hrvatski

Dinamički matematički model procesa dubinske filtracije

Deep bed filtration is commonly used for clarification of dilute suspensions of particles ranging in size about 0.1 to 50 micro m. Suspension carrying solid particles of different sizes is flowed through the porous bed of defined geometrical characteristics. It has been found that sizes of suspended particles and their distribution are very important physical parameters influencing deep bed filter efficiency. During the filtration process the bed porosity decreases and interficial velocity increases due to particle"s accumulation in filter bed. Mathematical model of deep bed filtration consists of balance and kinetics equation. Model is developed with assumption that plug flow model can approximate flow of suspension through the bed. Further assumption is that deposition kinetics is function of local suspension"s particle distribution and locally deposited particle distribution. In that way experimental data are obtained, that consists of the local suspension and deposit particle distribution values together with the local rate values. Distributions are approximated with standard Logarithm-Normal distribution function. Rate distribution parameters are formally dependent on the parameters that define suspension and deposit distribution and that relation is established using the generalised regression neural network (GRNN). Dynamical model of the deep bed filtration process can be solved for a given boundary conditions, approximating distributions with sums, and using orthogonal collocation method for transforming partial differential equation in the system of ordinary differential equations with initial conditions. Developed method can be applied for simulation of the process as long as the input concentration and distribution are in range of experimental values for the kinetics determination. The experiments were run using quartz- water suspension with constant concentration of 25 mg/l and filtration rate of 8 m/h. Experimental runs were conducted changing bed depths from 0.2 to 0.6 m. Suspensions were prepared using four quartz samples with different particle size distributions. Filter media was spherical polymer grains with initial porosity of 0.35. The results show that very complex process such as deep bed filtration can be successfully described combining usual analytical methods and neural network.

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