## 2 Methodology
### Reactor Modelling
#### 2.1.2 Gas Switching Partial Oxidation
For GSPOX H\({}_{2}\) production plants, in the subsequent reforming step (REF), a methane-steam feed with a molar ratio of 1 is fed to the reactor, thereby attaining more H\({}_{2}\) in the outlet (ratio of 3:1). During the reforming step, a negligible carrier conversion is observed due to the equimolar feed of methane and water that cause forward and backward reactions to take place at identical rates. The following oxidation step is carried out similarly to the GSR reactor, with only sufficient air to fully re-oxidize the carrier (no O\({}_{2}\) slippage). Finally, in the reduction step (RED), the PSA off-gas fuel is completely combusted to CO\({}_{2}\) and H\({}_{2}\)O. In Figure 4, a case corresponding to the GSPOX model designed for H\({}_{2}\) production is presented, whereas in Figure 5, a case for H\({}_{2}\)-power co-production is shown. In Figure 5, air is introduced in the oxidation step in excess, to allow subsequent extra firing to reach high gas turbine (GT) combustor outlet temperatures (COT) to maximize efficiency. The low-carbon fuel for the extra firing is generated by operating the water splitting (WS) step with a steam sweep (as opposed to the equimolar methane-steam feed to the reforming step), in order to obtain a relatively pure H\({}_{2}\) output. This latter strategy is not advisable for H\({}_{2}\) production only, since the H\({}_{2}\) purity of the product stream is approximately 90%, and therefore it would still require a cooldown and purification sequence, neglecting potential efficiency gains whilst increasing operational complexity. It was therefore decided to carry out the reforming as described earlier and mix the process stream outlets from the partial oxidation and reforming steps in Figure 4 before introducing them to the downstream WGS reactors. For the H\({}_{2}\)-power coproduction reactor profile (Figure 5), the maximum reactor temperature is attained in the oxidation step at the point where the carrier becomes fully oxidized, after which the reactor cools down and the O\({}_{2}\) concentration begins to increase. The mass flow rate of air is manipulated from the stationary simulation to reach autothermal operation (energy conservation across the cycle), while the initial reactor temperature was iteratively varied to reach the specified maximum temperature. On the other hand, the degree of oxygen carrier reoxidation during the WS step was manipulated in order to produce sufficient H\({}_{2}\) to reach the nominal COT value upon combustion with the O\({}_{2}\) depleted air stream from the oxidation step outlet. Figure 4: GSPOX reactor cycle composition and temperature profile for an H\({}_{2}\) plant case. (POX: 0–46.4 s, REF: 46.4–92.7 s, OX: 92.7–162.3 s, RED: 162.3–208.6 s). Figure 5: GSPOX reactor cycle composition and temperature profile for an H\({}_{2}\)-power co-production plant case. (POX: 0–97.8 s, WS: 97.8–111.7 s, OX: 111.7–363.1 s, RED: 363.1–405.0 s). The mole fraction at equilibrium of CO\({}_{2}\) and H\({}_{2}\)O for the kinetic expressions in Table 2 is determined as a function of the specified selectivity to CO and H\({}_{2}\) (assumed conservatively to be 95%) and the actual mole fraction of each gas species in the reactor at any given time, as shown in Equations (6) and (7). Where \(s_{k}\) indicates the selectivity towards a specific component \(k\). Reactions taking place in reduction and oxidation steps proceed to completion, while only methane in the partial oxidation step is fully converted. \[\frac{y_{H_{2}}}{y_{H_{2}}+y_{H_{2}O,eq}}=s_{H_{2}} \tag{6}\]  
\[\frac{y_{co}}{y_{co}+y_{co2,eq}}=s_{co}. \tag{7}\]