## 3 Result
### Anode Off-Gas Recycling  
Unreacted hydrogen in the anode off-gas from the PEMFC stack can be recycled as fuel for the steam reformer's burner, increasing the thermal efficiency of the fuel processer and PEMFC. The thermal efficiency of the combined system depends on the amount of hydrogen recycled, which is determined according to the fuel utilization ratio of the PEMFC. The calculated stack power is summarized in Table 5 and depends on the natural gas supplied to the fuel processor and the fuel utilization efficiency of the stack. In Table 4, the conditions for making more than 5 kW power are shaded. The power increases with a higher fuel utilization at the stack, with higher steam reformer operating temperatures, and with a higher flow rate of PNG. To increase the thermal efficiency of the fuel processor and PEMFC stack, anode off-gas is recycled to the burner. In Figure 12, it can be seen that recycling AOG increases the efficiency of the fuel cell system by 1.28 times compared to the case without it.  
However, some of the calculations are excluded by the details described below in Figure 13. Figure 13 shows the combustion energy generated by each process at various temperatures of the steam reformer. The flow rate of unreacted hydrogen in the anode off-gas varies depending on the fuel utilization (\(U_{f}\)) in the stack, which causes the combustion energy to vary. If the combustion energy of the anode off-gas is greater (red area in Figure 13) than the combustion energy of the natural gas, excess energy is supplied to the reactor, and the reactor temperature increases. Since the use of AOG in this section does  
Figure 12: Relationship between the overall system efficiency of the AOG recycling process and the AOG non-recycling process (S/C = 3, \(n_{\text{PNG}}\) = 0.9 mol/min).  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \(U_{f}\) (\%) & \(T_{\text{SR}}\) (\({}^{\circ}\)C) & \multicolumn{3}{c}{**70\%**} & \multicolumn{3}{c}{**75\%**} & \multicolumn{3}{c}{**80\%**} \\ \hline \(n_{\text{PNG}}\) **(mol/min)** & & **0.7** & **0.8** & **0.9** & **0.7** & **0.8** & **0.9** & **0.7** & **0.8** & **0.9** \\ \hline \multirow{8}{*}{\(P_{\text{stack}}\) (kW)} & 600 & 3.18 & 3.68 & 4.18 & 3.43 & 3.97 & 4.51 & 3.68 & 4.26 & 4.84 \\  & 650 & 3.87 & 4.48 & **5.09** & 4.18 & 4.83 & **5.48** & 4.48 & **5.18** & **5.88** \\ \cline{1-1}  & 700 & 4.25 & 4.91 & **5.58** & 4.5 not maintain the temperature, it is excluded from the result of a fuel utilization of 70% or less in this study. Conversely, if the combustion energy of the anode off-gas is smaller (blue area in Figure 13) than the required heat, additional natural gas to the burner must be introduced to maintain the temperature of the reactor.  
In Figure 14, the overall efficiency of the system is compared according to the temperature of the steam reformer for each process. Since 80% of the AOG has small combustion energy, it is possible to reach maximum efficiency by supplying additional natural gas. Finally, in the case of AOG 75%, the value was consistent with the required heat, showing that the reformer can be operated with only AOG and without an additional fuel supply. In other words, energy independence is possible under the conditions of 750 \({}^{\circ}\)C or more, a fuel utilization efficiency = 75%, and S/C = 3.  
Table 6 shows the final selected operating conditions and system efficiency for a 5 kW residential PEMFC. Consequently, the efficiency of the fuel cell system is recommended under the following conditions: S/C = 3 for maximum efficiency of fuel processor, fuel utilization efficiency without overheating of 75-80%, steam reformer temperature of  
Figure 14: Comparison of system efficiency at various temperatures in AOG recycling and non-recycling operation.  
Figure 13: Combustion energy according to the temperature of the steam reformer and the fuel utilization efficiency.  
700-800 \({}^{\circ}\)C, and a molar flow rate of PNG of 0.8-0.9 mol/min to produce more than 5 kW of power.