Development of a generalized mathematical model for two-stage reverse osmosis desalination systems

Abstract

This study presented a generalized mathematical model for a two-stage reverse osmosis (RO) system based on mass balance, the solution-diffusion model, and film theory. The model is user-friendly and can be customized for any membrane regardless of the manufacturer. A set of non-linear equations was solved in MATLAB to calculate the system arrangement, performance parameters, and the required feed pressure for the desired recovery ratio by incorporating membrane characteristics and design parameters. Actual data from a two-stage RO system were employed for model validation against ROSA software results. To optimize energy conservation, equal recovery rates are applied to both stages, resulting in lower calculated feed pressures than those obtained using ROSA software. The study reveals a strong agreement between the simulation results and those obtained from the ROSA software and alignment with the membrane manufacturer's recommendations, making the model a reliable tool for evaluating the system before implementation.