Analysis of a model for the operation of a vanadium redox battery

Although the vanadium redox battery (VRB) has recently attracted considerable interest as an energy storage technology, it has a relatively poor energy-to-volume ratio and a system complexity compared with other technologies; however, modelling can assist in optimizing cell and stack design. This paper analyzes a 2D time-dependent single-phase isothermal model for the operation of a single cell in a VRB. Unlike in all previous work, asymptotic methods are used to determine the characteristic current density scale in terms of operating conditions and cell component properties. Also, the analysis reveals that the fluid mechanics decouples from the electrochemistry, at leading order; an asymptotically reduced model is then proposed which preserves the original geometrical resolution. This approach is recommended for accurate and computationally efficient VRB stack models, as has been achieved for polymer electrolyte fuel cells; this will be a prerequisite for the use of modelling in stack design and thence large-scale commercialization of the VRB. Finite-element methods are used to compute results for the 1D steady state high-stoichiometry limit; although an idealized case, it is recommended for the in-situ experimental acquisition of VRB electrokinetic data that can then be used for the model when applied under more general operating conditions.