Plane-Strain Propagation of a Fluid-Driven Crack in a Permeable Rock with Fracture Toughness |
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Authors: | J. Hu D. I. Garagash |
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Affiliation: | 1Project Engineer, AMEC Geomatrix, Inc., 2101 Webster St., Oakland, CA 94612. 2Associate Professor, Dept. of Civil and Resource Engineering, Dalhousie Univ., 1360 Barrington St., Halifax NS, Canada B3J 1Z1 (corresponding author). E-mail: garagash@dal.ca
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Abstract: | 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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Keywords: | Cracking Porous media Leakage Numerical analysis Rocks |
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