An Open-Source Multiscale Transient Model for Numerical Characterization of Proton Exchange Membrane Fuel Cells

Mathematical modeling often compliments experimental studies and helps gain insight into various physical phenomena occurring in fuel cells that is difficult to obtain otherwise because of the small size of the components and lack of visual access. Many of the existing models for proton exchange membrane fuel cells (PEMFCs) are steady-state. These models cannot be used to study the behavior of PEMFCs during the normal testing process, which exhibits several time scales: a) milliseconds for the electrochemical processes; b) up to minutes for the mass transport; and c) up to hours for the heat transfer [1]. In recent years, various time-dependent models have been developed, e.g., [2-8]. These models, however, have critical drawbacks. Some of them, for instance, were developed for high-temperature PEMFCs and either do not consider water transport in the membrane [3] or neglect electro-osmotic drag [6]. Fuel cell models also commonly use simplified reaction kinetics [2,4-8] and neglect the capacitive current arising from double layer charging and discharging [3-8]. Effective diffusion coefficients for gases in the porous layers of fuel cells are typically computed using the Bruggeman approximation [2,4-6,8], which is not generally suitable for modeling transport phenomena in fuel cells [9]. Microstructure of the catalyst layers is seldom accounted for when estimating oxygen or hydrogen concentration at the reaction sites. In [7], an agglomerate and thin-film sub-model is only implemented for the cathodic side of the cell. In this work, a transient, two-dimensional numerical model of a PEMFC is developed in the open-source framework OpenFCST [10]. The model uses multi-step reaction kinetics [11-14] and accounts for water sorption and transport in the electrolyte, including electro-osmotic drag. Capacitive current due to double layer effects is taken into account in the model in order to increase its accuracy at small time scales. Effective gas diffusion coefficients are computed from the percolation theory [15,16], and a previously developed ionomer-covered catalyst particle sub-model [17,18] is incorporated that accounts for local transport resistances in the catalyst layers. The presented model is used for numerical PEMFC characterization by two common techniques: polarization curve experiments and electrochemical impedance spectroscopy. With this model, correlations between the operating conditions, voltage scan rates, and the magnitude of the polarization curve hysteresis are built in order to help experimentalists choose appropriate testing conditions and avoid the measurement uncertainties associated with the electrolyte hydration transients. The model also enables better understanding of the effect of the cell composition (e.g., catalyst loading and electrolyte content in the catalyst layers, thickness of the membrane and the catalyst layers) and different physical phenomena (e.g., electrolyte hydration, double layer charging and discharging) on the impedance spectrum of PEMFCs. References [1] T. Jahnke et al., J. Power Sources, 304 (2016): 207-233. [2] C. Bao and W. G. Bessler. J. Power Sources 275 (2015): 922-934. [3] X. L. Chen et al., Adv. Mat. Res. 625 (2013): 226-229. [4] P. Choopanya and Z. Yang, Proc. Int. C. Heat. Transf. Fluid Mec. Therm. (2014). [5] A. Jo et al., Int. J. Hydrogen Energ. 40.2 (2015): 1305-1315. [6] H. S. Kim et al., Int. J. Hydrogen Energ. 41.31 (2016): 13657-13665. [7] I. V. Zenyuk et al., J. Electrochem. Soc. 163.7 (2016): F691-F703. [8] A. Verma and R. Pitchumani, J. Fuel Cell Sci. Tech. 12.1 (2015): 011005. [9] B. Tjaden et al., Curr. Opin. Chem. Eng. 12 (2016): 44-51. [10] M. Secanell et al., ECS Transactions 64.3 (2014): 655-680. [11] J. X. Wang et al., J. Electrochem. Soc., 153.9 (2006): A1732-A1740. [12] M. Secanell, Ph.D. thesis, University of Victoria, 2007. [13] J. X. Wang et al., J. Phys. Chem. A, 111.49 (2007): 12702–12710 [14] M. Moore et al., J. Electrochem. Soc., 160.6 (2013): F670-F681. [15] M. Eikerling and A. A. Kornyshev. J. Electroanal. Chem. 453.1-2 (1998): 89-106. [16] P. Dobson et al. J. Electrochem. Soc. 159.5 (2012): B514-B523. [17] P. Wardlaw, M.Sc. thesis, University of Alberta, 2014. [18] M. Moore et al., J. Electrochem. Soc., 161.8 (2014): E3125-E3137. Figure 1

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