Study on the Evolution Law of Four-Dimensional Dynamic Stress Fields in Fracturing of Deep Shale Gas Platform Wells

Abstract

Compared with conventional gas reservoirs, deep shale gas reservoirs are characterized by developed faults and fractures, strong heterogeneity, high stress sensitivity, and complex in situ stress distribution. To address traditional 3D static models’ inability to predict in situ stress changes in strongly heterogeneous reservoirs during fracturing, this study takes the deep shale gas in the Zigong block of the Sichuan Basin as an example. By comprehensively considering the heterogeneity and anisotropy of geomechanical parameters and natural fractures in shale gas reservoirs, a 4D in situ stress multi-physics coupling model for shale gas reservoirs based on geology–engineering integration is established. Through coupling geomechanical parameters with fracturing operation data, the dynamic evolution laws of multi-scale stress fields from single-stage to platform-scale during large-scale fracturing of horizontal wells in deep shale gas reservoirs are systematically studied. The research results show the following: (1) The fracturing process has a significant impact on the magnitude and direction of the stress field. With the injection of fracturing fluid, both the minimum and maximum horizontal principal stresses increase, with the minimum horizontal principal stress rising by 1.8–6.4 MPa and the maximum horizontal principal stress by 1.1–3.2 MPa; near the wellbore, there is an obvious deflection in the direction of in situ stress. (2) As the number of fracturing stages increases, the minimum horizontal principal stress shows an obvious cumulative growth trend, with a more significant increase in the later stages, and there is a phenomenon of stress accumulation along the wellbore, with the stress difference decreasing from 15 MPa to 11 MPa. (3) The on-site adoption of the fracturing operation method featuring overall flush advancement and inter-well staggered fracture placement has achieved good stress balance; comparative analysis shows that the stress communication degree of the 400 m well spacing is weaker than that of the 300 m well spacing. This study provides a more reasonable simulation method for large-scale fracturing development of deep shale gas, which can more accurately predict and evaluate the dynamic stress field changes during fracturing, thereby guiding fracturing operations in actual production.

1. Introduction

China is rich in shale gas resources, with favorable exploration areas reaching 43 × 10⁴ km². According to preliminary evaluation results from the Ministry of Natural Resources, China’s total shale gas resources amount to 134.4 × 10¹² m³, with recoverable resources reaching 25 × 10¹² m³, ranking among the world’s highest. Notably, deep shale oil and gas resources account for a considerable proportion [1,2]. Deep (3500–4500 m) to ultra-deep (>4500 m) shale gas has now become an important replacement field for China’s shale gas development, with technically recoverable resources accounting for 56.63% of the total recoverable shale gas resources. Enhancing its exploration and development is of great strategic significance for ensuring national energy security. After more than a decade of theoretical innovation and practical development in shale gas exploitation, China has established technical capabilities for shale gas well extraction at depths shallower than 3500 m. Although significant progress has been made in supporting extraction technologies for depths of 3500–4000 m, commercial development remains distant, and the overall exploration level of deep shale gas is relatively low [3,4]. The Sichuan Basin and its surrounding areas contain 65.8% of China’s total recoverable deep to ultra-deep shale gas resources, making it the primary exploration and development base for domestic deep shale gas [5,6,7]. However, unlike medium-deep formations, deep shale exhibits significantly increased formation temperature, pressure, and stress with greater burial depth, along with more complex geological structures and in situ stress conditions, leading to substantially greater challenges in fracturing stimulation [7,8,9,10].

In situ stress has a significant impact on the productivity of a single well. For horizontal wells in deep shale gas, if well logging is not performed, the calculation parameters for in situ stress cannot be obtained. Therefore, it is urgent to carry out research on the modeling of the original three-dimensional stress field to support the optimization of the fracturing scheme. During hydraulic fracturing, changes in formation pore pressure, combined with interactions with natural fractures and induced fracture networks, generate a perturbed stress field, leading to real-time variations in the near-wellbore stress distribution; Refs. [11,12]. This may even lead to stress reversal, which directly affects the propagation direction and morphology of the hydraulic fracture network and changes the flow efficiency of oil and gas from the rock matrix to the wellbore [13,14]. At the same time, it will also cause formation deformation and activate faults, generating a disturbed stress field that can lead to fault slip-induced casing deformation [15,16], posing safety risks. After fracturing, both the fracturing well and offset wells experience significant changes in stress orientation. If initial stress data are still used for subsequent fracturing simulations of adjacent stages or wells, the results may be unreliable [17]. Thus, it is essential to investigate the dynamic evolution of in situ stress during deep shale gas fracturing.

The generation of hydraulic fractures alters the magnitude and orientation of in situ stresses around the fractures, an effect termed the “stress shadow” effect. Sneddon [18] derived an analytical expression for the stress field distribution around fractures under plane strain conditions in an infinite elastic medium, demonstrating that the impact on the minimum horizontal principal stress near the fracture is more pronounced than on the maximum principal stress. Crouch [19] pioneered the use of the displacement discontinuity method to investigate displacement discontinuities and the surrounding stress distribution in fractured rock media. Roussel [20,21] integrated the displacement discontinuity method with the finite element method, proposing that dynamic stress field variations induce pore volume and rock matrix compression, thereby influencing fluid flow and fracture propagation. Zhang et al. [22] found that both stress contrast and fracture initiation angle affect the propagation path of fractures, causing the orientation of new fractures to gradually deviate and eventually reorient toward the maximum horizontal stress direction after overcoming stress barriers. Wang et al. [23] employed the extended finite element method to analyze stress interference phenomena in sequential and alternate fracturing, revealing its dependence on the fracturing sequence.

For a long time, modeling dynamic stress fields in hydraulic fracturing has been a research hotspot both domestically and internationally: Biot [24] was the first to propose a seepage-stress coupled 3D in situ stress model based on elastic porous media; later, Geertsma [25] put forward the theory of pore-rock volume change to better understand the pressure–volume relationship of reservoir rocks, establishing connections between the porosity, rock volume compressibility of isotropic porous media, and the elastic and viscous deformation constants of rock matrix and materials; since simple isotropic models cannot describe real rock behavior, Lekhnitskii [26] proposed the theory of anisotropic elastic bodies; Pei et al. [27] established a 3D geomechanical–fluid flow coupling model for multi-layer reservoirs to analyze the impact of stress differences on infill well fracturing effects, though the model assumes steady-state fluid flow and static stress fields, ignoring the cumulative effect of stress shadows in multi-stage fracturing; Zhang et al. [28] proposed a workflow integrating microseismic monitoring and geomechanical modeling to study the correlation between induced seismicity and stress redirection in shale gas reservoirs; Glubok et al. [29] developed a physics-constrained machine learning algorithm that converts microseismic event distributions into near-real-time fracture propagation visualizations, reducing interpretation errors from 300% to 10%; Ibrahim et al. [30] used the Adaptive Neuro-Fuzzy Inference System (ANFIS) to predict horizontal in situ stress via logging data with a correlation coefficient (R) of 0.96; Khormall [31] applied artificial neural networks to analyze reservoir rock permeability changes caused by solid precipitation during water flooding; on this basis, Hatchell et al. [32,33,34] coupled reservoir simulators with seismic-driven geomechanical models to establish a 4D dynamic in situ stress model considering the time effect of production or injection processes; Zhu [35] constructed a 4D in situ stress evolution model for shale gas reservoirs, combining continuum mechanics with the Discrete Fracture Network (DFN) method to simulate stress field reconfiguration due to pore pressure decline during long-term exploitation; and Ma [36] proposed an integrated static and dynamic geomechanical modeling workflow for hydraulic fracturing optimization, conducting dynamic (4D) stress field simulations for tight oil reservoirs.

Existing studies have limitations in several aspects: analyses of stress fields mostly focus on static characteristics and fail to fully capture the dynamic reconstruction laws of stress fields during fracturing; existing 4D models mostly target isotropic reservoirs, ignoring the heterogeneity and anisotropy of reservoir geomechanical parameters and natural fractures, which leads to a significant deviation from the actual geological conditions of shale gas reservoirs; the application of machine learning methods in stress field prediction is still dominated by static or semi-static analyses, with insufficient dynamic adaptability and a lack of real-time linkage with fracturing operation parameters (such as injection rate and pressure), making it difficult to dynamically reflect stress evolution during the operation process; meanwhile, existing stress field studies mainly focus on stress changes caused by reservoir depletion in shallow shale gas and tight oil reservoirs, and there is a lack of research on real-time dynamic changes of stress fields during fracturing operations in deep shale gas.

Therefore, this paper first comprehensively considers the heterogeneity and anisotropy of geomechanical parameters and natural fractures in deep shale gas reservoirs and establishes a 4D in situ stress multi-physics coupling model for shale gas reservoirs based on geology-engineering integration. Then, by coupling geomechanical parameters with fracturing operation data, it systematically studies the dynamic evolution laws of multi-scale stress fields from single-stage to platform-scale during large-scale fracturing of horizontal wells in deep shale gas reservoirs, As shown in Figure 1. The research results can provide a certain scientific basis for optimizing fracturing design and improving shale gas recovery efficiency.

2. Regional Geological Overview and Geological Modeling

2.1. Geological Overview

The Panlongchang syncline is structurally located within the Ziliujing Depression of the Central Sichuan Uplift Belt, bounded by the Shengdengshan structure to the west and the Yundingchang structure to the east. With an area of 188.3 km², the syncline is delineated by secondary faults, featuring a major axis of 17.8 km and a minor axis ranging from 7.1 to 12.8 km. The structural low point at the base of the Longmaxi Formation reaches an elevation of −4100 m, with burial depths varying between 4000 and 4400 m. The workable area covers 169.2 km², while the deployable area spans 131 km². The study area is situated in the central part of the Panlongchang syncline. The syncline exhibits favorable fault stability, with only one weak-slip fault developed. The maximum horizontal principal stress exceeds the vertical principal stress, indicating a strike-slip stress regime. The location of well area is shown in Figure 2. Natural fractures in the Panlongchang syncline are predominantly oriented NE-SW and NW-SE. The NE-SW trending fractures include Fe1 through Fe13 (totaling 13 natural fractures), while the NW-SE trending fractures comprise Fw1 through Fw8 (totaling 8 natural fractures). The basic parameters of the study area are summarized in

Table 1. The key petrophysical parameters of the study area.

Formation Pressure/MPa	Permeability/mD	Porosity/%	Young’s Modulus/GPa	Poisson’s Ratio	Minimum Horizontal Stress/MPa	Maximum Horizontal Stress/MPa
85.6~90.8	0.001~0.002	2.7~4.5	27~45	0.17~0.27	80~104	100~121

.

2.2. 3D Geomechanical Modeling

Geological modeling serves as a crucial bridge connecting various geological understandings. The methodology integrates well data, test results, and seismic interpretation to establish structural models through refined stratigraphic correlation and fault/formation surface interpretation, while reservoir property models are built using conventional and specialized logging data (Figure 3). The study area contains two major NE-SW trending faults modeled with 3D Structural Framework technology to represent complex fault intersections, subsequently converted into a Pillar-Gridding corner-point grid fault model. Natural fractures were effectively characterized using ant-tracking seismic attributes in the Petrel integrated geological-engineering platform, demonstrating high consistency (Figure 4). Laboratory mechanical tests provided calibration for field logging data, enabling the development of accurate 1D geomechanical models with key parameters determined based on structural framework and formation properties. Employing Pillar Gridding technology within well-controlled favorable zones, the 3D structural model achieved 20 m × 20 m planar resolution with true north-oriented grids. The reservoir section features high-precision vertical gridding at 1 m intervals, ensuring robust simulation accuracy.

3. Methodology

3.1. Fluid–Solid Coupling Mathematical Model

In the process of oil and gas reservoir production, the most significant changes in the reservoir are caused by pore pressure increases resulting from stimulation measures such as fracturing and pore pressure depletion due to production. Based on the initial in situ stress field model and combined with regional formation pressure changes provided by reservoir simulation, the induced stress field considering production time is calculated to achieve four-dimensional in situ stress field modeling. In reality, the reservoir is a highly complex system. To solve the stress field in the reservoir, it is simplified here as a fluid–solid coupling problem in porous media.

For the rock matrix part (solid phase medium), the governing equations are as follows:

$${\sigma }_{ij}=2G{\epsilon }_{ij}+\lambda {\delta }_{ij}{\epsilon }_{kk}$$

(1)

where ${\sigma }_{ij}$ denotes the total stress tensor, Lamé constants $\lambda ={\displaystyle \frac{Ev}{\left(1+V\right)\left(1-2V\right)}}$, shear modulus $G={\displaystyle \frac{E}{2\left(1+V\right)}}$, and ${\delta }_{ij}$ is the Kronecker delta symbol.

For the fluid phase, the mass conservation equation for single-phase flow is expressed as follows:

$${\displaystyle \frac{\partial \left(\varphi P_{f}s\right)}{\partial t}}+\overrightarrow{\nabla }\cdot \left(p_f\overrightarrow{v}\right)=Q_m$$

(2)

In the equation, $\varphi$ represents porosity; $p_f$ denotes fluid density; $S$ indicates saturation; $t$ is time; $\overrightarrow{v}$ stands for flow velocity vector; $\overrightarrow{\nabla }$ is the gradient operator with respect to three-dimensional coordinates

The fluid velocity is described by Darcy’s law:

$$\overrightarrow{V}=-{\displaystyle \frac{k}{\mu }}\overrightarrow{\nabla }\left(p-p_{f}gD\right)$$

(3)

where $k$ represents permeability; $\mu$ denotes fluid viscosity; $p$ is fluid pressure; $g$ stands for gravitational acceleration constant; $D$ indicates depth with surface as reference zero point. Under the condition of negligible fluid density, Equation (2) simplifies to the following:

$${\displaystyle \frac{\partial \overrightarrow{\zeta }}{\partial t}}+\overrightarrow{\nabla }\cdot \left[{\displaystyle \frac{k}{\mu }}\overrightarrow{\nabla }\left(p-p_{f}gD\right)\right]=Q_V$$

(4)

where $Q_V={\displaystyle \frac{Q_m}{P_f}}$ represents the volumetric fluid flow rate per unit time, characterizing the fluid volume flux through a unit cross-section; $\zeta =\varphi s$ denotes the fluid content in porous media (dimensionless), defined as the ratio of fluid volume to total bulk volume.

According to the effective stress principle for porous media, the stress acting on the solid matrix is given by the following:

$${\sigma }_{ij}^{\prime }={\sigma }_{ij}-\alpha {\delta }_{ij}p$$

(5)

where ${\sigma }_{ij}^{\prime }$ denotes the effective stress.

To address the limitations of the conventional Biot coefficient α being treated as a constant, this model introduces a time-dependent equation to characterize matrix–fluid interactions during fracturing:

$$\alpha \left(t\right)=1-{\displaystyle \frac{K_{dry}}{K_{solid}}}\exp \left(-\beta t\right)$$

(6)

where $K_{dry}$ and $K_{solid}$ represent the bulk modulus of dry rock and solid matrix, respectively, and $\beta$ denotes the attenuation coefficient (range: 0.05–0.15 h⁻¹) [37] characterizing the dynamic stiffness variation of matrix caused by fracturing fluid imbibition. This enhancement enables the model to better capture the stress–seepage coupling characteristics of deep shale reservoirs.

Accordingly, based on poroelastic theory with total stress and fluid content as primary variables, the constitutive relations of porous media can be expressed as follows:

$${\sigma }_{ij}=2G{\epsilon }_{ij}+{\displaystyle \frac{2Gv}{1-2v}}{\delta }_{ij}{\epsilon }_{kk}+\alpha {\delta }_{ij}p$$

(7)

For porous media containing incompressible solid grains fully saturated with incompressible fluid (when α = 1.0, B = 1.0), Equation (4) becomes the following:

$${\displaystyle \frac{\partial {\epsilon }_{kk}}{\partial t}}+\overrightarrow{\nabla }\cdot \left[{\displaystyle \frac{k}{\mu }}\overrightarrow{\nabla }\left(p-\rho gD\right)\right]=-Q_V$$

(8)

Considering the equilibrium equations of the entire system:

$${\sigma }_{ij,j}+f_i=0$$

(9)

where $f$ represents external or body forces.

Based on the strain–displacement relationship, combining Equations (7) and (8) yields the following:

$$G{\nabla }^2{u}_i+{\displaystyle \frac{G}{1-2v}}{\left(u_{k,k}\right)}_{,i}+\alpha p_{,i}=f_i$$

(10)

$${\displaystyle \frac{\partial {\epsilon }_{kk}}{\partial t}}+\overrightarrow{\nabla }\cdot \left[{\displaystyle \frac{k}{\mu }}\overrightarrow{\nabla }\left(p-\rho gD\right)\right]=-Q_V$$

(11)

The system of equations composed of Equations (9)–(11), when supplemented with appropriate initial and boundary conditions, enables the complete solution for porous media behavior.

3.2. Fracture Propagation Criteria

During hydraulic fracturing, a main hydraulic fracture is generated along the wellbore. With the continuous injection of fracturing fluid, branch fractures are formed around the main fracture. The main fracture and branch fractures together constitute a complex fracture network, thereby improving the seepage capacity. The basic principle of fracture propagation is based on stress conditions and rock failure criteria. In the process of fracture propagation, two issues need to be clarified: whether the fracture propagates and extends, and the direction of propagation. The J-integral method is used to calculate the stress intensity factor at the fracture tip:

$$K_I^{eq}={\displaystyle \frac{1}{2}}\cos \left({\displaystyle \frac{\theta }{2}}\right)\left\{K_I\right.\left(1+\cos \left(\theta \right)\right)\left.-3K_{II}\sin \left(\theta \right)\right\}$$

(12)

where $K_I^{eq}$ is the equivalent stress intensity factor; $K_I$ is the Mode I stress intensity factor; $K_{II}$ is the Mode II stress intensity factor.

The propagation direction (angle θ) of the fracture is calculated according to the maximum circumferential stress criterion:

$$\theta =2\arctan {\displaystyle \frac{1}{4}}\left({\displaystyle \frac{K_I}{K_{II}}}-sign\left(K_{II}\right)\sqrt{{\left({\displaystyle \frac{K_I}{K_{II}}}\right)}^2+8}\right)$$

(13)

If there are natural fractures developed in the reservoir, the main hydraulic fractures will connect with the natural fractures during their propagation and extension. The Warpinski–Teufel criterion is a widely used failure criterion for tensile fractures at present:

$$p>{\sigma }_n$$

(14)

where $p$ is the pore pressure in the natural fracture; ${\sigma }_n$ is the normal stress on the wall of the natural fracture.

Whether shear slip occurs in the natural fracture is determined by the Mohr–Coulomb criterion, whose expression is as follows:

$$\left|\tau \right|>{\tau }_0+C_f\left({\sigma }_n-P\right)$$

(15)

where $\tau$ is the shear stress on the fracture wall; ${\tau }_0$ is the cohesion of the rock; $C_f$ is the wall friction factor.

Based on the theories of elasticity and fracture mechanics, the net pressures required for the generation of tensile fractures and shear fractures are as follows:

$$p_t>{\displaystyle \frac{{\sigma }_H-{\sigma }_h}{2}}\left(1-\cos 2\theta \right)$$

(16)

$$p_s>{\displaystyle \frac{1}{C_f}}\left[{\tau }_0+{\displaystyle \frac{{\sigma }_H-{\sigma }_h}{2}}\left(C_f-\sin 2\theta -C_f\cos 2\theta \right)\right]$$

(17)

where $P_t$ is the net pressure required for the generation of tensile fractures; $P_s$ is the net pressure required for the generation of shear fractures; ${\sigma }_H$ and ${\sigma }_h$ are the maximum and minimum horizontal principal stresses, respectively. The fluid loss rate of fracturing fractures is calculated by the Carter leak-off model:

$${\nu }_L={\displaystyle \frac{2C_L}{\sqrt{t-t_0}}}$$

(18)

where ${\nu }_L$ is the leak-off velocity; $t$ is time; $t_0$ is the initial time of leak-off; $C_L$ is the Carter leak-off coefficient. Using the cubic law, the continuity equation for the flow of fracturing fluid in the fracture considering fluid leak-off is as follows:

$${\displaystyle \frac{{\partial }_w}{{\partial }_t}}+\nabla \cdot \left(-{\displaystyle \frac{w^3}{12\mu }}\nabla P_f\right)+{\displaystyle \frac{2C_L}{\sqrt{t-t_0}}}=0$$

(19)

where $\mu$ is the viscosity of the fracturing fluid; $p_f$ is the pressure in the fracture. The criterion for determining the dynamic boundary position of pressure propagation caused by fracture propagation in volume-fractured horizontal wells under nonlinear seepage conditions is as follows:

$$\begin{array}{c}{\left.\left({\displaystyle \frac{\partial p}{\partial x}}-G_a\right)\right|}_{r=Rtx}=0\\ {\left.\left({\displaystyle \frac{\partial p}{\partial y}}-G_a\right)\right|}_{r=Rty}=0\end{array}$$

(20)

$$G_a={\displaystyle \frac{1-a}{b}}$$

(21)

where $Rtx$ and $Rty$ are the dynamic boundary positions in the x and y directions, respectively; $Ga$ is the critical start-up pressure gradient.

3.3. Research Methodology

During the long-term production of shale gas reservoirs, formation pressure continuously changes, and the reservoir stress state essentially represents the dynamic coupling between fracture–pore dual-medium seepage and matrix skeleton stress. Based on reservoir numerical simulation methods and geomechanical theory, a seepage–stress–fracture propagation coupling model is established, with research conducted using an integrated geological-engineering platform. The forms of coupled calculation can be divided into one-way coupling, iterative coupling, and full coupling [38]. Since one-way coupling has low calculation accuracy and full coupling has low calculation efficiency, the iterative coupling method is selected for calculation. The difference from conventional iterative coupling is that the seepage–stress–fracture propagation iterative coupling simulation solves the fracture morphology, pore pressure, stress, and strain at all time points in one iteration.

This methodology utilizes the Kinetix fracture propagation simulator, Intersect reservoir numerical simulator, and Visage finite element mechanical simulator to model fracture geometry, seepage field, and stress field, respectively. The process begins by generating an initial fracture network. During one iteration, pore pressure and saturation at each timestep are solved, followed by grid conversion. These results are then used as input conditions for the finite element model to calculate stress and strain data at each timestep. Subsequently, the computed fracture geometry, pressure, saturation, and stress data are updated to initiate the next iteration step. This cyclic computation is repeated to complete the coupled simulation of seepage–stress–fracture propagation across different development stages (Figure 5).

4. Study on the Evolution Laws of 4D Dynamic Stress Fields

During hydraulic fracturing operations, the dynamic evolution of reservoir stress fields directly influences fracture propagation patterns, stimulation volume, and inter-well interference levels, representing a core scientific issue for geology-engineering integration optimization. Traditional static stress field models struggle to reveal the spatiotemporal evolution characteristics of stress states under fracturing disturbances, which constrains the precision of large-scale fracturing designs. This chapter systematically investigates based on multi-scale coupling modeling methods: (1) study on single-stage stress field evolution, analyzing the dynamic coupling mechanism between fracture propagation and near-field stress redistribution; (2) study on single-well stress field evolution, revealing the stress accumulation effects of multi-stage fracturing; (3) study on pad-scale stress field evolution, clarifying the stress interference boundaries and balanced control principles during multi-well simultaneous fracturing.

By establishing a four-dimensional dynamic response model of “fracture–stress–fluid” interactions, this research provides theoretical foundations for stress field regulation and engineering optimization pathways for efficient shale gas development.

4.1. Study on Single-Stage Stress Field Variation Patterns

4.1.1. Fracture Propagation

The simulated treatment pressure for Stage 7 of Well 54-2 shows good agreement with actual field data. The actual shut-in pressure was 66.31 MPa, while the simulated shut-in pressure was 63.2 MPa, yielding an error of 4.7% (Figure 6). As shown in Figure 7, the spheres represent the values of the microseismic monitoring signals. The results correlate well with microseismic monitoring data, demonstrating that the simulated fractures accurately represent actual hydraulic fracture parameters and geometry, thereby validating the model’s accuracy.

The hydraulic fractures propagate relatively symmetrically on both sides of the wellbore, with fracture complexity near the wellbore showing minimal variation compared to the fracture tips. The average hydraulic fracture length is 223 m, average height is 47 m, and average width is 8.54 mm.

4.1.2. Stress Field Variation

(1)

Stress Magnitude Variation

Figure 8 shows the distribution of the minimum horizontal principal stress in the formation before and after fracturing in Stage 7 of Well 54-2. The figure clearly shows that after fracturing, the minimum horizontal principal stress in the formation around the fractures underwent significant changes, increasing by 3.4 MPa compared to the pre-fracturing state. Compare with the pre-fracturing conditions, the impact of fracturing on the surrounding formation can be divided into three zones. The first is the stress reversal zone, where the presence of hydraulic fractures causes stress reversal in a certain area around the fractures. In the formation close to the fracture faces, the minimum horizontal principal stress significantly decreases after fracturing. Additionally, there is an “elliptical” zone around the fractures where the minimum horizontal principal stress increases noticeably. Finally, on both sides of the fractures along the wellbore direction, there is a “triangular” zone where the minimum horizontal principal stress shows varying degrees of increase, with more pronounced stress elevation closer to the wellbore. After fracturing, the stress contrast decreases in regions far from the fractures, while it increases near the fracture faces. In comparison, the maximum horizontal principal stress shows a smaller increase of about 1.3 MPa, concentrated mainly at the fracture tips (Figure 9).

(2)

Stress Orientation Variation

After the fracturing operation, the opening of fractures causes changes in the displacement around the fractures, leading to the deflection of the directions of the maximum and minimum principal stresses. The degree of stress direction deflection is influenced by the net fracture pressure, which is related to parameters such as fracturing displacement and fluid volume. Figure 10 and Figure 11 shows the directional changes of the formation principal stresses before and after the fracturing of the seventh section of Well 54-2. where the arrow directions indicate the azimuth angles of in-situ stress and the color bands represent the magnitude of in-situ stress. The maximum deflection of the maximum horizontal principal stress occurs in the middle of the fracture, in the area perpendicular to the fracture. In contrast, the maximum deflection of the minimum horizontal principal stress occurs at both ends of the fracture. Post-fracturing, the maximum horizontal principal stress, originally parallel to the fracture extension direction, starts to deflect towards a direction perpendicular to the fracture extension. Conversely, the minimum horizontal principal stress, originally perpendicular to the fracture extension direction, begins to deflect towards a direction parallel to the fracture extension.

4.2. Single-Well Stress Field Evolution Study

Well 54-3 has abundant pre-fracturing seismic monitoring data and related information. Following the above methodology, fracture propagation and stress simulation were performed for Well 54-3. The main fracturing operation in Well 54-3 adopted large-stage multi-cluster, high-intensity, and multi-stage temporary plugging fracturing technology with the following perforation techniques: Stage 1 used coiled tubing perforation while the remaining stages employed cable-conveyed cluster perforation. The primary fluid system used was variable-viscosity slickwater, with low-viscosity slickwater accounting for approximately 90% of the total volume. During smooth operation phases, low-viscosity slickwater was predominantly used to minimize consumption of high-viscosity fluids. The proppant selection consisted of 70/140 mesh quartz sand mixed with 40/70 mesh ceramic particles at an 8:2 ratio. The perforation parameters for Well 54-3 were as follows: Stage 1 used coiled tubing perforation with a density of 8 holes per 0.5 m, each cluster having a 0.5 m perforation interval, totaling 40 holes; the remaining fracturing stages had 13 clusters with a density of 3 holes per 0.3 m, each cluster having a 0.3 m perforation interval, totaling 39 holes.

4.2.1. Fracture Propagation

The overall treatment pressure matching for Well 54-3 shows good agreement, with an actual average shut-in pressure of 65.75 MPa and a simulated average shut-in pressure of 68.06 MPa, resulting in an error of 3.5%. The results generally correlate well with microseismic monitoring data, demonstrating that the simulated fractures accurately represent the actual hydraulic fracture parameters and geometry (Figure 12). The average hydraulic fracture length is 267 m, average width is 5.3 mm, and average height is 47.8 m. Post-fracturing results indicate effective fracture geometry improvement, with sufficient fracture propagation achieved at all well locations. As fracturing fluid injection continued, energy gradually accumulated within the reservoir, ultimately inducing both tensile and shear failure in the formation.

4.2.2. Stress Field Changes

(1)

Stress Magnitude Changes

As the fractures in each fracturing stage propagate, the injection of formation energy causes corresponding adjustments in the in-situ stress in the adjacent areas of each fracturing stage. Figure 13 shows the changes in the minimum horizontal in-situ stress of Well 54-3 before and after fracturing. From the simulation results, it can be observed that in terms of the magnitude of stress change, due to the positive induced stress generated by the fracturing stages, the minimum horizontal in-situ stress increased significantly compared to the original stress during the fracturing process (ranging from 1.8 to 6.4 MPa), with an average increase of 4.2 MPa. As the number of fracturing stages increased, the minimum horizontal principal stress showed an obvious cumulative growth trend, and the increase amplitude became more significant in the later stages, with a phenomenon of stress accumulation along the wellbore. After 22 stages of fracturing, the cumulative increase in the minimum horizontal principal stress reached 6.4 MPa. Meanwhile, compared to the minimum horizontal principal stress, the maximum horizontal in-situ stress shows limited increase, ranging from 1.1 to 3.2 MPa (Figure 14). When considering both stress components, the horizontal stress contrast decreases after each fracturing stage. Figure 15 presents the variation in bi-directional stress contrast, which more visually demonstrates the differential impacts of fracturing on the maximum and minimum horizontal principal stresses. The figure shows that the pre-fracturing bi-directional stress contrast was about 15 MPa, which decreased to approximately 11 MPa after fracturing. Notably, significant stress reversal was observed in certain stages (e.g., Stage 11), where the minimum horizontal principal stress exhibited an anomalous decrease of about 1.1 MPa during fracturing. Through comprehensive analysis of microseismic event distribution characteristics and fracturing operation curves, this phenomenon is primarily attributed to the activation of natural fracture systems.

(2)

Stress Direction Changes

Based on the simulation results, the minimum and maximum directions of horizontal in-situ stress before and after fracturing are plotted, as shown in Figure 16 and Figure 17. Here, the arrow directions and color bands represent the direction and magnitude of horizontal in-situ stress, respectively. The analysis indicates that the morphology of the ultra-large-scale fracture network exhibits high complexity. During the hydraulic fracturing process, not only do the in-situ stress values change but the in-situ stress directions also show a certain degree of deflection. In general, the variation range of in-situ stress after fracturing is relatively small: the direction of the minimum horizontal principal stress changes by 0°~20°, and that of the maximum horizontal principal stress changes by 0°~10°. The influence is mainly within the range controlled by fractures, with the most obvious changes near the wellbore, and the directional variation decreases as the distance increases.

4.3. Platform Stress Field Evolution Study

The single-well simulation results of Well 54-3 indicate the following: After large-scale fracturing, significant changes occurred in the stress state (magnitude and direction) and fracture system of adjacent stages and wells in the horizontal well. Based on these changes, if the original stress and fracture data continue to be used for subsequent fracturing simulations of neighboring stages and wells, significant errors will occur, greatly interfering with the selection of subsequent fracturing methods and optimization of fracturing parameters.

Therefore, based on the concept of dynamic fracturing stress fields and the integrated geomechanics approach, this study employs the actual field fracturing sequence to conduct more reasonable simulations of subsequent horizontal well fracturing processes. The three-dimensional model is updated in real-time according to the in-situ stress field and fracture conditions after each stage of fracturing. In field operations, a coordinated zipper fracturing approach with staggered inter-well fracture placement was adopted. A total of five wells—two from Platform 53 and three from Platform 54—were fractured simultaneously. Due to the influence of natural fracture development, casing deformation was observed in certain intervals. To mitigate risks, some stages were either skipped or combined into larger intervals for modified fracturing treatment. Ultimately, a total of 105 stages were successfully executed.

4.3.1. Fracture Propagation

The specific fracture morphology after platform fracturing simulation is shown in Figure 18. The simulation results show that the average opening exceeds 5 mm, and due to stress concentration effects, the maximum width of local main fractures can reach 8–10 mm, providing sufficient flow channels for proppant injection. The main fracture extension distance exceeds 200 m, and secondary branch fractures exhibit multi-level bifurcation, forming a complex fracture network system that effectively expands the stimulated reservoir volume (SRV). After fracturing, the vertical extension height of fractures in each horizontal well exceeds 40 m, with some intervals showing sudden height changes (up to 55 m) due to natural weak planes, indicating that fracturing energy has effectively penetrated thin interlayers.

4.3.2. Stress Field Changes

(1)

Stress Magnitude Changes

As shown in Figure 19 and Figure 20, during the fracturing process, the minimum horizontal principal stress in the platform area changes in real time, showing an overall increasing trend. The increase range of the minimum horizontal principal stress is approximately 1.1–7.6 MPa, with an average increase of 3.8 MPa, while the influence range is mainly distributed around the fractures. The maximum horizontal principal stress also changes simultaneously, showing an overall increasing trend, with a slightly smaller increase magnitude than the minimum horizontal principal stress, increasing by about 0.3–3.5 MPa, with an average increase of 1.7 MPa. The stress influence range after platform fracturing is relatively large, with an average stress change range of 290 m. Comparative analysis shows that a 400 m well spacing (Platform 54) has better stress balance and fewer stress communication phenomena compared to a 300 m well spacing (Platform 53), effectively balancing reservoir stimulation efficiency and inter-well interference control.

(2)

Stress Direction Changes

Meanwhile, significant changes have occurred in the stress directions of both the fractured well and adjacent wells. It is more reasonable to conduct subsequent fracturing simulations on adjacent stages and wells based on these changes. The minimum and maximum directions of horizontal in-situ stress before and after fracturing are plotted in Figure 21 and Figure 22, where the arrow directions indicate the azimuth angles of in-situ stress and the color bands represent the magnitude of maximum in-situ stress. It can be seen that the ultra-large-scale fracture network is relatively complex. During the fracturing process, not only does the magnitude of in-situ stress change but the direction of in-situ stress also undergoes certain changes. Specifically, the greater the variation amplitude of pore pressure, the more obvious the deflection of stress direction. The direction of the minimum horizontal principal stress changes by 0°~45°, and that of the maximum horizontal principal stress changes by 0°~30°, forming a regional stress equilibrium zone. Near the red high-stress areas, the local stress direction changes more significantly after fracturing, indicating obvious fracture deflection and high fracture complexity.

Since the hydraulic fracturing stress field cannot be directly measured, the Instantaneous Shut-In Pressure (ISIP) is employed to characterize the stress field during fracturing, as illustrated in the Figure 23. After large-scale fracturing operations, the ISIP fluctuations observed in Platform 54 were significantly smaller than those in Platform 53, indicating a more balanced post-fracturing stress field in Platform 54.

5. Conclusions

Taking the deep shale gas in the Zigong block of the Sichuan Basin as the research object, this study comprehensively considers the heterogeneity and anisotropy of geomechanical parameters and natural fractures in shale gas reservoirs, and constructs a 4D in-situ stress multi-physics coupling model for shale gas reservoirs based on geology–engineering integration. By coupling geomechanical parameters with fracturing operation data, the dynamic evolution laws of multi-scale stress fields from single-stage to platform-scale during large-scale fracturing of horizontal wells in deep shale gas reservoirs are systematically studied. The research results are as follows:

(1)

The fracturing process has a significant impact on the magnitude and direction of the stress field. With the injection of fracturing fluid, both the minimum and maximum horizontal principal stresses show an increasing trend, with the minimum horizontal principal stress increasing by 1.8–6.4 MPa and the maximum horizontal principal stress increasing by 1.1–3.2 MPa; moreover, near the wellbore, the direction of in-situ stress deflects obviously.

(2)

As the number of fracturing stages increases, the minimum horizontal principal stress presents a significant cumulative growth trend, with a more prominent increase in the later stages. There is a phenomenon of stress accumulation along the wellbore, and the stress difference decreases from 15 MPa to 11 MPa.

(3)

The on-site adoption of the fracturing operation method featuring overall flush advancement and inter-well staggered fracture placement has achieved good stress balance; comparative analysis shows that the stress communication degree of the 400 m well spacing is weaker than that of the 300 m well spacing.

(4)

By studying the evolution laws of the stress field during fracturing and accurately identifying the distribution characteristics of the stress field, it is possible to guide the on-site real-time adjustment of the fracturing sequence, thereby improving the stress field balance and enhancing the fracturing stimulation effect. In future research, real-time in-situ stress measurement technology can be incorporated, and combined with the changes of the stress field during the production process, research on the stress field evolution throughout the whole life cycle of shale gas wells can be carried out.