Multiscale Homogenization of Pre-treatment Rapid and Slow Filtration Processes with Experimental and Computational Validations

Abstract

In this paper, we summarize on an approach which couples the multiscale method with the homogenization theory to model the pre-treatment depth filtration process in desalination facilities. By first coupling the fluid and solute problems, we systematically derive the homogenized equations for the effective filtration process while introducing appropriate boundary conditions to account for the deposition process occurring on the spheres’ boundaries. Validation of the predicted results from the homogenized model is achieved by comparing with our own experimentally-derived values from a lab-scale depth filter. Importantly, we identify a need to include a computational approach to resolve for the non-linear concentration parameter within the defined periodic cell at higher orders of reaction. The computational values can then be introduced back into the respective homogenized equations for further predictions which are to be compared with the obtained experimental values. This proposed hybrid methodology is currently in progress.