This paper presents an analysis of the propagation of a penny-shaped hydraulic fracture in an impermeable elastic rock. The fracture is driven by an incompressible Newtonian fluid injected from a source at the center of the fracture. The fluid flow is modeled according to lubrication theory, while the elastic response is governed by a singular integral equation relating the crack opening and the .uid pressure. It is shown that the scaled equations contain only one parameter, a dimensionless toughness, which controls the regimes of fracture propagation. Asymptotic solutions for zero and large dimensionless toughness are constructed. Finally, the regimes of fracture propagation are analyzed by matching the asymptotic solutions with results of a numerical algorithm applicable to arbitrary toughness.
Bibliographical noteFunding Information:
This research has been partially funded by the Graduate School of the University of Minnesota through the Doctoral Dissertation Fellowship awarded to AS, and by a grant from Schlumberger. This support is gratefully acknowledged. The authors would also like to thank Dr. Jean Desroches of Schlumberger for providing the results of the numerical simulations with Loramec; his general assistance to the research program in hydraulic fracturing at the University of Minnesota is also deeply appreciated.
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