## 4 Results and Discussion
### Correction Factors and New Empirical Correlation for the Equilibrium Constant

Table 10: Empirical correlation coefficient correction of reaction equilibrium constants. Figure 3: The graph represents the equilibrium of the original reaction and its modification to temperature. resulted in RMSE between 2.39 and 4.25 over 64 simulation scenarios. [PERSON] et al. [34] found similar values of RMSE by modifying the stoichiometric models. Table 12 presents the mean of the predicted composition of CO, CO\({}_{2}\), CH\({}_{4}\), H\({}_{2}\), and N\({}_{2}\) gas simulated using M1A-M6D. The models of M1D, M2C, and M3C accurately predicted composition of CO, CO\({}_{2}\), H\({}_{2}\), and N\({}_{2}\) (\(\alpha\) = 0.05 and t-crit value of 2.0687). M1B accurately predicted CO, H\({}_{2}\), and N\({}_{2}\). M2D and M3B accurately estimated CO\({}_{2}\), H\({}_{2}\), and N\({}_{2}\). The models M4C, M4D, M5C, M5D, M5B, M6C, and M6D correctly predicted CO, CO\({}_{2}\), and N\({}_{2}\). The predicted composition of CH\({}_{4}\) by all developed models (M1A-M6D) was lower than the experimental data. Based on the statistical analysis, the developed models M1D, M2C, and M3C are the models that may accurately predict CO, CO\({}_{2}\), H\({}_{2}\), and N\({}_{2}\) gas composition. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **CO** & **CO\({}_{2}\)** & **CH\({}_{4}\)** & **H\({}_{2}\)** & **N\({}_{2}\)** & **t-Stat** & **t-Stat** & **t-Stat** & **t-Stat** & **t-Stat** \\  & **(\%vol)** & **(\%vol)** & **(\%vol)** & **(\%vol)** & **(\%vol)** & **CO** & **CO\({}_{2}\)** & **CH\({}_{4}\)** & **H\({}_{2}\)** & **N\({}_{2}\)** \\ \hline M1O & 36.190 & 2.159 & 0.395 & 28.362 & 34.637 & & & & & \\ M1A & 17.399 & 13.998 & 0.261 & 14.985 & 51.666 & \(-\)0.943 & 2.960 & \(-\)8.836 & 2.829 & \(-\)1.827 \\ M1B & 20.736 & 11.913 & 0.458 & 16.110 & 49.539 & 4.787 & \(-\)0.373 & \(-\)7.995 & 5.045 & \(-\)4.460 \\ M1C & 18.065 & 13.486 & 0.313 & 14.031 & 52.358 & 0.214 & 2.145 & \(-\)8.631 & 0.882 & \(-\)0.956 \\ M1D & 18.582 & 13.332 & 0.528 & 13.903 & 51.956 & 1.043 & 1.816 & \(-\)7.694 & 0.525 & \(-\)1.408 \\ M2O & 25.002 & 9.124 & 0.307 & 21.165 & 44.403 & & & & \\ M2A & 17.489 & 13.926 & 0.311 & 14.920 & 51.702 & \(-\)0.877 & 2.857 & \(-\)8.707 & 2.756 & \(-\)1.742 \\ M2B & 19.121 & 12.804 & 0.389 & 14.505 & 51.639 & 2.329 & 1.051 & \(-\)8.431 & 1.954 & \(-\)1.834 \\ M2C & 18.710 & 13.071 & 0.360 & 14.424 & 51.835 & 1.519 & 1.478 & \(-\)8.516 & 1.765 & \(-\)1.590 \\ M2D & 19.448 & 12.633 & 0.611 & 14.418 & 51.440 & 3.015 & 0.774 & \(-\)7.183 & 1.817 & \(-\)2.078 \\ M3O & 24.924 & 9.133 & 0.363 & 21.511 & 44.040 & & & & \\ M3A & 17.764 & 14.190 & 0.321 & 15.164 & 52.562 & \(-\)0.359 & 3.252 & \(-\)8.725 & 3.231 & \(-\)0.683 \\ M3B & 19.120 & 12.785 & 0.323 & 14.543 & 51.673 & 2.348 & 1.022 & \(-\)8.760 & 2.037 & \(-\)1.811 \\ M3C & 18.727 & 13.077 & 0.443 & 14.357 & 51.819 & 1.560 & 1.494 & \(-\)8.111 & 1.635 & \(-\)1.605 \\ M3D & 19.461 & 12.656 & 0.761 & 14.302 & 51.408 & 3.049 & 0.807 & \(-\)6.087 & 1.563 & \(-\)2.105 \\ M4O & 36.402 & 1.747 & 0.386 & 29.540 & 34.193 & & & & \\ M4A & 17.144 & 13.802 & 0.320 & 16.189 & 51.471 & \(-\)1.374 & 2.610 & \(-\)8.678 & 5.173 & \(-\)1.983 \\ M4B & 20.152 & 12.021 & 0.582 & 17.405 & 49.162 & 4.071 & \(-\)0.191 & \(-\)7.144 & 7.348 & \(-\)4.523 \\ M4C & 17.598 & 13.364 & 0.386 & 15.061 & 52.498 & \(-\)0.541 & 1.840 & \(-\)8.259 & 3.137 & \(-\)0.771 \\ M4D & 18.344 & 12.949 & 0.634 & 15.036 & 52.054 & 0.635 & 1.220 & \(-\)6.885 & 3.139 & \(-\)1.328 \\ M5O & 24.520 & 9.061 & 0.273 & 21.994 & 44.128 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 12: The predicted values of producer gas and their statistical analysis.