## 3 Results and Discussion  
The temperature profiles associated with the analysed coaxial WBHE system configurations were obtained by making use of the specific ground properties of the selected case studies (the Villafortuna 1, Gela 38 and Tempa Rossa 1D hydrocarbon wells). Values relating to the thermal properties of the different rock formations have been attributed in accordance with references [11; 12] (Tables 1-3). For all cases analysed, the flow rate of the fluid and the inlet temperature were first considered as 3 kg/s and 50 \({}^{\circ}\)C, respectively. This temperature is a typical value for direct applications like production cycles in manufacturing and agricultural districts [2]. Subsequently, an analysis was conducted on the thermovector fluid temperature at the outlet as the inlet flow rate varied. The sizing of the inner and outer tubes, as well as the final casing size, were fixed according to the values proposed in Figure 6 and Table 5. The thermal conductivity value of the insulating material was set to 0.025 W/mK. In the first section of an external pipe of a coaxial WBHE system, the downward fluid is in thermal contact with both the ground on one side and the upward tube on the other. Because of its thermal properties, the ground in contact with the external piping provides a negative heat contribution, while the inner tube of a coaxial WBHE provides a positive one. As the negative contribution is usually larger, the water temperature (working fluid temperature) decreases slightly. This behaviour can be observed by analysing the obtained temperature profiles associated with the Gela 38 and Tempa Rossa 1D hydrocarbon wells, in which the thermovector fluid was cooled at depths of up to 1800 m and 1200 m, respectively. Unlike in the Gela 38 and Tempa Rossa 1D hydrocarbon wells, the thermovector fluid maintained a constant temperature (50 \({}^{\circ}\)C) for the first portion of the borehole (1400 m) in the Villafortuna 1 hydrocarbon well (Figures 7a, 8a and 9a). The presence of a thick stratigraphic horizon made up of terrigenous sedimentary deposits (Table 1), which are characterised by very low conductivity and specific heat values, negatively influenced the heat exchange and so limited heat dispersion. Figure 6: Coaxial WBHE geometry: considered configuration. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Tube Sizing** & **ID** & **OD** \\
**m** & **(mm)** & **(mm)** \\ \hline
3 inches & 77.9 & 88.9 \\ \hline
5 inches & 121.4 & 139.7 \\ \hline Casing 7 inches & 150.4 & 177.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: WBHE tube sizing—ID: internal diameter, OD: external diameter. Figure 7: **(a)** Temperature profile associated with the coaxial WBHE configuration considering the site-specific stratigraphy of Villafortuna 1 well. **(b)** Wellhead temperature behaviour as the flow rate changes. However, when the water and ground temperatures approached similar values in all three hydrocarbon wells, the negative contribution decreased, and water temperature increased. As the downward water profile line crossed the ground temperature line, the ground's heating process began, and the ground contribution became positive. Due to the presence of the insulating material, the heat exchange coefficient between the annulus and the inner tube was quite low, and the increase in the working fluid temperature could be mainly associated with the contribution of the ground. Using the fixed inlet working fluid temperature (50 \({}^{\circ}\)C) and the estimated fluid temperature at the outlet for the three case studies (Figures 7a, 8a and 9a), thermal power values were evaluated for 627.9 KW (100 \({}^{\circ}\)C, Villafortuna 1), 75.3 KW (56 \({}^{\circ}\)C, Tempa Rossa 1D) and 100.5 KW (58 \({}^{\circ}\)C, Gela 38). Considering a cascading exploitation mode of the heat accumulated by the working fluid water in Villafortuna 1 WBHE, it is correctly possible to hypothesize a multi-variant and comprehensive use of the resource.