Model of T-Type Fracture in Coal Fracturing and Analysis of Influence Factors of Fracture Morphology
Abstract
:1. Introduction
2. Derivation of the Model of T-Type Fracture
3. Model Validation
4. Analysis of Influence Factors of T-Type Fracture
4.1. Effect of Vertical Fracture Height on the Shape of T-Type Fracture
4.2. Influence of Coalbed Fracture Toughness on T-Type Fracture
4.3. Influence of Bedding Shear Strength on the Morphology of T-Type Fracture
5. Discussion
5.1. Principal Insights
5.2. Model Limitations
6. Conclusions
- (1)
- T-type fractures in coal fracturing are mainly caused by vertical fractures extending to the bedding plane and causing horizontal fractures to form on the bedding plane after stretching or shear failure.
- (2)
- The increase of the vertical fracture height can increase the length of the horizontal fracture, but when the vertical fracture height increases to a certain value, the effect of increasing the horizontal fracture length by increasing the vertical fracture height is no longer obvious.
- (3)
- The fracture toughness has certain influence on the length of horizontal fracture, but there is a threshold. When the fracture toughness is less than the threshold, the length of horizontal fracture remains unchanged, otherwise, the length of horizontal fracture increases rapidly with the increase of fracture toughness.
- (4)
- When the shear strength of the interface between the coalbed and the interlayer is enhanced, the length of the horizontal part of T-type fracture is rapidly reduced. It shows that the greater the stratification strength is, the more stable it is and the less favorable it is to the formation of T-type fracture.
Author Contributions
Acknowledgments
Conflicts of Interest
Nomenclature
σH | maximum horizontal principal stress, MPa; |
σh | minimum horizontal principal stress, MPa; |
σv | vertical stress, MPa; |
lf | length of horizontal fracture, m; |
Pr | fracture propagation pressure, MPa; |
C | the half height of the vertical fracture, m; |
Pnet(x) | the net pressure of the fluid at any point in the fracture, MPa; |
hi | the thickness of the i-th layer, I = 1, 2, …., n, m; |
σI | the horizontal minimum principal stress of the i-th layer, I = 1, 2, …., n, MPa; |
KICi | the fracture toughness of the i-th layer rock, I = 1, 2, …., n, MPa·m1/2; |
TVD | the true vertical depth, m; |
ρ | the fracturing fluid density, kg/m3; |
m | the density gradient, kg/m2·s2; |
dref | the vertical depth of perforation, m; |
Pref | the fracturing fluid pumping pressure at the perforation location, MPa; |
dmid | the vertical depth of the middle of the fracture, m; |
Pmid | the fracturing fluid pressure in the middle of the fracture, MPa; |
xd,I, xu,I | the bottom and top depth of the i-th layer respectively, m; |
α | the angle between horizontal bedding and vertical stress, (°); |
θ | the polar angle of any point in the polar coordinate system of the fracture tip deviating from the direction of the fracture extension line, (°); |
β | the angle between the horizontal bedding polar coordinate system and vertical fracture rectangular coordinate system, (°); |
σt | the tensile strength of the bedding plane, MPa; |
τs | the cohesion of the bedding plane, MPa. |
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No. | Parameters | Symbol | Unit | Value |
---|---|---|---|---|
1 | maximum horizontal principal stress | σH | MPa | 6 |
2 | minimum horizontal principal stress | σh | MPa | 4 |
3 | vertical stress | σv | MPa | 10 |
4 | length of vertical fracture | 2C | m | 0.25 |
5 | length of horizontal fracture | lf | m | 0.05–0.15 |
6 | fracture propagation pressure | Pr | MPa | 5.5 |
7 | fracturing fluid density | ρ | kg/m3 | 1050 |
No. 1 | No. 2 | No. 3 | ||||||
---|---|---|---|---|---|---|---|---|
Symbol | Unit | Value | Symbol | Unit | Value | Symbol | Unit | Value |
KIC | MPa·m1/2 | 0.94 | KIC | MPa·m1/2 | 0.94 | KIC | MPa·m1/2 | 0.94 |
τ | MPa | 0.84 | τ | MPa | 0.59 | τs | MPa | 0.48 |
lf | m | 0.05 | lf | m | 0.10 | lf | m | 0.15 |
No. of Layer | Top Depth (m) | Thickness (m) | Minimum Horizontal Principal Stress (MPa) | Vertical Stress (MPa) | Fracture Toughness (MPa·m1/2) | Tensile Strength (MPa) | Shear Strength (MPa) |
---|---|---|---|---|---|---|---|
1 | 900 | 50 | 20.70 | 21.60 | 1.42 | 0.91 | 3.49 |
2 | 950 | 20 | 16.40 | 22.80 | 0.71 | 0.32 | 0.85 |
3 | 970 | 50 | 22.30 | 23.30 | 1.42 | 0.93 | 3.62 |
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Li, Y.; Jia, D.; Li, W.; Zhang, K. Model of T-Type Fracture in Coal Fracturing and Analysis of Influence Factors of Fracture Morphology. Energies 2018, 11, 1196. https://doi.org/10.3390/en11051196
Li Y, Jia D, Li W, Zhang K. Model of T-Type Fracture in Coal Fracturing and Analysis of Influence Factors of Fracture Morphology. Energies. 2018; 11(5):1196. https://doi.org/10.3390/en11051196
Chicago/Turabian StyleLi, Yuwei, Dan Jia, Wei Li, and Kunpeng Zhang. 2018. "Model of T-Type Fracture in Coal Fracturing and Analysis of Influence Factors of Fracture Morphology" Energies 11, no. 5: 1196. https://doi.org/10.3390/en11051196