期刊
JOURNAL OF ENGINEERING MECHANICS
卷 136, 期 9, 页码 1152-1166出版社
ASCE-AMER SOC CIVIL ENGINEERS
DOI: 10.1061/(ASCE)EM.1943-7889.0000169
关键词
Cracking; Porous media; Leakage; Numerical analysis; Rocks; Fracture mechanics; Hydraulic fracture; Porous media; Leak-off; Asymptotic solution; Numerical analysis
资金
- Petroleum Research Fund [ACS-PRF 35729-G2]
A solution to the problem of a plane-strain fluid-driven crack propagation in elastic permeable rock with resistance to fracture is presented. The fracture is driven by injection of an incompressible Newtonian fluid at a constant rate. The solution, restricted to the case of zero lag between the fluid front and the fracture tip, evolves from the early-time regime when the fluid flow takes place mostly inside the crack toward the large-time response when most of the injected fluid is leaking from the crack into the surrounding rock. This transition further depends on a time-invariant partitioning between the energy expanded to overcome the rock fracture toughness and the energy dissipated in the viscous fluid flow in the fracture. A numerical approach is used to compute the solution for the normalized crack length and crack opening and net-fluid pressure profiles as a function of two dimensionless parameters: the leak-off/storage evolution parameter and the toughness/viscosity number. Relation of this solution to the various available asymptotic solutions is discussed. Obtained mapping of the solution onto the problem parametric space has a potential to simplify the tasks of design, modeling, and data inversion for hydraulic fracturing treatments and laboratory experiments.
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