Modeling of Ion Crossover in Vanadium Redox Flow Batteries: A Computationally-Efficient Lumped Parameter Approach for Extended Cycling

In this work, we have developed a zero-dimensional vanadium redox flow battery (VRFB) model which accounts for all modes of vanadium crossover and enables prediction of long-term performance of the system in a computationally-efficient manner. Using this model, the effects of membrane thickness on a 1000-cycle operation of a VRFB system have been investigated. It was observed that utilizing a thicker membrane significantly reduces the rate of capacity fade over time (up to ∼15%) at the expense of reducing the energy efficiency (up to ∼2%) due to increased ohmic losses. During extended cycling, the capacity of each simulated case was observed to approach an asymptote of ∼60% relative capacity, as the concentrations in each half-cell reach a quasi-equilibrium state. Simulations also indicated that peak power density and limiting current density exhibit a similar asymptotic trend during extended cycling (i.e., an ∼10–15% decrease in the peak power density and an ∼20–25% decrease in the limiting current density is observed as quasi-equilibrium state is reached).