Modeling of the consolidation stage in pressure filtration of compressible cakes

Abstract

High pressure filtration of fines and colloidal suspensions is determined by the structure of particle network in the flocculated suspension, its yield rheology, hindered settling, and flow through the compressible porous media. A realistic theoretical treatment of the process, incorporating the relevant material functions and transport phenomena, results in a nonlinear partial differential diffusion equation for local solid volume fraction with moving boundaries. Because of the complicated nature of numerical solution, deficiencies in the experimental data, and uncertainty inherent in numerical differentiation, among others reasons, the model equation and its approximate linearized version are not convenient for engineering analysis of industrial high pressure filtration cycles. An approximate model of the filter cake consolidation stage is proposed, taking cognizance of the facts that with filtration time the porosity and thickness of the compact bed decrease and the fluid stress drops continually. The model is significantly easier to implement and seemingly capable of simulating a wide variety of suspensions having diverse dewatering characteristics. Only one filtration run, which need not be driven to the end point, is required to estimate all model parameters for the pressure employed. The consolidation model is meant to supplement the more detailed and rigorous diffusion model of white and coworkers in those situations where data is limited in some way or where there is uncertainty in the measurement of the dewatering parameters. Because of its relatively simple mathematical structure, the model could be useful for engineering analysis and simulation of the filtration cycle, including model based control in the face of fluctuating feed properties.