing sand and a suspension of CaCO 3 particles
into a column. Then, a particle free KCl solution was injected into
the column.
In Figures 10-23 and 10-24 of Gruesbeck and Collins, their experi-
mental data and plots of Eq. 10-186 are given, respectively. Based on
Figure 10-24, they concluded that the particle mobilization rate can be
represented by

cte
= oca(«-« c) (10-187)

0.95CM/S
= 0.66 CM/S

RNES

10 20 25 30 35 50 GO
PORE VOLUMES

Figure 10-22. Deposition of fines in a porous medium of 30.48 cm pack of
840-2000 mm diameter sand grains (after Gruesbeck and Collins, ©1982
SPE; reprinted by permission of the Society of Petroleum Engineers).