Seepage and Heat Transfer of Dominant Flow in Fractured Geothermal Reservoirs: A Review and Outlook

: Deep geothermal reservoirs have great potential for exploitation and are characterized by high temperatures, high stress, and strong heterogeneity. However, these reservoirs contain widely and continuously distributed dominant flow channels with high permeability, predisposing these reservoirs to the formation of dominant flow, which notably decreases the efficiency of heat extraction. Focusing on the dominant flow in fractures, this study provides a definite concept, systematically reviews current studies, and puts forward suggestions for future research. It is expected that this study will serve as a reference for the sustainable, high-quality development of deep geothermal resources.


Introduction
With an increase in the exploitation depth, geothermal reservoirs with high temperatures, high stress, and strong heterogeneity have been found to generally host continuously distributed dominant flow channels with high permeability. Dominant flow channels refer to the channels with high permeability and continuous distribution in the fractures of highly heterogeneous geothermal reservoirs, and they can be as small as 10 −3 m on a pore scale and can be up to 10 6 m on a regional scale [1,2]. During the cyclic production and reinjection of geothermal energy, low-temperature tailwater enters geothermal reservoirs and accumulates toward the dominant flow channels at a high flow velocity, forming dominant flow [3]. Dominant flow influences the distribution of the flow velocity of geothermal water in the heterogeneous geothermal reservoirs, thereby controlling the mass transport and heat transfer in fractures and reducing the temperature difference in geothermal reservoirs (Figure 1). The substantial drop in the temperature of a production well occurring during the geothermal production and reinjection is referred to as a "thermal breakthrough" (also known as "thermal short circuit"). A thermal breakthrough will reduce the heat-extraction efficiency and production lifespan of geothermal reservoirs and even necessitate the shutdown of geothermal wells, resulting in economic losses amounting to tens of millions of Yuan [4,5]. Dominant flow is generally believed to be the dominant factor inducing thermal breakthroughs. It has been observed in many geothermal fields, including Geyser, Miravalles, Prieto, and Xianxian in Hebei, thus having received wide attention [6][7][8][9][10].
This paper presents the definition of dominant flow in fractured geothermal reservoirs. It systematically summarizes and analyzes the research progress in the seepage and heat transfer of the dominant flow and offers suggestions for further research. The aim of this paper is to expedite the sustainable, high-quality exploration of deep geothermal resources and to improve and enrich the research system for the scientific exploration and development of the deep Earth of the country. This paper also serves the purpose of promoting the implementation of the national strategy named Deep Earth Exploration as a preliminary study.
Water 2023, 15, x FOR PEER REVIEW 2 of 14 dominant factor inducing thermal breakthroughs. It has been observed in many geothermal fields, including Geyser, Miravalles, Prieto, and Xianxian in Hebei, thus having received wide attention [6][7][8][9][10]. This paper presents the definition of dominant flow in fractured geothermal reservoirs. It systematically summarizes and analyzes the research progress in the seepage and heat transfer of the dominant flow and offers suggestions for further research. The aim of this paper is to expedite the sustainable, high-quality exploration of deep geothermal resources and to improve and enrich the research system for the scientific exploration and development of the deep Earth of the country. This paper also serves the purpose of promoting the implementation of the national strategy named Deep Earth Exploration as a preliminary study.

Seepage and Heat-Transfer Mechanisms of Dominant Flow in Fractures of Geothermal Reservoirs
The presence of dominant flow is one of the most important characteristics of heterogeneous porous reservoirs. Accordingly, heterogeneous porous reservoirs yield completely different geothermal responses to the production-reinjection well system from homogeneous geothermal reservoirs even under the same reinjection conditions. Since deep geothermal reservoirs are highly heterogeneous in general, their seepage and heat-transfer processes cannot be characterized using homogeneous models or equivalent layered models [12]. Crooijmans et al. examined the seepage and heat-transfer processes of heterogeneous geothermal reservoirs under different geothermal production-reinjection schemes [13]. They proposed that the lifespan of geothermal well systems can only be accurately predicted using numerical models based on the heterogeneity of specific geothermal reservoirs. Ganguly et al. proposed that the heterogeneous geometry of the geothermal reservoirs significantly controls the anisotropy of the flow velocity and the non-

Seepage and Heat-Transfer Mechanisms of Dominant Flow in Fractures of Geothermal Reservoirs
The presence of dominant flow is one of the most important characteristics of heterogeneous porous reservoirs. Accordingly, heterogeneous porous reservoirs yield completely different geothermal responses to the production-reinjection well system from homogeneous geothermal reservoirs even under the same reinjection conditions. Since deep geothermal reservoirs are highly heterogeneous in general, their seepage and heattransfer processes cannot be characterized using homogeneous models or equivalent layered models [12]. Crooijmans et al. examined the seepage and heat-transfer processes of heterogeneous geothermal reservoirs under different geothermal production-reinjection schemes [13]. They proposed that the lifespan of geothermal well systems can only be accurately predicted using numerical models based on the heterogeneity of specific geothermal reservoirs. Ganguly et al. proposed that the heterogeneous geometry of the geothermal reservoirs significantly controls the anisotropy of the flow velocity and the nonlinear convective heat transfer [14]. Moreover, they developed an analytical model to characterize the transient temperature distribution and cold-front movement in geothermal reservoirs. Guo et al. found that high-permeability channels occur in heterogeneous geothermal reservoirs using a digital modeling method [15]. Furthermore, they pointed out that fluids accumulate and have a high flow velocity due to the heterogeneity of fracture apertures, resulting in a differential temperature drop in the rock matrix. The heterogeneity along the depth of geothermal reservoirs has a significant impact on the heat-extraction efficiency, and dominant flow is the main factor inducing thermal breakthroughs. Luo comparatively analyzed the influence of one and multiple dominant flow channels on the temperature field using an equivalent continuous model of discrete fractures [11]. He proposed that the inversion for dominant flow channels based on the breakthrough curves of conservative tracers is subjected to a multiplicity of solutions. Specifically, the concentration peak of the same tracer can be obtained through the fitting of two or three dominant flow channels ( Figure 2). In this case, the effects of the heat transfer of the dominant flow on thermal breakthroughs may potentially be incorrectly evaluated. Many studies on the enhanced geothermal system (EGS) show that three parameters of a discrete fracture network, namely aperture, rock matrix permeability, and wellbore radius, serve as important factors affecting thermal breakthrough [16,17]. thermal reservoirs using a digital modeling method [15]. Furthermore, they pointed out that fluids accumulate and have a high flow velocity due to the heterogeneity of fracture apertures, resulting in a differential temperature drop in the rock matrix. The heterogeneity along the depth of geothermal reservoirs has a significant impact on the heat-extraction efficiency, and dominant flow is the main factor inducing thermal breakthroughs. Luo comparatively analyzed the influence of one and multiple dominant flow channels on the temperature field using an equivalent continuous model of discrete fractures [11]. He proposed that the inversion for dominant flow channels based on the breakthrough curves of conservative tracers is subjected to a multiplicity of solutions. Specifically, the concentration peak of the same tracer can be obtained through the fitting of two or three dominant flow channels ( Figure 2). In this case, the effects of the heat transfer of the dominant flow on thermal breakthroughs may potentially be incorrectly evaluated. Many studies on the enhanced geothermal system (EGS) show that three parameters of a discrete fracture network, namely aperture, rock matrix permeability, and wellbore radius, serve as important factors affecting thermal breakthrough [16,17]. As indicated by Pandey et al. (2017), due to the rapid reactions of calcite, carbonate reservoirs are more significantly affected by heterogeneity than silicate reservoirs; accordingly, they show more complex seepage and heat-transfer processes [18]. The carbonate karst reservoirs in China enjoy considerable geothermal resources and are widely distributed in areas such as North China and northern Jiangsu, featuring high water yields and easy reinjection [9,19]. As shown by deep exploration in recent years, the karst geothermal reservoirs in the Jixianian Gaoyuzhuang Formation in North China have water yields of 25-110 m 3 /h and are characterized by high temperatures, high stress, and strong heterogeneity [8,20]. Under the action of compression and tectonism, deep karst geothermal reservoirs have spaces dominated by pores and fractures and generally have permeabilities of a few to tens of millidarcys, while parallel fractures with an aperture of 1 mm have permeabilities of hundreds of darcys [21][22][23]. Conservative tracer tests were conducted in typical geothermal fields in North China, such as Xiaotangshan in Beijing [24], Xiong an New Area [25], Xianxian in Hebei [7,26], and Donglihu in Tianjin [27]. The test results showed that karst geothermal reservoirs in North China contain dominant flow, which is liable to decrease the heat-extraction efficiency and even induce thermal breakthroughs. As mentioned earlier, dominant flow channels were identified. However, there is a lack of research on the formation and evolutionary laws of the dominant flow, as well as its As indicated by Pandey et al. (2017), due to the rapid reactions of calcite, carbonate reservoirs are more significantly affected by heterogeneity than silicate reservoirs; accordingly, they show more complex seepage and heat-transfer processes [18]. The carbonate karst reservoirs in China enjoy considerable geothermal resources and are widely distributed in areas such as North China and northern Jiangsu, featuring high water yields and easy reinjection [9,19]. As shown by deep exploration in recent years, the karst geothermal reservoirs in the Jixianian Gaoyuzhuang Formation in North China have water yields of 25-110 m 3 /h and are characterized by high temperatures, high stress, and strong heterogeneity [8,20]. Under the action of compression and tectonism, deep karst geothermal reservoirs have spaces dominated by pores and fractures and generally have permeabilities of a few to tens of millidarcys, while parallel fractures with an aperture of 1 mm have permeabilities of hundreds of darcys [21][22][23]. Conservative tracer tests were conducted in typical geothermal fields in North China, such as Xiaotangshan in Beijing [24], Xiong'an New Area [25], Xianxian in Hebei [7,26], and Donglihu in Tianjin [27]. The test results showed that karst geothermal reservoirs in North China contain dominant flow, which is liable to decrease the heat-extraction efficiency and even induce thermal breakthroughs. As mentioned earlier, dominant flow channels were identified. However, there is a lack of research on the formation and evolutionary laws of the dominant flow, as well as its heat-transfer process. This makes it difficult to scientifically predict and prevent thermal breakthroughs in deep geothermal exploitation.

Indoor Experiments and On-Site Tests on Seepage and Heat Transfer in Fractures
A small proportion of geothermal energy is stored in geothermal fluids, while more than 90% of it is stored in the rock matrix. The thermal energy in the rock matrix of deep geothermal reservoirs can be cyclically extracted by reinjecting low-temperature tailwater into reservoirs. Therefore, the heat transfer between geothermal fluids and the rock matrix is a hot research topic in the field of geothermal exploitation [28][29][30]. Presently, indoor experiments, which primarily focus on cores or a single fracture, are designed to investigate the mechanical, hydraulic, or heat-transfer properties of rock fractures. In contrast, field tests primarily include hydraulic tests and tracer tests. For on-site research, tracer tests are cost-effective and can yield site parameters, thus offering certain information for the establishment of analytical or numerical models. The numerical models for seepage and heat transfer in geothermal reservoirs established based on experiments and tests can be used for the effective inversion of dynamic water and heat transport in geothermal reservoirs since they are adapted to various geological structures, nonlinear parameters, and complex boundary conditions.

Laboratory Experiments
In the early days, indoor experiments were mostly carried out based on fractures bounded by smooth, straight, parallel plates with certain apertures, forming Navier-Stokes equations and the famous cubic law. According to the cubic law, the volumetric flux of water through a fracture is proportional to the cube of its aperture. However, the simplification of actual rough fracture surfaces into parallel plates might introduce certain errors [31,32]. To more accurately reflect the practical engineering conditions, researchers carried out tests to simulate natural fractures and made various modifications to the cubic law. They found that the measured roughness provides a more practical approach for characterizing the roughness of fracture networks. Barton proposed the empirical criteria for determining the joint roughness coefficient (JRC) and joint shear strength, while many researchers determined the JRC values based on mechanical experiments of samples [33][34][35]. Sisavath et al. (2001) characterized the roughness of fractures using symmetrical sinusoidal curves, established the relationships between the average aperture, roughness, and hydraulic resistance coefficient of fractures, and verified the relationships by comparison with relevant model experiments [36]. To quantitatively characterize the fracture roughness, various methods for characterizing the roughness have been proposed, such as statistical parameters, the standard deviation of fracture apertures, and fractal dimension [37][38][39][40][41][42][43]. Accordingly, the effects of rough geometry on the flow and heat transfer have been effectively investigated. However, the seepage mechanisms are highly complex under the influence of the fracture geometry. Therefore, it is necessary to conduct indepth research on the formation and evolutionary laws of dominant flow in the case of complex fracture geometries. Generally, laboratory experiments primarily focus on rock core samples or a single fracture, laying a solid foundation for research on the mechanical, hydraulic, or heat-transfer properties of rock fractures. However, their scales differ greatly from those of practical engineering.

Tracer Tests for Geothermal Production and Reinjection Projects
To reasonably characterize the seepage and heat transfer in geothermal reservoirs, reservoir information is frequently analyzed in combination with field tracer tests [8,44]. Tracers can be divided into two types based on their properties and functions, namely conservative tracers and active tracers (e.g., adsorption tracers and thermosensitive tracers; also known as reactive tracers). Conservative tracers, which are designed to analyze the flow connectivity and water residence time in geothermal reservoirs, have been widely applied [45][46][47][48][49][50][51][52][53][54]. Researchers previously assumed for a long time that the return rate of tracers is directly correlated with thermal breakthroughs. Later, after characterizing the heat transfer of the dominant flow channels using different types of tests (e.g., tracer tests, pressure transient tests, and nonisothermal injection tests), it was concluded that the rapid return of tracers does not necessarily imply a premature thermal breakthrough. Pruess and Bodvarsson (1984) held that the degree and time of the temperature drop in geothermal reservoirs depend not only on the duration of water transport between the reinjection and production wells (more specifically, the distribution of water residence time) but also on the heat transfer between the wells, as well as the average temperature and contact area of the flow channels [55]. However, the latter three characteristics can be scarcely reflected by conservative tracers.
As research deepens, active tracers have been used to obtain information about geothermal reservoirs. On the one hand, adsorption tracers are employed to identify the contact area of the geothermal reservoirs. Thermosensitive tracers, on the other hand, are used to indicate the temperature changes in tailwater's flow channels since they undergo irreversible hydrolysis reactions with an increase in temperature. However, the indicative function and specific processes of active tracers should be utilized in combination with at least a reference (conservative tracer). In other words, the use of active tracer-based identification and quantification of reaction processes should be conducted based on the water-transport process revealed via using conservative tracers. Owing to the advantages of different tracers, active tracers (e.g., adsorption and thermosensitive tracers) are used in combination with conservative tracers, which are referred to as multitracer tests. By comparing the flux concentration vs. time curves (i.e., breakthrough curves) of active and conservative tracers, the expected information can be obtained from tracer tests. This concept can be illustrated by the schematic breakthrough curves for the simulated tracer tests after a pulse injection, as shown in Figure 3. In these curves, the time shift or the reduction in the peak area (tracer mass) indicates retardation or degradation, respectively. Therefore, the measured breakthrough curves can be inversely interpreted using analytical equations or numerical models to estimate the values of control parameters, such as the distribution coefficient of the sorption process, the decay rate of the sorption process, or the decay rate of the thermal degradation process.
mal reservoirs depend not only on the duration of water transport between the reinjection and production wells (more specifically, the distribution of water residence time) but also on the heat transfer between the wells, as well as the average temperature and contact area of the flow channels [55]. However, the latter three characteristics can be scarcely reflected by conservative tracers.
As research deepens, active tracers have been used to obtain information about geothermal reservoirs. On the one hand, adsorption tracers are employed to identify the contact area of the geothermal reservoirs. Thermosensitive tracers, on the other hand, are used to indicate the temperature changes in tailwater s flow channels since they undergo irreversible hydrolysis reactions with an increase in temperature. However, the indicative function and specific processes of active tracers should be utilized in combination with at least a reference (conservative tracer). In other words, the use of active tracer-based identification and quantification of reaction processes should be conducted based on the water-transport process revealed via using conservative tracers. Owing to the advantages of different tracers, active tracers (e.g., adsorption and thermosensitive tracers) are used in combination with conservative tracers, which are referred to as multitracer tests. By comparing the flux concentration vs. time curves (i.e., breakthrough curves) of active and conservative tracers, the expected information can be obtained from tracer tests. This concept can be illustrated by the schematic breakthrough curves for the simulated tracer tests after a pulse injection, as shown in Figure 3. In these curves, the time shift or the reduction in the peak area (tracer mass) indicates retardation or degradation, respectively. Therefore, the measured breakthrough curves can be inversely interpreted using analytical equations or numerical models to estimate the values of control parameters, such as the distribution coefficient of the sorption process, the decay rate of the sorption process, or the decay rate of the thermal degradation process. Researchers revealed the contact area of geothermal reservoirs by combining conservative tracers with adsorption tracers. Their findings indicate that, given two different Researchers revealed the contact area of geothermal reservoirs by combining conservative tracers with adsorption tracers. Their findings indicate that, given two different flow channels with the same water residence time, the channel with a higher ratio of contact area to rock matrix volume exhibited an earlier temperature drop in the rock matrix. This phenomenon can be contributed to the more effective heat transfer from hot rocks to cold water when the ratio of the contact area to rock matrix volume is increased. The average temperature of a flow channel does not affect the time at which the geothermal reservoir temperature drops. However, it does affect the decreased amplitude of the geothermal reservoir temperature. The estimated ratio of the contact area to rock matrix volume and the average temperature of a flow channel are complementary and can be jointly used to estimate the timing and magnitude of the temperature drop in geothermal reservoirs. Thermosensitive tracers can indicate changes in the temperature of the tailwater's flow channel. These tracers, combined with the ratio of the contact area to rock matrix volume revealed by adsorption tracers, allow information such as the apertures of fractured rocks to be inferred. Accordingly, the distribution of seepage channels can be characterized, indicating the spatial distribution of the dominant flow. This can further constrain the nu-merical models of seepage and heat transfer, thus facilitating the accurate identification of dominant flow channels and enhancing the quantitative research on the controlling effects that the dominant flow has on the seepage and temperature fields [56][57][58][59][60][61][62][63][64]. Since the early 1990s, researchers have conducted a large number of indoor experiments and field tests of active tracers and have developed and tested multiple active tracers. Reimus et al. (2020) successfully estimated the seepage and heat-transfer characteristics of geothermal reservoirs using conservative tracers, thermal degradation tracers, and adsorption tracers [65]. They also discussed the uncertainties associated with combining multiple active tracers and the methods to reduce these uncertainties. Despite their advantages, active tracers are subjected to physical, chemical, and biological processes during transport compared to conservative tracers, which undergo a hydrodynamic transport process. To scientifically interpret the implications of the seepage and heat-transfer processes in the geothermal reservoirs based on tracer breakthrough curves, it is necessary to demonstrate the reaction rate between rocks and tracers through experiments prior to practical applications.
Fractures under experiments differ greatly from underground fractures in the order of magnitude. Therefore, the multiscale applications of microscopic mechanisms under experiments to macroscopic engineering are limited. However, such applications can be effectively achieved by combining indoor experiments and field tests. The areal contact rate-based correction method greatly simplifies the correction of the cubic law. Using this method, it is only necessary to understand the general contact of fractures while avoiding the difficulties of characterizing the distribution of bulges or fracture widths at each point on the fracture surface. In addition, this method also allows for measurements. For example, by applying adsorption tracers, the contact surfaces of fractures can be determined based on the absorption capacity of the tracer. By using the adsorption tracer technology to evaluate the contact area (also known as the effective heat-transfer area, which refers to the interface area between rock fractures and water) through indoor experiments and field tests, the multiscale seepage and heat-transfer mechanisms can be investigated by applying microscopic mechanisms to macroscopic engineering. Therefore, the permeability coefficient field under the influence of THMC coupling during the reinjection of deep karst geothermal reservoirs is a dynamic evolution process. The effects of the seepage field on the evolution of seepage, heat transfer, and thermal diffusion, which are difficult to investigate, are highlighted in studies on the seepage and heat-transfer mechanisms in geothermal reservoir engineering. However, fractures under experiments differ greatly from underground fractures in the order of magnitude. As a result, it is difficult to achieve the multiscale applications of microscopic mechanisms to macroscopic engineering, posing constraints on the optimal design of the productionreinjection schemes in deep geothermal exploitation.

Numerical Simulations
Deep geothermal reservoirs are located in a high-temperature and high-pressure environment with the mutual coupling of the seepage field, temperature field, stress field, and chemical field. Therefore, this environment differs greatly from that with a normal temperature and pressure. The multifield coupling in geothermal reservoirs is subjected to spatiotemporal dynamic changes during geothermal production and reinjection, making the seepage and heat transfer of the dominant flow even more complex [65,66]. With the rapid advancement in computer science, software such as COMSOL Multiphysics 6.1, FE-FLOW 7.2, TOUGHREACT v2.4, and FRACMAN v7.0 has seen significant development [9]. Consequently, numerical simulations have gradually become an indispensable tool in both scientific research and engineering applications [67]. To determine the accurate convective heat transfer in fractures, many researchers have investigated the multifield coupling in the field of geological engineering using methods such as analytical methods and numerical simulations based on experiments [4,[68][69][70][71][72][73][74]. Using the 1D model of the convective heat transfer in fractures, Zhao et al. developed a method for calculating the temperature distribution in fractures based on the assumptions of the local thermal equilibrium and local nonthermal equilibrium [67]. As a result, they obtained significantly different coefficients for convective heat transfer under both assumptions. Liu et al. established an anisotropic heat-transfer model for low-temperature fractured rock masses [7]. Liu and Xiang proposed a time-domain semi-analytical method for calculating the seepage and heat transfer in fractured rock masses [75]. He et al. proposed an analytical method to calculate the convective heat transfer between fluids and rock fractures by combining experiments and numerical simulations [76]. Bai et al. calculated the temperature and pressure distribution in rock fractures during the seepage process and proposed a calculation method for characterizing the local heat-transfer coefficients (LHTCs) of fractures [77]. Sun et al. investigated the distribution patterns of the temperature, seepage, and stress fields within geothermal reservoirs [78]. According to their results, for areas with fully developed seepage heat transfer, the efficiency of local heat transfer in rock fractures does not vary significantly with an increase in the flow velocity but is closely related to the distribution of flow rates. Based on the simulation analysis using a discrete fracture network model, Chen et al. suggested that the permeability of the rock matrix has a significant effect on the seepage properties of fractures [79]. Moreover, when the permeability of the rock matrix is six orders of magnitude lower than that of the fractures, seepage will accumulate in the fractures, forming dominant flow. For karst geothermal reservoirs, their fractured rock matrix has high pore permeability, leading to a relatively high permeability caused by pores and fractures. Therefore, it is necessary to determine the boundary conditions for the formation of dominant flow. The permeability coefficient field, as a complex composite of pore and fracture geometries and the porosity of the rock matrix, is a dynamic evolutionary process under the action of coupled multiple fields (e.g., such as temperature, stress, hydraulic gradient, and water-rock reactions) and the disturbance of production and reinjection activities [78,79]. For instance, as indicated by the numerical simulation of the thermohydro-mechanical coupling process carried out by the enhanced geothermal system (EGS) project at Soultz-sous-Forets, the changes in the stress field have significant effects on the injection well zones, permeability, and porosity. The numerical and simulation results also indicate the variations in permeability will affect the overall temperature and pressure of a geothermal system. Given that the seepage field in geothermal reservoir engineering is a dynamic evolutionary process, the influencing mechanisms of the dynamic evolution of the heat transfer and thermal diffusion in the seepage field are a key research topic [80,81].
Numerical simulations, which are adapted to changeable geological structures, nonlinear parameters, and complex boundary conditions, have received growing attention and have gradually become the most powerful tool for the analysis of multiple physical field coupling in a geothermal system. There are two types of multifield coupling models for geothermal reservoirs with different geometries, namely continuous medium models for porous media and discrete fracture network models. Among them, discrete fracture network models mainly include the fracture network model and the dual-fracture model, with the latter being widely applied due to its simple conceptual model and a small number of parameters [82]. However, the dual-fracture model oversimplifies the structure of thermal reservoirs and suffers some defects in its hypotheses about representative elementary volume (REV) and water-rock interactions. To gain a better understanding of the seepage, heat-transfer, and deformation mechanisms of rock fractures, a method for simplifying discrete fractures into a stochastic continuous model has been proposed. This method is more suitable for fracture propagation. Moreover, it takes into account the permeability of the rock matrix and is suitable for large-scale modeling. However, since it is difficult for this method to obtain parameters of deep reservoirs, the inversion-derived spatial distribution of hydraulic conductivity coefficients of aquifers features a strong multiplicity of solutions, and constraints from more experiments and experimental parameters are required [16,17,[80][81][82][83].

Existing Problems
Numerous researchers have conducted extensive studies on the seepage and heattransfer processes of geothermal reservoirs, achieving fruitful results [84][85][86][87][88][89][90][91][92][93][94]. With an increase in the geothermal exploitation depth, geothermal reservoirs with high temperatures, high stress, and strong heterogeneity have emerged. In the process of the production and reinjection of deep geothermal reservoirs, dominant flow is likely to pose challenges with the technologies of geothermal reservoir engineering, such as reduced heat-extraction efficiency, shortened production lifespans, and even thermal breakthroughs.
Previous researchers have recognized the impacts of the dominant flow in deep geothermal reservoirs on the heat-extraction efficiency and the lifespan of geothermal production and reinjection systems. However, the challenges of reconstructing the in situ high-temperature, high-pressure environment in deep geothermal reservoirs in experimental settings have resulted in the undefined formation and evolutionary laws and heat-transfer mechanisms of the dominant flow within these reservoirs [95,96]. These complications are particularly evident under the influence of coupled multiple fields, such as high temperature, high stress, complex pore-fracture geometries, and perturbation caused by geothermal production and reinjection. Moreover, the fractures in experimental settings differ greatly from subsurface fractures in the order of magnitude, making it difficult to study the multiscale applications of the microscopic mechanisms to macroscopic engineering. In addition, the effects of the seepage and heat transfer of the dominant flow on the evolution of the temperature field of the fracture network in geothermal reservoirs are yet to be ascertained. All these restrict the efficient and sustainable development of deep geothermal resources.
(1) The multifield coupling in geothermal reservoirs is a dynamic process in time and space during the operation of the geothermal production-reinjection system. Moreover, reconstructing the deep in situ high-temperature, high-pressure environment in experimental settings is challenging. All these lead to the unidentified formation and evolutionary laws of the dominant flow in deep geothermal reservoirs under coupled THMC fields. These laws include pore-fracture geometries, the spatial distribution of fracture networks, and the perturbation caused by geothermal production and reinjection. (2) The fractures in experimental settings differ greatly from subsurface fractures in the order of magnitude, making it difficult to study the multiscale applications of the microscopic mechanisms to macroscopic engineering. In addition, the effects of the seepage and heat transfer of the dominant flow on the evolution of the temperature field of the fracture network in geothermal reservoirs are yet to be ascertained. Accordingly, it is difficult to achieve the scientific design of the production-reinjection schemes for deep geothermal exploitation.

Suggestions for Further Research
Further research should focus on two critical scientific issues: (1) the first is to determine the formation and evolutionary mechanisms of the dominant flow in the fracture networks during the reinjection of deep karst geothermal reservoirs and to reveal the effects of THMC coupling on the permeability coefficient field of the fracture networks during geothermal reinjection; (2) the second is to achieve an accurate quantitative evaluation of the seepage and heat transfer of the dominant flow in the fracture networks during the reinjection of deep karst geothermal reservoirs and to reveal the evolutionary mechanisms of thermal convection and diffusion of the dominant flow in fractures under the influence of the seepage field.
To address the two critical scientific issues mentioned above, the following research should be conducted in the future: (1) The formation mode and heat-transfer process of the dominant flow in a single fracture The authors of this study recommend extracting and reconstructing the 3D structures of fractures in in situ rocks using representative rock samples from karst geothermal reservoirs; conducting multitracer tests for the seepage and heat transfer in a single fracture under the in situ temperature and confining pressure using an independently developed displacement system for high-temperature and high-pressure flow reactions and heat transfer; investigating the seepage and heat transfer of a single fracture under different porefracture geometries, stresses, reinjection temperatures, and flow velocities; ascertaining the controlling factors and critical conditions for the formation of the dominant flow; and proposing criteria for identifying the dominant flow based on the dynamic distribution characteristics of local permeability coefficients of fractures under the influence of multifield coupling. The authors also suggest establishing a simplified continuous THMC coupling model of discrete fractures taking into account factors such as the chemical reactions between rocks and active tracers; proposing the constitutive equation reflecting tracer breakthrough curves and contact area; and further quantitatively evaluating the heat transfer of the dominant flow and its effects on the temperature evolution of geothermal reservoirs.
(2) Evolutionary laws and accurate identification of the dominant flow in the fracture network of karst geothermal reservoirs The authors of this study recommend building a numerical THMC coupling model of the fracture networks and conducting multitracer tests for reinjection based on geological information, such as the pore-fracture geometries and the distribution and developmental patterns of fractures in typical karst geothermal reservoirs. Furthermore, the authors suggest quantitatively evaluating parameters such as the geothermal reservoir connectivity and contact area based on the breakthrough curves obtained from multitracer tests; conducting simulative analyses of the effects of the changes in parameters (e.g., connectivity, contact rate, stress, reinjection temperature, and flow velocity) on the permeability coefficient field of fractures, and revealing the evolutionary laws of the seepage field in the fracture network of in situ geothermal reservoirs. They also recommend accurately identifying the distribution of the dominant flow channels in the fracture network of in situ karst geothermal reservoirs and quantitatively evaluating the evolution of the dominant flow in the fracture network by combining criteria for determining the dominant flow in a single fracture.
(3) Heat transfer of the dominant flow in the fracture network of karst geothermal reservoirs and its quantitative evaluation The authors of this study present the following recommendations: (i) constraining and correcting the numerical model of the fracture network using parameters obtained from multitracer breakthrough curves (e.g., water residence time, fracture aperture, and contact area); (ii) solving the thermal convection and diffusion equations of the dominant flow in fractures under the influence of the seepage field using the lattice Boltzmann method; (iii) investigating the distribution of the geothermal reservoir temperature field under the temporal and spatial coupling of multiple fields, including complex pore-fracture geometries and different production-reinjection schemes (e.g., well network layout, production and reinjection temperatures, and flow velocity); (iv) comprehensively analyzing the effects of the fracture geometries and hydraulic conditions on the heat transfer of the dominant flow; (v) calculating the parameters used to characterize the seepage and heat-transfer effi- The authors of this study recommend analyzing the heat-transfer efficiency of the dominant flow and rock matrix in geothermal reservoirs; analyzing the influencing law of the dynamic heat transfer of the dominant flow on the evolution of the temperature field of geothermal reservoirs under different production-reinjection schemes by combining the ratio of the rock volume to contact area; clarifying the major factors controlling the temperature evolution of the fracture network in geothermal reservoirs; and determining the thresholds for thermal breakthroughs. Furthermore, they suggest establishing an index system for thermal sensitivity analysis based on a self-coded neural network of multilayer neurons; proposing a multiobjective optimization strategy for production-reinjection schemes while considering both the heat-extraction efficiency and production lifespan of geothermal reservoirs; and forming a regulation method for the balance between the heat-extraction efficiency and the production lifespan in deep geothermal exploitation.

Summary and Conclusions
This study reviews the research progress of the dominant flow in deep fractured geothermal reservoirs and presents a comparative analysis of the pros and cons of indoor experiments, field tests, and numerical simulations.
Dominant flow is liable to pose technical challenges to geothermal reservoir engineering during the production and reinjection of deep geothermal reservoirs. These challenges include a reduced heat-extraction efficiency, shortened production lifespans, and even thermal breakthroughs. To deal with these challenges, this study proposes conducting research on the seepage laws and heat-transfer mechanisms of the dominant flow in deep fractured geothermal reservoirs using multitracer techniques and a combination of indoor experiments, field tests, and numerical simulations. This study will play an important role in the sustainable and high-quality development of the exploitation of deep geothermal resources.

Conflicts of Interest:
The authors declare no conflict of interest.