A Novel Circuit-Based Model of Electrodialysis Avoiding the Use of Empirical Parameters
Authors: Ledingham Jack , Yip Ngai Yin , Sedransk Campbell Kyra , Campbell Alasdair 
Published: February 2024

Electrodialysis (ED) is an emerging membrane-based electroseparation technology for desalination, water treatment, and ionic pollutant removal. Compared to conventional separation methods such as reverse osmosis, ED offers several advantages including lower energy consumption, higher selectivity, and lower fouling propensity. Further, coupling ED with renewable electricity sources enables it to be far more sustainable than competing technologies (reverse osmosis and evaporation) across a wide range of scales. However, the design and operation of ED systems are still challenging due to the complex interactions between the membrane, the electrolytes, and the applied electric field. To address this issue, advanced process models are required to provide accurate predictions of ED performance and to guide system optimisation. Existing ED models tend to be highly dependent on empirical parameters and thus are only applicable to a narrow range of process conditions and require several data sets to validate. Therefore, in this work we aimed to develop a glabal model of ED without reliance on experimental training data.
Herein, we present a novel circuit-based model for ED. The model considers the membrane stack as a series of resistors, where the membranes and electrolytes are represented as separate resistive elements. Crucially, the membrane resistance is calculated directly from the electrostatic interaction between ions and fixed charge groups, rather than from manufacturer data or empirical sub-model. This allows for consideration of the ion identity and electrolyte concentration when determining the membrane resistance. Ohm's law is used to relate the applied voltage and stack electrical resistance to a current density, which is then converted to a flux using Faraday's law and current efficiency model. Historically, current efficiencies are calculated from transport numbers provided from membrane manufactures and assumed constant. A novel model for the current efficiency has been developed by us in which the current efficiency is a function of the trans-membrane concentration difference. A space-wise material balance is employed to determine the concentration profile along the stack, while a time-wise material balance tracks the changes in reservoir concentration for recirculating batch experiments.
To validate the model, desalination experiments were conducted on a PC BED 1-4 recirculating batch system and compared the model predictions with experimental data. The model demonstrated excellent matching on a range of variables across a range of conditions, including current density, current efficiency, and ion concentration.
The proposed model has various applications in ED process modelling, optimisation, and economic analysis. It can be used to evaluate the impact of different design parameters such as membrane thickness, membrane charge density, and flow rate on system performance as well as to optimise these.
In summary, the circuit-based model presented in this work offers a robust and versatile tool for ED process simulation and optimisation, which can be used for effective and efficiency desalination and water treatment. Two major advancements presented include models for the membrane electrical resistance and current efficiency, which have historically been considered constant.

Figure 1