An empirical carbon degradation reaction model for the high-speed computation in an integrated fuel cell system simulator and its validation by the accelerated stress test data of the commercial fuel cells
Authors: Hasegawa Shigeki , Kim Sanghong , Kageyama Miho , Kawase Motoaki 
Published: December 2024

Abstract

An empirical model to estimate the carbon corrosion rate was developed for a year-long and system-scale durability simulation in an acceptable accuracy and computational time for wide range of the cathode electrode potential, temperature, and humidity. The relative error of the overall carbon corrosion extent during a test pattern at 80 C and 100% RH was 5.5 %. The coefficient of determination (R2) of the increase in the concentration overpotential after 30000 voltage cycles was 6.1 %. The computational time with a standard laptop was 705 times faster than the actual experimental time.

Experimental:

The MEA and GDL of 2nd-generation MIRAI were used for the carbon corrosion rate measurement. The steady-state and transient carbon corrosion rates at 0.2–0.95 V, 20–100 % relative humidity, and 40–80 °C were measured by the experimental apparatus shown in Fig. 1. The cell voltage was controlled following the profile shown in Fig. 2 by potentiostat. H2 and N2 were supplied to the anode and cathode of the single cell with the active area of 25 cm2. The humidity of the supplied gas was controlled by the bubble humidifier. The carbon corrosion reaction rate was calculated from the measured IR absorbance measured at the cathode outlet with an FT-IR. A condenser was installed between the cathode outlet and the FT-IR and the temperature inside was controlled at 5 °C to prevent the water droplets from affecting the IR absorbance.

Modeling methods:

The following assumptions of the entire carbon corrosion reactions in the literatures [1][2] were adopted: The surface fractions of C=O/C–OH/C–H and PtO/PtOH/Pt are determined by the physical models consisting of electrochemical reaction rate and the mass balance; the carbon corrosion rate is calculated by the reaction rate equation from the surface fractions of C–OH and PtOH. In this study, only changes in the C–OH and PtOH surface fractions were considered by the simple empirical models described by Eqs. [1]–[7], Table 1, and Fig. 3. Solving the model equations does not require an iterative calculation for the convergence of the solution and high-speed computation in the integrated system simulator the current authors had presented [3] was expected. The parameters in Table 1 and Fig. 3 were calibrated by the experimental results of the steady state and transient behaviors of CO2 concentration. The model was implemented on MATLAB/Simulink environment as the open loop simulator.

Results and discussion:

The experimental results of the CO2 measurement are shown by the red lines in Figs 4(a)–4(c). The dynamic behaviors of the carbon corrosion rates were as follows: the measured CO2 mole fraction increased rapidly following the stepwise change in the voltage; its peaks were higher when the voltage was stepped up than when stepped down; its peaks were higher when the step width of the voltage was greater; its peaks were higher in cases of the higher humidity and higher temperature. The simulated CO2 mole fractions in a wide range of humidity and temperature are shown by the blue lines in Fig. 4(a)–4(c). The developed simulator reproduced the overall carbon corrosion extent within the relative error of 5.5 % as shown in of Fig. 4(a). The voltage cycle test using the MEA of 2nd-generation MIRAI at 0.95–0.6V, 80 °C, and 100 % relative humidity [4] was reproduced by the developed simulator. Fig. 5 shows the calculated carbon fractional retention after 500, 1000, 3000, 10000, and 30000 voltage cycles. As shown in Fig. 6, the increase in the concentration overpotentials caused by the carbon corrosion was expressed by the empirical function of the correction factors of the mass transfer resistance and agglomerate coefficient in the current authors’ FC stack model [5]. These correction factors were determined to reproduce the experimental polarization curves collected with the MEA of 2nd-generation MIRAI [5]. Fig. 6 shows the experimental and simulated increase in the concentration overpotential. The coefficient of determination (R2) of the increase in the concentration overpotential after 30000 cycles was 6.1 %. The computational speed was 705 times faster than the actual experimental time with a standard laptop (Toshiba dynabook G83/HS; Intel Core i7-1165G7 @ 2.80 GHz / 2.80 GHz CPU; 16 GB RAM).

References:

[1] A. Pandy et al., J. Electrochem. Soc., 160(9), F972–F979 (2013).
[2] N. Macauley et al., J. Electrochem. Soc., 165(6), F3148–F3160 (2018).
[3] S. Hasegawa et al., ECS Trans., 109(15), 15–70 (2022).
[4] K. Amemiya et al., PEFC&E 22 in 242nd. ECS Meeting (Atlanta, GA, US, Oct. 9–13, 2022), I01Z-1692. .
[5] S. Hasegawa et al., ECS Trans., 104(8), 3–26 (2021).

Figure 1