A feasibility study is carried out theoretically for the separation of different ionic species of the same charge sign via repeated permeation through ion-exchange membranes in a multi-stage electrodialysis system. In order to avoid depletion and accumulation of ionic species in the retentate and the permeate streams, reflux lines on both sides of the system return the non-product streams from each stage to the previous stage.
Two types of cascades are considered. In the first type, called the ‘cross type’, there are two center cells, and the reflux streams from the second set of cells are mixed and fed jointly to the center cells. In the second type, the ‘straight type’, there is one center cell, and the depleted and concentrated reflux streams from the second stages are mixed and fed to the center stage.
A set of generalized equations for the concentration of each ionic species at each stage is derived for both cascade types. For ion-exchange membranes with perm-selective coefficients for ionic species 2 compared to ionic species 1,
T21, of 2. 25, numerical calculations are carried out for systems with 6, 10, 14 and 18 total cell compartments. The separation is predicted for two ionic species of the same charge and identical concentration of 0.1 mol/
l. For the constant current of 30 A/m
2, the final mole fractions of species 1 in the depleted stream for 18, 14, 10 and 6 cell compartments in the crosstype system are 0.93, 0.86, 0.76 and 0.63, respectively, and 0.73, 0.71, 0.68 and 0.63 for the straighttype system.
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