Page 335 - Reservoir Formation Damage

Cake Filtration: Mechanism, Parameters and Modeling 315

20 30 40 50 60
Filtration Time, min.
Figure 12-21. Comparison of the filtrate volume for linear and radial constant
pressure filtration (Civan, R, 1998b; reprinted by permission of the AlChE,
©1998 AlChE. All rights reserved).

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filtration results are more pronounced and the cake thickness and filtrate
volume are less for the constant pressure filtration.
Tien et al. (1997) have solved their partial differential model numerically
using a ready-made Fortran subroutine for linear filtration at static
condition and reported numerical solutions along the filter cake only
at the 100- and 1000-seconds times. Their model generates numerical
solutions over the thickness of the filter cake, whereas, Civan's (1998b,
1999b) models calculate the thickness-averaged values. Therefore, Civan
averaged the profiles predicted by Tien et al. (1997) over the cake thick-
ness and used for comparison with the solutions obtained with the
thickness-averaged filter cake model. Because Tien et al. (1997) reported
numerical solutions at only two time instances, this resulted in only two
discrete values. Civan generated the numerical solutions with the linear
filtration model using the data identified as Data II in Table 12-2 for
constant rate and constant pressure filtrations. As can be seen by Civan's
(1998b) results presented in Figures 12-22 through 12-25, his ordinary
differential model can closely reproduce the results of the Tien et al.

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