Dynamic modeling of long-term operations of vanadium/air redox flow battery with different membranes

The crossover rate of vanadium ions through the membrane and oxygen transport determines the capacity of vanadium/air redox flow battery due to the ion diffusion and the side reactions and the electro-migration and convection. The battery's high reaction temperature also impacts the diffusion coefficient. In this paper, the electrolyte concentration change is predicted, and battery performances with different membranes, including Nafion 115, CMS, and CMX, in different working conditions are compared using the developed dynamic model: Mass balance for each reaction ions and reaction temperature are studied by Fick's Law and Arrhenius Equation to predict; the voltage change of the battery can be calculated by the Nernst Equation. The partial differential equations are applied to predict the performance of the battery. It is observed that with a low crossover rate, the capacity of the battery using CMS is almost unchangeable for over 400 h, while with Nafion 115 the capacity decreases around 2% in each cycle steadily. However, Nafion 115 with the lowest inner resistance achieves the highest efficiency (0.85), while CMS is 13% lower and CMX is 27% lower than N115, respectively. The V²⁺ concentration in contact with the electrode and catalyst is also predicted to monitor this working efficiency model.