Study on Rock Interface Stability in the Heat Exchange Channel of the Horizontal Section of U-Shaped Wells in Hot Dry Rock

Abstract

Enhanced Geothermal Systems (EGS) represent a promising direction for sustainable energy development, yet their efficiency and feasibility often suffer due to suboptimal heat extraction methods and interface instability in U-shaped wells. This study introduces an innovative volume encapsulation technology that aims to address these challenges. The proposed technology employs a combination of hydraulic fracturing and acidification to prepare the rock interface, followed by encapsulation using high-temperature liquid metal. Low-melting-point alloys are utilized as a heat exchange medium between the horizontal sections of the wells. This study meticulously analyzes the impact of formation stress, thermal shock stress, and liquid metal properties on rock interface stability. Advanced simulation tools and experimental setups were used to test the encapsulation process under various conditions. The application of liquid metal encapsulation demonstrated significant improvements in energy conversion efficiency and rock interface stability. In conditions simulating a dry and hot rock reservoir at depths up to 3000 m and temperature gradients reaching 2200 °C/m, the adjusted depth of horizontal sections and increased pumping pressure contributed to maintaining interface stability. The established failure criteria provide a robust theoretical foundation for the encapsulation process. Volume encapsulation technology using liquid metal not only enhances the operational efficiency of EGS but also stabilizes the rock interface, thereby increasing the feasibility of continuous geothermal energy extraction. This study offers valuable theoretical insights and practical guidance for future research and applications in geothermal energy technologies, creating new pathways for the efficient exploitation of geothermal resources.

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 does not require intermediate energy storage to address peak demand fluctuations, making it one of the most promising low-carbon resources to replace fossil fuels [4].

Current geothermal development mainly relies on shallow geothermal resources with vertical well circulation, which has the drawback of low heat exchange efficiency. For the development of energy resources in large reserves and deeper hot dry rock formations, energy developers have proposed Enhanced Geothermal Systems (EGS) [5], Downhole 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 Nian et al. showed that a geothermal reservoir at a depth of 3000 m and a temperature of 126 °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. However, in terms of large-scale heat extraction, the contact heat exchange area is the primary limitation hindering the widespread application of DHE technology. The ground source heat exchanger system can serve as a feasible alternative for wells with very low geothermal flow rates [13]. Alimonti collected existing literature on deep downhole heat exchangers to analyze their advantages and disadvantages. The analysis included heat transfer in simulated geothermal reservoirs, heat exchange between formations and wells, modeling of deep downhole heat exchanger design, and heat exchange in double-pipe systems, as well as performance analysis of deep downhole heat exchangers in producing thermal and/or electrical energy. It is evident that deep borehole heat exchangers can extract geothermal energy from deep wells, but the heat exchange flow is limited [14].

The SLGHP utilizes closed heat transfer technology based on phase change-free convection, differing from underground heat transfer techniques in principle [15]. This technology operates by transferring heat from the high-temperature end at a lower position to the low-temperature end at a higher position through the phase change of the heat transfer medium and the thermal convection of steam under the influence of gravity, without needing pump power [16,17,18,19]. The heat in the strata is transferred to the heat transfer medium, stored in the form of latent heat, and carried to the surface. The heat transfer medium does not experience a significant temperature increase with the amount of heat absorbed. The technical advantages of SLGHP are low energy consumption and low operational maintenance costs. However, applying this technology directly to heat extraction from ultra-deep hot dry rock formations poses challenges. Both domestic and international efforts have been made to utilize SLGHP technology for geothermal energy development. Experimental tests have been conducted on pipelines with lengths of 150 m and 3000 m by Kusama [16] and Zhang [20,21], respectively, outputting heat at steam temperatures of 80 °C and 34.3 °C, generating 90 kW and 174 kW of heat.

Based on the analysis of EGS, DHE, and SLGHP technologies, DHE has certain limitations in the scale of downhole heat exchange. SLGPH technology cannot be widely applied for heat extraction in ultra-deep hot dry rock formations. EGS technology involves the physical and chemical interactions between the heat exchange working fluid and rock during the fracture seepage process. The physical interaction includes rock fracturing due to thermal stress in hot dry rock formations, while the chemical interaction involves collapse caused by the dissolution of high-temperature heat exchange working fluid with the rock, with scaling and corrosion potential. To efficiently exchange heat in the horizontal section of new U-shaped wells while maintaining the overall stability of horizontal wells, using new efficient heat exchange working fluids and ensuring the rocks’ stability is necessary. The new U-shaped well differs from traditional U-shaped wells of equal diameter and does not have a single-well U-shaped heat exchange pipeline. Instead, it involves expanding the horizontal section of the U-shaped well to increase the heat exchange area. Therefore, improving existing horizontal wells and hydraulic fracturing technologies to enhance heat transfer between reservoirs and efficient heat exchange working fluids within the reservoir is essential. On the other hand, the application of new heat exchange working fluids is necessary to enhance heat exchange between high-temperature rocks and improve rock stability. Based on the above analysis, one of the key technologies in geothermal resource development is the effective sealing and storage of the fracture volume generated by hydraulic fracturing and acidizing in the horizontal section of U-shaped wells, achieving efficient heat conduction at the interface of high-temperature rock layers. Therefore, this paper proposes a volume storage and efficient heat exchange technology suitable for hot dry rock formations after hydraulic fracturing and acidizing. This new technology of storing U-shaped hydraulic fracturing and acidizing in horizontal sections avoids thermal fluid flow and chemical reactions in the formation. It directly transfers heat through thermal conduction between formation rocks and alloy metals, maintaining the overall stability of the U-shaped wellbore horizontal section.

2. Technology Description

This article proposes a volume storage technology for the horizontal section of U-shaped wells after hydraulic fracturing and reservoir acidification, forming an efficient heat exchange loop for efficient heat exchange, as shown in Figure 1.

Figure 1 shows that a network of fractures is formed near the wellbore in the ultra-deep dry hot reservoir after hydraulic fracturing. After small-scale fracturing in the U-shaped well, the formed fracture network consists of main fractures and microfractures, making it difficult to achieve closure of the horizontal section. Therefore, acid is injected into the formation through continuous tubing via surface acid injection equipment to acidify the dry hot rock formation, creating spatial volume post-hydraulic fracturing. Products after acidification can be returned through fluid flow to form a cavity with a diameter much larger than the wellbore diameter, as shown in Figure 1a.

After hydraulic fracturing and acidification, the horizontal section closes the channel of the formed horizontal section cavity. Before closing the cavity, water injection is required for pressure testing. If the pressure drops sharply, the leakage points of the horizontal section cavity must be plugged. While ensuring that the fluid medium does not leak, circulating air is injected underground to ensure a dry state.

A liquid alloy with a melting point higher than the formation temperature is heated until a phase change occurs to form liquid metal. The high-temperature liquid metal is injected from one side of the U-shaped well until the liquid alloy appears on the other side, and then the injection is stopped.

The liquid alloy with a melting point at the formation temperature is heated and undergoes a phase change to form a liquid metal. Then, it is injected into the closed loop to displace the liquid alloy with a melting point higher than the formation temperature, thereby achieving closure of the horizontal section cavity.

The horizontal section of the U-shaped well has significant advantages over volumetric storage technology by achieving heat conduction between hot dry rock at a high temperature and pressure and the flow channel of the thermal working fluid. Unlike EGS technology, the fluid within the hot dry rock formation flows through the wellbore to the surface for efficient heat exchange. The thermal working fluid circulating in the horizontal section of the U-shaped well is liquid alloy metal, which has high density, low melting point, and high boiling point characteristics. It is a more advantageous medium-to-low temperature phase change heat storage material and heat transfer material than water as a heat exchange medium. Utilizing liquid alloys as the heat exchange medium in the U-shaped well’s horizontal section cavity exploits this metal material’s excellent heat transfer properties. The low-melting-point liquid alloy Sn_17.8Cd_13.5Pb3^1.1Bi3_7.6 containing the metal elements Cd, Sn, Pb, and Bi has a thermal diffusion rate of approximately 13.72 mm²/s at 25 °C [22], whereas the thermal diffusion rate of water is 1.43 mm²/s. The thermal diffusion rate of the low-melting-point liquid alloy is 9.6 times that of water, showing promising prospects when applied to a closed-loop heat exchange system.

The core technology of circulating heat exchange in a U-shaped well using liquid metal as the heat exchange medium is to store volume in the horizontal section and increase the formation’s heat transfer area by improving thermal conductivity. Volume storage involves solidifying rocks in the dry hot rock formation with a liquid metal to isolate them, preventing fluids from entering the heat exchange channel in the formation and preventing loss of liquid metal fluid in the dry hot rock formation. Increasing the heat transfer area by improving the formation’s thermal conductivity essentially involves enlarging the diameter of the heat exchange medium flow to increase the contact area between the heat exchange medium in the heat exchange channel and the storage layer. An increase in the contact area of the storage layer implies an increase in the diameter of the horizontal section cavity in the U-shaped well. Due to high formation pressure, there is a pressure difference between the heat exchange media in the cavities of the horizontal section of the U-shaped well. Simultaneously, there are temperature gradients in the rocks surrounding the cavities, resulting in thermal stress differences in the rocks surrounding the cavities. Under the combined action of formation stress and thermal stress, the rocks stored in the cavities of the horizontal section may fracture, leading to significant instability in the flow channels of the heat exchange medium. Therefore, assessing the stability of the cavities in the horizontal section of the U-shaped well and optimizing the cavity radius is necessary.

3. Stability Analysis of Cavity Interface

Stability analysis of the horizontal section cavity of the dry hot rock U-shaped well involves sealing the cavity, where the geological heat passes through the metal material of the sealing layer and exchanges heat with the liquid alloy heat transfer medium, without any loss of fluid mass. However, the pressure in the dry hot rock formation and the thermal stress caused by cyclic heat exchange can lead to an imbalance between the rock pressure and heat transfer medium inside the heat exchange channel, potentially causing rock fracturing and instability in the heat exchange channel. To ensure the structural stability of the cavity in the horizontal section of the U-shaped well, the cavity structure must be optimized. The most stable cavity structure is a cylindrical structure with a smaller diameter; however, the horizontal section of the U-shaped well cannot form a cylindrical structure after hydraulic fracturing and acidification. Therefore, the cavity sealed in the horizontal section of the U-shaped well exhibits structural instability, and is especially prone to collapse during changes in formation pressure and thermal stress. This section mainly analyses and studies the stability of the surrounding rock of the cavity sealed in the horizontal section of the U-shaped well.

The interface between the metal lining layer and the rock within the cavity sealed in the horizontal section of the U-shaped well exhibits irregularity, as shown in Figure 1. Since the cavity sealed in the horizontal section extends along the length of the wellbore, structural issues crossing the wellbore section are simplified into a plane strain problem, as illustrated in Figure 2. The sealing layer is formed by injecting a high-temperature liquid alloy into the channel of the dry hot rock reservoir after undergoing heat conduction and cooling to solidify. The thickness of the sealing layer is determined by the time controlled by heat conduction between the high-temperature liquid alloy and the dry hot rock. Due to the irregular shape of the dry hot rock formed by small-scale hydraulic fracturing and acidification, the sealing layer also has an irregular shape. However, due to the similar heat conduction properties of the high-temperature liquid alloy, the sealing layer formed in the reservoir has thermal stability. The thickness of the sealing layer formed at the same heat conduction control time should be the same. Heat exchange occurs as the working fluid flows through the channel containing the sealing layer and directly exchanges heat with the inner lining. Since the dry hot rock exchanges heat directly with the sealing layer, the temperature of the sealing layer is higher than that of the heat exchange working fluid. A temperature gradient is formed between the heat exchange working fluid close to the sealing layer and the heat exchange working fluid in the direction of the central axis. The flow rate of the heat exchange working fluid effectively must be controlled effectively to achieve efficient heat exchange.

In Figure 2, the stability of the horizontal segment ring storage cavity is divided into the stability of the entire cavity body and the stability of the irregular interface between the cavity body and the rock. The stability of the cavity body is mainly controlled by the equivalent radius of the cavity, where a smaller equivalent radius results in higher stability of the cavity body. However, a smaller equivalent radius of the cavity body leads to a smaller contact area between the cavity rock and the lining of the ring storage alloy, reducing heat transfer efficiency. The stability of the irregular interface between the cavity rock and the rock is mainly controlled by the combined effect of thermal shock-induced thermal stress and the pressure of the heat transfer medium on the rock interface. The high-temperature damage to rock materials under unconstrained heating is mainly controlled by the tensile strength of the rock material at high temperatures. The material may only fail when the internal thermal stress exceeds the tensile strength at certain high-temperature moments. The formula for calculating thermal stress can be expressed as:

$$p_T=\alpha E\frac{dT}{dx}$$

(1)

This formula is used to calculate thermal stress caused by temperature gradients, where the symbols represent:

• $p_T$—thermal stress, MPa;
• $\alpha$—coefficient of thermal expansion;
• $E$—elastic modulus, GPa;
• $\frac{dT}{dx}$—temperature gradient of rock material, °C/m;

The horizontal segment of the ring storage cavity on the rock interface is mainly due to the pressure from the liquid alloy material’s gravity in a direction perpendicular to the formation and pressure differences between the injection and production wells in the U-shaped well. The water density is 1000 kg/m³, the water vapor density is 0.6 kg/m³, and the density of low-melting-point liquid alloys is generally around 8500 kg/m³. The force acting on the rock interface using low-melting-point liquid alloys as a heat exchange medium cannot be neglected due to the influence of gravity. The pressure on the rock interface by the heat exchange medium is expressed as:

$$p_a={\rho }_{a}g\left(h_{in}-h_{ex}\right)+\Delta p$$

(2)

where,

• $p_a$—represents the pressure of the thermal medium on the rock interface, Pa;
• ${\rho }_a$—the density of the low-melting-point liquid alloy, kg/m³;
• $h_{in}$—the depth of the injection well’s vertical section, m;
• $h_{ex}$—the depth of the production well’s vertical section, m;
• $\Delta p$—pressure difference between inlet pressure and outlet pressure, Pa.

In the horizontal section of a U-shaped well, within a high-temperature dry hot rock formation, heat conduction occurs from the inner lining layer to the lower-temperature heat transfer medium. The combined effect of thermal stress within the rock due to heat conduction and the pressure at the rock–heat transfer medium interface may exceed the tensile strength of the rock, leading to failure. Therefore, the criteria for determining the tensile failure of dry hot rocks can be expressed as:

$$p_T-p_a\ge p_{cri}\mathrm{R}\mathrm{o}\mathrm{c}\mathrm{k}\mathrm{F}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}$$

(3)

$$p_T-p_a<0\mathrm{I}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{R}\mathrm{o}\mathrm{c}\mathrm{k}$$

(4)

where $p_{cri}$ is the critical tensile strength of rock under a certain temperature environment in MPa. Formula (3) indicates that rock fragmentation occurs when the difference between thermal stress and pressure from the heat transfer medium in the thermal channel on the rock interface, at a certain depth and temperature gradient, exceeds the critical tensile strength of dry hot rock. Formula (4) indicates that when the pressure from the heat transfer medium on the rock interface is higher than the thermal stress, the rock is under compression and remains stable.

4. Results

The decrease in rock’s mechanical properties due to the thermal impact of the working fluid in the horizontal section of the loop storage cavity is caused by rapid temperature changes on the rock surface, creating temperature gradients. This process leads to the destruction of rock mineral bonding, the formation of microcracks within the rock, and potential penetration. High-temperature rocks may experience rapid fracturing at rock interfaces due to cooling by cold fluids, primarily resulting from the destructive force of thermal shock. When using water as a heat transfer medium in contact with granite in dry hot rock formations, significant thermal shock velocities are generated. For instance, the cooling rate of a 400 °C hot dry rock in 20 °C water within the first 20 s is 11.407 °C/s (the expression for thermal shock velocity is $v_T=\Delta T/\Delta t$, $\Delta T=T_1-T_2,\Delta t=t_1-t_2$. $t_1$ and $t_2$ represent time, while $T_1$ and $T_2$ represent the temperature corresponding to $t_1$ and $t_2$). The cavity in the horizontal section of the loop storage technology proposed in this paper has a metallic lining. By avoiding direct contact between the working fluid and the rock, the U-shaped well horizontal section loop storage technology effectively reduces thermal shock damage to the rock.

In hot dry rock formations, the main rock is granite, with a density of about 2.65–2.67 g/cm³, a thermal expansion coefficient of 9.0 × 10⁻⁶/°C, a compressive strength of 193.5 MPa for a sample size of ϕ50 mm × 100 mm at room temperature, and an elastic modulus of 14.79 GPa [23]. However, after cooling at different temperatures, the compressive strength decreases. For instance, in hot dry rock formations, when the temperature exchanges heat with water at 100 °C within the range of 250–600 °C, the compressive strength decreases from 105.59 MPa to 50.87 MPa, and the elastic modulus decreases from 11.30 GPa to 2.80 GPa [23]. The rock’s tensile strength decreases from 7.28 MPa to 2.31 MPa. This finding indicates that the decreased temperature of the surrounding rock mass in the horizontal section of the hot dry rock formation leads to significant changes in the compressive strength, tensile strength, and elastic modulus of the rock material. Therefore, calculating the thermal stress of hot dry rock materials in the heat conduction process, considering changes in parameters under different temperatures and times, is quite challenging. The calculation formula for thermal stress includes the temperature gradient $\frac{\mathrm{d}\mathrm{T}}{\mathrm{d}\mathrm{x}}$ of the rock material, which represents the rate of temperature change inside the rock under a fixed temperature difference. According to test data [24], $\frac{\mathrm{d}\mathrm{T}}{\mathrm{d}\mathrm{x}}$ decreases exponentially with an increase in heat conduction time. Thermal stress reaches its maximum only under high-temperature gradient conditions, and failure may occur only when thermal stress is at its peak. However, when maximum strain is used as the criterion for failure, considering variations in temperature gradient throughout the entire heat conduction process and calculating thermal strain in the direction of heat conduction is necessary. During stability analysis of the cavity interface, the criterion for the tensile failure of hot dry rock is determined based on the relationship between total stress and critical stress value. Therefore, this study only focuses on parameters with the highest temperature gradient, allowing for a fixed temperature gradient value. The maximum temperature gradients for 600 °C high-temperature granites under 20 °C water thermal shock and natural cooling are 57,204 °C/m and 3022 °C/m, respectively. However, in enclosed hot dry rock formations without direct contact between gas, liquid, and rock, the maximum temperature gradient is smaller than that of natural cooling. Temperature gradients of 2000 °C/m, 2200 °C/m, 2400 °C/m, 2600 °C/m, 2800 °C/m, and 3000 °C/m are considered for thermal conduction in enclosed hot dry rock formations. The relationship between temperature gradient and stress can be calculated using Formula (1), as shown in the following Figure.

Figure 3 illustrates a linear relationship between temperature gradient and stress. As the temperature gradient increases, thermal stress also rises, especially in the vicinity of the heat exchange medium and the rock contact surface, where localized high thermal stress is directly generated in high-temperature environments. Dry hot rocks generate thermal stresses at temperature gradients of 2000 °C/m, 2200 °C/m, 2400 °C/m, 2600 °C/m, 2800 °C/m, and 3000 °C/m are 266.2 MPa, 293.8 MPa, 319.5 MPa, 346.09 MPa, 372.7 MPa, and 399.3 MPa, respectively. As the temperature gradient changes from 2000 °C/m to 3000 °C/m, the thermal stress increases by 133.1 MPa.

In the horizontal segment cavities of dry hot rock formations at depths of 3000 m, the pressure of the heat exchange medium in the annular storage chamber is mainly determined by gravity and the pressure difference between the two vertical wells. The pressure caused by the gravitational force of liquid alloy metals can be calculated as 255 MPa using Formula (2), while the pressure caused by the gravitational force of water as the heat exchange medium is 30 MPa. Since both the injection and production wells in the U-shaped wells contain heat exchange media, fluid flow is not driven by the formation pressure but by the injection pressure ∆p at the injection wellhead. The pressure is highest at one end of the horizontal segment near the injection well, as calculated by Formula (2). Assuming an injection wellhead driving pressure of 20 MPa, the pressures on the rock interface caused by liquid alloy technology and water as heat exchange media, calculated using Formula (2), are 275 MPa and 20 MPa, respectively.

The tensile strength of rock can be obtained through experiments or empirical formulas derived from data analysis. In this study, the tensile strength of rock was measured as one-tenth of its compressive strength, which is $p_{cri}$ = 19.35 MPa [22]. At a heating rate of 2000 °C/m, the criteria for dry hot rock tensile failure can be observed.

$$p_T-p_a=266.2-275=-8.8<0$$

(5)

In a dry hot rock formation at a depth of 3000 m, the rock temperature gradient is 2000 °C/m. The interface rock will not be damaged by thermal stress generated by heat shock because rocks in deep formations have higher compressive strength and lower tensile strength, thus maintaining stability under certain conditions. In a dry hot rock formation at a depth of 3000 m with a temperature gradient of 2200 °C/m, the pressure at the interface of the stored rock is 293.8 MPa.

$$p_T-p_a=293.8-275=18.8>0$$

(6)

In a dry hot rock formation at a depth of 3000 m, the temperature gradient of the rock is 2200 °C/m. The stored interface rock will experience damage due to thermal stress caused by heat shock. Therefore, at higher temperature gradients, dry hot rock formations at a depth of 3000 m will lose stability due to thermal shock-induced damage.

5. Discussion

The stability of the interface rock stored in the horizontal section of the dry hot rock formation is related to factors such as temperature, temperature gradient, depth of the horizontal section, the density of the heat transfer medium, and surface injection pressure of the dry hot rock. Experimental studies indicate that higher temperatures in dry hot rock formations may have higher temperature gradients. To ensure stable interface rock stored in the horizontal section of a dry hot rock formation, the temperature must be considered comprehensively. To ensure the stability of interface rock stored in dry hot rock formations under high-temperature gradients, constructing horizontal section storage cavities in deeper formations or increasing surface injection pressure is considerable. To investigate the impact of formation depth on the stability of the interface rock stored in the horizontal section of dry hot rock formations, assuming that the formation temperature gradient and injection pressure are determined, the depth of the horizontal section formation must be designed so that the interface rock stored in the horizontal section formation cavity rock is stable. The critical value of the horizontal section depth of the U-shaped well under different temperature gradients at an injection pressure of 20 MPa can be determined using Formula (4) based on the criterion of dry hot rock tensile failure, as shown in Figure 4.

Under a pump injection pressure of 20 MPa, different temperature gradients affected the critical depth of the horizontal section of the U-shaped well, as shown in Figure 4. To maintain the interface stability of the horizontal section’s annulus cavity, the horizontal depth section must be above the critical line; otherwise, the rock may fracture. This finding indicates that the criterion Formula (4) for the tensile failure of dry hot rock provides an important basis for designing the depth of the horizontal section of the U-shaped well.

As shown in Figure 5, during the long-term thermal production process of the dry hot rock U-shaped well, cyclic thermal shocks can gradually reduce the tensile strength of the rock at the interface of the horizontal section storage cavity. To maintain the stability of the interface rock, increasing the injection well’s pump pressure in a timely manner is necessary. For example, with a 0.5 MPa decrease in tensile strength every 3 years, after 18 years of continuous heat extraction, the rock’s tensile strength will decrease from its initial value to 14.35 MPa. This process requires adjusting the pump pressure from 44.65 MPa to 49.65 MPa. This change demonstrates that by appropriately adjusting the pump pressure, even during continuous extraction of dry hot rock, the rock interface stability of the horizontal section storage cavity can be effectively maintained without significant pressure adjustments. In deep reservoirs within hot dry rock formations, the higher the depth, the higher the temperature, and the lower the critical strength, higher surface pressure is required. Therefore, current surface pumping equipment may have limitations for deeper hot dry rock reservoirs. This technology is not suitable for sandstone-type hot dry rock formations.

6. Conclusions

This study successfully proposed and validated a new technology for storing volume in the horizontal section of dry hot rock U-shaped wells, providing an innovative solution for effective dry hot rock energy development. By conducting hydraulic fracturing and acidizing in the horizontal section and sealing the rock interface with high-temperature liquid metal, this technology not only optimizes the heat exchange process but also achieves efficient energy conversion using low-melting-point liquid alloys as the heat transfer medium.

Furthermore, it thoroughly explores factors influencing rock interface stability in the horizontal section of U-shaped wells, including formation stress, thermal shock stress, as well as the gravity and pressure effects of liquid alloys. Establishing failure criteria for the rock interface lays a theoretical foundation for the application of storage technology in the horizontal section of U-shaped wells.

The study also analyzed the parameter sensitivity of rock stability at the interface of dry hot rock formations, indicating that adjusting the depth of the horizontal section can effectively maintain rock interface stability. These findings will provide important guidance for U-shaped wells’ design and optimization.

Moreover, research shows that cyclic thermal shock decreases rock tensile strength. However, by increasing pump injection pressure, the rock interface stability can be effectively maintained. These findings validate the feasibility and efficiency of storage cavity technology in the continuous extraction of dry hot rocks.

In summary, the findings of this study offer a new technological path for the efficient development of dry hot rock energy. They also provide important theoretical and practical guidance for future research and application of dry hot rock extraction technologies.

However, the rocks in the hot dry rock reservoir contain various minerals, which may undergo chemical reactions with alloys in high-temperature environments, potentially causing chemical corrosion to the alloys, leading to a decrease in their strength, and leakage of high-efficiency heat exchange fluid in the channels. Therefore, studying the chemical reactions between alloys and rocks in hot dry rock reservoirs and proposing measures to improve the alloys is necessary.