## 3 Results and Discussion
### Performance of the Integrated Geothermal System  
First, a parametric investigation was carried out, and the effect of the maximum temperature (T\({}_{\rm max}\)) on the ORC performance was analysed. The maximum pressure was fixed to 65.3 bar (1.80 \(p_{crit}\)) while the condensation temperature was set to 30 \({}^{\circ}\)C. As expected [29], a continuous increase in the ORC electric efficiency with the maximum temperature was noticed for both simple and regenerative configurations (Figure 4). The simple arrangement guarantees higher performance for temperature values lower than 165 \({}^{\circ}\)C and a plateau (\(\eta_{el}\approx\) 13.4%) was reached for T\({}_{\rm max}\) higher than 200 \({}^{\circ}\)C. Conversely, the IHE configuration guarantees a significant raise in the electric efficiency when the temperature moves from 140 \({}^{\circ}\)C to 220 \({}^{\circ}\)C (6.7% to 18.7%, respectively) while the maximum electric power (102.3 kW\({}_{\rm el}\)) is registered when the temperature at the turbine entrance is equal to 195 \({}^{\circ}\)C.  
Figure 4: Influence of the maximum temperature on ORC electric power and efficiency. Simple and IHE configurations. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Unit** & **Value** \\ \hline Investment Period & (Years) & 20 \\ Interest rate & (\%) & 2 \\ Specific revenue for the saved thermal energy & (c\(\xi\)/kWh\({}_{\rm th}\)) & 6.7 \\ Specific revenue for the saved electricity & (c\(\xi\)/kWh\({}_{\rm el}\)) & 18.8 \\ Specific value of the electricity injected into the grid & (c\(\xi\)/kWh) & 10.0 \\ Specific cost of the electricity withdrawn from the grid & (c\(\xi\)/kWh) & 18.8 \\ Specific cost of natural gas & (c\(\xi\)/kWh) & 6.0 \\ CEPCI\({}_{2001}\) & (-) & 397.0 \\ CEPCI\({}_{2019}\) & (-) & 607.5 \\ EUR/USD exchange rate & (EUR/USD) & 1.12 \\ Maintenance cost/Investment cost & (\%) & 2.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Further assumptions for the economic analysis. A multi-variable optimisation was adopted to select the most suitable configuration of the ORC geothermal-driven apparatus, and the electric power and efficiency have been considered as objective parameters. Figure 5 highlights that a Pareto frontier exists and the \"minimum distance\" criterion was adopted to define the proper ORC arrangement according to the literature [120; 121]. The method suggests selecting the system configuration that minimises the dimensionless distance to the ideal point (the red circle in Figure 5) that is characterised by the maximum ORC electric efficiency (\(\eta_{el,ORC\text{max}}\)) and the maximum electric power (\(P_{el,\text{max}}\)), according to the following equation:  
\[d=\text{min}\left(\sqrt{\left(\frac{\eta_{el,ORC\text{ max}}-\eta_{el,ORC\text{ \ \ \ }i}}{\eta_{el,ORC\text{ max}}-\eta_{el,ORC\text{ min}}}\right)^{2}+\left(\frac{P_{el,\text{ max}}-P_{el,\text{ \ \ }i}}{P_{el,\text{ max}}-P_{el,\text{ min}}}\right)^{2}}\right) \tag{16}\]  
The subscript \(k\) refers to the generic \(k^{\text{th}}\) ORC configuration that is characterised by the electric efficiency \(\eta_{el,ORC\text{ \ \ }k}\) and the electric power \(P_{el,k}\), whereas \(\eta_{el,ORC\text{ min}}\) and \(P_{el,\text{min}}\) corresponds to the minimum ORC electric efficiency and power on the Pareto frontier, respectively. In particular, the transcritical ORC with the internal heat exchanger (IHE) and temperature at the entrance of the turbine equal to 205 \({}^{\circ}\)C was selected as the most suitable configuration. The corresponding electric power and efficiency were equal to 101.4 kW and 17.4%, respectively. At full load, the geothermal mass flow rate (1 kg/s) was fully exploited in the ORC and the HEX thermal production is absent. At partial load the mass flow rate of the organic fluid was reduced and, as a consequence, a rate of the geofluid was used to drive the HEX sub-system. It is worth noting that a minimum geothermal flow is required for the proper operation of the HEX heat exchanger.