Fluid-Solid Coupling Mechanism of Shale Hydraulic Fracture Propagation Based on True Triaxial Test and Numerical Analysis

The fracture mechanics and geomechanics were used to study the interaction between water and rock, and the relationship between rock fracture and water pressure is determined. So the hydraulic crack propagation mechanism can be obtained to evaluate the effectiveness of hydraulic fracturing.

The circumferential stress of horizontal wells under in situ stress and hydraulic pressure was generally analyzed. And the fracture criteria were used to judge whether cracks are generated. Fluid infiltration and microfissures were combined to analyze the crack propagation. The expansion direction of cracks can be obtained from the theory of maximum circumferential stress [1, 2], strain energy [3], and critical energy release rate [4], but hydraulic fracturing factors were not considered. True triaxial hydraulic fracturing laboratory test is an intuitive method to monitor and observe the crack initiation and propagation of hydraulic fracturing. It is an effective and reliable means to understand fracture geometry and propagation law. Ito and Hayashi used a cube andesite rock block to perform a triaxial hydraulic fracturing test at a fixed flow rate and obtained the differential relationship between pore pressure and time during crack propagation [5]. Hou found that hydraulic fracture bifurcate and divert at weak bedding planes and gradually become perpendicular to the direction of the minimum horizontal principal stress by true-triaxial horizontal well fracturing tests [6]. Feng Yanjun [7] prefabricated cracks in rock samples. The propagation law of cracks was studied by true triaxial hydraulic fracture propagation test. It is found that under the condition of large stress difference, the final orientation of crack propagation is determined by the stress field. Guo et al. [8] studied the crack propagation pattern under hydraulic pressure. Tan et al. [9] proposed five models for the initiation and propagation of vertical cracks in horizontal bedding shales. Xu et al. and Sun et al. [10, 11] studied the effect of bedding on hydraulic fracturing and concluded that hydraulic fracture was jointly controlled by in situ stress conditions and bedding. Cheng et al. [12] verified that the variable flow can reactivate natural fractures and form complex fractures. The numerical analysis method was used to study the influence of natural cracks, stress shadows, and engineering conditions on the hydraulic fracture propagation. Keshavarzi and Mohammadi [13], Taleghani [14], and Wang et al. [15] used extended finite element method (XFEM) to study the mechanism of hydraulic crack propagation and analyzed the influence of hydraulic fracturing on natural cracks. Hou et al. [16] simulated the complex shape of hydraulic fracture propagation in a shale formation under the random distribution of natural cracks. Ben et al. [17-19] used discountinous deformation analysis (DDA) to study the effects of various parameters on hydraulic fracture propagation. Weng [20] and Kresse et al. [21] used the unconventional crack propagation model to study the parameters of hydraulic fracture propagation. Meyer et al. [22, 23] used a discrete mesh model to study the effects of various parameters on the hydraulic fracture geometry. Zhang [24, 25] applied the methods of experiment and numerical simulation to study the fracture extension.

Based on the fluid-solid coupling theory, the physical simulation experiments and numerical simulation methods were adopted to study the generation and expansion of shale cracks under water pressures. Acoustic emission (AE) technology is used to monitor the initiation and propagation of fracture during hydraulic fracturing. The Abaqus software was applied to study the fracture propagation law of shale with preset joints under water pressure.

Under hydraulic pressure, the rock crack tip around the horizontal well forms a tensile stress zone. When the tensile stress exceeds the strength, the rock will crack. The research on the hydraulic fracture propagation mechanism of shale needs to consider the stress state of the fracture and the discriminating criterion of the fracture. The surrounding rock of horizontal well is affected by the overburden pressure $σv$⁠, the horizontal maximum principal stress (MaxPS) $σH$⁠, and the horizontal minimum principal stress (MinPS) $σh$⁠. Only when the bottom hydraulic pressure is higher than the sum of the circumferential stress and the tensile strength, the rock will be fractured.

When horizontal cracks are generated, the following conditions $σθv=−σtv$⁠, $θ=90°$must be met, when vertical cracks appeared, the following conditions $σθh=−σth$⁠, $θ=0°$ must be met, and the rupture pressure $pF$ at the bottom of the well is

where $k1$ is the seepage effect coefficient, $k1=δ[α(1−2ν)1−ν−φ]$⁠, $δ$ is the calculation parameter, which is 0 when the wellbore is impermeable and 1 when the wellbore is permeable. $ϕ$ is the porosity, $α$ is the effective stress coefficient, $ν$ is the Poisson’s ratio. $σθh$ and $σθv$ are circumferential stresses on horizontal and vertical diameters; $σth$ and $σtv$ are the horizontal tensile strength and vertical tensile strength of the rock. $ps$ is the pore pressure.

Equation 1 considers the influence of rock tensile strength and pore pressure in different directions.

When hydraulic fracture encounters structural planes or faults, it may turn and form a shear plane. The expansion direction is controlled by the MinPS. Let $σ1`=σθ$ and $σ3`=σr$⁠, the fracture pressure under shear failure is

where $σ1`$ and $σ3`$ are the effective stress of the MaxPS and MinPS of the surrounding rock, $σθ$ and $σr$ are the circumferential and radial stresses in the horizontal wellbore, $C`$ and $ϕ`$ are the effective cohesion and the internal friction angle of the rock.

Equation 2 considers the combined effect of the change of rock permeability and the reduction of rock strength due to hydraulic action.

Based on the principle of similarity [26], the true triaxial hydraulic fracturing physics simulation and AE monitoring experiments were used to study the shale damage evolution and dynamic expansion under hydraulic conditions.

The true triaxial hydraulic fracturing physics simulation system was used to load in three directions, and constant-speed, constant-pressure fracturing fluid can be added. The Peripheral Component Interconnection 2 (PCI-2) AE system is used to monitor the internal hydraulic cracks. The shale is from the Longmaxi Formation in western China, and the size of the shale samples is 300 mm × 300 mm × 300 mm. A horizontal borehole with a steel casing is drilled in the middle of the rock sample to simulate a horizontal well. A ring-shaped induction joint is cut at the bottom of the hole to facilitate the cracking of the rock sample. Six AE probes are arranged at the corners of the rock samples, as shown in Figure 1.

The similarity criteria of Liu Gonghui [26] and Guo Tiankui [27] in hydraulic fracturing simulation test are used. The horizontal MinPS of the sample is 8 MPa, the horizontal MaxPS is 12 MPa, and the vertical principal stress is 11 MPa. After the confining pressure was stabilized, the fracturing fluid was applied, and the inlet displacement was 10 mL/min. A small amount of tracer was added to the fracturing fluid to facilitate the observation of the hydraulic crack propagation. Figure 2 shows the pump pressure curve during loading.

The surface cracks distribution is shown in Figure 3. The initial cracks on the six faces are shown in Figures 3(a) and 3(c), while the cracks after the experiment are shown in Figures 3(b) and 3(c). It can be seen that faces S1, S4, S2 and S6 developed new hydraulic fractures after the experiment. The direction of the fracture surface is perpendicular to the direction of the maximum principal stress and parallel to the direction of the minimum principal stress. The hydraulic fractures on S1 and S6 both run through the bedding surface. The strength of the bedding surface is high, and the water pressure is difficult to open the bedding surface.

Therefore, the hydraulic fractures may extend along the wellbore direction or perpendicular to the wellbore direction. The cracks caused by shear failure may extend along the wellbore, and the fracturing effect is poor. The hydraulic fractures have better fracturing effect in the multistage fracturing process.

There are four typical forms of cracks in horizontal well fracturing: longitudinal cracks, transverse cracks, turning cracks, and twisted cracks. The internal cracks distribution of the specimen is shown in Figure 4. The hydraulic fracture runs through the entire rock sample, and the hydraulic fracture is approximately perpendicular to the direction of the MaxPS and penetrates the bedding plane, as shown in Figure 4(a). When the difference of confining pressure is not large, the crack propagation will be affected by rock bedding and internal microcracks. The cracks are not necessarily perpendicular to the MinPS direction but along the initiation direction and the dominant fracture surface. The main crack extends along the wellbore and forms a bifurcated crack at the weak point, as shown in Figures 4(b) and 4(c). Figure 4(d) shows that the hydraulic fracture extends along the direction perpendicular to the MaxPS. A new bifurcation crack is formed near the wellbore and extends along the weak rock formation, which confirms that the bifurcation crack extends along the direction of the MinPS. Figure 4(e) reflects the main crack propagation at the wellbore. The crack developed along the wellbore extends to the outer wall and forms a main crack, which penetrates the bedding plane.

From the distribution of hydraulic fractures, the tensile failure at the fracture point will directly affect the direction of fracture propagation. When the tensile failure dominates, the direction of hydraulic fracture propagation may be perpendicular to the MaxPS direction. Hydraulic fractures are difficult to pass through the bedding, indicating that the bonding strength of the bedding is large. The presence of natural cracks and bedding may cause the hydraulic fracture to turn, approximately perpendicular to the direction of the weak structural plane.

Combining the pump pressure curve, surface cracks, and internal cracks, the crack propagation in the shale was analyzed through AE monitoring. The distribution of AE events was shown in Figure 5. A small number of AE events occurred during the initiation of hydraulic fracturing, which may be a sign of local natural fracture closure. At 527 seconds, the fracturing fluid may enter the natural crack inside the shale. The number of AE events is the largest, and the main crack gradually forms. The direction of the main crack is perpendicular to the bedding plane, approximately parallel to the direction of the wellbore. At 720 seconds, there are many AE events, and many bifurcation cracks appeared along the direction of the MaxPS. However, some bifurcated cracks may turn and extend along the direction of the MinPS. Afterward, the pressure rises slowly. The fracturing fluid enters the bedding plane and flows along the bedding plane. At 1200 seconds, the hydraulic pressure reaches the maximum, and the fracturing fluid passes through the bedding plane and flows out of the surface of the sample. And then the hydraulic pressure drops sharply to zero. The number of AE events is in good agreement with the pump pressure curve. From the perspective of positioning, the hydraulic crack reflected by the AE event is consistent with the actual crack expansion trend, as shown in Figures 5(b) and 5(c).

In general, the formation of fracture networks is closely related to natural cracks, bedding, and mineral cementation surfaces. In the process of shale gas extraction, the orientation and direction of the wellbore greatly affect the production.

The numerical simulation method was used to study the crack propagation under different parameters such as hydraulic pressure, bedding, and microfissure distribution.

According to the rock sample parameters, the hydraulic fracturing three-dimensional (3D) model is established by the extended finite element method, as shown in Figure 6. The elliptical vertical crack is preset inside the model. The 3D eight-node-reduced integral solid element C3D8RP is selected to mesh the model. The number of units is 8709. The reservoir is saturated, and the initial pore water pressure is 0 MPa. To facilitate the fast convergence calculation, the injection rate of the fracturing fluid is 1000 times larger than the experiment and is set to 1.67 × 10⁻⁷ m³/s. At 0–1 seconds, the injection rate rises from 0 to the specified value and then remains to 24 seconds. The MaxPS criterion is used to determine the initial damage evolution. Since the displacement of cracks during hydraulic fracturing is difficult to monitor, the strain energy release rate is used as the criterion for damage evolution. The parameters used in the numerical model of hydraulic fracturing are shown in Table 1.

The displacement of the crack tip unit after cracking and rupture is shown in Figure 7. When the crack occurs, the crack tip is subjected to tensile stress. The stress near the wellbore is concentrated, and the displacement is elliptical. The displacement is large when the shale sample is broken, reaching the millimeter level. The hydraulic fracture is in the vertical direction, perpendicular to the direction of the MinPS. Some of the cracks farther away from the wellbore are offset along the direction of the MaxPS.

There is a difference in the expansion of the crack around the wellbore and the crack at the tip. It can be seen from Figure 8 that the tensile stress gradually changes to a compressive stress during the crack propagation process around the wellbore, and the shear failure form occurs. The Mises stress reached a maximum of 9.21 MPa at 0.099 seconds. The pore water pressure gradually increases with the injection of the fracturing fluid, reaching a maximum value of 3.04 MPa at 0.099 seconds. After the crack starts, the pore water pressure will drop sharply. The displacement in the middle of the crack is the largest, reaching 4.32 µm, and the displacement near the boundary is close to zero.

As shown in Figure 9, the tip crack is mainly subjected to tensile stress. At 0.47 seconds, the rock mass at the crack tip breaks, and the crack expands. At this time, the Mises stress reached a maximum of 2.51 MPa but was significantly lower than the crack propagation pressure around the wellbore. The pore water pressure gradually increases with the injection of fracturing fluid, reaching a maximum value of 6.37 Mpa at 0.47 seconds. The stress increasement is larger than that of Mises and the crack propagation pressure around the wellbore. The tip crack opening displacement reached 8.69 µm. The displacement value of the tip crack is much larger than the crack around the wellbore, indicating that it is more difficult to extend the distal crack.

To discuss the influence of weak structures on hydraulic fractures, a weak structural layer was added to the above model, whose thickness is 2 mm and the position is 25 mm from the top surface. The number of units is 9189. Other parameters remain the same, as shown in Figure 10.

The comparison between the homogeneous model and the model with weak structural layers was shown in Figure 11. The rock with weak structural layers is destroyed faster than the homogeneous rock. Moreover, the fracturing fluid extends a distance along the weak structural plane and then flows perpendicularly to the weak structural plane, which is consistent with the physical test law. When the hydraulic crack intersects the weak structural plane at a large angle, it may expand in the weak structural layer or may extend directly through the weak structural layer.

It can be seen from Figure 12 that the shear failure occurs in the weak structural layer, and the cracking pressure is significantly lower than that of the homogeneous rock. The inhomogeneity of the shale leads to a complex force under water pressure, which increases the probability of shear damage. The displacement of the weak structural layer is greater than the expansion displacement of the crack around the wellbore and is smaller than the extended displacement of the crack tip. At 0.254 seconds, the difference in the total displacement of the weak structural layer is 2.55 µm, which is significantly higher than other displacement values. It indicates that the weak structural layer increases the displacement of shale under hydraulic fracturing.

In this paper, the hydraulic fracture propagation mechanism of shale was studied through theoretical analysis, experimental tests, and numerical simulation. The following conclusions were reached:

1. Shale containing many uneven beddings will be tensile failure or shear failure under water pressure. The strength criterion derived from this paper can be used to judge the crack initiation pressure and the type of failure.

2. Triaxial fracturing experiments of shale show that tensile or shear failure may occur locally in shale under water pressure. In the case of small confining pressure difference, the hydraulic fracture propagation may be along the direction of the MinPS or the MaxPS and is greatly affected by the microfracture or weak structural layer inside the shale.

3. In the crack initiation stage, the pump pressure rises sharply and then falls rapidly after reaching the fracture pressure. The AE energy increases sharply and fluctuates violently. In steady pressure propagation stage, the pump pressure curve fluctuated and then stabilized, the AE energy level is relatively low, and hydraulic cracks exhibit dynamic nonuniform expansion.

4. The stress of the homogeneous shale at the perforation is concentrated, and the displacement changes greatly. The Mises stress in the middle of the preset crack is large, and the pore pressure is small, while the preset crack tip is the opposite. The hydraulic fracture propagation is greatly affected by the weak structural plane. Cracks may pass through weak structural faces or turn along structural faces.

Due to the limitation of experimental conditions, there are still many problems to be solved.

1. Whether the hydraulic fracture will produce new cracks or extend along the structural weak surface of the rock layer still needs to carry out systematic macro- and micro-research.

2. The fracture direction is greatly affected by stress and bedding and can be changed at any time. The influencing factors of fracture propagation direction need further study.

This work was supported by the Science and Technology Cooperation Project of the CNPC-SWPU Innovation Alliance (Grant 2020CX020100) and National Science and Technology of the Ministry of Science and Technology of China (2017ZX05037001).

The authors declare that there are no conflicts of interest regarding the publication of this article.

The experimental test data used to support the findings of this study are available from the corresponding author upon request.