(749c) Modeling of the Pressure Drop Across Polydisperse Packed Beds in Depth Filtration

Authors: 
Zhang, S., University of Pittsburgh
McCarthy, J. J., University of Pittsburgh
Depth filtration is the process of separation that involves flow of solid-liquid (or liquid-liquid) mixture through a fixed (packed) bed of porous (or particulate) materials. The flow through such a device is commonly modeled using the so-called Kozeny-Carman equation in order to predict the pressure drop during the filtration process. In this work we assess the predictive power of this approach for systems operated at low Reynolds numbers and comparably high pressure drops (on the order of several bar). We find substantial agreement between model and experiment only for systems that result in well-ordered particle packings (i.e., those that have a tight distribution of void sizes). Dramatic disagreement is observed for particle beds that exhibit wide void size distributions. The cake structure is primarily influenced by the size ratio of the particles that compose the cake; specifically, particles with a size ratio where Rsmall/Rlarge is larger than 0.5 do not typically form an ordered pore structure. We propose a modified approach, based on a bimodal void distribution, by introducing two factors: the fraction of expanded voids (kappa) and the ratio of void sizes (beta). Discrete Element Method (DEM) simulations of the packing of poly-disperse spheres are used to analyze the bed structure for different size ratios of binary mixtures. Based on the simulation results, void size distributions of the simulated beds can be extracted by means of a radical Delaunay tessellation. The void structure is quantified in terms of probability density functions of pore and constriction sizes. By fitting the simulated void size distributions to a bimodal (two normal) distribution, the factors kappa and beta can be calculated based on different mean void sizes and probability density. The predicted flow dynamics from the modified equation with factors extracted from the simulation results are found to be much more similar to the experimental flow rates than those calculated using the unmodified Kozeny-Carman equation.