Unified model for the prediction of consecutive solid–liquid filtration and expression at the constant pressure

Abstract

AbstractUnified nonlinear model is proposed for the prediction of consecutive solid–liquid filtration and expression at the constant pressure. This model is based on the Darcy–Terzaghi filtration‐consolidation equations modified to consider power‐law pressure dependence of the specific cake resistance, and transforming Darcy law to the linear form. The model considers nonuniform structure of compressible filter cakes obtained by filtration and following expression. The profiles of local compressive pressure and local cake characteristics are simulated and compared for different moderately and highly compressible filter cakes (H.K. kaolin, CaCO3, silica, activated sludge) based on the analytical and numerical solutions of the model. It is shown that the behavior of solid–liquid expression depends from the initial structure of compressed materials. Consolidation ratio U of the filter cakes with initially nonuniform structure formed by filtration differs from that of semi‐solid materials with initially uniform structure. Different methods of determination of consolidation coefficient are analyzed and compared for nonuniformly structured filter cakes.