A Pore Network Model of Carbon-Based Electrodes for Redox Flow Batteries
Authors: Gayon Lombardo Andrea , Simon Benedict A. , Taiwo Oluwadamilola O. , Neethling Stephen J. , Brandon Nigel P 
Published: December 2020

Electrodes constitute one of the main components of Redox Flow Batteries (RFBs) since they represent the sites where the electrochemical reaction occurs. The development of optimized electrode microstructures is therefore crucial in the design of the next generation RFBs.[1] For this purpose, there has been a surge in interest to understand the effect of the reactive and mass transport processes occurring within electrodes. Previous authors have introduced pore-scale models which perform direct numerical simulations of the multi-physics processes over reconstructed images of electrode microstructure; however, these models require high processing power and take significant time to converge.[2] In search of computationally inexpensive models the pore-scale detail of the microstructure, pore network models (PNMs) are considered a compelling alternative. [3]

In this work, a computationally efficient PNM is developed to represent the multi-physics processes occurring within porous carbon electrodes at the pore-scale. The model solves the velocity field within the porous matrix and successively couples the mass transport equations (i.e. for convection, diffusion and migration) with the electrochemical reaction (i.e. Butler-Volmer equation). [4] The PNM algorithm is validated on a cubic framework to represent the cathode of a Vanadium Redox Flow Battery (VRFB) operating under discharge conditions at 400 A m-2. These results are compared against the reported values of half-cell potentials of the same system, showing a good fit [5] (Figure 1 (a)). The PNM is subsequently implemented on pore networks extracted from X-ray computed tomography (X-CT) images of two commercial porous carbon electrodes: Toray090 (Figure 1 (b)) and SGL29AA. In both cases, the results show non-uniformity in the concentration and pressure distributions across the electrode when considering the pure convective and diffusive transport processes. The existence of preferred electrolyte travel pathways through the interconnected pores and throats is simulated and visually shown. The migration and reactive processes are subsequently considered and are shown to be influenced by the rate at which the convective/diffusive flow permeates the electrode. These results demonstrate how the rate at which electrolyte is replenished is affected by the interconnectivity between pores: in both carbon electrodes, the regions with low interconnectivity induce slow replenishment, which leads to reactant. This process represents a pore-scale transport limitation that results in the localized reduction of current density upon discharge. Furthermore, the simulation was run for these two electrodes at two pressure drops () and show that, even at relatively high convective flow, the electrolyte follows preferred paths, leading to a non-uniform utilization of the electrode and the existence of “convection-limited ” where almost no electrolyte permeates, (Figure 1(c))

To conclude, this PNM algorithm pore-scale transport processes within the electrode showing the effect of interpore connectivity on electrode utilization. The results suggest that an electrode with higher interpore connectivity would allow an even distribution of electrolyte, reducing transport limitations and reactant starvation. The simulations were performed on a standard single core workstation, and converged in 15 minutes, highlighting the benefits of using a computationally inexpensive pore-scale model.

Chakrabarti, D. Nir, V. Yufit, F. Tariq, J. Rubio-Garcia, R. Maher, A. Kucernak, P. V. Aravind and N. P. Brandon, ChemElectroChem, 4, 194 (2017).

Qiu, A.S. Joshi, C.R. Dennison, K.W. Knehr, E.C. Kumbur and Y. Sun, Electrochimica Acta, 64, 46 (2012).

T. Gostick, M. A. Ioannidis, M. W. Fowler and M. D. Pritzker, Journal of Power Sources, 173(1), 277 (2007).

Gayon Lombardo, B.A. Simon, O.O. Taiwo, S.J. Neethling and N.P. Brandon, Journal of Energy Storage,
24, 100736 (2019).

You, H. Zhang, and J. Chen, Electrochimica Acta, 54(27), 6827 (2009).

Figure 1