Page 224 - Reservoir Formation Damage

204 Reservoir Formation Damage

when the pore throat-to-particle diameter ratio is below its critical value.
Civan (1990, 1994) recommended the following empirical correlation:

(10-103)

which is determined empirically as a function of the particle Reynolds
number:

(10-104)

The rate of deposition in the nonplugging tubes is given as the dif-
ference between the rates of surface deposition and sweeping of particles
(Civan, 1994):

V - T cr) (10-105)

subject to the initial condition

(10-106)

where o np is the volume fraction of particles in the suspension of
particles flowing through the nonplugging pathways. k d and k e are the
surface deposition and mobilization rate constants. k e = 0 when i w < i cr.
is the fraction of the uncovered deposits that can be mobilized from
r\ e
the pore surface, estimated by:

(10-107)

is the minimum shear stress necessary to mobilize the surface deposits.
i cr
is the wall shear-stress in the nonplugging tubes, given by the
i np
Rabinowitsch-Mooney equation (Metzner and Reed, 1955):

(10-108)

in which the interstitial velocity, v np, is related to the superficial velocity,
« v , by:

'np (10-109)