## 4 Simulation Results
### Determination of Experimental Coefficients  
The calculation of the energy efficiency of the storage system requires the identification of the values assumed by the experimental coefficients (\(a_{i}\), \(b_{i}\), \(c_{i}\), \(d_{i}\)) that appear in the formulas provided above. The first two coefficients (\(a_{i}\) and \(b_{i}\), with \(i\) = 0\(-\)3) are necessary for the calculation of \(A(w)\) (see Equation (2a)) and \(B(w)\) (Equation (2b)), which define the adsorbent-adsorbate equilibrium equation (Equation (1)), while \(c_{i}\) and \(d_{i}\) (with \(i\) = 0-2) are used to calculate the equivalent specific heat of the working pair, as shown in Equations (14), (15a) and (15b). These coefficients are identified experimentally by the calorimetric technique described in Ref. [17]. The experimental measurements were conducted on a thermo-gravimetric apparatus installed in the CNR-ITAE laboratories according to the method described in Refs. [23; 25]. This apparatus allows the replication of the main phases of the thermodynamic cycle, measuring the equilibrium curves and the heat flows. Once isobaric curves were measured, the coefficients of the equilibrium curves were determined through a fitting procedure. In particular, we started from the experimental plots of the sorption isobars at a constant uptake (\(w\)). Then, we derived the sorption isosterees which provide the dependence of the pressure from the temperature, at a constant uptake. These are represented in a Clapeyron diagram (\(ln(P)\) vs. \(\
u T\)), where they are approximated straight lines (see Equation (1)). Therefore, based on a commercial software for data analysis, it is possible to determine the values of \(A(w_{i})\) and \(B(w)\) for each specific value \(w_{i}\) of the uptake. Finally, these values are plotted and fitted with a third-order polynomial curve to determine the coefficients of Equations (2a) and (2b). Usually, to obtain a reliable estimate, we considered no less than seven (\(P\),\(T\)) pairs, and no less than eight uptake values, for a \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & & **Buildings** & **Transport** & **Industry** \\ \hline CM01 & Activated Carbon AC35 CECA & \(\checkmark\) & \(\checkmark\) & \(\times\) \\ CM02 & Composite CaCl\({}_{2}\)-silica & \(\times\) & \(\times\) & \(\times\) \\ CM03 & Methanol & Composite LiBr-silica & \(\checkmark\) & \(\checkmark\) & \(\times\) \\ CM04 & Composite LiCl-silica & \(\checkmark\) & \(\checkmark\) & \(\times\) \\ CM05 & & Zeolite CBV 901 & \(\checkmark\) & \(\checkmark\) & \(\times\) \\ \hline CM06 & Activated Carbon SRD 1352/3 & \(\checkmark\) & \(\checkmark\) & \(\times\) \\ CM07 & Ethanol & Carbon Fibers FR20 & \(\times\) & \(\times\) & \(\times\) \\ CM08 & & Composite LiBr-silica & \(\checkmark\) & \(\checkmark\) & \(\times\) \\ \hline CM09 & & Composite CaCl\({}_{2}\)-silica & \(\checkmark\) & \(\checkmark\) & \(\times\) \\ CM10 & & Composite LiBr-silica & \(\checkmark\) & \(\checkmark\) & \(\times\) \\ CM11 & & Zeolite 4A & \(\checkmark\) & \(\checkmark\) & \(\times\) \\ CM12 & & Zeolite AQSOA FAM Z02 & \(\checkmark\) & \(\checkmark\) & \(\times\) \\ CM13 & Water & Zeolite DDZ70 UOP & \(\checkmark\) & \(\checkmark\) & \(\times\) \\ CM14 & & Zeolite SAPO 34 Tianjin & \(\checkmark\) & \(\checkmark\) & \(\checkmark\) \\ CM15 & & Composite Ca(NO\({}_{3}\))\({}_{2}\)-silica & \(\times\) & \(\times\) & \(\times\) \\ CM16 & & Zeolite AQSOA FAM Z01 & \(\times\) & \(\times\) & \(\times\) \\ CM17 & & Silica gel Sorbsil & \(\checkmark\) & \(\checkmark\) & \(\checkmark\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Acceptable and unacceptable working pairs for the applications considered. total of about 60 experimental values for each adsorbent/adsorbate pair. Tables 3 and 4 show the coefficient values that were obtained for each working pair considered. As anticipated in the previous section, the coefficients \(c_{i}\) and \(d_{i}\) are available only for some working pairs (unlike \(a_{i}\) and \(b_{i}\), whose values are available for all solutions).