Numerical and Experimental Investigations of the Interactions between Hydraulic and Natural Fractures in Shale Formations
Abstract
:1. Introduction
2. Methods
2.1. Displacement Discontinuity Method
2.2. Fracture Initiation and Propagation
2.3. Mohr-Coulomb Joint Element
2.4. Numerical Procedure
3. Model Verifications
4. Case Studies
4.1. Displacements and Stresses along the Natural Fracture (NF)
4.2. Parametric Study of Stress Distribution and Unstable Tensile Zone along the NF
4.3. Effects of Natural Fracture on the Hydraulic Fracture (HF) Propagation Path
5. Experimental Investigation
5.1. Experimental Setup and Sample Preparation
5.2. Experimental Results and Analyses
6. Conclusions
- (1)
- The hydraulic fracture morphology of shale was strongly influenced by the characteristics of its natural fractures. The NF density, orientation, and cemented strength, are three main factors dominating the formation of complex fracture networks.
- (2)
- The cemented strength of the NF caused a noticeable nonlinear behavior for this problem. For an NF with a low strength, only shear failure occurred, and the HF was more likely to terminate. However, for an NF with a moderate strength, the hybrid failure model (tensile failure and shear failure co-existence, and conversion) may occur, and the HF is more inclined to step over at the contact.
- (3)
- The displacements and stresses along the NF all changed in a highly dynamic manner. During the stage of approach of the HF to an NF, the HF tip could exert a remote compressional and shear stress on the NF interface, which could lead to the debonding of the natural fracture. Meanwhile, a maximum principal stress peak is generated at the end of the opening zone, where a new tensile crack is more likely to occur.
- (4)
- The location and value of the stress is the function of NF inclination angle, far-field differential stress as well as HF net pressure. For small approaching angles, the stress peak is located farther from the intersection point, so a step over (offset) fracture is more likely to occur. The same effect can be found by a higher HF net pressure, because the stress perturbation ahead the NF is proportional to the fluid pressure in the HF.
- (5)
- Meanwhile, the HF was found to be more prone to deviate from its original propagation path and reoriented near the NF because the deformation of the NF.
Author Contributions
Funding
Conflicts of Interest
Appendix A
Appendix B
Nomenclature
length of the tip element (L) | |
empricial correction coefficient in Equation (4) | |
shear displacement discontinuity of the j-th element (L) | |
normal displacement discontinuity of the j-th element (L) | |
normalized displacement discontinuities | |
modulus of elasticity (ML−1T−2) | |
stress intensity factor of kind I (ML−1/2T−2) | |
stress intensity factor of kind II (ML−1/2T−2) | |
fracture toughness (ML−1/2T−2) | |
shear stress stiffness (ML−2T−2) | |
normal stress stiffness (ML−2T−2) | |
shear displacements of the i-th element (L) | |
normal displacements of the i-th element (L) | |
Poisson’s ratio | |
dimensionless coordinate in the x direction | |
dimensionless coordinate in the y direction | |
average of the horizontal stresses (ML−1T−2) | |
difference of the horizontal stresses (ML−1T−2) | |
shear components of stress at the midpoint of the i-th element (ML−1T−2) | |
normal components of stress at the midpoint of the i-th element (ML−1T−2) | |
initial shear stress (ML−1T−2) | |
initial normal stress (ML−1T−2) | |
yield shear stress (ML−1T−2) | |
fracture initiation angle | |
normalized gap between the two fractures | |
normalized net pressure | |
normalized horizontal stress difference |
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Parameter | Unit | Value |
---|---|---|
Initial length of natural fracture | m | 2.0 |
Inclination of natural fracture | ° | 40 |
Cohesion of natural fracture | MPa | 2.2 |
Friction angle of fracture | ° | 26.6 |
Normal stiffness of natural fracture | MPa/m | 0.5 × 106 |
Shear stiffness of natural fracture | MPa/m | 0.25 × 106 |
Initial Length of hydraulic fracture | m | 2.0 |
Fluid pressure in the hydraulic fracture | MPa | −3.9 |
Initial gap between the fractures | m | 0.1 |
Elasticity modulus | GPa | 14 |
Poisson’s ratio | - | 0.1 |
Maximum horizontal stress | MPa | −2.1 |
Minimum horizontal stress | MPa | −1.9 |
Specimen Number | Simulated Well Type | Liquid Type | σv (MPa) | σH (MPa) | σh (MPa) | Flow Rate (ML/s) |
---|---|---|---|---|---|---|
Y-7-1 | horizontal well | fresh water | 20.00 | 19.51 | 16.98 | 0.5 |
Y-7-3 | 1.0 |
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Chang, X.; Guo, Y.; Zhou, J.; Song, X.; Yang, C. Numerical and Experimental Investigations of the Interactions between Hydraulic and Natural Fractures in Shale Formations. Energies 2018, 11, 2541. https://doi.org/10.3390/en11102541
Chang X, Guo Y, Zhou J, Song X, Yang C. Numerical and Experimental Investigations of the Interactions between Hydraulic and Natural Fractures in Shale Formations. Energies. 2018; 11(10):2541. https://doi.org/10.3390/en11102541
Chicago/Turabian StyleChang, Xin, Yintong Guo, Jun Zhou, Xuehang Song, and Chunhe Yang. 2018. "Numerical and Experimental Investigations of the Interactions between Hydraulic and Natural Fractures in Shale Formations" Energies 11, no. 10: 2541. https://doi.org/10.3390/en11102541