## 5 Results and Discussion
### Parametric Studies
#### 5.3.1 Fuel Re-Distribution between the First and Second Stages  
In this case, the fuel distribution is changed by shifting 20% coal-slurry to the first stage (originally 100% at the second stage) and feeding recycled char at the second stage (originally at the first stage). The entire oxygen is still injected at the first stage like the base case. Two alternate fuel redistribution cases are studied, either with or without the condensation and re-vaporization sub-models. Results of syngas composition and exit temperature are compared in Table 9.  
As shown in Table 9, the effect of fuel re-distribution on syngas composition is noticeable but not large. The exit temperature increases for the fuel re-redistribution cases. To further examine the temperature distributions, the centerline temperature distributions along the height of reactor are compared in Figure 4. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Property** & **Species** & **Base Case \({}^{*}\)** & **Condensation Only** & **Both Sub-Models** \\ \hline \multirow{6}{*}{
\begin{tabular}{c} Mole fraction \\ (\%) \# \\ \end{tabular} } & CO & 36.91 & 35.42 & 38.8 \\  & H\({}_{2}\) & 24.48 & 21.46 & 26.7 \\  & CO\({}_{2}\) & 10.07 & 10.43 & 8.11 \\  & H\({}_{2}\)O & 20.61 & 19.98 & 18.33 \\  & CH\({}_{4}\) & 2.27 & 1.29 & 2.45 \\  & Volatiles (G) & 1.05 \(\times\) 10\({}^{-6}\) & 3.68 \(\times\) 10\({}^{-6}\) & 4.25 \(\times\) 10\({}^{-7}\) \\  & Volatiles (L) & - & 6.47 & 0 \\ \hline \multicolumn{3}{c}{Unreacted Char (\%)} & 20 & 11 & 18 \\ \multicolumn{3}{c}{Temperature (K)} & 1463 & 1598 & 1505 \\ \hline \hline \multicolumn{3}{c}{\# Some species with small fractions (e.g., N\({}_{2}\), C\({}_{2}\)H\({}_{2}\), SiO\({}_{2}\)) are not listed here. \({}^{*}\) Condensation and recycling of the} \\ \multicolumn{3}{c}{unreacted char are not included in this base case.} \\ \end{tabular}
\end{table} 
Table 8: Effect of condensation and re-vaporization sub-model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Property** & **Species** & **Base** & \begin{tabular}{c} **2-Stage Fuel with** \\ **Sub-Models** \\ \end{tabular} & \
\begin{tabular}{c} **2-Stage Fuel without** \\ **Sub-Models** \\ \end{tabular} \\ \hline \multirow{6}{*}{
\begin{tabular}{c} Mole fraction \\ (\%) \\ \end{tabular} } & CO & 36.91 & 36.42 & 34.41 \\  & H\({}_{2}\) & 24.48 & 24.16 & 22.63 \\  & CO\({}_{2}\) & 10.07 & 11.56 & 12.74 \\  & H\({}_{2}\)O & 20.61 & 18.58 & 20.24 \\  & CH\({}_{4}\) & 2.27 & 3.04 & 3.65 \\  & Volatiles (G) & 1.05 \(\times\) 10\({}^{-6}\) & 4.47 \(\times\) 10\({}^{-7}\) & 4.76 \(\times\) 10\({}^{-7}\) \\  & Volatiles (L) & - & 0 & - \\ \hline \hline \multicolumn{3}{c}{Unreacted Char (\%)} & 20 & 15 & 12 \\ \multicolumn{3}{c}{Exit Temperature (K)} & 1463 & 1615 & 1558 \\ \multicolumn{3}{c}{HHV (MJ/kg)} & 8.15 & 7.91 & 7.33 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Effect of fuel-redistribution on syngas composition and exit temperature with and without condensation and re-vaporization sub-models. The exit temperatures and the interior temperature distributions are quite different. In the base case, the average temperature in the first stage (with recycled char) is about 2200 K. In the case of fuel re-distribution, there is a low temperature region in the first stage since the recycled char is injected at the second stage. With 80% coal-slurry and recycled char, the temperature at the second stage is higher than that of base case. Therefore, using fuel re-distribution leads to lower first stage temperature and higher second stage temperature. Fuel-redistribution also results in higher outlet temperature. The temperature distribution of the base case is more preferable because the wall temperature is relatively low and the hot spot region is less noticeable, as illustrated in Figure 5; hence, the refractory can last longer. Figure 4: Effect of fuel re-distribution on temperature distributions with and without condensation and re-vaporization sub-models.