A Multi-Dimensional Vanadium Redox Flow Battery Performance Model Accounting for Species Crossover
Authors: Moro Federico , Bertucco Alberto , Giomo Monica , Guarnieri Massimo 
Published: February 2020

All-vanadium redox flow batteries (VRFBs) are attracting increasing interests, due to their potentials as a competitive energy storage technology in complementing the electric energy production from intermittent renewable sources in low- to large-scale applications for decarbonized smart grids. Their major advantages consist in power/energy independent sizing that allows for unparalleled discharge times among electrochemical storage devices, but also very long cycle life good efficiency, and room temperature operation. However, a number of challenges need to be tackled to allow successful market penetration, including increase of power and energy densities and minimization of side effects such as pumping losses and shunt currents, and reduction of solution imbalance from species crossover. High-performance materials, improved cell and stack designs, and optimal power management and system control are the tools for achieving such targets [1].
Multiphysics numerical models have an important role in this strategy while reduced models derived from them can allow tailoring the control and monitoring systems for interfacing the electric grid [2]. The 2D multiphysics multi-dimensional finite element model that we are going to present stems from previously developed work enhanced with new features. All the main components of the cell are modeled: the positive and negative current collectors, the porous electrodes, and the ion-conducing polymer membrane. The electric potentials in the electrodes and electrolytes and the ionic species concentrations in the porous electrodes have been chosen as independent variables of the problem.
The model is based on mass, momentum, charge and species conservation. Mass and momentum conservation describe the electrolyte flow in the porous electrodes and across the membrane, whereas charge conservation describes charge transport in the collectors, within the electrodes and across the membrane. In particular, the equilibrium electrode potentials are expressed under reversible thermodynamic conditions and the ionic and electronic potentials are deduced from the ohmic conduction law. The charged species transport in the porous electrodes and across the membrane is modeled by means of the species conservation. The transport of each species takes into account all three transport mechanisms (diffusion, convection and migration) according to the Nernst-Plank equation, whereas the Butler-Volmer equation describes electrochemical activity inside the porous electrodes and a kinetic model the side reactions deriving from crossover [3,4]. The effect of mass transport in the porous electrodes is taken into account by considering the gradients of the species concentrations between bulk and active interfaces inside the porous media. The variations of the vanadium ion concentrations during charge and discharge processes are modeled according to reservoir mass balance. The open circuit cell voltage is derived as a function of the State of Charge (SoC) during charge and discharge cycles and the load voltage is obtained by adding loss voltage drops. The cell runtime and the device round-trip efficiency are also computed. The model can be used in performing cost and convenience assessments [6]. As an example, Fig. 1 shows the effect of species crossover on the cell voltage as a function of the state of charge, both in charge and discharge.

References

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Figure 1