## 6 Conclusions  
This study presents a model concept for simulating the indirectly operated reactor concept. It is composed of two subdomains, one for the reactive bed and one for the heat transfer channel. Both submodels are coupled by exchanging a conductive heat flux. A major objective of this study was the calibration and validation of the numerical model. The simulation results were compared to experimental temperature data at distinct measurement points and to the overall conversion for a discharge reaction as presented in Reference [31]. The temperature in the experiment, however, falls below the temperature imposed in the heat transfer channel. In Reference [20], this was explained with heat losses occuring over the reactor casing. Our study reveals that introducing the hypothesized heat loss in the model concept is not sufficient to reproduce the experimental temperature profiles. Another important mechanism could be identified and is concerned with the decrease in the reaction rate with increasing conversion of the reactive material. To represent this effect phenomenologically in our model, we modified the reaction kinetics by introducing the factor \((1-X)^{k_{R2}}\). With the heat-transfer coefficient in the heat transfer channel, the temperature distribution outside of the reactive bed, the heat-loss coefficient, and two reaction-rate constants, we identified altogether seven model parameters as relevant to be included in a calibration for the envisaged simulation setup. They were inferred with the help of Bayesian inversion based on a Markov chain Monte Carlo algorithm. To accelerate the process, we replaced the numerical model by a PCE (polynomial chaos expansion) surrogate model that we trained with 500 simulation runs at varying parameters covering the parameter space. The Bayesian inference delivers a posterior parameter distribution with the mean being the most probable value. All the inferred parameters were Gaussian distributed in the posterior distribution. This confirms that our numerical model is sensitive to all of them. The simulation results of the calibrated surrogate model showed a good match with the measurements. A subsequent validation with a similar experiment at different boundary conditions confirms the model for the experimental setup. The new insights from this modelling study into the interpretation of the experimental temperature data and the conversion rates of the reactive material can be summarized as follows:  
In addition to the heat transported in the heat transfer channel, heat is lost over the reactor surface. As temperatures close to the equilibrium temperature limit the reaction, the heat losses in fact lead to an increased speed of reaction. A temperature difference between the surface of the reactive bed and the casing of the vapor vessel induces a heat transport by a combination of different heat-transport processes, notably heat conduction, free convection, and radiation. It is beyond the scope of our study to identify the amount of heat loss associated to each mechanism separately. But we inferred that with \(1.34\times 10^{3}\) kJ in total more heat is lost over the reactor surface than transported to the heat transfer channel (\(0.93\times 10^{3}\) kJ). Contrary to the statement of Reference [20] that the experimental results can be reproduced by only considering the heat losses occuring in the homogeneous reactive bed, we identified an additional process that requires consideration. Our results indicate that the agglomerates decelerate the reaction in the reactive bed of the indirectly operated reactor, as they limit the distribution of the reaction fluid. We represented this effect phenomenologically by modifying the reaction kinetics. A reduced reaction rate at later stages of progressed conversion permits reaching the equilibrium temperature at the beginning of the reaction and causes a flatter slope of the temperature jump at the end of conversion.