TITLE:
A Finite Element Stiffness Method for Modeling Solute Transport in Reverse Osmosis Membranes
AUTHORS:
Farah Najdawi
KEYWORDS:
Advection-Diffusion Model, Nernst-Planck Model, Finite Element Method, Stiffness Matrix Method, Mesh Sensitivity Analysis, Net Driving Force Pressure
JOURNAL NAME:
Engineering,
Vol.17 No.10,
October
22,
2025
ABSTRACT: With increasing freshwater demand and rising water scarcity, reverse osmosis (RO) has become a key method for seawater desalination; however, accurately modeling RO remains challenging due to its complex, nonlinear processes. This study develops a new mass transport model by coupling the Advection-Diffusion Model (ADM) with the Solution-Diffusion Model (SDM), and it is solved by using the Finite Element Method (FEM) with the linear stiffness approach. The extended ADM-SDM framework combines both advective and diffusive transport forces and calculates osmotic pressure. The model is validated against COMSOL simulations and commercial RO module data, finding accurate prediction of solute concentration and permeate flux, with errors as low as 0.7% for SW30-2514 and 2.6% for SW30-4021 compared to commercial RO module data. Unlike the traditional SDM, the extended ADM-SDM framework captures advective transport effects, leading to improved permeate flux estimation while maintaining 100% salt rejection. The numerical stability was further validated by mesh sensitivity analysis, which also demonstrated the robustness and effectiveness of the FEM stiffness implementation by showing that outlet flux errors successfully converged to zero across refinements.