Introduction
Previous hydrocarbon exploration experiences in the central Tarim Basin have indicated that the fractured–vuggy carbonate reservoirs develop along strike-slip faults (Yu et al. Reference Yu, Li and Yang2016; Lu et al. Reference Lu, Wang, Tian, Li, Yang, Li, Lv and He2017). The major breakthrough of the Northwest Oilfield Branch Company (SINOPEC) in the T-SH oilfield has further indicated that strike-slip faults play an important role in the development of Ordovician carbonate fractured reservoirs for oil and gas accumulation (Qi, Reference Qi2016; Jiao, Reference Jiao2017). The reservoir type in the middle of the Tarim Basin is a fault-controlled carbonate reservoir (Song et al. Reference Song, Li and Wang2013; Zhao et al. Reference Zhao, Zhao, Li, Deng and Zhang2019). Previous studies mainly focused on the geometric (Deng et al. Reference Deng, Li, Zhang, Wu and Zhang2018, Reference Deng, Li, Zhang, Zhang and Yang2019; Wang et al. Reference Wang, Gao, Fan, Shang, Qi and Yun2020) and kinematic characteristics of strike-slip faults in the central Tarim Basin (Han et al. Reference Han, Deng, Tang and Cao2017). However, little effort has been made regarding the present in situ stress distribution of the strike-slip fault system. Research on the distribution and application of present in situ stress has important guiding significance for petroleum engineering design, reservoir reconstruction and hydraulic fracturing (Gale et al. Reference Gale, Reed and Holder2007; Engelder et al. Reference Engelder, Lash and Uzcategui2009; Radwan et al. Reference Radwan, Abdelghany and Elkhawaga2021).
The present in situ stress field is affected by topography, lithology, structure, mechanical properties, fluid pressure and other factors (Nenna & Aydin, Reference Nenna and Aydin2011; Radwan & Sen, Reference Radwan and Sen2021 a, b). How to accurately obtain the present in situ stress field has always been a challenging problem for petroleum engineering (Hopkins, Reference Hopkins1997). The study of present in situ stress is usually carried out through in situ measurement and stress modelling (either analytical or numerical); in situ stress measurement is usually carried out through logging data, acid fracturing curve and rock experiment (Djurhuus & Aadnoy, Reference Djurhuus and Aadnoy2003; Cui and Radwan, Reference Cui and Radwan2022; Xie et al. Reference Xie, Zhou, Liu, Yin, Radwan, Lei and Cai2022), while stress modelling (either analytical or numerical) includes the finite-element method (Hampel & Hetzel, Reference Hampel and Hetzel2015; Khodaverdian et al. Reference Khodaverdian, Zafarani and Rahimian2015), the boundary element method (T Zhao et al. Reference Zhao, Jiang, Feng, Sun, Cheng and Zheng2021) and the discrete element method (Qu et al. Reference Qu, Shen, Fu, Zhang and Yang2011). The finite-element method is widely used in numerical simulations of the present in situ stress, due to its accurate quantitative and discrete approximation, and it is a key method for oil and gas exploration and development and fault formation mechanism identification (Bertoluzza & Perotti, Reference Bertoluzza and Perotti1997; Candela et al. Reference Candela, Mazzoli, Megna and Santini2015; Gao, Reference Gao2021). The distribution of the present in situ stress field can be applied to fracture prediction (Pollard & Segall, Reference Pollard and Segall1987; Zoback, Reference Zoback2007; Zhang et al. Reference Zhang, Zhang, Wang and Deng2018; Maerten et al. Reference Maerten, Legrand, Castagnac, Lefranc, Joonnekindt and Maerten2019), reservoir ‘sweet spot’ prediction (Zhou et al. Reference Zhou, Yin, Luo and Xiao2012) and mud window determination (Mousavipour et al. Reference Mousavipour, Riahi and Moghanloo2020).
The SB5 fault is the main dividing line of E–W zoning of the strike-slip fault system in the Tarim Basin. The fault strike in the west is mainly NW-trending, and the fault strike in the east is mainly NE-trending. The SB5 fault is an important target of oil and gas exploration at present, with full coverage of 3D seismic data. In this study, the SB5 fault was taken as the research object, and the geological model was established based on the interpretation results of 3D seismic data. The results of the regional present in situ stress magnitude and direction were taken as boundary conditions, and collected rock physical test reports provided model rock mechanical parameters. A 3D geomechanical model is implemented to better understand the control of faults and structures on the stress field. In situ stress analysed by the finite-element method, and stress measured in situ were used to calibrate the model. Based on the in situ stress distribution, the propagation direction of hydraulic fractures and effectiveness evaluation of natural fractures were studied.
Geological setting
The T-SH area is located in the north of the Shuntuoguole Low Uplift, a secondary structural unit located in the Tarim Basin, the largest intracratonic basin in China. The study area encompasses the Kataka Uplift to the north, the Shaya Uplift to the south, the Manjiaer Depression to the east and the Awati Depression to the west (Fig. 1). The T-SH area of the Tarim Basin is an Ordovician ultra-deep fault-controlled carbonate oilfield. Oil and gas resources are mainly contained in the marine carbonate formation of the middle and lower Ordovician in the platform basin. The target formation in the T-SH area is Ordovician carbonate rock of the Yijianfang Formation (Fig. 2). The thickness of the Yijianfang Formation is c. 160 m.
Fig. 1. (a) Simplified distribution map of the tectonic units in the Tarim Basin. (b) Detail of the strike-slip fault distribution at the top of the Middle–Upper Ordovician (interface T7 4) in the north of the Shuntuoguole Low Uplift.
Fig. 2. Stratigraphy of the central Tarim Basin correlated with the seismic reflecting interface (horizons), the timing of regional tectonic movements and petroleum system elements (sources, reservoirs, seals) (modified from Tang et al. Reference Tang, Huang, Qiu, Qi, Yang, Xie, Yu, Zhao and Chen2012).
The research objects of this paper are in the northern section of the SB5 fault. The SB5 fault is characterized by plane segmentation and vertical stratification (Jiao, Reference Jiao2018). It is N-NW-trending in the Shun 8 North 3D work area, which is divided into ten segments. These are mostly arranged in a left-stepping configuration, and overlapped areas are developed between the segments (Fig. 3b–d). It is inferred that the SB5 fault is dextral strike-slip at the T7 4 interface (top of the Ordovician Yijianfang Formation), and the left-stepping en echelon normal fault developed at the T7 0 interface (top of Ordovician Sangtamu Formation) is also dextral strike-slip (Deng et al. Reference Deng, Li, Zhang, Zhang and Yang2019). In the formation period, the translation segment formed under a single regional strike-slip event. The two strike-slip faults overlap in the step area and are in a state of tension torsion or compression torsion (Mcclay & Bonora, Reference Mcclay and Bonora2001; Woodcock & Rickards, Reference Woodcock and Rickards2003). The overlapping areas can be divided into pull-apart segments and uplift segments. The pull-apart segment is characterized by an extensional component, forming normal faults, extensional strike-slip dual structure and pull-apart basins. The uplift section is characterized by a compressive component, forming reverse faults, fold and uplift (Alsop, Reference Alsop2009). There are three deformation styles distributed along ten segments dividing up the northern section of the SB5 fault (Deng et al. Reference Deng, Li, Zhang, Zhang and Yang2019).
Fig. 3. (a) Plane coherence properties of north section of SB5 fault. (b) Pull-apart segment seismic profile. (c) Uplift segment seismic profile. (d) Translation segment seismic profile.
Data and methodology
Seven wells (S1–S7) were selected in the SB1, SB5 and SB7 faults, including log data, geological reports and core samples. The well-log datasets are wireline logs of gamma-ray, density, resistivity and sonic curves, and formation micro-imager (FMI) logs that were used for in situ stress analysis based on observed drilling-induced fractures and borehole breakout. The core samples are used for mechanical experiments to determine the rock mechanical parameters and in situ stress. When establishing the 3D geomechanical model, we focus on the influence of strike-slip faults on the stress field. The research workflow diagram is shown in Fig. 4. Firstly, the SB5 fault was interpreted according to the 3D seismic data, and the geological model was established. Secondly, the rock mechanical parameters were calculated using logging data, and different mechanical parameters were given to different layers and structural parts of the geological model (Table 1). The present in situ stress magnitude and direction of a single well were obtained by comprehensive use of logging data and rock mechanics experiment as the boundary conditions for model loading. Finally, based on the established geological mechanical model, the finite-element method was used to carry out the numerical simulation of the stress field, establish a three-dimensional in situ stress distribution model and verify it with the calculation results of a single well. The distribution of the present in situ stress of SB5 was clarified, providing a basis for the study of the fracture propagation law of hydraulic fracturing and the optimization of the targeted acid fracturing process.
Fig. 4. Adopted workflow to derive the distribution characteristics and application of present in situ stress.
Table 1. Assignment scheme of the rock mechanics parameters in the in situ stress simulation
Fault description based on seismic data
High-quality 3-D seismic volumes collected by SINOPEC cover the SB5, SB1 and SB7 faults. The seismic dataset used here has a bin spacing of 25 × 25 m with a main frequency of 30–40 Hz, which are favourable parameters for detailed structural mapping and seismic reservoir description. The processed seismic data (time-migrated) were used for interpretation. The seismic coherence technique was used to image fault-induced discontinuities (Bahorich & Farmer, Reference Bahorich and Farmer1995).
Rock mechanics parameters
Young’s modulus and Poisson’s ratio are elastic mechanical properties. In this study, the rock mechanical parameters were obtained through triaxial mechanical experiments.
The maximum confining pressure of a triaxial rock mechanics tester is 100 MPa, the maximum simulated well depth is 10 000 m and the system accuracy error is less than 0.0005 %. The simulated formations are ultra-deep (>6000 m). Due to the deep buried depth (about 7000 m), the real geological conditions are inaccessible, hence, only the experimental conditions with the highest temperature and pressure can be selected. The ones with confining pressure of 60 MPa and temperature of 140 °C were selected.
Present in situ stress magnitude
The distribution of present in situ stress is mainly reflected in its direction and magnitude. For a strike-slip fault, reliable in situ stress results can be obtained only by using a variety of effective methods. In this paper, the acoustic emission (AE) experiment and logging evaluation method were used to determine the in situ stress magnitude of the target layer.
Acoustic emission (AE) experiment
The principle of the AE experiment is based on the Kaiser effect. The Kaiser effect means that the internal strain energy of rock will be released quickly after deformation. When the stress reaches the maximum stress in history, the elastic wave release phenomenon will be very obvious (Kaiser. Reference Kaiser1950). Kanagawa et al. (Reference Kanagawa, Hayashi and Nakasa1977) first applied this method to the calculation of in situ stress. The present in situ stress results obtained by other methods can be used as the basis for calibration points (Lan et al. Reference Lan, Song, Li and Liu2021). A Triaxial Rock mechanics tester is used for loading, and a rock acoustic emission high-performance analyser is used to monitor the Kaiser point. Experiments were carried out under conditions of confining pressure 20 MPa, pore pressure 0 MPa and room temperature. According to the measured Kaiser effect point stress, the principal stress is calculated as follows:
\begin{align}&
\quad \quad \quad \quad \qquad {\sigma _v} + {\sigma _ \bot } + \alpha {p_p} - {p_c}\\
{\rm{ }}{\sigma _H} &= {{{\sigma _0} + {\sigma _{90}}} \over 2} + {{{\sigma _0} - {\sigma _{90}}} \over 2}{\left( {1 + {{\tan }^2}2\theta } \right)^{{1 \over 2}}} + \alpha {p_p} - {p_c}\\
{\rm{ }}{\sigma _h} &= {{{\sigma _0} + {\sigma _{90}}} \over 2} + {{{\sigma _0} - {\sigma _{90}}} \over 2}{\left( {1 + {{\tan }^2}2\theta } \right)^{{1 \over 2}}} + \alpha {p_p} - {p_c}\\
\textrm{tan 2}\theta &= {{{\sigma _0} + {\sigma _{90}} - 2{\sigma _{45}}} \over {{\sigma _0} - {\sigma _{90}}}}\end{align}
where
${\sigma _ \bot }$
(MPa) is the Kaiser point stress of the vertical coring rock sample,
${\sigma _0}$
(MPa) is the Kaiser point stress of 0° coring rock sample,
${\sigma _{45}}$
(MPa) is the Kaiser point stress of 45° coring rock sample,
${\sigma _{90}}$
(MPa) is the Kaiser point stress of 90° coring rock sample, Pp (MPa) is the pore pressure, P
C (MPa) is the confining pressure and α is the effective stress coefficient.
Logging evaluation
The vertical principal stress is determined by the gravitational gradient of the overlying strata and can be obtained by integrating the density logging curve using
$${\sigma _{\rm{V}}} = \mathop \int \nolimits_0^H \rho \left( z \right)g$$
where
${\sigma _{\rm{V}}}$
(MPa) is vertical stress, H (m) is burial depth and ρ(z) is rock density at burial depth z, which can be acquired from density logging data.
The horizontal principal stress is evaluated by Huang’s model, and the evaluation formula is as follows (Yin et al. Reference Yin, Ding, Zhou, Shan, Xie, Guo, Cao, Wang and Wang2017):
$${\sigma _{\rm{H}}} = \left( {{\mu \over {1 - \mu }} + {\omega _1}} \right)\left( {{\sigma _{\rm{V}}} - \alpha {P_{\rm{P}}}} \right) + \alpha {P_{\rm{P}}}$$
$${\sigma _{\rm{h}}} = \left( {{\mu \over {1 - \mu }} + {\omega _2}} \right)\left( {{\sigma _{\rm{V}}} - \alpha {P_{\rm{P}}}} \right) + \alpha {P_{\rm{P}}}$$
where
${\sigma _{\rm{H}}}$
(MPa) is the maximum horizontal principal stress,
${\sigma _{\rm{h}}}$
(MPa) is the minimum horizontal principal stress,
${\sigma _{\rm{V}}}$
(MPa) is the vertical principal stress,
${\omega _1}$
and
${\omega _2}$
are the horizontal in situ stress coefficients (the coefficient is obtained by fitting the sample stress obtained by the experiment with the logging curve at the same depth),
$\alpha $
is the Biot coefficient,
$\mu $
is the static Poisson’s ratio and
${P_{\rm{P}}}$
(MPa) is the pore pressure.
Present in situ stress direction
The present in situ stress direction in the T-SH area was based on the present regional in situ stress field direction diagram, combined with the borehole breakout method and drilling-induced fracture analysis method (Nelson et al. Reference Nelson, Meyer, Hillis and Mildren2005). Analyses of borehole breakout and drilling-induced fractures allow us to infer
${\sigma _{\rm{h}}}$
and
${\sigma _{\rm{H}}}$
directions (Zoback et al. Reference Zoback, Barton, Brudy, Castillo, Finkbeiner, Grollimund, Moos, Peska, Ward and Wiprut2003).
Borehole breakout method
The principle of the borehole breakout method is that the rock around the borehole is affected by the horizontal differential stress to form a breakout phenomenon. The
${\sigma _{\rm{h}}}$
direction is parallel to the major axis of the ellipse, while the
${\sigma _{\rm{H}}}$
direction is parallel to the minor axis (Nelson et al. Reference Nelson, Meyer, Hillis and Mildren2005)
Drilling-induced fracture analysis method
The principle of the drilling-induced fracture analysis method is that the rock will produce induced fracture under the influence of stress. The drilling-induced fracture strike is consistent with the
${\sigma _{\rm{H}}}$
direction (Zoback et al. Reference Zoback, Barton, Brudy, Castillo, Finkbeiner, Grollimund, Moos, Peska, Ward and Wiprut2003).
Results
Present in situ stress measurement
Present in situ stress direction
The in situ stress direction in the T-SH area is roughly NE–SW-trending (Heidbach et al. Reference Heidbach, Rajabi, Ziegler and Reiter2016). Due to the influence of fault, different lithology and structure, the in situ stress direction varies significantly. In order to accurately determine the present in situ stress direction in the T-SH area, the in situ stress direction of a single well in the study area was statistically analysed. Through various methods (borehole breakout method, drilling-induced fracture method, wave velocity anisotropy experiment, palaeomagnetic method and dipole acoustic logging data), the in situ stress direction of six wells (S1–S6) in the T-SH area was analysed.
Borehole breakout in well S1 (7774.8–7776.0 m, MD) indicated that the
${\sigma _{\rm{H}}}$
direction is NE25° (Fig. 5a). Borehole breakout in well S2 (7462.3–7464.3 m, MD) indicated that the
${\sigma _{\rm{H}}}$
direction is NE20° (Fig. 5b). According to the borehole breakout method, the
${\sigma _{\rm{H}}}$
direction of well S3 (7550.4–7552.4 m, MD) is NE30° (Fig. 5c). The
${\sigma _{\rm{H}}}$
direction of well S5 (7709.6–7713.2 m, MD) obtained by the borehole breakout method is NE50° (Fig. 5d). In the 7604.4–7606.3 m, MD section of well S1, the drilling-induced fracture rose diagram shows that the strike is NE30°, indicating that the
${\sigma _{\rm{H}}}$
direction is NE30° (Fig. 5e). The
${\sigma _{\rm{H}}}$
direction of well S1 obtained by the borehole breakout method and the elliptical borehole method is basically the same. The main strike of the drilling-induced fracture of well S4 is NE60° (Fig. 5f), indicating that the
${\sigma _H}$
direction is NE60°.
Fig. 5. Analysis of present in situ stress direction. (a) Borehole breakout direction of well S1 (7774.8 –7776.0 m); (b) borehole breakout direction of well S2 (7462.3–7464.3 m); (c) borehole breakout direction of well S3 (7550.4–7552.4 m); (d) borehole breakout direction of well S5 (7709.6–7713.2 m); (e) strike of drilling-induced fracture in well S1 (7604.4–7606.3 m); (f) strike of drilling-induced fracture in well S4 (7710.7–7712.9 m).
The palaeomagnetic method and the wave velocity anisotropy method were applied to 11 core samples from well S3. The core samples were taken from the Yijianfang Formation. According to statistics, the
${\sigma _{\rm{H}}}$
direction is NE74°. According to the anisotropy of wave velocity, the
${\sigma _{\rm{H}}}$
direction measured in well S6 is NE24.2°. The logging data collected show that the
${\sigma _{\rm{H}}}$
direction measured by the fast shear wave method in well S4 is NE43.3°.
Due to the influence of fault, lithology and structural characteristics, the
${\sigma _{\rm{H}}}$
direction measured in each single well changes greatly (Table 2). The direction of in situ stress obtained by a single well is consistent with the direction of regional in situ stress (NE-trending). Considering that the change of in situ stress direction in the study area and the data of
${\sigma _{\rm{H}}}$
obtained by each single well is small (except for well S3), the average value of these data is taken as the boundary condition of the present in situ stress direction (Table 2). Based on these methods, the present maximum horizontal principal stress direction in the T-SH area is NE41.4°, which is consistent with the present maximum horizontal stress direction NE–SW in the T-SH area.
Table 2. Statistics of the maximum horizontal stress direction for wells S1–S6 in the T-SH area
Present in situ stress magnitude
In this study, the rock acoustic emission test results of wells S3 and S5 and the logging data calculation results of well S7 are used as reference data to determine the present in situ stress magnitude in the T-SH area.
Well S5 is located near the SB5 fault. The experimental samples are cores with well depths of 7656.38–7656.46 m (MD) and 7656.46–7656.57 m (MD), which are within the target layer. The measured
${\sigma _{\rm{V}}}$
is 189.1 MPa, the
${\sigma _{\rm{H}}}\;$
is 191.52 MPa and the
${\sigma _{\rm{h}}}$
is 141.25 MPa (Table 3). The measured data of well S3 are from the acoustic emission test results of 12 core samples. The test shows that the average
${\sigma _{\rm{V}}}$
is 182.39 MPa, the average
${\sigma _{\rm{H}}}$
is 174.73 MPa and the
${\sigma _{\rm{h}}}$
is 133.27 MPa (Table 3). For the 7650–7690 m (MD) section of well S7, the present in situ stress is calculated using poro-elastic formation, and calibrated against the measured point. The present in situ stress is composed of rock mass self-weight stress, tectonic movement stress, fluid seepage stress and other stresses (geothermal, geochemical, etc.). The calculated average
${\sigma _{\rm{V}}}\;$
is 181.4 MPa, the average
${\sigma _{\rm{H}}}$
is 167.1 MPa and the
${\sigma _{\rm{h}}}$
is 136.5 MPa (Fig. 6). Based on these analysis and test results, the average
${\sigma _{\rm{V}}}$
is 184.57 MPa, the average
${\sigma _{\rm{H}}}$
is 177.78 MPa and the
${\sigma _{\rm{h}}}$
is 137.01 MPa (Table 3). The present in situ stress in the T-SH area is defined as the loading boundary condition.
Table 3. Present in situ stress test and calculation results for wells S3, S5 and S7
Fig. 6. Calculation of present in situ stress using conventional logging (acoustic logging, density logging) of well S7 (7650–7690 m). Column 1: shear sonic, acoustic and density logs; column 2: static Poisson’s ratio and Poisson’s ratio; column 3: shear modulus and bulk modulus; column 4: compressive strength and cohesive force; column 5: internal friction angle; column 6: minimum horizontal principal stress, maximum horizontal principal stress and vertical principal stress.
Present in situ stress field simulation
The primary steps of the 3D FEM include model-building, rock mechanical parameter assignment, meshing, stress loading, calculation and result analysis.
Model-building
The geological model takes the T7 4 interface (the top of the Ordovician Yijianfang Formation) as the top surface, and the layer depth is 1000 m. The depth of the T7 4 interface is determined according to the contour map of the northern section of the SB5 fault (Fig. 7). The model considers the attitude and style of the northern section of the SB5 fault (Fig. 8a, b). In order to consider the stress effect of the overlying formation on the target layer, an overburden from the surface to the buried depth of 9000 m is established. The purpose of the overburden is to realize the loading of vertical stress (gravity).
Fig. 7. Present buried depth map of T7 4 interface in the northern section of the SB5 fault.
Fig. 8. (a) 3D strike-slip fault model. (b) 3D strike-slip fault and target layer model. (c) Boundary conditions of stress simulation of the northern section of the SB5 fault.
To establish the geological model of the fault, firstly, according to the plane coherence properties (Fig. 3a), the key breakpoints of the fault were selected on the equidistant survey line. The X, Y and Z coordinates of the breakpoints were determined and imported into software to restore the strike and dip angle of the fault. Secondly, based on the interpretation of the corresponding seismic profile (Fig. 3b–d), we could clearly identify the dip direction. Combined with plane coherence properties and seismic profile, the occurrence of the northern section of the SB5 fault is inputted in software. For the formation near the fault, 50 equidistant data points with three-axis coordinates were derived from the contour map of the T7 4 interface (Fig. 7) in the X and Y directions. A total of 2500 data points were imported into the software and combined to form a whole, which has the actual buried depth. After these two kinds of geological models were established, the formation and fault were combined by overlap operation in the software (Fig. 8a, b).
Rock mechanics parameter assignments
The geological model of the northern section of the SB5 fault has established three types of units: fault, formation near the fault and overburden.
The fault is composed of fault gouge and broken breccia (Billi et al. Reference Billi, Salvini and Storti2003), and drilling results show that the SB5 fault has this characteristic. It is difficult to obtain samples inside the fault to carry out mechanical parameter experiments. Because the rock strength inside the fault is low, this simulation refers to the rock mechanics parameters of mudstone. The Young’s modulus and Poisson’s ratio of the fault are 10 GPa and 0.35 respectively.
The target formation is an ultra-deep formation (>6000 m) with high temperature and pressure. In order to achieve the real geological conditions, the samples used were those with confining pressure of 60 MPa and temperature of 140 °C in well S3 (Table 4). According to the selected sample data, the average value was taken as the rock mechanics parameters of the formation near the fault. The Young’s modulus is 58 GPa and the Poisson’s ratio is 0.287.
Table 4. Evaluation of the experimental results of rock mechanics in well S3
The overburden can be regarded as a geological body from the surface to 9000 m underground, and the overall temperature and pressure conditions are lower than those of ultra-deep formation. Therefore, the samples with confining pressure of 15 MPa and temperature of 30 °C in well S5 were selected as rock mechanics parameters (Table 5). The Young’s modulus and Poisson’s ratio of the overburden are 41 GPa and 0.295 respectively. The fault and target formation are embedded into this overburden.
Table 5. Evaluation of the experimental results of rock mechanics in well S5
Meshing
A key parameter of FEM is mesh generation. After determining the rock mechanics parameters and establishing the geomechanical model, according to the strain characteristics of different rocks different types of grid elements are selected for the division of geomechanical models to obtain the finite-element model. For the T-SH area, the Solid95 element is selected to grid the geological model. The Solid95 element constructs a 3D finite-element model through 20 nodes, each node having three degrees of freedom in the X, Y and Z directions, and the element has the capabilities of plasticity, creep, expansion, stress strengthening, large deformation and large strain, which is closest to the actual geological body (Sun et al. Reference Sun, Hou and Zheng2019). In the process of meshing, different models should be given different grid lengths. In order to more finely reflect the stress distribution of the strike-slip fault, the grid length of the strike-slip fault is smaller than that of the formation. The geological model (fault and formation) of the north section of the SB5 fault constitutes 94 444 elements and 142 218 nodes.
Based on the establishment of the geological model and determination of various rock mechanics parameters, the model can be loaded and solved according to the present in situ stress direction. The vertical direction of the model is Z-axis upward. The X-axis trends E–W, and the Y-axis N–S.
Distribution of the present in situ stress
Based on the requirements of FEM computation (the model has no overall translation and rotation, and can calculate and obtain the convergence solution), the loading conditions are imposed on the model (Fig. 8c). The loading method is to constrain the bottom surface of the footwall of the model and fix its displacement in the Z direction, which can reduce the deformation of the footwall base rock. The applied boundary forces include horizontal tectonic force and gravity. The
${\sigma _{\rm{h}}}$
and
${\sigma _{\rm{H}}}$
direction for loading at overburden are SE131.4°–NW311.4° and NE41.4°–SW221.4°, and the
${\sigma _{\rm{h}}}$
and
${\sigma _{\rm{H}}}$
magnitudes for loading at overburden are 137.01 MPa and 177.78 MPa. In the vertical direction, the loading stress is gravity, and the loading method is to apply the gravity acceleration of 9.8 N kg−1 on the overburden.
The distributions of the present in situ stress of the target formation are shown in Figure 9. The range of σ 1 in the formation around the strike-slip fault is 185 –195 MPa, the range of σ 3 in the uplift segment is 180 –190 MPa and the value of σ 1 near the strike-slip fault is larger than 200 MPa. The range of σ 2 in the formation around the strike-slip fault is 163–177 MPa, and the range of σ 1 in the uplift segment is 150 –165 MPa. The range of σ 3 in the formation around the strike-slip fault is 130 –145 MPa, the range of σ 3 in the uplift segment is 130 –135 MPa and the value of σ 1 near the strike-slip fault is larger than 150 MPa.
Fig. 9. Present triaxial stress magnitude in the northern section of the SB5 fault.
Discussion
Distribution of present in situ stress
The σ 1 direction near the strike-slip fault is vertical. However, the σ 1 direction in the uplift segment is horizontal. In seismic section, compared with the surrounding formation, the uplift amplitude of the uplift segment is larger than 20 ms, and the maximum value can exceed 60 ms. The reason for the change of stress direction is that the buried depth of the uplift segment in the strike-slip fault is shallower than that of the nearby formation. The horizontal stress is larger than the vertical stress in shallow formation. Brown & Hoek (Reference Brown and Hoek1978) provided statistics on the distribution law of the ratio of the global measured horizontal average principal stress to the vertical stress with the buried depth, as shown in the formula
$${{100} \over H} + 0.3 \le {{{\sigma _{\rm{H}}} + {\sigma _{\rm{h}}}} \over {2{\sigma _{\rm{V}}}}} \le {{1500} \over H} + 0.5$$
where
${\sigma _{\rm{H}}}$
(MPa) is the maximum horizontal principal stress,
${\sigma _{\rm{h}}}$
(MPa) is the minimum horizontal principal stress (MPa),
${\sigma _{\rm{V}}}$
(MPa) is the vertical principal stress and
$H$
(m) is buried depth.
The Anderson fault formation mechanism describes the mechanical state of different faults (Anderson, Reference Anderson1951). The fault primarily formed under a strike-stress regime, forming the strike-slip fault system. A change of stress state occurred in time, resulting in reactivating the system under a normal stress regime. According to the Anderson model, it is found that the strike-slip fault of the target layer in the T-SH area is now in the normal fault stress state, and the horizontal compression is significant. For the uplift segment, it is in a state of strike-slip stress, and the horizontal compression is more significant.
It is well established that fault perturbations will tend to deflect the stress in a certain trend (Husodon & Cooling, Reference Husodon and Cooling1988). Numerical analysis methods such as finite element (Matsukik et al. Reference Matsukik, Nakama and Sato2009; Bouatia et al. Reference Bouatia, Demagh and Derriche2020), discrete element (Stephansson & Zang, Reference Stephansson and Zang2012) and boundary element (Zhong et al. Reference Zhong, Xu, Chen and Ji2010) were also used to study the disturbance law of fault to local stress field.
Based on the borehole breakout method, the drilling-induced fracture method, palaeomagnetic experiment and wave velocity anisotropy analysis, it is determined that the average
${\sigma _{\rm{H}}}$
direction in the T-SH area is NE41.1° (Table 3). The finite-element numerical simulation of the maximum horizontal principal stress direction in the northern section of the SB5 fault is carried out using ANSYS software to study whether the fault interactions will perturb the stress orientation. The simulation results show that the σ
2 direction near the strike-slip fault is horizontal and the overall direction is NE–SW-trending. In the formation near the strike-slip fault, there is no obvious change in the σ
2 direction, which is consistent with the measured data. Near the strike-slip fault, the σ
2 direction deflects, and the closer it is to the fault, the greater the angular deflection. The deflection of the σ
2 direction has a trend parallel to the strike of the fault (Fig. 10a). For the uplift segment, in the nearby formation, the σ
2 direction is horizontal, which is consistent with the regional stress field direction. Near the fault, the σ
2 direction deflects anticlockwise, which is parallel to the strike of the fault. In the uplift segment, the σ
2 direction is vertical and the σ
3 direction is horizontal (Fig. 10b). The uplift segment is a structural high part formed under the combined action of shear stress along the fault strike direction and compressive stress. The buried depth is relatively shallow with the surrounding formation. The horizontal principal stress of the shallow buried formation is generally higher than the vertical principal stress (Brown & Hoek, Reference Brown and Hoek1978).
Fig. 10. Characterization of σ 2 in (a) the northern section of the SB5 fault and (b) the uplift segment. As shown, σ 2 starts deflecting from NE–SW-trending when approaching the strike-slip fault, until it switches from the horizontal to the vertical within the uplift segment.
In situ stress partitioning into several segments
Using the numerical simulation results for the northern section of the SB5 fault, the triaxial principal stress and stress anomaly range of the uplift segment, pull-apart segment and translation segment are compared (Fig. 11; Table 6). In each segment, the stress can be divided into three parts: inside the fault, inside the segment and near the fault. The stress differences for each of these three parts are compared. Inside the fault, the in situ stress magnitude of the three segments is smaller than that in the surrounding formation. The smaller value is similar in the three segments. Inside the segment, the in situ stress in the uplift segment and pull-apart segment is smaller than that in the surrounding formation. This is related to the fault activity and the mechanical property changes between the three deformation types and the surrounding formation. Near the fault, the σ 1 and σ 3 magnitude in the three segments is larger than that in the surrounding formation, the σ2 magnitude in the three segments is smaller than that in the surrounding formation. Although the abnormal values near different segmented faults are slightly different, the variation is the same. For the range of abnormal stress, the uplift segment is 250–300 m, the pull-apart segment is 150–300 m and the translation segment is 100–250 m. The overall anomaly range is largest in the uplift segment, next largest in the pull-apart segment and smallest in the translation segment.
Fig. 11. Triaxial principal stress distribution of different strain segments along the SB5 fault.
Table 6. Statistics of triaxial principal stress anomalies along different strain segments of the SB5 fault
Notes: ↑ indicates that the stress is more than the principal stress of the surrounding formation; ↓ indicates that it is less than the stress of the surrounding formation.
Present in situ stress application
Hydraulic fracturing
Rock is in a complex stress state composed of overlying formation pressure, tectonic stress, wall rock pressure and pore fluid pressure (Aadnoy, Reference Aadnoy1989; Marques et al. Reference Marques, Ranalli and Mandal2018). Due to the difference of in situ stress state, the rock has different fracture propagation patterns, resulting in the formation of a variety of fractures with different properties and occurrence (Schultz, Reference Schultz2000; Griffith et al. Reference Griffith, Becker, Cione, Miller and Pan2014; Lee et al. Reference Lee, Olson and Schultz2018). The present in situ stress state directly controls the occurrence and propagation trending of fractures produced by acid fracturing (K Zhao et al. Reference Zhao, Jiang, Feng, Sun, Cheng and Zheng2021).
According to the formation conditions, fractures can be divided into three types: shear fractures, tension fractures and mixed modes (Zhu & Song, Reference Zhu and Song1990; Zeng et al. Reference Zeng, Qi and Wang2007). The in situ stress controlling the formation of shear fractures is compressive stress, generally as a conjugate set of two fractures. The tensile fracture also has the characteristics of displacement direction perpendicular to and away from the fracture surface, and the minimum principal stress direction is perpendicular to the fracture surface, but the basic condition for forming the tensile crack is that at least one principal stress is the tensile stress.
The numerical simulation results show that the present in situ stress along the target formation of the SB5 fault is compressive stress. Therefore, the fractures produced by acid fracturing are mainly shear fractures, tensile fractures cannot be produced and the fracture surface is perpendicular or approximately perpendicular to the σ 3 direction. The σ 3 direction in the T-SH area is NW–SE-trending, resulting in high-angle fractures from acid fracturing. The propagation direction of hydraulic fractures is consistent with the σ 2 direction. Along the SB5 fault, except for the uplift segment, the present in situ stress state is: vertical σ 1, NE–SW-trending σ 2 and NW–SE-trending σ 3 (Figs 12d, 11e–i). Therefore, the fractures due to acid fracturing are mainly high-angle fractures, and the main propagation direction is NE–SW-trending (Fig. 13a). This kind of fracture has stronger horizontal communication ability and communicates more easily with multiple sets of fault–fracture reservoirs. The present in situ stress state in the uplift segment is: NE–SW-trending σ 1, vertical σ 2 and NW–SE-trending σ 3 (Fig. 12a–c). Under the control of such a stress state, although the fractures produced by acid fracturing are mainly high-angle fractures, their propagation direction is mainly longitudinal (vertical) (Fig. 13b). This type of fracture communicates more easily with deep reservoirs.
Fig. 12. (a) σ 1 direction in the uplift segment; the exterior is vertical, the interior is NE–SW-trending. (b) σ 2 direction in the uplift segment; the exterior is NE–SW-trending, the interior is vertical. (c) σ 3 direction in the uplift segment; the whole is NW–SE-trending. (d) σ 1 direction in the pull-apart segment; the whole is vertical. (e) σ 2 direction in the pull-apart segment; the whole is NE–SW-trending. (f) σ 3 direction in the pull-apart segment; the whole is NW–SE-trending. (g) σ 1 direction in the translation segment; the whole is vertical. (h) σ 2 direction in the translation segment; the whole is NE–SW-trending. (i) σ 3 direction in the translation segment; the whole is NW–SE-trending.
Fig. 13. Propagation mode for fractures from acid fracturing under different stress conditions along the SB5 fault. (a) σ 2 direction is horizontal; high-angle fracture propagates along horizontal direction. (b) σ 2 direction is vertical; high-angle fracture propagates along horizontal direction.
Effectiveness evaluation of natural fractures
Present in situ stress not only controls the propagation trend of fractures from acid fracturing, but also controls the opening trend of pre-existing natural faults and fractures. The smaller the angle between the natural fracture strike and the
${\sigma _{\rm{H}}}$
direction, the easier it is to open (Angelier et al. Reference Angelier, Slunga, Bergerat, Stefansson and Homberg2004; Zoback, Reference Zoback2007; Angelier & Baruah, Reference Angelier and Baruah2009; Zhao et al. Reference Zhao, Zhao, Kong, Deng and Li2020). Based on the numerical simulation of the present in situ stress field in the SB5 fault, the opening trend of the fault and fracture can be qualitatively evaluated. In this study, the natural fault–fracture opening trend of well S2 is qualitatively evaluated.
Well S2 has conducted four sidetracks: three of these are NE-trending, and mainly intersected NW–SE-trending faults and fractures, whilst the fourth sidetrack is NE-trending and mainly intersected NE–SW-trending faults and fractures.
A total of 21 fractures were identified by image logging; their strikes were both NE–SW-trending and NW–SE-trending, with the two sets showing both low and high dip angles (Fig. 14). The three sidetracks mainly encountered NW–SE-trending faults and fractures, with only a small total hydrocarbon display. The fourth sidetrack intersected mostly low-angle NE–SW-trending fractures, with larger total hydrocarbon display (Fig. 15). This is consistent with the medium–high permeability values (up to 162 md) of the formation. The
${\sigma _{\rm{H}}}$
direction is NE–SW-trending. Under this condition, NW–SE-trending fractures do not open, but NE–SW-trending fractures open, resulting in a larger display of total hydrocarbons. Therefore, present in situ stress direction can be used to evaluate the effectiveness of natural faults and fractures, and then provide a basis for drilling trajectory optimization and reservoir reconstruction measures.
Fig. 14. Dip angles (a) and strikes (b) of fractures encountered by well S2.
Fig. 15. (a) Sidetrack directions of well S2 in map view. (b) Vertical borehole S2 and the four sidetracks with different directions. (c) Hydrocarbon shows for the vertical well. (d–g) Hydrocarbon displays for the four sidetracks.
Conclusion
In the T-SH area, the σ 1 magnitude is 185 –195 MPa, the σ 2 magnitude is 163 –177 MPa and the σ 3 magnitude is 130–145 MPa. For strike-slip fault and surrounding formation, the σ 1 direction is vertical, and the σ 2 and σ 3 directions are horizontal, belonging to a normal fault stress state. For the uplift segment, due to the relatively low buried depth, the σ 2 direction is vertical and the σ 1 and σ 3 directions are horizontal, belonging to a strike-slip fault stress state.
The average
${\sigma _{\rm{H}}}$
direction in the T-SH area is NE41.1°. With the existence of a strike-slip fault, the
${\sigma _{\rm{H}}}$
direction will deflect. The
${\sigma _{\rm{H}}}$
direction near the fault tends to be consistent with the fault strike.
The segmentation of the strike-slip fault has only local influence on the present in situ stress. The present stress field is mainly affected by the shape, scale and quantity of pre-existing faults. It is shown that the triaxial principal stress is relatively small as a whole, and the range of stress anomaly is slightly different, being 2–6 times the width of the fault. The abnormal range of the uplift segment is the largest, the pull-apart segment is second largest and the translation segment is smallest.
Controlled by the present in situ stress, the propagation trend of fractures is different in different areas. In the uplift segment, the σ 1 direction is horizontal, and the fractures caused by acid fracturing mainly extended vertically. This type of fracture allows easier communication with the deep reservoir. In other areas, the σ 1 direction is vertical and the propagation direction of high-angle fractures caused by acid fracturing is NE–SW-trending. This kind of fracture has strong horizontal communication ability, and is therefore able to improve connectivity amongst fault–fracture reservoirs.
The smaller the angle between the natural fracture strike and the
${\sigma _{\rm{H}}}$
direction, the easier it is to open. Therefore, present in situ stress direction can be used to qualitatively evaluate the effectiveness of natural fractures, so as to provide a basis for drilling-trajectory optimization and reservoir reconstruction measures.
Acknowledgements
This work was financially supported by the National Natural Science Foundation of China (NSFC) (Grant No. 42072173) and the Joint fund for enterprise innovation and development of National Natural Science Foundation of China ‘Study on enrichment mechanism and key engineering technology of marine deep oil and gas’ (U19B6003). Dr Ahmed E Radwan thanks the Priority Research Area Anthropocene under the program ‘Excellence Initiative—Research University’ at the Jagiellonian University in Kraków.
Conflict of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
