## 3 Preliminary Calibration Attempt and Selection of Parameters for Optimization  
We ran preliminary simulations in the attempt to calibrate, and, eventually, validate the model based on expert knowledge and trial-and-error changes of parameters. This did not lead to satisfactory results, but we can use this preliminary attempt for selecting the parameters related to heat transfer, heat loss, and heat release that are later on used in the optimization procedure, and we also define their ranges. These simulations are based on the experimental setup representing Case S17, see Table 3. Results with a linear \(T_{BC}\) distribution (i.e., \(k_{1}=0\), \(k_{2}=-5.567\), and \(k_{3}=764.99\)) and the heat transfer parameters \(\alpha_{HTF}=275\) W/m\({}^{2}\)K and \(\alpha_{loss}=30\) W/m\({}^{2}\)K are shown in Figure 2 in orange. The simulated curves for the three temperatures T1, T3, and T7 roughly match the arrival time of the temperature jump after conversion in the respective region. However, the temporal temperature distribution differs between experiment and simulation. The slope at the temperature jump is much steeper in the simulation than in the experiment. This indicates that further processes occur at progressed conversion and overlap the release of heat due to the reaction, additionally to the heat loss and transport in the reactive bed. In order to identify those processes, we tested the influence of a variation in the following parameters on the simulation results: a porosity induced permeability alteration, the solid heat conductivity and the constants of the reaction kinetics. The changed parameters for each simulation are listed in Table 4. Figure 2 displays the simulation results. \begin{table}
\begin{tabular}{c c c} \hline
**Domain** & **Location** & **PriVar and Value** \\ \hline HTF channel & \(t=0\) & \(p=p_{HTF,init},T=T_{init}\) \\  & \(x=0\) & \(q_{air}=q_{air}T=T_{init}\) \\  & \(x=x_{max}\) & \(p=p_{HTF,init},q_{easy}=2q_{te}\) \\ Porous Bulk & \(t=0\) & \(p_{H_{\rm G}O}=p_{bulk,init};T=T_{init};\Phi_{\rm CAO}=0.1113\)\([-]\), \(\Phi_{\rm CA(OH)_{2}}=0.0[-]\) \\  & \(y=0\) & \(q_{\rm HCO}=q_{\rm CAO}=q_{\rm CAH}=0\) \\  & \(q_{energy}=q_{te}\) \\  & \(y=y_{max}\) & \(p_{H_{\rm G}O}=p_{bulk,init};\Phi_{\rm CAO}=q_{\rm CAH}=0\); \\  & \(q_{energy}=\frac{\mu_{\rm HO}K_{bulk}}{\mu_{\rm HO}}\
abla p_{y=y_{max}}\). \(h(H_{\rm G}O,T_{y=y_{max}})+(T(y)=y_{max})-T_{\rm BC})\mu_{loss}\) \\  & \(x=0\) \& \(x=z\) & \(q_{\rm HO}=q_{\rm CAO}=q_{\rm CAH}=0;q_{energy}=(T(xy)-T_{\rm BC})\mu_{loss}\) \\ \hline \end{tabular}
\end{table} 
Table 1: Boundary and initial conditions with: \(q_{air}\) source term for the component air, \(q_{\rm H_{\rm G}O}\) water source term, \(q_{\rm CA(OH)_{2}}\) Ca(OH)\({}_{2}\) source term, \(q_{\rm CAO}\) CaO source term, \(q_{e}\) energy source term. The initial temperature for all simulation cases is \(T_{init}=773\)\([\)K\(]\). \begin{table}
\begin{tabular}{c c c} \hline
**Property** & **Symbol** & **Value** \\ \hline Reference porosity (according to Reference [20]) & \(\phi_{\rm g}\) & 0.773 \\ Density Ca(OH)\({}_{2}\)[26] & \(\phi_{\rm Ca(OH)_{2}}\) & 2200 kg m\({}^{-3}\) \\ Density CaO [42] & \(\phi_{\rm CaO}\) & 3340 kg m\({}^{-3}\) \\ Permeability (according to Reference [20]) & **K** & 8.8\(\times\) 10\({}^{-12}\) m\({}^{2}\) \\ Specific heat capacity Ca(OH)\({}_{2}\)[26] & \(c_{\rm PCa(OH)_{2}}\) & 15300 kg\({}^{-1}\) K\({}^{-1}\) \\ Specific heat capacity CaO [26] & \(c_{\rm PCaO}\) & 934 kg\({}^{-1}\) K\({}^{-1}\) \\ Solid heat conductivity [8] & \(\lambda_{\rm s}\) & 0.4 W m\({}^{-1}\)K\({}^{-1}\) \\ Reaction enthalpy [8] & \(\Delta I_{\rm R}\) & 104.4 kJ mol\({}^{-1}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Material parameters. \begin{table}
\begin{tabular}{c c c} \hline
**Case** & **Vapor Pressure \(p_{bulk,init}\)** & **Air Flux \(q_{air}\)\([\frac{\rm kg}{\rm h}]\)** \\ \hline Case 17 (according to case A & 470 & 16 \\ in Reference [31]) & 270 & 25 \\ \hline \end{tabular}
\end{table} 
Table 3: Experimental setups, as basis for the simulations.