A Mean Phi Model for Pressure Filtration of Fine and Colloidal Suspensions

A working model for engineering analysis of pressure filtration is presented. Based on the filtration characteristics of fine and colloidal suspensions, the process was divided into two stages. A time-invariant spatially uniform volume fraction of solids approximation is invoked in the growing filter cake stage (stage 1). A time-dependent spatially uniform volume fraction of solids assumption is made in the cake consolidation stage (stage 2). The two models, named collectively as Mean Phi (M-P) model, have a common physical basis, seamless continuity between the stages and internal consistency. The M-P model has only three parameters: terminal or equilibrium volume fraction of solids in the filter cake that is related to its compressive yield stress, critical volume fraction of solids, which joins stage 1 and stage 2, and a permeability factor, which is common to stages 1 and 2. The model is validated with a large number of colloidal suspensions filtered under highly diverse physical-chemical process conditions. A Pareto profile is identified that relates the timescale of filtration and the extent of dewatering achieved, the two most important performance indices of the process.