Macrohomogeneous approach to a two-dimensional mathematical model of an industrial-scale electrodialysis unit

In this manuscript a novel way of mathematical modelling of the electrodialysis process, based on a macrohomogeneous approach, is introduced. It enables an industrial-scale unit to be described without unrealistic simplifications, thus providing information about the local distribution of various physical quantities inside this apparatus based on the operational parameters studied. The two-dimensional model presented takes into consideration a spatial variation of the effective flow cross-sectional area of the geometry of a real electrodialysis unit. The key feature of this macrohomogeneous model is the anisotropy of individual macrohomogeneous domains described by corresponding balance and transport partial differential equations. A classical Nernst-Planck model is used to describe NaCl transport inside the unit. The proposed model approach is experimentally validated for a medium degree of water desalination (up to 40 %). By means of this model the principal consequences of the non-uniform hydrodynamics in the electrodialysis unit are demonstrated. It is shown that non-uniform distribution of diluate in the individual diluate compartments results in (a) a significant decrease in overall process efficiency due to an increase in the value of parasitic current and (b) a concentration of the electric current in a narrow area. The latter aspect, in combination with locally lowered linear velocity of the solution, may lead to an enormous increase in temperature and subsequent deterioration of the membranes. Such a situation is, therefore, highly dangerous from the point of view of process reliability.