Mathematical modelling and numerical simulation of reverse-osmosis desalination

The reverse osmosis membrane module is a fundamental component of a desalination system, as it determines the overall performance of the desalination plant. The proportion of clean water that can be recovered through this process is often limited by salt precipitation, a critical factor affecting sustainability. In this work, we present a comprehensive computational model to study the complex interplay between flow, transport, and precipitation processes in reverse osmosis (RO) membranes, which collectively influence water recovery. The membrane is described using a reactive porous interface model with dynamically evolving porosity and permeability, allowing us to capture scaling and clogging effects. We outline the mathematical framework that governs the dynamic evolution of the filtration process, requiring only a few initial parameters (such as feed properties and reaction kinetics). We then discuss the implementation of our model in the widely used open-source finite-volume library OpenFOAM® , and demonstrate its applicability through numerical tests in representative scenarios. The results illustrate how this model can predict the decline in membrane flux caused by the accumulation of precipitated solids. The proposed formulation provides a unified approach to describe the interlinked mechanisms—fluid dynamics, solute transport, chemical reaction, scaling, and fouling—that collectively impact membrane performance.