An empirical/theoretical model with dimensionless numbers to predict the performance of electrodialysis systems on the basis of operating conditions

• Empirical predictive models for ED/EDR were developed using dimensionless numbers.
• Stanton number was a function of Peclet and dimensionless voltage in ED/EDR.
• Presented models can be utilized in large-scale applications.
• Selectivity of the ED/EDR process was defined in a new form based on Stanton number.

Among the different technologies developed for desalination, the electrodialysis/electrodialysis reversal (ED/EDR) process is one of the most promising for treating brackish water with low salinity when there is high risk of scaling. Multiple researchers have investigated ED/EDR to optimize the process, determine the effects of operating parameters, and develop theoretical/empirical models. Previously published empirical/theoretical models have evaluated the effect of the hydraulic conditions of the ED/EDR on the limiting current density using dimensionless numbers. The reason for previous studies' emphasis on limiting current density is twofold: 1) to maximize ion removal, most ED/EDR systems are operated close to limiting current conditions if there is not a scaling potential in the concentrate chamber due to a high concentration of less-soluble salts; and 2) for modeling the ED/EDR system with dimensionless numbers, it is more accurate and convenient to use limiting current density, where the boundary layer's characteristics are known at constant electrical conditions. To improve knowledge of ED/EDR systems, ED/EDR models should be also developed for the Ohmic region, where operation reduces energy consumption, facilitates targeted ion removal, and prolongs membrane life compared to limiting current conditions. In this paper, theoretical/empirical models were developed for ED/EDR performance in a wide range of operating conditions. The presented ion removal and selectivity models were developed for the removal of monovalent ions and divalent ions utilizing the dominant dimensionless numbers obtained from laboratory scale electrodialysis experiments. At any system scale, these models can predict ED/EDR performance in terms of monovalent and divalent ion removal.

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