## 1 Introduction
However, as the number of these systems increases, concerns about their impact become more significant. A more comprehensive assessment of thermal plume migration is essential for the design and management of GSHPs in urban areas, particularly in locations with high system densities or where aquifer resources are in close proximity [32; 33]. The effect of geo-exchange systems adds to other important anthropic systems in the urban environment, such as subway tunnels, industrial plants, and underground tanks. The resulting rise in temperature contributes to the urban heat island (UHI) effect. This was widely studied by many authors for different urban areas: [PERSON] and [PERSON] [34] demonstrated the existence of a UHI in the city of Breslava (Polonia); [PERSON] et al. [35] studied the impact of anthropic activities on groundwater temperatures in different cities of Germany (Berlin, Munich, Cologne, and Karlsruhe); [PERSON] et al. [5] showed an increase in groundwater temperature equal to 5 \({}^{\circ}\)C in the industrial area of the city of Cologne. The effects of UHI have important implications for human health, increasing the risk of mortality during summer heat waves and also negatively impacting ecosystems and water bodies [36; 37]. Numerical models are common tools used to quantitatively evaluate the effects of external stresses in the subsoil. There are many examples of their use in different fields, from groundwater resource extraction and management in complex geological settings [38; 39; 40] to groundwater pollution remediation [41; 42; 43], groundwater subsidence study [44; 45], or interaction between deep and shallow water [46] and their consequences on shallow sediment transport [47; 48]. Furthermore, numerical models can also be applied to evaluate the extension of the thermal interference in the subsurface [49]. [PERSON] et al. [50] presented an analysis of the anthropogenic and natural factors responsible for the thermal balance of the subsoil in Milan. [PERSON] et al. [9] developed a semi-analytical model to study the outlet fluid temperature of a BHE according to different hydrogeological settings. To evaluate the extent of thermal perturbation in different aquifers, [PERSON] and [PERSON] [51] proposed different simulations, considering groundwater flow velocities. An interesting analysis was conducted by [PERSON] and [PERSON] [52], which developed a finite numerical model to show the main parameters influencing the heat exchange between BHE and subsoil. [PERSON] et al. [53] reproduced finite elements numerical models simulating annual heating and cooling cycles to verify the sustainability of geothermal resources and the thermal impact induced by the BHEs during a long-term (20 years) operation. Predictive models of thermal plume behavior and groundwater temperature distribution, considering factors such as aquifer permeability, groundwater flow rates, and system configuration, are also essential to optimize the placement and operation of GSHPs [16]. Updating the thermal conditions of the ground with continuous temperature measurements can increase the optimization of the geo-exchange system: [PERSON] et al. [54] demonstrated the performance of a sequential optimization applied to two borefields with 5 and 26 BHEs over 15 years of operation. By incorporating these models, it will be possible to minimize the risks associated with thermal interference and ensure that the deployment of BHEs and GSHPs remains a sustainable and environmentally responsible solution. When a GSHP system is installed close to other operating wells, the induced thermal perturbation should be carefully evaluated to prevent negative effects on other uses of the groundwater resource. However, the evaluation of more than one BHE is unfeasible with classical techniques, making this task hard to accomplish.