Fractional Calculus-based Modelling of Membrane Filtration

Abstract

The aim of this work was to model the deep bed and cake filtration process using an alternative approach based on a fractional calculus (FC). The considered experimental data in this study were extracted from published studies. The data used in FC models contained two inputs - initial concentration and time, and volume of filtrate as an output. The FC kinetic constants were tuned by fitting the experimental and predicted data through Dragonfly algorithm implemented in MATLAB programming software. The performance of the developed models was assessed using different metrics by comparing the experimental against the predicted data. The developed fractional model with nth order presented very acceptable metrics in comparison to the pseudo-nth order and displayed strong potential for estimating the volume of filtrate.

Keywords

• fractional calculus
• dragonfly algorithm
• membrane filtration