Page 175 - Reservoir Formation Damage

Particulate Processes in Porous Media 157

subject to

(8-32)

is the critical shear stress and is an erosion rate constant given
i cr k e
by (Khilar and Fogler, 1987):

0 when > l (8-33)

and

(8-34)
= 0 otherwise
There are several alternative ways of expressing the hydraulic force.
The Rabinowitsch-Mooney equation for non-Newtonian fluid wall shear-
stress, i w , in pipes is given by (Metzner and Reed, 1955):

(8-35)
d* D

The non-Darcy equation can be modified by applying the capillary tubes
analogy and the procedure by Ikoku and Ramey, Jr. (1979):

(8-36)
V-e

where \L e is the effective viscosity given by

(8-37)

k' and n are some empirical parameters, which assume k' = \JL and n' = 1
for Newtonian fluids.
The critical shear stress, i cr, is a function of the particle stickiness to
the surface characterized by the k x constant and the particle concentration
at pore surface (Civan, 1990, 1996):

T =^c« (8-38)

where a is an empirical constant.