Advances in Mathematical Modelling, Mathematical Optimization and Simulation in Water Treatment

The ever-growing global need for clean water coupled with rampant pollution by emerging persistent contaminants, necessitates the use of advanced water treatment processes such as adsorption, advanced oxidation processes (AOPs) and membrane separation. These technologies, while effective, are often hindered by their reliance on sophisticated equipment, specialized materials, and complex chemical reactions, resulting in high costs and operational difficulties. Unlike previous studies, which primarily focused on technological aspects of the processes, this study takes a broader approach by analyzing of the entire process, proposing an innovative solution through the application of mathematical modelling, mathematical optimization and simulation techniques to enhance efficiency of water treatment processes. Mathematical modelling employed the Freundlich adsorption isotherm in adsorption, first order reaction kinetics in Advanced Oxidation Processes (AOPs) and Darcy – Hagen – Poiseuille equation, Carman – Kozeny equation, Nernst – Planck equation and solution – diffusion transport equation in microfiltration, ultrafiltration, nanofiltration and reverse osmosis respectively. The Newton’s method, direct differentiation and Simplex method was utilized in the optimization. The subsequent mathematical models and optimization techniques were applied to real world processes and simulated in C – programming language. The simulation results demonstrated optimality for the required adsorbent mass in adsorption, residence time and mass of catalyst in AOPs and effect of feed to pressure ratio on the operating flux in membrane separation processes. The findings of the study illustrate mathematical modelling and optimization and simulation as reliable approaches in the design and effective operation of advanced water treatment processes.