# Determination of a Complete Conversion Model for Gasification of Lignite Char
## 4 Results and Discussion
### Determination of Kinetic Parameters  
For the determination of the kinetic parameters, the objective function (11) was minimized for the Arrhenius equation and the L-H model in combination with all four kinetic models (VM, RM, RPM and JM) for both the CO\({}_{2}\) gasification as well as the steam gasification. The coefficients of determination \(R^{2}\) are listed in Table 5. The L-H model generally leads to significantly better results than the Arrhenius model with the coefficient of determination being larger for any given conversion model except from the GM for CO\({}_{2}\) gasification. In this case, R\({}^{2}\) is very similar for the Arrhenius and the L-H model. Regarding the conversion models, the JM is the most suitable for the selected char samples. Table 6 shows the kinetic parameters for the L-H model, the parameter \(\alpha\) of the JM and the parameter \(b\) for the mass influence. A closer look has to be taken at the activation energy \(E_{a,2}\), which is negative for both CO\({}_{2}\) and steam gasification. Negative activation energies have been observed for gasification before [6] and are a hint that the L-H model does not completely describe the reaction mechanisms during gasification. In the case of steam gasification, a possible reason is the hydrogen inhibition through the irreversible adsorption of hydrogen on the active char sites, described by [PERSON] et al. [24]. For both, steam and CO\({}_{2}\) gasification, the influence of ash acting as a catalyst is another explanation. Still, with a coefficient of determination at about 98% and 95% for steam and CO\({}_{2}\) gasification respectively, the confidence intervals are narrow enough for practical use. Figure 4 exemplarily shows the results of a steam gasification run in test configuration No. 2 with 20 mL/min steam and 35 mL/min hydrogen for a selection of temperatures with their error bar according to the Allan deviation. Additionally, the predicted reaction rates of the L-H model together with all four conversion models are plotted. For the JM, the 95% confidence interval is marked in the plot, too. The measurements show a digressive change in reaction rate between 900 \({}^{\circ}\)C and 970 \({}^{\circ}\)C that was observed in all measurements with steam. Only the JM satisfactorily models this characteristic, leading to the very high coefficient of determination. The results are in good agreement with the JM model, especially in the relevant range from 750 \({}^{\circ}\)C to 950 \({}^{\circ}\)C.  
Figure 5 shows the respective information for a trial with 33% CO\({}_{2}\) and 20% CO for the L-H reaction model together with all conversion models. Here, the L-H model emulates the measurements for the CO\({}_{2}\) gasification best, too. In addition, similarly to Figure 4, the change in reaction rate decreases between 900 \({}^{\circ}\)C and 950 \({}^{\circ}\)C. However, for the CO\({}_{2}\) gasification, the JM is not able to model this effect correctly. For very high conversions and temperatures, all models overestimate the reaction rate. These deviations are observed for most CO\({}_{2}\) measurements and lead to a smaller coefficient of \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(k_{1}\) & \(k_{2}\) & \(k_{3}\) & \(E_{a,1}\) & \(E_{a,2}\) & \(E_{a,3}\) & \(\alpha\) & \(b\) \\ \hline \([\)kPa\({}^{-1}\) min\({}^{-1}]\) & \multicolumn{3}{c}{\([\)kPa\({}^{-1}]\)} & \multicolumn{3}{c}{\([\)kJ/mol\(]\)} & \multicolumn{3}{c}{\([\)-\(]\)} \\ \hline \(CO_{2}\) _Gasification_ & & & & & & \\ \(3.70\times 10^{8}\) & \(4.04\times 10^{-6}\) & \(8.73\times 10^{9}\) & \(236.1\) & \(-87.8\) & \(256.7\) & \(1.41\) & \(7.7\) \\ _Steant Gasification_ & & & & & & & \\ \(1.39\times 10^{12}\) & \(5.14\times 10^{-3}\) & \(3.25\times 10^{12}\) & \(298.5\) & \(-39.8\) & \(287.5\) & \(1.89\) & \(10.8\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results for the L–H reaction model with the Johnson conversion model.