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Mathematical Modeling of Compressible Cake Filtration

by Scott A. Wells, Portland State Univ, United States,
Richard I. Dick, Portland State Univ, United States,



Document Type: Proceeding Paper

Part of: Environmental Engineering

Abstract:

A numerical and analytical model of cake filtration was derived from liquid and solid continuity and momentum equations. Constitutive relationships describing porosity as functions of effective stress and permeability were obtained from laboratory filtrations and studies at the Cornell High Energy Synchrotron Source (CHESS) using kaolin suspensions. The analytical model predicted the cake suspended solids profile as a function of z/L, where z is the distance from the filtration medium and L is cake length. Because the analytical model was unable to account for presedimentation and shrinkage phenomena observed during kaolin filtration experiments. The numerical model, though, was able to predict the suspended solids cake profile evolution as a function of time even when the average porosity was not constant.

Subject Headings: Numerical models | Filtration | Mathematical models | Porosity | Water treatment | Turbidity | Mathematics

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