Influence of Low-Temperature Fluid Thermal Shock on Hydraulic Fracture Propagation in Deep Shale

Abstract

Deep shale subjected to thermal shock from low-temperature fracturing fluid in high-temperature and high-pressure (HTHP) environments will severely affect the propagating behavior of hydraulic fractures. This study conducted hydraulic fracturing physical simulation experiments under HTHP conditions, as well as numerical simulations of thermal shock-induced shale cracking based on the cohesive zone model (CZM), to systematically investigate the initiation mechanisms and propagation behavior of thermal cracks under thermal shock. Experimental results indicate that as the rock temperature increases from 25 to 200 °C, the thermal shock effect becomes significantly enhanced. The stimulated rock area (SRA) increases from 1.00 to 1.75, and the fracture fractal dimension (FD) rises from 1.92 to 2.01. Meanwhile, the breakdown pressure at 200 °C decreases by approximately 9.8% compared to that at 25 °C. Numerical simulation results show that higher thermal shock rates (with a shock duration of 25 s) lead to an increased number of thermal cracks (up to 31 fractures). Moreover, multiple cycles of thermal shock (10 cycles) can enhance the average crack length by 51% through cumulative damage accumulation. By leveraging thermal shock effects, more advanced hydraulic fracturing techniques may be developed for deep earth energy reservoirs, with the potential to reduce breakdown pressure and enhance fracture network complexity. These findings provide laboratory-scale evidence and mechanistic insights for future fracturing process optimization.

1. Introduction

Deep and ultradeep shale gas resources have become key targets for reserve replacement and production enhancement in China. However, these formations are typically characterized by high-temperature and high-pressure (HTHP) conditions, under which the injection of large volumes of low-temperature fracturing fluid can induce strong thermal-shock effects. Such thermal shock not only alters reservoir properties, including porosity and permeability, but also diminishes critical mechanical parameters such as Young’s modulus, strength, and fracture toughness, − thereby affecting the initiation and propagation of hydraulic fractures. Consequently, elucidating the mechanisms by which thermal shock influences fracture growth under HTHP conditions is essential for improving fracturing performance and achieving effective stimulation in deep shale reservoirs.

Currently, studies on the influence of thermal shock on hydraulic fracture propagation remain relatively limited. − Nevertheless, some temperature-related investigations provide valuable insights into fracture behavior under thermal shock. Most studies on the influence of high-temperature on hydraulic fracture propagation has focused on hot dry rock reservoirs. And most existing experimental findings are concentrated on thermal-damage evolution and property degradation after heating–cooling treatments, whereas studies that directly connect thermal shock to the hydraulic-fracturing process response and to quantitative fracture-geometry outcomes remain insufficient, particularly under deep-shale HTHP in situ stress conditions. or instance, Zhou et al. found that elevated temperature induces microcracks inside rocks, transforming the hydraulic fracturing mode from brittle fracture to continuous fracture. Cheng et al. pointed out that the fracture initiation and breakdown pressures decrease significantly under high-temperature conditions. Although high-temperature can reduce the mechanical properties of rocks, its impact on fracture propagation is less pronounced than the thermal shock caused by low-temperature fracturing fluids. Thermal shock has a particularly significant effect on reducing rock breakdown pressure. Recent studies have shown that temperature fluctuations and thermal-shock treatments can regulate breakdown pressure by inducing microcrack damage and altering pore–fracture structure characteristics. On the one hand, as the number of thermal-shock cycles increases, rock strength and stiffness generally decrease, whereas pore density and permeability increase, indicating an accumulated thermal-damage effect. Moreover, the magnitude of these mechanical and structural changes tends to become more pronounced with increasing cycle number. On the other hand, the transient temperature gradient associated with thermal shock is prone to generating microcracks, thereby markedly reducing breakdown pressure in both sandstone and shale. Pore-scale NMR and MRI observations further suggest that damage accumulation arises from the coupled heating–cooling process, including mineral thermal expansion and possible phase transitions during heating, volumetric contraction during cooling, and water-mediated reactions such as clay hydration and swelling during water cooling. − Studies have shown that thermal shock exhibits a certain critical temperature threshold: below this threshold, fracture propagation is mainly stress-controlled; above the threshold, thermal fractures dominate the fracture evolution and can induce multiple branch fractures. ,− During the thermal shock process, fractures formed by cooling are generally wider, facilitating the connection of large-scale fractures. The mechanism underlying this phenomenon is that the propagation of thermal fractures after their initiation is still stress-controlled, with only local bending observed in the initial stage. In addition, the efficiency of thermal shock is closely related to rock type and mineral compositionrocks with higher brittleness exhibit more significant thermal shock effects. For hot dry rock reservoirs, explicitly stated that when the thermal shock temperature exceeds 300 °C, the fracturing effect can be significantly enhanced. Thermal fractures induced by thermal shock occur at multiple locations inside the rock, and the improvement of cooling efficiency can also lead to a competitive effect among fractures. , Meanwhile, the formation temperature disturbance caused by thermal shock enhances the stress interference effect during the propagation of multicluster fractures and also results in the unevenness of fracture propagation.

Although relevant studies have made progress, systematic evidence regarding the influence of thermal shock on fracture propagation in deep shale under HTHP in situ conditions is still limited. In particular, the links between thermal shock conditions, injection pressure response characteristics, and fracture spatial morphology remain unclear. This study combines HTHP true triaxial hydraulic fracturing experiments with numerical simulations of thermal shock induced fracture propagation, and provides complementary laboratory-scale evidence and mechanism explanations to explore how thermal shock affects fracture activation in the near-wellbore area and subsequent fracture propagation. Meanwhile, the limitations of extrapolating the present results to field-scale hydraulic fracturing are explicitly discussed. The research results provide a new theoretical basis and optimization ideas for deep shale hydraulic fracturing technology.

2. Methodology

2.1. Sample Preparation

Samples utilized in fracturing experiments were collected from natural outcrop shales in Chongqing, China (Figure a), which represent natural extensions of the Lower Silurian Longmaxi Formation shale reservoir. The outcrop shales predominantly consist of siliceous shale and graptolite-bearing black shale, characterized by well-developed bedding structures and severely weathered rock surfaces (Figure b). To ensure sample integrity and representativeness, the heavily weathered surface strata of the outcrop were first stripped to expose the shale with lower weathering intensity, larger volume, and higher quality. Subsequently, heavy machinery was employed to extract intact shale blocks (Figure c). The uniaxial compressive strength of the collected shale is 122.6 MPa, and the Young’s modulus is 25.6 GPa. Mineralogical analysis revealed approximately 69.2% brittle mineral content and 18.3% clay mineral content.

1.

Shale sample collection site.

Standard cubic shale samples (300 × 300 × 300 mm) were prepared by cutting from outcrop blocks (Figure a). All sample surfaces were precisely ground using a large-scale rock grinder, with surface flatness verified at multiple locations per face using spirit levels. Local irregularities were corrected with an angle grinder to meet experimental flatness requirements. A central borehole (25 mm diameter, 165–170 mm depth) was drilled into the cubic sample, followed by insertion of a diameter of 21 mm and a length of 160 mm wellbore casing into the borehole to create an open-hole section. The annulus between the casing and borehole wall was sealed with high-temperature resistant epoxy resin, which was cured at room temperature (25–30 °C) for 24 h (Figure b). The processed sample was then mounted into the HTHP hydraulic fracturing experimental system for subsequent fracturing experiments.

2.

Sample preparation and hydraulic fracturing experimental apparatus.

2.2. Experimental Setup and Testing Procedure

The experimental apparatus employed in this study is the newly developed real-time HTHP true triaxial hydraulic fracturing experimental system at Wuhan Institute of Rock and Soil Mechanics of the Chinese Academy of Sciences (Figure c). Primarily designed for 300 mm cubic samples, the system demonstrates scalability to accommodate 500 mm samples. It exhibits exceptional loading capacity with independent maximum principal stress application up to 88 MPa in all three orthogonal directions. The integrated heating module achieves uniform sample temperature elevation to 350 °C through an intelligent temperature control system. For fracturing operations, the apparatus supports slickwater injection with a maximum pumping pressure of 210 MPa and incorporates a supercritical CO₂ injection module.

The experimental procedure utilizing this system is outlined as follows: Samples were initially labeled and photographed for documentation, with loading stress magnitudes and directions recorded for each face. A high thermal conductivity heat dissipation silicone grease was uniformly applied to all loading plates of the triaxial chamber to mitigate end friction effects, enhance thermal conduction efficiency, and reduce stress concentration. Subsequently, the sample was hoisted and positioned into the triaxial chamber, where a 5 MPa preload stress was simultaneously applied to the sample. After installing the thermal insulation cover, the heating system was activated to elevate the temperature to the preset target, followed by 4 h isothermal hold to ensure temperature field equilibrium. Upon temperature stabilization, three directional stresses were synchronously loaded to target values according to the predetermined path, while fracturing fluid containing tracer was injected to initiate the experiment. Pumping was terminated once a sample fracture occurred and fracturing fluid emerged from the sample. After cooling to room temperature, the sample was disassembled for marking fractures, photographic recording, and anatomical analysis. Finally, a 3D optical scanning system was used to digitally reconstruct the fracture geometry.

2.3. Basic Theory of Numerical Simulation

Based on the theory of cohesive interface element simulation, namely the cohesive zone model (CZM), a numerical calculation script for simulating thermal crack propagation induced by thermal shock was written in Python. The visual simulation of the thermal crack initiation and propagation process was realized using the commercial finite element software ABAQUS.

2.3.1. Constitutive Model of Cohesive Zone Model

The crack propagation process in brittle materials such as rocks can be characterized by the cohesive zone model (CZM), and its mechanical behavior is typically simulated by introducing cohesive elements. The stress-displacement relationship of cohesive elements is generally described using a bilinear traction-separation constitutive model, which is divided into a linear stress increase phase and a damage softening phase, with the peak strength serving as the boundary. For two-dimensional problems, eq can be used to characterize the traction-separation relationship in the prepeak stage:

$$\left\{\begin{array}{l}{\sigma }_{\mathrm{n}}\\ {\tau }_{\mathrm{s}}\end{array}\right\}=\left[\begin{array}{ll}{E}_{\mathrm{nn}}& 0\\ 0& E_{\mathrm{ss}}\end{array}\right]\left\{\begin{array}{l}{\epsilon }_{\mathrm{n}}\\ {\epsilon }_{\mathrm{s}}\end{array}\right\}=\frac{1}{T_0}\left[\begin{array}{ll}{E}_{\mathrm{nn}}& 0\\ 0& E_{\mathrm{ss}}\end{array}\right]\left\{\begin{array}{l}{\delta }_{\mathrm{n}}\\ {\delta }_{\mathrm{s}}\end{array}\right\}$$ 1

where σ_n and τ_s are the nominal traction components: normal stress and shear stress; ε_n and ε_s are the two nominal strain components; δ_n and δ_s are the separation components: normal displacement and shear displacement; T ₀ the original thickness of the cohesive element; E _nn and E _ss are the initial normal and shear stiffness of the element, respectively.

When the normal and shear separation components of the cohesive element reach δ_n and δ_s , the cohesive interface initiates damage. According to eq , the damage initiation displacements can be calculated using eq :

$${\delta }_{\mathrm{n}}^0=\frac{{\sigma }_{\mathrm{nc}}}{K_{\mathrm{nn}}}\mathrm{and}{\delta }_{\mathrm{s}}^0=\frac{{\tau }_{\mathrm{sc}}}{K_{\mathrm{ss}}}$$ 2

where σ_nc and τ_sc are the normal stress and shear stress respectively when the interface undergoes type I and type II fractures. According to the bilinear traction-separation constitutive model, the δ_n and δ_s values at the time of separation displacement can be expressed by eq :

$${\delta }_{\mathrm{n}}^{\mathrm{f}}=\frac{2G_{\mathrm{n}}}{{\sigma }_{\mathrm{nc}}}\mathrm{and}{\delta }_{\mathrm{s}}^{\mathrm{f}}=\frac{2G_{\mathrm{s}}}{{\tau }_{\mathrm{sc}}}$$ 3

where G _n and G _s are the critical fracture energies of the interface in Type I and Type II fracture states. When the nominal stress of the cohesion interface reaches the maximum standard, the interface is damaged. The maximum nominal stress criterion can be used to represent the initial damage condition:

$$\max \{\frac{⟨{\sigma }_{\mathrm{n}}⟩}{{\sigma }_{\mathrm{nc}}},\frac{⟨{\tau }_{\mathrm{s}}⟩}{{\tau }_{\mathrm{sc}}}\}=1$$ 4

where ⟨·⟩ is the Macaulay bracket. When x ≥ 0, ⟨x⟩ = x, otherwise, it is 0.

When the damage criterion given by eq is satisfied, the traction stresses of the cohesive interface enter the postpeak linear softening phase. A scalar damage variable can be employed to characterize the stress degradation:

$${\sigma }_{\mathrm{n}}=(1-D){\mathrm{\sigma ̅}}_{\mathrm{n}}\mathrm{and}{\tau }_{\mathrm{s}}=(1-D){\mathrm{\tau ̅}}_{\mathrm{s}}$$ 5

where σ̅_n and τ̅_s are the nominal normal traction stress and shear traction stress predicted by the traction-separation model in the undamaged state of the cohesive element.

For mixed-mode fracture, the bilinear traction-separation model of the cohesive interface is characterized by the relative separation δ_m:

$${\delta }_{\mathrm{m}}=\sqrt{{⟨{\delta }_{\mathrm{n}}⟩}^2+{\delta }_s^2}$$ 6

For linear damage softening, the damage variable can be expressed by eq :

$$D=\frac{{\delta }_{\mathrm{m}}^{\mathrm{f}}({\delta }_n-{\delta }_{\mathrm{m}}^0)}{{\delta }_m({\delta }_{\mathrm{m}}^{\mathrm{f}}-{\delta }_{\mathrm{m}}^0)}$$ 7

where δ_m and δ_m are the effective separations at damage initiation and complete separation of the cohesive interface, respectively.

For mixed-mode fracture, the combination of fracture modes at the cohesive interface can be quantified by the ratio of the normal fracture energy­(G _n)­to the shear fracture energy­(G _s). Fracture energy represents the work done by the nominal traction stress under the corresponding separation, and thus the total mixed-mode fracture energy (G _t) can be defined. Two ratios, m ₁ and m ₂ are further defined as follows:

$$\begin{array}{l}{m}_1=\frac{G_{\mathrm{n}}}{G_{\mathrm{t}}}\mathrm{and}{m}_2=\frac{G_{\mathrm{s}}}{G_{\mathrm{t}}}\\ G_{\mathrm{t}}=G_{\mathrm{n}}+G_{\mathrm{s}}\end{array}$$ 8

The relationship between the fracture energy and the mixed-mode fracture can be defined by the power-law fracture criterion (eq ):

$${\left\{\frac{G_{\mathrm{n}}}{G_{\mathrm{n}}^{\mathrm{c}}}\right\}}^{\alpha }+{\left\{\frac{G_{\mathrm{s}}}{G_{\mathrm{s}}^{\mathrm{c}}}\right\}}^{\alpha }=1$$ 9

where G _n , G _s and G _s are material constants characterizing the fracture behavior of the cohesive interface.

2.3.2. Heat Conduction in Cohesive Interface Elements

The heat conduction of the cohesive interface element can be expressed as a function of the temperature difference between the upper and lower interfaces, which is defined by eq :

$$q=k_{\mathrm{cz}}({\theta }^{+}-{\theta }^{-})$$ 10

where q is the heat flux per unit area across the cohesive interface; θ⁺ and θ^– are the temperatures at the upper and lower surfaces of the interface; and k _cz is the thermal conductivity of the gap within the cohesive zone, which depends on the normal separation displacement (k _cz = k _cz(δ_n)). The thermal conductivity of the gap can be described by eq as follows:

$$k_{\mathrm{cz}}=\{\begin{array}{ll}{k}_{\mathrm{cz}0}-k{\delta }_{\mathrm{n}}& {\delta }_{\mathrm{n}}<k_{\mathrm{cz}0}/k\\ 0& {\delta }_{\mathrm{n}}\ge k_{\mathrm{cz}0}/k\end{array}$$ 11

where k _cz0 is the thermal conductivity in the undamaged state, which is consistent with that of the rock matrix, and k is the coefficient characterizing the decrease in thermal conductivity with increasing normal separation displacement. When the normal separation displacement exceeds the critical value (k _cz0/k), k _cz = 0.

2.3.3. Numerical Simulation Procedure and Model Setup

The thermal shock model is established as a 2D plane perpendicular to the wellbore (Figure a), with both length and width dimensions set at 300 mm to maintain consistency with hydraulic fracturing specimen geometries. Computational analyses focus on thermal shock temperature difference, cycles, and cooling rate. The numerical simulation initializes boundary conditions, including in situ stress distribution, fluid temperature profiles along the wellbore inner wall, and initial temperature fields of the rock mass. The complete computational workflow is presented in Figure b.

3.

Thermal shock numerical modeling and calculation workflow.

2.4. Physical Experiment and Numerical Simulation Scheme

In this paper, the deep shale gas reservoirs above 3500 m in the Sichuan area of China serve as the research background. The in situ stress state of the reservoir is mainly characterized by a strike-slip fault stress mechanism (maximum horizontal principal stress (SH) > vertical stress (SV) > minimum horizontal principal stress (Sh)). The horizontal principal stress difference is about 15 MPa, and the formation temperature exceeds 150 °C. To improve the representativeness of the laboratory scale, the injection rates were selected based on the dimensional-analysis scaling laws for hydraulic fracturing proposed by de Pater et al. , Accordingly, the laboratory injection rate of 20 mL/min corresponds to a field-scale pumping rate of approximately 8 m³/min, implying a geometric scale factor of about 74. With this scale factor, the cubic sample edge length of 300 mm corresponds to a characteristic field length of approximately 22 m. Accordingly, the following test schemes (Table ) was designed following a grouped controlled-comparison strategy. Specifically, H1, H3, and H4 were tested under the same stress state (SV/SH/Sh = 80/85/70 MPa) and injection rate (40 mL/min), with temperature as the sole variable for evaluating thermal shock response. In addition, the injection rate effect was examined by comparing H2 and H3 (same temperature and stress state). The horizontal stress difference effect was examined by comparing H4 and H5 (same temperature and injection rate). The corresponding numerical simulation scheme was listed in Table .

1. Physical Simulation Experiment Scheme for Hydraulic Fracturing.

no.	temperature (°C)	SV (MPa)	SH (MPa)	Sh (MPa)	stress difference (MPa)	injection rate (mL/min)	fracturing fluid type	tracer type
H1	25	80	85	70	15	40	water	red fluorescence reagent
H2	150	80	85	70	15	20	water
H3	150	80	85	70	15	40	water
H4	200	80	85	70	15	40	water
H5	200	80	85	60	25	40	water

2. Numerical Simulation Scheme of Thermal Shock.

no.	temperature (°C)	fracturing fluid temperature (°C)	shock time (s)	cycle
T1	100	20	25	1
T2	200	20	25	1
T3	300	20	25	1
T4	200	20	50	1
T5	200	20	100	1
T6	200	20	25	5
T7	200	20	25	10

The numerical model requires the input of fundamental physical, mechanical, and thermodynamic parameters of the shale. These include: SH of 85 MPa, Sh of 70 MPa, Young’s modulus of 25 GPa, and tensile strength of 8.96 MPa. Since no thermophysical experiments on shale have been performed in this study, the relevant parameters were adopted from the findings reported by Enayatpour et al. ,, Among these parameters are a coefficient of thermal expansion of 2.2 × 10^–5 K^–1, a thermal conductivity of 0.61 W·m^–1·K^–1, a specific heat capacity of 1.28 × 10³ J·kg^–1·K^–1, a normal traction modulus of 0.5 GPa, and a tangential traction modulus of 0.2 GPa; five damage parameters: a nominal normal traction stress of 1.8 MPa, a nominal shear traction stress of 5.2 MPa, a critical Mode I fracture energy of 150 N/m, and a critical Mode II fracture energy of 1500 N/m; and two thermal parameters for the cohesive interface model: an initial gap thermal conductivity of 1.5 W·m^–1·K^–1, and a gap thermal conductivity reduction coefficient of 0.3.

3. Results

3.1. Fracturing Experiment - Injection Pressure Curve

Figure a illustrates the temporal evolution of injection pressure under various fracturing test conditions, with five curves exhibiting significant disparities. Under room-temperature high-pressure (RTHP) conditions, the pressure remains stable during the initial injection stage (<100 s) as fracturing fluid fills the wellbore. Subsequently, pressure rises rapidly due to fluid compression effects. The first deviation from the quasi-linear pressurization stage is identified as the fracture initiation pressure (FIP). The first peak pressure is defined as the breakdown pressure (BP), typically followed by an abrupt pressure drop. After the pressure reaches its peak, the curve enters a violent oscillation stage and then tends to stabilize. At this time, the hydraulic fracture is completely formed and enters a stable seepage state. The postpeak violent oscillation characteristics under RTHP conditions fundamentally differ from the typical pattern of “rapid decline followed by stabilization after peak” observed in idealized injection pressure-time curves. This phenomenon likely arises from two mechanisms: (1) Intermittent propagation of hydraulic fractures. After rock initiation, fracturing fluid enters newly formed fractures, causing a pressure drop and reducing the fracture tip stress intensity factor. Fracture propagation temporarily halts and requires pressure to be boosted again to drive continued extension until completely penetrating the rock; (2) Fracture unblocking. Under high confining stress conditions, if fractures close after rock penetration due to insufficient pressure, they will only reopen when the injection pressure recovers to the fracture opening threshold. This oscillatory behavior is consistent with the cyclic opening–closure of fractures, which has also been directly observed using distributed fiber-optic strain sensing (OFDR) to track the evolution of fracture opening displacement in laboratory fracturing tests. Pressure oscillations correspond to transient disturbances caused by the unblocking of hydraulic fractures by high-pressure fracturing fluid. The injection pressure oscillations observed in the RTHP fracturing experiment can be attributed to the cyclic opening and closing of the fracture. This is confirmed by the ejection of red fracturing fluid at the rock boundary during the first oscillation.

4.

Injection pressure – time curve and breakdown pressure.

Under 150 °C HTHP conditions, the postpeak injection pressure curve shows two typical features. Taking a 20 mL/min injection rate as an example: the initial fluid filling stage lasts longer with an identifiable fracture initiation pressure point; after the peak, pressure drops rapidly and stabilizes, indicating fractures quickly enter stable seepage flow. This reflects possible natural fractures or weak planes in the sample’s open-hole section. During fluid filling, the fracturing fluid is lost quickly, and weak planes gradually reach a subcritical state during the pressure rise, becoming fully activated at the peak. Under the weak plane self-supporting effect, fracturing fluid rapidly achieves a stable seepage flow. When the injection rate increases to 40 mL/min, the postpeak pressure drop becomes smaller and the oscillation amplitude is attenuated. Notably, a higher injection rate does not necessarily eliminate the oscillations; instead, it can primarily shift the oscillation frequency/period because pressure is replenished more rapidly under constant-rate injection, leading to a change in the oscillatory characteristics of the curve. Under 200 °C HTHP conditions, the postpeak injection pressure curve shows two characteristics. At 15 MPa horizontal stress difference, the fracture initiation pressure point is clear and the postpeak oscillation frequency increases. The abrupt slope change indicates activation of local defects in the open-hole section, differing from gradual slope variation in conventional curves. Oscillation enhancement is related to the fracture opening-closing process on one hand, and influenced by fracturing fluid vaporization at high temperatures on the other. At 200 °C, the fracturing fluid vaporizes on the rock surface, accelerating its dissipation and causing rapid pressure fluctuations, thereby generating high-frequency oscillations. Sounds of water vapor ejection accompany each pressure oscillation in the experiment, and oscillations terminate when the sounds cease, further corroborating the vaporization effect. At a 20 MPa horizontal stress difference, the postpeak oscillation amplitude significantly decreases, indicating a transition from unstable to stable seepage characteristics in hydraulic fractures.

BP is determined as the first peak injection pressure on the pressure–time curve, as shown in Figure b. Theoretically, hydraulic fracture formation requires overcoming the sum of the minimum principal stress and rock tensile strength, allowing for BP calculation via eq . Since this experiment excludes pore pressure effects, theoretical calculations show reasonable agreement with the measured BP. BP exhibits a gradual decreasing trend with increasing temperature. Under the same injection rate and horizontal stress difference conditions, the BP at 150 and 200 °C decreases by approximately 3.6 and 9.8%, respectively, compared to 25 °C. As each condition was tested once, the observed BP reduction is discussed as a temperature-associated trend rather than statistical significance. This phenomenon is primarily attributed to the high-temperature weakening of shale matrix mechanical properties, including thermal crack initiation, intensification of wellbore wall damage, and enhanced activation potential of natural weak planes.

$$P_b=\min ({\sigma }_{\mathit{in}\mathit{situ}}+{\sigma }_t)-P_o$$ 12

where P _b is the breakdown pressure, P _o is the pore pressure, σ _t is the tensile strength, and σ _in situ is the in situ stress.

3.2. Fracturing Experiment - Hydraulic Fracture Morphology

Figure illustrates the fracture morphology after fracturing. Consistent with the injection pressure curve analysis, the fracture patterns include artificial hydraulic fractures, natural fractures, and secondary fractures. It should be noted that for the 150 °C-40 mL/min-15 MPa sample, a cylindrical sample with 100 mm diameter and 300 mm length was drilled along the wellbore axis for CT scanning to observe secondary fracture distribution around the primary fracture, hence its anatomical diagram is not included in Figure . Observations indicate that under RTHP conditions, fractures initiate from the open-hole section and propagate perpendicular to the Sh direction, penetrating through the sample with minimal deflection and a smooth fracture surface. At 150 °C and 20 mL/min, the open-hole section contains a natural fracture parallel to the Sh. This fracture is activated and penetrates the sample; the natural fracture exhibits significant surface roughness, partial cement spalling, and low cementation strength, making it prone to cracking under high-temperature conditions. CT results of the sample under 150 °C-40 mL/min conditions show that, apart from the main fracture, multiple parallel secondary fractures exist near the open-hole section. If the single injection of low-temperature fracturing fluid is regarded as a thermal shock, these secondary fractures are considered to be induced by thermal shock effects. Detailed analysis is provided in Section . Under 200 °C-15 MPa conditions, both fracture initiation and propagation directions are perpendicular to Sh. Two secondary fractures appear parallel to the main fracture but do not penetrate the sample. They only partially propagate before converging with the main fracture, forming spindle-shaped fractures. This phenomenon indicates that a single thermal shock can generate thermal fractures in the open-hole section. Furthermore, the amplitude of high-frequency injection pressure oscillations approaches the initial hydraulic fracture opening amplitude, intermittently providing driving force for thermal fracture propagation. After stable fracturing fluid seepage is established in the main fracture, the pressure within becomes insufficient to sustain thermal fracture extension, resulting in incomplete propagation and eventual intersection with the main fracture during the shear slip process. Compared to 150 °C, the thermal fracture propagation distance increases at 200 °C, indicating that larger temperature differences generate greater thermal stresses and more pronounced thermal shock effects. This results in more severe open-hole damage and enhanced thermal fracture propagation potential. Under 200 °C-25 MPa conditions, fracture initiation and propagation directions are also perpendicular to Sh, with relatively smooth fracture surfaces and no thermal fractures observed. The fracture directly crosses a low-angle natural fracture, demonstrating that high horizontal stress difference strongly controls fracture propagation direction and accelerates fracture extension.

5.

Hydraulic fracture morphology.

3.3. Fracturing Experiment – Statistics and Evaluation of Hydraulic Fracture

Although the fracture propagation scale in HTHP fracturing experiments is limited, the results still provide important references for fracturing engineering. To deeply analyze the morphological and structural characteristics of hydraulic fractures, quantitative evaluation of fracture complexity was conducted using the stimulated rock area (SRA) and fractal dimension (FD) based on 3D fracture morphology scanning data. SRA is defined as the total area of tracer-containing fractures within the sample. It classifies fracture types (hydraulic, natural, bedding planes) by the ratio of their area to the sample cross-section area, typically including four grades (0.25, 0.5, 0.75, and 1). As shown in Figure a, the hydraulic fracture penetrates the left side of the sample and partially communicates with bedding planes, while the right side is captured and diverted by natural fractures. Consequently, the SRA calculation follows: SRA = 0.75 (left hydraulic fracture: 0.5 + right hydraulic fracture: 0.25) + 0.5 (bedding plane) + 0.75 (natural fracture) = 2.0.

6.

Calculation method of SRA and FD.

FD, grounded in fractal theory, quantifies the irregularity and spatial filling capacity of fracture morphology in 3D space, representing a noninteger dimension. A higher FD indicates denser spatial distribution and more complex fracture patterns. FD is calculated using the box-counting method: the 3D fracture model is partitioned into cubic boxes with side length r, and the number of boxes covering the fracture surface is counted (Figure b). As the box side length approaches zero, the fractal dimension is determined by the ratio of the natural logarithm of the box count to the natural logarithm of the reciprocal of the box side length. The detailed calculation method is provided in eq .

$$\ln (N(r))=\mathit{FD}\ln \left(\frac{1}{r}\right)+C$$ 13

where N is the number of boxes, r is the box size, and C is the intercept (constant).

Figure illustrates the 3D morphology reconstruction results of hydraulic fractures. The fracture patterns can be categorized into three types: single hydraulic fractures, single natural fractures, and combined fractures of hydraulic and thermal fractures. The first two categories exhibit a double-wing symmetric pattern, while the combined fractures display a spindle-shaped structure. Detailed SRA statistical results are provided in Table .

7.

3D morphology reconstruction of hydraulic fractures.

3. SRA Evaluation Results of Hydraulic Fractures.

no.	temperature (°C)	SV (MPa)	SH (MPa)	Sh (MPa)	stress difference (MPa)	injection rate(mL/min)	SRA
H1	25	80	85	70	15	40	1
H2	150	80	85	70	15	20	1.5
H3	150	80	85	70	15	40	1
H4	200	80	85	70	15	40	1.75
H5	200	80	85	60	25	40	1

Under RTHP conditions, the fracture SRA was 1; at 150 °C, the average SRA rose to 1.25; and at 200 °C, it further increased to 1.375. The SRA increased with temperature; higher temperatures amplify the thermal shock effects and elevate the potential for activating and connecting thermal cracks/microcracks, which, under high-pressure fracturing fluids, tend to evolve into a more complex fracture network with a larger fracture surface area. Accordingly, a more complex fracture network may also cause greater pressure loss during intermittent opening/closing events, while the reopening pressure threshold under the same closure stress remains comparable, potentially resulting in larger postbreakdown oscillation amplitudes. For example, CT scans of sample H2 (Figure ) reveal numerous tiny cracks in the open-hole section. The classification of these fractures as thermal rather than natural is attributed to the absence of a distinct nonlinear stage during the pressurization process, indicating minimal fluid leak-off or a lack of natural fractures in the open-hole section. However, a transient pressure plateau suddenly emerged during the midstage of pressurization, suggesting the formation of minor new microcracks in the open-hole section. Although elevated temperature enhances thermal shock effects, the propagation extent of thermal fractures remains constrained. Theoretically, if all near-wellbore microfractures undergo synergistic propagation with the main fracture, the SRA would experience a substantial increase. Consequently, enhancing the controllability and utilization efficiency of thermal fractures constitutes a potential approach to improve reservoir stimulation volume in practical fracturing engineering. The 150 °C-20 mL/min sample primarily activated natural fractures with an SRA of 1.0, while the 150 °C-40 mL/min sample formed thermal fractures, elevating the SRA to 1.5. This suggests that elevated temperatures increase the natural fracture activation potential under low injection rates, although they result in reduced heat exchange efficiency and weakened thermal shock. The 200 °C-15 MPa sample achieved the highest SRA of 1.75 due to significant thermal fracture propagation, whereas the 200 °C-25 MPa sample showed an SRA of 1.0. This demonstrates that a higher horizontal stress difference, while facilitating the rapid propagation of main fractures, significantly inhibits the development of thermal fractures.

8.

Characteristics of thermal cracks in the open-hole section.

Although SRA effectively reflects the overall complexity of hydraulic fractures, it exhibits limitations in characterizing detailed fracture geometries. To further validate the efficacy of SRA, the FD was used as a complementary metric for comparative analysis. It should be noted that the box-counting analysis was performed using box sizes spanning 0.17–148 mm. The ln N(r) – ln­(1/r) linear fits show high goodness-of-fit, with R ² values ranging from 0.993 to 0.999. Figure illustrates the FD calculations for hydraulic fractures: Sample H1, with the single fracture formed under RTHP conditions, demonstrates an FD of 1.9183. For samples H3 and H5, which are also single fractures, FDs of 1.9220 and 1.9235 were observed, respectively. The former is attributed to the surface roughness of natural fractures, and the latter results from the deflection of hydraulic fractures. Thermal fracture samples H2 and H4 exhibit significantly higher FDs (1.9504 and 2.0126), indicating a positive correlation with the extent of thermal fracture propagation. This suggests that under the same hydraulic fracture propagation scales, FD effectively characterizes thermal fracture propagation. FD and SRA under HTHP conditions show good agreement in evaluating fracture complexity (Figure ). The integrated use of these metrics provides a more comprehensive method for analyzing thermal fractures.

9.

FD results of hydraulic fractures.

10.

Comparison of FD and SRA of hydraulic fractures.

3.4. Numerical Simulation - Thermal Crack Propagation Characteristics

Because direct temperature instrumentation at the borehole (e.g., injected fluid temperature in the borehole and the transient near-wellbore cooling rate) was not available in the true triaxial HTHP experiments, the thermal shock rate cannot be directly quantified from the experiments alone. Nevertheless, the experimental observations indicate that even a single thermal shock treatment under appropriate conditions can enhance fracture complexity, which suggests a potential pathway for optimizing hydraulic fracturing operations. To further interpret this effect and guide process design, two critical challenges should be addressed: (1) inducing thermal cracks with propagation potential at the open-hole; and (2) driving extended thermal fracture further while ensuring adequate hydraulic fracture propagation. A systematic investigation of cracking behaviors in the open-hole section under thermal shock effects is therefore essential. This section focuses on analyzing three key parametersthermal shock temperature difference, cooling rate, and cyclewhich correspond to field operational factors including formation temperature, fracturing fluid properties, and injection mode.

3.4.1. Thermal Shock Temperature Difference

Figure illustrates the distribution characteristics of thermal cracks under different thermal shock temperature differences. Here, the thermal shock temperature difference is defined as the borehole-wall rock temperature drop during cooling (from the initial borehole-wall temperature to the cooled temperature imposed in the simulation). In the left panel, the temperature field cloud after thermal shock is shown; in the right panel, the distribution of borehole damage state and thermal cracks is shown. The results demonstrate that thermal cracks predominantly develop uniformly around the borehole circumference, exhibiting a radial distribution pattern. As the thermal shock temperature difference increases, the cracks evolve from sparse to dense, and the degree of borehole damage is markedly exacerbated. Under a rock temperature of 100 °C, the number of thermal cracks is minimal, and both fracture openings and length remain limited, resulting in a low overall damage level.

11.

Characteristic of thermal cracks under thermal shock temperature difference.

In contrast, at 200 and 300 °C, crack abundance increases markedly, accompanied by larger openings and extended radial propagation distances. A greater temperature difference induces more intense thermal stresses, manifesting as significantly elevated tensile stresses along the borehole wall and thereby triggering more severe thermal rupture behavior at the rock surface. To further quantify the effect of thermal shock temperature difference on crack initiation and propagation, statistical analyses of crack count, mean fracture length, and mean openings were conducted (Figure ). At 100 °C, a total of 29 thermal cracks were generated, with a mean opening of 6.18 μm and a mean length of 3.86 μm, corresponding to a small-scale crack pattern. At 200 °C, crack count increased to 31; the maximum opening reached 29.90 μm, and the mean opening and length rose to 14.58 and 11.92 μmrepresenting approximately 135 and 208% increases, respectivelyindicative of a medium-scale crack pattern. At 300 °C, 57 thermal cracks were observed, with a maximum opening of 36.22 μm and a mean opening and length of 14.86 and 16.77 μm, respectively, corresponding to increases of 140 and 334% relative to the 100 °C case, and defining a large-scale crack pattern. Overall, both crack number and scale exhibit a pronounced upward trend with increasing thermal shock intensity. In theory, HTHP fracturing experiments should activate even more thermal cracks; however, not all cracks possess sufficient propagation potential.

12.

Size of thermal cracks under thermal shock temperature difference.

The size distribution of thermal cracks (Figure ) reveals that the crack sizes are not continuous and are mainly distributed in two intervals with obvious zoning characteristics. Large-scale thermal cracks are more readily driven by high fluid pressuresparticularly when their openings are sufficient to establish effective flow conduits. According to previous studies, , filled natural fractures require an opening greater than 50 μm to be effectively penetrated by the fracturing fluid, whereas unfilled natural fractures require an opening greater than 20 μm. Given that thermal cracks can be analogized to unfilled natural fractures, none of the cracks formed under 100 °C conditions possessed propagation potential. At 200 °C, nine thermal cracks exceeded the critical opening threshold, increasing to 18 fractures at 300 °C. This finding rationalizes why, in fracturing experiments, thermal fractures under 200 °C conditions achieve greater propagation distances compared with those generated at 150 °C.

3.4.2. Thermal Shock Cooling Rate

Figures and illustrate the distribution and size characteristics of thermal cracks under different thermal shock cooling rates. Overall, regardless of the cooling rate applied, thermal cracks continue to propagate uniformly around the borehole circumference. However, as the duration of thermal shock increases (i.e., the cooling rate decreases), the spacing between adjacent cracks progressively widens, and the cracks become sparser, leading to a marked reduction in overall crack density. Meanwhile, the dimensions of individual cracks exhibit an increasing trend. Statistical analysis indicates that 31 thermal cracks were generated at a thermal shock duration of 25 s. When the duration was extended to 50 and 100 s, the number of cracks decreased to 25 and 22, representing reductions of approximately 19.4 and 29.0%, respectively, compared to the 25 s condition. In terms of crack size, the mean opening and length at 50 s were 23.70 and 19.92 μm, respectively. At 100 s, the average opening further increased to 33.35 μm, and the mean length reached 23.71 μm. The former is characterized predominantly by large-scale cracks, while the latter exhibits a mixed mode of medium-scale and large-scale cracks. Regarding cracks with propagation potential, 19 were identified at 50 s, decreasing to 14 at 100 s.

13.

Characteristic of thermal cracks under thermal shock cooling rate.

14.

Size of thermal cracks under thermal shock temperature cooling rate.

As the thermal shock rate decreases, the number of thermal cracks possessing propagation potential displays an initially increasing and then declining trend. The formation mechanisms can understand this trend; thermal cracks originate when thermal stresses, generated by nonuniform temperature distributions, exceed the intrinsic tensile strength of the rock. Under rapid thermal shock conditions, cold fluid contacts the rock surface almost instantaneously, producing steep internal temperature gradients in highly permeable lithologies and thereby promoting the initiation of longer thermal cracks. However, in ultralow-permeability shales, cooling fluid cannot infiltrate deeply; heat conduction lags, confining significant temperature gradients to the rock surface. Although numerous surface fractures may form, their lengths remain limited and cannot penetrate the rock’s interior, resulting in relatively few fractures with propagation potential. , This explains why, at 25 s, crack count peaks, yet the number of cracks with propagation potential remains modest. Conversely, when the shock duration is extended, the cold fluid has sufficient time to conduct heat deeper into the rock matrix, establishing a temperature gradient from the outside to the inside that induces thermal stresses over a larger zone. While total crack count diminishes, individual cracks exhibit increased length and opening, thereby enhancing their propagation potential. It can be seen that a complex coupling exists between thermal shock rate and crack size, and effective thermal cracks require an optimal balance between crack abundance and crack scale.

3.4.3. Thermal Shock Cycle

Figures and illustrate the distribution and size characteristics of thermal cracks under different thermal shock cycles. With increasing cycles of thermal shock, not only do new, small-scale cracks emerge, but the lengths of some pre-existing cracks also increase significantly, and pronounced bifurcation is observed at crack tips. Statistical analysis reveals that after five thermal shock cycles, a total of 44 thermal cracks formed, with a maximum opening of 46.94 μm, a mean opening of 14.23 μm, and a mean length of 16.34 μm. Compared to a single shock, the increase in crack opening is modest, whereas the length increases by approximately 37.0%. After ten cycles, 52 thermal cracks were generated, with a maximum opening of 73.76 μm, a mean opening of 13.38 μm, and a mean length of 18.01 μmrepresenting a 51.0% increase in length relative to a single shock. Of these, ten cracks after five cycles and eight cracks after ten cycles possessed propagation potential. It can be seen that additional thermal shock cycles have limited effects on increasing the number of large-scale cracks but effectively promote increases in crack length. The relationship between cycle count and crack size is governed by a “cumulative-damage effect”: successive thermal shocks subject the rock to cyclic thermal stresses, driving intermittent crack propagation. Additionally, local stress concentrations at crack tips induce secondary cracking.

15.

Characteristic of thermal cracks under thermal shock cycles.

16.

Size of thermal cracks under thermal shock cycles.

4. Discussions

4.1. Mechanisms of Thermal Cracks Induced by Thermal Shock

Due to the limitation that we cannot directly observe the effects of the thermal shock effect through experiments, we can rely on the numerical simulations to evaluate its role. While a 2D plane strain model cannot fully capture the 3D fracture propagation encountered in the field, and because no dedicated sensitivity analysis was performed for the adopted rock thermophysical and interface parameters, the absolute simulated crack metrics may carry additional uncertainty, it is appropriate here as a mechanistic tool to interpret near-wellbore thermal cracks initiation and early growth. In single thermal shock fracturing experiments, the lack of visualization techniques hinders direct observation and quantification of crack geometry, thus failing to validate the numerical predictions. Fortunately, in our previous study, industrial CT imaging enabled the quantitative measurement of thermal cracks after 10 shock cycles, revealing thermal crack openings below 85 μm that were in good agreement with the current simulation outcomes and corroborated the credibility of the numerical simulation results in this study. It is clear that the fundamental mechanism of thermal crack genesis is based on microstructural damage in rocks induced by thermal stresses during heating and cooling. Thermal stresses provoke both intergranular and transgranular cracks within rock mineral particles. Under sustained thermal stress loading, these microcracks propagate, with their tips extending toward surrounding zones of stress weakness. Pores encountered along the propagation path may act as “bridges,” facilitating the connection of isolated thermal cracks and markedly enlarging crack sizes. At the microscale, the thermal stresses originate from thermal strain disharmony among the mineral grains. During heating, differential thermal expansion among quartz, feldspar, and clay minerals creates strain disharmony; in dense lithologies, constrained grain expansion generates significant compressive stresses. When the temperature of some rocks increases to approximately 200 °C, the thermal stress level increases significantly. Upon cooling, the previously expanded mineral grains contract rapidly; however, their shrinkage is impeded by neighboring grains, resulting in tensile stresses that readily initiate cracks at weak intragranular regions and grain boundaries. In addition, the fracture structure of the fracturing process may also be influenced by several other factors, such as (a) the unevenness of the rock and the anisotropy of bedding will shift the initiation and propagation of the fractures; (b) previously existing natural weak planes may alter the pressure response and promote the preferential activation of fractures; (c) the experimental boundary conditions and sample size effects may change the redistribution of stress in the area close to the wellbore. Future work will combine multifactor experiments and numerical simulations to unravel these interrelated influences.

4.2. Optimization Strategies for Thermal Shock Hydraulic Fracturing Processes in Deep Earth Energy Engineering

In addition to deep shale gas exploitation, hydraulic fracturing is extensively applied in deep coalbed methane development and the establishment of enhanced geothermal systems (EGS) in hot dry rock. In these contexts, effectively mobilizing near-wellbore thermal fractures that have not fully propagated represents a promising pathway to optimize fracturing technology and enlarge the stimulated reservoir volume (SRV). Hong et al. conducted laboratory-scale experiments using transparent poly­(methyl methacrylate) (PMMA) as the research subject, and observed that multiple rounds of low-temperature fluid thermal shock pretreatment can significantly enhance the complexity of the fracture network during subsequent fracturing (Figure a–c). Based on this concept, we discuss a potential strategy for deep earth energy extraction that combines: “Cyclic thermal shock + Main fracture temporary plugging + Repeated fracturing to induce thermal fracture propagation” (Figure d). The core idea involves multiple cycles of intermittent injection of cold fracturing fluid into the high-temperature formation, amplifying thermal shock effects in the wellbore, thereby generating a dense network of near-wellbore thermal fractures. An initial hydraulic fracturing stage then activates both the main fracture and part of the thermal fractures. Given the limited propagation capacity of thermal fractures, the main fracture is temporarily plugged following the first-stage treatment, followed by a second fracturing stage to promote further propagation and form a more complex fracture network. It should be noted that this strategy is conceptual and is primarily derived from laboratory-scale observations. In deep high-temperature wells, the injected fluid may be substantially heated during downhole flow, which can reduce the effective thermal shock at the reservoir; therefore, field implementation would require wellbore–reservoir heat-transfer evaluation and further field-scale validation. Admittedly, the effectiveness of the combined technology in actual formations and the propagation characteristics of thermal fractures after temporary plugging remain to be further verified, which will be the core research content of the subsequent phase of this study.

17.

Optimized hydraulic fracturing strategies based on thermal shock effects.

5. Conclusions

This study adopted a combined methodology of HTHP fracturing experiments and numerical simulations to systematically elucidate the initiation mechanisms of thermal fractures under thermal shock and their influence on hydraulic fracture propagation. The main conclusions are as follows:

• (1)Thermal shock effect reduces breakdown pressure and enhances fracture complexity. As the rock temperature increases from 100 to 300 °C, the intensity of the thermal shock effect rises, resulting in a continuous decline in shale breakdown pressure, while both the SRA and FD of hydraulic fractures increase significantly. The SRA reaches 1.75 under a 15 MPa stress difference at 200 °C. Whereas at a higher stress difference of 25 MPa, the main fracture preferentially propagates, thermal fracture propagation is constrained, and the SRA falls to 1.00.
• (2)Thermal shock parameters exert distinct control over thermal crack features. Temperature difference is the primary determinant of crack size; at 300 °C, the number of cracks with propagation potential nearly doubles relative to 100 °C. Faster thermal shock cooling rates result in a greater number of cracks, albeit with smaller openings and shorter lengths. Increasing the number of thermal shock cycles promotes the cumulative damage of cracks; ten cycles produce crack lengths that are 51% greater than those from a single shock and facilitate tip bifurcation.
• (3)Thermal cracks genesis arises from thermal strain disharmony among mineral grains within the shale. During thermal shock cooling, differential contraction between minerals induces localized tensile stresses; when these exceed the tensile strength of the minerals, intergranular and transgranular microcracks initiate. Thermal shock cycling exacerbates fatigue damage at crack tips, driving thermal cracks to propagate into the shale.

Glossary

Nomenclature

BP

breakdown pressure

CZM

cohesive zone model

FD

fractal dimension

HTHP

high-temperature and high-pressure

RTHP

room-temperature high-pressure

SRA

stimulated rock area

SV

vertical stress

SH

maximum horizontal principal stress

Sh

minimum horizontal principal stress

σ_n

normal stress

τ_s

shear stress

δ_n

normal displacement

δ_s

shear displacement

T ₀

cohesive element thickness

E _nn

normal stiffness

E _ss

shear stiffness

G _n

type I fracture energy

G _s

type II fracture energy

q

heat flux

θ

surface temperature

k _cz

thermal conductivity

W.G.: Writingreview and editing, writingoriginal draft, investigation, validation, methodology, conceptualization. Y.G.: Methodology, project administration, writingreview and editing, supervision, funding acquisition. M.W.: Methodology, data curation, visualization. Z.B.: Methodology, data curation, visualization. X.Z.: Data curation, visualization, formal analysis. S.T.: Data curation, visualization, formal analysis. C.Y.: Resources, supervision.

The authors declare no competing financial interest.