*4.1. Model Validation*

To demonstrate the reliability of the developed model, a model validation process is essential. Comparing the simulation results to the experimental data of the whole system is the best way to validate a model, however, the purpose of this paper was to estimate the performance depending on the system configuration. Thus, only the model of the most complex component, which is a SOFC stack, is demonstrated in this paper. A 1 kW class stack as described in Table 1 was used for the experiment. During the experiments, the fuel and air flow rates were constant regardless of the current. H2 and CO2 were supplied at 27.96 and 10.61 lpm, respectively, as fuel. The air flow rate was fixed at 66.10 lpm. The load current was varied from 0 to 29.92 A. The stack temperature was maintained at 1023.15 K during the experiment. The model validation results are displayed in Figure 2. As a result, the model was able to accurately predict the performance of the stack.

**Figure 2.** Comparison between the predictions and experimental data.

#### *4.2. Operating Conditions for Simulation*

The operating conditions for the simulation are presented in Table 9. Methane was used as fuel. The fuel and air flow rates were determined depending on the fuel/air utilization factor and operating current density. Steam flow rate was calculated based on the fuel flow rate and S/C ratio. The steam was generated at steam generator using thermal energy from off-gas. The PI controller adjusted the CC air flow rate so that the temperature of the CC did not exceed 1123.75 K. In this study, the performance of each system was investigated with various fuel/air utilization factors and recirculation ratios. We define the reference condition of the simulation as the condition with both a utilization factor of 0.6 and a recirculation ratio of 0.2.

**Table 9.** Operating conditions for the simulation.


#### *4.3. Result 1: The Effect of the Fuel/Air Utilization Factors*

#### 4.3.1. Reference System

The fuel flow rate changed from 6.42 to 2.41 lpm in accordance with the fuel utilization factor of 0.3 to 0.8. The air flow rate was fixed at 30.57 lpm. Figure 3a,b indicate the temperature of each component, the CC air flow rate and the heat transfer rate of each heat exchanger. As the fuel utilization factor increased, less fuel was supplied to the system. This decreased the combustion energy at the CC and the additional CC air flow rate for cooling. When the fuel utilization factor was 0.8, the temperature of CC became lower than 1123.15 K without additional air flow to the CC. The ESR was thermally integrated with CCOG in the reference system; therefore, the temperature of the ESR decreased. In Figure 3b, it was observed that the heat transfer rate from CCOG to ESR and the amount of recovered heat were rapidly reduced. On the other hand, the stack temperature increased due to the lowered internal reforming rate. The SMR process is a strong endothermic process,

so the more abundance the internal reforming reactions are, the lower the temperature of the stack.

**Figure 3.** The effect of fuel utilization factor on the reference system; (**a**) temperature of each component, (**b**) heat transfer rate at each heat exchanger (COG HE: steam generator, CCOG HE: air pre-heater, HR HE: heat recovery heat exchanger).

To examine the effect of the air utilization factor, the fuel utilization factor was fixed at 0.6 and the air utilization factor was changed from 0.3 to 0.8. The results are depicted in Figure 4a,b. A decreased stack air flow rate led to a temperature rise in the stack, and the raised temperature accelerated the internal reforming reaction. Consequently, the hydrogen molar flow rate to the CC increased, causing larger heat generation in the CC. Although extra air was supplied to the CC, the total amount of air diminished because the stack air flow rate decreased further. Less heat was transferred from the CCOG to the ESR, thus, the temperature of the ESR slightly decreased.

**Figure 4.** The effect of air utilization factor on the reference system; (**a**) temperature of each component, (**b**) heat transfer rate at each heat exchanger (COG HE: steam generator, CCOG HE: air pre-heater, HR HE: heat recovery heat exchanger).

4.3.2. SOFC System with AOGR #1

In this section, the AOGR #1 system is examined. As the condition described in Section 4.3.1, the fuel or air utilization factor was changed from 0.3 to 0.8. For the calculation, the recirculation ratio was held constant at 0.2. The results of the fuel and air utilization factors are presented in Figure 5a,b, respectively. Overall, the results are similar to those presented in Figures 3 and 4. By comparing the CC air flow rate, the generated heat of the CC of this system was slightly lower than that of the reference system. The AOGR system enhanced the efficiency of fuel utilization, so the available energy in CC becomes reduced. The temperature of the recirculation blower is also shown in Figure 5a,b, and it falls within the appropriate operating temperature. The recirculation blower temperature was between 691.79 and 745.86 K.

**Figure 5.** The effect of (**a**) fuel and (**b**) air utilization factors on the AOGR #1 system.4.3.3. SOFC System with AOGR #2.

The difference between the AOGR #1 and AOGR #2 systems is the heat supply method for the ESR. As mentioned in Section 2, the ESR applied in the system with AOGR #1 was thermally integrated with the CC to directly absorb heat from the CCOG. Meanwhile, the ESR used in the AOGR #2 system received the required heat only from the reactants. Fuel preheater 2 was also added to recover additional heat from the COG, as shown in Figure 1c. The effect of fuel and air utilization factors on component temperatures is presented in Figure 6a,b. The changes in temperature of the stack, ESR and CC were similar to those presented in Section 4.3.2. However, CCOG did not directly flow to the ESR, and the temperatures of the stack and CC in the AOGR #2 system became higher than those in the AOGR #1 system. When the fuel utilization factor was 0.8, the stack temperature slightly decreased. Under this condition, the effect of the stack temperature reduction because of the lowered inlet air temperature became greater than the effect of the stack temperature increase caused by the weakened internal reforming reaction.

With regard to the recirculation blower, the temperature of the recirculation blower increased to 728.02 K at the fuel utilization factor of 0.8. The heat supply amount at the fuel preheater diminished in accordance with the increase in the fuel utilization factor. On the other hand, the temperature of the recirculation blower decreased as the air utilization factor increased because of the reduced heat transfer rate in the steam generator.

**Figure 6.** The effect of (**a**) fuel and (**b**) air utilization factors on the AOGR #2 system.
