Mathematical modelling of water filtration

Abstract

Saline water can be desalinized with the use of reverse osmosis, wherein a mixture of water and dissolved salt molecules is forced by a high pressure pump through a semi-permeable membrane, preventing the bigger salt molecules from getting through the holes of the membrane but allowing the tinier water molecules to do so. The downside to this process is the build-up of salt (also known as membrane fouling) at the semi-permeable membrane due to the osmotic pressure applied, which restricts the flow of water and essentially decreases the efficiency of the system. To tackle this problem, the project aim is to develop a mathematical model to determine the build-up of salt concentration in a water filter. In visualizing the flow of water better, the overall design and efficiency of the system can be improved. The water filtration problem is first re-written in non-dimensionalised form as requiring the solution of its Partial Differential Equation (PDE) subjected to its boundary conditions. The problem is then solved using Finite Volume Method (FVM) and programmed up and plotted on MATLAB.