Mathematical Model to Study Vanadium Ion Crossover in an All-Vanadium Redox Flow Battery

The performance of an all-vanadium redox flow battery (VRFB) is affected by many factors, among which the crossover of the vanadium ion through the ion-exchange membrane plays an important role in distribution of the electrolyte concentration along the flow direction. In this study, a mathematical isothermal model is developed to investigate the effect of crossover of the vanadium ion on distributions of the electrolyte concentration, activation overpotential profiles, and cell potential. The chemical reactions of redox reaction between different oxidation states of vanadium ions are included in this model. The model is validated by fitting the charging and discharging curves with experimental data. The concentration distributions of different vanadium ions with and without crossover effect are presented and compared. Results show that distributions of concentration and potential are more uniform due to the balance for VO2+ being generated from VO2+ and reduced by V2+. Moreover, the Coulombic efficiency of the VRFB is reduced from 0.971 to 0.892. The voltage is decreased by 0.05 V at the SOC of 0.5 due to vanadium ion crossover.