A multiple state stochastic model for deep‐bed filtration

A one‐parameter stochastic model has been developed for the prediction of dynamic pressure drop in a deep‐bed filter. The model is based on a finite‐state and discrete‐time Markov chain method whereby the pressure drop in a deep‐bed filter can be estimated at discrete time intervals. The proposed model is simpler than the stochastic birth and death models available in literature. The bed is assumed to pass through different states of porosity during the filtration and it is spatially lumped in each state. For pressure drop calculation, the Carman‐Kozeny equation is used in conjunction with the Payatakes‐Tien‐Turian model. Model equations are simple and can be easily solved on a personal computer. The theoretical results agree well with the plant data as well as with the available experimental data.