## 2 Materials and Methods
### Closed-Loop Geothermal Energy Systems: WBHEs  
In current practice, two main types of closed-loop systems have been described for harnessing geothermal energy resources by taking advantage of disused boreholes in oilfields: U-tube and coaxial double-pipe WBHE technologies [33; 34].  
In U-tube heat exchangers, fluid is pumped through one tube string and comes out of the other. It is by this action of flowing through the well that the fluid in the U-tube can gain heat energy from the surrounding geological formations. The gaps between internal pipes are filled with an insulating material, and the bottom hole is sealed. On the other hand, the coaxial heat exchanger comprises two concentric pipes. Circulating working fluid is injected into the outer pipe (the injection pipe), flows down to the lower part of the exchanger and is gradually warmed by heat from the rocks. After the fluid reaches the bottom hole of the well, it flows upwards through a thinner pipe, which acts as the inner pipe (the extraction pipe). Both pipes are thermally insulated, and the bottom hole is sealed. Heat exchange occurs between the geological formation and the fluid in the injection pipe and between the fluid in the injection pipe and the fluid in the extraction pipe [10].  
For both closed-loop geothermal systems, the consequences of corrosion have to be considered in the selection phase of the working fluid. Due to its low cost, heat transfer  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Depth**} & **Litho-Stratigraphic** & **Age** & \(\mathbf{\lambda_{\mathrm{s}}}\) & \(\mathbf{\rho_{\mathrm{c_{s}}}}\) & \(\mathbf{\rho}\) \\ \hline m & & & W/mK & J/kgK & kg/m\({}^{3}\) \\ \hline
1632 &
\begin{tabular}{c} Terrigenous sedimentary \\ deposits-Sandy Clay \\ \end{tabular} & Holocene–Pleistocene & 1.61 & 1696 & 1890 \\ \hline
5451 & \
\begin{tabular}{c} Calcareous Marl \\ rocks—Calcarenite/Dolostone \\ \end{tabular} &
\begin{tabular}{c} Miocene–Middle Eocene \\ \end{tabular} & 2.17 & 830.1 & 1801 \\ \hline
6189 &
\begin{tabular}{c} Carbonate \\ rocks—Calcarenite/Dolostone \\ \end{tabular} & Upper Jurassi–Lower Jurassic & 3.50 & 810.5 & 2480 \\ \hline
6282 &
\begin{tabular}{c} Elastic sedimentary \\ rocks—Argillaceous Sandstone \\ \end{tabular} & Middle Triassic & 3.00 & 821.1 & 2330 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Trecate4 hydrocarbon well-lithost stratigraphic profile (Villafortuna–Trecate Oilfield, Western Po Plain).  
Figure 2: Temperature data visualisation for the Trecate4 hydrocarbon well: depth (m); temperature (\({}^{\circ}\)C).  
and stored capacity, water represents one of the most used working fluids. Moreover, operating parameters such as the fluid flow rate and pipe diameter have to be selected in order to guarantee transient turbulent flow conditions in the subsurface, thus facilitating heat transfer from the ground to the fluid [33].  
For properly evaluating the temperature profiles of the selected fluid (water) associated with both U-tube and coaxial double-pipe WBHE technologies, the models proposed below were implemented in a Python environment, identifying the best geothermal system configuration. Then, they were applied to the selected case study represented by the Trecate4 hydrocarbon well.