Mathematical and optimization modelling in desalination: State-of-the-art and future direction

The growing water demand across the world necessitates the need for new and improved processes as well as for a better understanding of existing processes. This level of understanding includes predicting system performance in scenarios that cannot always be evaluated experimentally. Mathematical modelling is a crucial component of designing new and improved engineering processes. Through mathematically modelling real life systems, we gain a deeper understanding of processes while being able to predict performance more effectively. Advances in computational capacity and the ease of assessing systems allow researchers to study the feasibility of various systems. Mathematical modelling studies enable optimization performance parameters while minimizing energy requirements and, as such, have been an active area of research in desalination. In this review, the most recent developments in mathematical and optimization modelling in desalination are discussed with respect to transport phenomena, energy consumption, fouling predictions, and the integration of multiple scaling evolution on heat transfer surfaces has been reviewed. Similarly, developments in optimization of novel reverse osmosis (RO) configurations have been analyzed from an energy consumption perspective. Transport models for membrane-based desalination processes, including relatively less understood processes such as nanofiltration and forward osmosis are presented, with recent modifications to allow for different solutes and solutions. Mathematical modelling of hybrid systems integrated with RO has also been reviewed. A survey of the literature shows that mathematical and optimization modelling of desalination processes is an exciting area for researchers in which future scholarship includes coupling of renewable energy systems with desalination technologies, as well as more advanced descriptions of fouling evolution other than that of cake filtration in membrane-based processes.