Page 326 - Reservoir Formation Damage

306 Reservoir Formation Damage

<£=, (12-156)
dt

Eqs. 12-154 or 12-156 can be solved numerically subject to the initial
condition
(12-157)

Applications

The applications of the linear and radial filter cake buildup models are
illustrated using the data given in Table 12-2.
Corapcioglu and Abboud (1990) obtained a numerical solution for the
linear constant rate filtration problem involving small particle invasion
at static condition, assuming that the cake is incompressible, the cake
porosity remains constant and all particles are filtered. Abboud (1993)
repeated a similar calculation, but also considered the effect of small
particles migration into the filter. Tien et al. (1997) considered both
constant rate and constant pressure-driven compressive cake filtrations in
a linear and static case only.
In the following, the applications by Civan (1998b, 1999b) to constant
rate and constant pressure-driven filtration processes in linear and radial
cases are presented and compared. The data considered are composed
from the data used by Corapcioglu and Abboud (1990), Tien et al. (1997),
and the missing data estimated by Civan (1998b), given in Table 12-2.
Civan obtained the best estimates of the missing data by fitting the model
to data as practiced by Liu and Civan (1996) and Tien et al. (1997).
The numerical solutions of the ordinary differential equations, Eqs. 12-
107, 108, and 110 for the linear model and Eqs. 12-97, 98, and 100
for the radial model, are obtained using the Runge-Kutta-Fehlberg four
(five) method (Fehlberg, 1969) to determine the filter cake thickness,
h = x w - x c for the linear and h = r w-r c for radial cases, and the volume
fractions of the jjmall particles retained in the cake and suspended in the
flowing slurry, e p2s and e p 2/, respectively. Eqs. 12-109 and 99 are used
to determine the filtrate carrier fluid volumetric flux, (M/)-. , for the
v * / jitter
linear and radial cases, respectively. First, using the data given in Table
12-2, identified as Data I, the numerical solutions are carried out with
the present, improved model for both linear and radial constant rate
filtrations. The results for all particles filtered, for which (c p2i) = 0>
as expected from an efficient filter, are compared and the effect of fine

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