## 2 Materials and Methods
### Operating Conditions  
The performances of the integrated energy systems have been investigated. To this purpose, 1 kg/s of geothermal water at 230 \({}^{\circ}\)C was considered as energy input [16]. The geofluid was used to drive both the ORC and HEX units depending on the energy request of the investigated users while the minimum reinjection temperature was fixed to 70 \({}^{\circ}\)C to prevent scaling and fouling problems within system components and pipes, according to the literature [82; 105; 106]. The thermal efficiency of the heating process from the geothermal source was fixed to 0.92 [80] and the minimum pinch-point temperature was considered equal to 10 \({}^{\circ}\)C [16]. This value was increased if the constraint on the minimum reinjection temperature was not fulfilled. The analysis was carried out adopting transcritical ORC units with and without the internal heat regenerator (simple and IHE configuration, respectively) owing to their high performance with geothermal sources [16]. Isobutane was selected as organic fluid due to its thermal stability, low specific cost and attractive efficiency, according to the literature [67; 107; 108]. Furthermore, isobutane is suitable for supercritical ORC applications with high-temperature geothermal sources [33; 68; 69], as already pointed out in the introduction section. The ratio between the critical temperature of the working fluid and the geothermal source temperature was equal to 0.81, within the suggested interval (0.8-0.9) to minimise the specific investment cost and the levelized cost of energy [62]. ORC condensation temperature was fixed to 30 \({}^{\circ}\)C while the maximum pressure was set to 65.32 bar, corresponding to 1.80 times the critical value (\(p_{crit}\) = 36.29 bar). At part load operations, the maximum pressure can be reduced up to 1.03 \(p_{crit}\) depending on the energy request. The temperature at the entrance of the turbine varies with the pressure and the maximum value was fixed to 220 \({}^{\circ}\)C, based on the geothermal source temperature. For the investigation, the maximum turbine and pump efficiencies were imposed equal to 0.80 and 0.70 [109], respectively, while the electro-mechanical efficiencies were 0.95 [110]. The effectiveness of the internal heat exchanger was set to 95% and the vapour temperature at the IHE exit (_point 4_*) was 10 \({}^{\circ}\)C higher than the condensation temperature [16; 111]. The efficiency and head of the pump used for the cooling circuit were equal to 80% and 10 m, respectively, while the corresponding pinch point temperature was 5 \({}^{\circ}\)C [81; 106]. Table 1 summarises the operating conditions and the main assumptions adopted for the analysis. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Parameters**} & \\ \hline Mass flow rate of geothermal fluid & (kg/s) & 1 \\ Temperature of geothermal fluid & (\({}^{\circ}\)C) & 230 \\ Minimum reinjection temperature & (\({}^{\circ}\)C) & 70 \\ Pinch-point temperature in geothermal circuit & (\({}^{\circ}\)C) & 10 \\ Geothermal heat exchanger efficiency & (-) & 0.92 \\ Geothermal pump efficiency & (-) & 0.70 \\ ORC configuration & & Transcritical \\ ORC working fluid & & Isobutane \\ ORC maximum temperature range & (\({}^{\circ}\)C) & 140.0–220.0 \\ ORC maximum pressure range & (bar) & 37.38–65.32 \\ ORC condensation temperature & (\({}^{\circ}\)C) & 30.0 \\ ORC condensation pressure & (bar) & 4.05 \\ Maximum ORC pump efficiency & (-) & 0.70 \\ Maximum ORC turbine efficiency & (-) & 0.80 \\ Electro-mechanical efficiency & (-) & 0.95 \\ Cooling pump efficiency & (-) & 0.80 \\ Head of cooling pump & (m) & 10 \\ Pinch-point temperature in cooling system & (\({}^{\circ}\)C) & 5 \\ Heat exchanger inner tube diameter & (mm) & 10.92 \\ Heat exchanger outer tube diameter & (mm) & 12.70 \\ Gas-fired auxiliary boiler efficiency & (-) & 0.90 \\ Natural gas lower heating value & (MJ/Sm\({}^{3}\)) & 34.54 \\ Reference thermal efficiency & (-) & 0.92 \\ \hline \hline \end{tabular}
\end{table}