A Hybrid Finite Volume and Extended Finite Element Method for Hydraulic Fracturing with Cohesive Crack Propagation in Quasi-Brittle Materials
Abstract
:1. Introduction
2. Methodology
2.1. Conceptual Model
2.2. Deformation Model
2.3. Fracture Flow Model
2.4. Fracture Propagation Model
2.5. Discretization and Solution Algorithms
2.5.1. Discretization of Equilibrium Equation
2.5.2. Discretization of the Fracture Flow
2.6. Fluid–Solid Coupling Procedure and the Picard Iteration Approach
3. Results and Discussion
3.1. Khristianovic–Geertsma–de Klerk (KGD) Model
3.2. Hydraulic Fracturing Test
3.3. Hydraulic Fracturing in a Concrete Gravity Dam
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Young’s modulus | E = 17.0 GPa |
Poisson’s ratio | ν = 0.2 |
Tensile strength | ft = 1.25 MPa |
Cohesive fracture energy | Gc = 120 N/m |
Water density | ρw = 1000 kg/m3 |
Water dynamic viscosity | μ = 1.00 × 10−4 Pa s |
Fluid injection rate | Q0 = 5.00 × 10−4 m2/s |
Young’s modulus | E = 27.25 GPa |
Poisson’s ratio | ν = 0.173 |
Tensile strength | ft = 2.01 MPa |
Cohesive fracture energy | Gc = 140 N/m |
Water density | ρw = 1000 kg/m3 |
Water dynamic viscosity | μ = 1.00 × 10−6 kPa s |
Young’s modulus | E = 25.0 GPa |
Poisson’s ratio | ν = 0.167 |
Tensile strength | ft = 2.05 MPa |
Cohesive fracture energy | Gc = 150 N/m |
Water density | ρw = 1000 kg/m3 |
Water dynamic viscosity | μ = 1.00 × 10−6 kPa∙s |
Solid density | ρw = 2400 kg/m3 |
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Liu, C.; Shen, Z.; Gan, L.; Jin, T.; Zhang, H.; Liu, D. A Hybrid Finite Volume and Extended Finite Element Method for Hydraulic Fracturing with Cohesive Crack Propagation in Quasi-Brittle Materials. Materials 2018, 11, 1921. https://doi.org/10.3390/ma11101921
Liu C, Shen Z, Gan L, Jin T, Zhang H, Liu D. A Hybrid Finite Volume and Extended Finite Element Method for Hydraulic Fracturing with Cohesive Crack Propagation in Quasi-Brittle Materials. Materials. 2018; 11(10):1921. https://doi.org/10.3390/ma11101921
Chicago/Turabian StyleLiu, Chong, Zhenzhong Shen, Lei Gan, Tian Jin, Hongwei Zhang, and Detan Liu. 2018. "A Hybrid Finite Volume and Extended Finite Element Method for Hydraulic Fracturing with Cohesive Crack Propagation in Quasi-Brittle Materials" Materials 11, no. 10: 1921. https://doi.org/10.3390/ma11101921