(239f) Modeling of the Flow Dynamics of High Porosity Filter Media in Depth Filtration

Depth filtration is a separation process that selectively removes either solids or fine liquid droplets from another liquid phase. The analysis of this process is well developed, being widely applied in groundwater flow, oil transport in porous rock and other engineering applications. Specifically, the Kozeny-Carman (KC) model is commonly used to predict the flow dynamics during such processes. In recent work, however, we have found that the KC model cannot be directly applied to the flow through certain poly-disperse particle beds or, more generically, porous materials that have complex pore size distributions. In these cases, the KC model requires both aphysical average particle sizes and/or tortuosities in order to fit our experimental data. In contrast, our modified model introduced two intuitive fitting parameters that describe the cake/pore structure – the fraction of expanded voids (kappa) and the ratio of void sizes (beta) – and was found to dramatically improve predictions of flow through packed spheres. Here we adapt this model to beds comprised of high void fraction materials (diatomaceous earth). 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 KC model and show that this approach is viable for both statically formed and evolving (dynamic) beds. Interestingly, for a best fit, we find that the model predictions require that we ignore the pores that are intrinsic to the individual filter media particles and instead only account for pores formed between particles. Finally, 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 are deposited. 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, and pressure requirements from simple measurements of the size distribution of both the filter media pores as well as the contaminant particles/droplets.