A compressional rheology model of fluctuating feed concentration during filtration of compressible suspensions

Filtration is a common process used to perform solid–liquid separation. This work addresses a previously overlooked yet significant aspect of filtration when the feed solids concentration varies on the same timescale of the filtration process. This affects the filtration rate and therefore the throughput of the filter. Existing one-dimensional models of fixed-cavity and flexible-membrane plate-and-frame filtration based on compressible suspension theory, in which the cake concentration as a function of thickness and time is given by a hyperbolic second-order diffusion equation, are expanded here using a filtrate volume dependent feed concentration. The key material properties are the compressive strength and the solids diffusivity. Two limiting approximations for the suspension flow behaviour above the filter cake are considered; perfect mixing and plug flow. Three case studies are presented exploring different aspects of fluctuating feed. Modelling results indicate that fluctuations in feed concentration can have a large effect on solids throughput as a function of final cake solids concentration. A key result is that, when processing a fixed volume of suspension, dilute feed followed by concentrated feed leads to faster overall filtration than the reverse case. The two limiting approximations of suspension flow behaviour show no significant difference under the examined conditions since the filtration kinetics are dominated by the rate of fluid flow through the cake, not the suspension.

► Filter model of feed concentration fluctuating on the process timescale.
► Accounts for compressible filter cakes.
► Considers extremes of perfect mixing and plug flow above the filter cake.
► Feed can be networked or un-networked and increasing or decreasing.
► Three case studies used to illustrate the effect of fluctuating feed concentrations.