## 3 Results
### Model Results  
Properties of the zeolite 13X and the operational conditions adopted for the simulation analysis are listed in Table 2. In all simulations, it was assumed that the zeolite reactor started from an equilibrium condition, where the initial temperature is given by the average of the temperatures detected by the 4 thermocouples immersed in the zeolite bed, while the vapour pressure is equal to that detected by the two piezoelectric sensors. From this, it follows that the initial state vector depends only on these two quantities, since it is possible to determine the water-uptake from the corresponding equilibrium isotherm (Equation (13)) and the masses of vapour inside and outside the zeolite bed from the respective state equations. In order to assess the effects of the inconstancy of the operative initial conditions on the reactor performance, a sensitivity analysis applied to the initial state vector was performed. The results show that a deviation within the expanded uncertainty (\(\pm\)1.3 \({}^{\circ}\)C) of the initial average bed temperature causes variations in the estimate of the adsorption/desorption heat between 3% and 5%, respectively. Similarly, a deviation within the expanded uncertainty (\(\pm\)1.4 mbar) of the measured initial reactor pressure produces variations in the energy output between 1% and 3%. Figure 8 shows two examples of simulation outputs evaluated in the following conditions:  
1. Adsorption phase with the zeolite bed at an initial temperature of 90 \({}^{\circ}\)C and HTF temperature, entering in the finned tube heat-exchanger, of 30 \({}^{\circ}\)C. The analysis was performed for different values of the fin effectiveness in order to evaluate the influence of this parameter on the performance of the reactor. \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Bed porosity \(\varepsilon_{b}\) & 0.38 \\ Particle porosity \(\varepsilon_{p}\) & 0.32 \\ Mean particle radius \(R_{p}\) & 2.2 mm \\ Density of dry zeolite \(\rho_{z}\) & 990 kg/m\({}^{3}\) \\ Heat capacity of zeolite \(C_{p,z}\) & 831 J/kg K \\ Conductivity \(k\) & 0.2 W/m K \\ HTF flow rate & 0.3 kg/s \\ \hline \end{tabular}
\end{table} 
Table 2: Properties of the zeolite 13X and process parameters. Figure 7: Adsorption results: zeolite temperatures during the test. (**a**) Adsorption—Test 4 and (**b**) Adsorption—Test 5. * **Description phase with the zeolite bed at an initial temperature of 30 \({}^{\circ}\)C and HTF temperature, entering in the finned tube heat-exchanger, of 90 \({}^{\circ}\)C. The analysis was performed for different values of the vapour pressure inside the reactor in order to evaluate the sensitivity of the model to the variation of this process parameter. **  
In Figure 9, the simulation results, obtained applying the model to the adsorption case study (Test 5), are compared with the experimental results. This test was selected because it was characterised by a very constant trend of the reactor pressure. The comparison of numerical and experimental temperatures shows a good agreement. The calculated bed temperatures show a faster decrease during the first 60 min of the test, and subsequently, the values follow the same trend. This is probably because there is an overestimation of the heat transfer between the zeolite bed and the finned heat-exchanger. Despite this initial  
Figure 8: Results of sensitivity analysis: (**a**) Effects of fin effectiveness on the temperature profile of zeolite bed during adsorption process (value of fin effectiveness equal to 1 corresponds to a not finned tube). (**b**) Effects of vapour pressure inside the reactor on the temperature profile during desorption process. Figure 9: Comparison of numerical (red) and experimental (blue) temperature trends of zeolite bed for the adsorption Test 5.  
discrepancy, the maximum difference recorded between the temperatures measured and those calculated remained below 2.5%.