Start-stop model

Equations (11), (12), and (13) can be solved for three unknowns 0e,Power, e.Load, and / s,cath with reference to (ps an = 0 (set arbitrarily) when the difference in electrolyte phase potential between anode and cathode electrodes is negligible, which is a good assumption at a very low current density. However, anode and cathode electrolyte phase potentials can be differentiated by adding two more equations, namely 

Carbon corrosion current density can be further reduced by controlling the cell voltage at a low level during the start-stop process.25,27 Neglecting /qer, Eq. (12) is simplified to 

Measured Start-Stop Degradation Rates at 1.2 A/cm2 Normalized to H2/02 Front Residence Time on a 50 cm2 Cell at 80 °C, 66% RHj, 150 kPa.lhs, Compared to the Modeled 

Anode Pt loading (mgpt/cm2) Carbon support Degradation rate (mV/cycle/s) Gain Experiment Model 

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THE START-STOP MODEL OF CAVE CALCITE PRECIPITATION... 

Modeling of Membrane-Electrode-Assembly Degradation in Proton-Exchange-Membrane Fuel Cells - Local H2 Starvation and Start-Stop Induced Carbon-Support Corrosion... 

In this chapter, we will review the fundamental models that we developed to predict cathode carbon-support corrosion induced by local H2 starvation and start-stop in a PEM fuel cell, and show how we used them to understand experiments and provide guidelines for developing strategies to mitigate carbon corrosion. We will discuss the kinetic model,12 coupled kinetic and transport model,14 and pseudo-capacitance model15 sequentially in the three sections that follow. Given the measured electrode kinetics for the electrochemical reactions appearing in Fig. 1, we will describe a model, compare the model results with available experimental data, and then present... 

The two-dimensional, coupled kinetic and transport model can also be used to simulate start-stop processes. Figure 14 plots cathode potential and carbon corrosion current distribution at three instants when the H2/02 front passes through 10, 50, and 90% of anode flow path during the start process. As H2 displaces air in the anode flow-field, the size of the power source increases and the load size decreases accordingly. The balanced current density becomes larger, causing higher carbon corrosion current density. 

Figure 15. Predicted accumulated carbon loss distribution along anode flow-field over a complete start-stop cycle for a controlled start-stop experiment as shown above the plot at 80 °C, 101 kPaabs, 66% RHjn, and residence time of 1.5 s based on anode void volume (including flow-field and diffusion medium). The model predicts nearly symmetric carbon loss at anode inlet and outlet because the stop process essentially mirrors the start process by switching H2 and air periodically at anode inlet.

Therefore, for equal H2/air-front residence times, the pseudo-capacitive model would suggest lower rates of carbon-support oxidation, i.e., lower rates of C02 formation for the stop process if compared to the start process, which is consistent with on-line C02 measurements of the air exiting the cathode flow-field during H2/air-front start-stop events, as shown in Fig. 16. 

Here / is the current density with the subscript representing a specific electrode reaction, capacitive current density at an electrode, or current density for the power source or the load. The surface overpotential (defined as the difference between the solid and electrolyte phase potentials) drives the electrochemical reactions and determines the capacitive current. Therefore, the three Eqs. (34), (35), and (3) can be solved for the three unknowns the electrolyte phase potential in the H2/air cell (e,Power), electrolyte phase potential in the air/air cell (e,Load), and cathode solid phase potential (s,cath), with anode solid phase potential (Sjan) being set to be zero as a reference. The carbon corrosion current is then determined using the calculated phase potential difference across the cathode/membrane interface in the air/air cell. The model couples carbon corrosion with the oxygen evolution reaction, other normal electrode reactions (HOR and ORR), and the capacitive current in the fuel cell during start-stop. 

Figure 19. Predicted carbon loss distribution along anode flow-field channel over a complete H2/air-front start—stop cycle using the pseudo-capacitance model in comparison with one-dimensional, normalized mass activity from Fig. 17. The pseudo-capacitance value used in the model is obtained from AC-impedance measurements as described in references (42, 43).

Gu W, Carter RN, Yu PT, Gasteigta- HA (2007) Start/stop and local H2 starvation mechanisms of carbon corrosion model vs. experiment. ECS Trans ll(l) 963-973... 

In order to deal with the problem of carbon corrosion due to start-stops, it is necessary to understand the critical parameters associated with the start-stop process, as well as the critical specifications that need to be placed upon the materials. What is required to do this is to have a validated model of carbon corrosion and its dependence on the critical parameters temperature, pressure, flow rate, and composition. Such a model has been developed, to the first order, by Meyers and Darling [63] in which the potentials driving the reaction are linked to the spatial concentrations of oxygen and hydrogen in the flow channels. 

The actual lifetime of a fuel cell in a vehiele undergoing driving and start/stop cycles may or may not be accurately predieted by these protoeols. More studies are needed to link the AST results to the aetual lifetime, ineluding identifying failures, understanding failure mechanisms, and modeling data to prediet the lifetime of products. 

The impact of carbon-support materials on the two most severe cathode carbon corrosion cases in automotive operation, i.e., start/stop and local anode starvation, can in general be determined by a simple kinetic model on the basis of (3), as was suggested previously in the literature (Reiser et al. 2005, Meyers and Darling 2006). However, it needs to be stressed that the predictions of such models very strongly depend on the fidelity of the kinetic parameters required to describe the COR and the OER. Unfortunately, these are not very well known, so the rates of the COR and the OER which have been used for previous models (see Meyers and... 

Darling 2006) are very different from our measurements as shown in Fig. 19. Therefore, in general, it is advisable to measure the relevant COR and OER kinetics which are used for the start/stop and local starvation models discussed next. 

Fundamental model analyses incorporating the measured carbon corrosion kinetics were developed for conditions of start/stop or local starvation. The combination... 

Before we could start to model the nucleation and growth of the ZnO nanopartides we needed to determine the reaction kinetics. This was realized by stopped-flow measurements with high time resolution (ms). The solid concentration was derived from PSDs determined by absorbance measurements. Thereby we used the effect that prior normalization the spectra provide information on the particle concentration [14, 68]. From the initial reaction rates in dependence of the zinc acetate precursor concentration c(Zn " ) the reaction rate constant was determined for T = 20 C to be 51.6 1.1 m kmor s (R = 0.997). The overall reaction kinetics are described by... 

Various life-cycle models may be utilized in defining the start, stop, and process activities appropriate to the life-cycle stages. Figure 2.2 shows three of the best practice life-cycle models used in systems engineering. These are known as... 

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