## 2 Materials and Methods
### Closed-Loop Geothermal Energy Systems: WBHEs  
Exploiting the geothermal energy resources associated with decommissioned hydrocarbon wells requires that the borehole to be retrofitted with a heat exchanger. In current practice, two main types of closed-loop systems are used to harness geothermal energy resources by taking advantage of disused boreholes in oilfields: U-tube and coaxial double-pipe WBHE technologies [20; 21]. Both kinds of systems allow for the extraction of heat from the ground without extracting or re-injecting any geothermal fluids. In U-tube heat exchangers, fluid is pumped through one tube string and comes out the other, while coaxial heat exchangers are composed of two concentric pipes, as shown in Figure 5 and Table 4. In coaxial WBHEs 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). The gap between internal pipes is filled with an insulating material, 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. Figure 4: Temperature data visualisation for the Gela 38 hydrocarbon well: Depth (m); Temperature (\({}^{\circ}\)C). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Depth** & **Litho-Stratigraphic Formation** & \(\lambda_{\text{s}}\) & \(pc_{\text{s}}\) & \(\rho\) \\
**m** & **Litho-Stratigraphic Formation** & **W/mK** & **kJ/m3K** & **kg/m3** \\ \hline
1772 & Marls, clays and gypsum & & & \\
2117 & Marl, calcareous marl and clays & 3.16 & 1937 & 2359 \\ \hline
2556 & Limestone and marl & & & \\
2582 & Limestone & 2.17 & 1495 & 1801 \\ \hline
2860 & Limestone, dolomitic limestone and marl & 3.12 & 2010 & 2480 \\ \hline
3156 & Limestone, marl and dolomite & & & \\
3446 & Marls, clays and gypsum & 2.17 & 1495 & 1801 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Gela 38 hydrocarbon well-lithost stratigraphic profile (Gela Field, Sicily). Corrosion must be considered when selecting this type of system; it may be ideal for heat exchange, but it may also reduce the system's operational life. Due to its low cost and its heat transfer and storage capacity, water is still one of the most commonly used fluids. The operating parameters of subsurface closed-loop systems, such as fluid flow rate and pipe diameter, should be selected to guarantee transient turbulent flow conditions, since these conditions facilitate heat transfer, and low hydraulic head losses, since this indicates lower energy expenditure on circulation pumping. Compared to U-tube heat exchangers, coaxial heat exchangers have a higher surface area and a higher volume of the working fluid through which heat exchange occurs. As a result, under the same injection rate conditions (q), the fluid flow velocity in the coaxial pipe system and the hydraulic pressure required for fluid circulation can be lower, resulting in decreased energy consumption from pumping [21]. The coaxial geometry of a double-pipe heat exchanger also has the advantage of reducing thermal resistance between the circulating fluid and the wellbore. In this paper, in order to evaluate and analyse the temperature profiles of the selected fluid (water) associated with a coaxial double-pipe WBHE technology, the simplified models proposed below were implemented in MATLAB and applied to the selected case studies: the Villafortuna 1, Tempa Rossa 1D and Gela 38 hydrocarbon wells. For the elaborated model, two main assumptions were considered: the propagation of heat in the reservoir occurs by means of conduction (convection phenomena are neglected),