Page 169 - Reservoir Formation Damage

Paniculate Processes in Porous Media 151

The pore throat diameter can be estimated as a fraction, /, of the hydraulic
tube diameter according to (Ohen and Civan, 1990, 1993):

D,=fD (8-19)

Then, the ration of the particle to pore throat diameters can be approxi-
mated by:

D
F = 1 = P =
5 (8-20)
p D, o.
King and Adegbesan (1997) state that the ratio of the median particle
diameter to pore throat diameter is given by (Dullien, 1979):

(8-21)

A comparison of Eqs. 8-20 and 21 implies that, even if / = 1.0, Eq.
8-21 is applicable for tight porous media with a porosity of the order of
4 = 0.04.
The value of the parameter F s or its reciprocal (3 indicates that the
flow of a particulate suspension into porous media may lead to one of
the following phenomena (King and Adegbesan, 1997):

a. P < 3 , external filtercake formation
b. 3<(3<7, internal filtercake formation
c. p>7, negligible filtercake involvement

Pautz et al. (1989) point out that these rules-of-thumb have been derived
based on experimental observations. The values 3 and 7 denote the critical
values or P cr . Note these values are very close to the values of 2 and 6
indicated by Figure 8-5 given by Gruesbeck and Collins (1982) for
bridging of particles in perforations.
Civan (1990, 1996) determined (3 cr empirically by correlating between
two dimensionless numbers. In the pore throat plugging process, the mean
pore throat diameter, D t, mean particle diameter, D p, particle mass
concentration, c p, viscosity of suspension, |o,, and the interstitial velocity
of suspension, V = M/<|), are the important quantities. Therefore, a dimen-
sional analysis among these variables leads to two dimensionless groups
(Civan, 1996). The first is an aspect ratio representing the critical pore
throat to particle diameter ratio necessary for plugging given by: