DYNAMIC MATHEMATICAL-MODEL OF DEEP BED FILTRATION PROCESS

Deep bed filtration is commonly applied in clarification of dilute sus pensions of particles ranging in size from about 0.1 to 50 mu m. A sus pension carrying solid particles of different sizes is passed through the porous bed of defined geometrical characteristics. It has been fou nd that sizes of suspended particles and their distribution are very i mportant physical parameters that influence deep bed filter efficiency . During the filtration process the bed porosity decreases, whereas in terficial velocity increases due to the particle accumulation in filte r bed. Mathematical model has been developed under the assumption that the plug flow model approximates flow of suspension through the bed. The second assumption is that a deposition kinetics is a function of l ocal suspension's particle distribution and locally deposited particle distribution. In order to obtain the experimental data needed for det ermination of the process kinetics, a set of experiments has been carr ied out. So obtained experimental data consisted of the local suspensi on and deposit particle distribution values and also of the local rate values. All three empirical distributions are approximated by standar d Logarithm-Normal distribution function. Each distribution is defined by two LN function parameters. Rate distribution parameters are forma lly dependent on the parameters that define suspension and deposit dis tribution. This relation has been established using the general regres sion neural network (GRNN). Thus defined model enables solving the sys tem within given boundary conditions by approximating distribution fun ctions with sums and using orthogonal collocation method for transform ation of partial differential equations into a system of ordinary diff erential equations. Developed method can be applied in process simulat ion as long as the input concentration and distribution are within the range of experimental values for the kinetics determination. To test the developed method, experiments were conducted on the pilot scale de ep bed filter having total height of Im and diameter of 0.1m. The resu lts show that a very complex process, as is deep bed filtration, can b e successfully described using hybrid neural network.