The vanadium redox flow battery: An asymptotic perspective

Asymptotic methods are used to analyze a time-dependent two-dimensional (2D) model for the operation of a vanadium redox flow battery-an energy storage technology that has attracted much attention recently. The model takes into account mass, momentum, and charge conservation involving a total of seven ionic species in two porous electrodes that are separated by a proton exchange membrane and attached to external recirculating tanks. In particular, we demonstrate a self-consistent asymptotic reduction of the original model. From this, we identify the presence of concentration boundary layers in each porous electrode at its interface with the membrane, and are able to explain the linear evolution in time of the inlet concentrations of the reacting ionic species-an assumption used in earlier models but never justified. The results of the asymptotic model, which ultimately requires only the numerical solution of four coupled nonlinear ordinary differential equations, are found to compare favorably with those of the original 2D transient problem, which involves 11 coupled nonlinear partial differential equations and two algebraic relations. The solution of the fully reduced asymptotic model is found to require around 300 times less computational time than that of the original model.