## 2 Modeling
### Fuel Processor Description  
Simulations were performed for a combined system of a fuel processor and HT-PEMFC with a recycle stream of anode off-gas to a burner installed in the SR (steam reformer). Figure 2 shows the simulation process for the combined system of a fuel processor and HT-PEMFC. ### Fuel Processor Description  
Simulations were performed for a combined system of a fuel processor and HT-PEMFC with a recycle stream of anode off-gas to a burner installed in the SR (steam reformer). The fuel processing system consists of a steam reformer, two water-gas shift reactors (a high-temperature shift reactor and a low-temperature shift reactor), and heat exchangers. Figure 3 shows the process flow diagram by Aspen Hysys(r). PNG (process natural gas)  
Figure 2: Simulation block diagram, (**a**) overall block diagram for the fuel processor and HT-PEMFC and (**b**) block diagram for the P\({}_{\text{stack}}\) calculation. is introduced to the reformer and reacted with steam to form hydrogen. Q\({}_{\rm H1}\) is the heat required to raise the PNG to the reaction temperature of the steam reformer. Q\({}_{\rm H2}\) is the heat required to turn water into steam up to the reaction temperature of the reformer. The product gas from the steam reformer is cooled down by a heat exchanger (cooler 1 in Figure 3) to the high-temperature water-gas shift reactor (HTS) operating temperature and then introduced to the HTS. CO is then converted into CO\({}_{2}\) with steam at the HTS and the concentration of CO in the HTS product gas is lowered to less than 3%. To reduce the CO concentration lower than 1%, the HTS product gas is cooled again and introduced to the low-temperature water-gas shift reactor [27]. The heat released in the process is named Q\({}_{\rm C1}\), Q\({}_{\rm C2}\), and Q\({}_{\rm C3}\). Q\({}_{\rm SR}\) is the energy required for the reaction at the steam reformer. Q\({}_{\rm HTS}\) is the heat of the reaction at the high-temperature water-gas shift reactor and Q\({}_{\rm LTS}\) is the heat of the reaction at the low-temperature water-gas shift reactor. In the steam reformer, two main reactions are considered [28; 29; 30]: the steam reforming reaction (Equation (1)) and the WGS reaction (Equation (2)). It is assumed that the reaction proceeds to equilibrium conditions in each reactor, and the equilibrium reactor is used for the simulation with the equilibrium constants (\(K_{SR}\) and \(K_{WGS}\)) calculated in Equations (3) and (4). \[\text{Steam methane reforming:}\;CH_{4}+H_{2}O\leftrightarrow\text{CO}+3H_{2} \tag{1}\]  
\[\text{Water-gas shift reaction:}\;\text{CO}+H_{2}O\leftrightarrow\text{CO}_{2}+H_{2} \tag{2}\]  
\[K_{SR}=\frac{P_{CO}p_{H_{2}}^{3}}{p_{CH_{4}}p_{H_{2}}}atm^{-2}=\frac{1}{\exp(Z (Z(2(0.2513Z-0.3665)-0.58101)+27.1337)-3.2770)} \tag{3}\]  
\[K_{WGS}=\frac{p_{H_{2}}p_{CO_{2}}}{p_{H_{2}}p_{CO}}atm^{-2}=\exp(Z(Z(0.63508-0. 29353Z)+4.1778)+0.31688) \tag{4}\]  
\[Z=\left(\frac{1000}{T}\right)-1 \tag{5}\]  
Equations (3) and (4) are empirical equations presented by [PERSON] [31], and the equilibrium constants (\(K_{SR}\) and \(K_{WGS}\)) are expressed as a function of temperature (\(Z\) and \(T\)) instead of each partial pressure. The WGS reactor applied \(K_{WGS}\) within the temperature range of the reactor. The equilibrium constants calculated for each reaction are summarized in Table 1.  
Figure 3: Aspen hysys® flowsheet of the fuel processor. To calculate the thermal energy and heat of the reaction in each component, energy balances are applied. As shown in Figure 4, the fuel processor consists of two independent parts. One is the reaction part and the other is the thermal energy supply part. The thermal energy required is calculated as the enthalpy difference between the inlet stream and the outlet stream (Equations (6) and (7)), which can be supplied by the methane burner via combustion.