One Dimensional Mathematical Modelling of the All-Vanadium and Vanadium/Oxygen Redox Flow Batteries

A simple stationary, isothermal one-dimensional (1-D) volumetric model for the all-vanadium redox flow battery (VRFB) and the vanadium/oxygen system (VORFB) is presented in this work. The model incorporates species conservation equations along with an advection term to describe the concentration changes in the porous electrodes. In addition, a complete Nernst equation, which accounts for proton concentrations in the VRFB is also included to improve the cell voltage prediction without using any arbitrary fitting contact voltage. In addition, the model is coupled with the electrochemical reaction kinetics of the vanadium species and the gaseous oxygen. The 1-D model is validated against experimental data from the literature and the ability of the model to predict the cell performance is investigated. The cell voltage prediction compares surprisingly well with higher-dimensional models. This enhanced 1-D model is also capable of capturing the cell performance at different electrolyte flow rates, especially evidenced by the polarization curves. The effect of the electrolyte flow rate and the carbon porous electrode design employed for the vanadium half-cells on the overall cell performance are also detailed for the VORFB. The results form an important basis to determine the optimum electrolyte flow rate range and the design modifications for carbon porous electrode as to further improve the performance. Some possible improvements for both of the systems and future works are suggested.