## 2 Methodology
### Reactor Modelling
#### 2.1.2 Gas Switching Partial Oxidation  
The modeling of the La-Fe-based oxygen carrier for GSPOX is based on the promising experimental results obtained in [31]. Good performance has also been achieved in a fluidized bed, increasing confidence in the application to gas switching reactors [38]. The original oxygen carrier possesses an oxygen storage capacity of \(\sim\)9 wt.% and thermodynamic properties such that \(\sim\)96.5% of its redox-active lattice oxygen is selective for the partial oxidation of methane to syngas (in the reduction step) and \(\sim\)95% of steam (or CO\({}_{2}\)) can be converted to H\({}_{2}\) (or CO), in the oxidation step. The aim is to develop and assess the application of this oxygen carrier in an H\({}_{2}\) production plant, benchmarking it against the former GSR plant and the reference technology: SMR process. For this purpose, certain ideal performance assumptions have been taken, as further detailed below. The chemical reactions and kinetic expressions considered for each step are presented in Table 2 for the GSPOX reactor, where the fully oxidized oxygen carrier is denoted by XO, while the reduced oxygen carrier is referred to as X. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Step** & **Reaction** & **Kinetics** \\ \hline \multirow{3}{*}{POX and REF/WS} & \(CH_{4}+0.74 XO_{1.35}\to 0.74X+CO+2H_{2}\) & \(R_{CH_{4}}=\frac{1}{\tau}n_{CH_{4}}n_{XO}\) \\  & \(0.74X+CO_{2}\leftrightarrow 0.74 XO_{1.35}+CO\) & \(R_{CO_{2}}=\frac{1}{\tau}\left(y_{CO_{2}}-y_{CO_{2},e_{1}}\right)n_{gas}n_{X}\) \\  & \(0.74X+H_{2}O\leftrightarrow 0.74 XO_{1.35}+H_{2}\) & \(R_{H_{2}O}=\frac{1}{\tau}\left(y_{H_{2}O}-y_{H_{2}O,e_{2}}\right)n_{gas}n_{X}\) \\ \hline \multirow{3}{*}{OX} & \(1.48X+O_{2}\to 1.48 XO_{1.35}\) & \(R_{O_{2}}=\frac{1}{\tau}n_{O_{2}}n_{X}\) \\ \cline{1-1} \cline{2-3}  & \(0.74 XO_{1.35}+H_{2}\to 0.74X+H_{2}O\) & \(R_{H_{2}}=\frac{1}{\tau}n_{H_{2}}n_{XO}\) \\ \cline{1-1} \cline{2-3}  & \(0.74 XO_{1.35}+CO\to 0.74X+CO_{2}\) & \(R_{CO}=\frac{1}{\tau}n_{CO}n_{XO}\) \\ \cline{1-1}  & \(CH_{4}+2.96 XO_{1.35}\to 2.96X+CO_{2}+2H_{2}O\) & \(R_{CH_{4}}=\frac{1}{\tau}n_{CH_{4}}n_{XO}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Reactions and kinetic expressions for GSPOX. Figure 3: GSR reactor cycle composition and temperature profile. (REF: 0–146.3 s, OX: 146.3–209.0 s, RED: 209.0–271.7 s). The proposed cycle includes a two-step reduction. In the first step, the oxygen carrier shows full selectivity to CO\({}_{2}\) and H\({}_{2}\)O and fully oxidizes all fuel gases fed to the reactor. In the second step, the oxygen carrier has 95% selectivity to H\({}_{2}\) and CO, by partially oxidizing CH\({}_{4}\) and reducing H\({}_{2}\)O or CO\({}_{2}\) fed to the reactor. It is assumed that the transition point between these two steps (i.e., to what degree the oxygen carrier is reduced when the selectivity of the oxygen carrier changes from total to partial oxidation) can be tuned according to the requirements of the process, e.g., by decreasing the ratio of La:Sr in the oxygen carrier [31], or by adding other combustion oxygen carriers such as ilmenite to the formulation [39]. The modeling results reveal that approximately half of the lattice oxygen that is consumed during reduction (case dependent) must fully oxidize the fuel to achieve adequate step lengths. Since the overall degree of oxygen carrier reduction was limited in all cases below 70%, and due to the higher resistance of these materials to carbon deposition [40], it was neglected in the kinetic model. In the partial oxidation step (POX) two moles of H\({}_{2}\) are present per mole of CO produced. Unlike in the reforming step in the GSR, a large flow of steam is not required to ensure high methane conversion. An oxygen carrier conversion of 30% in addition to that for the reduction step (where full combustion of the fuel takes place) is specified for the POX step.