Design of electrodialysis desalination plants by considering dimensionless groups and variable equivalent conductivity

Electrodialysis desalination plants, for brackish water, are designed based on different parameters such as feed concentration, current density, and stack construction. Among the various model assumptions, the constancy of the equivalent conductivity of the diluate and concentrate streams is considered a prominent one. In this paper, this assumption is relaxed at different levels and closed-form solutions are obtained to ascertain its effects. It is shown that previously published results can be replicated. Also, a comparison between the lumped and staged model shows that using the inlet flow rate in the lumped model instead of the product flow rate provides more accurate results. Further analysis reveals a non-dimensional number, termed the electrodialytic Biot number, which is the ratio of the total to exit concentration based average cell pair volume resistance. It was found to be physically equivalent to the number of stacks. This provided a clear criterion as to when the lumped model should be used. Specifically, as long as the electrodialytic Biot number is (less than or) equal to 1, the lumped model should be used, otherwise the staged model is a more appropriate choice. It also provides direction for future research. A design chart is also developed to facilitate the calculation procedure.