Upscaling of Reactive Mass Transport through Porous Electrodes in Aqueous Flow Batteries

Porous electrodes (PEs) are an important component of modern energy storage devices, such as lithium-ion batteries, flow batteries or fuel cells. Their complicated multiphase structure presents a considerable challenge to modeling and simulation. In this paper, we apply the volume-averaging method (VAM) as an efficient approach for the evaluation of effective macroscopic transport parameters in PEs. We consider the transport of electro-active species coupled to heterogeneous Butler-Volmer type reactions at the electrode surface. We identify the characteristic scales and dimensionless groups for the application to aqueous flow batteries. We validate the VAM-based model with direct numerical simulation results and literature data showing excellent agreement. Subsequently, we characterize several simplified periodic PE structures in 2D and 3D in terms of hydraulic permeability, effective dispersion and the effective kinetic number. We apply the up-scaled transport parameters to a simple macroscopic porous electrode to compare the overall efficiency of different pore-scale structures and material porosity values over a wide range of energy dissipation values. This study also reveals that the Bruggeman correction, commonly used in macroscopic porous electrode models, becomes inaccurate for realistic kinetic numbers in flow battery applications and should be used with care.