An improved one-dimensional membrane-electrode assembly model to predict the performance of solid oxide fuel cell including the limiting current density
Introduction
Fuel cells are considered attractive alternatives to combustion engines because of their high theoretical efficiency. Solid oxide fuel cells (SOFCs) have special advantages over low temperature fuel cells such as polymer electrolyte membrane fuel cells because they exhibit high conversion efficiency at high temperatures while consuming hydrocarbons directly. Current SOFC research focus areas include reducing the operating temperature and eliminating the need for reformers while utilizing hydrocarbon fuels. In order to achieve these objectives while improving the finite current efficiency and optimizing the design of SOFCs, mathematical models are indispensable.
The limiting current density is an important characteristic quantity in SOFCs. Efforts to predict the limiting current density have not been successful. The high concentration overpotential, determined by the reactants and products transport limitations that reduce the reactants’ concentrations at the three-phase boundary (TPB), is often used to explain the limiting current density. The concentration overpotential depends on the transport properties of the electrodes including their porosities and tortuosities. To predict the measured limiting current density, some membrane-electrode assembly (MEA) models assume anode tortuosities in the range of 10–17. These values are too high, considering that the reported range for porous sintered ceramics is 2–10, and most often below 6 [1]. To avoid making this assumption, Williford et al. [1] introduced surface diffusion effects into Fick’s diffusion model, by adjusting the diffusion coefficients assuming that the competitive adsorption and surface diffusion contribute to the concentration overpotential. The adjusted diffusion coefficient was introduced by combining a gas diffusion coefficient and a surface diffusion coefficient, and was applied to the gas species transport throughout the entire thickness of electrodes. This approach overestimated the diffusion resistance because: (i) the diffusion coefficient adjusted using the surface diffusion coefficient is applied to the gas species transport; and (ii) the adjusted coefficient is applied to the whole electrode even though surface diffusion plays a role only in the vicinity of the TPB, within tens of nanometers.
In this paper, we propose other mechanisms that can explain the cell behavior around the limiting current density. For this purpose, we develop an accurate transport–chemistry interaction model for the MEA, using the dusty-gas model (DGM) to describe transport; a detailed mechanism for the thermochemistry in the anode; and multistep reaction mechanisms to model the charge-transfer reactions at the anode and the cathode surfaces. We show that the model can predict the polarization curve accurately over most of the range of current density, while using the assumption that hydroxyl ion oxidation reaction is the limiting step in the anode electrochemistry model. However, this assumption fails to predict the limiting current density accurately. We explore other rate limiting reactions at high current density and show that hydrogen adsorption at the anode can become sufficiently slow to cause rapid increase of the activation overpotential at high currents. Using a modified approach to the selection of the rate limiting reaction, we obtain better prediction of the limiting current density.
In the following sections, a detailed model to calculate each overpotential and the way to implement them in the simulation code will be described. We will validate the model against available experimental results and propose a new rate-limiting switch-over model to improve the prediction of the limiting current density. The paper ends with conclusions and suggestions for future work.
Section snippets
Model description
The objective of the model is to calculate the polarization curve of a SOFC over the entire operating range of voltage–current density, and for different fuel concentrations. We adopt a one-dimensional approach to model transport–chemistry interactions within the MEA and limit our validation to button cell results. Extension to multi-dimensional models will be attempted in the future. We assumed that the temperature is constant and uniform through the MEA.
The equilibrium potential, Erev, is
Simulation procedure
The model described in Section 2 is used to determine the cell voltage for a given current density, from zero current to the limiting current. The cell potential is expressed as the difference between the equilibrium potential Erev and the sum of all the relevant overpotentials, which depend on the current density.
The solution proceeds as follows.
- (1)
We calculate the equilibrium potential based on the global electrochemical reaction at zero current.
The equilibrium potential depends on the fuel and
Simulation results
Among the numerous 1D MEA models developed to describe the transport–chemistry interaction within the different elements, the model of Zhu et al. [9] is the most detailed one. Our model, while using the same equations, modifies the transport and activation overpotential models to improve their accuracy, as shown below. In order to evaluate the effect of each improvement, we compute i–V curve using a single rate-limiting reaction mode across the entire current density range, similar to that used
Conclusions
The model presented in this paper, which is similar in construction to the model presented in [9], is based on the DGM, detailed heterogeneous thermo-chemistry models, and detailed electrode kinetics models. We corrected the effective Knudsen diffusion coefficient and the permeability values, and showed improved predictive accuracy. We additionally analyzed the possibilities that a different intermediate step in the hydrogen electrochemical oxidation model is rate-limiting and proposed the
Acknowledgements
Won Yong Lee wishes to acknowledge the support of the Samsung Scholarship. The work was also supported by a grant from the MIT School of Engineering.
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