## 2 Materials and Methods
### Economic Analysis  
The economic viability of the integrated geothermal system has been evaluated. To this purpose, the costs of the different components were calculated, adopting the bare module equipment methodology, which takes into account direct and indirect costs [113]. In particular, the reference purchased cost \(C_{j}^{0}\) (in US dollar) of the generic component \(j\) was evaluated according to the following equation:  
\[\log C_{j}^{0}=K_{1,j}+K_{2,j}\log S_{j}+K_{3,j}\Big{(}\log S_{j}\Big{)}^{2} \tag{11}\]  
Figure 3: Electric and thermal demand of the investigated commercial centre.  
where \(S\) is the size or capacity parameter of the component \(j\) and it corresponds to the area (in m\({}^{2}\)) of heat exchangers or to the power (in kW) of pumps and turbines [113]. The superscript \(0\) refers to the base conditions with carbon steel material and ambient operating pressure, whereas the coefficients \(k_{1,j}\), \(k_{2,j}\) and \(k_{3,j}\) vary with the selected sub-systems (Table 2).  
The reference purchased costs of pumps and heat exchangers are corrected to take into account the adopted construction materials and operating pressures:  
\[C_{j}=C_{j}^{0}\ \left(B_{1,j}+B_{2,j}\ F_{M,j}\ \ F_{P,j}\right) \tag{12}\]  
where the coefficients \(b_{1,j}\) and \(b_{2,j}\) depend on the equipment type, while \(F_{M,j}\) and \(F_{Pj}\) represent the material and the pressure factors of the generic component \(j\). Specifically, the pressure factors are evaluated according to:  
\[\log F_{P,j}=C_{1,j}+C_{2,j}\log p_{j}+C_{3,j}\big{(}\log p_{j}\big{)}^{2} \tag{13}\]  
where \(p_{j}\) is the operating pressure. The coefficients \(b_{1,j}\), \(b_{2,j}\), \(c_{1,j}\), \(c_{2,j}\), \(c_{3,j}\) and the material factors \(F_{M,j}\) are shown in Table 2[19; 88; 89; 90].  
The turbine purchased cost was evaluated as a function of the corresponding reference cost [60; 114; 115]:  
\[C_{j}=C_{j}^{0}\ \ F_{BM,j} \tag{14}\]  
where the corresponding bare module factor \(F_{BM}\) is in Table 2[19; 88; 89; 90].  
Finally, the total cost (in euro) of the integrated geothermal system was calculated according to the following equation:  
\[C=\frac{CEPCI_{2019}}{CEPCI_{2001}}\ \cdot e_{EUR/USD}\cdot\ \sum_{j=1}^{N}C_{j} \tag{15}\]  
Here, the chemical engineering plant cost indexes (\(CEPCI\)) are used to account for inflation and update to 2019 the parameters of Table 2 (referred to as 2001). Specifically, \(CEPCI\) indexes correspond to 397.0 and 607.5 for 2001 and 2019, respectively [113; 116; 117]. Furthermore, the European Central Bank reference exchange rate (\(e_{EUR/USD}\)) from euro (EUR) to US dollar (USD) is adopted to express the total cost of the geothermal combined system in euros [118].  
Other assumptions for the economic analysis are summarised in Table 3. In particular, the investment period has been set to 20 years and the interest rate to 2%. The electricity and natural gas prices are based on Italian tariffs for non-domestic users [119] and the maintenance costs of the integrated geothermal-driven system have been assumed to be equal to 2% of the initial investment [28]. The reference exchange rate from euro to US dollar is 1.12 \(\upcels\)(1 July 2020 value) [118].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Heat Exchanger** & **Pump** & **Turbine** \\ \hline \(k_{1}\) & 4.3247 & 3.3892 & 2.2476 \\ \(k_{2}\) & \(-\)0.3003 & 0.0536 & 1.4965 \\ \(k_{3}\) & 0.1634 & 0.1538 & \(-\)0.1618 \\ \(c_{1}\) & 0.0388 & \(-\)0.3935 & 0 \\ \(c_{2}\) & \(-\)0.1127 & 0.3957 & 0 \\ \(c_{3}\) & 0.0818 & \(-\)0.0023 & 0 \\ \(b_{1}\) & 1.63 & 1.89 & - \\ \(b_{2}\) & 1.66 & 1.35 & - \\ \(F_{M}\) & 1.00 & 1.60 & - \\ \(F_{BM}\) & - & - & 3.5 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Equipment cost assumptions for bare module methodology.