Separation of monovalent salts by reverse osmosis modules: A 2D mass transport model based on solution friction theory

Developing a detailed two-dimensional (2D) theoretical framework for mass transport in a spiral wound reverse osmosis (RO) module is crucial to better understand membrane processes. In this study, we developed a 2D mass transport model for a monovalent binary symmetric salt (1:1) using the solution friction theory. Mass and volume balances were used to define cross-flow velocity and salt concentration along the module length. The numerical simulations analyzed local RO module performance, such as fluxes, pressures, axial velocity, mass transfer coefficient, water recovery, and salt rejection. The simulation results demonstrated that hydraulic pressure loss along the module length has a minor effect on a single module's local and overall performance. Conversely, the effect becomes significant when several modules are stacked in a pressure vessel (PV). The performance optimization for brackish water and seawater desalination membranes was conducted using low-salinity feed water (50 mM NaCl). This involved a detailed parametric study on the operational conditions, membrane geometry, and number of module elements in a PV.