where Ede,spc is the specific desalination energy, t is the time of operation, Cind and Cinc are the equivalent concentrations of the diluate and the concentrate at the cell inlet, Coutd and Coutc are the concentrations of the diluate and the concentrate at the cell outlet, L is the equivalent conductivity of the salt solution, ram and rcm are the area resistances of the anion- and cation-exchange membrane, D is the cell thickness, X is the current utilization, Qdell is the diluate flow rate in a cell, Acdl is the cell pair area, Nceu is the number of cell pairs in a stack, and Vpro is a volume product water.
Eq. (28) shows that the energy dissipation due to the resistance of the solutions and membranes increases with the current density. The electrical energy for a given resistance is proportional to the square of the current, whereas the salt transfer is directly proportional to the current. Hence, the power necessary for the production of a given amount of product increases with the current density. However, the required membrane area for a given capacity is decreasing with the current density as illustrated in Fig. 15, which shows the total costs of desalination, the membrane costs, and current density-related costs as a function of the current density. The figure shows that at a certain current density, the total desalination cost reaches a minimum. However, in a practical application, the operating current density must be lower than the limiting current density.
The operation of an electrodialysis unit requires one or more pumps to circulate the diluate, the concentrate, and the electrode rinse solution through the stack. The energy required for pumping these solutions is determined by the volumes of the solutions to be pumped and the pressure drop. It can be expressed by
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