Abstract
This paper considers the problem of a hydraulic fracture in which an incompressible Newtonian fluid is injected at a constant rate to drive a fracture in a permeable, infinite, brittle elastic solid. The two cases of a plane strain and a penny-shaped fracture are considered. The fluid pressure is assumed to be uniform and thus the lag between the fracture front and the fluid is taken to be zero. The validity of these assumptions is shown to depend on a parameter, which has the physical interpretation of a dimensionless fluid viscosity. It is shown that when the dimensionless viscosity is negligibly small, the problem depends only on a single parameter, a dimensionless time. Small and large time asymptotic solutions are derived which correspond to regimes dominated by storage of fluid in the fracture and infiltration of fluid into the rock, respectively. Evolution from the small to the large time asymptotic solution is obtained using a fourth order Runge-Kutta method.
Original language | English (US) |
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Pages (from-to) | 175-190 |
Number of pages | 16 |
Journal | International Journal of Fracture |
Volume | 134 |
Issue number | 2 |
DOIs | |
State | Published - Jul 2005 |
Bibliographical note
Funding Information:Support has been provided by a Graduate Assistance in Areas of National Need fellowship from the United States Department of Education and the University of Minnesota Department of Civil Engineering. Further support has been provided by CSIRO Division of Petroleum Resources in Melbourne, Australia.
Keywords
- Asymptotic expansions
- Hydraulic fracturing
- Numerical methods