Modeling Depth Filtration of Activated Sludge Effluent Using a Synthetic Compressible Medium

Abstract

A new filter employing a compressible filter medium has been evaluated for the filtration of secondary effluent. The ability to adjust the properties of the filter medium by altering the degree of the bed compression is a significant departure from the conventional depth filtration technology. Unlike conventional filters, it is possible to optimize the performance of the Fuzzy Filter during the filtration cycle by adjusting the medium properties (i.e., collector size, porosity, and depth) to respond to the variations in the influent quality. Because the use of a compressible filter medium is a new development, none of the existing filter models can be used to predict the performance of the Fuzzy Filter. The development of a predictive model that can be used to describe the filtration performance of the Fuzzy Filter is presented and discussed in this paper.A new equation, based on the conservation of mass principle and depth filtration kinetics, was developed taking into account the fact that the properties of the filter medium change with time and depth. The inherent nonlinearity of the problem, caused by the dependency of the concentration, the accumulation of solids within the filter medium, and the medium properties on each other was considered when deriving and solving the new equation. The following hyperbolic type second order nonlinear partial differential equation, which governs the concentration of particulate material as a function of filter medium depth and time, was derived:where C = concentration of particulate material, t = time, x = medium depth in the direction of the flow, v = approach filtration velocity, max σ = maximum mass amount of particulate material that can be accumulated within the medium (usually referred as specific deposit) λ = filter coefficientThe modeling results obtained for different filtration conditions are presented in this paper. The model does not depend on variable empirical coefficients, and can be used to predict the performance of full scale installations.

Development and Solution of Depth Filtration Equation

“…The modeling results were compared with the field observations obtained from several experiments (26 experiments) conducted at filtration rates between 10 gal/min-ft 2 and 20 gal/min-ft 2 and at medium compression ratios from 15 percent to 40 percent (Caliskaner, 1999). Some important findings derived from the development and solution of the depth filtration equation presented in this study are as follows:…”

“…A solution was developed for the depth filtration equation given above using the explicit finite difference numerical method (Caliskaner, 1999). The solution method is outlined below.…”

“…(13)] for total suspended solids concentration values as a function of medium depth and time. The algorithm and the computer program are presented elsewhere (Caliskaner, 1999).…”

Modeling Depth Filtration of Activated Sludge Effluent Using a Compressible Medium Filter

“…Therefore, must be solved numerically. was solved using the explicit‐upstream, finite‐difference method ( Caliskaner, 1999 ). The solution of the two equations (eqs 2 and ) simultaneously would give identical results, with the solution of , as is a combination of the two.…”

“…Both definitions are acceptable, as long as a proper conversion is used between the two parameters, when necessary. Maximum specific deposit is expressed in terms of mass‐per‐unit volume in this study, because mass accumulation of TSS particles within the unit filter volume can be calculated directly by the use of continuous online measurements of turbidities for the influent stream and at a selected medium depth ( Caliskaner, 1999 ). It should be noted that the MSD is a variable coefficient (in depth), because it increases with the medium depth ( Caliskaner, 1999 ).…”