Predictive model of constant rate expression for dewatering of semi-solid materials

Abstract

Nonlinear predictive model of constant rate expression is developed for dewatering semi-solid materials and industrial filter cakes. Nonlinear consolidation equation is expressed on the base of a power-law θ-function linearising Darcy law. Analytical solutions of consolidation equation are obtained under the constant rate condition. Presented model permits obtain the local solid and liquid pressure profiles during constant rate solid–liquid expression, as well as the internal distributions of liquid flow rate, local specific cake resistance and void ratio. Proposed analytical model and numerical simulations were used in worked examples for the highly compressible filter cakes of silica and activated sludge, as well as for the moderately compressible filter cake of CaCO3. It is shown that the value of applied expression rate is determinant for the process efficiency. Expression rate should be very low in case of highly compressible filter cakes of silica and activated sludge to avoid very rapid pressure rise and excessively high expression pressure. Obtained results permit verify and confirm Shirato’s hypothesis that internal structure of filter cake compressed under the instantaneous pressure in a constant rate operation is practically the same as that compressed under such a pressure in a constant-pressure operation.