Modelling and simulation of deep-bed filtration: a stochastic compartmental model

Abstract To gain insight into the performance of a deep-bed filter, it is essential to determine the spatial distribution of suspended particles in the bed as a function of time. More often than not, a filtration process behaves stochastically rather than deterministically; therefore, a stochastic compartmental model is proposed to simulate the concentration dynamics of suspended particles in the liquid and solid parts over the different sections of the filter. In this study, the filter bed is divided into an arbitrary number of compartments in the direction of flow. The model yields the distribution of suspended particles along the bed at any time t , including those exited from the bed up to that time, and the mean and variance of the distribution. The parameters of the model are estimated by fitting the model to the experimental data. The reasonably good agreement between the simulated results and experimental data ensures the applicability of the present model.

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