Optimal current and voltage trajectories for minimum energy consumption in batch electrodialysis

Abstract

Cost-effective operations of a batch electrodialyzer for removal of salt from a single salt solution are investigated. It is desired to minimize the operating cost for a particular batch. The operating cost for an electrodialysis (ED) stack is comprised of cost related to energy consumption and cost of maintenance of the ED stack. In effective operations of an ED stack, the maintenance cost is a small fraction of the total operating cost. The bulk of the operating cost is therefore proportional to total energy consumption, which is the sum of the electrical energy needed for salt removal and the energy required to pump various solutions through the ED stack. For fixed feed composition and the desired percent salt recovery, the total energy required is influenced by trajectories of current flowing through and the voltage applied across the ED stack and the operating time. In this regard, the following operations are studied: (I) constant current operation, (II) constant voltage operation, (III) constant current operation followed by constant voltage operation, (IV) constant voltage operation followed by constant current operation, and (V) operation with time-variant current and voltage. For arbitrary relations among salt concentration, current utilization, and stack resistance, optimal current and voltage trajectories that lead to minimum energy requirement are identified for each of the five operations. It is established analytically that operation V is superior to operations III and IV, which in turn are superior to operations I and II. Numerical illustrations reveal that the performance differences in these operations are enhanced as the percent salt recovery is increased.