1 Introduction

Shale gas is an important component of unconventional oil and gas resources, and the successful development of shale gas in the United States has enabled it to get rid of its dependence on foreign oil and gas resources, realize energy independence, and initiate a “shale gas revolution” in the world (Zou et al. 2020a, b; Jarvie et al. 2007; Zou et al. 2010; Bowker 2007). As clean and efficient energy, increasing the development and utilization of shale gas is of great significance for environmental protection. However, due to the low porosity and low permeability of shale reservoirs (Jarvie et al. 2007; Loucks et al. 2012), shale gas transport is limited, resulting in low shale gas production from a single well in its natural state, which hinders the commercial development of shale gas. Given this, hydraulic fracturing technology has been introduced into the oil and gas industry to improve oil and gas recovery, the core idea of the technology is to pump high-pressure fluids through a wellbore into a shale reservoir, where the fluids act on the surface of the rock and destroy it, creating effective fracture channels along which shale gas can flow to the wellbore and ultimately be extracted (Estrada and Bhamidimarri 2016; Vidic et al. 2013; Zhang et al. 2016). The first application of hydraulic fracturing technology to the oil and gas industry was in 1947, when the state of Kansas, USA, conducted the first successful hydraulic fracturing operation on the Hugoton gas field to increase the effectiveness of well fracturing and stimulation (Clark 1949; Gandossi and Von Estorff 2013; Grebe and Stoesser 1935). Since then, hydraulic fracturing has grown considerably in the oil and gas industry, and by 1955, over 100,000 hydraulic fracturing operations had been conducted across the United States (Hubbert and Willis 1957). Nowadays, hydraulic fracturing has become a key technology for unconventional oil and gas development and contributed significantly to the development of the energy industry. However, due to the complex geological conditions of deep underground shale, it is difficult to accurately predict the propagation paths of hydraulic fractures during the fracturing process, and it is not possible to adjust the hydraulic fracture propagation direction in real-time, which results in a limited complexity of the generated fracture network, thus limiting the oil and gas production.

In the past decades, scholars have conducted numerous researches on the accurate prediction of hydraulic fracture propagation paths in the hydraulic fracturing process and achieved certain conclusions and understanding (Borden et al. 2012; Zhao et al. 2020). Lamont and Jessen (1963), Daneshy (1974, 1978), and Blanton (1982, 1986) investigated the interaction process between discontinuities such as bedding and cracks and hydraulic fractures based on physical modeling tests of hydraulic fracturing, put forward the propagation criterion of hydraulic fractures in discontinuities, and pointed out that the difference of geostress and the angle of approximation (the angle of hydraulic fracture and natural fracture) are the main controlling factors affecting the interaction between hydraulic fractures and natural fractures., Renshaw and Pollard (1995) used a numerical method to establish a criterion for the interaction between hydraulic fractures and natural fractures under orthogonal action, and Gu and Weng (2010), Gu et al. (2012) extended it to the non-orthogonal case. In addition, scholars have investigated the effect of the widely distributed bedding structure in shale on hydraulic fracture propagation, pointing out that the bedding structure is the key to the generation of a complex network of seams by hydraulic fractures (Tan et al. 2018; Suo et al. 2020). Besides discontinuities, researchers have also investigated the effects of shale mineral composition and connections between mineral grains on hydraulic fracture propagation behaviors, pointing out that mineral composition indirectly affects hydraulic fracture propagation paths by influencing shale characteristics such as inhomogeneity, anisotropy, mechanical properties, and pore structure (Bakhshi et al. 2020; Chen 2022a; Li et al. 2020; Miao et al. 2021, 2023; Sun et al. 2021; Xiong et al. 2021; Zeng et al. 2019; Liang et al. 2019). Then, scholars also analyzed the stress state of the subsurface shale and found that the length of hydraulic main cracks becomes larger with the increase of the main stress difference (Blanton 1982, 1986; Renshaw and Pollard 1995; Gu and Weng 2010; Gu et al. 2012). The combined effects of geostress, stress shadowing between hydraulic fractures, pore pressure, fluid pressure, and other forces drive the hydraulic fractures to extend along the weaker structures in the rock, and ultimately drive the hydraulic fractures to extend along the direction of the maximum principal stress (Bakhshi et al. 2020; Blanton 1982, 1986; Duan et al. 2020; Huang 1981). Moreover, to forces, subsurface shale is also affected by temperature, and the degree of temperature effect on shale increases gradually with depth. Studies have confirmed that increasing temperature leads to a decrease in rock mechanical properties, an increase in plasticity and toughness, organic matter pyrolysis, and the development of micro-cracks, which reduces the rock fracture pressure, and consequently affects the extension behavior of hydraulic fractures (Huang et al. 2016; Isaza et al. 2021; Maruvanchery et al. 2022; Shen et al. 2020; Zhao et al. 2020). In addition, temperature affects the performance of the fracturing fluid during the fracturing process, which in turn indirectly affects the propagation of hydraulic fractures (Fu et al. 2019; Shen et al. 2019; Hou et al. 2016; Wen et al. 2022).The above remarks point out that geological factors have an important influence on the propagation of hydraulic fractures. However, different scholars have mainly focused on analyzing the influence of individual geological factors on hydraulic fracture propagation behavior, and most of the analyses are not comprehensive enough (Gou et al. 2021; Hageman et al. 2021a, b; Fu et al. 2020; Chen et al. 2022a). In particular, there are fewer studies on the interaction between geological factors, which in turn affect the hydraulic fracture extending behavior (Liu et al. 2021a, b; Zhao et al. 2022a; Ham et al. 2019; Zhang et al. 2021). Therefore, this paper firstly reviews the current literature on the influence of geological factors on hydraulic fracture propagation behaviors and combines its research to preferentially select five geological factors, namely, the mineral composition of shale, the connection between mineral particles, defects in the rock, geostress and temperature, analyzing the mechanism of their influences on hydraulic fracture propagation behaviors, and investigating the hydraulic fracture propagation behaviors under the combinations of these factors. The following part of this paper will discuss the mechanism of their influence on hydraulic fracture propagation from these five aspects respectively, to deepen the understanding of the mechanism of geological factors on hydraulic fracture propagation behavior, revealing the mechanism of hydraulic fracture propagation, and providing guidance for the prediction of hydraulic fracture propagation paths and fracture design.

2 Analysis of geological factors

Hydraulic fracturing technology has become the core technology for unconventional oil and gas reservoir stimulation due to its advantages of low cost and easy operation (Clark 1949; Hubbert and Willis 1957; Vidic et al. 2013). For hydraulic fracturing of reservoirs, it is necessary to analyze the propagation pattern of hydraulic fractures during the hydraulic fracturing process and clarify the propagation mechanism of hydraulic fractures to improve the prediction accuracy of hydraulic fracture propagation paths, adjust the turning direction of hydraulic fractures, and form a complex fracture network to ultimately obtain a higher volume of reservoir stimulating and a higher single-well oil and gas production (Beugelsdijk et al. 2000; Fu et al. 2013; Olson et al. 2012).

Currently, many scholars have studied the propagation pattern of hydraulic fractures during hydraulic fracturing and explored its influencing factors, which can be classified into two categories: geological factors and engineering factors through analysis of these influencing factors (Chen et al. 2022a; Hageman et al. 2021a, b). Among them, geological factors refer to the factors related to the shale itself in its natural state, such as the mineral composition, cementation type, and pore structure of the shale (Daneshy 1974; Warpinski et al. 1987; Bernabé et al. 1992; He et al. 2012; Chen et al. 2013); engineering factors mainly refer to the influence of the fracturing technique and construction parameters on the expansion behavior of hydraulic fractures during the development of shale oil and gas (Bunger et al. 2012; Guo et al. 2014; Hou et al. 2014a, b; Liu et al. 2014a, b; Fallahzadeh et al. 2015). Among them, geological factors are the most basic influencing factors, which are determined during the tectonic evolution; engineering factors are determined by the fracture design engineer and can be changed for actual conditions during the development process. The geological factors are decisive for the engineering factors. As different geological factors will select different fracturing techniques, a detailed and comprehensive analysis of the geological factors should be carried out to select the appropriate fracturing technique. In this paper, through extensive research into the literature on the behavior of fracture expansion by hydraulic fracturing, the geological factors affecting the behavior of fracture propagation by hydraulic fracturing are divided into five secondary factors: the mineral composition of the shale, the connections between mineral grains, defects in the shale, geostress and temperature, which are analyzed in detail below.

2.1 Influence of mineral composition

Minerals are the material basis of shale, and different mineral components and their contents and particle sizes determine the heterogeneous and anisotropy of shale and have an important influence on the propagation behavior of hydraulic fractures during fracturing (Guo et al. 2013; Li et al. 2013; Akbradoost et al. 2014; Zhou et al. 2016a, b; Ren et al. 2021). At present, the research on the influence mechanism of shale mineral components on hydraulic fracture propagation is limited by the research method, resulting in less relevant research content, and the existing research mainly uses X diffraction experiments to obtain the shale mineral composition and its content, and then establishes a mathematical model based on the theoretical analysis, and solves the model using numerical methods, to investigate the hydraulic fracture propagation pattern under the different mineral component ratios, thus revealing the influence mechanism of mineral components on hydraulic fracture propagation.

X-ray diffraction analysis revealed that shale is mainly composed of minerals such as quartz, feldspar, carbonate, clay minerals, and pyrite (Fig. 1) (Sun et al. 2021; Gong et al. 2021; Ye et al. 2022), and different mineral compositions have different properties, which affect the physical, mechanical and fracture toughness properties of the shale, and are determinative of its brittleness (Kang et al. 2020; Zhang et al. 2013). Brittleness (Meng et al. 2021; Dong et al. 2021; Liu et al. 2020) is an important characteristic of shale, mainly referring to the content of brittle minerals in shale, and is commonly characterized by the brittleness index. A higher brittleness index corresponds to a higher number of natural fractures and facilitates the formation of complex fracture networks (Guo et al. 2012). The mineral composition method and the rock mechanics parameter method are common methods for calculating the brittleness index of shales (Ye et al. 2019; Xia et al. 2017). The higher the brittle mineral content of shale, the higher its modulus of elasticity, the lower its Poisson's ratio, and the lower its fracture toughness, which is conducive to the generation of complex fracture networks (Zeng et al. 2019; Li et al. 2017; Xiong et al. 2019). Meantime, an increase in brittle mineral content also leads to higher initiation and initial fracture pressures in shales (Dou et al. 2022). Although brittleness is a good characterization of shale rock mechanics, the definition of brittle minerals is still controversial, and different scholars disagree on the definition of brittle minerals (Table 1), so the selection of brittle minerals becomes an important research element when analyzing shale brittleness. Currently, different scholars define brittle minerals based on the characteristics of the target shale reservoir in their research area, and then select the corresponding minerals as brittle minerals by integrating the geological characteristics of the study area (Xia et al. 2017; Zhang et al. 2017a, b; Lai et al. 2019). Although there is disagreement on the selection of brittle minerals, there is consensus on quartz as the brittle mineral, and the remaining brittle minerals are then selected based on their respective findings to characterize the brittleness of the shale (Ye et al. 2019; Lai et al. 2019). In addition to brittle minerals, clay minerals, an important component of shale, also have an impact on the propagation of hydraulic fractures. It was noted that as the clay content increases, shale ductility increases, and shale gas-filled pores are restricted, resulting in higher construction pressure required for fracture initiation and expansion during hydraulic fracturing, which is not conducive to shale fracturing (Bowness et al. 2022; Ren et al. 2014). Meanwhile, increased clay mineral content also leads to increased Poisson’s ratio, increased fracture toughness, reduced Young’s modulus, and reduced brittleness in shales, which is not conducive to fracture stimulation to generate complex fracture networks (Guo et al. 2013; Ren et al. 2014). Therefore, brittle minerals in shale are favorable for hydraulic fractures to form complex fracture networks, while clay minerals are not favorable for fracture stimulation, and hydraulic fractures should be designed to follow the brittle minerals and away from clay minerals as far as possible (Li et al. 2017; Borden et al. 2012, 2014; Ambati et al. 2015).

Fig. 1
figure 1

Mineral fractions and their contents of long 7 fault shale in southern Ordos Basin (Li et al. 2022a)

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Table 1 Definition of brittle minerals by different scholars
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In addition to shale mineral composition, shale mineral grain size and its distribution influence the propagation behavior of hydraulic fractures. Shale mineral grain size and its distribution have an important influence on fracture propagation and energy release, with the relative abundance of rougher mineral grains favoring compaction locally when the largest mineral grain size does not exceed five times the smallest mineral grain size, accompanied by both less fragmentation and energy release (Xiong et al. 2021). For different mineral compositions, the particle size and distribution determine the degree of the denseness of the shale. When the shale mineral compositions and their particle size combinations are better matched, the less heterogeneous and stronger the shale is and the more brittle the shale is, making it easier to fracture and stimulate (Li et al. 2017; Dou et al. 2022). Meanwhile, shale heterogeneity changes rock strength and stress distribution (Zou et al. 2020b), which ultimately affects the propagation behavior of hydraulic fractures. That is, shale mineral fractions and their grain size ultimately affect the propagation behavior of hydraulic fractures by influencing shale heterogeneity and its strength characteristics. Therefore, heterogeneity is often used as an indicator to evaluate the mineral composition of shale and its particle combination, and heterogeneity is positively correlated with the dominant mineral combination of the shale. The physical properties of shale such as porosity and permeability are also influenced by its mineral composition and its grain size. It was found that the tensile strength of the rock decreases with increasing particle diameter (Fig. 2), meaning that too large a particle size of the minerals comprising the rock reduces the strength of the rock and is not conducive to fracture stimulation (Chen 2022a). In addition, when the shale mineral particle combinations are better matched, the denser the resulting shale is, the smaller its porosity and permeability, and the poorly developed pore structure of the shale, which is not conducive to shale gas transport and development (Dou et al. 2022; Liu et al. 2021a). Therefore, the mineral composition and its particle sorting together determine the strength, elasticity, fracture toughness, pore permeability, and other properties of the shale (Li et al. 2022a, b; Erarslan et al. 2016). It was found that the more brittle minerals the shale contain and the more pore fractures are developed, the better the fracture modification is in facilitating the generation of complex fracture networks. In addition to the mineral composition, shale also contains some cementing substances, the presence of which can also have an impact on the strength, elasticity, fracture toughness, pore permeability, plasticity, and other properties of the shale (Erarslan et al. 2016). Therefore, when analyzing the influence of the mineral composition of shale on hydraulic fracture propagation, the joint influence of the mineral composition and its intergranular cement should be analyzed fully. In addition to minerals and their cement, shale also contains a small amount of organic matter, which shows ductile damage during hydraulic fracturing, and temperature changes also lead to the decomposition of organic matter, increasing shale porosity. Given the above characteristics of organic matter, when analyzing the influence of shale composition on hydraulic fracture extension behavior, the combined influence of mineral composition, inter-mineral cement, and its cementation strength and organic matter should be combined, and the joint influence of these factors should be analyzed comprehensively, to better guide the fracturing design and improve the effect of shale reservoir stimulation.

Fig. 2
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Tensile strength of shale as a function of mineral grain size (Chen 2022b)

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2.2 Influence of connection method

The composition of shale matter includes, in addition to the minerals, the cement that holds the mineral grains together. The mineral composition of shale and cement together determine the strength, physical, elastic, and fracture toughness properties of the rock (Liang et al. 2019; Pihu et al. 2012; Taylor et al. 2010). Therefore, in addition to the influence of shale mineral composition, the analysis of cement and its strength of the effect is also important when analyzing the influence of geological factors on hydraulic fracture propagation behavior. At present, the research on the influence mechanism of shale mineral components on hydraulic fracture propagation is limited by the research method, resulting in less relevant research content, and the existing research is mainly to use scanning electron microscopy to obtain the content of cement and its distribution, and then establish a mathematical model based on theoretical analysis, and use numerical methods to solve the model, to investigate the hydraulic fracture propagation of different types of cement and its intensity of action, thus revealing the influence mechanism of cement on hydraulic fracture propagation.

The cement content and cementation influence the strength, elasticity, fracture toughness, and other properties of the rock. As the cement content increases, cement is deposited in the pores between mineral grains and their contacts, impeding the relative sliding and rotation between mineral grains, which has an inhibitory effect on rock yielding and increases the strength of the rock (Bernabé et al. 1992). In addition, the filling of the pores between the mineral grains of the shale by the cement, which results in a large reduction in the pore space of the rock, reduces the local stress concentration, the shale becomes dense, the porosity and permeability are significantly reduced, and the density of the rock increases, again increasing the strength of the shale (Fig. 3) (Hangx et al. 2019). Based on an analysis of cement types, it was found that siliceous and ferruginous cemented rocks were stronger, followed by calcareous, and muddy cemented rocks were the least strong. In addition to cement type, the strength of shale cementation also influences the propagation behavior of hydraulic fractures (Taylor et al. 2010). When cementation is weak, shale mineral grains are more likely to rotate and move relative to each other during the fracturing process, and the rock becomes dense, forming local compaction zones. Therefore, cementation can influence local strain by controlling local compaction zones. In addition, weak cementation corresponds to low tensile stresses during rock failure and hydraulic fractures tend to spread along weakly cemented areas. Conversely, when cementation is strong, the shale mineral particles are firmly linked to the cement, and even undergo a series of physical and chemical changes that cause the shale mineral particles to bond to the cement, greatly increasing the strength of the rock and requiring higher tensile stresses to break the rock, while also resulting in poorly developed pore penetration and discouraging gas transport. Of course, the combination of strong cement, strong mineral grains and strong cementation significantly strengthens the rock, minimizes porosity and permeability, and increases rock density significantly, while also increasing the fracture pressure during fracturing construction, making it more difficult to extend hydraulic fractures in the area. Therefore, when analyzing the influence of geological factors on hydraulic fracture propagation behavior, the shale mineral components and the cement between mineral grains and their mode of action are important research aspects, and detailed compositional and strength analyses should be carried out in conjunction with shale characteristics in the specific study area to understand as much as possible the mechanism of the influence of these factors on hydraulic fracture propagation behavior, to better guide fracture design.

Fig. 3
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Combination between mineral grains and cement in shale (Li et al. 2022c)

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2.3 Impact of defects

The main defects in shale are faults, joints, bedding, fractures and natural fissures (Warpinski et al. 1987; Wang et al. 2022). Of these, they can be classified by size into large size faults and joints, and small size bedding, natural fractures and fissures. Defects are areas of stress concentration in the rock and are therefore more likely to break down during the fracturing process and become fracture initiation points. For dense shale reservoirs, most scholars have conducted extensive research on the influence of discontinuities such as bedding and natural fractures on the propagation behavior of hydraulic fractures, analyzing the interaction mechanism between discontinuities and hydraulic fractures using theoretical analysis, physical model tests, mining experiment, and numerical simulations, and proposing guidelines for the interaction between hydraulic fractures and discontinuities (Warpinski et al. 1987; Liu et al. 2022b; Wang et al. 2019).

  1. (1)

    Mechanism of interaction between natural fractures and hydraulic fractures

    The development of various scales of natural fractures in shale will influence the propagation behavior of hydraulic fractures, and determine the complexity of the resulting fracture network. It has been found that when a hydraulic fracture encounters a natural fracture, the hydraulic fracture at the contact interface may pass through the natural fracture, be stopped by the natural fracture, extend along the natural fracture, or penetrate the natural fracture while also bifurcating along it (Fig. 4) (Wang et al. 2019; Liu et al. 2022a; Li et al. 2022b). Which specific behavior occurs depends on the horizontal stress difference (the difference between the maximum horizontal principal stress and the minimum horizontal principal stress) and the orientation angle (the angle between the natural fracture and the hydraulic fracture) (Liu et al. 2022a; Li et al. 2022b; Gong et al. 2022; Guo et al. 2015; Zhou et al. 2017). According to the criterion for the intersection of hydraulic and natural fractures: at high levels of stress difference and orientation angle, hydraulic fractures tend to pass directly through natural fractures, forming longer single main fractures with fewer branching cracks and less fracture complexity; at moderate or low-stress differences and orientation angles, hydraulic fractures tend to deviate along or be arrested by natural fractures, forming complex fracture networks (Fig. 5) (Ai et al. 2018; Bakhshi et al. 2019). In addition to the orientation of natural fractures, the density, size, and strength of natural fractures and their location also influence the propagation pattern of hydraulic fractures (Liu et al. 2015; Behnia et al. 2015). When the natural fracture density (number of natural fractures per unit area) in a shale reservoir is higher, the more conducive it is to generating a complex fracture network (Zhao et al. 2013). The size of the natural fractures determines the volume of the shale reservoir it controls; when the size of the natural fractures is larger, the volume of the shale reservoir it controls is larger, so when the hydraulic fractures interact with them, the more complex the fracture network formed and the larger the volume of reservoir modification; conversely, when the size of the natural fractures is smaller, the volume of the shale reservoir it controls is smaller, and when the hydraulic fractures interact with them, they tend to cause the natural fractures to collapse or expansion along the natural fracture, and it is considered that the smaller natural fracture size has less impact on the overall direction of hydraulic fracture expansion, and therefore the modification volume is limited. The greater the natural fracture strength, the more the hydraulic fracture interacts with the natural fracture as shown in Fig. 4, but the energy required for the hydraulic fracture to pass through or open the natural fracture increases, and the threshold pressure to activate the natural fracture increases, meaning that it becomes more difficult to activate the natural fracture and more difficult to form a complex fracture network (Cheng et al. 2015; Li et al. 2022b). Natural fractures near the wellbore eliminate stress concentrations around the wellbore wall, reducing the hydraulic fracture initiation and propagation pressure, and changing the direction of hydraulic fracture propagation; away from the wellbore, the effect of natural fractures on hydraulic fracture propagation behavior depends on factors such as horizontal stress difference and natural fracture orientation angle (Wasantha et al. 2017; Dehghan et al. 2016). A large number of natural fractures of different scales exist in shales, and the presence of natural fractures has an important influence on the expansion path of hydraulic fractures. To accurately predict the expansion path of hydraulic fractures, the location, size, strength, orientation, density, and other characteristics of natural fractures present in shale need to be investigated and decided, thus better guiding the fracturing design.

    Fig. 4
    figure 4

    Results of the interaction between hydraulic and natural fractures (Gong et al. 2022)

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    Fig. 5
    figure 5

    Guidelines for the interaction of hydraulic and natural fractures (Blanton 1982, 1986)

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  2. (2)

    Mechanism of interaction between beddings and hydraulic fractures

    In addition to the interaction between natural fractures and hydraulic fractures, there are a lot of bedding in shales, which are discontinuous surfaces like natural fractures, and the interaction between the beddings and hydraulic fractures has an important influence on the creation of complex fracture networks. The interaction between beddings and hydraulic fractures has been studied extensively (Xu et al. 2015; Tan et al. 2017). The mechanism by which beddings influence the propagation behavior of hydraulic fractures is found to be similar to that of natural fractures: when a hydraulic fracture propagates into a bedding, the hydraulic fracture may pass through the bedding, or be arrested by the bedding, or be branched along the bedding, or branch along the bedding while passing through the bedding (Fig. 6) (Blanton 1982, 1986; Renshaw et al. 1995; Gu et al. 2012; Olson et al. 2012). Exactly which behavior occurs depends on the combination of stress difference and orientation angle (Bahorich et al. 2012; Sun et al. 2016). Also, factors such as the orientation, strength, and size of the beddings have an important influence on the propagation behavior of hydraulic fractures (Xu et al. 2015; García et al. 2013; Wang et al. 2021). When the stress difference is not considered, the hydraulic fracture always extends along the bedding when the angle between the bedding plane and the hydraulic fracture is small; as the angle increases, the hydraulic fracture gradually tends to pass through the bedding plane. The beddings, as stress concentrations in the rock, also have strict requirements for their strength. When the strength of the beddings is high, the hydraulic fracture tends to pass through the beddings; when the strength of the beddings is low, the fracturing fluid tends to flow towards the beddings, opening them and branching the hydraulic fracture towards the beddings (Tan et al. 2018). The larger the bedding size, the more hydraulic fractures tend to turn along the bedding plane, forming a complex fracture network. In addition to the nature of the beddings themselves, the angle between the beddings and the direction of the injection holes also has an important influence on the expansion of the hydraulic fractures; the smaller the angle between the injection casing and the bedding plane, the better the fracturing effect (Zheng et al. 2022). The beddings are one of the most developed structures in shale and thus have an important influence on the propagation behavior of hydraulic fractures. Therefore, further analysis is needed to identify the effects of various characteristics of the beddings on the propagation behavior of hydraulic fractures, such as the location, size, size and strength of the beddings in the rock, for better guidance of fracture design, formation of complex fracture networks, and achievement of reservoir volume stimulation Maximization.

    Fig. 6
    figure 6

    Interaction of hydraulic fractures with laminated surfaces (Fisher et al. 2012; Gu et al. 2022)

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In summary, the nature of the mechanisms affecting the behavior of hydraulic fracture propagation is the same for defects in shale, such as bedding, natural fractures, fissures, and other structures. Because these structures are discontinuities, there must be stress concentrations at these structures, leading to a complex series of interactions when hydraulic fractures extend into these discontinuities. The outcome of the interaction depends on the characteristics of these discontinuities, such as size, orientation, strength, etc. Therefore, when analyzing the influence of defects in rocks on the propagation behavior of hydraulic fractures, the size, direction, strength, and location of the defects should first be analyzed, to clarify the relevant characteristics of defects at different scales in shales, and then to analyze their influence on the propagation behavior of hydraulic fractures and identify the mechanism of their influence, hence providing more favorable supporting evidence for predicting the propagation path of hydraulic fractures. Of course, the presence of these defects is difficult to detect with current technology due to the denser shale deep underground and the small size of certain defects in the rock, which hinders the accurate prediction of hydraulic fracture propagation paths. Therefore, research on auxiliary techniques such as acoustic emission monitoring and CT scanning should be enhanced, to improve the resolution and accuracy of these auxiliary techniques, so that they can more accurately characterize the hydraulic fracture propagation behavior, thus providing technical support to achieve the goal of maximizing the volume of the stimulated reservoir.

2.4 Effect of in-situ stress

Forces are the fundamental cause of deformation and damage in rocks. When the force applied to the rock exceeds the strength limit of the rock, the rock will be deformed and damaged. This is also the case with hydraulic fracturing, where the fluid pressure applied to the surface of the rock is continuously increased by the continuous injection of fracturing fluid, and the rock is damaged when the applied fluid pressure exceeds the strength limit of the rock. Currently, studies on the influence of geostress on hydraulic fracture propagation are mainly based on hydraulic fracturing physical modeling experiments, numerical simulation methods, and mine site experiments. Among them, hydraulic fracturing physical modeling experiments and numerical methods are the most common used methods, while mine site experiments are limited in their application due to their high cost.

Numerous studies have confirmed, the direction of initiation and propagation of the hydraulic fracture during fracturing depends mainly on the magnitude and direction of the geostress on the rock, and the propagation direction of the fracture is always perpendicular to the direction of the minimum principal stress (Huang 1981). Therefore, before conducting hydraulic fracturing operations, it is necessary to conduct a force analysis of the subsurface shale in its natural state. Through the force analysis, the direction and magnitude of the in-situ stress on the subsurface rock can be determined, and then the appropriate fracturing technique and construction parameters can be selected to maximize the volume of reservoir stimulation. Generally, the in-situ stresses applied to subsurface rocks can be divided into three axes of stresses (Fig. 7), namely the maximum horizontal principal stress (σH), the vertical stress (σV), and the minimum horizontal principal stress (σh), which are perpendicular to each other and act together to determine the stress state of subsurface rocks (Huang 1981; Wei et al. 2021). Among them, when σV > σH > σh, the vertical stress plays a dominant role and the tectonic stress plays a weak role, which is a normal ground stress state; when σH > σV > σh, the tectonic stress plays a dominant role and the vertical stress plays a weak role, which is a local tectonic stress state (Hou et al. 2018). The different stress states have an essential influence on the expansion path of the hydraulic fracture and determine the selection of the injection direction and construction parameters (Hou et al. 2014a).

Fig. 7
figure 7

Three-way ground stresses on subsurface rocks (Wei et al. 2021)

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The direction of hydraulic fracture propagation is determined by analyzing the stress state of the subsurface rock. When the subsurface rock is under normal ground stress (σV > σH > σh), the horizontal stress difference (the difference between the maximum horizontal stress and the minimum horizontal stress) has a significant influence on the propagation of the hydraulic fracture, which is often expressed as a stress difference coefficient K (the ratio of the difference between the maximum horizontal stress and the minimum horizontal stress to the minimum horizontal stress). When the stress difference coefficient is small (i.e. the horizontal stress difference is small), the hydraulic fracture will propagate along the direction of the maximum horizontal principal stress, and when it encounters a natural fracture, it will easily turn along the natural fracture, reactivate the natural fracture, produce more branches, form a complex fracture network, and increase the stimulation volume of the reservoir; when the stress difference coefficient is large (i.e. the horizontal stress difference is large), the hydraulic fracture will propagate along the direction perpendicular to the minimum horizontal principal stress, and when it encounters a natural fracture, it will easily penetrate the natural fracture directly, with fewer branches, forming a longer single fracture reservoir reformation effect is poor (Fig. 8) (Hou et al. 2018; Ai et al. 2018; Ren et al. 2014; Guo et al. 2014). In addition, the propagation behavior of hydraulic fractures under vertical stress differences (the difference between vertical stress and minimum horizontal stress) was also analyzed and similar conclusions were derived for horizontal stress differences, i.e. low vertical stress differences favored the generation of a complex fracture network, and high vertical stress differences favored the generation of a long simple fracture. The behavior of hydraulic fracture propagation in subsurface rocks under tectonic stress state (σH > σV > σh) is similar to that of hydraulic fracture propagation under normal stress, i.e. with a large horizontal or vertical stress difference, the fractures will propagate in the direction of the maximum horizontal principal stress and tend to produce a long simple fracture; with a small horizontal or vertical stress difference, the fractures will propagate in the direction perpendicular to the minimum horizontal principal stress and tend to produce a complex fracture network. Meanwhile, the interaction between the hydraulic fracture and the natural fracture will become more intense due to the tectonic stresses, and the hydraulic fracture will deflect and distort significantly in the vertical direction.

Fig. 8
figure 8

Crack network generated at different stress differences (Tan et al. 2017)

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In addition to the difference in in-situ stress affecting the expansion behavior of hydraulic fractures, the direction of in-situ stress also influences the propagation of hydraulic fractures. The direction of propagation of a hydraulic fracture is always along the direction of the maximum principal stress and perpendicular to the direction of the minimum principal stress. Therefore, the direction of in-situ stress also heavily influences the propagation behavior of hydraulic fractures and, together with the ground stress difference, determines the complexity of the resulting fracture network. Currently, the stress angle (the direction of the maximum principal stress to the natural fracture) is commonly used to characterize the in-situ stress direction (Zhang et al. 2021). Under the condition of not considering the horizontal stress difference, when the stress angle is small, the maximum horizontal stress is approximately the same as the direction of the natural fracture, and the hydraulic fracture tends to propagate along the natural fracture and reactivate it, leading to the generation of a complex fracture network; when the stress angle is large, the hydraulic fracture tends to pass through the natural fracture and generate a simple long straight fracture, making it difficult to generate a complex fracture network (Zhang et al. 2018). Consider the effect of stress difference and stress angle together: when the stress difference is small, easier it is for the hydraulic fracture to turn along the natural fracture and activate the natural fracture, thus generating a complex fracture network, when the stress angle has less influence; when the stress difference is large, if the stress angle is large, the hydraulic fracture will go directly across the natural fracture, and the stress angle is too small, which will result in the generated hydraulic fracture generating a shorter length, which is not conducive to the generation of complex fracture networks. Therefore, to generate complex fracture networks, the appropriate stress angle range is 45–60° (Zhang et al. 2018, 2017b; Zhou et al. 2016a, b; Wang et al. 2016; Zou et al. 2016a, b).

The above focuses on the effect of stress difference and stress direction on the expansion behavior of hydraulic fractures. In addition, hydraulic fracture propagation is also influenced by stress anisotropy and stress shadowing (Ju et al. 2020; Duan et al. 2020). When the stress anisotropy is smaller, resulting in a smaller stress difference, it the more conducive to the generation of complex crack networks; conversely, a larger stress anisotropy results in a larger stress difference, making hydraulic fractures tend to generate simple cracks (Li et al. 2017). Stress shadowing is due to the interference effect of the first generated hydraulic fracture on the expansion of the later generated hydraulic fracture when multiple fractures expand simultaneously, i.e. the mutual interference of multiple hydraulic fractures in the expansion process, also known as the stress shadow effect (Wu et al. 2022; Chang et al. 2022; Kresse et al. 2012). When multiple cracks are extended, the cracks at both ends will dominate due to the stress-shadow effect, while the extension length and width of the internal cracks are inhibited, and the stronger the stress-shadow effect is as the crack spacing decreases, the more obvious the inhibition of the crack length and width is; conversely, when the distance between cracks increases, the stress-shadow effect will gradually diminish until the crack spacing is greater than its crack height, and the mutual The interference tends to disappear as the distance between cracks increases (Fig. 9) (Kresse et al. 2013; Han et al. 2020). Also, stress anisotropy affects the stress shadow effect. When the stress anisotropy is small, the stress shadowing effect will lead to crack diffusion due to mutual crack disruption; when the stress anisotropy is large, the stress anisotropy will offset some of the stress shadowing effects, resulting in limited crack diffusion and crack expansion along the direction of the maximum principal stress (Han et al. 2020; Guo et al. 2013). However, regardless of the degree of fracture diffusion, the stress-shadow effect will have a strong effect on the hydraulic fracture width, which will have an impact on the later fracturing.

Fig. 9
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Interaction between cracks as multiple cracks expand (Kresse et al. 2013)

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2.5 Effect of temperature

Shales are generally located deep underground (typically greater than 1500 m), with those developed in the Luzhou area of the Sichuan Basin in China buried at depths over 4000 m. For shales at greater depths, the temperature at which they are buried will also increase significantly. Therefore, when fracturing shales using hydraulic fracturing techniques, it is important to consider the effect of temperature changes on the fracture propagation behavior of hydraulic fracturing. Currently, studies on the mechanism of temperature influence on hydraulic fracture propagation mainly include hydraulic fracturing physical modeling experiments, numerical simulation methods, and mine site experiments. Among them, numerical methods are the most commonly used methods, while physical modeling experiments and mine site experiments are limited by research equipment, which results in their limited application.

It has been found that increasing temperature will change the mechanical properties of the rock. As the temperature increases, the brittleness, elasticity, and strength of the rock gradually weaken, plasticity and fracture toughness increase, and the mechanical properties of the rock gradually decrease (Fig. 10a, b) (Liu et al. 2014a, b; Huang et al. 2016; Shen et al. 2020); also, the organic matter in the rock will be pyrolyzed with the increase in temperature, and the conversion of organic matter into liquid or gas will increase the internal pressure of the shale, making the rock more prone to rupture, i.e. the fracture pressure of the rock will increase with the temperature during hydraulic fracturing. The rupture pressure of the rock will decrease as the temperature increases (Fig. 10c). Shale is a rock composed of multiple minerals and there are differences in the coefficients of thermal expansion between the minerals, so an increase in temperature will cause the various minerals to expand unequally, resulting in micro-fractures within the rock. The higher the temperature, the more the micro cracks will develop, and when defects in the rock are encountered, the microcracks will develop further and even evolve into microfractures, which will significantly reduce the strength of the rock (Fig. 10b) (Zhao et al. 2020), and the curvature of the fracture surface and the permeability coefficient of the shale will also increase (Xie et al. 2022).

Fig. 10
figure 10

Interaction of hydraulic fractures with laminated surfaces (Liu et al. 2014a, b; Kumari et al. 2018)

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In addition to its effect on the shale, temperature also affects the performance of the fracturing fluid. When the temperature of the fracturing fluid pumped into the shale is changed, the performance of the fracturing fluid changes, which affects the propagation behavior of the hydraulic fracture (Li et al. 2019). Based on physical model tests, it was found that low-temperature fluids drive hydraulic fractures to expand in a path opposite to the fluid pressure and reduce the curvature of the fracture surface, which is not conducive to hydraulic fracture expansion; as the fluid temperature increases, the viscosity of the fracturing fluid decreases, the fluid molecular activity becomes intense, and fluid kinetic energy increases, which will more easily rupture the rock and facilitate the expansion of hydraulic fractures (Shi et al. 2022). In addition, warming reduces the viscosity of the fracturing fluid, which reduces the sand-carrying capacity of the fracturing fluid, resulting in larger particles of proppant being difficult to transport to fractures further away from the wellbore and instead accumulating near the wellbore, to the detriment of forming a complex fracture network. Therefore, temperature can alter the performance of the fracturing fluid during hydraulic fracturing and, affecting the distribution of proppant and hence the extending behavior of the hydraulic fracture.

Therefore, the temperature can change not only the characteristics of shale reservoirs but also the performance of fracturing fluid during fracturing, thus affecting the propagation behavior of hydraulically fractured fractures during fracturing. In addition, temperature increases gradually with increasing reservoir burial depth. Therefore, the deeper the shale is buried, the higher the temperature and pressure it is subjected to, and the more intense the reaction that occurs in the rock (Xie et al. 2022). Different temperature ranges affect shales with varying intensity, with global shale burial depths ranging from a few hundred meters to several thousand meters or even tens of thousands of meters, and hence temperature variations from tens to hundreds of degrees Celsius. Faced with such a wide range of temperature variations, it is necessary to analyze in detail the mechanism of temperature variations on hydraulic fracture expansion behavior, establish a correlation model between temperature and hydraulic fracture propagation patterns, reveal the characteristics of hydraulic fracture expansion behavior with temperature during fracturing in shale reservoirs in different regions and at different depths, realize accurate prediction of hydraulic fracture expansion paths, and ultimately maximize the efficiency of reservoir stimulation. Of course, as shales are heterogeneous and anisotropic, there may be differences in the response of shales to temperature changes in different regions and at different depths, therefore, the model we build must have a sufficient number of data samples to minimize errors and improve the accuracy of hydraulic fracture expansion path prediction.

3 Discussion

When hydraulically fracturing shales, the expansion behavior of the hydraulic fractures is influenced by some factors that work together to determine the complexity of the generated fracture network. Analysis of the factors affecting hydraulic fracture extension reveals that the main factors are the mineral composition of the shale, mineral grain connectivity, defects in the rock, geostress, temperature, fracturing fluid, injection rate, injection holes, and fracturing sequence (Han et al. 2020; Chen et al. 2022a; Zhao et al. 2022a, b). Among these, the first five factors are mainly present in their natural state and are mainly related to the nature of the shale itself and the environment in which it is located, and can therefore be attributed to geological factors. The last four are factors involved in carrying out the shale gas development process and are primarily determined by the fracture design engineer and are therefore classified as engineering factors. Regarding the research on the mechanism of hydraulic fracture propagation by geological factors, scholars have conducted a lot of research on it by using hydraulic fracturing physical modeling experiments, numerical simulation methods, and site experiments, and have obtained certain conclusions and understanding. Different geological factors are subject to their action mechanisms, and thus the selected research methods are also different. Among them, the numerical simulation methods such as finite element method, discrete element method, and boundary element method are still dominated by the effects of shale mineral components, connections between mineral grains, and temperature on hydraulic fracture propagation, whereas hydraulic fracturing physical modeling experiments and site experiments are limited in their application due to their failure to reveal the mechanism of hydraulic fracture propagation. The effects of defects in shale and geostress on hydraulic fracture propagation are mainly studied by hydraulic fracturing physical modeling experiments and numerical simulation methods. Through hydraulic fracturing physical modeling experiments, the effects of geostress and discontinuity on hydraulic fracture propagation are investigated, and the mechanism is clarified; then, appropriate numerical simulation methods are selected and corresponding numerical models are established, and the numerical simulation methods are used to verify the results of the physical modeling experiments. The hydraulic fracturing site experiments, on the other hand, are less applied due to their high cost. However, the results obtained from hydraulic fracturing site experiments are the most accurate research method, and the results obtained from this method can well validate the results obtained from physical modeling experiments and numerical simulation methods. Therefore, more and more scientific research institutes and oil and gas companies have begun to cooperate to get real fracturing data by conducting hydraulic fracturing tests in the field and verifying the results of indoor experiments and numerical simulation methods, which in turn will promote the advancement of hydraulic fracturing research theories and methods, and then optimize the design of fracturing in the field, promoting the advancement of fracturing renovation theories and techniques.

Shale is formed by the gradual evolution of a variety of minerals, cement, and organic matter through long periods of sedimentation and diagenesis. The composition of the substances that constitute the shale, the connection between the different minerals and their strength of action, and the defects in the rock together determine the mechanical properties such as strength, elasticity, and brittleness of the shale (Beugelsdijk et al. 2000; Bunger et al. 2005; Liu et al. 2020; Pu et al. 2020), which in turn influence the propagation of hydraulic fractures. During the fracturing process, hydraulic fractures tend to propagate along brittle minerals such as quartz and dolomite, while ductile minerals such as organic matter and clay minerals are unfavorable to the propagation of hydraulic fractures. The strength and cementing effect of cement is stronger, and the propagation of hydraulic fracture is hindered at the boundary of mineral particles; Meanwhile, the connection between mineral particles and cement is more solid, and the mineral particles can not rotate freely, and the rock becomes dense, and the pore structure is not developed, which generates the shale with greater strength, and then increases the shale rupture pressure. Therefore, shale reservoirs with relatively large content of brittle minerals and weak cementation should be selected for fracturing (Belytschko and Black 1999; Ren et al. 2021; Zhao et al. 2014; Zhou et al. 2016b). Thus, when analyzing the factors affecting hydraulic fracture expansion during fracturing, it is not only necessary to consider the influence of individual factors on the fracture expansion behavior, but also to analyze their combined effects.

Defects are stress concentration sites in rocks. When hydraulic fractures extend to defects, their propagation pattern will become complex, which in turn increases the complexity of the generated fracture network. By extensive research on the interaction of natural fracture, bedding, and other discontinuities with hydraulic fracture, it has been confirmed that hydraulic fracture may undergo complex behaviors such as termination, diversion, and crossing at discontinuities. Based on this, scholars have proposed a criterion for the interaction of hydraulic fractures with natural fractures (Blanton 1982, 1986; Gu and Weng 2010; Gu et al. 2012; Renshaw and Pollard 1995; Zheng et al. 2022). The criterion states that the stress and angle of approximation control the propagation pattern of hydraulic fractures at discontinuities and that hydraulic fractures exhibit different propagation behaviors at discontinuities under different combinations of stress and angle of approximation. However, through further research, scholars found that factors such as fracturing fluid, proppant materials, and construction parameters also affect the expansion of hydraulic fractures at discontinuities. Multiple influencing factors act together to determine the propagation pattern of hydraulic fractures at the discontinuity. During the fracturing process, when hydraulic fractures encounter discontinuities, relatively small fracturing fluid viscosity, construction displacement, and proppant particles are advantageous combinations to improve the complexity of the generated fracture network. Meanwhile, the angle between the hydraulic fracture and the discontinuity is relatively large, which is more conducive to the communication of natural fractures and the generation of complex fracture networks.

Shales located deep underground are subjected to high pressure at depth, resulting in a series of reactions and changes. As the depth of burial increases, the pressure on the rock increases, leading to a corresponding increase in its geostress (Aliha et al. 2012; Isaza et al. 2021; Yang et al. 2021). It is found that the complexity of the generated fracture network decreases gradually with the increase of the principal stress difference during the fracturing process. Especially when encountering discontinuities, the smaller principal stress difference drives the hydraulic fractures to turn along the natural fractures, which in turn increases the complexity of the generated fracture network. In addition, the direction of the geostress also affects the hydraulic fracture propagation path, and the hydraulic fracture propagation direction will gradually tend to the direction of the maximum principal stress with the increase of the propagation time (Zhou et al. 2018; Long et al. 2011). In addition to the geostress, the interaction between cracks also exacerbates the complexity of the hydraulic crack propagation pattern. It is proved that the strength of interaction between cracks increases with the decrease of crack spacing. Therefore, selecting a perforation spacing that is compatible with the geostress is a prerequisite for generating a complex fracture network. Therefore, to improve the complexity of the generated fracture network during hydraulic fracturing operations, shale reservoirs with low-stress anisotropy should be selected for stimulation as much as possible, and the appropriate perforation spacing should be chosen as much as possible when perforation.

As the depth of shale increases, the temperature at which it is located gradually deepens, which in turn affects the relevant physical properties of shale. It is found that as the temperature rises, the mechanical properties of shale such as strength and elasticity gradually weaken, and ductility gradually increases, which in turn reduces the rock rupture pressure. In addition, heating will also promote the pyrolysis of organic matter in shale and the uneven expansion of minerals, which will lead to the development of a series of microcracks in shale, reducing the strength of the rock. Besides affecting the mechanical properties, material composition and other characteristics of the rock, temperature also affects the performance of the fracturing fluid, which in turn affects the expansion behavior of the hydraulic fracture (Maruvanchery and Kim 2022; Zhou et al. 2008; Long et al. 2011). It has been found that an increase in temperature increases the kinetic energy of fracturing fluid molecules, decreases the viscosity, and makes the rock easier to fracture. However, increasing temperature also reduces the sand-carrying capacity of the fracturing fluid, which is detrimental to the proppant transport. Therefore, during the fracturing process, temperature controls the hydraulic fracture extension behavior by affecting the shale physical properties and fracturing fluid properties, which in turn enables the control of hydraulic fracture extension behavior. During the hydraulic fracturing process, when the shale reservoir is located at a high temperature, relatively small proppant particles, construction displacement, and relatively large proppant combinations should be selected for fracture modification to increase the reservoir stimulation volume as much as possible.

During the fracturing process, the mineral composition of shale, the connection between components, the defects in the rock, the geostress, and the temperature are simultaneous, which together affect the hydraulic fracture extension, which in turn leads to the complexity and variability of the hydraulic fracture extension paths. Therefore, when analyzing the influence mechanism of geological factors on hydraulic fracture extension, in addition to analyzing the hydraulic fracture extension pattern under the action of a single factor, it is more important to analyze the extension pattern of hydraulic fracture under the combined action of multiple factors. Research shows that relatively high brittle mineral content and temperature, small stress anisotropy, cementation strength, and more developed natural fracture networks are favorable conditions for generating complex fracture networks. In the process of fracturing, shale reservoirs with relatively high brittle mineral content and temperature, small stress anisotropy and cementation strength, and more developed natural fracture network should be selected for fracturing and reforming as much as possible to generate complex fracture networks. In addition, the above research on the influence of geological factors on hydraulic fracture extension behavior is still mainly based on qualitative analysis to understand the relevant patterns of hydraulic fracture extension under the action of different influencing factors. Then, the quantitative research on the mechanism of the influence of each geological factor on hydraulic fracture extension behavior is relatively few and hinders the accurate prediction of hydraulic fracture extension paths. During the fracturing process, due to the many factors affecting the hydraulic fracture extension behavior and the different strengths of each influencing factor, quantitative research on the influence of each influencing factor on the hydraulic fracture extension behavior is necessary for the accurate prediction of hydraulic fracture extension paths, and it is also an important direction for the future hydraulic fracturing research. In addition, the characterization of hydraulic fracture extension patterns is also the focus of hydraulic fracturing research. Only by truly describing the expansion pattern of hydraulic fractures during the fracturing process can we provide a theoretical basis for the prediction of hydraulic fracture expansion paths. Therefore, real-time fracture characterization techniques such as micro-seismic monitoring and fiber-optic monitoring, as well as post-fracture fracture morphology characterization techniques such as CT scanning, are also the focus of future hydraulic fracturing research.

4 Conclusion

  1. (1)

    The geological factors affecting the hydraulic fracture propagation behavior during shale fracturing are mainly the mineral components of shale, the connection between mineral particles, the geostress, the defects in the rock, and the temperature. The influence mechanism of different geological factors on hydraulic fracture propagation behavior varies, and each influencing factor affects each other, which makes it difficult to predict the hydraulic fracture propagation path accurately.

  2. (2)

    During the fracturing process, the relatively high brittle mineral content and temperature in the shale, the small stress anisotropy and cementation strength, and the more developed natural fracture network are favorable conditions for the generation of a complex fracture network.