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mass balances in the compartments, electrical phenomena, etc. Several different modelling approaches have been presented so far in the literature, each one addressing in a different way and to a different extent all these aspects. In most cases, the aim was to develop effective design and optimisation tools for ED and RED1 processes. In the present section, the different modelling approaches will be critically presented, starting with a classification into simplified and advanced modelling tools. The first class of process models is characterised by a highly simplified approach based on neglecting most non-ideal phenomena (e.g. DBL, non-Ohmic effects, salt diffusion, water fluxes, etc.) and on the use of lumped parameters equations (i.e. the use of average compartment concentrations to estimate all process variables). Simplified models are commonly adopted for a first rough design of ED equipment, allowing the estimation of figures such as the membrane area required for a given separation problem, and for simplified economic analysis of the process. In this case, empirical coefficients are applied in order to somehow account for all non-idealities, often summarized by a simple current utilisation factor (or current efficiency). The second, and wider, class of process models can be divided into 2 sub-categories: 1) rigorous Nernst–Plank (N-P) or Stefan–Maxwell (S-M) based models and 2) semi-empirical models. In both cases, non-ideal phenomena are accounted for and models typically include mass balance differential equations in order to describe the variation or process parameters along the flow direction. The main difference between the two sub-categories is related to the mathematical description of trans- membrane phenomena. N-P based models (S-M models are even more complex and accurate, with this respect) contain rigorous equations able to almost predictively describe all transport phenomena inside the membrane at the microscopic level (though even in this case some membrane features, such as ions diffusivity, ions mobility, fixed charge density etc. have to be based on empirical information). The simulation is often carried out using Finite Element Methods (or similar approaches) and the process model is practically merged with thermodynamics and mass transfer models, including the description of the fluid dynamics. A limitation of this approach is the very large computational power required to solve the model, which limits the application to very simple channel geometries or to a very small computational domain, thus making the tool unsuitable for whole-stack simulation purposes. 1 Models developed for RED are based on the same physical principles governing the ED process and are, therefore, useful to complete the scenario of modelling tools for electromembrane processes. 50PDF Image | Electrodialysis for water desalination
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