Solution of Granular Bed Filtration Equations

Mathematical models based on filtration theory may play an important role in pilot plant studies of granular bed filtration. A semianalytical solution of such a model is presented, solving the material balance and the kinetic equations to provide concentration, specific deposit and gradient variations with filtrate volume and bed depth. A transformation of the filtration equations yields a quasilinear hyperbolic partial differential equation which is solved numerically using the method of characteristics. The method, the numerical analysis and the computer program are explained in detail. The solution enables the use of filtration equations to predict filter performance and optimize design by feeding the computer with the filtration parameters obtained by pilot experiments. It is also applicable to other accumulation processes, i.e., fixed-bed adsorption, which have a similar conservation equation.