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Cake Filtration: Mechanism, Parameters and Modeling 291

filtrate volumes with reasonable accuracy in view of the uncertainties
involved in the estimated values of the missing data. Fisk et al. (1991)
did not report any results on the filter cake thickness and therefore a
comparison of the cake thicknesses could not be made by Civan (1998a)
in the radial filtration case.

Conclusion

The models presented in this section offer practical means of inter-
preting experimental data, estimating the model parameters, and simulat-
ing the linear and radial, incompressive cake filtration processes at static
and dynamic filtration conditions. The simplified forms of these models
conform with the well-recognized simplified models reported in the literature.
These models are capable of capturing the responses of typical laboratory
filtration tests while providing insight into the governing mechanisms.

Compressive Cake Filtration Including Fines Invasion

The applicability of the majority of the previous models, such as those
by Corapcioglu and Abboud (1990), Liu and Civan (1996), Tien et al.
(1997) and Civan (1998b), is limited to low rate or low pressure difference
filtration processes because these models facilitate Darcy's law to describe
flow through porous media. However, filtration at high flow rates and
high overbalance pressure differences may involve some inertial flow
effects, especially during the initial period of the filter cake formation.
In the literature, the initial non-linear relationships of the filtrate volume
versus the square root of time has been attributed to invasion and clogging
of porous media by fine particles during filtrate flow into porous media
prior to filter cake formation. The cumulative volume of the carrier fluid
(filtrate) lost into porous media during this time is usually referred to as
the spurt loss (Darley, 1975).
Based on an order of magnitude analysis of the relevant dimensionless
groups of the general mass and momentum balances of the multiphase
systems involving the cake buildup, Willis et al. (1983) concluded that
non-parabolic filtration behavior is not caused by non-Darcy flow. Instead,
it is a result of the reduction of the permeability of porous media by
clogging by fine particles. Their claim is valid under the conditions of
their experimental test conditions. The phenomenological models for filter
cake buildup involving fine particle invasion have been presented by Liu
and Civan (1996) and Civan (1998b) for low rate filtration. However, a
close examination of most filtration data reveal some non-Darcian flow
effect during the short, initial period of filtration depending on the
magnitude of the filtration flow rate and/or the applied pressure difference.