Refined 3D Numerical Simulation of In Situ Stress in Shale Reservoirs: Northern Mahu Sag, Junggar Basin, Northwest China

Abstract

The shale oil reservoirs of the Lower Permian Fengcheng Formation in the northern Mahu Sag are promising targets. However, complex geology and strong heterogeneity in the area pose great difficulties in the numerical simulation of in situ stress fields, which have for a long time been poorly understood. This study provides a systematic and accurate 3D in situ stress numerical simulation workflow based on comprehensive data. In this research, optimized ant tracking was applied to construct refined geological models. Acoustic impedance is taken as what we refer to as “hard” data to reflect variations in geomechanical parameters. Logging and mechanical tests were taken as “soft” data to restrict the numerical range of the geomechanical parameters. With the integration of “hard” data and “soft” data, accurate 3D geomechanical models can be attained. The finite element method was ultimately utilized to simulate the 3D in situ stress field of the Fengcheng Formation. Numerical simulation results reveal that the stress state of the Fengcheng Formation is quite complicated. The magnitude of the horizontal principal stress, horizontal stress difference and horizontal stress difference coefficient are correlated with burial depth, faults, and geomechanical parameters to some degree. The parameter Aφ was introduced in this research to better analyze the stress regime, the result of which demonstrates that the main stress regime in the study region is the reverse faulting stress regime. By evaluating the fault stability, it was found that there is basically no possibility of slippage regarding the faults in northern Mahu Sag. The results of this research provide evidence for well deployment optimization, borehole stability, and so on, all of which are of great significance in hydrocarbon exploration and exploitation.

1. Introduction

Shale oil, characterized by the integration of source rocks and reservoirs, refers to the prospective hydrocarbon resources that exist in shale in a free or adsorbed state [1,2,3]. The exploration and development of abundant shale oil resources are crucial globally. Energy independence has been achieved by the United States through the Black Shale Revolution, significantly increasing shale oil production, which now constitutes 50% of the nation’s total crude oil production [4]. In recent years, China has also made substantial progress in exploiting shale oil resources. Commercial shale oil reserves have been discovered in the Junggar Basin, Ordos Basin, Qaidam Basin [5,6,7], and numerous other petroliferous basins (Figure 1). However, shale oil reservoirs present challenges due to their poor physical properties, complex pore structures, rapid lithological changes, and strong heterogeneity. These factors contribute to the considerable challenges of exploitation [7,8]. Fracturing based on the natural fracture networks of shale oil reservoirs during later stages of development has proven effective in enhancing industrial oil and gas production. Previous studies have highlighted the significant influence of rock mechanical properties and in situ stress on fracture propagation, underscoring the critical importance of studying these factors for shale oil development. Currently, research on the tectonics, mineral composition, and organic geochemistry of shale oil reservoirs in the Mahu Sag has been comprehensive [9,10,11]. However, research on the distribution of in situ stress, which is crucial for predicting sweet spots and determining well trajectories in shale oil reservoirs, remains insufficient. This gap in understanding hampers shale oil reservoir exploration and development. Therefore, urgent research is needed on rock mechanics analysis and precise stress quantification to address the challenges in hydrocarbon exploitation and generate economic value [12].

In recent years, research has proven the widespread presence of source rocks with rich organic matter in the lower Permian Fengcheng Formation of Mahu Sag. Due to the superposition of multiple tectonic movements, the stress distribution in the research area is complex [13]. Additionally, the strong reservoir heterogeneity poses challenges in identifying sweet spots. Exploiting industrial oil and gas from unconventional reservoirs often involves deploying directional and horizontal wells [14,15]. However, the poor reservoir quality poses challenges for maintaining stable production, despite the deployment of horizontal wells. Therefore, establishing effective fracture network systems through fracturing transformation, which are significantly influenced by in situ stress, is advisable [16]. Previous research on in situ stress in this region has primarily focused on logging calculations and mechanical experiments. While these methods accurately reflect in situ stress to some extent, they do not capture the stress distribution across the entire research area. Furthermore, typical 3D numerical simulations of stress fields often concentrate on regional faults and terrain undulations. Homogeneous geomechanical parameter models are employed during the simulation process, which means the influence of these complex variables has not been fully considered. Consequently, the stress state in the formation cannot be adequately represented by numerical simulation results. Nowadays, the technology for simple 3D in situ stress simulations has significantly advanced. Accurately depicting geomechanical models with strong anisotropic characteristics and constructing in situ stress models under complex geological conditions are pressing issues that require solutions. Mechanical experiments, seismic data, volume attributes, and other data were used in the numerical simulation process to enhance the results.

This study focuses on the shale oil reservoir of the lower Permian Fengcheng Formation in the north of Mahu Sag. Firstly, a detailed geological model of the study area was constructed by using ant tracking. Then, precise 3D geomechanical parameter models for the target layers were established by integrating mechanical experiments, logging calculations, and inverted acoustic impedance. Additionally, imaging logging was utilized to determine the orientation of maximum horizontal stress (σ_hmax). Finally, the in situ stress state of the target layer in the study area was determined through finite element simulation. A corresponding analysis was conducted based on the final results.

2. Geological Settings

The northern region of Mahu Sag is situated in the northwest of the Junggar Basin in northwestern China (Figure 2A). The tectonic evolution of the northern Mahu Sag is consistent with that of the Junggar Basin. From the late Paleozoic to the Quaternary, the region experienced three tectonic phases: Hercynian, Indosinian-Yanshanian, and Himalayan. In the early Permian, strata in the southern Mahu area were rapidly deposited under an extrusion environment, forming the prototype of the Mahu Sag. During the Middle and Late Permian, the sedimentary center continuously migrated northward, leading to the formation of thick, fine-grained sediments. Tectonic extrusion caused local structures in the Mahu area to uplift. In the early Triassic period, the basin underwent uplift and erosion, resulting in the absence of some strata in the Mahu Sag. The Late Jurassic Depression was uplifted as a whole, with weak tectonic activity beginning in the Cretaceous, after which the basin entered a continuous burial stage.

As mentioned earlier, the Mahu Sag was formed during the sedimentation period of the Early Permian, with the Jiamuhe Formation, Fengcheng Formation, Xiazijie Formation, and Ulmu Formation developing from bottom to top [17,18]. The source rock of the Fengcheng Formation is mainly composed of bacteria and algae (Figure 3). The Fengcheng Formation was formed under alternating seasonal humid and arid environments, resulting in the development of typical dolomitic rock deposits [19,20]. There are two types of faults with different orientations in the Mahu Sag. Some faults are northeast-trending reverse faults, roughly parallel to the boundary faults, and were mainly formed during the Hercynian-Indosinian period. These faults are arranged en echelon in a planar view and exhibit a typical nose structure in the vertical profile. The other faults are east-west trending strike-slip faults, roughly perpendicular to the boundary fault. These faults mainly formed during the Indosinian period and continued to be active until the Yanshan period.

3. Data and Methods

3.1. 3D Geological Models

Conventional fault interpretation relies on manual observation, which is time consuming and labor intensive in areas with complex structures. Ant tracking, an innovative approach that has emerged in recent years, can effectively identify horizon discontinuities [21,22]. The concept originates from the foraging behavior of ants in nature. Ants choose routes based on pheromone concentration. As they pass, the pheromone concentration on the path increases, but it also evaporates over time. The formula for updating pheromone concentration on each path is as follows:

$${\tau }_{ij}\left(t+n\right)=\left(1-\rho \right){\tau }_{ij}\left(t\right)+∆{\tau }_{ij}$$

(1)

$${∆\tau }_{ij}={\sum }_{k=1}^m{∆\tau }_{ij}^k$$

(2)

where ρ (0 < ρ < 1) is the evaporation coefficient of pheromones on the path; 1-ρ is the maintenance coefficient of pheromones on the path; ${\Delta \mathsf{\tau }}_{\mathrm{i}\mathrm{j}}^{\mathrm{k}}$ is the amount of pheromones left by ant k from node i to node j (If ant k did not follow this route, then ${\Delta \mathsf{\tau }}_{\mathrm{i}\mathrm{j}}^{\mathrm{k}}$ = 0).

The principle of ant tracking involves using electronic ants to search for and label discontinuous values in a region, attracting neighboring ants to track along the outliers [23,24]. Mutation values represent faults and fractures, and using this tracking marker intuitively identifies faults and fractures. There are two typical types of ant tracking: aggressive ant tracking and passive ant tracking. Aggressive ant tracking can identify more discontinuities, while passive ant tracking identifies fewer fractures and faults [25]. The outcomes of ant tracking are generally controlled by six parameters, determined based on geological backgrounds (

Table 1. Ant tracking parameters of different types.

Ant Tracking Parameters	Initial Ant Boundary	Ant Track Deviation	Ant Step Size	Illegal Steps Allowed	Legal Steps Required	Stop Criteria
Range	1–30	0–3	2–10	0–3	0–3	0–50
Passive ant	7	2	3	1	3	5
Aggressive ant	5	2	3	2	2	10

). This method not only allows for subtle interpretation of fractures and faults but also effectively eliminates the subjective influence of manual fault interpretation. Considering the practicality and applicability of ant tracking, this technology was used in this research to assist in identifying faults and constructing detailed geological models of the entire study area (Figure 4).

3.2. Mechanical Tests

Before simulating the in situ stress, it is essential to analyze the mechanical parameters, which are critical for the accuracy of the simulation results. Reliable simulation of in situ stress fields can only be achieved by conducting numerical simulations based on precise mechanical parameters. Currently, the analysis of the mechanical properties of rocks under different temperature and pressure conditions typically uses triaxial compression tests [26,27]. In this research, 15 samples without fractures from different depths of the Fengcheng Formation were collected for triaxial compression tests. According to international rock mechanics experimental standards, the diameter of the cylindrical sample is 2.5 cm, and the height is 5 cm.

Besides triaxial compression tests, acoustic emission tests are another essential method for a better understanding of the in situ stress state (Figure 5A). Acoustic emission tests can be categorized into uniaxial and triaxial acoustic emission tests [28], both of which can determine the magnitude and stage of paleostress by identifying the Kaiser point [29,30]. However, samples in uniaxial acoustic emission tests often undergo damage before the Kaiser point appears. Consequently, the collected signal may not be a genuine Kaiser signal but rather a rock sample rupture signal [31,32,33]. Therefore, increasing the confining pressure and determining the stress through triaxial acoustic emission tests is preferable. The sampling method is illustrated in Figure 5B, with three samples selected vertically and nine selected horizontally. Based on well-established test principles and selective samples, the vertical stress and horizontal principal stresses of the research target can be acquired.

3.3. 3D Geomechanical Modelling

The experimental results obtained from triaxial tests are called static geomechanical parameters, which are known for their high accuracy [34]. However, due to sample discontinuities, acquiring continuous data solely through experiments remains unattainable. Dynamic geomechanical parameters can be derived using logging data such as p-wave time difference, s-wave time difference, and density (Figure 6). The limitation of logging calculations is the inherent inaccuracy of dynamic geomechanical parameters. The calculation formulas are as follows:

$${\mu }_d={\displaystyle \frac{∆t_s^2-2∆t_p^2}{2(∆t_s^2-∆t_p^2)}}$$

(3)

$$E_d={\displaystyle \frac{\rho }{∆t_s^2}}\times {\displaystyle \frac{3∆t_s^2-4∆t_p^2}{∆t_s^2-∆t_p^2}}$$

(4)

where Δt_s is the p-wave time difference, s/m; Δt_p is the s-wave time difference, s/m; and ρ is the rock density, g/cm³.

By integrating mechanical experimental data with logging calculations, a successful relationship between dynamic and static geomechanical parameters in the study area was established, mitigating the limitations of individual methods and ensuring continuous and credible results (Figure 6).

The heterogeneity and anisotropy of the formation, rapid lithological changes, and sudden fractures can lead to variations in velocity, density, and geomechanical parameters. According to the definition of acoustic impedance, this variable’s magnitude correlates closely with velocity and density, offering insights into geomechanical parameter trends. In this study, static geomechanical parameters serve as constraints, guided by acoustic impedance trends. Geostatistical analyses such as Cokriging and sequential Gaussian simulation were employed to develop complex and accurate 3D heterogeneous rock mechanics models of the study area [35,36,37,38].

3.4. Logging Calculation of In Situ Stress

Various methods exist for determining the orientation of in situ stress, including the strike of borehole breakouts, drilling-induced fractures, and hydraulic fracturing, all of which are derived from imaging logging [39,40]. The azimuthal anisotropy of shear waves provides an alternative method to determine the orientation of in situ stress. Considering the available data, this research plotted rose diagrams of borehole breakout strikes and drilling-induced fractures to determine the orientation of maximum (σ_hmax) and minimum horizontal stress (σ_hmin).

In situ stress magnitude may vary due to external factors, but the stress gradient tendency should be similar within a specific area. Logging offers advantages for calculating in situ stress, including low cost, straightforward data acquisition, and continuous evaluation (Figure 6). Several models are used for stress magnitude calculation, with the most commonly employed being as follows:

$${\sigma }_v={\int }_0^H\rho \left(H\right)gdH$$

(5)

$${\sigma }_{hmin}={\displaystyle \frac{\mu }{1-\mu }}{\sigma }_v+{\displaystyle \frac{1-2\mu }{1-\mu }}\alpha p_p+{\displaystyle \frac{E}{1-{\mu }^2}}{\epsilon }_h+{\displaystyle \frac{E\mu }{1-{\mu }^2}}{\epsilon }_H$$

(6)

$${\sigma }_{hmax}={\displaystyle \frac{\mu }{1-\mu }}{\sigma }_v+{\displaystyle \frac{1-2\mu }{1-\mu }}\alpha p_p+{\displaystyle \frac{E}{1-{\mu }^2}}{\epsilon }_H+{\displaystyle \frac{E\mu }{1-{\mu }^2}}{\epsilon }_h$$

(7)

where σ_v is the vertical stress, MPa; σ_hmin is the maximum horizontal stress, MPa; σ_hmax is the horizontal minimum stress, MPa; ρ(H) is the bulk density varying with depth, g/cm³; E is the Young’s modulus, GPa; μ is the Poisson’s ratio; ε_h is the σ_hmin correction coefficient; ε_H is the σ_hmax correction coefficient; α is the Biot coefficient; and p_p is the pore fluid pressure, MPa.

3.5. Numerical Simulation of 3D In Situ Stress

Shale oil reservoirs exhibit strong heterogeneity and anisotropy, compounded by the presence of natural fractures that complicate geomechanical parameters. Consequently, accurately constructing geomechanical models presents challenges. Unlike previous 3D stress field numerical simulations, this study has established a precise 3D model of rock mechanics parameters through logging, seismic data, and mechanical experiments (

Table 2. Comprehensive data used in the numerical simulation.

Data	Utilization
Post-stack seismic data	Extraction of ant tracking from post-stack seismic data for constructing 3D geological models.
Well logging	P-wave time difference, S-wave time difference, and density were primarily used to calculate dynamic mechanical parameters and in situ stress.
Formation MicroScanner Image (FMI)	To determine the orientation of the in situ stress field.
Triaxial compression tests	To calibrate the static mechanical parameters, which can be used to adjust dynamic mechanical parameters.
Acoustic emission	To determine the maximum and minimum horizontal principal stress.

). Consideration was given to the heterogeneity and anisotropy of the formation. Furthermore, the construction process of fault models was optimized, enhancing the accuracy and reliability of the models. Numerical simulations of in situ stress in shale reservoirs were conducted using the finite element method (Figure 7). The simulations have two prerequisites: (1) The stress field deformation is linear elastic without artificial intervention [41,42]. (2) In situ stress results from gravity, whereas paleostress is influenced by plate movements and tectonic deformation [43].

4. Results

4.1. In Situ Stress Measurement

Triaxial compression tests reveal that the static Young’s modulus of the Fengcheng Formation ranges from 31.62 GPa to 56.42 GPa, and the static Poisson’s ratio ranges from 0.21 to 0.31. Dynamic geomechanical parameters at the same burial depth were calculated using Equations (1) and (2). These dynamic parameters, derived from logging data, generally exceed their static counterparts obtained through experiments (Figure 8).

Conducting rock mechanics tests is costly and time consuming, despite the accuracy of the data obtained. Moreover, this method collects scattered points that may not fully represent the overall variation in geomechanical parameters. In contrast, calculating geomechanical parameters via logging is simpler and more efficient. Considering the applicability of static geomechanical parameters and the continuity of dynamic geomechanical parameters, linear regression analysis was conducted in the research area to obtain precise and continuous data (Figure 8). Consequently, trend lines were fitted, from which conversion formulas were derived as follows:

E_s= 1.1996 × E_d − 43.964

(8)

μ_s = 0.314 × μ_d + 0.1208

(9)

where E_s is the static Young’s modulus, GPa; E_d is the dynamic Young’s modulus, GPa; μ_s is the static Poisson’s ratio; μ_d is the dynamic Poisson’s ratio.

Acoustic emission experiments indicate that σ_hmax, σ_hmin and the horizontal stress difference in the study area are approximately 90 MPa, 80 MPa, and 8 MPa, respectively (

Table 3. In situ stress from acoustic emission tests.

Depth, m	σhmin, MPa	σhmin gradients, MPa/hm	σhmax, MPa	σhmax Gradients, MPa/hm	Δσ, MPa
4553	79.8	1.75	86.3	1.90	6.4
4560	82.2	1.80	89.3	1.96	7
4562	78.5	1.72	86	1.89	7.6
4572	81.1	1.77	90	1.97	8.9
4667.5	82.6	1.77	90.7	1.94	7.1

). According to Figure 9, the σ_hmax and σ_hmin increase gradually with depth. Indeed, there is a weak positive correlation between horizontal principal stress and burial depth. The weak correlation between burial depth and horizontal principal stress does not imply that the test results are incorrect and therefore does not affect the accuracy of the numerical results and conclusions. Since the magnitudes of σ_hmax and σ_hmin can be influenced by various factors, such as lithology, the presence of fractures, and mechanical parameters, test results of in situ stress are needed to establish boundary conditions for numerical simulations. The test results indicate that depth is not the sole influencing factor of in situ stress. Factors that may influence in situ stress are considered during numerical simulations. That is the reason why this numerical simulation is accurate.

4.2. Distribution of 3D Geomechanical Parameters

Geological models characterize the spatial structure of strata and the relationships between layers and faults. These models not only depict reservoirs precisely but also provide a solid foundation for geomechanical modeling. Four layers were constructed through manual interpretation, spanning from the bottom of P₁f¹ to the top of P₁f³ (Figure 10A). Based on post-stack seismic data, aggressive and passive ant tracking were combined to identify faults and establish fault frameworks in the research area (Figure 10B).

Three-dimensional (3D) rock mechanics models in the research area were constructed by adopting geostatistical theory and integrating geological functions and deterministic seismic attributes. Variogram serves as the dominant function, with geomechanical parameters calculated via logging used as deterministic data in this research. A 3D rock mechanics model is established using Co-Kriging under the constraint of acoustic impedance (Figure 11A).

Post-stack deterministic inversion, which accurately reflects the original seismic waveform changes, primarily relies on post-stack amplitude information. To ensure accurate inversion models, wavelet sidelobes and tuning effects must be eliminated during this process. Figure 11 depicts the complex internal properties of the fault-controlled reservoir, characterized by strong heterogeneity and anisotropy in the target layer, in the study area. Acoustic impedance values are approximately normally distributed, ranging mainly between 11,800 and 13,200 m/s × g/cm³. Inverted geomechanical models show Young’s modulus ranging from 35 to 55 GPa, predominantly concentrated between 42.5 and 50 GPa (Figure 12), consistent with mechanical test results. Poisson’s ratio ranges from 0.2 to 0.28, with a predominant focus between 0.23 and 0.26 (Figure 13). Comparing inversion models of geomechanical parameters with acoustic impedance reveals that acoustic fluctuation is more closely related to Poisson’s ratio (Figure 12). Alterations in geomechanical parameters near faults and fractures are also observed.

4.3. Orientation and Gradient of In Situ Stress

Based on imaging logging, the orientation of the horizontal principal stress in the Mahu Sag can be accurately and efficiently determined. During the drilling process, the original stress balance in the formation is disrupted. Consequently, in situ stress is redistributed around the shaft lining. This phenomenon, known as stress concentration, may expand the cross-sectional area of wellbores. According to this theory, the relationship between the orientation of fractures and the strike of the horizontal principal stress can be determined. In this research, the orientation of drilling-induced fractures and wellbore collapse was determined from FMI logging. As illustrated in Figure 14, the orientation of σ_hmax and σ_hmin is approximately 28° and 297°, respectively. In areas where fractures exist, the stress magnitude at the same well depth decreases.

Acoustic emission tests, beneficial indicators illustrating general fluctuations of in situ stress, demonstrate that the stress gradient of σ_hmax in the target layer ranges from 1.89 to 1.97 MPa/hm, while the σ_hmin gradient varies between 1.72 and 1.80 MPa/hm (

Table 4. Simpson ratio and stress regime.

Aφ	Stress Magnitude	Stress Regime
0	σv > σhmax ≈ σhmin	Radial extension
0.5	σv > σhmax > σhmin	NF
1	σv ≈ σhmax ~ σhmin	NF to SS
1.5	σhmax > σv > σhmin	SS
2	σhmax > σv ≈ σhmin	SS to RF
2.5	σhmax > σhmin > σv	RF
3	σhmax ≈ σhmin > σv	Radial compression

). However, due to sample limitations, the range of stress gradients calculated by the experiments may not completely represent the overall trend in the study area. Utilizing logging data to calculate the in situ stress gradient is advisable to address deficiencies in the experiment. Based on logging evaluation and experimental analysis, it can be concluded that the stress gradient of the maximum principal stress in the study area is 1.95–2.32 MPa/hm, while that of the minimum horizontal principal stress is 1.62–1.95 MPa/hm (Figure 6).

4.4. Characteristics of 3D In Situ Stress

Based on the simulation results, the in situ stress of the Fengcheng Formation in the study area can be thoroughly analyzed. Generally speaking, the alterations and distribution of the in situ stress state are intricate. As shown in Figure 15, the simulation results conform to the acoustic emission experiment results. Most of the σ_hmin exceeds 78 MPa, with the majority of σ_hmax exceeding 90 MPa. The variation tendencies in σ_hmax and σ_hmin are identical, both displaying low values in the north and high values in the south, with the lowest stress magnitude located in the western part of the study area. The maximum horizontal principal stress is mainly concentrated between 98 and 124 MPa, accounting for 68.7% of the stress distribution (Figure 16). Similarly, the minimum horizontal principal stress is mainly centered between 85 and 100 MPa, making up 60.3% of the stress distribution (Figure 16). The orientation of σ_hmax is NE, and the strike of σ_hmin is approximately perpendicular to that of σ_hmax (Figure 17). To sum up, the in situ stress state in the study area changes rapidly, with the orientation of horizontal principal stress varying near certain faults.

5. Discussion

5.1. Influencing Factors of In Situ Stress

The in situ stress state is affected by various influencing factors, leading to a complex in situ stress distribution in the research area. According to the simulation results, burial depth, geomechanical parameters, and faults have a controlling effect on the in situ stress.

Regardless of the fault strike, the stress on the hanging wall of the reverse fault in the study area is generally lower than on the footwall. According to Figure 18, the magnitude of horizontal principal stress is correlated with geomechanical parameters. In areas where Young’s modulus increases and Poisson’s ratio declines, horizontal principal will change with these two parameters. The influence of geomechanical parameters on horizontal principal stress is not as strong as that of burial depth. As depth increases, the magnitude of horizontal principal stress tends to increase. Faults also impact the direction of horizontal principal stress, and the dip azimuth of horizontal principal stress consistently shows variation near northeast and southeast-oriented faults (Figure 19).

5.2. Stress Difference and Stress Difference Coefficient

In shale oil reservoirs with natural fractures, the propagation of artificial fractures is not only related to the stress state but also closely connected with the horizontal stress difference (Δσ) and horizontal stress difference coefficient (K_h). These two parameters comprehensively determine whether hydraulic fractures and natural fractures can jointly form beneficial fracture network systems [44]. The following formulas represent the horizontal stress difference and horizontal stress difference coefficient, respectively:

$$∆\mathsf{\sigma }={\sigma }_{hmax}-{\sigma }_{\mathrm{h}\mathrm{m}in}$$

(10)

$$K_h={\displaystyle \frac{{\sigma }_{hmax}-{\sigma }_{\mathrm{h}\mathrm{m}in}}{{\sigma }_{\mathrm{h}\mathrm{m}in}}}$$

(11)

where Δσ Is the horizontal stress difference; K_h is the horizontal stress difference coefficient; σ_hmax is the maximum horizontal stress; and σ_hmin is the horizontal minimum stress.

Figure 20 shows the planar distribution of the horizontal stress difference in P₁f² and P₁f³. The horizontal stress difference is generally greater than 12 MPa, mainly distributed between 16 and 20 MPa. There is a correlation between horizontal stress difference and burial depth. As shown in Figure 10A, the terrain in the study area is higher in the north and lower in the south. In contrast, the horizontal stress difference coefficient, lower in the north and higher in the south, displays an opposite characteristic in the research area. Therefore, as depth increases, the stress difference exhibits an upward trend. The magnitude of the stress difference is directly proportional to depth. Conversely, the shallower the formation, the smaller the magnitude of horizontal stress difference. As shown in Figure 10B, there are two types of faults with different orientations in the study area. Some are northeast oriented, while others are southeast oriented. As illustrated in Figure 20, there is an increase in horizontal stress difference near the faults. In addition, the geomechanical parameters also influence the horizontal stress difference to some degree. In areas where Young’s modulus and Poisson’s ratio are both high, the horizontal stress difference shows high numerical values (Figure 18, Figure 21 and Figure 22). Therefore, the horizontal stress difference is positively correlated with Young’s modulus and Poisson’s ratio.

The horizontal stress difference coefficients, concentrated between 0.17 and 0.23, are generally greater than 0.14 (Figure 23). The horizontal stress difference coefficient is not significantly affected by burial depth. There is no evident correlation between burial depth and the stress difference coefficient (Figure 18). However, faults may affect the magnitude of stress difference coefficients. The stress difference coefficient increases when there is a fault nearby (Figure 23). Furthermore, the increase in horizontal stress difference coefficient near northeast-oriented faults is more dramatic than near southeast-oriented faults.

5.3. Commplex Stress Regime

The conventional stress regime analysis is based on the Anderson model [45,46], which classifies stress types on the basis of the relative magnitude of principal stress [47,48,49,50]. In accordance with this theory, Simpson (1997) proposed an innovative parameter A_φ to classify stress regimes (Table 4). A_φ is a continuous variable ranging from 0 to 3, in which A_φ = 0.5 for NF, A_φ = 0.5 for SS, and A_φ = 0.5 for RF stress regimes.

In this research, the A_φ values in the study region are all beyond 2 (Figure 24), indicating that most of the stress regimes are RF, with a small portion transitioning from SS to RF in certain areas. Although the stress regime is not complex, there are still distinct differences in the numerical values distributed throughout the region. High values are mainly distributed along the NE-SW orientation. An increase in A_φ can be observed adjacent to the faults. The stress regime transitioning from SS to RF is mainly distributed in the southeast of the study area, with some scattered in the south. The reverse faulting type gradually converts to a strike-slip faulting stress regime as depth increases in the deeply buried southeastern area. The stress regime of the NE–SW-oriented faults in the research area is RF. By contrast, there is a stress regime transitional zone from RF to SS in the NW–SE-oriented faults (Figure 25). Therefore, apart from depth, the orientation of the fault also affects the stress regime to a certain degree. Additionally, there is a clear correlation between A_φ and K_h. As Kh increases, the value of A_φ also rises (Figure 25).

5.4. Fault Stability Analysis

Previous researchers proposed the Mohr–Coulomb criterion based on the analysis of rock rupture characteristics. According to this criterion, fault stability is contingent on the relationship between normal stress, shear stress, and friction coefficient [51,52]. By introducing the concept of effective stress, the following formula can be obtained:

$$k={\displaystyle \frac{{\sigma }_1-P_0}{{\sigma }_3-P_0}}={\left[{\left({\mu }^2÷1\right)}^{0.5}+\mu \right]}^2=K_{\mu }$$

(12)

where σ₁ is the maximum principal stress; σ₃ is the minimum principal stress; P₀ is the pore pressure; and μ is the friction factor.

If the ratio of maximum effective principal stress to minimum effective principal stress is less than the friction coefficient-related value, i.e., k < K _μ, then the fault is stable with little tendency for slippage. Nevertheless, on condition that k > K _μ, the fault may be unstable, with the possibility of slippage.

The primary issue in determining fault stability is the assessment of frictional strength. Based on laboratory experimental data, it is concluded that μ values for most rocks range between 0.6 and 1.0. Therefore, the critical value μ = 0.6 is used as the calculation standard in this study. As shown in Figure 25, more than 90% of the k-K _μ values are less than 0. Therefore, the faults are quite stable, with a low possibility of fault motion in the research area. Two typical faults (F1 and F2) were selected within the region for detailed analysis. The F1 fault has not yet reached the threshold for fault slippage overall (Figure 26). However, the deeper part of the fault exhibits stronger activity than the upper region, indicating a possibility of fault slippage in certain areas below. The general situation of the F2 fault, which exhibits no significant possibility of fault slippage, is roughly the same as the F1 fault, though the F2 fault is more stable overall (Figure 26). As K_μ is an increasing function of μ, when μ takes the minimum value of 0.6, K_μ is also at its minimum value. Under this condition, the minimum value of K_μ is still greater than most of the k values in the study area. Therefore, it can be concluded that the faults in the study area are stable, with essentially no risk of activation.

6. Conclusions

Based on selected seismic attributes, an accurate geological model was established. Similarly, 3D geomechanical models were constructed in accordance with the geological model by integrating various data, such as mechanical experiments, logging, and acoustic impedance. Along with determining the orientation of horizontal principal stress, a quantitative analysis was conducted on the 3D in situ stress of the Fengcheng Formation in the Mahu Sag.

The influencing factors of the in situ stress field are complex, with the magnitude affected to some degree by Young’s modulus and Poisson’s ratio. However, the magnitude of horizontal principal stress is more affected by burial depth than by mechanical parameters. The deeper the burial depth, the higher the magnitude of horizontal principal stress. Additionally, the orientation of horizontal principal stress is mainly correlated with faults. Regardless of the fault strike, the dip azimuth of in situ stress will increase if a fault is nearby.

The horizontal stress difference and horizontal stress difference coefficient impact the fracture network system, controlling the patterns and development of fractures. As the burial depth increases, the horizontal stress difference also increases. However, the horizontal stress difference coefficient, mainly influenced by geomechanical parameters, is not significantly affected by burial depth. In the vicinity of faults, both the stress difference and the stress difference coefficient may vary to some extent.

To thoroughly understand the stress regime of the research area, A_φ is introduced to quantitatively describe the stress regime. According to the research results, most of the stress regimes in the study area are of the reverse faulting type, with a small number of SS to RF types mainly distributed near the SE–NW-oriented faults.

The fault slip potential analysis was conducted from a 3D perspective. By comparing the values of k and K_μ, it was found that most faults display high stability throughout the region with nearly no risk of slippage. However, in the lower part of certain faults, fault slippage is still possible.