Page 318 - Reservoir Formation Damage

298 Reservoir Formation Damage

assuming p p is constant and substituting Eq. 12-112. The present
Eqs. 12-106 and 12-109 simplify to their Eqs. 24 and 28, substituting
Eq. 12-113 for e p2l«e l. Also, Corapcioglu and Abboud (1990) did not
distinguish between the rates of deposition of small and all (large plus
small) particles over the progressing cake surface (i.e., R p2s and R° s) and
used Rp 2s = Rp S in their Eq. 24. This assumption is not valid because most
small particles migrate into the cake and only a little fraction of the small
particles can deposit by the jamming process over the slurry side of the
filter cake, such as described by Civan (1996). The filter cake is essen-
tially formed by the deposition of the large particles and the deposition
of the small particles over the progressing cake surface is negligible. The
deposition of the small particles more dominantly occurs within the
cake matrix as the suspension of small particles flows through the
cake. Therefore, there is a large order of magnitude difference between
the rates of the small and large particles deposition over the filter cake
(i.e., Rp ls » Rp 2s and, thus, R° s = Rp ls). However, it is more accurate to
use Eq. 12-91.

Pressure-Flow Relationships

3
2-
The slurry carrier fluid flow rate «, (cm /cm s) can be expressed
using the effluent fluid pressure p e(atm) at the outlet side of the filter,
the pressure p c(atm) at the slurry side cake surface, and the harmonic
average permeability of the cake and filter system.
Forchheimer's (1901) law of flow through porous media for the linear
case is given by

(12-116)
dx k
The pressure differences over the filter cake and the porous media can
be expressed by integrating Eq. 12-116, respectively, as (Civan, 1999b):

-
Pc-P»=\T-Uc+f>£c"?\(Xw-Xc) (12-117)

P W~Pe = (12-118)

The instantaneous volumetric fluxes and densities of the suspensions of
fine particles flowing through the cake matrix and porous formation are