Multiscale Homogenization of Pre-treatment Rapid and Slow Filtration Processes with Experimental and Computational Validations
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.
KeywordsHomogenization theory Multi-scale perturbation Porous media filtration Computational and analytical modelling
The lab-scale rapid pressure filter setup employed in this study is funded by Singapore-MIT Alliance for Research and Technology (SMART) while the lab-scale slow pressure filter setup is funded by the internal core funding from the Nanyang Environment and Water Research Institute (NEWRI), Nanyang Technological University (NTU), Singapore. The first author is also grateful to NTU for the 4-year Nanyang President Graduate Scholarship (NPGS) for his PhD study.
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