A CFD-Informed Surrogate Modelling Framework Linking Spacer-Scale Simulations to Process-Scale Reverse Osmosis Modelling

Abstract

The global water shortage has increased the importance of seawater desalination technologies, with reverse osmosis (RO) emerging as the most widely used process. However, the performance of RO membrane modules is significantly influenced by the trade-off between concentration polarisation and pressure drop, both of which are strongly affected by the geometry and arrangement of spacers. In this study, a computational fluid dynamics (CFD)-based surrogate model was developed to quantitatively capture the influence of spacer geometry on RO performance and subsequently integrated into module- and process-level simulations. Process-level economic optimisation was performed as a demonstration of the proposed framework. Water and salt fluxes at the membrane surface, as well as the pressure drop, were obtained from three-dimensional CFD simulations at the unit-cell level. These results were generalised into regression-based surrogate models and integrated with process models at the module and stage levels. Subsequently, optimal operating conditions were determined to minimise freshwater cost. The analysis showed that freshwater cost converged within a narrow range of approximately 0.62–0.63 $/m³, depending on the spacer geometry, while the resulting process configurations varied significantly (e.g., total module counts ranging from 1,981 to 2,193). Through this framework, spacer effects can be explicitly incorporated into process-level models, where they are typically treated as fixed constants (e.g., mass transfer coefficients and friction factors) in simplified mathematical models.