Formation of Complex Networks

Abstract

When a hydraulic fracture interacts with multiple natural fractures (such as bedding planes, faults, weak interlayers, and formation interfaces) in the formation, arrests, bifurcations, crossings, and openings may occur, contributing to forming a complex fracture network (referred as CFN). Shale differs from other types of rocks due to its apparent bedding anisotropy, making it easier to form complex fracture networks during hydraulic fracturing. A mass of field hydraulic fracturing data and laboratory studies have confirmed that the hydraulic fractures generated in shale reservoirs are not bi-wing planar fractures in homogeneous media, but multi-dimensional, asymmetric, and non-planar complex hydraulic fractures (as shown in Fig. 9.1) (Liu et al. in Guti Lixue Xuebao/Acta Mech Solida Sin 37:34–49, 2016; Xiao in Research of hydraulic fracturing dynamic propagation in fractured reservoirs, 2014; Guo and Wang in J Eng Geol 26:118–128, 2016).

1 Introduction

When a hydraulic fracture interacts with multiple natural fractures (such as bedding planes, faults, weak interlayers, and formation interfaces) in the formation, arrests, bifurcations, crossings, and openings may occur, contributing to forming a complex fracture network (referred as CFN). Shale differs from other types of rocks due to its apparent bedding anisotropy, making it easier to form complex fracture networks during hydraulic fracturing. A mass of field hydraulic fracturing data and laboratory studies have confirmed that the hydraulic fractures generated in shale reservoirs are not bi-wing planar fractures in homogeneous media, but multi-dimensional, asymmetric, and non-planar complex hydraulic fractures (as shown in Fig. 9.1) [1,2,3].

Fig. 9.1

Hydraulic fracture morphology retained by injecting fluid into the particulate material matrix

Although many scholars have investigated hydraulic fracture propagation and evaluated its spatial geometry through field and laboratory tests, most of the problems related to the control and reconstruction of hydraulic fracture networks are still empirical. Since there is no reliable standards to evaluate hydraulic fracturing effectiveness, it is difficult to adjust parameter settings and guide the construction process according to the hydraulic fracture network. Using a conventional hydraulic fracture model to simulate and guide fracturing design may lead to poor fracturing effectiveness or even the failure of fracturing. To qualitatively assess the hydraulic fracturing effectiveness, previous scholars have mainly divided the morphologies of hydraulic fracture into the following categories [4, 5]: (a) single transverse hydraulic fracture; (b) main Arc fracture; (c) fishbone-like complex fracture; (d) complex fracture network (see Fig. 9.2).

Fig. 9.2

Different types of hydraulic fracture morphology

Research on the formation mechanism of complex fracture networks and effective fracture network reconstruction (number and connectivity of HF) have a pronounced impact on enhancing fluid infiltration and improving the extraction rate of shale gas [6]. However, technically limited by hydraulic fracturing (e.g., working pressure and flow), the recovery rate of shale reservoirs fluctuates from 5 to 60%), and the initial recovery rate is quite low (5–15%). The core reason is the stress shadow effect between different hydraulic fractures, which makes it fail to form a fracture network in which multiple fractures simultaneously propagate. Effective fracture networks are fundamental to maximizing the production of shale gas [7, 8]. In addition, high-pressure injection during hydraulic fracturing reduces the effective stress of the local formation, which may induce fault activation and seismic slip [9]. The infiltration of fracturing fluid via secondary fractures can also deteriorate the pollution of groundwater. Therefore, it is particularly important to understand the formation mechanism of the complex fracture networks.

Based on experimental set-ups used for uniaxial and true triaxial hydraulic fracturing described in Chap. 2, this chapter investigated the deformation and hydraulic fracture propagation in different types of shales (Longmaxi shale and Lushan shale), bedding inclinations (β = 0°, 45° and 90°) and stress levels (uniaxial stress state (σ_H > σ_v = σ_H = 0), normal-faulting stress regime (σ_v > σ_H > σ_h), strike-slip faulting stress regime (σ_H > σ_v > σ_h) and reverse faulting stress regime (σ_H > σ_h > σ_v), and qualified the formation mechanism of the complex fracture networks. The results can provide experimental references for hydraulic fracturing design and optimization of the fracturing parameters to obtain the optimal fracturing effectiveness, so as to enhance reservoir permeability and improve reservoir recovery.

2 Effect of Bedding Anisotropy on Hydraulic Fracturing

Shales are intrinsically anisotropic and heterogeneous sedimentary rocks due to the preexisting bedding planes and microfractures. Bedding anisotropy directly affects hydraulic fracture behaviors. Available data indicate that the propagation of hydraulic fractures perpendicular to the bedding plane requires higher injection pressure than that parallel to the bedding plane [10]. The change of bedding inclination will disturb the propagation pattern of hydraulic fractures, resulting in crossing, sliding, arresting and even opening at the intersection. Lin et al. [11] explored the effect of shale anisotropy on the propagation of hydraulic fractures using Longmaxi shale samples. They found that when the bedding inclination is greater than 60°, hydraulic fractures would propagate along the bedding plane, while when the bedding inclination is small, the hydraulic fractures will deflect into the bedding direction. Guo et al. [10] performed triaxial hydraulic fracturing tests with anisotropy Longmaxi shale. The results demonstrate that the breakdown pressure of rock decreases with increasing bedding inclination, and the complex hydraulic fracture networks are prone to be created at the bedding inclination of 0–30°. Wang et al. [12] quantitatively analyzed the hydraulic fracturing characteristics of anisotropic shale based on the fractal dimension and the equivalent fracture width. They found that with the increase of bedding inclination, the fractal dimension and equivalent fracture width showed an “S” shape (i.e. decrease-increase-decrease). However, previous studies do not reveal the relationship between shale anisotropy and acoustic emission evolution during hydraulic fracturing. In addition, limited by sample size (100–300 mm), current observation and description of fracture morphology mostly focus on the main hydraulic fracture. In fact, there are many micro-cracks around hydraulic fractures, so it is necessary to carry out micro-scale observation of fractured shale samples to deepen our understanding of the influence mechanism of anisotropic bedding planes.

In this section, the acoustic emission technique is used to monitor fracturing characteristics of anisotropic shales (β = 0°, 45° and 90°) in real time. Meanwhile, microscopic observations of hydraulic fractures are conducted on a stereomicroscope. Moreover, the hydraulic fracturing results of the Longmaxi shale and the Lushan shale are compared to clarify the impact of bedding anisotropy and rock heterogeneity on the hydraulic fracturing characteristics of shale.

2.1 Pump Pressure and Deformation

The evolution of shale hydraulic fractures is a complicated three-dimensional process. When pump pressure exceeds the bearing capacity of the surrounding rock, hydraulic fractures initiate. To gain an in-depth understanding of hydraulic fracture initiation and propagation, axial and circumferential strain gauges were used to measure the deformation in the process of hydraulic fracturing. Taking the results under an injection rate of 12 mL/min as an example, the effects of bedding anisotropy and matrix heterogeneity on the hydraulic fracturing fracture process are analyzed in the following part.

Figure 9.3 shows the evolution of pump pressure, deformation and acoustic emission of the Longmaxi shales and the Lushan shales with different bedding inclinations during hydraulic fracturing. It can be seen from Fig. 6.3 that as the bedding inclination increases from 0° to 90°, the breakdown pressure and instantaneous deformation (including circumferential (ΔD_c) and axial (ΔD_a)) of the two kinds of shale show a first increasing and then decreasing trend, which reaches the maximum at 45° bedding. This tendency agrees with the conclusions of Chong et al. [13] and Zhao et al. [14], who stated that the relationship between breakdown pressure and anisotropic angle approximately was characterized by a quadratic polynomial. Thus, we can conclude that the variation of shale anisotropy could mainly affect the breakdown pressure and instantaneous deformation during hydraulic fracturing.

Fig. 9.3

Fracturing results of anisotropic shale samples

Matrix heterogeneity would seriously complicate the effect of bedding anisotropy on the deformation and breakdown process. Comparing Fig. 9.3a–c and d–f, it can be found that in Longmaxi shale with good homogeneity, the hydraulic fracture initiation and propagation state can be identified according to the variation of AE cumulative energy. The fracture initiation and propagation pressures (15.10 MPa and 20.59 MPa) of the 0° sample are higher than those of 90° sample (11.67 MPa and 18.10 MPa). This can be attributed to the case that the 0° bedding is perpendicular to the axial stress. Initiation of micro-cracks induced by fluid injection must overcome axial stress limitation, so higher injection pressure is required. However, in the Lushan shale reservoirs with poor homogeneity, the AE count rate and cumulative energy increase steeply when the fluid pressure reaches the breakdown value. There is no microfracture initiation and propagation phenomenon before the injection pressure reaches the breakdown pressure, indicating that the Lushan shale matrix shows typically brittle characteristics. Concerning the AE count rate and the cumulative energy, for the Longmaxi shale, when the bedding inclination increases from 0° to 90°, the AE peak count rate always keeps increasing, which is 2.55 × 107 s⁻¹, 3.13 × 107 s⁻¹ and 5.4 × 107 s⁻¹, respectively, while the cumulative energy of AE first decreases and then increases. However, for the Lushan shale, with the increase of bedding inclination, AE peak count rate and AE cumulative energy increased first and then decreased. Du et al. [15] show that the AE counting rate reflects the initiation and propagation behavior of microcracks in the sample, and the AE cumulative energy reflects the energy consumption and fracturing degree of the sample. Therefore, it can be inferred that rock heterogeneity could suppress the effect of bedding anisotropy and make it mainly reflect in the initiation and evolution state of microfractures and the final rupture degree of the sample.

2.2 Acoustic Emission Response of Microfracture

As described in Sect. 4.2 of Chap. 4, the evolution characteristics of the dominant frequency band of the acoustic emission waveform can reflect the microfracture mechanism inside the rock. Specifically, the low-frequency signal corresponds to the tensile fracture, the medium-frequency signal reflects the tension-shear mixed fracture, and the high-frequency signal reflects the shear fracture. Figure 9.4 shows the time-varying frequency domain evolution curve of acoustic emission during hydraulic fracturing of anisotropic shale. Comparing Fig. 9.4a–c (or d–f), the evolution law of the induced microfractures is closely related to the bedding inclination during fluid injection. The proportion of low-frequency bands in anisotropic shales is generally more significant than the sum of the medium and high-frequency bands, indicating that tensile micro-fractures are mainly produced in the entire hydraulic fracturing process. Taking Longmaxi shale as an example, when the bedding inclination (β) is 0°, the proportions of low and high dominant frequency bands are 55.9% and 43.7%, respectively; When β is 45°, the low and high dominant frequency bands account for 80.59% and 17.3%, respectively; When β is 90°, the proportions of low and high dominant frequency bands are 87.5% and 2.5%, respectively. These phenomena indicate that with the increase of bedding inclination, the proportion of tensile micro-fractures increases, whereas the proportion of shear micro-fractures decreases. This is because under the action of the initial axial stress (without confining pressure), hydraulic fractures mainly initiate and propagate along the axial direction (i.e., the direction of the maximum principal stress). For samples with 0° bedding, hydraulic fractures will frequently intersect with beddings in their propagation path. More shear fractures are prone to be produced in the branching, initiation, and re-propagation at the intersection. For the samples with a bedding inclination of 90°, since the propagation direction of hydraulic fractures is consistent with the direction of the bedding plane, the tensile fractures are mainly generated in the 90° samples. In addition, in the time-varying frequency domain of acoustic emission of 45° samples, there is no stable propagation stage (III) of low-frequency and low-amplitude signals, indicating that the samples with 45° bedding are entirely fractured, and no closed crack reopening or new cracks initiation can occur.

Fig. 9.4

Time-varying features of AE frequency domain of anisotropic shale samples during the fluid injection process

Comparing Fig. 9.4a–c and d–f), the difference in shale heterogeneity not only affects the evolution characteristics of mixed tension-shear micro-fractures, but also changes the relative size of each dominant frequency band. Specifically, for the homogeneous Longmaxi shale, the proportion of medium frequency band signals and the amplitude of each frequency band keep increasing with the increase of bedding inclination. However, for the heterogeneous Lushan shale, the proportion of the medium frequency band decreases with the increase of the bedding angle, and the low-medium- and high-frequency amplitudes show a trend of increasing first and then decreasing. In addition, the influence of matrix heterogeneity can also be reflected by the time-domain distribution difference of frequency band signals. For example, the dominant frequency and amplitude detected in the Longmaxi shale concentrate mainly before the fluid pressure reaches the breakdown pressure. But in the Lushan shales with 0° and 45°, although the dominant frequency and amplitude have the same distribution trend as those of the Longmaxi shales when the bedding of Lushan shale is 90°, accumulation of dominant main signals are not visible before the injection pressure reaches the breakdown pressure. The reason for this phenomenon may be that the injected fluid directly activated the micro-cracks in the case of 90° bedding so no obvious signals appeared before the injection pressure reached the breakdown pressure.

2.3 Hydraulic Fracture Morphology

The anisotropic bedding plane of shale has a great impact on the hydraulic fracture propagation behavior. Figure 9.5 shows the macroscopic fracture propagation morphology on the sample surface after hydraulic fracturing. By exposing the sample to ultraviolet light, the fluorescent fracture path can be discerned. Overall, the hydraulic fracture propagation behavior is significantly different under different bedding inclinations. For the samples with a bedding inclination of 90°, the hydraulic fractures mainly spread along the bedding direction, resulting in vertical failure perpendicular to the fluid-injection direction. The propagation of the hydraulic fracture with a 45° bedding finally deflects toward the bedding plane. In the two types of shale, it can be observed that the hydraulic fractures are both 45° inclined to the horizontal plane. When the bedding plane of the sample is 0°, there are two propagation patterns. One is that hydraulic fractures propagate vertically and intersect with the bedding planes (Fig. 9.5a); The other is that the hydraulic fracture spread horizontally along the bedding plane (Fig. 9.5b).

Fig. 9.5

Morphology of hydraulic fracture on sample surface

Comparing Fig. 9.5a and b, it can be seen that the hydraulic fractures in Lushan shale are basically along the bedding plane regardless of varying bedding inclinations. By contrast, the fracture morphology in Longmaxi shale is relatively complex. Specifically, the hydraulic fracture of 90° Longmaxi shale bends to the direction perpendicular to the shale bedding, which is different from fractures parallel to bedding orientation in the 90° Lushan shale. For 45 shale, the hydraulic fracture oblique to the bedding finally deflects towards the axial direction. When the bedding inclination is 0°, the hydraulic fracture crosses the bedding and further extends vertically to the bedding plane. These differences can be attributed to the abundant and randomly-distributed microcracks and defects in Lushan shale (see Sect. 3.2 for microscopic observation). Initiation of hydraulic fractures will promote the rupture, coalescence and overlapping of these defects, forming a preferable way for hydraulic fracture to propagate in the bedding direction. On the contrary, Longmaxi shale a relatively homogeneous and bedding plane is not developed. Thus, hydraulic fractures are confined to grow along the mechanically preferential way, which results in axially growing hydraulic fractures.

To further analyze the influence of bedding anisotropy and matrix heterogeneity on hydraulic fracture propagation, the microscopic morphology of hydraulic fracture was observed by a stereomicroscope (500 μm). The results are shown in Figs. 9.6 and 9.7. Compared with 0° and 90°, 45° shale has the most twisted fracture path, and the fracture opening is the largest. Since these tests are carried out without confining pressure, the propagation of hydraulic fractures is mainly affected by the bedding planes, matrix homogeneity and axial stress. When the main hydraulic fracture spreads along the bedding, there will also be associated micro-fractures extending in the longitudinal direction. This conclusion can be verified by observing the fractures in Fig. 9.6c and 9.7b. In addition, whether the hydraulic fracture is parallel to or perpendicular to the bedding direction, the fracture opening varies slightly (Fig. 9.6b), indicating that the changes in fracture opening are probably dominated by the difference of individual samples rather than the bedding plane.

Fig. 9.6

Surface morphology of hydraulic fracture of anisotropic Longmaxi shale samples

Fig. 9.7

Surface morphology of hydraulic fracture of anisotropic Lushan shale samples

From Figs. 9.6 and 9.7, it can be found that the presence of defects in Lushan shale causes hydraulic fractures to propagate along the boundary of matrix defects (Fig. 9.7a) or through the shale matrix (Fig. 9.7c), and then the hydraulic fractures are slipped, branched or diverted. Especially, when the bedding inclination is 45°, an obvious shear spall zone appears near the main hydraulic fracture. The hydraulic fractures neat the matrix defects show “discontinuous and intermittent” on a microscopic scale (Fig. 9.7c). The hydraulic fractures in the discontinuous part are mainly connected with the shear dislocation zone (marked with red ovals in Fig. 9.7), forming complex hydraulic fractures.

Figure 9.8 summarizes the roughness parameters of the anisotropic shale fracture surface: (see Sect. 3.2.1 in Chap. 3 for definitions of these parameters). It is easy to find that with the increase of bedding inclination, the standard deviation (SD) of fracture surface elevation and the three-dimensional average inclination angle (θ_s) both show a first increasing and then decreasing trend. When the hydraulic fractures are inclined to the bedding planes (β = 45°), a relatively rough fracture surface is created. By contrast, the fracture surfaces generated by the propagation of hydraulic fractures perpendicular to the bedding planes (β = 0°) are rougher than those along the bedding planes (β = 90°). In addition, the surface roughness of Longmaxi shale is generally larger than that of Lushan shale. Due to the difference in matrix properties, the hydraulic fracture in Lushan shale propagates primarily along the bedding direction, while the fracture in Longmaxi shale mostly grows vertically confined by the axial stress. These two different propagation patterns lead to differences in the roughness of the fracture surface. From another point of view, this phenomenon also shows that the surface roughness of hydraulic fractures will decrease when they propagate along the bedding, while the propagation through the bedding is more conducive to the formation of rough and complex hydraulic fracture morphology. Therefore, in the actual fracturing operation, the induced hydraulic fractures should be designed to cross the shale beddings as much as possible to promote the formation of complex fracturing fracture networks with larger fracture surfaces, so as to provide a good channel for the effective migration of natural gas and improve the permeability and production of shale reservoirs.

Fig. 9.8

Evolution of fracture toughness parameters of anisotropic shale samples

3 Effect of Different In-Situ Stress States and Wellbore Orientations on the Formation Mechanism of Complex Fracture Networks

The true triaxial hydraulic fracturing tests can restore the three-dimensional stress state of reservoir rock, and more truly simulate the process of initiation and propagation of hydraulic fractures and the formation of fracture networks in shale-gas reservoirs. During the tests, the in-situ stress state (magnitude and direction) has an important influence on the formation of the fracture networks. The current hydraulic fracturing tests mainly focus on the effect of the in-situ stress magnitude (difference) on the propagation law and the complexity of fracture networks. Based on the true triaxial hydraulic fracturing tests, the research results of Ma et al. [16], Guo [17] and Zeng et al. [18] show that with the increase of the in-situ stress difference, the hydraulic fractures change from vertical fractures to horizontal fractures, and mainly propagate along the weak beddings to form a relatively simple hydraulic fracture morphology. In fact, when the magnitudes of the three principal in-situ stresses are the same, there are three stress states, as shown in Fig. 9.9, due to the different in-situ stress directions: normal faulting stress state (σ_v > σ_H > σ_h), strike-slip faulting stress state (σ_H > σ_v > σ_h) and reverse faulting stress state (σ_H > σ_h > σ_v). However, there are relatively few studies on the fracture network formation process in the context of the anisotropic stress state of the reservoirs. Zhou et al. [19] discussed the influence of the normal faulting stress state and strike-slip faulting stress state on hydraulic fracture morphology based on true triaxial hydraulic fracturing tests. The results show that under the normal faulting stress state, the hydraulic fractures mainly expand vertically with more branches along the way, while under the slip faulting stress state, the hydraulic fractures are tortuous and have fewer branches. However, Guo et al. [20] insisted that horizontal beddings are easier to be activated under a strike-slip faulting stress state, resulting in more branched hydraulic fractures. By analyzing the field data, Salvage and Eaton [21] found that the field hydraulic fracturing operations may change the direction of the principal stress of the formations, resulting in the stress state of the deep formations changing from the stress state of strike-slip faulting to the stress state of reverse faulting. Therefore, it is necessary to further analyze the influence of reverse faulting stress state on hydraulic fracture propagation and fracture network formation.

Fig. 9.9

Anisotropy of in-situ stress regime in shale reservoirs (revised from [22, 23])

The wellbore orientation also plays a key role in the propagation of hydraulic fractures. Guo et al. [10] compared the effect of wellbore orientations including horizontal and vertical wellbores on fracture propagation law and found that the breakdown pressure of horizontal wellbore fracturing was lower than that of vertical wellbore fracturing, and horizontal wells mainly produce horizontal transverse fractures while vertical wells mainly produce vertical fractures. These phenomena are obvious at small bedding inclinations. However, the tests of Guo et al. [10] were carried out on cylindrical samples, so the fracture propagation is limited by the length in the radial direction of the samples. In this section, based on previous studies, the differences in bedding inclinations, in-situ stress states and well orientations were taken into account to more truly simulate the fracturing process in shale reservoirs. By analyzing the results of the true triaxial hydraulic fracturing test and quantitatively characterizing the shape and complexity of the fracture network with the help of statistical methods, the formation mechanism of the complex hydraulic fracture network in reservoir rock shale is revealed.

The results of the true triaxial hydraulic fracturing test are summarized in Table 9.1. By comparing samples #1 and #2, we can get the effect of the normal-faulting stress state and strike-slip faulting stress state on hydraulic fracturing results, as shown in Fig. 9.10a and b. The effect of the normal faulting stress state and reverse faulting stress state on hydraulic fracturing can be studied by comparing samples #3 and #4, as shown in Fig. 9.10a and b. samples #5 and #6 are used for hydraulic fracturing of horizontal wells under the assumption that the vertical stress is applied along the Z-axis, as shown in Fig. 9.10e and f.

Table 9.1 Hydraulic fracturing schemes and observation of experimental results

Fig. 9.10

Curves of pump pressure and sample displacement with time under different beddings and true triaxial stress conditions

3.1 Characteristics of Fluid Pressure and Deformation

• (1) Fluid Pressure Response

The fluid pressure curves under various conditions can be described by four typical stages, which are the slow pressurization stage (stage I), rapid pressurization stage (stage II), pressure releasing stage (stage III), and pressure stabilization stage (stage IV), respectively (see Sect. 3.5.3 for details). However, there are still significant differences in injection pressure curves under different conditions, mainly reflected in stages II and IV. According to the division criteria of each stage of the injection pressure curve in Chapter II, stage II corresponds to the process of injection pressure increasing rapidly until reaching the breakdown pressure, and stage IV corresponds to the process of injection pressure stably fluctuating. We considered two in-situ stress states (normal faulting and strike-slip faulting) when investigating the hydraulic fracturing effectiveness of vertical wells (samples #1 and #2) whose wellbore is perpendicular to the bedding plane. In stage IV, there are two stages of pressure drop, pressure stability and pressure rise in sample #1, which may be caused by the pressure holding, re-initiation, and arrest of hydraulic fractures.

Compared with the injection pressure curve of sample #1, the injection pressure of sample #2 appears at an approximate climbing stage before reaching the breakdown pressure (P_b = 25.85 MPa), and the time for sample #3 to reach the stabilized pressure is 55 s longer than that of sample #1. The reason for the above phenomenon of sample #2 may be that the fluid pressurization causes the local cracking of the sample, resulting in the leakage of fluid through the crack, which eventually leads to the slow process of pressurization and pressure stabilization. Similarly, the injection pressure of sample #3 with an angle of 45° between the wellbore and bedding plane shows a phenomenon of slow decline and fluctuating rise before reaching the breakdown pressure, which can also be explained by the local cracking of the sample. The difference between the injection pressure changes of samples #2 and #3 in stage II can be attributed to the relative time difference between fluid pressure release and pressure holding caused by different crack cracking degrees. The difference between the injection pressure changes of samples #2 and #3 in stage II can be attributed to the difference in the relative time difference between fluid pressure release and pressure holding, which is caused by the difference in the crack cracking degree of samples #2 and #3. For sample #4 with 45° bedding, under the reverse faulting stress state, the injection pressure appears at the second peak which is defined as the secondary breakdown pressure (P_b = 19.19 MPa) after the breakdown pressure (P_b = 21.51 MPa), which reflects that the sample is not fully fractured at 21.51 MPa, and the subsequent injection can continue to hold pressure. When the injection pressure reaches 19.19 MPa, sample #4 is fully fractured, and then the pump pressure remains stable. Further, when the wellbore is parallel to the bedding plane (horizontal well fracturing), the evolution trend of the pump pressure evolution curve of the two samples (sample #5 is in normal faulting stress, and sample #6 is in tectonic stress state) is similar. The injection pressure curves of samples #5 and #6 maintain the characteristics of the above four stages, but there are still differences in breakdown pressure and pressure stabilization time due to different in-situ stress directions. These phenomena show that the stress mechanism will directly affect the variation trend of injection pressure by disturbing the crack initiation process. The deformation along the direction of the minimum principal stress is less than those along the directions of the middle and maximum principal stress.

• (2) Deformation Response

It can be seen from Fig. 9.10 that the sample deformation caused by pumping is abrupt, which mainly occurs at the moment of fracturing (P_inj = P_b). Under different stress conditions, the deformation characteristics of samples induced by pumping are different. When the wellbore is perpendicular to the bedding, under the normal faulting stress state (Sample #1), the deformations in X-, Y- and Z-directions increase at the moment of breakdown, while under the strike-slip faulting stress state (Sample #2), at the moment of breakdown, the deformation in the X-direction is basically unchanged, the deformation in the Y-direction increases, and the deformation in the Z-direction decreases. When the wellbore is 45° with the bedding, at the moment of breakdown, sample #3 has no deformation in the X-direction, while the deformations in the Y- and Z-directions decrease. For sample #4 whose wellbore direction is consistent with the direction of the minimum principal stress, the deformations of sample #4 in three directions did not change when the injection pressure reached the breakdown pressure but began to decrease synchronously after 170 s from the breakdown point. When the wellbore is parallel to the bedding, the deformations of samples #5 and 6# in X-, Y- and Z-directions show a decreasing trend at the moment of sample breakdown. Therefore, different stress conditions significantly affect the deformation caused by injection pressure. On the one hand, in the process of constant flow pressurization, the fluid pressure acting on the wellbore is non-uniform distribution, which leads to a different release of injection pressure in different directions at the moment of breakdown, and eventually leads to uneven deformation of the wellbore. On the other hand, due to the heterogeneity caused by the micro-cracks, beddings and other defects distributed in the shale, it is difficult to unify the initiation direction of hydraulic fractures at the moment of fracturing, which directly affects the propagation of subsequent fractures, and then affects the deformations of samples.

3.2 Hydraulic Fracture Propagation Modes

As summarized in Table 9.1, the morphology of hydraulic fractures can be mainly classified into four types in terms of different causes: (i) a single bi-wing hydraulic fracture (samples #3 and #6) generated by opening a weak bedding plane, which is called M-I; (ii) the multiple hydraulic fractures formed by cracking shale matrix and then coalescing with bedding planes, called M-II (e.g., sample #4); (iii) the multiple hydraulic fractures formed by activating natural fractures and then coalescing with bedding planes, which are called M-III (e.g., sample #1); (iv) the multiple hydraulic fractures formed by first cracking shale matrix and activating natural fractures and then coalescing with the bedding planes, called M-IV (e.g., samples #2 and #5). These experimental results are consistent with the observations of Warpinski et al. [24], Hou et al. [25], and Jiang et al. [26], who also conducted hydraulic fracturing experiments using similar anisotropic shale blocks.

For the convenience of analyzing, we introduced several symbols to characterize and distinguish the type of fractures induced by hydrofracturing. Fractures formed by cracking the shale matrix are defined as the main fractures M_i. Note that i hereafter refers to the fracture number of the specified fracture type (0 ≤ i ≤ N, N is the total number of fractures). The bedding planes opened by fracturing fluid are denoted as BP, the hydraulic fractures are represented by H_i, and the natural fractures activated by fluid injection are denoted as N_i.

Figure 9.11 shows the typical unfolded surface morphology of type M-I hydraulic fractures in the X–Z plane. The induced hydraulic fractures in samples #3 and #6 propagated along the direction of the bedding plane. The difference in bonding properties between beddings can cause the twisting of induced fractures, while the main fracture propagation direction did not turn and branch. Possible reasons for forming M-I type hydraulic fractures can be summarized as follows: (i) there is a fully developed bedding plane near the open hole section of the wellbore; (ii) no pre-existing natural fractures, joints and other weak bedding planes are distributed along the trajectory of induced hydraulic fracture; (iii) the tensile strength of shale matrix and the cohesion strength of other bedding planes are higher than the activated bedding plane.

Fig. 9.11

Unfolded surface morphology of hydraulic fractures that belong to type M-I

Figure 9.12 depicts the unfolded surfaces of M-II multiple fractures by taking sample #4 as an example. Under the confinement of the maximum in-situ stress (σ_max), two main fractures (M₁ and M₂), parallel to the direction of the maximum in-situ stress, were formed in the shale matrix. The fluid pressure opened a bedding plane (45° BP) near the open hole section of the wellbore and formed a hydraulic fracture H₁. In the propagation process of fractures M₁ and M₂, the fluid pressure successively opened two bedding planes, forming hydraulic fractures H₂ and H₃. The propagation path of the M-II type main fracture is relatively short, and the main fracture produces branches with the same propagation direction at the bedding. As shown in Fig. 9.12, the main fractures M₁ and M₂ only appear on the surface of X₂ of sample #4. When hydraulic fractures (M₁ and M₂) intersect with bedding planes, two fracturing effectiveness will occur: (1) hydraulic fractures are arrested by the bedding plane and open the bedding plane (H₃); (2) hydraulic fractures cross directly bedding planes and open bedding planes (H₁ and H₂). The activation of bedding will divert the fluid in the matrix fracture. Because the fluid is divided at H₁ and H₂, the fluid pressure is insufficient to make the matrix fractures (M₁ and M₂) cross the bedding plane when matrix fractures propagate to H₃, resulting in more fluid flowing into the bedding (H₃) and promote H₃ to propagate to other surfaces of sample #4. The main causes for this kind of hydraulic fracture (M-II) are as follows: (i) microcracks are highly developed in the rock matrix near the open hole section of the wellbore; (ii) the direction of the maximum in-situ stress is not parallel to the bedding plane but at an inclination angle of θ = 45°; (iii) the initiation pressure of microcracks in the rock matrix is less than the cohesion strength of the bedding planes, so that the hydraulic fractures propagate along the direction of the maximum in-situ stress in the matrix before propagating along the bedding; (iv) the cohesion strength of the bedding planes is lower than the tensile strength of the rock matrix, which causes the matrix fractures M₁ and M₂ to cross and open the bedding planes (H₁, H_2, and H₃).

Fig. 9.12

Unfolded surface morphology of hydraulic fractures that belong to type M-II (Sample #4, β = 45° and σ_H > σ_h > σ_v)

The M-III fracture morphology represented by sample #1 is displayed in Fig. 9.13. The cyan dotted line on the Z₂ surface in Fig. 9.13 is the location of the wellbore. It can be seen that hydraulic fractures (H₁, H₂, H_3, and H₄) are formed by the activation of bedding planes located in the open hole section of the wellbore due to fluid injection pressurization. It should be noted that the direction of the maximum principal stress is perpendicular to the direction of the bedding plane, and the hydraulic fractures propagating along the bedding plane first need to overcome the limitation of the maximum principal stress. Under the limit of the maximum principal stress, the range of each hydraulic fracture propagating along the bedding plane is small. For example, H₂ only propagates to the Z₂ surface, H₁ and H₃ only appear on the X₁ and Z₂ surfaces, and although H₄ appears on the four surfaces (X₁, X₂, Z₁, and Z₂), its propagation path does not completely connect the bedding planes where it is located. In addition, an obliquely propagating natural fracture N₁ is generated near the open hole section of the wellbore. The natural fracture is mainly distributed on the surfaces of X₂, Z₂, and Y₂, and is a branch of H₄ after the termination of its propagation at a 0° bedding, whose propagation direction is determined by the interaction of the maximum principal stress and the fluid pressure. The causes of M-III type fractures are as follows: (i) the fluid pressure first opens the bedding plane in the open hole section of the wellbore; (ii) the natural fracture in the open hole section of the wellbore is activated; (iii) when the fracturing fluid encounters a bedding plane in the activation process of a natural fracture, fluid pressure will directly open the bedding plane.

Fig. 9.13

Unfolded surface morphology of hydraulic fractures that belong to type M-III

Unfolded surfaces of M-IV type hydraulic fracture morphology after fracturing is shown in Fig. 9.14. This type of hydraulic fracture includes cracked shale matrix, opened bedding planes, and activated natural fractures. The hydraulic fractures are connected and overlapped with each other to form a complex fracture network. The formation process and network morphology of hydraulic fractures significantly differ under different matrix and bedding structures. For example, there are three matrix fractures M₁, M₂, and M₃ propagating obliquely in sample #2. From the perspective of fracture penetration on the surface, M₁ is directly overlapped with the wellbore and mainly appears on Y₁ and Z₁ surfaces, M₂ appears on Y₁ and X₂ surfaces, and M₃ only appears on Z₁ surface. The matrix fractures appear intermittently and are mainly connected with the bedding plane (H₁ and H₂) and the natural fracture (N₁). When there are hydraulic fractures formed by opening bedding and hydraulic fractures formed by cracking the matrix at the same time near the wellbore, the tensile strength of the matrix is generally higher than the cohesion strength of the bedding, so the former usually give priority to cracking. It can be inferred that for this type of hydraulic fracture, the natural fracture (N₁) is activated in the process of hydraulic fracture propagating along the bedding, and finally, the hydraulic fracture extends along the matrix. Due to the different degrees of disturbance by opening bedding, the hydraulic fractures formed by cracking the matrix are not continuous. Similarly, in sample #5, the hydraulic fractures (H₁, H₂ and H₃) propagating along beddings near the wellbore activate the natural fracture (N₁) during their propagation process and induce the matrix to crack, forming a main fracture (M₁). The reason for M-IV type hydraulic fractures are as follows: (i) the bedding planes with similar cohesion strength near the wellbore are fully developed, resulting in multiple bedding planes being opened; (ii) natural fractures exist in the rock matrix, which is the key to the evaluation of the propagation behavior of the main fractures and the formation of complex fracture networks.

Fig. 9.14

Unfolded surface morphology of hydraulic fractures that belong to type M-IV

In summary, hydraulic fractures in shale reservoirs primarily propagate along the bedding plane. However, due to different in-situ stress states and the distribution of natural fractures, hydraulic fractures may have different propagation modes, forming different fracture network morphology. Based on the initiation and propagation mode of hydraulic fractures in anisotropic shale reservoirs, hydraulic fracture morphology could be divided into four categories in detail: (1) a single bending hydraulic fracture formed by propagating along the bedding (Fig. 9.15a); (2) fishbone-like hydraulic fractures formed by hydraulic fractures crossing the beddings (Fig. 9.15b); (3) dendritic fractures formed by hydraulic fractures first propagating along the beddings and then activating natural fracture (Fig. 9.15c); and (4) a complex fracture network formed by hydraulic fractures opening and crossing the beddings and activating natural fractures (Fig. 9.15d).

Fig. 9.15

Classification of fracture networks after hydrofracturing in anisotropic shale reservoirs

3.3 Quantitative Evaluation of Fracture Morphology

To quantitatively evaluate the morphological characteristics of the hydraulic fracture network under various working conditions, the three-dimensional hydraulic fracturing effectiveness is quantitatively evaluated by counting the induced fracture occurrence and stimulated rock area (SRA) [25].

• (1) Induced Fracture Occurrence

In order to better display the distribution of hydraulic fractures in the fractured samples with three bedding inclination angles, a polar coordinate axis is established with the wellbore center as the origin as shown in Fig. 9.16. The distribution angle between the induced fracture and horizontal bedding plane is defined as β. When the fracture is parallel to the horizontal bedding plane, β is 0°, and the sign of β is assumed to be positive in the clockwise direction.

Fig. 9.16

Schematic diagram of hydraulic fracture statistical method

The statistical results of the induced fractures for each sample were quantitatively presented in the form of a rose diagram (Fig. 9.17) in accordance with the method suggested by Taleghani and Olson [27] and Ezati et al. [28]. It is easy to see that the main reasons for the formation of multiple hydraulic fractures (M-II, M-III and M-IV) are the simultaneous initiation of multiple bedding planes in the open hole section of the wellbore and the generation of main fractures propagating along the shale matrix. The reason for the formation of a single bending fracture (M-I) is that there is only one hydraulic fracture propagating along a bedding plane near the wellbore. In addition, it can be found that the number of hydraulic fractures in the sample with activated natural fractures is more than that in the sample without activated natural fractures, which indicates that the activation of natural fractures leads to more branches and more complex fracture networks.

Fig. 9.17

Rose diagram of hydraulic fractures occurrence in each sample

• (2) Stimulated Rock Area

The fracture network generated by hydraulic fracturing of shale samples is composed of one or more combinations of the main fractures, the activated natural fractures (turning, opening or crossing), and the opened bedding planes. Since the hydraulic fracture morphology of the sample is the observation result under the condition of three-dimensional complete unloading, the traditional method of calculating the stimulated reservoir volume [29] is no longer applicable, so the “stimulated reservoir area (SRA)” proposed by Hou et al. [30] is used to evaluate the hydraulic fracturing effectiveness. According to Hou et al., the SRA was the total area of the main fractures, the opened bedding planes and the activated natural fractures, which were divided into four grades based on the fracture area: 1.0 (approximately 200 mm × 200 mm), 0.75 (approximately 150 mm × 150 mm), 0.5 (approximately 100 mm × 100 mm), and 0.25 (approximately 50 mm × 50 mm). Moreover, larger SRA resulted in a larger fracture area in the reservoir, which was conducive for complex fracture formation and gas migration. Using identical method, we analyzed the shale fracturing effectiveness under different conditions.

The SRA of various types of fractures calculated by fracturing samples is shown in Fig. 9.18. The SRA actually reflects the extent of fracture propagation, while the counted number of hydraulic fractures represents the complexity of fractures. On the whole, the SRA of four types of hydraulic fracture (M-I, M-II, M-III and M-IV) in Sect. 9.3.2 increases successively, and the complexity of the four types of hydraulic fracture also increases correspondingly. The M-IV type fractures (samples #2 and #5) with activated natural fractures and opened bedding planes have the best effectiveness in increasing and stabilizing production. There is an overall good correspondence between the SRA value and the counted number of hydraulic fractures. However, it is insufficient to evaluate the hydraulic fracturing effectiveness only by SRA value or the counted number of hydraulic fractures. For example, the SRA values of samples #2 and #4 are 0.5, but the number of the main fractures is 3 and 2, respectively (Fig. 9.18a). In opened bedding planes, the SRA of samples #1 and #2 are 1.25 and 1.5, whereas the number of (activated) bedding planes is 4 and 3 (Fig. 9.18b). Although samples #1, #2, and #4 have the same counted number of natural fractures, their SRA values are different (Fig. 9.18c). These differences may be related to the limitation of the sample size. Although a large-scale shale sample with a side length of 200 mm has been used in the tests, such a sample size is still insufficient to reflect the state of reservoir rocks. Therefore, in the process of hydraulic fracturing tests, once hydraulic fractures propagate to the surface of the sample, the fracturing fluid is likely to leak directly through the induced fractures, resulting in the instantaneous reduction of fluid pressure, which cannot drive other fractures to continue to propagate. In other words, the SRA value is essentially related to the time when the hydraulic fracture propagates to the surface of the sample. The larger the sample size is, the larger the SRA value of each type of hydraulic fracture will be. Therefore, the SRA value and the counted number of hydraulic fractures are synchronously adopted as the quantitative evaluation indexes to evaluate the hydraulic fracturing effectiveness.

Fig. 9.18

SRA and fracture number distribution of the fractured shale samples

3.4 Effects of Bedding Planes

By comparing the fracture morphology of sample #1 (the bedding is orthogonal to the wellbore), sample #3 (the bedding is oblique to the wellbore (45°)), and sample #5 (the bedding is parallel to the wellbore), the influence of anisotropic bedding on the fracture network morphology is analyzed. It can be seen from Table 6.1 that samples #1, #3 and #5 are in a normal faulting stress state.

When the bedding is vertical to the wellbore, the fracture network of sample #1 belongs to dendritic hydraulic fractures (M-III type) that propagate along the beddings and activate natural fractures. We found five hydraulic fractures in sample #1, four of which (H₁, H₂, H₃, and H₄) propagate along the 0° bedding planes, and one of which (N₁) is an activated natural fracture. The calculated SRA of all fractures in sample #1 is 1.5 in line with Fig. 9.18. However, under the same stress state, when the angle between the bedding and the wellbore is 45°, only a single hydraulic fracture (M-I) is produced in sample #3, and the calculated SRA is 0.75, which is 50% lower than that of the sample #1. When the bedding is parallel to the wellbore, the hydraulic fracture morphology of sample #5 is M-IV complex fracture network morphology, and compared with samples #1 and #3, sample #5 has the largest SRA value and the counted number of hydraulic fractures, which are 2.5 and 6 respectively.

Comparing the SRA values of samples #1, #3, and #5, it can be found that the hydraulic fracturing effectiveness is the smallest when the bedding inclination is 45°, which seems to be in contradiction with Sect. 9.2 of this chapter. However, it should be noted that the sample size used in the true triaxial fracturing tests is larger than that used in the uniaxial tests. During the sampling process, it is inevitable to produce differences in individual properties, resulting in the fracture morphology of sample #3, not in line with expectations. Therefore, the difference between the bedding and fracture morphology of shale before and after the test is compared to explain the cause of this phenomenon. As shown in Fig. 9.19a, comparing the photos before and after the test of sample #1, it can be found that although the beddings of sample #1 propagate horizontally as a whole, the propagation track is not straight, and the spacing and distribution of beddings are also extremely uneven. The beddings on the Z₁ surface do not appear in the X₁ surface, indicating that the beddings on the Z₁ surface are not fully developed. For these reasons, after multiple beddings are opened instantaneously to form hydraulic fractures, they will not always propagate along the bedding of Z₁ surface, but will deflect or terminate under the disturbance of the maximum principal stress. The actual propagation morphology of sample #1 (Fig. 9.13) also confirms this conclusion. However, it can be seen from Fig. 9.19b that there is obvious bedding that completely extends to the surface of sample #3, resulting in the tendency of the sample to slip along 45° during the loading process of three-dimensional stress. In addition, during the fluid injection process, new cracks initiate near the weak bedding, and the fracturing fluid flows into the bedding plane, further reducing the effective stress of the bedding. Once the sample breaks slightly along the bedding plane, the fluid pressure is released instantly and drives the hydraulic fracture to propagate along the bedding plane, forming a single hydraulic fracture propagating along the 45° direction. In Fig. 9.19c, the local details of sample #5 whose bedding is parallel to the wellbore before and after fracturing are compared. It is easy to find that there is no obvious weak bedding before the test in the sample #5, and beddings with the same width are densely distributed near the wellbore. Shale with this structure is prone to crack at many places during hydraulic fracturing to form multiple hydraulic fractures propagating along beddings. In addition, there is no obvious weak bedding in sample #5, which ensures that the hydraulic fractures can propagate along their mechanical optimal direction and the bedding direction. This process may lead to the initiation of fracture matrix, activation of natural fractures, and forming an M-IV type of complex fracture network. It should be noted that since the wellbore of sample #5 is arranged horizontally, in addition to the bedding plane, the wellbore orientation may also be a factor in the generation of the M-IV fracture network, which will be discussed in Sect. 9.3.6.

Fig. 9.19

Effect of bedding on hydraulic fracture networks

In conclusion, hydraulic fractures in anisotropic reservoirs mainly initiate and propagate along the bedding plane. The complexity of the hydraulic fracture network depends on the distribution of beddings and the difference in bedding strength and is less affected by the change of bedding inclination angle. When a bedding plane is developed, a hydraulic fracture directly penetrates the bedding to form a single hydraulic fracture, while when the bedding planes are uniformly distributed or locally developed, it is easier to form a relatively complex fracture network. In the actual fracturing, to prevent fluid leak-off into the beddings near the wellbore, the plugging agents are widely used, and the fracturing parameters (injection rate, injection pressure, fluid viscosity) can be adjusted to make fracture reorientation.

3.5 Effects of In-Situ Stress

Under a normal faulting stress state (σ_V > σ_H > σ_h), the dendritic hydraulic fractures (M-III) formed by activating natural fractures and then coalescing with bedding planes are generated in sample #1. The SRA value and the counted number of hydraulic fractures of sample #1 are 1.5 and 5, respectively. However, under the strike-slip faulting stress state, a complex fracture network (M-IV) with activated natural fractures and open bedding planes is generated in sample #2. The SRA value and the total number of fractures are 2.25 and 7, respectively. In comparison, the fracture area and fracture complexity of sample #2 are higher than those of sample #1, which indicates that it is easier to form tortuous and complex hydraulic fracture morphology under the strike-slip faulting stress state. The bedding inclination angle and in-situ stress difference of samples #1 and #2 are the same, but the direction of the maximum in-situ stress is different. Concretely, the direction of the maximum principal stress of sample #1 is perpendicular to the bedding plane, while the direction of the maximum principal stress of sample #2 is parallel to the bedding plane. In the process of hydraulic fracturing, the maximum principal stress in the normal faulting stress state inhibits the initiation and propagation of hydraulic fractures along the 0° bedding, while the maximum principal stress in the strike-slip faulting stress state is easier to make hydraulic fractures propagate horizontally along the bedding plane. Therefore, under the strike-slip faulting stress state, the resistance of hydraulic fracture propagating along 0°bedding is small, and more fractures propagating along bedding may be generated. When the beddings of shale are not developed, under the combined action of fluid pressure and maximum principal stress, multiple bedding planes may occur, resulting in multiple hydraulic fractures propagating along the bedding inclination. During the propagation of hydraulic fractures along the bedding plane, fluid activates natural fractures and even induces the cracking of the shale matrix. Therefore, under the strike-slip faulting stress state, the morphology of hydraulic fracture is more complex. This conclusion is consistent with the indoor true triaxial test observations by Guo et al. [20], Zhou et al. [19], and Hou et al. [31].

In the case of horizontal well fracturing, the fracture patterns under the normal faulting and strike-slip faulting stress are also compared. The M-IV complex fracture network is produced in sample #5 under the normal faulting state, while a single hydraulic fracture is generated in sample #6 under the strike-slip faulting stress state. This is because there is a well-developed bedding plane in sample #6 (Fig. 9.20), which leads to the fact that in the process of hydraulic fracturing, a hydraulic fracture directly cracks and propagates along this bedding plane without multiple fractures forming complex fractures. However, under the strike-slip faulting stress state, the propagation path of the main fracture of sample #6 is tortuous (as shown in Fig. 9.11b), and its tortuosity is higher than that of the main fracture of sample #5 (Fig. 9.14b), which is consistent with the conclusion that the sample in the stress state of strike-slip faulting is more likely to produce tortuous hydraulic fracture.

Fig. 9.20

Bedding distribution of end faces of Sample 6# before fracturing tests

When the bedding inclination angle is 45°, the influence of the normal faulting stress state and reverse faulting stress state on the morphology of hydraulic fracture can be analyzed by comparing those of samples #3 and #4. It can be seen from Sect. 9.3.2 of this chapter that sample #3 has a single hydraulic fracture (M-I), under a normal faulting stress state. Because there is obvious bedding in sample #3 (Fig. 9.19b), under the action of the maximum vertical principal stress and fluid pressure, the hydraulic fracture mainly initiates and propagates along the bedding, forming a single hydraulic fracture. However, under the reverse faulting stress state (σ_H > σ_h > σ_V), the maximum principal stress is arranged along the horizontal direction, while the vertical in-situ stress is the minimum principal stress. Under the reverse faulting stress state, hydraulic fractures of sample #4 propagate along bedding planes and induce the activation of natural fractures to form dendritic hydraulic fractures (M-II). The SRA value and the counted number of hydraulic fractures are 2 and 5 respectively, which are higher than those of sample #3 (0.75 and 1 respectively) under a normal faulting stress state, indicating that the fracture morphology of sample #4 is more complex and the fracturing effectiveness of sample #4 is better. This phenomenon also shows that compared with the normal faulting stress state, the reverse faulting stress state is also conducive to the formation of complex hydraulic fractures in shale reservoirs. In addition, since the vertical stress has the least restriction on the sample, the shale matrix in sample #4 is cracked along the direction of the maximum principal stress, and two main fractures connecting the parallel bedding planes are generated (M₁ and M₂ in Fig. 9.12), forming dendritic hydraulic fractures.

3.6 Effects of Wellbore Orientations

It can be seen from Table 6.1 that samples #1 and #5 simulate the hydraulic fracturing of vertical and horizontal wells, respectively, under a normal faulting stress state, while samples #2 and #6 simulate the hydraulic fracturing of vertical and horizontal wells, respectively, under a reverse faulting stress state. In addition, the breakdown pressures of vertical well hydraulic fracturing are higher than those of horizontal well hydraulic fracturing, which accords with the experimental observations of triaxial hydraulic fracturing in shale performed by Guo et al. [10].

However, due to the pre-existing obvious bedding planes and natural fractures in sample #6, it becomes inappropriate to use sample #6 for comparison. Therefore, we compared sample #1 to sample #5 to investigate the effects of wellbore orientations on hydraulic fracture morphology.

The SRA value and the total number of fractures of the vertical well (sample #1) are 1.5 and 5, respectively. The SRA value and the total number of fractures of the horizontal well (sample #5) are 2.5 and 6, which increased by 66.7% and 20% compared with the fracturing of vertical wells. Since the wellbore direction is vertical to the bedding plane direction, hydraulic fracturing of vertical wells often produces fractures propagating vertically or horizontally along the bedding [32]. Since the maximum principal stress acts vertically on the wellbore, when the fractures around the wellbore crack, under the limitation of the maximum principal stress, the hydraulic fractures will propagate perpendicular to the bedding, resulting in main fractures (such as M₁ in sample #5). This process is conducive to the formation of a complex fracture network.