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

Abstract

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%.

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

“…22 In this formulation of the migration term, the dilute solution approximation is used and thus the ionic mobility in the electrolyte, is represented using the Nernst-Einstein equation:…”

“…Also, it's important to note that the viscosity values are assumed to be constant. 22 The main source for change in vanadium concentrations is the applied or drawn current. The source terms are specified in each half cell individually, giving the source terms for V(II) and V(III) in negative half-cell as…”

“…22 Using this model, the effects of each species transport mechanism on crossover and capacity fade were investigated. Accordingly, several strategies to mitigate the capacity fade have been proposed, such as tailoring membrane properties 26 and running VRFB under constant pressure 27 or asymmetric current density 28 mode depending on the membrane properties.…”

“…22 Among these, only the diffusivity of V 2+ across the membrane is changed compared to the previous study in order to achieve closer agreement for the ionic transport through the membrane and to compensate the dimensional limitations of this model. More detailed information about the model including governing equations, initial and boundary conditions, and constant parameters can be found in our group's earlier studies.…”

“…More detailed information about the model including governing equations, initial and boundary conditions, and constant parameters can be found in our group's earlier studies. 22,26,28 …”