Multicomponent mass transport modeling of water desalination by reverse osmosis including ion pair formation

Reverse Osmosis (RO) is one of the main membrane technologies currently used for the desalination of seawater and brackish water to produce freshwater. However, the mechanism of transport and separation of ions in RO membranes is not yet fully understood. Besides acid-base reactions (i.e., including the H⁺-ion), at high concentrations, the salt ions can associate and form ion pairs. In this study, we investigate how to include the formation of these ion pairs in the extended Donnan steric partitioning pore model. We study the desalination of a water source where three ion pairs can be formed (NaCl, MgCl⁺, and MgCl₂) and also include water self-dissociation and the carbonate system. The model assumes infinitely fast reactions, which means that the participating ions are locally at chemical equilibrium with one another. A square stoichiometric reaction matrix composed of active species, moieties, and reactions is formulated. As the final constraint equation, we use the charge balance. The model predicts profiles in concentration, flux, and reaction rates across the membrane for all species and calculates the retention per group of ions. Ion pair formation has an influence on the fluxes of individual ions and therefore influences the retention of ions.