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An electrochemical reduced order model (ROM) has been developed in this study to simulate the performance of syngas-fueled anode-supported SOFCs with coupled bulk chemical reactions and multi-species gas diffusion in the electrodes. Experimental V-I curves with syngas fuel were used to validate the model to ensure its high fidelity. The model was used to investigate the effects of fuel composition and temperature on the electrochemical performance of the cell, chemical reaction rate and concentration distributions of gaseous species across the anode. The results show that H2 electro-oxidation dominates the overall cell performance, and that CO contributes to the performance indirectly via water gas shift (WGS) reaction, especially at low CO:H2 ratio and low current densities. Increasing the temperature enhances the performance of syngas-fueled SOFCs by increasing the rates of total electrochemical oxidation and the WGS reaction. The present work provides fundamental knowledge and framework for future performance simulations of large-scale and more complex syngas-fueled SOFC systems.

Solid oxide fuel cells (SOFCs) offer high efficiency pathways to producing electricity from fuels.14 Systems are being developed for a variety of applications, operating on a range of fuels from hydrogen to natural gas to syngas.59 Computational models that can accurately describe the gas phase reactions, electrochemistry, and the heat and mass transfer within SOFC cells and modules are an invaluable tool for the design of efficient and cost-effective systems.1017

Models described in the open literature can be generally grouped into three categories - classical semi-empirical models, full-order models (FOM) and reduced-order models (ROM). The categories differ in how they manage the trade-off between accuracy and computational effort. Semi-empirical models estimate the cell voltage by subtracting the overpotentials resulting from activation, ohmic and concentration polarizations from the Nernst potential.18 Three major simplifications are typically used: 1) the Butler-Volmer equations are approximated by either linear or Tafel equations; 2) the concentration overpotential is correlated to gas diffusion using empirical or semi-empirical relationships; and 3) the model ignores cell geometry. These approximations simplify the analysis, but have several drawbacks: 1) coupling between the gas diffusion and activation/concentration losses is ignored, which is particularly problematic for systems using syngas fuel; 2) the exchange current density at the triple-phase-boundary (TPB) is more complicated for multi-step elementary reactions, also problematic for systems in which chemical reactions such as reforming or water-gas-shift are occurring; and 3) the limiting current density is obtained by an empirical relation, which means the effects of cell and stack design are not always captured accurately.

Full order models were first introduced in the 1990s.19 These approaches include all the relevant physical and chemical processes in the cell, including gas diffusion through the porous electrodes, mass and momentum conservation in the channels, charge transport within electrodes and the electrolyte as described by Ohm's law, and charge-transfer kinetics as described by the Butler-Volmer equation. Early versions described the H2 electro-oxidation reaction using global reactions by a finite volume method.19,20 More recent FOMs have incorporated the microscale elementary reactions occurring near TPBs with cell performance.2123 FOM approaches offer the highest resolution and accuracy (short of complete 3-D models), but are more computationally expensive than semi-empirical approaches, which could be an issue when applied to 3D SOFC stack simulations.

Reduced order models attempt to retain much of the accuracy of FOMs while reducing the computational burden. This is accomplished in several ways. A common approach is to simplify the physics, such as the gas diffusion or the electrochemical reactions. Specifically, the diffusion could be simplified to a single dimension, typically in the flow direction2427 or anode-thickness direction.2831 This captures some of the physics due to 1D gas diffusion and heterogeneous reactions at the solid/gas interfaces, while significantly reducing the computational effort required. Another more widely used approach to reducing the model order is by projection-based mathematical reduction, in which a set of data is mapped into sub-set with certain accuracy. One interesting ROM developed in this way by PNNL32 uses a sub-model to predict the performance and response of a SOFC stack. The sub-model was constructed using a simple empirical relationship generated from sampling a limited number of input parameters, ranking of input parameters, constructing relations between inputs and outputs, and studying sensitivity of inputs in different regions. Such an approach can be used to rapidly explore performance under specific scenarios to aid in the design process. Here, we use the first approach to developing ROMs, but instead of simplifying the diffusion procedure, we lowered the order of model by reducing the electronic/ionic charge transfer and the electrochemical reactions from the 3D electrode domains to the 2D electrode/electrolyte interface. Meanwhile, the electrolyte is treated as an interface between anode and cathode by a pure ionic resistor. Since the concentration of gas species varies significantly along the direction of gas flow and thickness, the 3D diffusion feature in the electrode domains is kept in this study for further development of stack model.

ROMs have been used successfully to explore the competition between different physical processes. Friedrich et al.33,34 developed a ROM that includes detailed H2-oxidation elementary reactions for coupled charge-transfer and surface chemistry in the anode, and gas diffusion in the flow direction and cell thickness direction were decoupled and calculated separately. Another ROM developed by Campanari et al.35 simulated the combined electrochemical oxidation of CO and H2 (relevant to this work) with the assumption that exchange current density for CO oxidation is 0.4 times the H2 oxidation without validation and the diffusion through the thickness was significantly simplified. Further progress can be made in several areas to increase the utility of ROMs, particularly for hydrocarbon or syngas fuels. First, additional experimental validation is needed to further demonstrate the usefulness of ROMs. Second, ROMs can be extended to explore the competition between direct electrochemical oxidation of fuel and indirect oxidation of fuels through chemical conversion to form hydrogen. This second issue is of particular interest in practical systems where the relative importance of internal reforming or water-gas-shift reactions can vary through the stack.

In this paper, we address these issues by developing a ROM for anode-supported SOFCs. We begin with a derivation of the ROM, and validate it using experimental data from the literature. We then explore the impact of syngas composition and temperature on the relative importance of direct and indirect oxidation modes. This paper is the first of a series of papers, aiming to lay the ground for systematically investigating the effects of pressure, temperature-field coupling and flow patterns on the performance of commercial-size planar SOFC stacks operated on syngas fuel.

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Jin, X., Ku, A., Verma, A., Ohara, B., Huang, K., & Singh, S. (2018). The Performance of Syngas-Fueled SOFCs Predicted by a Reduced Order Model (ROM): Temperature and Fuel Composition Effects. Journal Of The Electrochemical Society, 165(10), F786-F798. doi: 10.1149/2.0511810jes