Simulation of Fracture Propagation and Permeability Enhancement in Heterogeneous Coal Seams During Hydraulic Fracturing Using a Thermo-Hydro-Mechanical-Damage Coupling Model

Abstract

The development of deep coalbed methane is hindered by the strong heterogeneity of coal mechanical properties and complex hydraulic fracturing behavior. To identify the key factors controlling fracture geometry and permeability enhancement, this study developed a thermo-hydro-mechanical-damage coupled model within a COMSOL Multiphysics 6.3-MATLAB R2022b co-simulation framework, incorporating a Weibull random field to characterize mechanical heterogeneity. Sensitivity analysis demonstrates that tensile strength is the predominant factor governing both the fracturing damage zone and permeability-enhanced area, with its damage area extreme difference (10.094) and coefficient of variation (0.85) significantly surpassing those of other parameters. Poisson’s ratio and elastic modulus emerge as key secondary parameters, while compressive strength shows the lowest sensitivity. The parametric influences exhibit distinct patterns: tensile strength shows a strong negative correlation with damage and permeability-enhanced areas (up to 85% reduction), whereas the maximum permeability enhancement rate follows a non-monotonic trend, peaking at 215 when tensile strength reaches 3.33 MPa. Compressive strength minimally affects the damage area (~15%) but steadily improves the maximum permeability enhancement rate (7.5% increase). Elastic modulus exhibits an optimal value (8.93 GPa) for maximizing damage area, while negatively correlating with maximum permeability enhancement rate (9.1% decrease). Fracture morphology is differentially controlled by multiple parameters: low compressive strength promotes fracture deflection and branching, elastic modulus regulates fracture network complexity, and low Poisson’s ratio enhances coal brittleness to effectively activate natural fractures, thereby facilitating complex fracture network formation.

1. Introduction

As an important unconventional natural gas resource, coalbed methane holds strategic significance for optimizing energy structure, ensuring coal mine safety, and promoting green and low-carbon energy transition [1,2,3]. However, most coal seams in China are characterized by low permeability, strong heterogeneity, and complex pore-fracture structures [4,5,6,7]. These characteristics severely restrict gas desorption, migration, and production. Hydraulic fracturing serves as the core technology for enhancing coal seam permeability. It aims to create complex fracture networks to fundamentally improve reservoir conductivity and gas recovery. Accurate simulation and optimization of this process not only concern technical effectiveness but also carry significant sustainability value. By increasing per-well production and resource extraction efficiency, we can obtain clean energy with a smaller ecological footprint. This approach also improves project feasibility economically and provides solid support for energy security and low-carbon transition socially. Nevertheless, coal’s heterogeneity, elastoplastic mechanical behavior, and its thermo-hydro-mechanical (THM) coupling with fracturing fluids make fracture propagation extremely complex and morphology highly unpredictable [8,9,10,11]. This complexity directly limits accurate evaluation and further improvement of fracturing effectiveness.

In recent years, researchers worldwide have conducted extensive studies on the mechanisms of hydraulic fracture propagation. In numerical simulation, numerous coupled multi-physics models have been developed to reveal the underlying physical mechanisms. For instance, one study employed a Thermo-Hydro-Mechanical (THM) model coupled with the Discrete Element Method and Computational Fluid Dynamics (DEM/CFD) [12]. This approach revealed significant influences of two-phase flow and temperature differences on fracture morphology at the pore scale, finding that the temperature difference between the rock matrix and injected fluid markedly alters fracture propagation patterns. Meanwhile, the phase-field method, based on variational principles, has been successfully extended to thermo-poro-elastic media, providing a continuum framework for simulating complex fracture networks [13]. Research using this method indicates that the initial formation temperature and in situ stress ratio play decisive roles in fracture initiation and propagation. Furthermore, studies on heterogeneous deep formations, such as glutenite, highlight that the presence of stiff inclusions (e.g., gravels) induces stress concentrations. This leads to fracture deflection, branching, or termination, significantly altering failure modes and wellbore stability [14]. These findings highlight the critical importance of accounting for material heterogeneity and multi-physical field coupling to accurately predict fracture behavior. Physical simulation studies have further synthesized the influence of key operational parameters, such as confining pressure, stress difference, and fracturing fluid viscosity, on fracture complexity [15].

Specifically for coal seam hydraulic fracturing, coal is a typical heterogeneous elastoplastic material. Its internal cleats, random distribution of mineral components, and varying mechanical properties collectively dominate the initiation and propagation paths of hydraulic fractures. Studies show that using the Finite-Discrete Element Method (FDEM) combined with a Weibull distribution to characterize coal heterogeneity can effectively simulate fracture branching and deflection. The heterogeneity degree coefficient is identified as the key parameter controlling fracture complexity [16]. Similarly, in shale reservoirs, the strength, spacing, and density of bedding planes intensely interact with hydraulic fractures. This directly influences the vertical propagation and complex morphology of the fracture network [17]. Furthermore, coupled simulations integrating hydraulic fracturing with subsequent gas–water two-phase flow demonstrate that the created complex fracture network effectively depressurizes coalbed methane and expands the productive area. This effect is controlled by multiple factors, including initial water saturation and adsorption characteristics [18]. Heterogeneous factors such as mineral composition and pore structure are also confirmed to be critical in controlling the final fracture morphology [19].

Despite the fruitful achievements in existing research, studies that integratively couple thermal effects, fluid flow, solid deformation, damage evolution, and heterogeneity, and systematically quantify their impacts on fracture propagation and the ultimate permeability enhancement in coal seams remain relatively scarce. Constructing a fully coupled thermal-hydraulic-mechanical-damage (THMD) model to precisely reveal the interaction mechanisms among temperature, seepage, stress, and damage fields in heterogeneous coal seams represents a current research challenge and frontier.

Based on this, this study establishes a fully coupled THMD numerical model. The heterogeneity of coal mechanical properties is characterized using a Weibull random field, and the model is solved via COMSOL-MATLAB co-simulation. By comparing fracture geometry, damage area, and permeability enhancement under different mechanical parameters, the dominant mechanical factors controlling fracture propagation in heterogeneous coal seams under multi-field coupling are revealed. This work provides a theoretical foundation and technical support for the efficient development of deep CBM.

2. Establishment and Verification of the THMD Coupling Model

2.1. Basic Assumptions of the Mathematical Model

The following assumptions are made:

(1) Coal is treated as a porous medium with strong heterogeneity and is assumed to follow the effective stress principle of poroelasticity; (2) The processes of gas adsorption/desorption and chemical reactions between the fracturing fluid and the coal matrix are neglected; (3) The fracturing fluid is an incompressible, single-phase Newtonian fluid; (4) The coal body undergoes only small displacements and strains during the fracturing process; (5) Fluid acceleration effects and non-Darcy flow in the porous medium are ignored; (6) The influence of gravity on fracture propagation is neglected.

2.2. Mathematical Models

2.2.1. Fluid Flow Governing Equation

Considering the influence of strain and thermal effects on seepage flow, the governing equation for fluid transport within the fractures, based on the mass conservation law [20,21], is formulated as

$${\rho }_w({\varphi }_m\chi +\left({\alpha }_B-{\varphi }_m\right){\displaystyle \frac{1-{\alpha }_B}{K_d}}){\displaystyle \frac{\partial p}{\partial t}}+\nabla \cdot \left(-{\rho }_w{\displaystyle \frac{k}{{\mu }_w}}\nabla p\right)+{\rho }_w{\alpha }_B{\displaystyle \frac{\partial {\epsilon }_V}{\partial t}}=-Q_m$$

(1)

where ρ_w is the fluid density (kg/m³); ϕ_m is the coal matrix porosity; χ is the fluid compressibility coefficient (1/Pa); μ_w is the fluid dynamic viscosity (mPa·s); k is the coal permeability (m²); ε_V is the volumetric strain; Q_m is the source/sink term; K_d is the drained bulk modulus (Pa).

2.2.2. Stress Field Governing Equation

Considering the strains induced by thermal effects and seepage flow, the stress–strain relationship for a non-isothermal coal seam [22,23,24] is expressed as

$$G{\nabla }^2{u}_i+{\displaystyle \frac{G}{1-2\nu }}{u}_{j,ji}-{\alpha }_B{p}_{,i}-{\alpha }_{T}K\left(T_{,i}-T_0\right)+F_i=0$$

(2)

where G is the shear modulus (Pa); K is the bulk modulus (Pa); α_B is the Biot coefficient (dimensionless); α_T is the linear thermal expansion coefficient of the rock skeleton (K⁻¹); v is Poisson’s ratio (dimensionless); F_i is the body force per unit volume (Pa/m).

2.2.3. Temperature Field Governing Equation

Accounting for heat convection between coal and the fluid, heat conduction, and the strain energy of the coal, the thermal energy balance governing the coal seam [24,25] is formulated as

$$\left(\rho Cp\right){\displaystyle \frac{\partial T}{\partial t}}+(T0+T)K{\alpha }_T{\displaystyle \frac{\partial {\epsilon }_T}{\partial t}}+{\rho }_w{C}_w(T_0+T){\displaystyle \frac{k}{{\mu }_w}}\nabla p=({\lambda }_m(1-{\varphi }_m)+{\lambda }_w{\varphi }_m){\nabla }^{2}T$$

(3)

where ρCp is the effective volumetric heat capacity of the fluid-saturated porous medium (kJ·m⁻³·K⁻¹); ε_T is the volumetric thermal strain; C_w is the specific heat capacity of the fluid (J·kg⁻¹·K⁻¹); λ_m is the thermal conductivity of the coal matrix (W·m⁻¹·K⁻¹); λ_w is the thermal conductivity of the fluid (W·m⁻¹·K⁻¹).

$$\rho Cp={\rho }_m{C}_s(1-{\varphi }_m)+{\rho }_w{C}_w{\varphi }_m$$

(4)

where C_s is the specific heat capacity of the coal solid grains (J·kg⁻¹·K⁻¹).

2.2.4. Damage Evolution Equation

Under the high-temperature and high-pressure conditions of deep reservoirs, the Mohr–Coulomb criterion is suitable for describing the shear failure state of coal. Combined with the maximum tensile stress criterion to determine coal damage [23,24], the damage evolution is defined by Equation (5):

$$\left\{\begin{array}{l}{F}_T={\sigma }_1-f_T\\ F_C=-{\sigma }_3-f_C+{\displaystyle \frac{1+\sin \theta }{1-\sin \theta }}{\sigma }_1\end{array}\right.$$

(5)

Tensile failure occurs when F_T ≥ 0; shear failure occurs when F_C ≥ 0.

Where f_T is the uniaxial tensile strength of the coal (Pa); f_C is the uniaxial compressive strength of the coal (Pa); θ is the internal friction angle of the rock (°); σ₁, σ₂, σ₃ are the first, second, and third principal stresses, respectively (MPa).

Within the damage evolution law, the extent of damage is characterized by the damage variable D [10,26,27], which is defined as

$$D=\left\{\begin{array}{l}0, \begin{array}{cc} & \end{array}{F}_T<0, F_C<0\\ 1-{({\displaystyle \frac{{\epsilon }_{t0}}{{\epsilon }_1}})}^2,\begin{array}{cc} & \end{array}{F}_T=0, d{F}_T>0\\ 1-{({\displaystyle \frac{{\epsilon }_{c0}}{{\epsilon }_3}})}^2,\begin{array}{cc} & \end{array}{F}_C=0, d{F}_C>0\end{array}\right.$$

(6)

where ε_t0 is the ultimate tensile strain at tensile failure, given by, ε_t0 = σ_t/E₀; ε_c0 is the ultimate shear strain at shear failure, given by, ε_c0 = σ_c/E₀; ε₁, ε₃ are the major and minor principal strains, respectively.

2.2.5. Coupling Relationship Equations

The degradation of the coal’s elastic modulus due to damage incurred during the fracturing process is accounted for by the following relationship [28]:

$$E=E_0\left(1-D\right)$$

(7)

where E₀ is the initial elastic modulus of the coal (Pa).

The evolution of coal porosity and permeability, influenced by both damage and stress changes during fracturing, is described by the following equations [29,30]:

$${\varphi }_m=\left({\varphi }_{m0}-{\varphi }_{me}\right)\exp \left(-{\alpha }_{\varphi }\overline{{\sigma }_{eff}}\right)+{\varphi }_{me}$$

(8)

$$k=k_0{\left({\displaystyle \frac{{\varphi }_m}{{\varphi }_{m0}}}\right)}^3\exp \left({\alpha }_{k}D\right)$$

(9)

where ϕ_m0 is the initial coal porosity; α_ϕ is the porosity stress-sensitivity coefficient; ϕ_me is the residual porosity; σ_eff is the mean effective stress; k₀ is the initial coal permeability (m²); α_k is the permeability stress-sensitivity coefficient.

The variation in the coal’s thermal conductivity with damage is considered using the expression:

$${\lambda }_m(T,D)={\lambda }_m(T)\exp \left(D/{\alpha }_T\right)$$

(10)

In summary, Equation (1) through (10) collectively constitute the fully coupled THMD mathematical model for deep coal seams.

2.3. Model Validation

The accuracy of the model was verified by comparing experimental simulations with numerical simulations. Based on the experimental study by Zhou et al. [31]. (Figure 1a), this study established a 300 mm × 300 mm numerical model (Figure 1b), with initial conditions and boundary conditions (normal constraints on the left and bottom boundaries, application of the minimum and maximum horizontal principal stresses on the top and right boundaries, respectively) consistent with the literature. The simulation results show good agreement with the experimental outcomes: in both cases, fractures propagated perpendicular to the minimum principal stress direction.

The simulation results showed good agreement with the experimental data. Specifically, the fracture propagation zone in the numerical simulation aligned well with the actual fracture morphology observed in the physical experiment in terms of overall distribution and the upward/downward propagation trend from the borehole (Figure 1). This consistency indicates that the numerical model can accurately capture the initiation and propagation behavior of fractures during hydraulic fracturing. Thus, the proposed numerical approach is validated as a suitable and reliable tool for investigating hydraulic fracturing mechanisms and predicting fracture geometry.

To verify the stability of the results, a mesh independence verification was conducted. As the number of mesh elements increased from 15,486 to 42,472 (through continuous mesh refinement), the simulated hydraulic fracturing damage results showed no significant variation (Figure 2). This demonstrates that the current mesh (with at least 15,486 elements) satisfies the “mesh independence” requirement. Subsequent simulations can therefore utilize this computationally efficient and stable mesh configuration without further refinement.

To further validate the model’s accuracy, a second numerical model (Model 2) was constructed. This model measured 200 mm × 200 mm, contained a wellbore with a diameter of 20 mm, and included two natural fractures. Roller supports were applied to the left and bottom boundaries, while the maximum and minimum horizontal principal stresses were applied to the top and right boundaries, respectively. The simulation parameters were consistent with those used in Model 1. To investigate the influence of the angle (θ) between the natural fractures and the maximum horizontal principal stress on hydraulic fracture propagation, four simulation scenarios with different natural fracture angles were designed. The results demonstrate that when the hydraulic fracture approaches a natural fracture, its propagation path is governed by the stress contrast and the orientation of the natural fracture. Specifically: When the natural fracture was oriented at 90° to the maximum principal stress direction, the hydraulic fracture crossed through it. At an angle of 60°, the hydraulic fracture propagated along the natural fracture but eventually broke through it at the fracture tip, continuing to propagate in the direction of the maximum principal stress. For angles of 45° and 30°, the hydraulic fracture primarily propagated along the natural fracture. Furthermore, a smaller angle between the natural fracture and the maximum principal stress direction resulted in a greater fracture length (Figure 3). These simulation results show good agreement with findings from previous studies (Figure 4) [32,33,34,35].

3. Construction of a Numerical Model for a Heterogeneous Coal Seam

3.1. Computational Model

Referring to the geometric dimensions (200 mm × 200 mm) of Model 1 and Model 2, Model 3 was constructed incorporating the heterogeneity of coal’s natural fractures. To reconstruct the distribution of natural fractures in coal, 120 random natural fractures were generated using MATLAB R2022b based on the Monte Carlo method. Each fracture has a length of 20 mm and is randomly distributed within the geometric model, with a random field grid resolution of 0.5 mm. The left and bottom boundaries of the model are assigned roller supports, while the maximum horizontal principal stress is applied to the top boundary and the minimum horizontal principal stress to the right boundary (Figure 5a). The model was discretized using free triangular meshes, with local refinement around the wellbore. The mesh consists of 274,569 domain elements and 4632 boundary elements (Figure 5b), with an average element quality of 0.82 to ensure simulation accuracy.

3.2. Numerical Scheme

The development of natural fractures and the mechanical properties of coal exhibit significant heterogeneity [36]. Therefore, in this model, parameters including tensile strength, compressive strength, elastic modulus, and Poisson’s ratio were assigned random distributions following the Weibull distribution. According to the definition of the Weibull distribution, the shape parameter *m* must be greater than 1.0. The spatial distributions of tensile strength, compressive strength, elastic modulus, and Poisson’s ratio for a model with *m* = 5 are shown in Figure 6. Concurrently, the mechanical properties at the locations of natural fractures were weakened, while their permeability was enhanced [35].

To investigate the influence of coal mechanical properties on hydraulic fracture propagation, four key parameters—tensile strength, compressive strength, elastic modulus, and Poisson’s ratio—were selected for a sensitivity analysis based on previous research [15]. This analysis aims to identify the dominant mechanical parameters governing fracture growth in coal (

Table 1. Simulation schemes.

Simulation Parameters	Value
Tensile Strength/MPa	NF = 0.06, CM = 1.99	NF = 0.08, CM = 2.66	NF = 0.10, CM = 3.33	NF = 0.12, CM = 3.99	NF = 0.14, CM = 4.66
Compressive Strength/MPa	NF = 0.80, CM = 30	NF = 1.20, CM = 40	NF = 1.50, CM = 50	NF = 1.80, CM = 60	NF = 2.10, CM = 70
Elastic Modulus/GPa	NF = 1.72, CM = 5.36	NF = 2.29, CM = 7.14	NF = 2.86 CM = 8.93	NF = 3.43, CM = 10.71	NF = 4.00, CM = 12.50
Poisson’s Ratio	NF = 0.18, CM = 0.13	NF = 0.24, CM = 0.18	NF = 0.30, CM = 0.22	NF = 0.36, CM = 0.27	NF = 0.42, CM = 0.31

).

3.3. Initial and Boundary Conditions

The initial and boundary conditions applied to the computational model for simulating the hydraulic fracturing process are defined as follows:

(1) Temperature Field: The initial reservoir temperature is set to 60 °C (

Table 2. Key Parameters for numerical simulation.

Parameter	Value	Parameter	Value
Natural Fracture Permeability/m2	1.15 × 10−15	Coal Thermal Expansion Coefficient/K−1	2.5 × 10−6
Matrix Permeability/m2	3.7 × 10−17	Coal Thermal Conductivity/W·(m·K)−1	4
Porosity	0.045	Coal Specific Heat Capacity/J·(kg·K)−1	960
Internal Friction Angle/°	40	Water Density/(kg/m3)	1000
Initial Reservoir Temperature/°C	60	Water Viscosity/Pa·s	1.0 × 10−3
Water Specific Heat Capacity/J·(kg·K)−1	4187	Coal Density/(kg/m3)	1350
Water Thermal Conductivity/W·(m·K)−1	0.6	Residual Porosity	0.039
porosity stress-sensitivity coefficient	5	permeability stress-sensitivity coefficient	5

). The outer boundaries maintain a constant temperature of 60 °C, while the fluid is injected at a temperature of 20 °C.

(2) Seepage Field: The initial reservoir pressure is 10 MPa. A constant pressure of 10 MPa is applied to the outer boundaries. The fracturing fluid is injected at a constant flow rate of 1 × 10⁻⁴ kg/s.

(3) Stress Field: Roller supports are applied to the left and bottom boundaries. The maximum horizontal principal stress (σ_H = 15 MPa) is applied to the top boundary, and the minimum horizontal principal stress (σ_h = 10 MPa) is applied to the right boundary.

(4) Damage Field: The initial damage state is set to 0.

4. Results

4.1. Influence of Tensile Strength

As shown in Figure 7 and Figure 8, a significant negative correlation exists between tensile strength and both the damage area and permeability-enhanced area. When the tensile strength increases from 1.99 MPa to 4.66 MPa, the damage area sharply decreases from 11.903 cm² to 1.8088 cm² (a reduction of 84.8%), while the permeability-enhanced area decreases from 11.666 cm² to 1.5598 cm² (a reduction of 86.6%). This indicates that coal rock with lower strength is more easily fractured, allowing fluid-driven fractures to more readily generate complex fracture networks, thereby forming extensive damage and permeability-enhanced zones. In contrast, high-strength coal exhibits greater resistance to fracturing, resulting in restricted fracture propagation and a reduced stimulation area.

The maximum permeability enhancement rate (k/k₀) exhibits a non-monotonic trend with increasing tensile strength, first rising and then declining, reaching a peak value of 215 at 3.33 MPa. In the low-strength stage (1.99–3.33 MPa), although the damage zone is extensive, the fractures may be too widespread to open adequately, or the created fracture network may possess limited flow conductivity. An optimal balance is achieved around 3.33 MPa, resulting in effective fractures with high flow capacity. When the strength further increases (>3.33 MPa), fracture propagation becomes severely restricted, hindering the formation of efficient flow pathways and causing the maximum permeability enhancement rate (k/k₀) to decrease by approximately 12%.

4.2. Influence of Compressive Strength

No clear monotonic trend was observed between compressive strength and the damage/permeability-enhanced areas. The data fluctuated around mean values (approximately 4.67 for damage area and 4.18 for permeability-enhanced area) with standard deviations of 0.49 and 0.50, respectively, indicating relatively stable variation. When compressive strength increased from 50 MPa to 80 MPa, the damage area changed by only about 15% (Figure 9). This suggests that within the investigated parameter range, compressive strength is not the dominant factor controlling the damage extent. Fracture propagation during hydraulic fracturing appears to be primarily governed by tensile stress, while the confining pressure effect may not have emerged as the dominant mechanism in this dataset.

The maximum permeability enhancement rate (k/k₀) showed a steady, slight increasing trend with rising compressive strength, growing from 201 (at 30 MPa) to 216 (stabilizing beyond 60 MPa), representing an increase of approximately 7.5%. This improvement can be attributed to the fact that higher compressive strength likely indicates a more robust coal matrix structure. Under closure stress, fractures created through hydraulic fracturing can better maintain their aperture in such stronger coal, thereby sustaining enhanced flow capacity (Figure 10).

In summary, higher compressive strength restricts the propagation of hydraulic fractures and results in a smaller damage area. However, under low compressive strength conditions, fracturing tends to generate short, wide fractures or even cause localized pulverization, leading to poor sustainability of the enhanced permeability.

4.3. Influence of Elastic Modulus

As the elastic modulus increased from 5.36 GPa to 8.93 GPa (a 66.6% increase), the damage area expanded from 3.403 to 5.1067 (peak value, representing a 50% growth). However, when the modulus further increased to 12.5 GPa, the damage area decreased to 4.2909. This pattern can be explained by different mechanical responses: low-modulus coal tends to undergo substantial deformation, absorbing more energy and consequently hindering far-field fracture propagation. Medium-modulus coal (8.93 GPa) achieves an optimal balance between energy transfer and fracture extension. In contrast, high-modulus coal exhibits stronger brittleness, potentially resulting in simpler fracture patterns with reduced branching, ultimately leading to a smaller damage zone (Figure 11).

A distinct negative correlation is observed between the maximum permeability enhancement rate (k/k₀) and the elastic modulus. The value decreased from 220 at 5.36 GPa to 200 at 12.5 GPa, representing a reduction of approximately 9.1% (Figure 12). Although low-modulus coal rock is less prone to developing long fractures, the fractures that do form tend to be wider, resulting in superior flow capacity and consequently higher maximum permeability enhancement rates (k/k₀).

4.4. Influence of Poisson’s Ratio

The relationship between Poisson’s ratio and the damage/permeability-enhanced areas exhibits a complex nonlinear pattern. Within the range of 0.13 to 0.18, both area metrics show a decreasing trend. Beyond this interval, they continuously increase with rising Poisson’s ratio, reaching maximum values at 0.3. An increase in Poisson’s ratio indicates that coal rock undergoes more significant lateral expansion under compression, potentially creating a larger compression zone at the fracture tip that inhibits initial fracture propagation (explaining the trough observed at 0.18). However, higher Poisson’s ratios (>0.22) may also promote shear failure and complex multi-fracture competition, thereby expanding the overall damage zone (Figure 13).

The maximum permeability enhancement rate (k/k₀) exhibits an overall negative correlation with Poisson’s ratio. It reaches its peak value of 221 at a Poisson’s ratio of 0.13, then fluctuates and declines, eventually stabilizing at 200 for ratios of 0.27 and 0.3 (Figure 14). A lower Poisson’s ratio is typically associated with more pronounced tensile fracturing, which generates fractures with larger apertures and consequently higher flow capacity. In contrast, damage under higher Poisson’s ratios may predominantly result from shear and plastic deformation. Fractures formed through these mechanisms generally exhibit relatively lower flow capacity.

In summary, a low Poisson’s ratio enhances coal brittleness, facilitating the formation of a wider and more complex fracture network and leading to more effective reservoir stimulation. This significantly improves the efficiency of methane desorption and flow.

5. Discussion

5.1. Sensitivity Analysis

The preceding results demonstrate that various mechanical parameters of coal significantly influence the effectiveness of fracturing stimulation. Conducting a systematic analysis and sensitivity assessment of key mechanical parameters—including tensile strength, compressive strength, elastic modulus, and Poisson’s ratio—on fracture propagation is essential for elucidating the intrinsic mechanical mechanisms governing fracture initiation, propagation, and morphology. This understanding is crucial for the precise design and optimization of fracturing operations. Given that the data analysis is primarily factor-oriented, a combined methodology of range analysis and sensitivity coefficients is employed for quantitative comparison.

Through range analysis, the variation range of output results caused by each parameter within its variation range was calculated. A larger range indicates that the output result is more sensitive to changes in that parameter.

R = Maximum Value − Minimum Value

The range analysis results (

Table 3. Range analysis results.

Mechanical Parameter	Damage Area Range	Permeability-Enhanced Area Range	Maximum Permeability Enhancement Rate Range
Tensile Strength	10.094	10.106	26
Compressive Strength	1.183	1.158	15
Elastic Modulus	1.704	1.404	20
Poisson’s Ratio	2.667	2.392	2

) show that for both the damage area and the permeability-enhanced area, the range of tensile strength (>10) is significantly higher than those of the other parameters (<3), indicating its overwhelmingly dominant sensitivity. Poisson’s ratio and elastic modulus exhibit a secondary influence, while compressive strength has the weakest effect. For the maximum permeability enhancement rate, the ranges of the four parameters are relatively close (15–26), with tensile strength having the largest range (26), suggesting it also exerts the most significant influence on the maximum permeability enhancement rate.

To eliminate the influence of parameter dimensions and numerical ranges, we calculated the coefficient of variation for each parameter and conducted the sensitivity analysis based on this metric.

Cv = Standard Deviation/Mean

where Cv represents the coefficient of variation, i.e., the ratio of the standard deviation to the mean.

The results of the sensitivity coefficients (

Table 4. Sensitivity coefficients.

Mechanical Parameter	Cv of Damage Area	Cv of Permeability-Enhanced Area	Cv of Maximum Permeability Enhancement Rate
Tensile Strength	0.85	0.88	0.06
Compressive Strength	0.11	0.11	0.04
Elastic Modulus	0.17	0.16	0.05
Poisson’s Ratio	0.24	0.25	0.05

) indicate that: For the damage/permeability-enhanced area: The coefficient of variation for tensile strength (0.85) exceeded those of other parameters by an order of magnitude, further confirming it as the most sensitive and critical parameter controlling the fracturing extent. Poisson’s ratio (~0.25) ranked second in sensitivity, followed by the elastic modulus (~0.17), while compressive strength (~0.11) was the least sensitive.

For the maximum permeability enhancement rate: The coefficients of variation for all four parameters were relatively small (0.04–0.06), indicating that the maximum permeability enhancement rate itself exhibits relatively minor fluctuations across different parameter levels. Among them, the sensitivity coefficient for tensile strength (0.06) remained the highest, identifying it as the primary factor influencing the enhancement effect. The influence degrees of compressive strength, elastic modulus, and Poisson’s ratio were very similar.

5.2. Engineering Implications

This study demonstrates that coal mechanical parameters exert significantly different influences on hydraulic fracturing outcomes. Tensile strength emerges as the dominant factor, showing the highest sensitivity to both the stimulation area and permeability enhancement effectiveness, thereby serving as the core indicator for reservoir evaluation and interval selection. Poisson’s ratio functions as a key secondary parameter, exhibiting complex effects on fracture propagation morphology and necessitating the identification of its optimal range. The elastic modulus presents a dual effect: a trade-off exists between increasing the stimulated volume and reducing fracture conductivity, requiring balanced optimization. Compressive strength demonstrates the weakest influence and can be considered an auxiliary reference. Consequently, fracturing design should prioritize tensile strength and Poisson’s ratio, while carefully managing the bidirectional implications of the elastic modulus to guide the optimization of operational parameters. Thereby enhancing per-well production and resource extraction efficiency, obtaining clean energy with a smaller ecological footprint, and providing solid support for energy security and the low-carbon transition.

5.3. Limitations

Since the data were obtained from single-parameter variation simulations, it is recommended that future studies employ a full factorial design (such as Latin Hypercube Sampling) to acquire more comprehensive sensitivity analysis results. Additionally, as the simulation results are based on laboratory-scale models, further investigation is required for field-scale models.

6. Conclusions

This study established a fully coupled THMD model using the finite element method to investigate the influence of different mechanical parameters on fracture propagation and permeability enhancement during hydraulic fracturing in heterogeneous coal seams. The model’s accuracy was verified against physical experiments and numerical benchmarks. The main findings are summarized as follows:

(1) Tensile strength is the predominant factor controlling both the fracturing extent and permeability enhancement, with its damage area range (10.094) and coefficient of variation (0.85) significantly exceeding those of other parameters. Poisson’s ratio (range: 2.667, Cv: 0.25) and elastic modulus (range: 1.704, Cv: 0.17) are key secondary parameters, where the elastic modulus exhibits a trade-off relationship between stimulation volume and flow conductivity. In contrast, compressive strength (range: 1.183, Cv: 0.11) shows the lowest sensitivity.

(2) Tensile strength primarily governs fracture propagation. As it increases from 1.99 MPa to 4.66 MPa, both the damage area and permeability-enhanced area sharply decrease by approximately 85%. However, the maximum permeability enhancement rate peaks at 215 when tensile strength reaches 3.33 MPa, exhibiting a non-monotonic trend. Compressive strength has a minor influence on the damage area (~15% variation) but steadily improves the maximum permeability enhancement rate (7.5% increase). The elastic modulus exhibits an optimal range (peak at 8.93 GPa), where the damage area first increases and then decreases, while the maximum permeability enhancement rate declines by about 9.1% with increasing modulus. Poisson’s ratio also demonstrates a nonlinear influence, with lower values (e.g., 0.13) favoring the formation of highly conductive fractures (maximum permeability enhancement rate: 221).

(3) Different mechanical parameters govern the fracture morphology and propagation path through distinct mechanisms. Low compressive strength promotes fracture deflection and branch development, whereas high strength guides fractures to extend along the principal stress direction. The elastic modulus primarily regulates the complexity of the fracture network, with an optimal range existing for maximizing the permeability-enhanced area. A low Poisson’s ratio, by enhancing coal brittleness, facilitates the activation of natural fractures and the formation of a complex fracture network system, thereby significantly improving the effectiveness of reservoir stimulation.