Mathematical modelling of water filtration

Abstract

Water is a vital resource for life and is essential for many aspects of daily living. Due to the lack of fresh water in the world, desalination has been vital to convert sea water into fresh water. However, during desalination, salt buildup near the semi-permeable membrane reduces efficiency. The main objective of this study is to analyze the buildup of salt concentration along the membrane during water filtration. This project aims to design a mathematical model for water filtration through a semi-permeable membrane. A mathematical formulation will be derived to solve a convection-diffusion problem. The model is developed using FVM, where the solution domain is partitioned into many control volumes, and partial differential equations (PDE) are converted into a set of algebraic equations that can be solved numerically using MATLAB.