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Abstract

Practical and improved ordinary differential models for compressible filter cake buildup involving small particle invasion and deposition inside the cake at static and dynamic conditions are developed by averaging particle and carrier fluid transport equations over the filter cake thickness. The models are simplified by considering that the panicles and carrier fluids involving many practical applications are incompressible. The results of radial and linear filtration cases are compared for constant rate and constant pressure drive filtrations. This thickness-averaged ordinary differential model reproduces the predictions of the Tien et al. (1997) partial differential model rapidly with less computational effort. Parametric studies indicate that the particle screening efficiency of the filter is an important factor on the filter cake properties and filtration rate, and differences between linear and radial cake filtration performances are more pronounced, and the cake thickness and filtrate volume are smaller for constant pressure filtration than constant rate filtration. The equations of the thickness-averaged linear and radial filter cake formation models are simple requiring less computational effort over the reported partial differential models for the analysis, design and optimization of the industrial cake filtration processes involving plate and drum filters.