(596a) Modeling of the Flow Dynamics through Incompressible Porous Media in Solid-Liquid Filtration

Solid-liquid filtration is a long-standing engineering practice and has been widely used in the chemical, process and mineral industries. Current models are semi-empirical in nature, thus they require significant experimental and/or computational resources in order to determine the empirical quantities. In contrast, in this work we provide a model to predict the dynamic behavior for both the liquid and solid phase of a filtration process without the requirement of empirical parameters. Instead, our model relies solely on the to-be-captured particle size distribution of contaminants as well as the pore size distribution of the filtration media. Our new algorithm is capable of describing filtration based on both “’steric” capture of contaminants as well as capture within dead-end pores in the material. Here we we show the performance of this model in modeling beds comprised of high void fraction materials (diatomaceous earth) that is used for the removal of multi-modal mixtures of contaminant. By formally accounting for the complex pore size distribution, we predict flow dynamics that are much closer to our experimental results than the predictions of the traditional Kozeny-Carmen (KC) model and show that this approach is viable for both statically formed and evolving (dynamic) beds. In an effort to understand the relationship between flow dynamics and pore size distribution more fully, we built a dynamic filter cake model that continuously modifies the pore size distribution as contaminants (polydispere spheres) are deposited. In short, the predicted flow dynamics of this new model match the dynamic experimental results remarkably well, setting the stage for a priori prediction of filtration times, flow-rates, particle capture, and pressure requirements from simple measurements of the size distribution of both the filter media pores as well as the contaminant particles/droplets.