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. 2024 Jan 16;9(4):4635–4646. doi: 10.1021/acsomega.3c07862

Influence of Engineering Parameters on Fracture Vertical Propagation in Deep Shale Reservoir: A Numerical Study Based on FEM

Shikun Zhang †,‡,*, Songze Liao §, Shuangming Li †,‡, Jinghong Hu §
PMCID: PMC10832007  PMID: 38313496

Abstract

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The geometry of hydraulic fractures in deep shale facies is significantly affected by the longitudinal inhomogeneity of rock physical properties and stresses. Numerous studies have been conducted on the influence of the longitudinal inhomogeneity of rocks on fracture morphology. However, there is still a lack of research that simultaneously considers the reservoir dip, bedding plane interface, and longitudinal inhomogeneity of the reservoir. To fill this gap, a three-dimensional (3D) numerical model of multireservoir hydraulic fracturing, which takes into account the bedding plane interface, was developed using the finite element method (FEM). The Drucker–Prager elastic-plasticity criterion was incorporated to accurately represent the plasticity of deep shale. The research revealed the influence of the formation dip angle on fracture morphology. Additionally, the perforation layer position and pump rate were optimized based on the actual geological parameters in North Jiangsu shale reservoir. The study findings indicate that reservoir fractures with a formation dip are easily detected by the interface. However, it is not necessarily true that the larger the formation dip, the easier it is for fluids to enter the interface. Fracturing from high-strength and stress reservoirs to lower reservoirs promotes the propagation of fracture height and the connectivity of multiple reservoirs. On the other hand, fractures initiated from low-strength and stress reservoirs tend to be confined to adjacent reservoirs more easily. The pump rate significantly affects the vertical propagation of fractures. At high interface strength, fractures with pump rate below 2.4 m3/min can only propagate at the perforation layer. The limited fracture height in shale reservoirs is likely due to substantial energy consumption by the fracturing fluid at the bedding plane interface. These studies offer theoretical guidance for understanding the vertical propagation of fractures in a deep multilayer reservoir.

1. Introduction

Deep shale reservoirs are typically defined as oil and gas reservoirs that are buried at depths greater than 3500 m.1 China’s deep oil and gas resources make up a significant portion of the total, with a low rate of detection and high potential.2,3 The predicted resources of shale oil are approximately 2.974 billion tonnes.4 Similarly, the technically recoverable resources of deep shale gas are estimated to be 19.36 trillion cubic meters, representing 56.63% of the total shale gas resources.5 As the burial depth increases in deep reservoirs, there is a corresponding increase in the ground pressure. The rocks in these reservoirs primarily exhibit a strengthening of elastic modulus and compressive strength, while brittleness is weakened.6,7 These changes in physical parameters and mechanical properties of deep shale, compared to shallow shale reservoirs, can result in variations in the propagation of hydraulic fractures and communication behavior with the bedding plane.8−10 These variations have a significant impact on the effectiveness of fracturing.

Hydraulic fracturing is a crucial technology for enhancing production in deep reservoirs.11−13 It enables the extraction of deep oil and gas by creating fracture channels within the reservoir.14 This process involves the propagation of hydraulic fractures driven by high-pressure fluids, as well as complex physical phenomena such as the interference of hydraulic fractures and the interaction between hydraulic fractures and the interfaces of the reservoir layers.15,16 When conducting hydraulic fracturing in deep shale formations, it is important to consider the varying layers of cementation between reservoirs of different properties.17 These differences can lead to the loss of fracturing fluid, which can significantly impact the effectiveness of reservoir modification.18−21 Therefore, it is important to not overlook the role of interface cementation during the hydraulic fracturing construction process.

A lot of research has been carried out on the fracturing of multilayer reservoirs. Xie et al.22 established a multilayer hydraulic fracturing model by using the boundary element displacement discontinuity method and the finite difference method. However, the multilayered rocks in this model do not show differences in their physical properties. Sun et al.23 established a three-dimensional (3D) model of hydraulic fracturing in multiple reservoirs by finite element method (FEM). The study analyzed the influence of the inclination angle of the formation on the fracture penetration. However, the model did not consider the nonhomogeneity of stress while considering the nonhomogeneity of physical properties of multilayer reservoirs. Fu et al.24 established a 3D model of multilayer hydraulic fracturing of coal beds based on FEM. However, the model did not consider the role of bedding plane interface. Hou et al.25 established a two-dimensional (2D) propagation model of hydraulic fracturing cross layers in a coal shale bedded reservoir based on a finite element platform. Although the model considered the role of stratification, the shale constitutive model used was still an elastic model. Qin et al.26 developed a 3D model of hydraulic fracturing in layered rock based on circumferential dynamics and simulated the growth of fracture height. The model takes into account the difference in physical properties of rocks in different layers and the influence of the bedding plane. However, the scale of the model is only the laboratory scale and fails to reflect the anisotropy of multilayer rock forces. Bai et al.27 developed a reservoir model with bedding plane and investigated the propagation behavior of hydraulic fractures under the bedding plane and ground stress. The mechanism of hydraulic fractures penetrating the shear-damaged and tensile-damaged bedding planes was analyzed. Although the model takes into account the nonhomogeneity of the forces on different layers of rock, it is not able to take into account the differences in the physical properties of the rock. In-depth investigation of the previous research shows that the previous researchers are insufficient in considering the elastic-plasticity of the deep rocks, the bedding plane, the differences in the physical properties of the rocks in multiple layers, and the differences in the stress of the rocks in multiple layers at the same time.28−30 The simultaneous consideration of the above factors is the key to simulating the hydraulic fracture morphology of actual multilayer shale reservoir fracturing.

This study aims to investigate the mechanism of the vertical propagation of fractures in deep shale multilayer reservoirs. The model takes into account the elasticity and plasticity of the deep rock, the bedding plane interface, the differences in the physical properties of the multilayer rock, and the differences in the stress of the multilayer rock. A 3D model of hydraulic fracturing was established using FEM. The study reveals the influence of the bedding plane angle on the hydraulic fracture morphology of multilayer shale reservoirs. Finally, based on the geological parameters of deep shale reservoirs in the North Jiangsu Basin, the perforation layers and construction pump rate were optimized. This optimization can provide theoretical guidance for understanding the interaction behavior of hydraulic fractures and the bedding plane interface on the oilfield scale.

2. Reservoir Geological Background of Jiangsu Oil Field

The shale oil reservoir in the North Jiangsu HY1 well is a deep lake-phase sedimentary reservoir that is thick and has a dense shale composition. The lower part of the reservoir is primarily composed of mudstone/gray mudstone, which exhibits development of a bedding plane. The average porosity of the reservoir is 5.27–5.32%, and the permeability is 0.1 md. The mineral composition consists of 19.6% quartz, 28.8% carbonatite, 20.3% clay, and 68.06% brittle minerals. The rock friction angle is 30°, and the yield strength is 4 MPa. The longitudinal lithology of the reservoir is characterized by alternating layers of altered and nonhomogeneous rock, with thin mudstone interlayers that are interbedded with a well-developed bedding plane interface of sandstone-mudstone. The rock layers have an inclination angle of approximately 15°. Longitudinally, the reservoir can be divided into L1–L5 based on fine stratification. Based on well logging data of oil production and oil content, the reservoir can be further divided into Class I and Class II reservoirs. The recoverability of the Class I reservoir is better than that of the Class II reservoir. The target area of the study is a contiguous reservoir with a burial depth ranging from 3660 to 3713 m and a thickness of 53 m.

Figure 1 illustrates that L1, L3, and L5 are identified as high-stress areas (minimum horizontal stress), while L2 and L4 are classified as stress areas. The longitudinal section of the reservoir exhibits intricate lithology, resulting in significant variations in rock mechanical characteristics and stress conditions, as shown in Figure 2. The stress discrepancy between layers can reach up to 3 MPa. The overall vertical stress surpasses the horizontal stress, which is a typical characteristic of vertical hydraulic fractures. In comparison to traditional single-lithology reservoirs, the complex bedding environment and stress state of multilithology thin interlayers pose significant challenges to the vertical propagation of hydraulic fractures.

Figure 1.

Figure 1

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Geological characteristics of the HY1 well in the shale reservoir of the Jiangsu oilfield.

Figure 2.

Figure 2

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Stress distribution of HY1 well in the shale reservoir of Jiangsu oilfield.

3. Mathematical Model

3.1. Solid Field Model

When the boundary of a porous medium is subjected to an external load, the solid skeleton will deform to produce effective stresses at the contact surfaces. Using an effective stress system to consider the influence of fluid pressure, the relationship between total stress and effective stress is31

3.1. 1

where σ is the effective stress, MPa, σ* is the total stress, MPa, χ is the Boit coefficient, pw is the matrix fluid pressure, MPa, and I is the second-order identify tensor.

The significant stress concentration at the fracture tip during hydraulic fracturing will form a large plastic zone, the mechanical behavior of which cannot be accurately described using linear elasticity theory and needs to be analyzed using elastic-plastic theory.32 The Drucker–Prager model is used to describe the plastic deformation behavior of the rock:33

3.1. 2
3.1. 3

where F is the yield criterion of the Drucker–Prager elasto-plastic model, I1 is the first invariant of the stress tensor, J2 is the second invariant of stress bias, c is the yield strength, MPa, and φ is the friction angle, °. Both α and k are constants related to the friction angle and yield strength of geotechnical materials. Using the incremental plasticity theory to establish the elastic-plastic ontological relationship, the rock’s yield condition can be expressed as

3.1. 4

where σij is the stress state, MPa, and K is the hardening function. In the incremental plasticity theory, the strain increment is divided into an elastic increment and plastic increment:

3.1. 5

Elastic strain increment dεe can be obtained from Hooke’s law. The plastic strain increment dεp is obtained using the associated flow law:

3.1. 6
3.1. 7

where λ is the plastic multiplier which is equal to the generalized plastic shear strain increment, and G is the plastic flow potential, which can be written as

3.1. 8

For the elastic stiffness matrix De and plastic stiffness matrix Dp, the expression is

3.1. 9
3.1. 10
3.1. 11

The elasto-plastic constitutive equation can be obtained by combining eqs 9 and 10.

3.2. Fluid Field Model

To characterize the flow of the fracturing fluid in the fracture, Poiseuille flow is used to represent the fluid flow in the fracture, which can be expressed as34

3.2. 12

where q is the tangential flow rate, m3/s, d is the opening width of the cohesive element, m, μ is the viscosity coefficient of the fracturing fluid, mPa·s, and p is the fluid pressure within the cohesive element, MPa.

Considering the filtration loss of the fracturing fluid along the hydraulic fracture to the upper and lower surfaces of the rock, the flow equation is35

3.2. 13

where qt and qb are the flow velocities of the fluid flowing into the upper and lower surfaces of the cohesive element, m3/s, respectively, ct and cb are the filtration coefficients of the two surfaces, and pt, pb, and pi are the fluid pressures on the two surfaces of the cohesive element and the fluid pressure on the middle surface of the cohesive element, MPa.

As the fracture initiates, the fluid within the fracture generates a flow field and the original seepage field in the rock changes. The Reynold’s equation for fluid flow is satisfied:36

3.2. 14

where Q(t) is the injection amount of fracturing fluid, m3/s, and t is time, s.

The seepage of fracturing fluid in a porous medium can be expressed as

3.2. 15

where the seepage velocity satisfies the following equation:

3.2. 16

where J is the volume change rate of the porous medium, vw is the seepage velocity vector, m/s, n is the porosity, k is the permeability tensor, m/s, pw is fluid pressure, MPa, ρw is the fluid density, kg/m3, and g is the gravitational acceleration vector, m/s2.

3.3. Cohesive Zone Model

During cohesion evolution, when the normal or tangential traction reaches a critical strength, the damage starts to occur and this damage initiation law is expressed as37

3.3. 17

where σn is normal stress, σs and σt are tangential stresses in two directions, MPa, and < > indicates that there is no damage when the viscous unit is subjected to tensile stress and compressive stress. The superscript max indicates critical.

The BK fracture criterion was adopted as the damage evolution criterion.38 The BK fracture criterion accurately describes the evolution of damage during fracture extension when the critical energy of deformation of the Cohesive unit along the first and second shear directions is the same:39

3.3. 18

where GnC and GsC are the critical fracture energies in the normal and shear directions, N/m, Gn, Gs, and Gt are the energies consumed in the normal, first, and second shear directions, N/m, respectively, and η is the rock-related constant and takes the value 2.40

4. Numerical Model and Validation

4.1. Model Verification

To evaluate the reliability of the current model in simulating the fracture propagation process, a numerical model was established based on the test conducted by Llanos et al.41 The multilayer hydraulic fracturing test, depicted in Figure 3a, consisted of six thin plates measuring 40 cm × 36 cm × 6 cm and one thin plate measuring 40 cm × 36 cm × 12 cm. The 12 cm thick plate was positioned in the middle, flanked by three 6 cm thin plates on each side. The modulus of elasticity of the thin plates was 7 GPa, with a Poisson’s ratio of 0.28. The thin plate was subjected to a uniform peripheral pressure of 8 MPa in both the X and Z directions. A blue fluid with a viscosity of 1 mPa·s was injected from the center point at a flow rate of 0.0158 mL/s with a total volume of 40 mL. The test results are shown as white outlines in Figure 3b. Since the injected fluid only affected thin plates No. 3–5, the numerical modeling process focused solely on these plates, resulting in the model shown in Figure 3a. The comparison between the numerical and experimental results in Figure 3b demonstrates a good fit, indicating the reliability of the model in simulating hydraulic fracture penetration in multilayer reservoir fracturing.

Figure 3.

Figure 3

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Comparison between numerical and experimental models: (a) numerical model and (b) experimental and numerical results.

4.2. Model Construction

Formation dip refers to the angle at which the formation is inclined from the horizontal plane. When shale formations are deeply buried, they often exhibit a formation dip. To extract oil from the shale, horizontal wellbores are drilled. However, due to the influence of the formation dip, these wellbores may not align perfectly parallel to the horizontal plane. During the fracturing process, fractures can be formed that either penetrate the formation or are confined within the interface, depending on the different dip angles of the bedding surfaces. Therefore, the angle of formation dip becomes an important factor influencing fracture morphology. In this section, two model cases are presented to investigate the vertical propagation morphology of hydraulic fractures in multilayer shale reservoirs.

The schematic diagram of Case 1’s theoretical model is presented in Figure 4. The reservoir model consists of a rectangular shape with dimensions of 50 m (length), 20 m (width), and 40m (height). The middle layer in the model has a thickness of 10 m, and the angle of the rock layer ranges from 0 to 30° to represent different inclinations. Variations in the mechanical properties of the rock were considered as shown in Table 1, assigning different elastic modeling, Poisson’s ratios, and tensile strengths to the vertically oriented rock layers (L1–L3). Due to the difficulty of obtaining strength parameters for the interface, the interface strength was set as a multiple of the matrix strength in this case. The tensile strength of the layer-to-layer interface in Case 1 was set to 0.5 MPa and the shear strength to 5 MPa. And the layers in the model have the same permeability of 0.1 md, porosity of 10%, friction angle of 30°, and yield strength of 4 MPa.

Figure 4.

Figure 4

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Theoretical model of shale reservoir considering bedding dip: (a) 3D view of the model and (b) X–Z plane view of the model.

Table 1. Base Rock Parameters for Case 1.

layer elastic modulus (GPa) Poisson’s ratio Sh (MPa) SH (MPa) Sv (MPa) tensile strength (MPa) shear strength (MPa)
L1 19 0.2 62 72 76 2 20
L2 20 0.2 60 70 76 2.5 20
L3 22 0.2 65 75 76 4 20
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Additionally, different layers experience minimum horizontal stress in the X direction and maximum horizontal stress in the Y direction. As the vertical stress remains relatively constant at this model’s scale, the same vertical stress value is applied in the Z direction. Fracturing fluid with a viscosity of 5 mPa·s was injected at a pump rate of 2.4 m3/min for a duration of 30 s. The injection point was located in the L2 layer, as depicted in Figure 4a. By observation of the fracture morphology at various formation dip angles, the impact of the formation dip angle on the vertical propagation of the fracture can be determined.

In Figure 5, the 3D model of Case 2 is presented, which is based on the geological parameters of the deep shale reservoir in the North Jiangsu Basin. The model incorporates the geological information from Chapter 2 and establishes a five-layer reservoir model with a rock dip of 15°. The overall shape of the model is a rectangle measuring 80 × 53 × 20 m, with layers L1–L5 arranged from top to bottom. Similar to Case 1, each layer from L1 to L5 has different rock mechanics and stress parameters, as indicated in Table 2. In addition, the strength of each interface is set to a constant value, where the interface with high cementation strength is set in this paper to have an interfacial tensile strength of 1.4 MPa and a shear strength of 14 MPa. The interface with low cementation strength is set in this paper to have an interfacial tensile strength of 0.4 MPa and a shear strength of 4 MPa. Fracturing fluid of 5 mPa·s was pumped from the perforation point for 150s. The red lines in Figure 5a represent the potential paths for fracture formation. To ensure accuracy, the entire model was divided into 190,880 cells and 228,420 nodes through fine meshing, effectively reducing arithmetic errors caused by coarse meshing. The optimization of the engineering parameters involves adjusting the perforation position and pump rate.

Figure 5.

Figure 5

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Mineral field model of the shale reservoir in North Jiangsu: (a) 3D view of the model and (b) meshing of the model.

Table 2. Base Parameters for Case 2.

layer elastic modulus (GPa) Poisson’s ratio Sh (MPa) SH (MPa) Sv (MPa) tensile strength (MPa) Shear strength (MPa)
L1 23.1 0.2 67.0 76.8 83 2.7 30
L2 19.9 0.17 65.4 75.2 83 1.9 30
L3 22.0 0.19 66.7 77.0 83 2.8 30
L4 18.9 0.16 65.2 75.1 83 2.1 30
L5 21.9 0.19 67.0 76.9 83 2.8 30
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5. Results and Discussion

5.1. Influence of Reservoir Dip

Figure 6a–d depicts the simulation results of fracture morphology for rock dip angles ranging from 0 to 30°. Assuming that the rock mechanical parameters are consistent with the ground stress, the hydraulic fracture can traverse the upper bedding plane interface from the L2 layer to the L1 layer when the rock layer has an inclination angle of 0°. However, due to the nonhomogeneous nature of the ground stress, it becomes challenging for the fracture to penetrate the lower bedding plane interface and reach the L3 layer. At a dip angle of 15°, the hydraulic fracture is more prone to being captured by the bedding plane. Furthermore, it is crucial to note that the fracturing fluid has a higher possibility of entering the high-angle interface.

Figure 6.

Figure 6

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Effect of the bedding plane angle on fracture morphology: (a) 0° formation dip, (b) 15° formation dip, (c) 30° formation dip, and (d) 45° formation dip.

Figure 6c,d demonstrates that the fracture area of the interface decreases as the dip of the formation increases. This indicates that it becomes more challenging for the fracturing fluid to enter the bedding plane with higher angles. The fracturing fluid tends to expand along the fracture length in the perforation layer. The above findings suggest that the possibility of hydraulic fracturing across the bedding plane is high when the formation dip angle is close to 0°. However, the presence of a formation dip significantly increases the difficulty of creating a penetrating fracture. A slight angle of formation dip may result in the fracture being trapped within the formation and unable to connect with neighboring reservoirs. Fracturing fluid enters the formation to a lesser extent at a high formation dip compared to a low formation dip, leading to longer fracture lengths. Therefore, the impact of formation dip angle cannot be overlooked when modeling fracture propagation in multilayer shale reservoirs.

5.2. Optimization of Perforation Layers

The impact of fracturing layers on the longitudinal propagation of fractures in shale oil reservoirs in the North Jiangsu Basin was investigated. Rock mechanics and stress parameters were analyzed from Layer 1 to Layer L5. Since low cementation strength interfaces may result in fractures being unable to cross the layer, the interface strength in this section is assumed to be as general as the high cementation strength is for the strength of the matrix. The elastic modulus of rock in Layer L3 was found to be significantly higher compared with the adjacent Layer L2 and L4 locations. In terms of stress direction, the minimum horizontal stress affecting fracture opening was significantly lower in layers L2 and L4 compared to those in the other three layers. Therefore, the five layers can be categorized into three high-strength layers (L1, L3, and L5) and two low-strength layers (L2 and L4). Four perforation locations were designated: two in the upper part of layers L2 and L3, and two in the lower part of layers L2 and L3, as shown in Figure 7.

Figure 7.

Figure 7

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Optimization of the perforation program.

This section presents the fracture morphology observed after fracturing in the L2 layer position at the upper layer of the rational surface cementation strength. Figure 8a,b illustrates the process of fracture propagation when perforation occurs at the upper L2 layer. Figure 8a shows that the fracture intersects the layer interface at 10.4 s. Throughout the simulation, two bedding planes are connected. Similarly, when perforation in the lower L2 layer, only two bedding planes can be traversed. However, fracturing in the lower L2 layer allows for a higher fracture height. The limitation of crossing only two reservoirs when fracturing from L2 is due to the lower rock mechanical parameters and minimum horizontal ground stress in L2 compared to those in L1 and L3. As a result, the fracturing fluid lacks sufficient energy for longitudinal flow, and its flow is restricted along the direction of fracture length, requiring relatively less energy. Regarding fracture width, the distribution of fracture widths in the upper L2 layer (Figure 8b) indicates that wider fractures are mostly concentrated in the L2 layer, with the widest point reaching 8.7 mm. On the other hand, fracturing in the lower L2 layer results in the red-colored area spreading across the L2 and L3 layers, with the widest point measuring 8.1 mm.

Figure 8.

Figure 8

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Fracture morphology of perforation at the L2 layer: (a) fracturing in the upper L2 layer for 10.4 s, (b) fracturing in the upper L2 layer for 50 s, (c) fracturing in the lower L2 layer for 8.2 s, and (d) fracturing in the lower L2 layer for 50 s.

Figure 9 illustrates the fracture morphology resulting from fracture from the upper and lower parts of L3. When fracturing from the upper part of L3, the fracture crosses the L2 to L3 layers, while fracturing from the lower part of L3 results in the fracture connecting the L2–L4 layers. It is important to note that fracturing from the lower L3 can traverse three reservoirs, which is advantageous compared to fracturing in the L2 layer in terms of enhancing fracture height. Regarding fracture width, the maximum widths of fractures from the L3 layer are 7.9 and 7.6 mm, which are not significantly different from those from the L2 layer. The reason why fracturing from the L3 layer can achieve higher fracture heights than fracturing from the L2 layer may be attributed to the fact that the L3 layer is characterized by high stress and strength. Consequently, when fracturing from the high-strength L3 layer to the low-strength L2 and L4 layers, it becomes easier for the fracturing fluid to penetrate the bedding interface and enter the adjacent reservoirs.

Figure 9.

Figure 9

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Fracture morphology of perforation at L3 layer: (a) fracturing in upper L3 layer for 12.5 s, (b) fracturing in upper L3 layer for 50 s, (c) fracturing in lower L3 layer for 11.8 s, and (d) fracturing in lower L3 layer for 50 s.

From the statistical graphs of the fracture area in different layers when fracturing from L2 and L3 layers in Figure 10, it is observed that there is no significant change in the total area of the fracture. However, the change in fracture height is more noticeable. Fracturing from the L3 layer results in a fracture height of more than 30 m, whereas fracturing from the L2 layer only achieves a height of 23–25 m. This represents a more than 20% enhancement in fracture height. Therefore, based on the findings of this study, the optimized perforation layer is the L3 layer. Furthermore, the study reveals that when fracturing from low-strength layers, the longitudinal flow of fracturing fluid requires a large amount of fluid accumulation to generate higher energy for penetrating across the layers. However, while accumulating energy, the conditions for cracking in the fracture length direction may have already been met, leading to the transfer of energy in that direction. Consequently, the longitudinal flow of fracturing fluid becomes more challenging, and the fracture height becomes severely limited. On the contrary, when fracturing from high-strength layers, the fracturing fluid easily expands vertically after reaching the upper energy limit. This is because the perforation layer experiences more stress compared to the neighboring layers, making it more difficult to fracture the rock in the perforation layer than in the neighboring layers.

Figure 10.

Figure 10

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Effect of the perforation layer on fracture height and area.

5.3. Optimization of Pump Rate

This section investigates the effect of pump rate on the vertical propagation of the fracture, based on the optimized upper L3 injection layer discussed in Section 5.2. Figure 11 illustrates the adjustment of injection rate and injection time using a constant fluid volume, with the pump rate ranging from 2.4 to 9.6 m3/s. To account for the uncertainty of interfacial cementation strength, a separate analysis was conducted for cases of strong and weak interfacial cementation.

Figure 11.

Figure 11

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Fracturing program with different pump rates.

The behavior of fractures across the bedding plane affected by different pump rates at high interface strength is shown in Figure 12. A high-strength interface indicates that the interface has relatively high tensile and shear strengths. Figure 12a demonstrates that when the single-cluster fracture pump rate is lower than 2.4 m3/min, the fracturing fluid can flow only in the perforation layer and cannot penetrate the layers. However, when the single-cluster fracture pump rate is increased to 4.8 m3/min and above, hydraulic fracturing achieves varying degrees of layer penetration.

Figure 12.

Figure 12

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Fracture morphology at different pump rates during strong cementation when perforation at the L3 layer: (a) pump rate, 2.4 m3/min; (b) pump rate, 4.8 m3/min; (c) pump rate, 7.2 m3/min; and (d) pump rate, 9.6 m3/min.

From Figure 12b,c, it can be observed that the fractures connect the L2 and L3 layers. When the pump rate is further increased to 9.6 m3/min, the fracture breaks through the L1 layer and connects three layers. Figure 13 shows that the pump rate has little effect on the total area of the fracture. However, it significantly increases the fracture height. Compared with the fracture height at a pump rate of 2.4 m3/min, the fracture height with a pump rate of 9.6 m3/min is more than doubled. During the fracturing of reservoirs with high interfacial strength, the fracturing fluid requires less energy for crossing the bedding plane interface. High pump rate injection of fracturing fluid means that more fluid is gathered at the same time, allowing for quick accumulation of enough energy to cross the bedding plane interface. Therefore, the pump rate has a more significant effect on the vertical penetration of the fracture.

Figure 13.

Figure 13

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Effect of pump rate on fracture height and area during strong cementation when perforation at the L3 layer.

Figure 14 demonstrates the fracture morphology at different pump rates for a weak interfacial strength. The blue region at the interface in Figure 14a–c indicates an increase in the slip of the fracturing fluid as the pump rate increases. The variation in fracture lengths among the three cases can also be attributed to the differing slip at the interface. This study considers the nonhomogeneity in the vertical direction of the reservoir and the effect of formation dip, resulting in a Z-shaped fracture instead of the T-seam observed by previous authors when the formation dip angle is not considered. In the cases of pump rate from 2.4 to 7.2 m3/min, the fractures failed to penetrate the formation. Only when the pump rate was increased to 9.6 m3/min did the fracturing fluid accumulate enough energy for penetration to occur. The penetration difficulty of weakly laminated cementation strength reservoirs is significantly higher than that of strongly laminated cementation strength reservoirs. Figure 15 shows that the fracture heights of the cases with pump rate lower than 9.6 m3/min were consistently 13 m of the reservoir height, while the fracture heights of the cases with pump rate higher than 9.6 m3/min increased by approximately 30%.

Figure 14.

Figure 14

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Fracture morphology at different pump rates during low cementation when perforation at the L3 layer: (a) pump rate, 2.4 m3/min; (b) pump rate, 4.8 m3/min; (c) pump rate, 7.2 m3/min; and (d) pump rate, 9.6 m3/min.

Figure 15.

Figure 15

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Effect of pump rate on fracture height and area during low cementation when perforation at the L3 layer.

Fracture height restrictions in shale reservoirs are primarily attributed to energy depletion resulting from fracturing fluid slippage at the formation interface. Reservoirs with weak interfacial cementation strength necessitate a high pump rate in order to achieve fracture penetration. Therefore, it is advisable to assess the strength of the interface in the target reservoir before initiating the fracturing process. Table 3 demonstrates the theoretical pump rate for a single fracture during multifracture fracturing. In cases of multifracture fracturing with single-cluster fractures less than 2.4 m3/min, the fracture height is likely to be limited when the interfacial cement strength is high. Due to a fixed total pump rate, the theoretical pump rate into each cluster decreases with more clusters. Consequently, there may be some fractures in which the fluid does not have enough energy to connect with the adjacent layers. This phenomenon is particularly noticeable when the cementation strength of the interface is weak. The weak interfacial strength, combined with fracture shunting, necessitates greater displacements per cluster of fractures in order to facilitate vertical penetration of the fractures through the layer. Therefore, controlling the number of clusters and increasing the pump rate are significant ways to favor the vertical propagation of the fracture.

Table 3. Single Fracture Pump Rate for Different Number of Clusters.

total pump rate 2 clusters 4 clusters 6 clusters 8 clusters 10 clusters
8 m3/min 4 m3/min 2 m3/min 1.8 m3/min 1 m3/min 0.8 m3/min
12 m3/min 6 m3/min 3 m3/min 2 m3/min 1.5 m3/min 1.2 m3/min
16 m3/min 8 m3/min 4 m3/min 2.6 m3/min 2 m3/min 1.6 m3/min
20 m3/min 10 m3/min 5 m3/min 3.3 m3/min 2.5 m3/min 2 m3/min
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7. Conclusions

A 3D finite element model was developed to study hydraulic fracturing in layered shale reservoirs. The model considered factors such as rock elasticity and plasticity, bedding plane interface, physical property differences of multilayered rocks, and stress variations. The study focused on examining the impact of the formation dip angle on the longitudinal propagation of fractures. By utilizing the geological parameters of the shale oil reservoir in North Jiangsu Province, the optimal perforation location and pump rate were determined through numerical simulation. The following conclusions were drawn from the study:

  • (1)

    The influence of formation dip cannot be ignored. When there is formation dip, hydraulic fractures are more prone to being trapped by the interface, resulting in the Z-shaped fracture. If the formation dip is too large, it can impede the access of fracturing fluid to the formation interface.

  • (2)

    Fracturing from high-strength and stress layers facilitates connection with more reservoirs by increasing the fracture height. Conversely, fracturing from a low-strength layer restricts the fracture height due to the presence of adjacent high-strength layers, causing the fracturing fluid to preferentially flow in the perforation layer.

  • (3)

    Increasing the pump rate can effectively increase the vertical propagation height of fractures. However, when there is high interfacial strength, the fracture height may be limited if the pump rate of a single cluster is less than 2.4 m3/min. This implies that too many clusters may result in inadequate fracture height to establish connection with the adjacent oil-bearing layer.

  • (4)

    Fracture height restrictions in shale reservoirs are primarily attributed to energy depletion resulting from fracturing fluid slippage at the interface. Reservoir with weak interfacial strength necessitate a high pump rate to cross the layer. Therefore, it is advisable to assess the strength of the interface in the target reservoir before fracturing.

Acknowledgments

This work was supported by National Natural Science Foundation of China (U19B6003 and 52074248), Young Elite Scientists Sponsorship Program by BAST (BYESS2023414), and Fundamental Research Funds for the Central Universities (2652022207), Program by SINOPEC (P23194).

The authors declare no competing financial interest.

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