A Mathematical Model of the External Circuits in a Bipolar Membrane Electrodialysis Stack: Leakage Currents and Joule Heating Effect

Leakage currents existing in a bipolar membrane electrodialysis (EDBM） stack cause loss of coulombic efficiency, ranged from approximately 0.9% to 12%, and create undesirable heat that impairs its operation. A model for predicting leakage currents in a EDBM stack was developed by considering the electrochemical process as an electrical analog circuit. Current and potential balance equations are used to define the equivalent network, and differential calculus is used to solve these equations. Leakage currents model is validated with experimental and simulated results. On this basis, leakage currents and Joule heating effect in a pilot-scale EDBM stack are analyzed. The results reveal that leakage currents in external circuits are distributed symmetrically around the membrane stack and are significantly affected by the number of cell pairs, current density, and element resistivity. Moreover, Joule heating effect in the external circuit in the stack is quantitatively analyzed and the temperature effect is dominated by the slot closed to the electrode cell in the acid compartment. This was most pronounced (raised by 12.18 ℃ in 0.3 s) during the termination stage. Using these findings, EDBM stacks can be improved and the optimal spacers and a more reasonable process can be designed, which could boost the development of EDBMs.