Hierarchical modelling of electrodialysis desalination process

In recent years, thanks to the development of ion exchange membranes (IEMs) manufacturing industry, Electrodialysis (ED) is spreading as a viable alternative to the more common membrane desalination processes. Therefore, many research efforts have been recently devoted to studying this process both via experimental and modelling activities. In the present work a novel mathematical model for ED was developed using a multi-scale approach. This method allows to build a hierarchical simulation tool that is able to gauge the impact of all the phenomena involved in the process. The lower-hierarchy model describes the behaviour of the elementary unit of an ED stack, namely cell pair. This model is based on differential mass balance equations and accounts for transport phenomena including salt migration and diffusion as well as water osmosis and electro-osmosis. In addition, Kirchhoff’s law together with the Nernst’s law for the non-Ohmic voltage drop was used to determine the electrical behaviour of the equivalent circuit. Interestingly, the model makes also use of CFD correlations from a lower scale as input data in order to predict the effect of concentration polarization. In the higher-hierarchy model the whole stack was described, allowing the simulation of multiple cell-pairs together with the end electrode compartments. Again, CFD correlations were used to include the contribution of pumping loss in the overall energy consumption. The model was implemented in PSE gPROMS Modelbuilder. Several simulations were carried out by changing flow arrangement (co-current, counter-current and cross-flow), operating conditions and stack features. Results showed that the model is able to reliably predict the effect of these variables on the performance of the ED unit investigated. In particular, the model was found capable of estimating the distribution of current density/voltage and concentration along the channels. In addition, stack resistance, overall and specific energy requirements were computed. Collected findings suggest that the model proposed might be a powerful tool to improve and optimise ED process.