Modeling of Compressible Cake Filtration

• Published in: Journal of colloid and interface science 1993-10, Vol.160 (2), p.304-316
• Main Authors: Abboud, Nelly M., Corapcioglu, M.Yavuz
• Format: Article
• Language: English
• Subjects: 01 COAL, LIGNITE, AND PEAT; 010800 - Coal, Lignite, & Peat- Waste Management; 320303 - Energy Conservation, Consumption, & Utilization- Industrial & Agricultural Processes- Equipment & Processes; Chemistry; Colloidal state and disperse state; COMPRESSIBILITY; DIMENSIONS; ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION; Exact sciences and technology; FABRIC FILTERS; FILTERS; FILTRATION; General and physical chemistry; GRANULAR BED FILTERS; LAYERS; MATERIALS; MATHEMATICAL MODELS; MECHANICAL FILTERS; MECHANICAL PROPERTIES; PARTICLES; PARTICULATES; PERMEABILITY; Physical and chemical studies. Granulometry. Electrokinetic phenomena; POROSITY; POROUS MATERIALS; SENSITIVITY ANALYSIS; SEPARATION PROCESSES; THICKNESS
• ISSN: 0021-9797; 1095-7103
• DOI: 10.1006/jcis.1993.1401

The transport of suspended solid particles in a liquid through porous media has importance from the viewpoint of engineering practice and industrial applications. Deposition of solid particles on a filter cloth or on a pervious porous medium forms the filter cakes. Following a literature survey, a governing equation for the cake thickness is obtained by considering an instantaneous material balance. In addition to the conservation of mass equations for the liquid, and for suspended and captured solid particles, functional relations among porosity, permeability, and pressure are obtained from literature and solved simultaneously. Later, numerical solutions for cake porosity, pore pressure, cake permeability, velocity of solid particles, concentration of suspended solid particles, and net rate of deposition are obtained. At each instant of time, the porosity decreases throughout the cake from the surface to the filter septum where it has the smallest value. As the cake thickness increases, the trends in pressure variation are similar to data obtained by other researchers. This comparison shows the validity of the theory and the associated solution presented. A sensitivity analysis shows higher pressure values at the filter septum for a less pervious membrane. Finally, a reduction in compressibility parameter provides a thicker cake, causes more particles to be captured inside the cake, and reduces the volumetric filtrate rate. The increase of solid velocity with the reduction in compressibility parameter shows that more rigid cakes compress less.