Anode exchange current density

The electrochemical conversions due to the cathodic and anodic exchange current densities are... 

The cathode exchange current density is typically four orders of magnitude greater than the anode exchange current density and supported by Choi and Berning in Ref. 24 and 25. The anode side is therefore limiting the reaction and dominates the activation overpotential. 

Then, a deeper analysis has been made by performing a parameter estimation, allowing an analysis of the local anode activation effects with variable local fuel utilization and temperature the anode exchange current density of every sector has been the estimated parameter, and its strict relation to the local fuel utilization of every sector (Paragraph 3.1) has been outlined. 

Nevertheless, the activation contribution to the cell voltage sensitivity to FU is neglected in this part of the analysis because of its small effect of the voltage drop [16,21]. In the next Paragraph 6, dealing with parameter estimation of some terms of the cell polarization model, the anode exchange current density will be estimated and a correlation with the local fuel utilization will be outlined. 

The anode exchange current density has been considered as a fitting parameter. For the estimation of its first attempt value in the fitting analysis, the equation (19) has been considered. 

Estimation of the Local Anode Exchange Current Density... 

The parameter estimation procedure involved the anode exchange current density, considered in the expression of the anode activation overpotential (equation (18)). As already noticed, in literature there are some expressions which describe the anode exchange current (equations (19) and (20) according to these equations, this parameter should be significantly affected by the fuel utilization values, and the aim is to outline how the distribution of the local fuel utilization (that is, the distribution of fuel) inside the generator affects the activation of the reaction at the anode side in the various sectors. 

The procedure of parameter estimation consisted in the evaluation of the values of the anode exchange current density in each sector of the generator, in order to obtain its distribution inside the stack. In the estimation, the local values of fuel utilization evaluated in... 

Figure 27. Distribution of the estimated values of the anode exchange current density.

Figure 28. 95% confidence region for the anode exchange current density estimation. 

It is possible to notice a symmetric trend centered on the row 6 for the Power Leads side and on the row 7 for the Ejectors side. The behaviour for the two side is nearly the same lower value of anode exchange current density at the boimdary rows of the generator, and higher values for the center sectors. 

This behaviour is the direct and logic consequence of the distribution of fuel utilization inside the generator. There are high values of fuel utilization at the boundaries of the generator while at the center of the generator the values of fuel utilization are lower. Therefore, the activation of the anode reaction is favoured at the center rows, while the kinetic is reduced at the boundary rows. This behaviour is expressed by the values of the anode exchange current density. 

The 95% confidence region is very small and the error on the estimated value is very low (below 2%). The regression produces a very good estimate of the anode exchange current density. 

In Figure 29 the correlation between the local anode exchange current density and the local fuel utilization (as usual, divided in Power Leads and Ejectors side) is shown. 

Figure 29. Correlation between the local anode exchange current density and the local fuel utilization.

The anode exchange current density depends not only on the local fuel utilization, but it is also influenced by the local temperature. A higher temperature should have a increasing effect on the anode exchange current density. Therefore, in Figure 30 the correlation between the local anode exchange current density and the local temperature (as usual, divided in Power Leads and Ejectors side) is shown. It seems that the correlation with the local temperature is less evident than the correlation with the local fuel utilization, especially at the Ejectors side (fuel inlet). Thus, it seems that the effect of the local fuel utilization is more significant than the effect of the local temperature on the activation of the anodic reaction. 

As a conclusion, the effect of fuel utilization distribution on the anode exchange current density is predominating, while the temperature distribution attenuates this behaviour. 

Based on the proposed electrochemical model, the percentage values of the overpotential contributions of the considered electrochemical model (with the anode activation overpotential calculated using the estimated values of the anode exchange current density) at about 180 mA/cm are shown. In Figure 31 the percentage values of the overvoltages for every sector at about 180 mA/cm are shown. 

Figure 32. Percentage weight of the overvoltage eontributions at 180 mA/cn (evaluated for the value of anode exchange current density find in Hterature and the values find by the regression on the SOFC...

Probably, it could be due to the fact that the literature equations are proposed for planar cells, and their behaviour is towards an underestimation of the anode exchange current density, with the consequence of overestimating the activation losses. 

Finally, in Figure 33 a correlation between the anode exchange current density and the local temperature (grouped by sector running hours), and the mean values for the miming horns (the cell pedigree), are shown. 

As a general comment, it can be noticed that in the new sectors the anode exchange ciurent density is lower compared to the old sectors. Therefore, it is possible to conclude that the effect of the position of the sector inside the generator predominates on its pedigree in fact, the boundary sectors (sectors 1 and 24) have a very low anode exchange current density compared to other sectors with the same pedigree disposed in different positions in the generator. 

The limiting current density of CI2 reduction (which is not assignable to mass transport limitations) equals anodic exchange current density related to the 30 mV slope,... 

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