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- Conflict of Interest
- In relation to this article, we declare that there is no conflict of interest.
- Publication history
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Received April 14, 2026
Accepted July 1, 2026
Available online November 25, 2026
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This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/bync/3.0) which permits
unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
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A CFD-Informed Surrogate Modelling Framework Linking Spacer-Scale Simulations to Process-Scale Reverse Osmosis Modelling
https://doi.org/10.1007/s11814-026-00782-4
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 signifcantly infuenced
by the trade-of between concentration polarisation and pressure drop, both of which are strongly afected by the geometry
and arrangement of spacers. In this study, a computational fuid dynamics (CFD)-based surrogate model was developed to
quantitatively capture the infuence 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 fuxes 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 confgurations varied signifcantly (e.g.,
total module counts ranging from 1,981 to 2,193). Through this framework, spacer efects can be explicitly incorporated
into process-level models, where they are typically treated as fxed constants (e.g., mass transfer coefcients and friction
factors) in simplifed mathematical models

