Review on Thermal Stimulation in Deep Geothermal Reservoirs: Thermo-Mechanical Mechanisms and Fracture Evolution

Abstract

Enhanced geothermal systems (EGS) are a key technology for developing deep geothermal resources, yet they face significant challenges in constructing efficient thermal reservoirs within high-stress, high-strength, and low-permeability crystalline rock formations. Traditional hydraulic fracturing (HF) techniques encounter deep challenges in these environments, including excessively high fracturing pressures, limited fracture network patterns, and the risk of induced seismicity. This paper reviews the multi-scale thermal-mechanical mechanisms, fracture evolution patterns, and control strategies associated with thermal stimulation and permeability enhancement in the modification of deep geothermal reservoirs. Research indicates that thermally induced fracturing triggers intergranular and transgranular cracks at the microscopic scale due to mineral thermal expansion mismatches, which macroscopically manifests as nonlinear degradation of rock strength and modulus. The redistribution of the thermal elastic stress field significantly lowers the breakdown pressure, while matrix thermal contraction increases fracture aperture, leading to an exponential enhancement of permeability following a cubic law. However, the high confining pressure constraints, true triaxial stress anisotropy, and thermal short-circuiting risks present substantial suppression and challenges to the effectiveness of thermal stimulation in deep in situ environments. Different fracturing media, such as water, liquid nitrogen (LN₂), and supercritical CO₂, exhibit varying advantages in thermal stimulation efficiency due to their unique thermal-flow characteristics. Future research should focus on the thermal-mechanical coupling mechanisms under true triaxial stress conditions, and develop intelligent control strategies for permeability enhancement and thermal short-circuiting risk mitigation. This study synthesizes existing analyses and proposes potential engineering strategies for stimulating deep EGS reservoirs, offering significant strategic value for the development of geothermal energy as a baseload renewable resource.

1. Introduction

1.1. Deep Geothermal Reservoir Development: Strategic Dilemmas and Opportunities

Against the backdrop of a global transition to a low-carbon energy structure, the pursuit of baseload renewable energy sources capable of replacing fossil fuels has become an international consensus [1]. Despite the rapid development of wind and solar energy, their inherent intermittency and volatility limit their contribution to the grid’s baseload capacity [2]. In contrast, geothermal energy is regarded as a key component of future clean energy systems due to its availability in all weather conditions, high stability, and gigawatt-scale energy potential [3]. As shown in Figure 1, since the 1980s, both the installed capacity and electricity generation from geothermal power have exhibited a continuous and stable growth trend, with generation increases closely aligned with capacity expansions. This reflects the high capacity factor and operational reliability of geothermal energy. Such characteristics enable it to serve as an irreplaceable baseload support within a renewable energy system primarily dominated by wind and solar power.

However, traditional hydrothermal geothermal systems heavily rely on naturally occurring heat-water-reservoir conditions, and their commercial development is primarily limited to tectonic plate boundaries and areas with active volcanic activity. This stringent geographical limitation significantly hinders the global-scale application of geothermal energy [5]. To overcome this resource bottleneck, the forefront of geothermal engineering has gradually shifted from shallow hydrothermal resources to deep EGS, especially targeting hot dry rock resources that lack natural fluid conduction capabilities [6].

The core concept of EGS is to artificially create commercially viable thermal reservoirs within deep (typically 3–6 km), high-temperature (150–350 °C), and low-permeability crystalline basement rocks, such as granite or granodiorite, via engineered interventions [7]. To intuitively illustrate the engineering implementation of EGS in hot dry rocks, Figure 2 provides a conceptual diagram of a typical EGS development model [8]. While these deep crystalline rock formations contain enormous thermal energy reserves, their inherent characteristics include extremely high in situ stress, exceptional mechanical strength, and very low intrinsic hydraulic conductivity. Therefore, the primary and fundamental challenge in the development of deep EGS lies in how to economically and effectively construct a long-term stable volumetric fracture network system with sufficient heat exchange area in such an extreme mechanical environment characterized by high temperature-high pressure-high strength. This challenge not only poses significant difficulties for engineering implementation but also represents a theoretical bottleneck that urgently needs to be addressed at the intersection of rock mechanics and geothermal engineering.

1.2. The Deep Dilemma of Traditional HF

Historically, reservoir stimulation techniques for geothermal development have largely been adapted from conventional oil and gas operations, with HF serving as the principal approach [9,10]. The fundamental mechanical principle underlying conventional HF is the establishment of a fluid pressure-controlled regime, in which pressurized fluids are introduced into the wellbore at levels sufficient to overcome both the minimum principal stress of the reservoir and the rock’s tensile capacity, consequently generating tensile fractures. Although this purely mechanically driven approach has proven highly effective in the extraction of hydrocarbons from sedimentary basins, its deployment in the deep crystalline rock settings characteristic of EGS encounters substantial geomechanical difficulties, particularly in three key areas: fracture initiation behavior, fracture network geometry, and environmental implications [11].

Firstly, the fracture initiation barrier caused by the high in situ stress environment at depth is the primary challenge for engineering implementation. The target formations for EGS are typically composed of granite or metamorphic basement rocks located at depths of 3–6 km [12,13]. These dense rocks not only possess extremely high intrinsic tensile strength but are also subjected to substantial triaxial confining pressure. According to classical fracture mechanics theory [14], the breakdown pressure required to initiate a fracture increases linearly with confining pressure. In some EGS cases, the injection pressure required at the wellhead often approaches or even exceeds the limits of surface pumping equipment and the safe pressure threshold of the well casing, thereby significantly undermining the technical feasibility and economic viability of relying solely on mechanical HF.

Secondly, the fracture network simplicity driven by stress severely restricts thermal extraction efficiency. Under the significant confinement imposed by the anisotropic deep in situ stress regime, the propagation of hydraulic fractures preferentially occurs along orientations orthogonal to the least principal stress, resulting in the formation of geometrically straightforward bi-wing planar fractures, rather than the desired intricately connected volumetric fracture networks [15]. The existence of such a fracture morphology can create low-resistance conduits that enhance communication between the injection and production wells, leading to preferential flow. The circulating working fluid travels rapidly through these highways, failing to achieve sufficient thermal exchange with the surrounding high-temperature rock matrix, resulting in the phenomenon known as thermal short-circuiting and premature temperature decay in the production well. Ultimately, this leads to low thermal extraction rates over the entire lifecycle of EGS projects [16].

Finally, the risk of induced seismicity caused by high-pressure injection cannot be ignored [17]. To overcome the high strength of deep rock formations, traditional fracturing often requires the injection of massive hydraulic energy. Such high-pressure disturbances can easily alter the effective normal stress state on fault planes, activating naturally occurring faults or fractures that are in a critical stress state, leading to shear slip. In recent years, several EGS operations, notably the Pohang project in South Korea, have been suspended as a result of felt induced earthquakes. This indicates that relying solely on high-pressure hydraulic drive in high-stress areas not only faces technical bottlenecks but also significant challenges related to social acceptance [18]. Therefore, exploring a novel fracturing mechanism that can lower the fracture initiation threshold, increase fracture network complexity, and be environmentally friendly has become an urgent need for the development of EGS technology.

1.3. Introduction of Thermal Stimulation and Scope of Review

Given the limitations of purely hydraulic driving in deep hard rock environments, thermal stimulation has gradually evolved from a secondary supportive measure to an indispensable core technology in the enhancement of deep reservoirs [19]. Unlike traditional HF, which relies on fluid overpressure to open fractures, thermal stimulation utilizes the significant temperature difference (ΔT) between the injected fluid (cold) and the reservoir rock (hot) to induce severe thermal shock effects within the rock mass. This non-equilibrium thermodynamic process leads to rapid contraction of the rock matrix, generating induced tensile thermal stress that can overcome the confining pressure of the formation, fundamentally altering the stress state in the near-wellbore region [20,21,22].

The most notable engineering value of thermal shock lies in its depressurization and permeability enhancement effect. Both theoretical and practical evidence suggest that the introduction of thermal stress can significantly reduce the breakdown pressure of the rock, making it possible to initiate fractures at lower injection pressures and thereby avoiding the engineering risks and seismic hazards associated with high-pressure operations [23,24]. More critically, the fracture propagation driven by thermal stress tends to be influenced by the heterogeneity of the rock’s microstructure, favoring the activation of natural microfractures and forming complex fracture networks rather than single planar fractures. This contributes significantly to enhancing the reservoir’s heat exchange performance. To illustrate the physical processes involved in fracture evolution under thermal stimulation conditions more intuitively, Figure 3 schematically shows the thermal shrinkage, dissolution, and geometric deformation of fracture surfaces caused by thermal flow during the thermal extraction process, as well as the resulting evolution of flow capacity [25]. It is evident that the opening, closing, and permeability changes in fractures are not merely mechanical responses but are closely coupled with heat conduction, fluid migration, and water-rock reaction processes.

Although the engineering potential of thermal stimulation has been validated in pioneering projects such as Soultz and Fenton Hill, a systematic theoretical framework that governs the cross-scale physical mechanisms—from microscale thermal damage accumulation to macroscale permeability evolution—remains absent in the current academic literature [26,27]. Existing research largely focuses on single-scale phenomenological descriptions, lacking a comprehensive framework that bridges the causal chain from mineral thermal expansion mismatch and microcrack nucleation to macroscopic mechanical degradation and, ultimately, fracture network conductivity enhancement. In view of this, this paper provides a structured narrative review synthesizing the thermo-mechanical (T-M) mechanisms governing rock behavior during thermal stimulation. We synthesize existing research on the fracturing mechanisms in deep crystalline rocks under thermal shock, summarize the nonlinear effects of thermal damage on rock strength and permeability, and discuss the engineering implications for achieving precise control over the permeability of deep EGS reservoirs. Ultimately, this review seeks to bridge the knowledge gap between purely hydraulic-driven and coupled thermo-hydraulic-driven reservoir stimulation, offering holistic insights for future engineering practices.

2. Literature Search and Methodology

2.1. Search Strategy

To ensure a comprehensive and rigorous coverage of the literature, we conducted a systematic search across primary academic databases, primarily relying on the Web of Science Core Collection.

The search strategy utilized a combination of Boolean operators (AND, OR) and targeted keyword clusters. The core search string was formulated as follows:

TS = ((“enhanced geothermal system*” OR EGS OR “hot dry rock” OR HDR OR geothermal) AND (“thermal stimulation” OR “thermal shock” OR “thermal cracking” OR “thermal stress” OR “thermal damage” OR “cooling-induced” OR cooling OR thermal) AND (“granite” OR “crystalline rock*” OR “hard rock” OR rock)).

2.2. Inclusion and Exclusion Criteria

To maintain the precise scope and high quality of this review, clear eligibility criteria were established. Studies were included if they were peer-reviewed and published in English in scholarly journals or authoritative conference proceedings, explicitly focused on deep crystalline rock reservoirs (e.g., granite, granodiorite, gneiss), typically defined as formations at depths exceeding 3 km or subjected to high-temperature conditions (>150 °C), and specifically addressed multi-scale thermo-mechanical mechanisms, thermal damage evolution, laboratory experimental simulations, or field applications of thermal stimulation techniques. Conversely, studies were excluded if they focused solely on shallow hydrothermal systems or sedimentary formations (e.g., sandstone, shale, carbonate rocks), involved only pure chemical stimulation or conventional hydraulic fracturing without a significant thermal cooling component, or were non-peer-reviewed materials, dissertation chapters, or technical reports lacking rigorous peer review.

2.3. Data Screening and Extraction

Based on the search strategy and selection criteria described above, this paper employs a systematic review methodology to conduct a stepwise screening of the literature. The specific process includes initial retrieval, removal of duplicate records, title and abstract screening, and full-text evaluation.

A total of 4011 records were identified from the Web of Science database, with no records retrieved from registers, and no studies were removed before screening. After initial screening of all 4011 records, 463 studies were excluded due to irrelevant topic or focus, leaving 3548 records for full-text retrieval; no studies were not retrieved during the full-text acquisition process. Eligibility assessment was performed on the 3548 successfully retrieved full-text studies, and 980 conference abstracts without available full-text were excluded. Finally, 2568 studies were included in the systematic review.

The entire screening process follows the reporting guidelines for systematic reviews and is presented in the form of a flowchart, as shown in Figure 4. This flowchart provides a detailed account of the changes in the number of records from initial identification to final inclusion, along with the reasons for exclusion, thereby ensuring the transparency and reproducibility of the research process.

3. Theoretical Fundamentals of Thermal Shock

3.1. Thermo-Elasticity Mechanism

The core physical essence of thermal shock fracturing lies in the transformation of intense disturbances in the temperature field into a restructured stress field [28]. According to linear thermo-elasticity theory, when solid materials experience a temperature change (ΔT), they undergo volumetric expansion or contraction. However, deep EGS reservoir rocks are not free bodies; they are subjected to significant overburden pressure and strict constraints from far-field horizontal stresses. Under these boundary-constrained conditions, the rock matrix cannot freely undergo thermal strain, resulting in the constrained thermal strain being directly converted into induced thermal stress. Assuming a linear elastic, isotropic medium under plane strain conditions, the induced thermal stress can be described by the thermally elastic extension of the generalized Hooke’s law [29]:

$${\sigma }_t={\displaystyle \frac{E{\alpha }_T\Delta T}{1-\nu }}$$

(1)

where E represents the Young’s modulus of the rock, characterizing the material’s stiffness; ${\alpha }_T$ is the linear thermal expansion coefficient; $v$ is the Poisson’s ratio; and ΔT is the instantaneous temperature difference.

This equation highlights the pronounced sensitivity of crystalline rocks like granite to thermal shock. In deep granites, the inherently high stiffness (high Young’s modulus) and the considerable thermal expansion coefficient, which is largely attributable to quartz content, mean that even moderate temperature differences can generate substantial induced tensile stress. Moreover, the term (1 − ν) in the denominator reflects the Poisson effect under biaxial constraints, further amplifying the magnitude of thermal stress in the uniaxial direction.

The correction effect of cooling-induced shrinkage on breakdown pressure is a key theoretical basis for the engineering application of thermal stimulation. Traditional HF theory posits that the tangential stress (Hoop Stress) at the wellbore must be overcome by the injection fluid pressure and transformed into a tensile state for fractures to initiate. With the introduction of thermal shock, the induced tensile stress resulting from cooling superimposes on the in situ stress field, creating a thermal unloading effect that effectively relaxes the compressive stress concentration around the wellbore [30].

This mechanism is mathematically expressed as a modification of the classical fracture pressure equation. Based on linear elastic fracture mechanics and porous media theory, Haimson & Fairhurst (1967) proposed the classic criterion for HF initiation pressure [31]. For porous rock media, considering the pore pressure effect, the fracture pressure at the wellbore wall can be expressed as:

$$P_b=3{\sigma }_{h\min }-{\sigma }_{H\max }+{\sigma }_T-{\alpha }_B{P}_p$$

(2)

where ${\sigma }_{h\min }$ is the minimum horizontal principal stress; ${\sigma }_{H\max }$ is the maximum horizontal principal stress; ${\sigma }_T$ is the tensile strength of the rock; ${\alpha }_B$ is the Biot effective stress coefficient; and P_P is the pore pressure. This equation establishes the fundamental control of in situ stress, pore pressure, and rock strength on the fracture pressure. On this basis, the introduction of thermal stress induced by thermal shock necessitates further modification of the classical equation. Considering the thermo-poroelastic coupling effect, the revised fracture pressure P_b can be expressed as [32]:

$$P_b=3{\sigma }_{\mathrm{hmin}}-{\sigma }_{\mathrm{Hmax}}+{\sigma }_T-{\alpha }_B{P}_P-{\sigma }_t$$

(3)

where ${\sigma }_t$ represents the absolute value of the thermally induced tensile stress. It is evident that thermal stress acts as a subtractive term directly in the fracture criterion. Physically, this implies that the injection of cold fluid functions as an invisible wedge—by reducing the circumferential compressive stress on the borehole wall, it significantly lowers the fracture threshold that would otherwise require extremely high hydraulic pressure to achieve. Under extreme temperature differentials (such as during LN₂ quenching), ${\sigma }_t$ may even exceed the sum of the in situ stress and the tensile strength of the rock, leading to spontaneous fracturing under zero net hydraulic pressure. This mechanism provides a robust theoretical foundation for achieving low-pressure fracturing in ultra-deep, high-stress environments.

To theoretically elucidate the influence of directional thermal shock on the stress field of surrounding rock, Zhang et al. [33] established a novel model, as illustrated in Figure 5. This figure schematically depicts the stress redistribution around the borehole wall, highlighting the three orthogonal stress components. These are the axial stress (${\sigma }_z$), which is governed by the overburden pressure; the radial stress (${\sigma }_r$), which equals the wellbore fluid pressure at the borehole wall; and the tangential stress (${\sigma }_{\theta }$), which induces a pronounced stress concentration effect at the borehole wall and serves as the dominant factor controlling fracture initiation. When the tangential tensile stress exceeds the tensile strength of the rock, fractures initiate and propagate in the direction perpendicular to the minimum principal stress. In the thermal stimulation for permeability enhancement in deep EGS reservoirs, the thermal stress (${\sigma }_t$) induced by cold fluid injection superimposes onto the in situ stress field, generating a thermal unloading effect. This modifies the effective tangential stress to ${\sigma }_{\theta }-{\sigma }_t$, thereby substantially reducing the fluid pressure required for fracture initiation and providing a theoretical basis for low-pressure fracturing. Although this model is based on assumptions of linear elasticity, homogeneity, and isotropy, it still offers valuable qualitative guidance and quantitative references for wellbore stability analysis and fracturing parameter optimization in deep crystalline rock reservoirs.

3.2. Fracture Mechanics Criteria and Initiation Mechanisms

Traditional breakdown pressure theories are grounded in the assumption of continuous media, while linear elastic fracture mechanics (LEFM) offers a more microscopic and fundamental perspective by introducing the concept of pre-existing defects [34]. According to Griffith’s energy balance theory and the criterion of fracture toughness [35], the failure of rock does not commence with the exhaustion of overall strength; rather, it initiates once the value of the stress intensity factor K_I at the crack tip exceeds the material’s fracture toughness K_IC. During the thermal shock process, the injection of cold fluid generates an extremely steep transient temperature gradient (ΔT), at the surface of the rock and along the walls of the cracks, which subsequently introduces a transient tensile stress field that decays with depth near the wall surface. For microcracks present on the surface, the cooling shrinkage of the matrix forces the cracks to open, resulting in a mode I (tensile) stress intensity factor. The variation in this stress intensity factor over time can be expressed as the integral of thermal stress along the crack surface [36]:

$$K_{\mathrm{I}}(t)={\displaystyle {\int }_0^a{\sigma }_{\mathrm{thermal}}}(x,t)m(x,a)dx$$

(4)

where a represents the crack length, and m(x, a) is the weighting function that depends on the geometric shape of the crack. When the stress intensity factor $K_{\mathrm{I}}(t)$ resulting from thermal shock exceeds the intrinsic fracture toughness K_IC, the crack undergoes unstable propagation. This process indicates that even when the macroscopic injection pressure has not reached the formation breakdown pressure, localized thermal stress concentrations are sufficient to drive the nucleation and growth of microcracks.

Iyare et al. [37] quantitatively characterized the geometric evolution features of fractures under shear, focusing on the opening behavior of fractures in different samples as shear displacement increases. The mechanical aperture of the fractures can directly reflect the shear–dilation effect and its impact on subsequent permeability. Figure 6 shows the correlation of mechanical aperture to shear displacement for different samples.

From the perspective of the physical nature of the driving mechanisms, there are fundamental differences between thermal cracks and traditional hydraulic fractures.

Hydraulic fractures are primarily driven by internal fluid pressurization. The mechanical logic behind this is that fluid pressure directly acts on the crack walls, effectively pushing the rock apart like a wedge, with the direction of propagation controlled by the minimum principal stress direction, favoring the formation of single, through-going deep planar fractures [38]. Thermal cracks, on the other hand, are driven by bulk matrix contraction. The mechanical logic here is that the surrounding rock mass experiences volumetric shrinkage due to cooling, resulting in a pulling effect. The constraint imposed by the hotter rock mass surrounding it results in the passive opening of fractures.

This mechanistic difference leads to distinctly different fracture network topologies. Specifically, hydraulic drive tends to form simple winged fractures, while thermal drive favors the formation of high-density networks of microcracks (thermal crazing) at the cooling front. Although thermal cracks may initially be confined to the near-wellbore region or the shallow walls of major fractures, they serve as high-energy stress concentration points, significantly reducing the energy barrier for subsequent macroscopic fracture propagation and providing a critical nucleation basis for constructing complex volumetric fracture networks [39].

4. Multi-Scale Thermal Damage Mechanisms

To comprehensively understand the macroscopic mechanical response of deep reservoir rocks such as granite, it is essential to delve into their microstructure and explore the interactions between constituent minerals. Granite is not regarded as a homogeneous continuous medium; instead, it is composed of a polycrystalline aggregate of several minerals, such as quartz, feldspar (including both orthoclase and plagioclase), and mica. The significant differences in thermodynamic properties among these minerals constitute the microphysical basis for fracture initiation due to thermal shock [40,41].

4.1. Micro-Structural Heterogeneity: Mismatch of Thermal Expansion

The heterogeneity of the mineral coefficients of thermal expansion (CTE) serves as the fundamental driving force behind micro-damaging processes. Tomás et al. [42] provided a two-dimensional schematic that simplifies the understanding of the multi-scale and multi-mechanism physical processes occurring within crystalline rocks under temperature effects, illustrating the evolution of thermally induced rock damage (Figure 7). This figure summarizes the primary microphysical mechanisms of thermal damage from several aspects, including crystal anisotropic thermal expansion, mismatch of thermal expansion between different minerals, polymorphic phase transitions in minerals, local phase transition sintering, and pore gas pressure induced by mineral decomposition.

To quantify the role of mineral thermal expansion mismatch in driving thermal damage, we systematically compiled the TM properties of primary granitic rock-forming minerals sourced from a wide range of experimental studies (

Table 1. Meta-analysis of thermal expansion coefficients for major minerals in granite.

Mineral	Parameter	Sample Size	Mean
Quartz	α (10−6 K−1)	3	23.87
K-feldspar	α (10−6 K−1)	4	10.73
Plagioclase	α (10−6 K−1)	4	12.05
Biotite	α (10−6 K−1)	4	12.08
Quartz	E (GPa)	36	89.6

Note: Sample sizes represent the number of independent experimental data sets reviewed. The reported ranges for α values are generally measured over the temperature range of 25–300 °C.

) [41,43,44,45,46,47]. A comprehensive review of these studies demonstrates a significant discrepancy in the reported ranges of the CTE. For instance, the CTE of quartz typically ranges from 23.11 to 24.63 × 10⁻⁶ K⁻¹, which is substantially higher than the reported ranges for feldspar-group minerals (typically 8.33 to 13.11 × 10⁻⁶ K⁻¹). This pronounced contrast in TM properties provides robust cross-study support for the central hypothesis that mineral thermal expansion mismatch drives micro-scale damage [48,49].

The damage evolution pattern exhibits a distinct temperature dependence, characterized by a transition from intergranular cracks to transgranular cracks. Under relatively low temperature thresholds or moderate cooling rates, thermal stress levels remain comparatively modest. In such regimes, failure predominantly follows the weakest-link principle and occurs along grain boundaries [50]. Contracted quartz grains undergo debonding from adjacent feldspar grains, giving rise to intergranular cracks that propagate tortuously along the grain boundaries. Although such cracks contribute to an increase in rock porosity, they tend to remain isolated and offer only limited enhancement to permeability.

As thermal shock intensity intensifies—under conditions such as temperatures exceeding 600 °C or cryogenic quenching in LN₂—the strain energy density accumulated within the rock increases dramatically, reaching levels sufficient to overcome the atomic bond strength inherent to the mineral crystals themselves. Under such conditions, cracks no longer propagate preferentially along grain boundaries but instead transect the mineral lattice directly, resulting in the formation of transgranular fractures. Microstructural characterization, including scanning electron microscopy (SEM), confirms that these transgranular cracks exhibit straighter trajectories and greater continuity. Unlike intergranular cracks that propagate exclusively along grain boundaries, transgranular cracks are capable of directly penetrating mineral grains themselves, thereby breaking the physical barriers between adjacent grains and establishing continuous fluid pathways across grain boundaries. This connectivity at the grain scale significantly reduces the tortuosity of fluid flow paths and constitutes a critical microstructural foundation for the formation of macroscopic high-conductivity channels. To intuitively illustrate the progressive evolution of microstructural damage in crystalline rocks during thermal treatment, Mo et al. [51] presented optical micrographs of specimens before and after heat exposure (Figure 8). The imagery reveals the initiation, propagation, interconnection, and closure of thermally induced microcracks. Intergranular cracks are widely observed, including those along plagioclase–plagioclase boundaries (Figure 8b), biotite–plagioclase interfaces (Figure 8f), and biotite–quartz contacts (Figure 8h). In comparison, transgranular cracks are relatively scarce. Notably, the layered structure inherent to biotite facilitates the genesis of thermal cracks along its cleavage planes (Figure 8b,d,f).

In addition, the α–β phase transition of quartz represents a critical abrupt mechanism that cannot be overlooked in high-temperature thermal stimulation of hard crystalline rocks. As the reservoir temperature crosses the critical threshold of 573 °C, quartz undergoes a displacive phase transformation from the trigonal (α-phase) to the hexagonal (β-phase) crystal system. This transition is accompanied by a sudden change in linear dimensions and an instantaneous volumetric expansion or contraction [52]. During thermal shock cooling, such reversible volumetric discontinuities induce catastrophic internal structural stresses within the rock matrix, resulting in intense comminution of quartz grains and the generation of high-density microcrack networks around them. This phase-transition-induced damage far exceeds the effects of purely linear thermal contraction, thereby offering a highly promising permeability-enhancement mechanism for the exploitation of super-hot geothermal resources.

4.2. Macro-Scale Mechanical Degradation

Thermal damage at the microstructural level inevitably manifests at the macroscopic scale as a pronounced deterioration in the physicomechanical characteristics of rocks. For EGS engineering design, the evolution of parameters such as uniaxial compressive strength (UCS), tensile strength (UTS), elastic modulus (E), and acoustic wave velocity (V_P) not only constitutes key indicators for evaluating reservoir stimulation efficiency but also serves as direct input for numerical modeling and optimization of operational parameters [53,54,55].

The threshold effect of strength parameters and experimental evidence of nonlinear decay indicate that the degradation of rock strength caused by thermal shock does not follow a simple linear pattern, but rather exhibits a significant nonlinear critical temperature characteristic, known as the threshold effect [56]. Taking granite as an example, its strength typically evolves in a reverse S shape or hockey stick pattern with changes in magnitude of the thermal shock [57]. In the lag phase, which occurs at temperature differences below 200 °C, the change in rock strength is minimal, and there can even be a counterintuitive slight thermal strengthening phenomenon due to the increase in friction caused by the evaporation of pore water and the closure of microvoids from mineral thermal expansion [58]. When the temperature difference exceeds 200 °C, the accelerated deterioration phase begins, during which microcracks at grain boundaries start to accumulate and the strength begins to show a downward trend, although the overall integrity of the rock framework remains intact. The catastrophic failure phase typically occurs above 400 °C to 600 °C, with 400 °C generally regarded as the turning point for damage accumulation. Once this threshold is exceeded, especially when crossing the quartz phase transition temperature (573 °C), transgranular crack networks rapidly form, leading to a cliff-like drop in unconfined compressive strength (UCS), with residual strength often falling below 50% of the initial value [45]. It is noteworthy that, compared to compressive strength, tensile strength (UTS) is highly sensitive to thermal microcracking. Since tensile failure heavily depends on material continuity, even a small amount of microcracking can significantly disrupt stress transfer pathways. Brazilian splitting tests indicate that at 400 °C, the reduction in UTS often far exceeds that of UCS, suggesting that thermally treated rocks are more prone to tensile failure under hydraulic drive, thereby effectively lowering the breakdown pressure required for engineering applications.

Accompanied by the macroscopic loss of strength, the deformation behavior of the rock undergoes a fundamental structural transformation. Intact deep crystalline rock typically exhibits pronounced hard-brittle behavior, characterized by a sharp post-peak stress drop [59]. However, following intense thermal shock (e.g., >600 °C), the post-peak stage of the stress–strain curve develops a noticeable yielding plateau, displaying semi-ductile characteristics. Meanwhile, the degradation rate of elastic modulus (E) generally exceeds that of strength. This stiffness softening effect yields unique engineering positive externalities for EGS reservoir creation: As derived from linear elastic fracture mechanics, under the same driving fluid pressure, rock with a lower modulus can develop larger fracture apertures. This implies that thermally softened rock masses are more conducive to proppant acceptance or the maintenance of wider self-propping flow channels, thereby enhancing reservoir conductivity.

Given the logistical challenges of in situ core sampling at significant depths, compressional wave velocity (P-wave velocity, V_P) is commonly employed as a non-destructive proxy indicator for assessing the degree of thermal damage [60]. Microcracks within the rock matrix constitute acoustically mismatched interfaces (solid–air or solid–fluid boundaries); as acoustic waves propagate through thermally damaged rock, they are forced to detour around such interfaces or undergo scattering, resulting in extended propagation paths and energy attenuation.

Xi et al. [61] established a quantitative relationship between the damage variable D and the reduction in wave velocity:

$$D=1-{\left({\displaystyle \frac{V_{pT}}{V_{p0}}}\right)}^2$$

(5)

where V_pT and V_p0 denote the wave velocities after thermal shock and in the initial state, respectively. Experimental data confirm that P-wave velocity is highly sensitive to variations in microcrack density. Under thermal shock conditions exceeding 600 °C, the reduction in V_P can reach over 60%, a trend that closely aligns with the exponential increase in crack porosity observed in micro-computed tomography (μ-CT) scans [62]. This strong correlation makes it feasible to invert the extent of the borehole-scale thermal halo and assess the degree of pre-fracturing damage using acoustic logging data. To further quantify the controlling effect of thermal damage on macroscopic mechanical deformation, a TM constitutive equation can be established based on the principles of Continuum Damage Mechanics. According to the strain equivalence principle in damage mechanics, the strain exhibited by a damaged rock specimen is equivalent to the strain exhibited by an undamaged specimen subjected to an effective stress [63]. The strain can be expressed as:

$$\epsilon ={\displaystyle \frac{\sigma }{\Delta E}}={\displaystyle \frac{\sigma }{E(1-D)}}$$

(6)

where $\sigma$ represents the nominal stress, $\Delta E$ denotes the elastic modulus of the damaged rock specimen, E is the elastic modulus of the undamaged granite, and $\epsilon$ corresponds to the effective strain.

Therefore, the damage constitutive equation for granite can be expressed as:

$$\sigma =E(1-D)\epsilon$$

(7)

This constitutive equation clearly reveals how the accumulation of microcracks (increase in D) leads to macroscopic stiffness degradation. When D approaches 1, the rock loses its load-bearing capacity, corresponding to the catastrophic failure phase discussed earlier. This mathematical formulation tightly bridges the aforementioned micro-scale mechanisms with macro-scale deterioration, providing a critical constitutive relationship input for numerical simulations.

It is important to acknowledge the significant variability in reported threshold temperatures for thermal damage across existing studies. For typical crystalline rocks (e.g., granite), microcrack initiation typically occurs at 300–400 °C, while the quartz α-β phase transition (~573 °C) serves as a critical threshold marking a qualitative change in the thermal damage mechanism [45,56,57,58]. Rather than representing contradictory findings, this range reflects the high sensitivity of thermal damage to boundary conditions and loading paths. Rapid cooling rates (thermal shock) tend to lower the effective threshold compared to slow heating, and heterogeneous mineral compositions (e.g., varying quartz content) shift the onset of microcracking. Therefore, these threshold values should be interpreted not as fixed material constants but as context-dependent parameters influenced by the specific thermal-mechanical loading path.

4.3. Statistical Variability in Rock Properties and Experimental Data

A critical consideration in synthesizing thermal stimulation research is the inherent variability in rock properties and experimental conditions across different studies. This variability arises from multiple sources and must be acknowledged when drawing generalized conclusions. The primary sources of data dispersion in the compiled literature include mineralogical heterogeneity, grain size and texture, and differences in experimental protocols. Mineralogical heterogeneity manifests in the significant variation in granite compositions across geological formations, quartz content, for instance, ranges from 20% to 40% in typical EGS target formations, directly influencing thermal expansion mismatch and damage thresholds [41,43,44,45,46,47]. Grain size and texture also play a key role, as coarse-grained granites (grain size > 2 mm) exhibit more pronounced intergranular cracking compared to fine-grained variants (<1 mm), leading to up to threefold variability in permeability enhancement under identical ΔT conditions [51,56]. In addition, differences in experimental protocols contribute substantially to data dispersion, cooling rates vary by orders of magnitude across studies (from 1 °C/min in furnace cooling to >1000 °C/s in LN₂ quenching), significantly affecting crack density and propagation modes [57,64].

5. Fracture Network and Permeability Evolution

5.1. Aperture Enhancement Mechanism via Matrix Thermal Contraction

During the stimulation and operation of deep EGS reservoirs, the most direct and pronounced physical response induced by cold fluid injection consists of thermal contraction of the rock matrix along the fracture walls [65]. Unlike HF, which relies on fluid overpressure to push the fracture surfaces apart, thermal shock induces thermoelastic strain, causing the rock matrix to retract inward from the fracture centerline. In rock mechanics, this phenomenon is what is referred to as the thermal unloading effect [30]. Even under the strong compressive confinement of far-field high in situ stress, such localized matrix contraction effectively counteracts the normal closure stress acting on the fracture surfaces, thereby significantly increasing the mechanical aperture of the fracture [66]. Though seemingly minor, this physical displacement exerts a decisive influence on the fluid transport capacity of the reservoir, the underlying mechanism of which is governed by the cubic law in fluid mechanics. According to this law, the volumetric flow rate Q through a parallel-plate fracture is proportional to the cube of the fracture aperture. This implies that a small increment in aperture translates into an exponential increase in permeability. Theoretical models indicate that, under ideal elastic conditions, the change in aperture Δb is linearly related to the temperature drop ΔT and the CTE. However, given the nonlinear behavior of deep-seated rocks, the actual permeability enhancement factor often exhibits a stronger sensitivity to temperature, with micron-scale thermal contraction being sufficient to elevate macroscopic hydraulic conductivity by several orders of magnitude.

Zhang et al. [67] conducted high-temperature (200 °C) seepage experiments and coupled THM-D numerical simulations to explore how thermal stress and thermally induced cracks affect fracture damage and permeability following cryogenic fluid injection (Figure 9). Their results indicate that, at elevated temperatures, fracture permeability initially increases rapidly due to thermal cracking, followed by a decline attributable to the clogging of flow pathways by crack debris. Increasing the injection rate and fracture heterogeneity both promote the development of thermal cracks, whereas higher confining pressure suppresses debris migration and thus alleviates the clogging effect.

Furthermore, in high-temperature geothermal environments, the evolution of fracture aperture is governed not only by TM processes but also by competing thermo-chemical (TC) effects [68]. Injecting cold fluid upsets the pre-existing geochemical equilibrium, potentially triggering mineral dissolution or precipitation (e.g., amorphous silica or calcite scaling), the latter of which tends to clog pore throats. It is worth noting that while engineered precipitation techniques, such as Microbially Induced Calcite Precipitation (MICP), have been successfully employed to enhance shear strength in shallow soil formations through carbonate bonding [69], their application in deep EGS is severely constrained by high-temperature limitations (>80 °C) that inhibit microbial activity. This contrasts with thermal stimulation, which leverages high-temperature gradients as the primary driving force. However, during the active injection stage, the mechanical thermal contraction effect driven by a strong temperature difference (ΔT) remains dominant. Simulation results indicate that while mineral precipitation may reduce permeability by approximately 0.5 orders of magnitude, matrix thermal contraction can enhance permeability by nearly 2 orders of magnitude [70]. This provides compelling evidence that thermal stimulation is not merely a transient fracturing mechanism but also the primary physical driver capable of sustaining EGS injectivity and prevailing over geochemically induced damage mechanisms.

5.2. Non-Linear Permeability Enhancement

As a core parameter governing the thermal extraction efficiency of EGS reservoirs, permeability does not evolve in a simple linear fashion with increasing thermal shock intensity [71]. Consistency between theoretical derivations and experimental data reveals a pronounced exponential growth relationship between temperature differential (ΔT) and permeability. This nonlinear response mechanism provides a robust physical basis for low-pressure permeability enhancement in deep tight reservoirs.

It is crucial to reconcile the apparent contradiction between the exponential permeability increases reported in laboratory studies (often 10–100×) and the more moderate enhancements observed in field projects like Soultz and Fenton Hill (typically 1.35–7.5×) [72,73]. This discrepancy does not invalidate the thermal stimulation mechanism but rather reflects the profound influence of boundary conditions. Laboratory experiments are frequently conducted under unconfined or low-confinement conditions, allowing thermal cracks to open freely. In contrast, deep reservoirs are subjected to high in situ stresses (40–60 MPa) that mechanically clamp fracture apertures. Additionally, laboratory measurements typically reflect matrix permeability of small, homogeneous samples, whereas field performance is governed by the connectivity of large-scale fracture networks within heterogeneous rock masses. Therefore, laboratory data should be interpreted as the upper bound of potential enhancement, while field outcomes represent the constrained reality modulated by geomechanical conditions.

5.3. Data Normalization and Cross-Study Comparison Framework

To enable quantitative synthesis across heterogeneous experimental studies, we adopted a normalization approach based on existing analyses, taking into account differences in initial rock properties, stress conditions, and measurement protocols. All permeability data were expressed as a dimensionless ratio k/k₀, this normalization removes the influence of absolute permeability magnitude and focuses on relative enhancement. The temperature difference was scaled by the reference temperature (in K) to define a normalized temperature differential, facilitating comparison across studies with different baseline temperatures. Cheng et al. [64] conducted a series of experiments, and based on these we plotted the relationship between the permeability enhancement ratio and the temperature difference by using the data in the literature, as shown in Figure 10.

Further analysis with reference to Figure 10 reveals that the thermal stimulation effect exhibits a pronounced scale dependency. Under unconfined or low-confining-pressure conditions in laboratory experiments, the permeability typically increases by a factor of 10 to 100 over a temperature difference (ΔT) range of 200–400 °C, owing to the opening and coalescence of numerous microcracks induced by thermal contraction. In contrast, field-scale observations (e.g., from the Soultz and Fenton Hill projects) indicate that while localized permeability enhancement may occur in the near-wellbore region, the effective permeability increase at the reservoir scale is generally modest (approximately 1.35 to 7.5 times). This disparity stems from differences in the dominant controlling mechanisms across scales: laboratory-scale behavior is governed by the generation and propagation of microcracks, whereas reservoir-scale behavior is controlled by the spatial connectivity of fracture networks and in situ stress anisotropy. Furthermore, during long-term operation, TC coupling effects (e.g., mineral dissolution and precipitation) may further modulate the permeability evolution trajectory, resulting in more conservative overall enhancement outcomes.

Thermal unloading experiments conducted at the laboratory scale have revealed the sensitivity of granite permeability to temperature variations. Studies indicate that the permeability enhancement factor (R), representing the ratio of cooled-to-uncooled permeability, exhibits an empirical exponential relationship with ΔT (Absolute temperature differential). For typical granite specimens subjected to cooling over a temperature range of 200–600 °C, this relationship can be fitted as follows [74]:

$$R=e^{0.0045 \Delta T}$$

(8)

It is noteworthy that under extreme thermal shock conditions—such as LN₂ quenching—where macroscopic transgranular fractures are induced, the observed permeability increase can exceed two orders of magnitude, far surpassing the predictions of purely elastic models [75]. This nonlinear characteristic has been incorporated into advanced thermo-hydro-mechanical (THM) coupled numerical simulators. The permeability evolution model no longer depends solely on mechanical stress, but instead adopts an effective stress formulation modified to include a thermal stress term [76]:

$$k=k_{0 }\exp [-\beta ({\sigma }^{\prime }+{\displaystyle \frac{E{\alpha }_T\Delta T}{1-\nu }})]$$

(9)

where k represents transient permeability; k₀ is the initial intrinsic permeability; $\beta$ is the stress sensitivity coefficient describing the dependence of permeability on effective stress; and ${\sigma }^{\prime }$ represents the effective stress acting on the rock matrix. In this formulation, $\Delta T$ takes a negative value during cooling. The exponential function magnifies the permeability enhancement by reducing the effective normal stress acting on fractures. Consequently, the model explains how sustained cold fluid circulation alone can lead to a continuous increase in injectivity, even without additional hydraulic stimulation. However, Equation (8) only describes the empirical relationship between temperature difference and permeability, without explicitly incorporating the rock damage state. Within the generalized framework of continuum damage mechanics, and by integrating the cubic law with fracture network evolution models, the transient permeability k in fractured rock masses can be conceptually correlated with the initial intrinsic permeability k₀ and the cumulative damage variable D [77]:

$$k={\displaystyle \frac{k_0}{{\left(1-D\right)}^{\xi }}}$$

(10)

where k₀ is the initial intrinsic permeability; $\xi$ is a coefficient related to the material. Equations (9) and (10) constitute the core of the fully coupled TM-hydrological framework.

The enhanced permeability effect induced by thermal stimulation has been confirmed not only under controlled laboratory conditions but also macroscopically validated in field-scale EGS projects, despite differences in boundary conditions. Under unconfined or low confining pressure conditions, cooling a granite core from 325 °C to 25 °C can significantly increase its permeability solely through matrix contraction [78]. If combined with thermochemical fracturing technologies, the enhancement can even reach several orders of magnitude through the extensive generation of microcrack networks.

Field Scale: In the Soultz-sous-Forêts project in France [72], the reservoir temperature is approximately 200 °C, and the long-term reinjection temperature is controlled within the range of 60–65 °C. Following chemical stimulation (RMA acid treatment), the injectivity index increased by approximately 35%, and numerical simulations indicate that the near-wellbore porosity increased from 10% to 17%. However, at the field scale, permeability is governed by the fracture network, making it difficult to characterize effective permeability with a single parameter. Microseismic monitoring and tracer tests indicate that the reservoir conductivity was significantly improved after combined hydraulic and chemical stimulation.

In the Fenton Hill project in the United States [73], the reservoir is located at a depth of 3.6 km, with an initial temperature of 230 °C and an injection temperature of 100 °C, resulting in a sustained thermal drawdown of approximately 130 K. Field monitoring shows that when the bottomhole injection pressure exceeds a critical threshold (~74 MPa), injectivity increases significantly, and under constant pump pressure, the injection rate continues to rise, confirming the mechanical mechanism of thermally induced fracture propagation. The microseismic cloud migrates in an NNW-SSE direction, with dimensions of approximately 1 km × 1 km × 300 m, revealing the evolution characteristics of the fracture network under the stimulation of hybrid mechanisms.

In summary, whether at the microscopic core scale or the macroscopic reservoir scale, thermal shock exhibits a strong nonlinear driving capability for permeability. This characteristic implies that in EGS projects, optimizing the temperature and rate of injected fluids to trigger an exponential jump in permeability through thermal-mechanical coupling effects is an effective approach to overcoming the fracturing bottleneck in deep reservoirs.

To resolve the apparent discrepancy between exponential permeability increases observed in laboratory settings and the more moderate improvements documented in field projects, we propose a unified interpretation framework based on multi-scale constraints. Within this framework, reservoir permeability evolution is conceptualized as the net outcome of competing enhancement and suppression mechanisms across scales.

First, at the mechanical constraint level, laboratory samples are typically tested under unconfined or low confining pressure, allowing thermal stress to fully open microcracks. In contrast, deep reservoirs are subject to high in situ stress, where overburden pressure acts as a persistent clamping force that suppresses thermally induced crack apertures. Thus, thermal stress must first overcome the initial compressive stress before any net permeability gain can occur, resulting in a mechanically dampened enhancement relative to laboratory conditions.

Second, at the spatial scale, laboratory specimens are relatively homogeneous and small, enabling thermal shock to affect the entire volume. Field reservoirs, however, are heterogeneous with natural fracture networks. Thermal stimulation often exhibits a skin effect, wherein significant damage is confined to the near-wellbore region, preventing the exponential permeability jumps observed in core samples from translating directly to the reservoir scale.

Third, at the temporal scale, laboratory tests capture short-term responses immediately after thermal shock, whereas field operations involve long-term fluid circulation accompanied by TC interactions. Processes such as mineral precipitation, fines migration, and asperity degradation can induce pore clogging and permeability loss over time, partially offsetting initial thermal gains.

Finally, flow pathway localization plays a critical role. In the field, fluid tends to channel through a few dominant fractures due to positive feedback, leading to thermal short-circuiting. Although these pathways may exhibit high local conductivity, the effective permeability of the entire reservoir remains limited by the untreated matrix blocks. Therefore, the moderate field improvements reflect a system-level equilibrium among thermal enhancement, stress confinement, heterogeneity, chemical clogging, and flow localization, rather than a failure of the thermal stimulation mechanism itself.

6. Challenges in Deep In Situ Environments

Although laboratory scale studies have thoroughly confirmed the fracturing potential of thermal shock, caution must be exercised when directly extrapolating these conclusions to deep EGS engineering sites. Deep reservoirs are not free surfaces; they are subjected to extreme triaxial stress conditions. Ignoring the mechanical constraints of in situ environments may lead to misjudgments regarding the effects of thermal stimulation.

6.1. Inhibitory Mechanism of Confining Pressure and Scaling Implications

Existing research on thermal damage is largely based on rock samples tested under unconfined or low confining pressure conditions, which fundamentally differs from the actual conditions of EGS reservoirs, typically located at depths greater than 4 km and subjected to geological confining pressures of several tens of megapascals. In the in situ environment, high confining pressure acts as a stable clamping force, exerting a significant mechanical inhibition effect on the nucleation and propagation of thermal cracks. From the perspective of stress superposition, the thermal stress tensor is superimposed onto the in situ stress tensor, leading to a redistribution of both the magnitude and orientation of the principal stresses within the rock. The prerequisite for thermal shock-induced fracturing is that the induced tensile stress must be sufficient to overcome the local compressive stress field, thereby altering the principal stress state [79]. Under such conditions, the net stress tensor acting on a rock micro-element can be expressed as:

$${\sigma }_{ij}^{net}={\sigma }_{ij}^T+{\sigma }_{ij}^{in-situ}, i, j=1, 2, 3$$

(11)

where ${\sigma }_{ij}^T$ represents the thermal stress tensor, and ${\sigma }_{ij}^{in-situ}$ represents the in situ stress tensor.

This tensor superposition process not only alters the magnitudes of stresses but may also rotate the directions of the principal stresses. Fracture initiation is no longer governed by the offset of confining pressure in a single direction; instead, it depends on whether the superposed minimum principal stress satisfies the tensile failure criterion. Cracks can only open when the absolute value of ${\sigma }_{ij}^{net}$ not only exceeds the intergranular cohesive strength of the rock but also effectively counteracts the in situ compressive stress component in that direction. This implies that under deep high-confining-pressure conditions (e.g., >50 MPa), moderate-intensity thermal shock may fail to trigger the microcrack networks that are readily observable in laboratory tests on unconfined specimens [80]. Consequently, damage models based solely on surface laboratory experiments are highly likely to overestimate the actual fracturing efficiency of thermal stimulation in deep reservoirs. Triaxial compression experiments further confirm the existence of this inhibition effect. Comparative studies show that granite samples subjected to thermal shock under high confining pressure (e.g., 25 MPa) exhibit significantly less degradation in mechanical properties compared to samples tested under low confining pressure (e.g., 5 MPa). This phenomenon is described as strength recovery or apparent toughness enhancement, and its physical mechanism is attributed to high confining pressure forcing the rough surfaces of thermally induced microcracks to remain in close contact, thereby fully mobilizing the frictional resistance between the crack surfaces under shear loads. This mechanism indicates that the resilience of deep rock structures under thermal shock far exceeds traditional expectations. Future engineering designs must revise predictive models based on unconfined data to account for the shielding effect of confining pressure on thermal damage.

6.2. Anisotropic Response Under True Triaxial Stress Conditions

The mechanical essence of deep geological environments is the true triaxial stress state [81]. Currently, the vast majority of experimental studies on thermal shock are based on conventional triaxial tests, a simplified assumption that overlooks the critical role of the intermediate principal stress in fracture mechanics, leading to potential discrepancies between theoretical predictions and actual deep subsurface conditions. To understand the source of this discrepancy, it is first necessary to establish the constitutive behavior and crack evolution benchmark of granite under true triaxial conditions. As illustrated in Figure 11, under true triaxial compression, the differential stress-strain curve of granite can be divided into five stages. Specifically, the figure identifies the critical stress thresholds for crack initiation (${\sigma }_{ci}$) and damage (${\sigma }_{cd}$), corresponding to the entire process of crack closure, initiation, propagation, and eventual failure. Concurrently, the evolution of crack volumetric strain clearly reflects the damage progression from compaction to dilatancy [82].

In deep rock masses, the magnitude and orientation of ${\sigma }_2$ directly govern the stress concentration pattern around wellbores and the preferred orientation of potential failure planes. Although theoretical fracture mechanics predicts that thermal cracks tend to initiate perpendicular to the direction of maximum local tensile stress, the lateral clamping effect exerted by ${\sigma }_2$ in a true triaxial stress field may substantially alter crack propagation trajectories or even suppress thermal crack nucleation along specific orientations. It remains unclear whether the presence of ${\sigma }_2$ promotes unidirectional thermal crack extension, thereby inducing a highly anisotropic damage pattern—a critical uncertainty that directly impedes accurate quantification of fracture network complexity [83].

Second, stress anisotropy inevitably induces directionality in permeability evolution. Although matrix shrinkage induced by thermal shock may be approximately isotropic at the grain scale, the resulting permeability enhancement is strictly modulated by the tectonic stress field at the reservoir scale. The total effective stress state arises from the superposition of isotropic thermal stress and anisotropic in situ geostress [84]. Mechanical principles dictate that natural fractures or newly generated thermal cracks oriented perpendicular to the minimum principal stress experience the minimum normal closing stress, rendering them most susceptible to opening under thermal stimulation and thus achieving the greatest enhancement in flow conductivity.

This stress-thermal-hydraulic coupling causes the permeability tensor of the reservoir to exhibit a pronounced ellipsoidal distribution, rather than the idealized spherical isotropic diffusion. Microseismic monitoring data from the Rosemanowes EGS field experiment, analyzed by Li et al. [85], corroborate this observation. Due to mechanistic differences between shear slip and tensile opening, the enhanced preferential flow pathways tend to elongate along the direction of the maximum principal stress. This finding carries profound engineering implications for wellbore placement optimization in EGS. Specifically, production wells should be aligned with the major axis of the permeability ellipsoid to maximize reservoir hydraulic connectivity and extend the economic lifespan of heat extraction.

6.3. Dynamic Evolution Risks: Positive Feedback Mechanisms and Thermal Short-Circuiting

Thermal stimulation enhances reservoir permeability, but its dynamic evolution characteristics introduce a critical trade-off—the risk of thermal short-circuiting. Throughout the long-term operation of EGS, permeability is not a static parameter; it evolves in time and space as the thermal front progresses. If this evolution lacks effective control, it can easily trigger a self-reinforcing positive feedback mechanism, leading to catastrophic declines in the system’s thermal extraction efficiency [86].

Driven by the inherent heterogeneity within EGS reservoirs, a positive feedback loop is triggered, which inevitably exacerbates the formation of several preferential seepage pathways within the initial flow field. When cold working fluid is injected, the rock matrix adjacent to these pathways cools preferentially and undergoes substantial thermal contraction [87]. According to thermoelastic theory and the cubic law, this matrix contraction leads to an enlargement of fracture apertures, thereby significantly reducing fluid resistance along these pathways. This process immediately triggers a critical positive feedback loop. As flow resistance decreases, a greater proportion of cold fluid is diverted into the same fracture set, leading to flow focusing. The resulting increase in fluid flux accelerates cooling along the fracture walls. In turn, intensified cooling induces further aperture widening and shear slip, causing the fractures to open continuously. Driven by the iterative nature of these THM processes, initially uniform and ordinary fractures progressively evolve into highly localized, preferential flow pathways [88].

Once a preferential flow pathway is established, it effectively serves as a superhighway connecting the injection well and the production well. The majority of the circulating working fluid is rapidly transported through these low-resistance channels, bypassing the surrounding high-temperature, low-permeability matrix rock. This hydrodynamic short-circuiting significantly decreases the retention time of the working fluid within the reservoir and drastically compromises the effective heat exchange area between the fluid and the hot rock. To further elucidate, from a structural perspective, the detrimental impact of preferential flow pathway on EGS thermal extraction efficiency, it is necessary to simplify the highly complex fracture network present in actual reservoirs through an equivalent representation. As illustrated in Figure 12, panel (a) presents a conceptual schematic of the complex fracture connectivity structure between injection and production wells in an EGS, which is then idealized as a set of parallel flow channel models. Based on this simplified representation, panel (b) compares two extreme fracture distribution scenarios under identical total permeability conditions, highlighting the critical fact that permeability enhancement and effective heat exchange surface area are not necessarily positively correlated [89].

The macroscopic direct consequence is the occurrence of premature thermal breakthrough in production wells: the outlet fluid temperature experiences a sharp decline early in the project’s lifespan, resulting in a significant reduction in power output from the plant, while a substantial portion of the reservoir’s thermal energy remains locked within the unaffected rock matrix [90]. Therefore, a critical control problem that future EGS reservoir management must address is how to utilize thermal stimulation to enhance permeability while suppressing the detrimental localization of fluid pathways.

6.4. Confining Pressure Scaling and Dimensionless Analysis

Table 2. Laboratory-field performance comparison under different confining pressure conditions.

Parameter	Laboratory	Field Scale
Confining Pressure	7 MPa	40–60 MPa
Temperature Differential	40–600 °C	130–180 °C
Permeability/Injectivity Enhancement	R = 1.5–100	I = 1.3–7.5

presents a quantitative comparison of thermal stimulation performance between laboratory and field scales (the data are from the literature [64,72,73]). Laboratory data are derived from controlled thermal shock experiments conducted on intact granite specimens, whereas field data are obtained from operating EGS projects, including Soultz and Fenton Hill. Within comparable temperature difference ranges ($\Delta T\approx$ 130–180 °C), existing field data show injectivity enhancement ratios (I = 1.3–7.5) that are comparable to, or even higher than, the lower end of laboratory permeability enhancement ratios (R = 1.5–100) observed under similar temperature differences. This observation is somewhat unexpected given the anticipated suppressing effect of high confining pressure in deep reservoirs. Possible explanations include the following. First, the presence of natural fracture networks in field reservoirs provides additional flow pathways that are absent in intact laboratory specimens. Second, the combined effects of hydraulic, chemical, and thermal stimulation during field operations may produce synergistic enhancement. Third, the limited field dataset may not be representative of the broader population of EGS projects.

However, it must be explicitly acknowledged that the available field data points are limited (n = 2) due to the sparse public reporting of quantitative injectivity or permeability measurements from operating EGS projects. The current data availability precludes definitive conclusions regarding the magnitude of the confining pressure scaling effect. Future field experiments with systematic permeability monitoring under controlled thermal stimulation conditions are required to quantitatively validate these preliminary observations and refine the scaling relationships.

7. Selection of Fracturing Media and Thermo-Fluid Characteristics

The engineering efficacy of thermal stimulation depends not only on the magnitude of the temperature differential (ΔT) but is also governed by the thermophysical properties of the fracturing fluid. The viscosity, density, specific heat capacity, and surface tension of the fluid directly determine its ability to infiltrate micro-fractures (permeability) and its heat exchange rate with the rock wall (heat transfer coefficient). Currently, three mainstream or emerging working fluids are primarily involved in EGS development: water, LN₂, and supercritical carbon dioxide (SCCO₂) [91]. Furthermore, other technical approaches, including in situ methane blasting, have effectively enhanced reservoir permeability through controlled blasting operations [92]. To systematically evaluate the suitability of these fluids for specific engineering objectives, we compare their performance across three key dimensions. Heat transfer efficiency, determined jointly by the fluid’s specific heat capacity, thermal conductivity, and convective heat transfer coefficient. High heat transfer efficiency implies the ability to rapidly cool the rock mass, generating a larger thermal stress gradient per unit time and driving fracture propagation. Hydraulic penetrability, controlled by the fluid’s viscosity and surface tension. Fluids with low viscosity and low surface tension can overcome capillary sealing effects, infiltrate micron-scale fracture tips, and activate more extensive microcrack networks. Reservoir compatibility, referring to the chemical and physical compatibility of the fluid with reservoir minerals, native formation fluids, and ambient temperature-pressure conditions, including the swelling risk of water-sensitive minerals, phase transition behavior, and thermosiphon potential.

As the traditional baseline medium, water is the most widely applied working fluid in current EGS projects due to its low cost, broad availability, and extremely high specific heat capacity. Its heat transfer efficiency is exceptionally high; per unit mass, it can carry and remove substantial thermal energy, enabling deep and sustained cooling of the rock mass surrounding the borehole and generating extensive zones of thermal stress. However, water possesses relatively high viscosity and significant surface tension, which hinders its ability to invade micron-scale or nano-scale natural micro-fracture tips, giving rise to the so-called capillary sealing effect. Consequently, the water medium is most suitable for long-term heat extraction and macro-fracturing scenarios, particularly in granite reservoirs with good permeability and no risk of clay swelling. In formations containing expansive clay minerals, water sensitivity may lead to permeability damage, necessitating the addition of anti-swelling agents or consideration of alternative working fluids.

LN₂ serves as a cryogenic fracturing fluid that leverages its extremely low boiling point (approximately −196 °C) to generate a steep temperature gradient on the rock surface [93]. Its core advantage lies in its ability to deliver an ultra-high instantaneous temperature differential exceeding 400 °C. This intense thermal shock can induce spontaneous rock fragmentation even in the absence of hydraulically driven pressure, thereby substantially reducing the breakdown pressure required for fracture initiation. From the perspective of hydraulic penetrability, the extreme thermal stresses generated by LN₂ fracturing can induce a high-density microcrack network, resulting in exceptional penetration capability. However, the primary physical obstacle associated with LN₂ fracturing is the Leidenfrost effect [94], wherein a vapor film immediately forms at the interface when the cryogenic fluid contacts the hot rock, hindering direct liquid–solid contact and reducing heat transfer efficiency during the initial stage. Nevertheless, once this vapor film collapses, the ensuing thermal shock leads to catastrophic rock failure. Therefore, LN₂ is most suitable for use in extreme near-wellbore preconditioning stages to reduce the breakdown pressure of tight hot dry rock, although injection strategies such as pulse injection require optimization to overcome the initial heat transfer barrier.

SCCO₂ is regarded as a highly promising next-generation working fluid for EGS, particularly for hot dry rock development. When temperature and pressure exceed the critical point (31.04 °C, 7.38 MPa), CO₂ enters the supercritical state, combining the low viscosity of a gas with the high density of a liquid [95]. Its viscosity is approximately one-tenth that of water, and its surface tension is nearly zero, conferring superior diffusivity that enables it to readily penetrate micro-fracture tips inaccessible to water, thereby inducing more complex microcrack networks rather than single dominant fractures. Along the dimension of hydraulic penetrability, SCCO₂ exhibits optimal performance. In terms of heat transfer efficiency, the specific heat capacity of SCCO₂ (1.1–2.5 kJ/kg·K) is lower than that of water, but varies dynamically with temperature and pressure conditions. As a non-aqueous medium, it avoids issues related to clay swelling. Additionally, due to the high sensitivity of fluid density to temperature variations, it generates a strong thermosiphon effect, thereby reducing the power consumption of circulation pumps.

8. Conclusions and Perspectives

8.1. Concluding Remarks

This paper provides a comprehensive synthesis of the rock mechanics fundamentals and engineering application potential of thermal stimulation technology in EGS development. It integrates fragmented findings into a coherent body of existing knowledge to guide future engineering practices. Faced with the extreme geological conditions of deep crystalline rock reservoirs characterized by high confining pressure, high strength, and low permeability, traditional HF techniques encounter inherent limitations due to excessively high fracture initiation pressures and singular fracture network geometries. Thermal Shock, as a non-contact fracturing mechanism, successfully facilitates a paradigm shift from purely hydraulic-driven to THM coupled approaches by introducing steep temperature gradients. The core insights synthesized from existing literature are summarized as follows:

The physical basis for thermal damage lies in the thermal expansion mismatch at the mineral scale. The uncoordinated deformation of quartz and feldspar during cooling contraction induces inter-granular microcracks.

When the temperature difference exceeds a critical threshold, the crack propagation mode transitions from intergranular extension to transgranular fracture, resulting in a catastrophic loss of rock skeleton strength. This conclusion is supported by consistent microstructural observations from multiple independent studies.

The matrix contraction induced by thermal stress effectively counteracts the in situ confining pressure of the deep formation, significantly reducing the breakdown pressure of the rock and enabling low-pressure fracturing. Simultaneously, this contraction effect directly increases the mechanical aperture of fractures, resulting in a nonlinear exponential enhancement of permeability according to Darcy’s law.

Unlike HF, which tends to form single planar fractures, thermal stimulation promotes the activation of natural micro-fractures and induces shear slip, facilitating the formation of multi-scale, highly interconnected volumetric fracture networks. Moreover, the rough shear fracture surfaces provide critical self-propping capabilities, thereby reducing dependence on artificial proppants.

8.2. Challenges and Future Perspectives

Although thermal stimulation holds significant potential for application, achieving the transition from random fracturing to engineered reservoir creation requires future research to focus on the following key bottlenecks.

The first is true triaxial thermo-mechanical testing. Existing thermal damage models are predominantly based on experiments conducted under unconfined or conventional triaxial stress conditions, which largely neglect the controlling role of the intermediate principal stress on crack propagation. In deep in situ environments, the presence of this factor significantly alters the nucleation direction and propagation pathways of thermal cracks. Future experimental investigations must return to authentic deep geomechanical conditions by conducting real-time thermal shock experiments under true triaxial stress states, with emphasis on exploring the interaction mechanisms between stress anisotropy and thermal gradients, thereby refining current damage prediction models that are subject to overestimation or misinterpretation.

The second is intelligent control. Thermal stimulation entails competing mechanisms; while it enhances permeability, it can readily lead to the formation of preferential flow channels due to positive feedback mechanisms, resulting in thermal short-circuiting and premature thermal breakthrough. Future engineering control strategies must shift from passive monitoring to active intervention. Regarding smart diversion mechanisms, it is essential to develop temperature-responsive temporary plugging agents or degradable diverting materials capable of autonomously sealing primary flow channels before severe localized cooling occurs, thereby forcing fluid to redirect toward undrained, high-temperature matrix regions. This approach aligns with the concept of real-time feedback-based adaptive control employed in complex energy systems [96]. Regarding cyclic injection-production schemes, pulsed injection or cyclic thermal shocking should be adopted instead of continuous low-temperature injection to suppress the detrimental growth of localized flow channels and maximize reservoir thermal sweep efficiency. Drawing on parameter optimization methods from process automation, future efforts can further develop machine learning-based predictive models of thermo-hydraulic responses to enable dynamic closed-loop regulation of injection and production parameters.

The third is failure cases and boundary conditions. Identifying failure cases is essential for defining the operational envelope of thermal stimulation. Drawing inspiration from geotechnical foundation design [97], future EGS engineering should develop similar ΔT-${\sigma }_3$-K (temperature differential-confining pressure-permeability) interaction diagrams to quantify the safe operational boundaries of thermal stimulation. Regarding seismicity-induced termination, the Pohang EGS project exemplifies a critical boundary condition where stimulation-induced seismicity exceeded socially acceptable limits, leading to project suspension. This underscores that permeability enhancement cannot be pursued in isolation from seismic risk assessment, particularly in areas adjacent to faults. Regarding thermal short-circuiting, premature thermal breakthrough observed in projects such as Fenton Hill and Soultz illustrates a failure mode in which permeability enhancement becomes localized rather than volumetric [87,88]. This defines a boundary condition: thermal stimulation yields limited effectiveness in reservoirs lacking sufficient natural fracture heterogeneity to distribute flow, or in the absence of active flow control mechanisms. Regarding confining pressure suppression, as discussed in Section 6.1, there exists a mechanical boundary beyond which in situ stress completely suppresses thermally induced microcracking. In such highly confined environments, thermal stimulation alone is insufficient and must be combined with hydraulic or chemical methods. Acknowledging these contradictions and boundary conditions helps prevent overly optimistic extrapolations and provides guidance for developing engineering strategies aimed at risk mitigation.

The fourth point is multi-scale interface characterization. Drawing from recent advances in geotechnical interface mechanics where finite-slip coupled (FSC) constitutive models have been developed to characterize grout-soil interface behavior [98], future EGS research should develop similar thermal-rock interface constitutive models that account for the coupled effects of temperature differential, confining pressure, and mineralogical heterogeneity. Such models would enable more accurate prediction of fracture aperture evolution and permeability enhancement in thermally stimulated reservoirs.