A robust model of brackish water electrodialysis desalination with experimental comparison at different size scales

This paper presents a robust analytical model for brackish water desalination using electrodialysis (ED), with prediction of the desalination rate, limiting current density, and total energy use including pumping energy. Several assumptions reduce computation time and accurately model ED system behavior. The predicted desalination rate, limiting current density, and total energy usage agree with measurements across two diverse ED stack designs, differing in total membrane area (0.18 m², 37.1 m²), membrane manufacturers (GE Water, PCA GmbH), and flow channel spacers. The commercial-scale stack was additionally tested with real groundwater, demonstrating that brackish groundwater may be modeled as an equivalent concentration NaCl solution. Sensitivity to the membrane diffusion coefficient, area available for ion transport, level of discretization along the flow channel length, boundary layer and membrane resistances, and water transport are analyzed to guide empirical characterization when higher accuracy is required. No single existing model for pressure drop in the membrane spacers could accurately predict pumping power in both stacks. One model for each stack was found to reasonably approximate pressure drop, however experimental validation of specific spacer designs is recommended. The fully quantitative, parametric description of electrodialysis behavior presented forms a useful tool to design, evaluate, and optimize ED systems.