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Cake Filtration: Mechanism, Parameters and Modeling 265

Civan (1998b) developed improved ordinary differential, linear and
radial filtration models incorporating the effects of filter cake compaction,
small particle invasion and retention at static and dynamic conditions. He
applied filter cake thickness averaging by extending the methodology by
Corapcioglu and Abboud (1990) and Civan (1994, 1996). The new models
alleviate the aforementioned problems associated with the previous
models. Civan (1998b) also derived the simplified forms of his models,
considering that the particles and carrier fluid can be assumed incom-
pressible for many practical applications. He presented the applications
to radial and linear filtration processes and compared the results. The
thickness-averaged ordinary differential filter cake model reproduced the
predictions of the Tien et al. (1997) partial differential model rapidly with
less computational effort.
In most filtration models, the flow through porous media is represented
by Darcy's law. Consequently, the applicability of these models is limited
to filtration undergoing at low flow rate or low pressure difference
conditions. Civan (1999a,b) also developed linear and radial filtration
models incorporating a non-Darcy flow behavior and applicable at static
and dynamic filtration conditions by extending Civan's (1998a,b) model
considering Darcy behavior. The non-Darcy behavior is represented by
Forchheimer's (1901) law. In this chapter, the filtration models are
presented by including the non-Darcy effects. However, the models also
apply for Darcy flow because the non-Darcy effects diminish at low flow
rates. Civan (1998a) also developed and verified several methods for
determining the parameters of these incompressible cake filtration models
from experimental data by constructing diagnostic charts of linear types.
However, some parameters should be either directly measured or deter-
mined by a least-squares regression of experimental data with the filtration
models as demonstrated by Civan (1998a,b). In this chapter, Civan's
(1998a,b, 1999a,b) filtration models are presented.

Incompressive Cake Filtration

In this section, models for interpretation and prediction of incom-
pressible filter cake thickness, and filtrate volume and rate data for linear
and radial filtration cases, at static and dynamic conditions, are presented.
Methods for determining the model parameters from experimental filtra-
tion data are presented. Model assisted analyses of three sets of experi-
mental data demonstrate the diagnostic and predictive capabilities of the
model. These models provide insight into the mechanism of incompres-
sible cake filtration and offer practical means of interpreting experimental
data, estimating the model parameters, and simulating the linear and radial
filtration processes.