Mathematical modelling of vanadium-based redox flow batteries

Abstract

Electrochemical energy storage could facilitate the integration of intermittent renewable sources, such as wind and solar, allowing for a more stable, reliable and flexible electrical grid. Vanadium redox flow batteries (VRFBs) are an attractive technology due to their capability to decouple power and energy, however they have displays limited deployment, which has been limited by cost. Hybrid-type redox flow batteries such as a Regenerative Hydrogen-Vanadium Fuel Cell (RHVFC) could allow to overcome the cost dependency of all-vanadium systems with regards to the vanadium requirements. Modelling and simulation appear as an indispensable tool to support the design and optimisation of these systems, saving time and reducing costs. On the other hand, physical-based models can capture the dependency of the cell performance on the operating conditions and physico-chemical properties. This thesis investigates the performance behaviour of RHVFC by means of mathematical representations of the system. Firstly, the conventional approach involving unit cell modelling for VRFBs is studied and implemented to understand the interplay of different phenomena and the possible similarities with the system of interest. Then, a unit cell model for a RHVFC is proposed, giving special attention to the equilibrium and kinetics equation used in describing the limiting electrode. A complete Nernst equation is derived to estimate the equilibrium potential, while a Butler- Volmer kinetics including the effect of concentration of protons and mass-transport limitations is used to describe the cathodic kinetics. This model is then modified to include the crossover phenomena, by means of a simplified treatment of transport of species in the cation-exchange membrane by means of diffusive, convective and migration mechanisms. The transport of species across the membrane controls the loss in capacity of the cell when continuous cycling operation is tested. This model allowed for the characterisation of a laboratory scale cell of a hydrogen-vanadium system and the simulation of its performance, where extensive experimental data of single-cycle charge-discharge potential, power density and cycling performance was studied. It was observed that the crossover effect was not fully captured for a unit cell model, reproducing the trends during continuous operation but showing some discrepancies with the experimental results. These results indicated the need for a more complex model, such a continuum approach, to describe the transport of species across the electrodes and membrane. Therefore, a time-dependant model considering a Poisson-Nernst-Planck one-dimensional approach to describe the cathode and membrane of a RHVFC was implemented. Initial results allowed to assess the evolution of concentration and potential profiles across the model domains, capturing the interfacial behaviour that appears due to the selectivity of the membrane. These interfacial phenomena produced a steep change in the value of ionic potential and concentrations across a narrow thickness of nano-meters. The model was used to indicate the dependency of crossover fluxes of species across the membrane when the applied current density increases. The mass-transport limitations effects on the cell performance, which were strongly affected by the transport parameters of species, were displayed by the model. This initial crossover model is the first part of a more extensive study of crossover, which will include the testing of the model capability in predicting cell potential over continuous operation, as well as the assessment of alternative modelling approaches such a Donnan-Nernst-Planck model.