Polarization curve performance modeling

This chapter is devoted entirely to performance models of conventional catalyst layers (type I electrodes), which rely on reactant supply by gas diffusion. It introduces the general modeling framework and employs it to discuss the basic principles of catalyst layer operation. Structure-based models of CCL rationalize distinct regimes of performance, which are discernible in polarization curves. If provided with basic input data on structure and properties, catalyst layer models reproduce PEFC polarization curves. Consistency between model predictions and experimental data will be evaluated. Beyond polarization curves, performance models provide detailed maps or shapes of reaction rate distributions. In this way, the model-based analysis allows vital conclusions about an optimal design of catalyst layers with maximal catalyst utilization and minimal transport losses to be drawn. 

Validation is performed in two steps first an experimental polarization curve, obtained with a fixed inlet gas flow rate, is compared with the calculated values, thus allowing the determination of some unknown parameter values (model calibration). Afterwards, three polarization curves, obtained at constant fuel and oxygen utiliza-... 

All impedance measurements should begin with measurement of a steady-state polarization curve. The steady-state polarization curve is used to guide selection of an appropriate perturbation amplitude and can provide initial hypotheses for model development. The impedance measirrements can then be made at selected points on the polarization curve to explore the potential dependence of reaction rate constants. Impedance measurements can also be performed at different values of state variables such as temperature, rotation speed, and reactant concentration. Impedance scans measured at different points of time can be used to explore temporal changes in system parameters. Some examples include growth of oxide or corrosion-product films, poisoning of catal5dic surfaces, and changes in reactant or product concentration. 

Omran et al. have proposed a 3D, single phase steady-state model of a liquid feed DMFC [181]. Their model is implemented into the commercial computational fluid dynamics (CFD) software package FLUENT . The continuity, momentum, and species conservation equations are coupled with mathematical descriptions of the electrochemical kinetics in the anode and cathode channel and MEA. For electrochemical kinetics, the Tafel equation is used at both the anode and cathode sides. Results are validated against DMFC experimental data with reasonable agreement and used to explore the effects of cell temperature, channel depth, and channel width on polarization curve, power density and crossover rate. The results show that the power density peak and crossover increase as the operational temperature increases. It is also shown that the increasing of the channel width improves the cell performance at a methanol concentration below 1 M. 

The total cell current is equal to the ionic current in the electrolyte, Jq. The voltage required to perform complete conversion of jo from ionic into electronic form is t]o (Figure 23.1) (see [3] for more details). The polarization curve of the CL is the equation r]o jo) and the task of modeling is to rationalize this dependence. 

The influence of CO poisoning at the anode of an HT-PEFC was investigated by Bergmann et ul. [28]. The dynamic, nonisothermal model takes the catalyst layer as a two-dimensional plane between the membrane and gas diffusion layer into account. The effects of CO and hydrogen adsorption with respect to temperature and time are discussed in detail. The CO poisoning is analyzed with polarization curves for different CO concentrations and dynamic CO pulses. The analysis of fuel-cell performance under the influence of CO shows a nonlinear behavior. The presence of water at the anode is explicitly considered to take part in the electrooxidation of CO. The investigation of the current response to a CO pulse of 1.31% at the anode inlet showed a reversible recovery time of 20 min. 

The cell-level numerical models can directly predict the fuel-ceU performance, that is, the power output The cell performance can be evaluated in two respects one is the overall polarization curve that plots the cell voltage as a function of the current density, and the other is the local fuel-cell performance as measured... 

To verify these predictions the measurements of DMFC polarization curves in conditions -C A , J 1 were performed (Kulikovsky et al., 2005b). The results are shown in Figure 4.32(b). Comparing Figures 4.32(a) and 4.32(b), we see that the experimental polarization curves reproduce, remarkably well, the two main features of the model curves the drastic change in the slope at a current density J, where the jumper forms (large diamonds in Figure 4.32(b)) and the constancy of the product A°J J s for A° = 8,4 and 2 are related nearly as 1 2 4. 

The performance of a PEMFC can be expressed through the analytical formulation of the polarization curve. Simultaneous estimation of the parameters through analysis of the polarization curve can be helpful in diagnosis of PEMFC degradation and identification of degradation mechanism. Some models and testing methods have been developed to characterize PEMFC performance through polarization curve analysis [25,26]. 

Prediction of the Steady-State Polarization Curves Figure 3.18 shows the predicted and experimentally tested polarization curves for the test cell across the full range of toluene concentrations encompassed by the model. The top curve (solid black) is the baseline polarization curve (i.e., no toluene contamination). Curves below that indicate decreasing performance as the toluene concentration increases. 

Once the mathematical problem has been formulated and solved, the numerical results should be compared to experimental results. In PEM fuel cell modeling, experimental data of the polarization curve are normally used for comparison reasons. The polarization curve is a measure of the performance of the PEM fuel cell. There are two types of performance measures, a full cell polarization curve and a half-cell polarization curve. In many cases, which is also the case in CO poisoning, mass transport is simulated in only half of the cell. One of the most widely used experimental datasets for CO poisoning was collected by Lee et al. [96]. In their study, they investigated the performance of the cell exposed to CO and studied the behavior of the performance depending on the electrode used. Baschuk and Li [21] compared their numerical results to the results from Lee et al. [96]. The comparison is shown in Figure 7.7 and Figure 7.8. 

The numerical model developed by Karimi and Li [109] is used to understand the effects of CO2 poisoning on the performance of a fuel cell stack. The result of their model in the form of polarization curves is shown in Figure 7.26. 

Numerical models of the contamination of the anode by CO2 and H2S are not as abundant as their counterparts for CO poisoning. The numerical models found in literature, which take into account the presence of carbon dioxide, are focused on understanding the reverse water-gas shift reaction (WGSR) and its effects on the performance of the cell. The effect of hydrogen sulfide presence on the polarization curve and liquid water distribution in the cell is also studied numerically. It is found that with trace amounts of H2S, the cell performance can be dramatically decreased. The effects of H2S poisoning can be sometimes very severe and cannot be reversed, unlike their counterparts of CO poisoning. 

The characterizations which we shall present below are the plot of the polarization curve, impedance spectroscopy response to current value steps and responses to large amplitude current sweepings. These are all non-intrusive characterizations on the scale of the component (or of each cell), and are intended to characterize its electrical behavior in the static and dynamic states in real operating conditions. These characterizations will enable us, on the one hand, to appreciate the performances of the electrolyzer, and on the other, if we cross them, to parameterize the different models presented above. 

The choice of electrochemical techniques that can be implemented in a tribocorrosion test and the development of relevant models for the interpretation of the tribocorrosion mechanism are determined by the mechanical contact conditions being continuous or reciprocating. Electrochemical measurements can be performed with both types of tribometers. However, to be implemented under conditions that allow the interpretation of results, some methods require stationary electrochemical conditions, at least prior to starting up the measurements. In the case of continuous sliding, a quasi-stationaiy electrochemical surface state can often be reached, and all the electrochemical techniques available for corrosion studies (polarization curves, impedance spectroscopy, electrochemical noise,...), can be used. On the contrary, when reciprocating contact conditions prevail, the interpretations of experimental results are more complex due to the non-stationary electrochemical conditions. Measuring techniques suitable for the recording of current or potential transients will be used preferentially (Mischler et al., 1997 Rosset, 1999). 

The performance portrait of the fuel cell is the polarization curve illustrating how much of the open-circuit potential has to be spent in order to generate a given load current. The product of the cell current density by the available cell potential gives the cell power density, that is, power generated by a unit cell active area. Understanding the contribution of every transport and kinetic process in the cell to the potential loss, is a key task of performance modeling. 

There is a great variety of approaches to fuel cell performance modeling. The simplest approach used in system simulations deals with the semiempirical polarization curves of the cell or stack under investigation. Such curves are obtained by fitting a simple analytical model equation to measured data. This philosophy is very useful in the optimization of FC systems with numerous peripheral components (blowers. 

The goal of DFT modeling is to understand the chain of elementary reaction events in the electrochemical conversion and to calculate the rate constants for these steps. The reaction mechanism and the rate constants, obtained from DFT, are then used to establish and parameterize time-dependent mass balance equations for the adsorbed/desorbed species. The steady-state solution of the surface coverage equations provides the conversion function, which can be used in the simplified current conservation equation in the CL model. The solution of the CL performance model yields the CL polarization curve, which can be used in the fuel cell or stack model. The chain of information transfer looks schematically like... 

FIGURE 4.6 (a) Effect of the Nafion weight fraction, 7 /, in CCL with uniform composition on the fuel cell voltage, Eceih evaluated at different values of the current density, yo. Experimental data taken from Passalacqua et al. (2001) (crosses) are shown for comparison. (b) Comparison of polarization curves, calculated in the model of composition-dependent performance, with experimental data of Uchida et al. (1995a,b). 

FIGURE 4.9 Polarization curve calculated with a CCL model that accounts for the full coupling between porous structure, liquid water accumulation, and performance. The dashed lines represent Hmiting scenarios corresponding to the ideally wetted state and the fuUy saturated state. Bistability occurs in the transition region. (Reprinted from Electrochim. Acta, 53(13), Liu, J., and Eikerling, M. Model of cathode catalyst layers for polymer electrolyte fuel cells The role of porous structure and water accumulation. 4435 1446. Copyright (2008), Elsevier. With permission.)... 

The coupled hierarchical model was evaluated by comparison with experimental data of Suzuki et al. (2011) and Soboleva et al. (2011). Both of these studies provided experimental data on CL structure as well as electrochemical performance, which were used to parameterize the model. The pore size distributions of the catalyst layers are depicted in Figure 3.42. Figure 4.12a shows polarization curves from both experimental studies compared to the curves obtained from the hierarchical model. Experimental trends are reproduced within the model. It is evident that flooding of the GDL is responsible for the knee in fuel cell voltage at high current density. 

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