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only convection-diffusion phenomena inside the channels. In this case, simulations took 3-8 h by using a workstation with 96 GB RAM. Therefore, building up a comprehensive simulation tool for an electromembrane process would be a very hard task and the direct simulation of the complete system by one single tool adopting the N-P approach appears to be almost impossible with currently available computing facilities. As an alternative to the rigorous N-P-based models, several “semi-empirical” models have been developed, based on a mix of mass and energy balance equations, equations linking electrical and physical variables, and some empirical equations, which are able to predict the voltage drop over the cell pair and, in a more or less rigorous way, a number of physical phenomena characterising the system. This will be discussed in the next section. 5.2 Semi-empirical models In the present section we have grouped all the models that renounce to resolve the Nernst–Planck equation, but simulate IEMs by using only macroscopic, experimentally accessible, properties (such as transport numbers, Ohmic resistance, salt permeability, osmotic permeability), and allow the channel geometry to be taken into account in a more realistic way. In most cases, semi-empirical models are based on a system of algebraic and differential equations divided into: 1) thermodynamic and electrical equations, leading to the calculation of cell pair potential and resistance, electric current, etc.; 2) mass balance equations accounting for the variation of flow rates and concentrations along the main flow directions and strictly linked with mass transfer equations; 3) transport equations providing mass flux of ions and water through the membrane, on the basis of empirical or separately calculated values for quantities like the Sherwood numbers; 4) other equations allowing the calculation of macroscopic performance parameters such as power requirements, pumping losses, efficiencies, etc., on the basis of empirical or separately calculated values for quantities like the friction factors. Figure 18 schematically represents a unit cell pair with indication of mass fluxes and of inlet-outlet variables typically adopted in semi-empirical models. 55PDF Image | Electrodialysis for water desalination
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