Introduction

With increasing depletion of conventional natural resources, more attention has been focused on deep and ultra-deep reservoirs, and natural gas from these reservoirs has become an important contributor to global reserve growth and deliverability construction. Currently, the critical depth for deep and ultra-deep reservoirs varies among different countries, and a standard and unified definition has not emerged because of geological differences (Dyman et al. 1998; Zhang et al. 2015; Feng et al. 2016). In western China, a “deep reservoir” is generally considered to correspond to a burial depth larger than 4500 m, and an “ultra-deep reservoir” corresponds to a depth over 6000 m (Wang 2012). Recent exploration indicates that natural gas resources are abundant within deep and ultra-deep reservoirs in western China, especially the Kelasu tectonic zone of Kuqa Depression, Tarim Basin (Tian et al. 2020; Xu et al. 2020; Zeng et al. 2020).

During drilling process and further development of deep and ultra-deep natural gas resources, an accurate understanding of the distribution of present-day in situ stresses is important to effectively prevent borehole collapses, reduce drilling costs, guide hydraulic fracturing, and improve reservoir management (Zoback et al. 2003; Tingay et al. 2009; Kingdon et al. 2016; Rajabi et al. 2016; Ju et al. 2017, 2018a). Common descriptions of the present-day in situ stress state are based on the magnitudes of vertical stress (Sv), horizontal maximum principal stress (SHmax), horizontal minimum principal stress (Shmin), and the orientation of SHmax (Zoback et al. 2003; Rajabi et al. 2016). The present-day in situ stress state in a sedimentary basin may change both laterally and vertically due to the development and distribution of faults, lithological differences, etc. Anderson delineated three types of stress regimes based on their relative stress magnitudes: the normal faulting stress regime (Sv>SHmax>Shmin), strike-slip faulting stress regime (SHmax>Sv>Shmin), and reverse faulting stress regime (SHmax>Shmin>Sv) (Anderson 1951).

The Bozi 3 Block of Kelasu tectonic zone is a typical deep sandstone reservoir in the Kuqa Depression, which is characterized by low permeability, low porosity, and strong heterogeneity. Therefore, natural gas within this block cannot be produced naturally and production intervention is required to obtain commercial quantity of gas (Holditch 2006; Ju and Wang 2018). Hydraulic fracturing is an important production intervention approach that has proven to be effective for commercial gas development. This approach depends partially on the present-day in situ stress (Zoback 2007; Rajabi et al. 2016; Ju et al. 2020); hence, accurate prediction of the present-day stress field is extremely significant for effective gas production in the Bozi 3 Block of Kuqa Depression.

The present-day in situ stress data can be obtained from actual measurements; however, measured data for the Bozi 3 Block are limited and widely spread over a large scale, precluding discernment of the overall characteristics of the stress distribution. Therefore, the objective of this study is to delineate the present-day in situ stress state of the Bozi 3 Block of Kuqa Depression, based on stress indicator interpretation, well log calculation, and numerical simulation, and to analyze the effects of stress distribution on deep resource development. The results are expected to provide geological references for natural gas production in the study area.

Geologic setting

The Kuqa Depression, known as the Kuche Depression, is located along the northern margin of Tarim Basin with an ENE-WSW trend (Fig. 1). Based on tectonic characteristics, the Kuqa Depression is laterally divided into the northern monocline belt, Kelasu-Yiqikelike structural belt, Baicheng and Yangxia sags, and Qiulitage structural belt from north to south (Fig. 1; Allen and Vincent 1999; Zeng et al. 2010; Ju and Wang 2018). Faults and folds are well developed in the Kelasu-Yiqikelike structural belt (Fig. 1). Furthermore, the Kelasu structural belt can be divided into the Keshen segment, Dabei segment, Bozi segment, and Awate segment from east to west, where the Bozi 3 deep sandstone reservoir is located in the Bozi segment (Fig. 1).

Fig. 1
figure 1

(a) Structural simplified map of the Kuqa Depression in the Tarim Basin; (b) Structural framework of the Kelasu structural belt

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The Bozi 3 Block is a diamond-shaped, deeply buried area in the Kuqa Depression (Fig. 2), within which, the main natural gas production layers are the Cretaceous deposits, including the Bashijiqike (K1bs) Formation and Baxigai (K1bx) Formation. The formations mainly consist of a series of sandstone and mudstone (Fig. 3). Reservoir test results for the entire Bozi segment indicate that the Bashijiqike Formation is characterized by low porosity and permeability. The effective porosity mainly ranges from 3.5 to 10.0% with an average of 6.30%. The matrix permeability varies between 0.10 and 0.50 mD (Wei et al. 2020). These results suggest that technologies, such as hydraulic fracturing, are required to obtain high natural gas production from the Bozi 3 deep sandstone reservoir.

Fig. 2
figure 2

Structural map of the top Cretaceous in the Bozi 3 Block of Kuqa Depression. The area with yellow background in this figure indicates the Bozi 3 Block

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Fig. 3
figure 3

Stratigraphic column of the Cretaceous in the Bozi 3 Block of Kuqa Depression

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Interpretation of the S Hmax orientation

Many methods can be applied to determine the SHmax orientation. The most commonly used approach in petroleum and natural gas industry is the interpretation of drilling-induced tensile fractures (DITFs) and borehole breakouts from imaging logs (Zoback 2007; Ju et al. 2017). DITFs generally exhibit two patterns: (1) Pattern I, which symmetrically aligned fractures lie parallel or subparallel to the borehole axis on opposite sides of the borehole wall (Fig. 4a); and (2) Pattern II, in which en-echelon fractures lie around the borehole with traces that are 180° apart (Fig. 4b). Borehole breakouts commonly appear in imaging logs as broad, parallel conductive zones separated by approximately 180° (Fig. 4c).

Fig. 4
figure 4

Drilling-induced tensile fractures and breakouts from borehole imaging logs in the Bozi 3 Block of Kuqa Depression. (a) Well Z3, drilling-induced tensile fractures, pattern I; (b) Well Z3, drilling-induced tensile fractures, pattern II; (c) Well Z1, borehole breakouts

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Previous studies have proven that borehole breakouts have a perpendicular orientation to the SHmax, and DITFs indicate the orientation of SHmax (Zoback et al. 2003; Rajabi et al. 2016; Ju and Wang 2018).

In this study, DITFs and borehole breakouts were interpreted from imaging logs of Well Z1, Well Z2, and Well Z3 (Fig. 4). Overall, the SHmax orientation indicated a dominant NNW-SSE direction (Fig. 5). Additionally, the orientation showed minor variations in different geological locations, which may result from the development of small faults, folds, natural fractures, lithological transitions, or differences (Martin and Chandler 1993; Bell 1996; Ju et al. 2018b).

Fig. 5
figure 5

The SHmax orientation interpreted from DITFs and breakouts in the Bozi 3 Block of Kuqa Depression

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In situ stresses calculated from wells

Method

Generally, the Sv magnitude is the weight of the overburden, which can be calculated by integrating the rock density from the surface to the measured depth (Zoback et al. 2003; Brooke-Barnett et al. 2015; Ju and Wang 2018) using Eq. (1).

$$ {S}_v={\int}_0^z\rho (h)g\ dh $$
(1)

where g is the gravitational acceleration, m/s2; ρ(h) is the density of the overburden rock as a function of burial depth, kg/m3; h is the burial depth from the surface to a particular depth underground, m; z is the target depth, m.

The density logs for the study area are not obtained from the ground level; hence, based on rock mechanics experiments from surface rocks, an extrapolation method with a gradient of approximately 23 kPa/m is used here to determine the Sv magnitude for segments without density logs.

The magnitudes of SHmax and Shmin in this study are calculated using the revised Anderson model (Eq. 2).

$$ \left\{\begin{array}{c}{S}_{\mathrm{Hmax}}=\frac{\mu }{1-\mu}\left({S}_v-\alpha {P}_0\right)+{\alpha P}_0+{S}_T\\ {}{S}_{\mathrm{hmin}}=\frac{\mu }{1-\mu}\left({S}_v-\alpha {P}_0\right)+{\alpha P}_0+{S}_t\end{array}\ \right. $$
(2)

where SHmax and Shmin are horizontal maximum and minimum principal stress, respectively, MPa; α is the effective stress coefficient (also the Biot coefficient), unitless; μ is the Poisson’s ratio, unitless; P0 is the pore pressure, MPa; ST and St are the additional tectonic stress corresponding to SHmax and Shmin, respectively, MPa.

The first term on the right hand of Eq. (2) is a linear elastic term for transforming the vertical stress to horizontal stresses. The second term corresponds to the fluid pressure. The third term is related to external sources of stress, such as the tectonic stress.

In situ stress distribution from log calculations

In this study, the log calculation results for Well Z1 show that the SHmax and Shmin magnitudes in the Cretaceous deposits range between 126 and 176 MPa, and 99 and 149 MPa, respectively (Fig. 6). The majority of calibrated stress profiles suggest a dominant strike-slip faulting stress regime in the Cretaceous Baxigai Formation (Fig. 6).

Fig. 6
figure 6

Distribution of the present-day in situ stress magnitudes in Well Z1 of Bozi 3 Block based on well log calculations. Symbols: DEN, rock density, g/cm3; CAL, borehole diameter, cm; GR, gamma ray, API; units for stress magnitude are MPa

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Distribution prediction of in situ stresses

Method

A numerical simulation is performed based on the finite element (FE) technique, where a single complete geometric model is firstly built and discretized into a finite number of continuous elements connected by nodes (Ding et al. 2012). Then, different rock mechanical parameters are assigned to different elements in the geometric model to create a geological model (Ding et al. 2012; Jiu et al. 2013; Ju and Sun 2016). A numerical solution is obtained by transforming the continuous field function of the entire geological body into a node function including basic variations in the stress, strain, and displacement caused by external forces (Ding et al. 2012; Liu et al. 2020).

Elastic mechanics theory is used to express the relationship between the strain and the displacement given in Eq. (3):

$$ \left\{\begin{array}{c}{\varepsilon}_{\mathrm{xx}}=\frac{\partial i}{\partial x},\kern0.5em {\gamma}_{\mathrm{xy}}={\gamma}_{\mathrm{yx}}=\frac{\partial i}{\partial y}+\frac{\partial j}{\partial x}\\ {}{\varepsilon}_{\mathrm{yy}}=\frac{\partial j}{\partial y},\kern0.5em {\gamma}_{\mathrm{yz}}={\gamma}_{\mathrm{zy}}=\frac{\partial j}{\partial z}+\frac{\partial k}{\partial y}\\ {}{\varepsilon}_{\mathrm{zz}}=\frac{\partial k}{\partial z},\kern0.5em {\gamma}_{\mathrm{zx}}={\gamma}_{\mathrm{xz}}=\frac{\partial k}{\partial x}+\frac{\partial i}{\partial z}\end{array}\right.\kern0.5em $$
(3)

where εxx, εyy, and εzz are the linear strain components, and γxy, γyz, and γzx are the shear strain components.

The matrix form is derived as follows (Eq. (4)).

$$ \left[\varepsilon \right]=\left[B\right]\left[\delta \right] $$
(4)

where [δ] is the nodal displacement matrix, [B] is the geometric matrix.

The physical equation can be used to derive the stress and strain given by Eq. (5):

$$ \left[\sigma \right]=\left[D\right]\left[\varepsilon \right] $$
(5)

where [D] is the elasticity matrix.

Geological model setup

The geometric model (Fig. 7a) used in this study was established utilizing finite element ANSYS software (version 14.5; Ansys Inc., Houston, USA) following a forward (dot-line-area-volume) setup order based on the basic conditions shown in Fig. 2, which is generally labor-intensive. The building procedure consists of the following steps: (i) choosing an appropriate element type, (ii) generating different solid model features, and (iii) applying Boolean operators or specific number controls to join separate solid model regions together as appropriate.

Fig. 7
figure 7

The geological model (a) and meshing results (b) of Bozi 3 Block of Kuqa Depression

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Then, the mechanical parameters of sedimentary layers were obtained from the results of rock mechanics experiments, and their average values were used in the established geometric model making a geological model (Table 1). Faults inside the model were represented by weakness zones with relatively low Young’s moduli (Fischer and Henk 2013; Ju and Sun 2016). The magnitude of Young’s moduli are 85% of the corresponding layer based on previous studies (e.g., Jiu et al. 2013; Ju et al. 2018b).

Table 1 Rock mechanics parameters used in this numerical study
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To reduce the calculation complexity and improve the accuracy, all the units in the geological model were discretized using primarily three-node triangular elements (Fig. 7b). Meshing controls were set to obtain the desired mesh density, and nodes and elements were created by meshing the solid model. The entire meshed model contained 80825 nodes and 473069 elements.

Boundary conditions

The study area was nested within a larger rectangular parallelepiped to reduce boundary effects on the modeling results (Fig. 8). The whole geological model was subjected to gravity loading in the vertical direction, which was automatically applied by the software. Based on previous studies (e.g., Zeng et al. 2010; Ju et al. 2018b; Xu et al. 2020), a compressive SHmax magnitude of approximately 165 MPa and a Shmin magnitude of 140 MPa were laterally applied in the ~NNW-SSE and ~ENE-WSW directions, respectively. Appropriate displacement constraints were applied to the geological model to prevent rotation and rigid displacement. In the numerical modeling results presented in Fig. 8, compressive and tensile stresses are indicated by negative and positive values, respectively.

Fig. 8
figure 8

The nested model used in this numerical analysis. The Bozi 3 Block is nested within a larger volume to reduce boundary effects and help apply forces

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Results and error analysis

The simulated results indicated that the SHmax magnitude ranged from − 150 to − 178 MPa, and the Shmin magnitude varied between − 121 and − 157 MPa in the target Cretaceous layers of Bozi 3 Block (Fig. 9a, b). The SHmax and Shmin showed similar distributions, where the negative values indicate that the Bozi 3 deep sandstone reservoir is subjected to compressive stresses. Gravity and boundary stresses play a major role in the study area. The stress values increased with the burial depth (Fig. 9).

Fig. 9
figure 9

The calculated SHmax (a) and Shmin (b) magnitudes in the Bozi 3 Block of Kuqa Depression

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The Bozi 3 Block is currently in the exploration and initial development stage; hence, wide-spread fracturing and horizontal wells have not yet been deployed. Based on the above stress modeling results, an error analysis was carried out using Eq. (6): the errors between the measured and calculated stress magnitudes were extremely low, generally less than 2% (Table 2), which suggests that the modeling results were credible.

$$ r=\frac{\left|\ \mathrm{calculated}\ \mathrm{stress}\ \mathrm{value}-\mathrm{measured}\ \mathrm{stress}\ \mathrm{value}\ \right|}{\mathrm{measured}\ \mathrm{vstress}\ \mathrm{alue}}\times 100\% $$
(6)

where r is the error between the calculated and measured value.

Table 2 Error analysis of numerical stress results in the Bozi 3 Block
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Implications for natural gas development

Effects of the stress field on natural fractures

In deep sandstone reservoirs, natural fractures favorably aligned with the present-day in situ stress field contribute considerably to subsurface fluid flows (Hillis 1997; Rajabi et al. 2016; Ju et al. 2020). Hence, the interpretations presented above show that fluid flows may be enhanced for natural fractures with strikes in the NNW-SSE direction. In addition, hydraulic fracturing is commonly required to increase gas production in deep sandstone reservoirs. During the hydraulic fracturing process, injecting fluids into target subsurface reservoir rocks may produce many geomechanically induced effects, such as the reactivation of natural fractures (Reynolds et al. 2003; Ju et al. 2020).

In this study, reactivation risk plots based on the Mohr’s circle criterion (Mildren et al. 2002) are introduced to analyze the risk of natural fracture reactivation in the Bozi 3 deep sandstone reservoir. The location and pattern of the Mohr’s circle in the shear stress-effective normal stress system is determined by the present-day in situ stress field calculated above. In the Mohr’s Circle, dots (representing fractures) located on the right of the red critical line are stable and not reactivated (Fig. 10). In this study, Well Z3 and the natural fractures developed within this well are selected as examples for analysis. The plots are shown in Fig. 10 with warm colors (red) indicating the highest reactivation risk.

Fig. 10
figure 10

Lower hemisphere stereonet plots and three dimensional Mohr circles showing critically stressed natural fractures in Well Z3 of Bozi 3 Block. The fracture orientations are plotted as the pole of planes with different colors representing the relative ease of fracture susceptibility as the amount of pore pressure increase required to reactivate a fracture. The red colors show the high likelihood of fracture reactivation, while the blue colors indicate the low likelihood of reactivation for all possible fractures in the present-day stress state. Black and white dots in the stereonet plots are normal and critically stressed natural fractures, respectively. In the Mohr circles, black and red dots are normal and critically stressed natural fractures. SG is specific gravity, δp indicates the pore pressure increase

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The interpreted natural fractures with varying orientations clearly indicate different conditions under the present-day in situ stress state (Fig. 10). Natural fractures are generally stable in the present stress field. Injecting fluids into the reservoir rocks, shifting the Mohr’s circle to the left, which increases the reactivation risk for natural fractures. In this study, when the specific gravity reaches 2.15, approximately 75% of all the interpreted natural fractures in Well Z3 are reactivated (Fig. 10), contributing to gas production.

Effects of stress state on hydraulic fractures

The present-day in situ stress field can influence hydraulic fracturing operations. Generally, a newly generated hydraulic fracture will propagate along the path that requires the minimum force (Kingdon et al. 2016). Hence, new horizontal wells should be drilled parallel to the Shmin orientation. Based on the interpreted stress orientation (Fig. 5), horizontal wells in the Bozi 3 deep sandstone reservoir should be drilled following the ENE-WSW trend.

The parameter of the horizontal stress difference coefficient (K; Eq. (7); Liu et al. 2020) is commonly used to determine the propagation of hydraulic fractures.

$$ K=\frac{S_{\mathrm{Hmax}}-{S}_{\mathrm{hmin}}}{S_{\mathrm{hmin}}} $$
(7)

Equation (7) can be used to obtain the spatial distribution of K in the study area. The main distribution of K can be described as follows: (1) the K values range from 0.14 to 1.53; and (2) the K values are controlled by depth, and are high in structurally high areas (Fig. 11). Generally, a small K facilitates the production of fracture networks (Liu et al. 2020). Based on the distribution pattern shown in Fig. 11, the areas around Well Z1 in the Bozi 3 Block are indicative of low K values, which may be viewed as engineering “sweet spots” for subsequent natural gas development.

Fig. 11
figure 11

Distribution of the horizontal stress difference coefficient in the Bozi 3 Block of Kuqa Depression

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Conclusions

Knowledge of the present-day in situ stress field can facilitate deep gas exploration and development in the Bozi 3 Block of Kuqa Depression. In this study, the variation in stress magnitudes and stress orientations were analyzed based on well log calculations and numerical simulations, drilling-induced tensile fractures and borehole breakouts.

  1. (1)

    The SHmax orientation indicates a dominant NNW-SSE direction in the Bozi 3 Block, and it shows minor variations in different geological locations due to lithological differences and the development of faults and natural fractures.

  2. (2)

    Finite element stress simulation results show that the SHmax and Shmin magnitudes in the Cretaceous layers of Bozi 3 Block range between − 150 and − 178 MPa, and − 121 and − 157 MPa, respectively, indicating compression. Burial depth has considerable controlling effects on the stress magnitude distributions. Larger depths generally indicate higher stress magnitudes. The dominant stress regime indicates a strike-slip faulting type in the Cretaceous layers based on well log calculations.

  3. (3)

    Under the present-day in situ stress field in the Bozi 3 Block, horizontal wells should be drilled along the ENE-WSW trend. Nearly 75% of natural fractures are reactivated when the specific gravity reaches approximately 2.15. The areas around Well Z1 are the engineering “sweet spots” for gas development in the Bozi 3 Block.