## 3 Results and Discussion  
In this study, the numerical model of a SRU thermal reactor is constructed using an unstructured grid. Five cell densities--10,826 cells, 187,354 cells, 342,856 cells, 683,672 cells and 1,124,627 cells--are tested to ensure a grid-independent solution. The computational results show that the sizes of the corner recirculation zone in zone 1 and zone 2 and the cross-sectional average temperature profiles obtained using the last two meshes almost coincide, with a deviation of less than 0.5%. Therefore, the mesh of 683,672 cells is used for the subsequent discussion. Figure 2 shows the numerical model of the SRU thermal reactor investigated. In Figure 2, the heat exchanger section consists of 19 cooling tubes, which have a diameter of 0.5 m, as shown schematically in Figure 3. The heat absorption rate for each heat exchanger tube is 40,000 W/m\({}^{2}\) and the other walls are adiabatic. No slip condition is applied on all solid walls. The exit of the heat exchanger section is connected to other equipment at 300 K and 1 atm by a pipe that is 1.372 m in diameter and 11.5 m in length. Figure 2: The numerical model for the SRU thermal reactor investigated. In this study, two types of oxygen supplies are investigated: an oxygen-normal supply and an oxygen-rich supply. An oxygen-rich supply increases sulfur recovery. The design conditions (including the species compositions, the temperature, the pressure and the velocity) at the acid gas inlet holes of zone 1 and zone 2 and at the air inlet hole are listed in Table 1. These conditions are practical operating conditions that are used by a petrochemical corporation in Taiwan. The turbulence kinetic energy is 10% of the inlet mean flow kinetic energy and the turbulence dissipation rate is computed using Equation (16). \[\varepsilon=C_{\mu}^{3/4}\frac{k^{3/2}}{l} \tag{16}\]  
where \(l\) = 0.07\(L\) and \(L\) is the hydraulic diameter. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline \multirow{2}{*}{**Location**} & \multicolumn{4}{c}{**Oxygen-Normal Supply**} & \multicolumn{4}{c}{**Oxygen-Rich Supply**} \\ \cline{2-7}  & **Acid Gas to** & **Acid Gas to** & **Air Inlet** & **Acid Gas to** & **Acid Gas to** & **Air Inlet** \\ \cline{2-7}  & **Zone 1** & **Zone 2** & & **Zone 1** & **Zone 2** & \\ \hline Species & & & & & \(x\) (\%) & \\ \hline O\({}_{2}\) & 0 & 0 & 19.87 & 0 & 0 & 23.85 \\ N\({}_{2}\) & 0 & 0 & 74.98 & 0 & 0 & 71.26 \\ H\({}_{2}\)O & 7.83 & 4.12 & 5.15 & 4.12 & 27.97 & 4.89 \\ CO\({}_{2}\) & 1.27 & 1.5 & 0 & 1.48 & 0 & 0 \\ H\({}_{2}\)S & 82.06 & 89.88 & 0 & 89.9 & 39.61 & 0 \\ CH\({}_{4}\) & 2.28 & 2.7 & 0 & 2.7 & 0 & 0 \\ C\({}_{2}\)H\({}_{6}\) & 1.52 & 1.8 & 0 & 1.8 & 0 & 0 \\ NH\({}_{3}\) & 5.04 & 0 & 0 & 0 & 32.42 & 0 \\ \hline \(T\) (K) & 319.92 & 316.15 & 403.15 & 313.15 & 316.15 & 397.15 \\ \hline \(P\) (N/m\({}^{2}\)) & 76,920 & 75,068 & 74,382 & 75,068 & 75,068 & 89,572 \\ \hline \(V\) (m/s) & 11.62 & 2.08 & 12.4 (Radial) & 11.46 & 1.88 & 10.8 (Radial) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The design conditions at the acid gas inlet holes and the air inlet hole. Figure 3: An illustration of the arrangement of heat exchanger tubes. To validate the numerical methods used in this study, the simulation results were compared with available practical data. The exit sulfur mole fractions from the SRU thermal reactor of a petrochemical corporation in Taiwan were measured with the design conditions listed in Table 1. The results are shown in Table 2. It can be seen that the respective deviations are 1.3% for an oxygen-normal supply and 8.3% for an oxygen-rich supply, which are acceptable from a viewpoint of engineering applications. To determine the effect of the fuel mass fraction, the zone 1 fuel mass fraction is defined as the mass ratio of the zone 1 acid gas to the total acid gas (acid gas to zone 1 plus acid gas to zone 2). The design zone 1 fuel mass fractions, calculated from Table 1, are 0.875 for an oxygen-normal supply and 0.895 for an oxygen-rich supply.