# Numerical Investigation of Hydraulic Fracture Network Formation of Jointed Shale with Oriented Perforation

Authors: Xiaoxi Men; Kaiyu Wang
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

This paper aims at exploring the fracture evolution as well as capturing the fracture network formation of jointed shale during hydraulic fracturing process by numerical simulation using the Rock Failure Process Analysis System of Flow (RFPA—Flow). The simulations were successfully completed following two stages. In the first stage, a series of simulations are performed to investigate the influence of different angle-oriented perforations on fracture initiation and propagation. The simulation results agreed well with the experimental results confirming the validity of the RFPA-Flow code in the application. In the second stage, extensive hydraulic fracturing simulations on jointed shale with different angled-joint planes and different angle-oriented perforations were performed. The simulation results demonstrated that the fracture evolution changes significantly as the magnitude ofα (the angle between perforation and the joint plane) increased. It was found that a large α value could lead to a larger the tensile stress region around the fracture tip resulting in more joint planes pulled apart. It could also induce more secondary fractures and hence a more complex fracture could be formed. As a result, the α value of 60° to 90° were found to aid in the fracture network generation. On the other hand, the angle β being the angle between the parallel joints and the maximum stress direction was another important factor in fracture evolution. Its influence on fracturing performance was similar to angle α. It was found that the initiation and breakdown pressure of jointed shale were in proportional to the magnitude of angle β. Therefore, this paper introduced an efficient approach to promote the formation of a complex fracture network in jointed shale with the presence of oriented perforation, which could offer valuable guidance for the design of unconventional reservoir reconstruction.


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## Body

## 1. Introduction

The unconventional reservoirs construction in shale has become popular globally. Shale nevertheless exhibits a strong heterogeneity, low porosity, and low permeability leading shale reservoir development to be more challenge than conventional reservoirs construction. In 2006, Mayerhofer et al. [1] proposed a concept and calculation method based on the SRV (Stimulated Reservoir Volume) referring to the total volume of reservoir rock that has been hydraulically fractured. The greater the SRV value was, the higher the gas and oil production would be. However, many engineering projects indicated that the SRV was not accurate enough in reservoir development evaluation. Later on, Jia et al. proposed the concept of ESRV (Effective Stimulated Reservoir Volume) in 2012 [2, 3], and Hou et al. proposed the concept of SRA (Stimulated Reservoir Area) In 2014 [4]. In addition, there are some other evaluation methods, such as EPV (Effective Propped Volume) [5], APV (Active Production Volume) [6, 7], ect. Although these reservoir development evaluation methods are different, they shared a common characteristic being a large quantity of induced fractures or a massive fracture network could lead to a bigger stimulated volume [8]. Therefore, how to create such a massive fracture network in the shale becomes a global attention in the research contents of shale reservoir development [9].Joint is a structural plane of discontinuities formed by sedimentation, and it is widespread in shale reservoirs. As a common rock structure, joints influence the physical properties, failure patterns, and fracture propagation behavior of the shale [10]. Heng et al. [11] established a true triaxial hydraulic fracturing simulation testing system to reveal the evolution of hydraulic fractures and their nonplanar behavior at joint planes. It was found that the mechanical properties of the joint primarily determine whether a hydraulic fracture penetrates or is deflected at the joint. Men and Jin [12] studied the hydraulic fracture evolution of jointed shale specimens under different confining pressures and the results indicated that the fracture evolution was predominantly affected by the maximum principal stress when the confining pressure is high whereas it was significantly influenced by the joint plane if the confining pressure is low. The oriented perforation is a common technique in hydraulic fracturing. Appropriate selection of perforation location on a well can improve the fracture intensity and quantity [13, 14]. Bai et al. [15] investigated hydraulic fracturing from oriented perforations at the microscale using hydro mechanical hybrid finite-discrete element method (FDEM) and it was found the perforation orientation, differential stress, and injection rate significantly affect the breakdown pressure and hydraulic fracture geometry. Huang et al. [16] simulated 3D lattice modeling of hydraulic fracturing initiation and near-wellbore propagation based on different perforation models, and the results showed that the perforation tunnels guide the generation of initial microcracks at the roots of the perforation tunnels once the injection starts; however, the subsequent fracture propagation is controlled by the relative locations of perforation tunnels and the stress interference among different perforation tunnels. It could be concluded that both joint plane and oriented perforation can contribute to the fracture network generation. However, the studies on the hydraulic fracture network formation considering both joint and oriented perforation are limited. As such, in this paper we employed the oriented perforation technique to improve the fractures complexity in jointed shale to increase the shale reservoir stimulated volume. The research outcomes would be helpful in determining the most appropriate hydraulic fracturing methods and production designs in the field through a better control of the fracture growth geometry in jointed shale reservoirs.In this paper, the RFPA2D-Flow code which was developed for heterogeneous material was used to simulate the fracture propagation process during the hydraulic fracturing of shale and jointed shale with oriented perforation. It was completed following three steps. Firstly, the RFPA-Flow code was introduced briefly. Secondly, the numerical models for three groups of specimens (different values of θ, α, and β) were established. Lastly, the numerical simulation results of three groups were analyzed leading to a suggested methodology to promote the formation of a complex fracture network in jointed shale by oriented perforation.


## 2. Brief Introduction of the RFPA-Flow Code

The RFPA code is developed by professor Tang et al. since 1995 [17, 18]. it can simulate the failure process of heterogeneous materials such that it is different to most of the other codes that were based on continuous and homogenous assumption. The calculation method of the RFPA was based on finite element theory and statistical damage theory [19, 20]. The RFPA code considered the heterogeneity of material properties and the randomness of defect distribution in the heterogeneous materials (such as rock) and combined the statistical distribution assumption with the finite element numerical computing methods. The elements exceeding the given strength criterion (such as the Mohr–Coulomb criterion, maximum tensile stress criterion, and double shear strength criterion) are defined to fail so that the numerical simulation of the failure process of the heterogeneous materials can be achieved. In the comparison of physical experiment and numerical simulation results, the creditability of RFPA simulation has been solidly proven [21–26].As a typical heterogeneous material, the rock contains mineral particles, crystal grains, pores, and other structures. It is such a heterogeneity and the existence of microscopic defects that lead to the final failure of rock. As shown in Figure1, the RFPA code fully considered the heterogeneity of materials. In modeling, RFPA imitates rock material and gives different mechanical properties to different mesoscopic elements by obeying a statistical distribution (e.g., normal distribution and Weibull distribution). The weak elements fail first in the loading process and are shown in black, then more and more elements fail and connect to each other leading to the formation of macro fractures as load increases (Figure 2).Figure 1
Comparison of rock and RFPA model. (a) Rock (b) RFPA model.
(a)(b)Figure 2
Failure process of rock Brazilian splitting simulation by RFPA-basic code.The RFPA-Flow model is based on the following five basic assumptions:(1)
The fluid in rock medium follows Biot consolidation theory(2)
The rock medium is an elastic-brittle material with residual strength, and its mechanical behavior during loading and unloading conforms to the elastic damage theor(3)
The maximum tensile strength criterion and Mohr–Coulomb criterion are used as damage thresholds to determine the damage of the element(4)
In the elastic state, the stress-permeability coefficient relationship of the material is described following a negative exponential equation(5)
The mechanical parameters (elastic modulus and compressive strength, etc.) of mesostructure of material are assigned according to Weibull distribution [27](1)fa=ma0aa0m−1exp−aa0m,wheref(a) is the statistical distribution density of the mechanical parameter of the mesoscopic elements, and a is the mechanical parameters (e.g., Young’s modulus, Poisson’s ratio, tensional strength, and compressive strength) of the elements, and a0 denotes the scale parameters related to the average values of the mechanical parameters. The indice m is the heterogeneity index that is used to describe the heterogeneity of solid materials in RFPA code. As shown in Figure 3, A high m value indicates the presence of highly homogenous materials whereas a small m value denotes the existence of highly heterogeneous material.Figure 3
Weibull’s distribution of the mechanical parameters of materials with different heterogeneity (m) value indices (Figure 3 is reproduced from Xiaoxi Men et al. numerical investigation on the hydraulic fracture evolution of jointed shale. Advances in materials science and engineering. 2021).


## 3. RFPA Numerical Model Establishment

The numerical simulations were completed in two stages. The first stage involved a physical experiment [28] of hydraulic fracturing in a shale with different angle-oriented perforations to validate the RFPA-Flow code. The size of the specimen was 300 mm × 300 mm that was further discretized into 160000 elements. A wellbore with a diameter of 15 mm was located at the center of the models, and a casing pipe made of steel with an external diameter of 20 mm was located around the wellbore (Figure 4). The θ was the angle between perforation and the maximum principle stress direction and it was set to 0°, 15°, 30°, 45°, 60°, 75° and 90°, respectively. The confining pressures of σH = 4 MPa and σh = 1 MPa were applied on the boundaries of the models. An increasing water pressure starting from 4 MPa at 0.1 MPa increment per step, was applied to the wellbore. The second stage involved numerical simulations of jointed shales with different dip angle-oriented perforation. The specimen size and wellbore setting were the same as in the first stage. As shown in Figure 4, α was the angle between the oriented perforation and joint plane, and β was the angle between the joint plane and the maximum principle stress direction. The spacing of the adjacent parallel joint planes was 30 mm. To investigate the influence of joint angle on fracture evolution, the angle α of 0°, 15°, 30°, 45°, 60°, 75° and 90° were simulated, respectively. Moreover, the angle β of 15°, 45° and 75° at constant α (15°) were simulated to investigate the influence of the maximum principle stress orientation on fracture propagation. The confining pressures of σH = 12 MPa and σh = 10 MPa were imposed on the boundaries of the models. An increasing water pressure of starting from 12 MPa increasing at 0.2 MPa increments per step was injected in the well. The shale and joint parameters input in the simulations were shown in Table 1. Figure 5 demonstrated the methodologies used in this study. Considering that the simulations are two-dimensional, the plane-strain calculation was adopted.Figure 4
Schematic of the model set.Table 1
Physico-mechanical parameters of shale and joint employed in simulations.
ParametersUnitShaleJointHeterogeneity index (m)32Young’s modulus (E)GPa303Poisson’s ratio (ν)0.230.23Friction angle (φ)o3737Compressive strength (fc)MPa808Permeability coefficient (K)md−10.0008640.00864Figure 5
Flowchart of methodologies used in this study.


## 4. Numerical Simulation

### 4.1. Fracture Evolution of Shale Models with Differentθ Values

In order to study the influence of perforation orientation on fracture evolution and verify the reliability of the RFPA-Flow code, seven models with differentθ values are simulated in this section. The results showed that the initiation and propagation of fractures significantly changed when the oriented perforation’s dip angle increased (Figure 6), and the initiation and breakdown pressure of specimens were influenced by the θ value (Figure 7).Figure 6
Simulation results of shale models with different angle oriented perforation.Figure 7
Initiation and breakdown pressure of shale models with differentθ value.As shown by the pore pressure field in Figure6, the hydraulic fracture was only initiated in the tip of the perforation because of the exits of the oriented perforation. This conforms to the function of oriented perforation and is consistent with the experiment [28]. The minimum principle stress distribution in Figure 6 showed that in the process of hydraulic fracturing, there is a tensile stress region likes umbrella (highlighted in green) emerges around the propagating fracture tip indicating that the hydraulic fractures were formed due to tension. In addition, the fracture evolution changed significantly as θ increased. When θ was small (0°, 15°, 30°), the fracture propagated along the direction of the maximum principal stress directly after initiated. When θ was large (45°, 60°, 75°, 90°), the fracture turns obviously, leading to generate more secondary fractures. On the other hand. Regardless of the magnitude of θ, the hydraulic fracture eventually would propagate along the horizontal direction confirming the significant role of the maximum principle stress in the fracture propagation.As shown in Figure7, an increase in θ value only led to a marginal change in the initiation pressure of 7 specimens. When the θ value is 0° to 60°, the initiation pressures are basically unchanged, while when the θ value is 75° to 90°, the initiation pressure exhibited a minor variation. On the other hand, the influence of θ values on breakdown pressure seems more significant than that on initiation pressure. When the θ value is 0° to 30°, the breakdown pressures were small and close to the initiation pressure value. When the θ value is 45° to 90°, the breakdown increased with the θ value at a greater rate than that for initiation pressures. It is noteworthy that a greater breakdown pressure indicates a longer and more complex fracturing path, it is consist with the hydraulic fracture evolution in Figure 6.Figure8 and Table 2 are the comparison of numerical simulation results and experimental results. In Figure 8, it can be found that the fracture initiation, propagation, and turning in the numerical simulation agreed well with that in the experimental results. When θ is 0°, the fracture is a straight line; whereas when θ is 60°, the fracture is an antisymmetry wing fracture with a deviated propagation. As shown in Table 2, the turning radiuses of simulations are consistent with the experiment values. Overall, the fracture evolution in the numerical simulations and experiments agreed well with each other confirming the validity of the RFPA-Flow code.Figure 8
Comparison of numerical and experimental results. (a) 0° (b) 60°.
(a)(b)Table 2
Turning radius of numerical simulation results and experimental results.
θ (o)Experiment results (mm)Simulation results (mm)0——1539403075804588936010610875—12090—159


### 4.2. Fracture Evolution of Jointed Shale Models with Differentα Values

It was found that more secondary fractures were generated whenθ is 90° and it would be easier to form a fracture network. Therefore, the angle θ which is the angle between oriented perforation and the maximum principal stress direction is set at 90° and remain constant in this section. The angle α which is the angle between the joint plane and oriented perforation was set at 0°, 15°, 30°, 45°, 60°, 75°, and 90°, to study the influence of α on the formation of a complex fracture network.As shown in Figure9, the magnitude of α value has a significant influence on the hydraulic fracture evolution due to the existence of the joint plane. When α was 0°, the fracture initiated and propagated closely along the joint plane. When α increased to 15°, 30° or 45°, the fracture initiated in the perforation tip and propagated toward to the nearest joint plane until connecting with the joint. The fracture propagated along the joint thereafter. When α increased to 60°, 75°, and 90°, the fracture initiated and propagated along the perforation direction until connecting to any nearest joint planes, then the fracture continued to propagate along the joint plane. Except for α being 0° and 90°, the hydraulic fractures were generated in the shape of an antisymmetry wing which were consistent with the numerical simulation results in the previous section. The only difference was these fractures are more regular because of the existence of the joint plane.Figure 9
Simulation results of jointed shale models with differentα values.From the minimum principle stress distributions in Figure9, it could be found that the fracture propagated due to the tensile stress (highlighted in green) leading to form a fracture tip. As the α value increased, more secondary fractures were generated. Therefore, the angle α was another influential factor in the fracture network formation in addition to the angle θ. It could be seen that a larger α value would lead to a greater the tensile stress zone around the fracture tip as well as more joint planes being pulled apart, and hence the antisymmetry wing fracture becomes more complex.As shown in Figure10, the initiation and breakdown pressures remained unchanged regardless of any variation in α value. It is determined by the hydraulic fracture propagation mode: no matter how the α value changes, the fracture always propagates along the joint plane eventually.Figure 10
Initiation and breakdown pressure of jointed shale models with differentα value.


### 4.3. Fracture Evolution of Jointed Shale Models with Differentβ Values

In addition toθ and α, the angle β which is the angle between joint plane and the maximum principal stress direction might be another important factor in the evolution of hydraulic fractures. In this case, the angle α was set constantly at 15° whereas the angle β was set at 15°, 45° and 75°, respectively.As shown in Figure11, the hydraulic fracture evolutions in the three specimens seems the same. The fracture was initiated in the oriented perforation tip and turned towards the nearest joint plane until connecting with the joints. Thereafter, the fractures propagated along the joint plane. As the magnitude of β increased, the tensile stress region (highlighted in green) in the fracture tip became larger, the number of the joint plane which be pulled apart increases, and the hydraulic fracture is more tortuous and complex.Figure 11
Simulation results of jointed shale models with differentβ value.Figure12 is illustrates the influence of β values on the initiation and breakdown pressure in a jointed shale. It could be seen that the initiation and breakdown pressures would increase with the magnitude of β.Figure 12
Initiation and breakdown pressure of jointed shale models with differentβ value.


## 4.1. Fracture Evolution of Shale Models with Differentθ Values

In order to study the influence of perforation orientation on fracture evolution and verify the reliability of the RFPA-Flow code, seven models with differentθ values are simulated in this section. The results showed that the initiation and propagation of fractures significantly changed when the oriented perforation’s dip angle increased (Figure 6), and the initiation and breakdown pressure of specimens were influenced by the θ value (Figure 7).Figure 6
Simulation results of shale models with different angle oriented perforation.Figure 7
Initiation and breakdown pressure of shale models with differentθ value.As shown by the pore pressure field in Figure6, the hydraulic fracture was only initiated in the tip of the perforation because of the exits of the oriented perforation. This conforms to the function of oriented perforation and is consistent with the experiment [28]. The minimum principle stress distribution in Figure 6 showed that in the process of hydraulic fracturing, there is a tensile stress region likes umbrella (highlighted in green) emerges around the propagating fracture tip indicating that the hydraulic fractures were formed due to tension. In addition, the fracture evolution changed significantly as θ increased. When θ was small (0°, 15°, 30°), the fracture propagated along the direction of the maximum principal stress directly after initiated. When θ was large (45°, 60°, 75°, 90°), the fracture turns obviously, leading to generate more secondary fractures. On the other hand. Regardless of the magnitude of θ, the hydraulic fracture eventually would propagate along the horizontal direction confirming the significant role of the maximum principle stress in the fracture propagation.As shown in Figure7, an increase in θ value only led to a marginal change in the initiation pressure of 7 specimens. When the θ value is 0° to 60°, the initiation pressures are basically unchanged, while when the θ value is 75° to 90°, the initiation pressure exhibited a minor variation. On the other hand, the influence of θ values on breakdown pressure seems more significant than that on initiation pressure. When the θ value is 0° to 30°, the breakdown pressures were small and close to the initiation pressure value. When the θ value is 45° to 90°, the breakdown increased with the θ value at a greater rate than that for initiation pressures. It is noteworthy that a greater breakdown pressure indicates a longer and more complex fracturing path, it is consist with the hydraulic fracture evolution in Figure 6.Figure8 and Table 2 are the comparison of numerical simulation results and experimental results. In Figure 8, it can be found that the fracture initiation, propagation, and turning in the numerical simulation agreed well with that in the experimental results. When θ is 0°, the fracture is a straight line; whereas when θ is 60°, the fracture is an antisymmetry wing fracture with a deviated propagation. As shown in Table 2, the turning radiuses of simulations are consistent with the experiment values. Overall, the fracture evolution in the numerical simulations and experiments agreed well with each other confirming the validity of the RFPA-Flow code.Figure 8
Comparison of numerical and experimental results. (a) 0° (b) 60°.
(a)(b)Table 2
Turning radius of numerical simulation results and experimental results.
θ (o)Experiment results (mm)Simulation results (mm)0——1539403075804588936010610875—12090—159


## 4.2. Fracture Evolution of Jointed Shale Models with Differentα Values

It was found that more secondary fractures were generated whenθ is 90° and it would be easier to form a fracture network. Therefore, the angle θ which is the angle between oriented perforation and the maximum principal stress direction is set at 90° and remain constant in this section. The angle α which is the angle between the joint plane and oriented perforation was set at 0°, 15°, 30°, 45°, 60°, 75°, and 90°, to study the influence of α on the formation of a complex fracture network.As shown in Figure9, the magnitude of α value has a significant influence on the hydraulic fracture evolution due to the existence of the joint plane. When α was 0°, the fracture initiated and propagated closely along the joint plane. When α increased to 15°, 30° or 45°, the fracture initiated in the perforation tip and propagated toward to the nearest joint plane until connecting with the joint. The fracture propagated along the joint thereafter. When α increased to 60°, 75°, and 90°, the fracture initiated and propagated along the perforation direction until connecting to any nearest joint planes, then the fracture continued to propagate along the joint plane. Except for α being 0° and 90°, the hydraulic fractures were generated in the shape of an antisymmetry wing which were consistent with the numerical simulation results in the previous section. The only difference was these fractures are more regular because of the existence of the joint plane.Figure 9
Simulation results of jointed shale models with differentα values.From the minimum principle stress distributions in Figure9, it could be found that the fracture propagated due to the tensile stress (highlighted in green) leading to form a fracture tip. As the α value increased, more secondary fractures were generated. Therefore, the angle α was another influential factor in the fracture network formation in addition to the angle θ. It could be seen that a larger α value would lead to a greater the tensile stress zone around the fracture tip as well as more joint planes being pulled apart, and hence the antisymmetry wing fracture becomes more complex.As shown in Figure10, the initiation and breakdown pressures remained unchanged regardless of any variation in α value. It is determined by the hydraulic fracture propagation mode: no matter how the α value changes, the fracture always propagates along the joint plane eventually.Figure 10
Initiation and breakdown pressure of jointed shale models with differentα value.


## 4.3. Fracture Evolution of Jointed Shale Models with Differentβ Values

In addition toθ and α, the angle β which is the angle between joint plane and the maximum principal stress direction might be another important factor in the evolution of hydraulic fractures. In this case, the angle α was set constantly at 15° whereas the angle β was set at 15°, 45° and 75°, respectively.As shown in Figure11, the hydraulic fracture evolutions in the three specimens seems the same. The fracture was initiated in the oriented perforation tip and turned towards the nearest joint plane until connecting with the joints. Thereafter, the fractures propagated along the joint plane. As the magnitude of β increased, the tensile stress region (highlighted in green) in the fracture tip became larger, the number of the joint plane which be pulled apart increases, and the hydraulic fracture is more tortuous and complex.Figure 11
Simulation results of jointed shale models with differentβ value.Figure12 is illustrates the influence of β values on the initiation and breakdown pressure in a jointed shale. It could be seen that the initiation and breakdown pressures would increase with the magnitude of β.Figure 12
Initiation and breakdown pressure of jointed shale models with differentβ value.


## 5. Summary and Conclusions

An approach which can promote the formation of a complex fracture network in jointed shales by oriented perforation is proposed in this study. The findings as seen in the followings can offer valuable guidance to the design of unconventional reservoir reconstruction and the control of the fracture growth geometry in jointed shale reservoirs.(1)
The angleθ affects the evolution of the hydraulic fracture and the breakdown pressure in the shale. A larger magnitude of θ would lead to a larger turning radius of the propagation path and hence a greater breakdown pressure. As a result, the more the secondary fractures would be generated leading to more complex the hydraulic fractures.(2)
The angleα affects the fracture initiation and propagation of jointed shale. A larger magnitude of α would lead to a larger tensile stress region around the fracture tip and more joint planes being pulled apart. Consequently, more the secondary fractures would be generated leading to more complex the fractures.(3)
With the sameα value, the evolution and shape of fractures remains the same regardless of the magnitude of θ.(4)
A largerβ value would lead to a larger tensile stress region is and more joint planes being pulled apart. Consequently, more tortuous and complex hydraulic fractures would be generated. In addition, the initiation and breakdown pressure in the jointed shale would increase with the magnitude of β.



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*Source: 2685236-2022-10-13.xml*