1 Introduction

Unconventional tight-sandstones oil and gas reservoirs are characterized by low permeabilities, usually less than 0.1 mD, (Law & Curtis 2002; Zhang et al. 2015). The economic recovery of these reservoirs is seeing increased success worldwide, largely attributed to two principal technologies: multi-stage hydraulic stimulation and horizontal drilling. Hydraulic stimulation is commonly utilized to generate a complex network and enhance permeability through increased contact area (Virues and Ehiriudu 2016). During hydraulic fracturing, proppant-laden fluid is pumped into a well to initiate and propagate fractures, thereby improving reservoir conductivity (Fan et al. 2022; Huang et al. 2017). These technologies have been successfully implemented in development of unconventional oil and gas plays, particularly in North America, Australia, and China (Ma et al. 2012; Rahman et al. 2007; Valko and Economides 1995).

Nevertheless, the full potential of hydraulic fracturing has yet to be realized. In some casess, it has failed to produce the desired fracture network (Rahman et al. 2007). Studies show that the performance of hydraulic stimulation jobs can be influenced by various factors. These include engineering-related conditions, such as types of fracturing fluids, injection pressure, type, size, and shape of proppant, injection displacement. Geological conditions, like bedding planes and reservoir conditions (e.g., mineralogical composition, matrix permeability, presence of natural fractures) also play a role (Mollanouri-Shamsi et al. 2018; Nailing et al. 2019; Parvizi et al. 2017). A comprehensive understanding of the reservoir’s geomechanical behavior and geological conditions can significantly improve economic gains by optimizing the extraction of oil and gas resources (Li et al. 2020).

Most studies on tight sandstone hydraulic fracturing mainly focus on fracture orientation, toughness, propagation, and how these fractures interact with natural fractures. Fracture propagation process is influenced by in-situ stress field and orientation, and the fractures propagate generally along the direction of maximum principal stress (Wright and Conant 1995). Another central aspect that affects fracture propagation is the pumping rate. It is hypothesized that introducing pauses during the pumping process is thought to influence the fracture growth path, thus determining the effectiveness of the stimulation process (Yu et al. 2019). According to Zhang et al (2014), rock brittleness plays a significant role in hydraulic fracturing. Brittleness, defined as the total energy stored in rocks before failure, is an intricate function of fracturing fluid type, rock elastic properties, strength, and lithological properties of the formation. Brittle rocks, due to their propensity to fracture easily, can produce complex fracture networks (Dubey et al. 2019). A significant factor in creating these networks is shear slip, determined by the surface roughness, or frictional strength, of the fracture surface (Wang et al. 2020; Yan et al. 2016).

The in-situ stress state, the angle at which hydraulically generated fractures approach the natural fractures, and rock mass shear strength significantly impacts the entire process of hydraulic fracturing (Wasantha and Konietzky 2017). Ideally, hydraulic fractures are expected to propagate along the direction of maximum horizontal stress. However, this is not necessarily true. If the differential stresses are generally small while the angle of approach between natural and hydraulic fractures is relatively tiny, the hydraulic fractures tend to propagate in the same direction as natural fractures. If the stress levels remain low while the angle of approach increases, the hydraulic-induced fractures will either propagate over the natural fracture or penetrate through them (Blanton 1986).

In unconventional blocks, the aim is to create a complex fracture network and, more specifically, a self-supporting network of shear and slide fractures (Fig. 1). Previous studies suggested that slip and shear dilations in the fracture surfaces can create permanent matrix permeability enhancement (Maxwell et al. 2002; Moos et al. 2013). Johri and Zoback (2013) note that hydraulic conductivity and reservoir fluid flow enhancement can only occur when hydraulic fractures are appropriately propped and when there's shear-stimulating pre-existing faults and natural fractures. Hence, hydraulic fracturing doesn't merely induce tensile fractures into reservoir rocks; it also activates slippage on the existing natural fractures and faults planes. This activation significantly expands the hydraulically conductive zone responsible for reservoir productivity.

Fig. 1
figure 1

Illustration of a complex fracture networks in unconventional plays

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When hydraulic pressure is applied, it mitigates the effects of the normal stress acting upon the fracture surface and subsequently decreases the friction coefficient (Wang et al. 2019; Yan et al. 2016). Such a reduction in effective stress and friction coefficient can significantly enhance the potential for shear sliding and crack propagation in tight sandstone. In tight sandstones, the natural fractures' shear and slip predominantly rely on inherent shear strength and frictional properties. Based on their mineralogy (clay, quartz, and other minerals), tight sandstones will have differing frictional properties, which can further be altered between the interaction of the minerals and the fracturing fluid. The fracturing fluids not only create fractures and transport proppant, but they also minimize the fracture surface frictional strength by decreasing their frictional coefficient and effective normal stress. Nevertheless, studies focusing on the shearing and sliding of sandstone plays during hydraulic fracturing, particularly its frictional properties due to the influence of fracturing fluids, are few. One well-known reaction is related to a change in frictional properties of the creviced surface, whereby its stiffness and hardness characteristics are tremendously altered (Liu et al. 1994). Regardless of whether fluid-rock interaction induces the surface softening or liquid film effects, the frictional properties of the fractures are likely to be altered, and thus the shear and slip network of the reservoir rocks will be affected. Consequently, the investigation of frictional characteristics of tight sandstone, mainly due to the effect of fracturing fluids, should be given adequate attention to advance our understanding of generating complex fracture networks during the hydraulic stimulating of unconventional sandstone plays.

In this paper, by analyzing tight sandstone samples’ mineralogy content and determining the proportionate mineralogical content on each sample (especially clay composition proportion) and by considering different fracturing fluids, the friction characteristics of tight sandstone samples are investigated by friction experiments. Further, the effects of varying the friction coefficients are studied via numerical simulation studies to determine the optimal value of the friction coefficient which can form a complex network. In addition, this study can enhance hydraulic fracture optimization by guiding how to select fracturing for tight sandstone depending on its mineral content, so as to achieve the desired productivity.

2 Experimental study frictional characteristics of tight sandstone

2.1 Experimental setup

An indoor rock friction testing apparatus was designed and manufactured (Fig. 2), which has a precision of horizontal displacement of 2.0 μm. The spherical joints ensure the normal stress perpendicularly to the sliding direction under all conditions. The design of liquid cells facilitates testing of rock friction characteristics in a fluid environment, with an integrated data acquisition system that can automatically record the drag force, micro-displacement, and normal pressure throughout the test.

Fig. 2
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A newly designed rock friction testing device. a schematic diagram; b photograph

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2.2 Tight sandstone samples’ geological characteristics and test methodologies

Test samples for this study, shown in Fig. 3, were sourced from the Changqing formation in the Chang7 tight sandstone oil play (commonly known as CQ tight sandstone). The mineralogy of the sample was determined by X-ray diffraction analysis, specific mineral content in all the samples includes plagioclase, dolomite, clay, and quartz.

Fig. 3
figure 3

Friction test tight sandstone samples

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As shown in Fig. 4, The clay content among the three samples is highest in sample C (30%), while sample A has the lowest amount at 20%. Further, the analysis results show that illite is the predominant clay mineral accounting for over 60 wt% in sample C, while sample B has the lowest at just under 50%. Other major clay components include illite/smectite, chlorite, and kaolinite.

Fig. 4
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Absolute clay minerals of the samples A, B, and C tight sandstone

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For this investigation, rock samples were separated and pretreated into three groups: tight sandstone dried at 105 °C for 24 h, tight sandstone saturated in deionized water (DI) for 5–10 min, and tight sandstone saturated in slickwater for 5–10 min. The experiment was conducted at 25 °C (room temperature). The frictional coefficient test matrix was shown in Table 1.

Table 1 Frictional coefficient test matrix
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2.3 Microstructure of the samples

Figure 5 shows the failure surface along a natural interlayer for each of the three samples, and traces of clay minerals can be observed clearly on the surface morphology. The microstructure of the samples was examined with a model TM3030 table scanning electron microscope, whose representative petrographic images are illustrated in Fig. 6. Even though our samples might not necessarily exemplify absolute end-members of the vast Chang7 play, it can be seen that the surface of the rock samples is covered with mud. More so, the variation in particle distribution depicts the variation in samples’ mineralogical content and probably the distribution of clay minerals. This can also imply roughness on the failure plane, which is essential because the friction characteristics of polished and unpolished rock surfaces behave differently when rock samples interact with a liquid medium. The friction coefficient of rocks on the polished surface increases when they are saturated with water, while rocks on the rough surface generally decrease (Byerlee 1967).

Fig. 5
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The original morphology of the three rock samples

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Fig. 6
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Surface electron microscope images of the three rock samples

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On the other hand, the surface morphology test patterns of the three experimental rock samples before and after friction sliding under 36 mesh emery conditions are shown in Fig. 7. Figure 7a, c and e are the three rock samples before friction sliding test and Fig. 7b, d, and f are the samples after fiction sliding test. There is a wide range of ripples in rocks surface, commonly referred to as "Asperities". Compared with before friction sliding, the sliding contact surface after friction is relatively smoother, and the contact area will be closer to the surface area of the sliding surface.

Fig.7
figure 7

Surface topography of the three rock samples before and after friction test. a and b are rock sample A; c and d of rock sample B; and e, f are rock sample C. (a), (c), (e) before friction test and (b), (d), (f) after friction test

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2.4 Normal stress effect on tight sandstone frictional behavior

It is observed that normal stress affects the rock frictional coefficient and its sliding mode, which is consistent with the findings of Carpenter et al. (2016). Three experimental rock samples were polished with 36-purpose sand and dried at 105 °C for 24 h (dry condition) for rock micro-sliding friction experiments. Effective normal stresses of 0.25 MPa, 0.50 MPa, and 1.00 MPa were applied to evaluate the influence of these stresses on rock sliding friction. Figure 8 illustrates the friction coefficient-displacement curves of the one experimental rock samples under different effective normal stresses. The normal stress influences the sliding friction coefficient (SFC) of Chang7 sandstone. As the sliding displacement increases, the friction coefficient exhibits significant fluctuations. These fluctuations are likely attributable to the effects of surface asperities on the rock sliding friction. The differences in the peak height, peak shape, and self-intensity of the asperities determine the different ways and strengths of the asperities interact, and the degree of fragmentation is also different, which leads to the continuous change of the sliding mode and friction strength. The coefficient is unstable and fluctuates accordingly; however, the unstable fluctuation of the kinetic friction coefficient is stable from a macroscopic point of view and usually fluctuates around a specific value. The average value of the coefficient is characterized, which can well reflect the macroscopic sliding friction characteristics and overall friction strength of rocks. The average value of the coefficient is characterized, SFC, about 0.7, which can well reflect the macroscopic sliding friction characteristics and overall friction strength of rocks. The sample exhibits a roughly stick–slip mode behavior defined by a maximum value at the conclusion of the static friction stage (Kaproth & Marone 2013), followed by the beginning of the sliding friction stage and a generally steady curve.

Fig. 8
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Effect of Normal stress on the sliding friction of Chang7 sandstone samples (air-dried condition)

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2.5 Liquid infiltration and mineral components effect on tight sandstone frictional behavior

The dry air environment’s effects on the samples’ friction coefficients are illustrated in Fig. 9. The coefficient of friction appears to fluctuate; however, the rock sample A attains a stable coefficient of about 0.61, while a stable coefficient of rock samples B and C are slightly lower at approximately 0.55. The influence of the dry air environment on the friction coefficient of tight sandstone is negligible regardless of the variations in mineral content and proportion of clay components. Like normal stress effects, a stick–slip mode behavior in dry air is observed with small peak values appearing at the end of the static friction stage, and the curves tend to smooth out.

Fig. 9
figure 9

Sliding friction behavior of Chang7 sandstone in a dry environment (0.5MPa Normal stress)

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After the surface of the sample was wetted with DI water, the maximum static and sliding friction coefficients decreased from 0.58 to 0.46. Figure 10 shows the variation of the friction coefficient of tight sandstone in a deionized water (DI) environment. With the increase of the sliding displacement, the friction coefficient still shows strong fluctuation, which indicates that the existence of liquid greatly influences the asperities. However, compared with the dry conditions, the friction coefficient is significantly reduced, which indicates that the liquid infiltration reduces the frictional resistance and plays a lubricating effect; at the same time, the liquid infiltration and the existence of quartz make the rock sliding mode from stable sliding. The friction coefficient of rock sample A (low in clay content) is higher than those of the other samples that have higher clay content. In the DI environment, the amount of clay mineral in the samples significantly impacts their friction coefficient values decreasing with increasing clay content. In addition, the friction coefficient curves appear to fluctuate more in a deionized water environment with peak values at the end of the static friction stage.

Fig. 10
figure 10

Sliding friction behavior of Chang7 sandstone in DI water environment (0.5MPa Normal stress)

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Figure 11 depicts the behavior of friction coefficients of sandstone samples in a slickwater environment. The average coefficients of friction for rock samples A, B, and C are correspondingly 0.53, 0.48, and 0.45. It was noticed that slickwater made sliding smoother, and the peak value (highest static frictional coefficient) disappeared (Yan et al. 2016). With the presence of clay inhibitors in slickwater, the growth of clay minerals is inhibited; hence, hard particles such as quartz and feldspar present in the samples have the greatest influence on the friction coefficient. Slick water transformed the frictional mode into steady sliding.

Fig. 11
figure 11

Sliding friction behavior of Chang7 sandstone in Slickwater environment (0.5 MPa Normal stress)

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The average friction coefficient of each rock sample in various fluid environments is presented in Table 2. For rock sample A (with low clay content of 20%), the average friction coefficient in DI water and slickwater reduces less than 8.2% compared to dry environment. In this case, the clay content in different fluid environments has little influence on the friction coefficient; in other words, the friction properties of the samples are primarily controlled by the amount of quartz, feldspar, and other hard particles. Due to the fluid wetted effect in DI water and slickwater environment, the hard surface particles in sample A only experienced the shear expansion, which could explain the smaller friction coefficient difference in the wetted environments and the dry environment. The average value of the friction coefficients of Sample B in dry environment is higher than the DI water environments about 12% and higher than the slickwater environment about 14.6%. Under dry and DI water environment, the difference in the friction coefficients of sample C is relatively bigger. Compared to the average friction coefficient in a slickwater environment, the values in dry and DI environments are approximately 22% higher. The clay content of this sample plays a predominant role in its frictional characteristics.

Table 2 The average friction coefficient of each rock sample in various fluid environments
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3 Numerical simulation and result analysis

At least five parameters must be correlated simultaneously to model the propagation of hydraulic fractures in a naturally fractured formation: (1) fracture initiation and propagation; (2) fluid movement within the fracture; (3) on fracture surfaces, fluid pressure induces rock deformation; (4) frictional activities of nature fracture; and (5) the interactions between hydraulic fractures and pre-existing natural fractures. To achieve this purpose, an explicit temporal integration–based pore pressure cohesive zone (Explicit PPCZ) model was created. As shown in Fig. 12, triangular components are used to discretize the rock domain. Between triangular components, zero-thickness cohesive elements are introduced to depict fracture formation and fluid flow with fractures. By employing this meshing strategy, the issues resulting from the intersection of hydraulic and natural cracks may be avoided (Li et al. 2019).

Fig. 12
figure 12

Mesh discretization for Explicit-PPCZ model

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3.1 Cohesive zone model

Considering the complexity and variability of the actual process of hydraulic fracturing and the mechanical state of reservoir rocks, the cohesive zone model (CZM) is a simulation method compatible with ABAQUS. It introduced by Barenblatt (1959) and Dugdale (1960), in order to overcome the stress singularity at the fracture tip, which is a problem with conventional linear fracture mechanics. According to the CZM, the mechanical behavior is dictated by the traction–separation law in the fracture process zone before the fracture tip. Cohesive zone models are described in further depth in previous research (Li et al. 2019; Wu et al. 2021). Since friction between fracture surfaces significantly contributes to the shear activation of natural fractures in rock-like materials, a CZM with frictional contact capability is used to model fracture initiation and growth in this study. As shown in Fig. 13, the bilinear traction–separation law be utilized to calculate the normal and cohesive traction in interface element.

$$\sigma = \left\{ {\begin{array}{*{20}l} {\frac{{\overline{\sigma }}}{{\delta_{n}^{0} }}\delta_{n} ,} \hfill & {{\text{if }}\delta_{n} < \delta_{n}^{0} } \hfill \\ {\frac{{\delta_{n}^{1} - \delta_{n} }}{{\delta_{n}^{1} - \delta_{n}^{0} }}\overline{\sigma },} \hfill & {{\text{if }}\delta_{n}^{0} \le \delta_{n} < \delta_{n}^{1} } \hfill \\ {0,} \hfill & {{\text{if }}\delta_{n} \ge \delta_{n}^{1} } \hfill \\ \end{array} } \right.$$
(1)
Fig. 13
figure 13

Cohesive zone model: a tension; b shear. (Li et al. 2019)

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$$\left| \tau \right| = \left\{ {\begin{array}{*{20}l} {\frac{{\overline{\tau }}}{{\delta_{t}^{0} }}\delta_{t} + \tau_{f} ,} \hfill & {{\text{if }} \left| {\delta_{t} } \right| < \delta_{t}^{0} } \hfill \\ {\frac{{\delta_{t}^{1} - \delta_{t} }}{{\delta_{t}^{1} - \delta_{t}^{0} }}\overline{\tau } + \tau_{f} ,} \hfill & {{\text{if }}\delta_{t}^{0} \le \left| {\delta_{t} } \right| < \delta_{t}^{1} } \hfill \\ {\tau_{f} ,} \hfill & {{\text{if }}\left| {\delta_{t} } \right| \ge \delta_{t}^{1} } \hfill \\ \end{array} } \right.$$
(2)

in which

$$\tau_{f} = \left\{ {\begin{array}{*{20}c} { - \mu \sigma ,} & {{\text{if }}\sigma < 0} \\ {0,} & {{\text{if }}\sigma \ge 0} \\ \end{array} } \right.$$
(3)

where \(\overline{\sigma }\) and \(\overline{\tau }\) are interface element cohesive tensile and shear strength. \(\delta_{n}\) is a normal separation and \(\delta_{t}\) is a shear separation of an interface element at any given moment. \(\delta_{n}^{0}\) and \(\delta_{t}^{0}\) are the normal separation and shear separation at damage initiation, respectively. \(\delta_{n}^{1}\) and \(\delta_{t}^{1}\) are the normal and shear relative displacements rep at the total failure, respectively. \(\tau_{f}\) is the interfacial friction.

In Fig. 13a, The region under the traction separation curve is referred to as \(G_{IC}\), which represents the energy of fracture per unit region of the fracture surface.

3.2 Numerical model setup

On-site data analysis was performed to obtain the necessary parameters (Table 3) for the numerical simulation. Based on the cohesive zone model mentioned above, a 2-D (two-dimensional) formation model by 40 m × 40 m is constructed (Fig. 14). Around the model’s center, which is set as the injection point, 30 and 20 pieces of 6m and 4m natural cracks are arranged anti-symmetrically, and the least horizontal ground stress is applied in the x-direction, while the highest horizontal ground stress is applied in the y-direction. Further, the triangular meshing method is adopted with a total of 3558 triangle meshes and 5257 interface Elements, while the boundary conditions for this model are fixed displacement and impermeable conditions.

Table 3 Numerical simulation input parameters
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Fig. 14
figure 14

A schematic representation of 2-D stratigraphic model

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3.3 Numerical simulation results analysis

The simulation result investigated the effect of the fracture surface friction coefficient on the fracture propagation morphology by altering the natural fracture surface friction coefficients (0.3, 0.4, 0.5, 0.6, 0.7, and 0.8). The results of this study are shown in Fig. 15.

Fig. 15
figure 15

Numerical simulation results of fracture propagation (×100 times)

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By Setting the frictional coefficient of the natural fracture surface at 0.3, 0.4, 0.5, and 0.6, the hydraulic fracture appears to turn and propagates along the natural fracture (Fig. 15a–d). In contrast, when the friction coefficient of the natural fracture surface is set to between 0.7 and 0.8, the hydraulic fracture propagates straight through the natural fracture in the direction of the highest horizontal in situ ground stress. (Fig. 15e–f).

The impact of varying the friction coefficient on the fracture propagation pattern can be examined more intuitively by considering the nature of the seam network, which is defined by the rate of the surface seam and the crack inclination angle dispersion. The surface fracture rate can be expressed as the ratio of the summation of the fracture areas to the summation of the surface area of the core lithology:

$${R}_{f}=\sum\limits_{i=1}^{n}\frac{{S}_{i}}{{S}_{l}}$$
(4)

where \({R}_{f}\) is the surface crack rate, dimensionless; \({\varvec{n}}\) is total number of cracks; \({{\varvec{S}}}_{{\varvec{i}}}\) is the area of the i crack, \({{\varvec{S}}}_{{\varvec{l}}}\) is the side surface area of the core, both units are pixels.

The dispersion of crack dip angle can be expressed as the variance of all crack dip angles:

$${D}_{a}=\sqrt{\frac{{\sum }_{i=1}^{n}{\left({A}_{i}-\overline{A}\right)}^{2}}{n}}$$
(5)

where \({D}_{a}\) is the dispersion of crack dip angle, dimensionless; \(n\) is total number of cracks; \({A}_{i}\) is the dip angle of the i crack, \(\overline{A}\) is the average inclination, both units are degrees.

The normalized surface fracture rate \({R}_{f}\) and fracture dip dispersion \({D}_{a}\) are given by:

$${R}_{fn}=\frac{{R}_{fi}}{{\sum }_{i}^{n}{R}_{fi}}$$
(6)
$${D}_{an}=\frac{{D}_{ai}}{{\sum }_{i}^{n}{D}_{ai}}$$
(7)

where \({R}_{fn}\) is the normalized surface crack rate; \({R}_{fi}\) is the surface crack rate of the i crack; \({D}_{an}\) is the normalized dispersion of crack dip angle; \({D}_{ai}\) is the dispersion of crack dip angle of the i crack.

The fracture complexity can be expressed as:

$${F}_{c}=\frac{1}{2}\left({R}_{fn}+{D}_{an}\right)$$
(8)

\({F}_{c}\) is the dimensionless fracture complexity and its value is directly related to quality of the fracturing.

In order to comprehend how different natural fracture surface friction coefficients at the ending of fracturing could affect the fracture propagation pathway and its length, the locations and failure units were extracted, and their plots were constructed, as shown in Figs. 16 and 17, respectively. It is evident from the location plots that the increase in the friction coefficient of the natural fracture surface decreases the length of the activated natural fracture, and so does the total fracture length. It is further obvious that the propagation of hydraulic fractures along with the natural fractures, mainly when the frictional coefficients are set to 0.3, 0.4, 0.5, and 0.6, makes the length of the activated natural fractures more extensive when compared to the length of induced hydraulic fractures. In this case, the sum of the natural and hydraulic fracture lengths makes up the total length of fractures. However, the natural fracture activation length has the most significant influence on the total fracture length.

Fig. 16
figure 16

The effects of different natural fracture surface friction coefficients on fracture propagation paths

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Fig. 17
figure 17

The effects of different natural fracture surface friction coefficients influence fracture length

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On the other hand, direct passing of the hydraulic fracture through the natural fracture and its further extension (when the frictional coefficient is 0.7 and 0.8) markedly decreases the activation length of the natural fracture. Thus, the total fracture length is predominately dependent on the hydraulic fracture. Therefore, an increase in the induced hydraulic fracture length tends to increase the total fracture length.

The results of the fracture complexity calculations under different values of the natural fracture surface friction coefficients (0.3, 0.4, 0.5, 0.6, 0.7, 0.8) are presented in Fig. 18. First, as the friction coefficient increases from 0.3, the fracture complexity tends to increase, peaking at 0.4. At the same time, fracture rate and dip dispersion are at their peak values. In addition, compared with the two interaction cases of hydraulic fracture and natural fracture, when the hydraulic fracture directly extends through the natural fracture, the fracture complexity is significantly lower because the total length of the fracture is smaller and the fracture morphology is single (the fracture is almost a straight fracture). The subsequent increase in the natural fracture friction coefficient decreases the value of the fracture complexity.

Fig. 18
figure 18

Fracture length statistics under different natural fracture surface friction coefficients

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4 Conclusions

In this study, the frictional characteristics of three kinds of tight sandstone were tested using an indoor rock micro-friction setup. According to the results of the tight sand friction tests, the composition of the tight sandstone, particularly the content of clay and the fluid environment, affects the friction coefficient correspondingly. The key findings can be summarized as follows:

  1. (1)

    The tight sandstone with low clay content, such as rock sample A (clay content is 20%), has a high friction coefficient under different fluid environments. Under the fluids wetted condition, it does not experience the asperities shear stage, and its friction coefficient is higher in DI water and slickwater as well.

  2. (2)

    When the tight sandstone clay content is higher, such as rock sample C (clay content is 30%), clay swelling by water absorption (in DI environment) reduces its friction coefficient. In slick-water environment the friction coefficient of the three kinds of the samples is slightly decrease due to the additive of large molecular polymer (resistant reducer).

  3. (3)

    Combined with friction experiment, the numerical simulation result shows that an internal friction coefficient of 0.4 is the most favorable for generating a complex fracture network in a tight sandstone reservoir. Thus, it would be beneficial to control the type of injected fluid in different reservoir blocks of varying clay content to ensure that the internal friction coefficient remains at around 0.4.

  4. (4)

    When the target reservoir blocks have low clay content (less than 20%), waterless fracturing fluid could be the most suitable fracture stimulation agent, while when the clay content in the target reservoir blocks is high (more than 30%), DI water or slickwater with low clay inhibitor content can be used for fracturing purposes. Finally, for blocks with 22% clay content, slickwater can produce the desired fracture complexity.