Modelling filtration with superimposed sedimentation

Abstract

Filtration at moderate rates is often superimposed by sedimentation. This work shows that classical cake filtration equations can be complemented by an additional sedimentation term to model cake filtration measurements with significant sedimentation. Algorithms are derived for zone as well as clarifying sedimentation. In contrast to the classical filtration theory not the absolute values but the differentials of cake height and filtrate volume are set into a proportional relation. The resulting set of equations can be solved numerically. If the porosity is expressed as a function of the cake height and the Carman–Kozeny relation is employed, the model may be extended to compressible cakes. Experiments with the system ‘lactose in ethanol’ justify the model. Experimental data can be fitted much better with the new model than with equations of the classical filtration theory alone. In contrast with other filtration models that include sedimentation, no additional parameters need to be introduced, and the physical meaning of constants such as cake resistance, specific cake volume and, settling velocity is maintained.