A Transient Vanadium Flow Battery Model Incorporating Vanadium Crossover and Water Transport through the Membrane

This paper presents a 2-D transient, isothermal model of a vanadium redox flow battery that can predict the species crossover and related capacity loss during operation. The model incorporates the species transport across the membrane due to convection, diffusion, and migration, and accounts for the transfer of water between the half-cells to capture the change in electrolyte volume. The model also accounts for the side reactions and associated changes in species concentration in each half-cell due to vanadium crossover. A set of boundary conditions based on the conservations of flux and current are incorporated at the electrolyte|membrane interfaces to account for the steep gradients in concentration and potential at these interfaces. In addition, the present model further improves upon the accuracy of existing models by incorporating a more complete version of the Nernst equation, which enables accurate prediction of the cell potential without the use of a fitting voltage. A direct comparison of the model predictions with experimental data shows that the model accurately predicts the measured voltage of a single charge/discharge cycle with an average error of 1.83%, and estimates the capacity loss of a 45 cycle experiment with an average error of 4.2%.