## 2 Methodology
### Reactor Modelling  
Two oxygen carriers were employed in the reactor models built in Scilab, which incorporated an in-house thermodynamic database (Patitug) for property calculations of the gas phase. The first reactor principle consists of gas switching reforming (GSR) using Nickel as an oxygen carrier, inspired in past studies from some of the authors [22]. The second reactor principle incorporates the novel oxygen carrier which achieves partial oxidation of methane, referred to henceforward as gas switching partial oxidation (GSPOX). For the solid property estimation, suitable data sources were employed [32; 33]. The oxygen carrier used in the GSPOX schemes had the chemical composition La\({}_{0.85}\)Sr\({}_{0.15}\)Fe\({}_{0.95}\)Al\({}_{0.05}\)O\({}_{3}\). Generally, thermodynamic data for such compositions are scarce, therefore the specific heat  
Figure 2: Simplified process diagram of the GPOX H\({}_{2}\)-power plant. capacity was estimated based on literature data for species that represent the components in the fully oxidized and fully reduced states of the oxygen carrier, respectively. For the oxidized oxygen carrier, the specific heat capacity reported for LaFeO\({}_{3}\) was used [34]. The composition of the reduced oxygen carrier consisted of 50.2 wt.% La\({}_{2}\)O\({}_{3}\), 23.0 wt.%. Fe and 26.8 wt.% La\({}_{3}\)Sr\({}_{2\text{-}\text{x}}\)Fe\({}_{\text{y}}\)Al\({}_{1\text{-}\text{y}}\)O\({}_{4}\)[31]; the mixed oxide phase La\({}_{\text{x}}\)Sr\({}_{2\text{-}\text{x}}\)Fe\({}_{\text{y}}\)Al\({}_{1\text{-}\text{y}}\)O\({}_{4}\) was assumed to possess the same physical properties as LaFeO\({}_{3}\). The specific heat capacity of the individual components was thus averaged using published data and interpolated across the operating temperature range of the reactor [32]. The specific enthalpy of reduced or oxidized species at each reactor temperature was estimated based on the experimental value for the partial oxidation of methane with the oxidized species, and equal to 222.25 kJ/mol of CH\({}_{4}\) at 900 \({}^{\circ}\)C [31], assuming an enthalpy origin of the reduced species at 298.15 K. Further property details of this oxygen carrier and cluster modeling assumptions are provided in Table 1 in Appendix A. Each reactor has a 1 m diameter and an aspect ratio of 3, which resulted in fluidization velocities of approximately 0.6-0.8 m/s for operating temperatures between 900-1100 \({}^{\circ}\)C. A pressure drop of 0.5 bar in each reactor was assumed in all cases. With a similar approach as in [22], additional thermal mass in the form of steel rods was introduced in the reactor to mitigate the temperature variation across the GSR and GSPOX cycles. The steel rods were assumed to occupy 25% of the reactor volume for all simulations. The specific heat of the carbon steel rods was assumed from [35], constant in the range of reactor operating temperatures. The carbon steel rods did not actively participate in the redox reactions (such that gas would be converted or produced), but only acted as a medium for storing heat. Both for GSR and GSPOX reactors, the dynamic molar species Equation (1) and energy Equation (2) balances are solved to determine the reactor profile (temperature and compositions) and outlet flows, assuming the fluidized bed behaves as a continuous stirred tank reactor (CSTR), in virtue of the high degree of mixing attained in industrial practice:  
\[\frac{dn_{k}}{dt}=F_{int}y_{int,k}+F_{out}y_{out,k}+\sum_{r=1}^{R}v_{r,k}\zeta _{r} \tag{1}\]  
\[\frac{dT}{dt}=\frac{-F_{int}\sum_{k}y_{int,k}\int_{T_{in}}^{T}c_{p,k}dT+\sum_{ r=1}^{R}\zeta_{r}(-\Delta H_{r,T})}{\sum_{k}n_{k}c_{p,k}}. \tag{2}\]  
The CSTR model assumes that both chemical and thermal equilibrium is reached. Thermal equilibrium is a realistic assumption in fluidized bed reactors and experimental work has shown that chemical equilibrium is also a reasonable approach for the highly reactive Ni-based oxygen carrier used in GSR [21].