Electrochemical Modeling of PEM Fuel Cells
Authors: Sulzer Valentin , Siegel Jason B , Mohtat Peyman , Srivastava Vishal , Duraisamy Karthik 
Published: December 2020

New alternatives to traditional petrol vehicles are required to reform the transport industry, which currently contributes nearly 30% of all greenhouse gas emissions in North America. One such alternative is Fuel Cell Electric Vehicles. Fuel cells directly convert chemical energy contained in fuels, such as hydrogen, into electricity, and hence provide a hybrid solution that combines the advantages of internal combustion engines and battery. However, the higher cost, lower durability, and lack of fueling infrastructure have typically hindered their commercialization. In order to address the first two challenges, it is crucial to understand the electrochemical behavior of fuel cells via mathematical models. Such models range from lumped models, which provide simple formulas for voltage-current response curves, to full CFD simulations, which can resolve complex physical phenomena in space and time but come at a high computational cost. The aim of this work is to provide intermediate models for proton-exchange membrane (PEM) fuel cells that are as accurate as possible while solvable in real-time.
In this work, we begin with a two-dimensional model of a PEM fuel cell based on Refs. [1] and [2]. The two dimensions are the “along-the-channel” dimension, and the “through-cell” dimension, which is much thinner. This model characterizes mass- and heat-transport related phenomena and hence facilitates water management in cells and membrane electrode assemblies. By nondimensionalizing the model and considering various physically relevant parameter limits, we derive a simplified reduced-order model that accurately reproduces the results of the full model at a much smaller computational cost. The reduced-order model has distributed states along the channel and lumped states in the through-plane dimension.
We compare our final reduced-order model to experimental measurements of spatial channel and GDL water distributions obtained using neutron imaging [3]. We find generally good agreement but identify some innate discrepancies. In order to improve the accuracy of our model, we use the Field Inversion and Machine Learning (FIML) modeling paradigm [4, 5]. This consists of inverse modeling to identify the spatial distribution of model discrepancies, and machine learning to learn the dependence of these fields on other model states and hence allow predictive modeling. A key advantage over purely data-driven methods is that the solutions must always satisfy physical laws enforced by the mathematical model, and so only limited data is required. We apply the FIML methodology to our PEM fuel cell model, and hence learn corrections that reduce discrepancies with the experimental data. We show that improved agreement with the experimental data can be obtained in operating conditions that were not used to train the model.

The authors acknowledge funding from Toyota Motor Engineering and Manufacturing North America.

References

[1] R. Vetter and J. O. Schumacher, “Free open reference implementation of a two-phase PEM fuel cell model,” Computer Physics Communications, vol. 234, pp. 223–234, 2019.
[2] J. B. Siegel, S. V. Bohac, A. G. Stefanopoulou, and S. Yesilyurt. Nitrogen Front Evolution in Purged Polymer Electrolyte Membrane Fuel Cell with Dead-Ended Anode. Journal of the Electrochemical Society (2010) 157(7): B1081-B1093.
[3] J. B. Siegel, D. A. McKay, A. G. Stefanopoulou, D. S. Hussey, D. L. Jacobson, “Measurement of Liquid Water Accumulation in a PEMFC with Dead-Ended Anode,” Journal of The Electrochemical Society (2008), 155 (11) B1168-B1178. DOI: 10.1149/1.2976356
[4] E.J. Parish and K. Duraisamy. A paradigm for data-driven predictive modeling using field inversion and machine learning. Journal of Computational Physics 305 (2016): 758-774.
[5] A.P. Singh, S. Medida and K. Duraisamy. Machine-learning-augmented predictive modeling of turbulent separated flows over airfoils. AIAA Journal (2017): 2215-2227.