## 3 Results and Discussion
### Reactor Hygrothermal Behavior  
The comparison of the hygrothermal behavior of the reactor between the fixed packed and the moving bed modes is shown in Figures 5-8. The curves with \"\(\bigcirc\)\" and \"\(\bigcirc\)\" markers refer to the fixed bed (test 1). These curves represent the typical behavior of an open sorption packed bed reactor and thus can be used as a reference to compare with the moving bed operating mode. Since the shape of the curves in test 1 is quite smooth, it was concluded that the material was densely packed in the reactor which resulted in a homogeneous sorption throughout the bed (see Figures 5-8). At the initial time instant \(t=0\) min the material had the lowest hydration state, less than 0.01 kg/kg (see Table 3, test 1) that corresponded to the initial Polanyi adsorption potential \(\Delta F_{0}>10\) kJ/mol (see Figure 4). Before the hydration reaction was initiated, the adsorption potential \(\Delta F_{1}{}^{\prime}=RT\ \ln(p_{\rm vs}/p_{v})\) in the reactor inlet conditions was equal to \(\Delta F_{1}{}^{\prime}=1.7\) kJ/mol. The difference \(\Delta F_{0}-\Delta F_{1}{}^{\prime}\) thus determined the maximum possible loading lift of the material with water, which was close to 0.81 kg/kg (see Figure 4). The difference of adsorption potentials, being high, produced the temperature lift of 16.6 \({}^{\circ}\)C between the inlet and outlet air temperature in the reactor within 4 min (see Figure 5, test 1), corresponding to 461 \(\pm\) 37 W of the thermal power (see Figure 8, test 1). At the same time, the outlet water vapor pressure sharply dropped down to 2 mbar (see Figure 6, test 1). The maximum of the thermal power of 551 W, as well as the minimum of the water vapor pressure of 1 mbar in the outlet conditions, were reached in 10 min. By this time, the material was loaded with water up to 0.04 kg/kg (see Figure 7, test 1). The distinct decrease on 50 W of the thermal power appeared after 14 min of work (see Figure 8, test 1), before the heat recovery was activated. The thermal power continued to decrease after the activation of the heat recovery (see Figure 8, test 1). The main driving factor behind the decrease in the thermal power in the fixed packed bed is the extinction of the sorption phenomenon related to the saturation of the material by water (see Figure 7, test 1). The dynamic adsorption potential \(\Delta F(t)=RT(t)\ \ln(p_{\rm vs}/\overline{p_{v}}(t))\) related to the air conditions on the reactor inlet and outlet with \(\overline{p_{v}}(t)\approx\frac{1}{2}(p_{v,in}+p_{v,out})\), and to the solid temperature \(T(t)\), also varied during the experiment and modified the sorption capacity. Due to the solid heating, the adsorption potential changed to \(\Delta F_{1}=5.6\) kJ/mol at 4 min, which caused the dynamic shift of the virtual equilibrium from 0.81 kg/kg to 0.25 kg/kg (see Figure 4). As soon as the solid was cooled down, the adsorption potential sprang back to 3.7 kJ/mol that corresponded to 0.44 kg/kg as the virtual equilibrium water uptake. As follows from Figures 5 and 6, the heat dissipated by the in-line fan and the activation of the heat recovery brought also the slight swing in the operating conditions (the inlet air temperature and water vapor pressure). The adsorption potential, due to the heat dissipated by the fan, was \(\Delta F_{2}=5.6\) kJ/mol, while after the activation of the heat recovery, it was \(\Delta F_{3}=5.1\) kJ/mol. The value of \(\Delta F_{2}\) is fully equivalent to \(\Delta F_{1}\), but the potential \(\Delta F_{3}\) is lower than \(\Delta F_{1}\). The difference between the potentials \(\Delta F_{3}<\Delta F_{1}\) was clearly produced by the reaction advancement (see Figures 5-7, test 1), but not by the activation of the heat recovery. Therefore, the contributions from the heat dissipated by the fan or from the heat recovery to the sorption performance of the fixed packed bed are negligible. Moreover, there are no non-linearities in the water mass uptake curve (see Figure 7, test 1), which could be linked to the effects described above.