## 2 Preparation for the Numerical Analysis
### Parametric Study  
Table 4 shows the numerical results for all the cases, and Figure 6 presents the temperature distributions of the EBS for the representative cases.  
In case 1, the peak temperatures of the buffer at thermal conductivity values of 1.0 W/(m\(\cdot\)K) and 1.2 W/(m\(\cdot\)K) were 88.85 \({}^{\circ}\)C at 11.5 years and 85.15 \({}^{\circ}\)C at 15.7 years, respectively (Figure 7a). While there was no significant difference in the peak temperature values with respect to the thermal conductivity values, the peak temperature of the buffer when the thermal conductivity was 1.0 W/(m\(\cdot\)K) decreased by 6% compared to that when  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Cases** & \multicolumn{2}{c}{**Thermal Conductivities (\(\lambda\), W/(m\(\cdot\)K))**} \\ \cline{2-4}  & **0.8** & **1.0** & **1.2** \\ \hline Tunnel spacing: 40 m & Max.temperature (T, \({}^{\circ}\)C) & 94.53 & 88.85 & 85.15 \\ \cline{2-4} Hole spacing: 7.5 m & Time to reach max.T (years) & 11.3 & 11.5 & 15.7 \\ \cline{2-4} Tunnel spacing: 30 m & Max.temperature (T, \({}^{\circ}\)C) & 108.28 & 103.66 & 100.76 \\ \cline{2-4} Hole spacing: 6.0 m & Time to reach max.T (years) & 20.4 & 26.1 & 34.9 \\ \cline{2-4} Tunnel spacing: 20 m & Max.temperature (T, \({}^{\circ}\)C) & & \\ Hole spacing: 4.5 m & Time to reach max.T (years) & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Maximum temperature of the buffer surface facing the canister with conditions.  
Figure 5: Validation result compared to the reference result for temperature of the buffer based on the R-SNF condition.  
the thermal conductivity was 0.8 W/(m-K). In contrast, the time required to reach the peak temperature of the buffer at the thermal conductivity of 1.2 W/(m-K) was at least 4 years longer than that when the thermal conductivity was 1.0 W/(m-K).  
Figure 6: Representative numerical results for temperature distribution of the engineered barrier system according to the spacing.  
Figure 7: _Cont._  
Figure 7: Temperature of buffer surface facing the canister with time according to the tunnel and hole spacing and thermal conductivity of the buffer: (**a**) tunnel and hole spacing are 40 and 7.5 m, respectively, (**b**) tunnel and hole spacing are 30 and 6.0 m, respectively, (**c**) tunnel and hole spacing are 20 and 4.5 m, respectively.  
For the different spacing case 2, the peak temperatures of the buffer at thermal conductivity values of 0.8 W/(m\(\cdot\)K), 1.0 W/(m\(\cdot\)K), and 1.2 W/(m\(\cdot\)K) were 108.28 \({}^{\circ}\)C after 20.4 years, 103.66 \({}^{\circ}\)C after 26.1 years, and 100.76 \({}^{\circ}\)C after 34.9 years, respectively (Figure 7b). In this case, because the peak temperature of the buffer exceeds 100 \({}^{\circ}\)C for all the three thermal conductivity values, the thermal conductivity of the buffer should be higher than 1.2 W/(m\(\cdot\)K) to satisfy the thermal requirements of the disposal system.  
In case 3 (Figure 7c), the temperature of the buffer increased continuously without attaining peak temperature within 55 years for all the thermal conductivities, and the temperature of the buffer exceeded 100 \({}^{\circ}\)C within 2.7 years for all the three thermal conductivity values because of insufficient spacing to emit the generated heat.