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(1997) partial differential model. Note that, as indicated in Table 12-2,
the values of the parameters at the present cake thickness-averaged level
should be different than those for the formulation at the local level
considering the spatial variations, such as by Tien et al. (1997).

Conclusions
Because of the improved phenomenological description and convenient
cake thickness-averaged formulation, the ordinary differential models can
provide faster numerical solutions with reduced computational effort and,
therefore, offer certain practical advantages over the partial differen-
tial models for the analysis, design, and optimization of the cake filtra-
tion processes.
The applicability of the models by Corapcioglu and Abboud (1990) and
Abboud (1993) is limited to static and low pressure filtration of dilute
suspensions and their assumption of the same rates for the deposition of
the small and large particles over the progressing cake surface is not
reasonable. The Tien et al. (1997) model can alleviate these problems but
it is computationally intensive and also limited to static filtration. These
models are for linear filtration and may sufficiently approximate radial
filtration only when the cake and the filter are much thinner compared
to the radius of the filter surface exposed to the slurry. However, the radial
model developed by Civan (1998a,b, 1999a,b) can better describe the
radial filtration involving thick filter cake and filter media.
The filtration models presented in this section provide insight into the
mechanism of compressive cake filtration and a convenient means of
simulation with additional features.

References

Abboud, N. M., "Formation of Filter Cakes with Particle Penetration at
the Filter Septum," Paniculate Science and Technology, Vol. 11, 1993,
pp. 115-131.
Adin, A., "Prediction of Granular Water Filter Performance for Optimum
Design," Filtration and Separation, Vol. 15, No. 1, 1978, pp. 55-60.
Arshad, S. A., "A Study of Surfactant Precipitation in Porous Media with
Applications in Surfactant-Assisted Enhanced Oil Recovery Processes,"
Ph.D. Dissertation, University of Oklahoma, 1991, 285 p.
Chase, G. G., & Willis, M. S., "Compressive Cake Filtration," Chem.
Engng. ScL, Vol. 47, No. 6, 1992, pp. 1373-1381.