Plane-Strain Propagation of a Fluid-Driven Crack in a Permeable Rock with Fracture Toughness
Publication: Journal of Engineering Mechanics
Volume 136, Issue 9
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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Acknowledgments
The writers thank Dr. José I. Adachi for insightful discussions on the numerical methods. Acknowledgment is made to the donors of The Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research under Grant No. UNSPECIFIEDACS-PRF 35729-G2.
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Information
Published In
Journal of Engineering Mechanics
Volume 136 • Issue 9 • September 2010
Pages: 1152 - 1166
Copyright
© 2010 ASCE.
History
Received: Jan 29, 2009
Accepted: Mar 18, 2010
Published online: May 6, 2010
Published in print: Sep 2010
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