1 INTRODUCTION

Hot dry rock (HDR) refers to rock formations that contain minimal or no water and predominantly consist of metamorphic or crystalline rocks. These formations are typically found buried at depths ranging from 3 to 10 km beneath the Earth's surface, with temperatures not falling below 180°C. In comparison to other carbon-based fuel sources, HDR boasts of substantial energy storage capacity and minimal environmental impact, which makes it a highly promising renewable energy resource (Wan et al., 2005). It is estimated that the heat stored in the Earth's interior is about 170 million times the global coal reserves, of which the amount available is equivalent to nearly 5000 trillion tons of standard coal. In China, the HDR resources located within land areas at depths of 3–10 km are estimated to possess energy equivalent to 856 trillion metric tons of standard coal. Based on international HDR standards and assuming a 2% extractable resource quantity, this is approximately 4000 times the total national energy consumption in 2015 (Liu et al., 2019). The geothermal energy sector is projected to contribute an additional 140 TWh of electricity annually by 2050, accounting for approximately 3.5% of global power generation and resulting in 800 million tons of carbon dioxide emission reduction (Pan et al., 2019). With the advancement of the national economy, deep geothermal energy development and utilization technologies in China have matured, leading to an increasing focus on HDR thermal energy development. Since the 12th Five-Year Plan, the Ministry of Science and Technology has initiated the 863 research program titled “Key Technologies for HDR Thermal Energy Development and Integrated Utilization” and formulated the “National Survey and Development Demonstration Implementation Plan for HDR.” The objective is to achieve commercial operation of HDR geothermal power generation around 2030.

Enhanced geothermal system (EGS) serves as the primary method for extracting geothermal energy from deep HDR reservoirs. The construction of an EGS involves several key steps. Initially, the underground hot rocks are fractured to create a fractured zone. This is followed by the injection and circulation of a closed-loop fluid between injection and production wells to extract heat energy (Figure 1). The low-temperature fluids, including water, nitrogen gas, and supercritical carbon dioxide (ScCO2), are injected into the high-conductivity pathways created by hydraulic fracturing. Subsequently, the fluid is heated by the surrounding hotter rock mass and circulated through production wells for electricity generation or other applications (Guo et al., 2019; Zhang et al., 2013). The establishment of an effective and stable inter-well fracture network stands as a crucial element in HDR reservoir stimulation, ensuring sustained and efficient heat exchange. In the context of EGS, this article provides an initial overview of the methods employed for HDR reservoir stimulation, as well as the fluids utilized for heat exchange. Furthermore, it conducts a comprehensive analysis of the impact of different well patterns, types, fracture layouts, and fracturing parameters on the efficiency of heat extraction. Finally, this article explores the limitations of numerical simulation research on HDR reservoirs and presents recommendations for future development.

2 EGS

The EGS is the main approach for extracting geothermal energy from deep HDR formations. The construction of an EGS begins with fracturing the underground hot rocks to create a fractured zone, followed by circulating closed-loop fluids between injection and production wells to extract heat energy. This process involves reservoir stimulation to increase permeability, thus ensuring adequate fluid involvement in heat exchange.

2.2 The working fluids of EGS

Water is the most widely used working fluid for EGS due to its high heat capacity and good thermal conductivity (Ashena, 2023). In addition to water, supercritical CO2 and N2O are also used. By comparing the productivity and heat breakthrough time of water and CO2 as working fluids, Mahmoodpour et al. (2022) evaluated the potential of using supercritical CO2 for geothermal energy extraction. The results indicated that supercritical CO2 exhibits the highest heat transfer efficiency. In the temperature range of 200–250°C, the density viscosity ratio of ScCO2 is approximately twice that of water, which allows for higher mass flow rate and improves the thermal extraction efficiency of EGS. Figure 2 shows a comparison of mass flow rates between ScCO2 and H2O, where the mass flow rate of ScCO2 is over three times that of water. As time goes on, the ratio of their mass flow rates gradually increases (Pruess, 2006). Therefore, during long-term operation, the high mass flow rate under ScCO2 injection can enhance the thermal extraction efficiency of EGS. Additionally, CO2 possesses high compressibility, reducing the operational power of EGS. Finally, as a heat transfer fluid, CO2 not only realizes the exploitation of geothermal energy but also achieves the geological storage of CO2. N2O is also a typical greenhouse gas, and the performance characteristics of ScN2O are similar to those of ScCO2. The life span of N2O-EGS is about 8 years longer than H2O-EGS, and the output power is approximately 2 MW higher than CO2-EGS (Huang et al., 2016).

3 ADVANCEMENTS IN UNDERSTANDING THE IMPACT OF WELL AND FRACTURE LAYOUTS ON HEAT EXTRACTION EFFICIENCY IN EGS

The fracture network and well layouts are crucial for achieving efficient heat extraction of HDRs. EGS increases rock permeability by hydraulically or chemically stimulating rock mass to form fracture networks. Multiple wells are employed to further expand the heat exchange surface area, enabling the establishment of fluid circulation for heat extraction.

3.1 The impact of well pattern on heat extraction efficiency in EGS

Well pattern design affects the heat extraction efficiency of EGS. Chen and Jiang (2015) conducted a study on optimizing well positions in EGS, exploring various layouts for two, three, and five wells (Figure 3). Their findings revealed that the triangular three-well layout (Figure 3c) exhibited the highest heat extraction efficiency, while the linear three-well layout (Figure 3b) rendered the lowest efficiency. Compared with the standard dual-well layout, the five-well layout improved heat extraction efficiency by 3.2%. However, when compared with the triangular three-well layout, the five-well layout only resulted in a 0.5% increase in heat extraction efficiency. This suggests that simply increasing the number of geothermal wells may not necessarily enhance the heat extraction performance of EGS. Comprehensive optimization of both well and fracture layouts is essential. Additionally, it is advisable to position injection wells at the reservoir's edge to ensure an adequate flow path for injected fluids and minimize filtration.

3.2 The impact of well type on heat extraction efficiency in EGS

The rational design of well type can increase the hydraulic connection between reservoir fracture and wellbore and improve the efficiency of geothermal system. Huang et al. (2016) investigated the influence of well depth on heat extraction efficiency in EGS. The study found that the depth of the production well directly affects heat extraction. By simulating heat extraction efficiency in production wells located in the middle and bottom sections of the artificial fracture system, the study demonstrated that the production well placed in the middle section achieved the highest heat extraction efficiency. This outcome can be attributed to the longer flow path of injected fluid within the fracture system, resulting in a larger effective heat exchange area. Song et al. (2018) conducted a three-dimensional study on the multilateral-well EGS (MLWGS) using a comprehensive model (Figure 4). The model encompassed the overlying layer, modified volume, HDR layer, and underlying layer, simulating the system from top to bottom. The findings obtained confirmed that the MLWGS, with multiple branch wells, exhibited higher heat extraction efficiency compared with the standard dual-well layout. The authors recommended extending the length of branch wells to enhance the average production temperature and prolong the system's life span.

3.3 The impact of fractures on heat extraction efficiency in EGS

A thermal breakthrough occurs in EGS when cold water injected into the system reaches the production well more rapidly than anticipated. This phenomenon leads to a reduction in output temperature and heat production. Shi et al. (2019) investigated the influence of fracture network geometry, primary fracture number, and fracture complexity on heat extraction efficiency in a MLWGS (Figure 5). The results from COMSOL simulations indicated that the geometric parameters and complexity of fractures significantly affect the heat extraction efficiency of MLWGS. Compared with orthogonal fractures, nonorthogonal fractures promote greater enhancements in heat extraction efficiency. Increasing fracture complexity enhances the contact area between the working fluid and rock, thereby improving heat extraction efficiency. However, an excessive number of branch fractures can lead to thermal breakthroughs and reduce the flow velocity of the working fluid in the reservoir. Li et al. (2019) analyzed the heat production capacity of HDR reservoirs using a discrete fracture model, and they identified that zigzag fractures between producing and injection wells can cause channeling. The authors proposed several mitigation methods: (1) positioning horizontal wells at greater distances to create longer flow channels; (2) alternating the activation of injection and production well segments; and (3) optimizing fluid circulation strategies through parameter adjustments.

In conclusion, current research primarily relies on numerical simulations, and further experimental validation is necessary. Whereas the influence of fracture network geometry and well layout on heat extraction efficiency has been examined, geological backgrounds and rock properties have not been fully considered. To enhance the reliability and stability of EGS, it is crucial to conduct in-depth research on the causes and preventive measures of thermal breakthrough and channeling.

4 PROGRESS IN UNDERSTANDING THE INFLUENCE OF FRACTURE PARAMETERS ON HEAT EXTRACTION EFFICIENCY IN EGS

The heat extraction efficiency of EGS is influenced by multiple factors. Achieving high heat extraction efficiency and economic feasibility in geothermal energy exploitation depends on parameters such as fracture permeability, injection flow rate, injected fluid temperature, and initial reservoir temperature. Therefore, a comprehensive analysis of the impact of these parameters on heat extraction efficiency in EGS is required, along with the optimization of HDR fracturing parameters.

Zeng et al. (2013) conducted a study using TOUGH2 to simulate the heat production capacity of a single vertical fracture in the Desert Peak geothermal field over 20 years. The study revealed that fracture permeability is the primary parameter affecting heat extraction efficiency. Properly optimizing fracture permeability and injection rate during the design of fracture parameters may lead to an ideal heat extraction state.

Hadgu et al. (2016) investigated the impact of fracture orientation on production temperature. Simulation results indicated that fracture orientation significantly influences reservoir thermal decline, with vertical and deviated wells experiencing more pronounced effects compared with horizontal wells.

Aliyu and Chen (2017a) optimized parameter combinations to meet temperature requirements at the wellhead. Their findings revealed that injection fluid temperature exerts a considerable influence on energy recovery, while injection fluid pressure notably affects reservoir cooling. In the same year, Aliyu and Chen (2017b) studied the impacts of injection flow rate, injection fluid temperature, and lateral well spacing on production capacity and system life span. Their impacts are ranked as follows: injection fluid temperature, injection flow rate, and lateral well spacing. As injection temperature rises, production capacity decreases, but life span increases. Higher injection flow rates enhance energy extraction efficiency while shortening system life span. The influence of lateral well spacing on heat extraction rate and life span is similar. Determining optimal injection parameters and selecting suitable injection strategies can prevent premature thermal breakthroughs (Zinsalo et al., 2020).

Xu et al. (2018) discussed the impact of fracture spacing, fracture permeability, and injection fluid temperature on the performance of EGS. The results indicated that within a certain range, reducing the fracture spacing effectively increases the temperature and thermal productivity of the produced water. Higher fracture permeability can reduce flow resistance and internal energy consumption. However, excessively low injection temperatures may lead to scaling or chemical deposition, while too high injection temperatures may affect electricity generation. Various evaluations have been made for heat extraction from differently conceptualized geothermal well systems. However, when the spacing between fractures is smaller than the fracture radius, the mechanical interaction between the fractures can influence the system's production rates (Slatlem Vik et al., 2018).

Asai et al. (2019) studied the impact of injection flow rate, injection temperature, fracture width, and fracture permeability on the performance of EGS. They found that EGS is highly sensitive to injection flow rate and temperature, and that an increase in injection flow rate can possibly lead to a faster temperature decline. Changing the fracture width may not cause a temperature decline when the fracture flow capacity remains unchanged. The authors also suggested that when high fracture flow capacity is required in the EGS, it is advisable to reduce the fracture width and maintain it within the range of 1–10 mm. In the same year, Zhang et al. (2019) established a thermal-fluid-solid coupled model based on the local nonequilibrium theory and studied the influence of different fracture network morphologies on heat extraction efficiency in EGS. The fracture network morphologies included fracture number, average fracture length, fracture length variance, and fracture orientation. The study revealed that increasing the number of fractures can improve the number of effective flow paths, thus enhancing heat extraction efficiency. Additionally, increasing the average fracture length can also improve the length of effective flow paths, thus enhancing heat extraction efficiency. However, increasing the fracture length variance reduces the uniformity of fracture distribution and lowers heat extraction efficiency. Fracture orientation affects fluid flow direction and flow resistance, thereby influencing heat extraction efficiency. The study found that when the angle between the fracture orientation and the connection direction of the injection-production wells is 45°, the optimal heat extraction efficiency can be achieved.

Ma et al. (2020b) proposed an EGS model with multiwell injection. Simulation results indicated that injection flow rate and injection temperature are the main factors affecting the heat extraction performance of EGS. Increasing the injection temperature can lower the injection pressure, thereby enhancing the injection mass flow rate (kg/s) per unit time. Assuming that continuous production lasts for 30 years, the heat extraction efficiency would decrease from 77.7% to 71.8% when the injection temperature increases from 273.15 to 293.15 K. Similarly, when the injection mass flow rate increases from 80 to 160 kg/s, the heat extraction efficiency increases from 57.6% to 84.7%. In the same year, Ma et al. (2020a) analyzed the impact of fracture parameters on the thermal production performance of EGS in fracture reservoirs. The study revealed that the heat extraction efficiency increases with the rise of fracture length but is negatively correlated with the fracture aperture. Increasing the number of fractures can improve heat extraction performance to some extent, but an excessive number of fractures may trigger adverse effects. The combination of fracture parameters yielding the highest heat extraction efficiency is found to be a fracture aperture of 0.05 mm, an average fracture length of 120 m, and a total of 94 fractures. Different geothermal well layouts are shown in Figure 6, where Case 1 exhibits the highest heat extraction efficiency.

Overall, fracture flow capacity, injection flow rate and temperature, fracture spacing, and fracture network morphology all exert some impact on the performance of EGS. Optimizing these factors can enhance the heat extraction efficiency of EGS. However, most existing research fails to consider the impact of thermal stress on reservoirs during long-term exploitation. For EGS, significant temperature variations and thermal stresses can occur after prolonged fluid circulation, which has a profound impact on fracture growth and the stability of geothermal reservoirs.

5 THE LIMITATIONS OF CURRENT NUMERICAL SIMULATION OF HDR RESERVOIRS

Fracturing is the primary method for reservoir stimulation in EGS. For high-temperature reservoirs, the coupling of thermo-hydro-mechanical and chemical processes poses significant challenges. In HDR reservoirs, a complex interplay between temperature field, seepage field, stress field, and chemical reactions controls both fracture expansion and fluid circulation. To investigate multifield coupling and mechanisms of action in the reservoirs, the fracture network model has evolved from equivalent continuous medium models, dual-medium models, and multiple-medium models to discrete medium models capable of accurately characterizing fracture behavior (Sang et al., 2016; Warren & Root, 1963). Research on thermo-hydro-mechanical coupling in EGS has advanced from two-dimensional numerical simulations to three-dimensional numerical simulations of underground complex fracture networks (Liu et al., 2023; Sun et al., 2016). Three-dimensional numerical simulations based on multifield coupling require significant computation and data processing, which exceed the limited computing power of any single CPU computing core. This limitation hinders the efficient characterization of artificial fractures needed for modern hydraulic fracturing. Unlike CPU, GPU has a large number of computing cores, and GPU-based numerical simulation calculations exponentially improve processing efficiency while greatly reducing simulation time. This provides technical support for real-time prediction and intelligent optimization of fracture parameters in actual complex hydraulic fracturing engineering, improving production efficiency and economic decision-making power.

During the thermal extraction process in geothermal reservoirs, the heat exchange between the injected low-temperature fluid and the rock matrix can significantly lower the matrix temperature. The cooling of the bedrock near fractures can lead to matrix contraction, thereby reducing the contact stress on the fracture surface and increasing the fracture aperture (Salimzadeh et al., 2018). This change in aperture diminishes the flow path between the injection well and production well, resulting in a reduced heat transfer area, lower heat transfer performance, and a faster temperature decline in the production well (Fox et al., 2015; Pandey et al., 2017). Furthermore, Gee et al. (2021) conducted further research on the “short-circuiting mechanisms” within and between fracture surfaces. Short-circuiting fluid circulation may cause premature “thermal breakthrough” and reduce heat extraction efficiency.

Alternating cycles of hot and cold fluids can lead to significant temperature variations (≥100°C), resulting in substantial thermal-induced stresses. Taking granite as an example, with a temperature change of, ΔT = 120°C a thermal expansion coefficient of ${�}_{�}=7.8\times {10}^{-6}/\mathrm{K}$ , Young's modulus of E = 35 GPa, and Poisson's ratio of $�=0.23$ , the thermal-induced tensile stress, $�$ , resulting from the temperature change of ΔT = 120°C is calculated to be $�=����/\left(1-�\right)=42.6\mathrm{MPa}$ . In the initial stage of fluid injection, the fracture system is primarily influenced by poroelastic effects. However, after prolonged injection periods, thermoelastic stress becomes the dominant factor (Ghassemi & Zhou, 2011). After the completion of hydraulic fracturing, a significant number of microseismic events are still detected during fracture monitoring, indicating that microcracks continue to propagate under the prolonged influence of thermal stress (Chen et al., 2019). Consequently, considering the influence of thermal-induced stresses on the stability of artificial fracture networks in EGS becomes crucial during the long-term (≥30 years) heat extraction from HDR reservoirs. However, presently, there are no analytical or numerical methods available for studying the stability of artificial fracture networks in EGS during long-term heat extraction processes.

6 CONCLUSION AND RECOMMENDATIONS

CONFLICT OF INTEREST STATEMENT

The authors declare no conflict of interest.