Development and Solution of Depth Filtration Equation

An innovative filter, which involves the use of compressible synthetic fiber porous material, was evaluated for the filtration of secondary effluent. Because existing filter models can not be used to predict the performance of the compressible medium filter (CMF), a new depth filtration model was developed to predict the removal performance of the CMF and the effect of the medium compression ratio. The following hyperbolic type second order nonlinear partial differential equation was derived to model depth filtration (Caliskaner and Tchobanoglous, 2005):∂2C/∂t∂x − 1/C ∂C/∂x ∂C/∂t + V/σmax λC ∂C/∂x − 1/λ ∂λ/∂t ∂C/∂x = 0WhereC = Concentration of particulate material (TSS in wastewater),t = Filtration time,x = Medium depth in the direction of the flow,σmax = Maximum specific deposit,λ = Filter coefficient, andV = Approach filtration velocity.A solution was developed for the depth filtration equation given above using the explicit finite difference numerical method. The solution method is presented and discussed in this paper