## 1 Introduction  
Geothermal energy is one of the most promising energy directions with the potential to achieve carbon neutrality and peak carbon goals, sparking enthusiasm among energy development researchers [1]. According to the World Energy Assessment (WEA), global geothermal resources are estimated to be around 600,000 EJ per year [2]. Geothermal resources have potential not only in their vast availability on the Earth's surface but also in their long-term stable supply [3]. Unlike solar, wind, and tidal energy, geothermal energy that one not require intermediate energy storage to address peak demand fluctuations, making it one of the most promising low-carbon resources to replace Heat Exchangers (DHE), and Super Long Geothermal Heat Pipe (SLGHP). EGS essentially involves creating artificial heat reservoirs using hydraulic fracturing technology to increase the permeability of hot dry rock formations [6; 7]. This process is typically achieved by connecting two parallel vertical or horizontal wells to natural and artificial fractures. Cold water at a lower temperature is injected into the reservoir through one well. Driven by the pressure difference in the formation, the water flows through the fractures, carrying away heat from the formation to the surface for heat exchange through another well. Although this technology has been demonstrated in various pilot projects worldwide, the associated technical risks, such as fluid loss during injection, pipe scaling, pipe corrosion, and micro-seismic events induced by formation collapse, have hindered its large-scale implementation to date [8; 9]. Considering resource utilization, environmental protection, and geological disaster prevention, the use of existing hydraulic fracturing for reservoir modification requires a significant amount of land and water resources. Construction and related infrastructure development on the ground necessitates a considerable amount of land resources. During the hydraulic fracturing process, a considerable amount of water resources is consumed, and the formation may contain natural fractures leading to water loss. The flow of water in the formation causes the loss of pressure balance, triggering numerous micro-earthquakes, resulting in a short lifespan for the hot dry rock development project and substantial destruction of surface infrastructure. Therefore, exploring new methods for hot dry rock development is a crucial task. Enhanced geothermal systems initially accelerate heat extraction but experience reduced extraction later on. Increasing injection rates diminish hydraulic fracturing benefits. The potential for enhanced geothermal systems exists in the basal Cambrian sandstone unit in Alberta, Canada. Conducting hydraulic fracturing before geothermal operation enhances the permeability of the heat reservoir, reducing the pressure drop required for fluid circulation [10]. Later water loss occurrences, however, lead to decreased efficiency in heat extraction. The DHE system is essentially a technology for extracting heat from individual wells, using a U-tube or casing system to transfer heat near the wellbore to the surface for heat exchange [11]. It is a closed-loop heat extraction technology that addresses challenges such as pipeline corrosion, scaling, and fluid medium losses. However, due to the relatively small heat exchange surface area in the DHE system, the amount of heat extracted is significantly lower than that of EGS systems. Research by [PERSON] et al. showed that a geothermal reservoir at a depth of 3000 m and a temperature of 126 \({}^{\circ}\)C could extract 700 KW of heat annually when operated for 3 months [12]. In the DHE system, the working fluid circulates in a sensible heat form to store the extracted geothermal energy, with its temperature rapidly increasing along the flow path. The temperature difference between the heat source and the working fluid is one of the key factors in controlling the total heat extraction rate from the heat source.