Propagation of a penny-shape hydraulic fracture in an impermeable rock

Alexei Savitski, Emmanuel M Detournay

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations

Abstract

This paper deals with the self-similar solution of a penny-shape hydraulic fracture propagating in an impermeable elastic rock. Growth of the fracture is driven by injection of an incompressible Newtonian fluid at the center of the fracture, at a flow rate varying according to a power law of time (which includes the practically important case of a constant injection rate). The solution is restricted to the so-called viscosity-dominated regime where it can be assumed that the rock has zero toughness. In this regime, the fracture tip is characterized by a singularity which is weaker than the classical square root singularity of linear elastic fracture mechanics. The paper describes the construction of a semi-analytical similarity solution, which incorporates the known singularity of the fluid pressure at the center of the fracture and at the tip and which is based on series expansions of the fracture opening and fluid pressure in terms of Jacobi polynomials. It is shown that very few terms in the expansions are needed to capture the solution accurately.

Original languageEnglish (US)
Title of host publicationVail Rocks 1999 - 37th U.S. Symposium on Rock Mechanics (USRMS)
Editors Kranz, Smeallie, Scott, Amadei
PublisherAmerican Rock Mechanics Association (ARMA)
Pages851-858
Number of pages8
ISBN (Print)9058090523, 9789058090522
StatePublished - Jan 1 1999
Event37th U.S. Symposium on Rock Mechanics, Vail Rocks 1999 - Vail, United States
Duration: Jun 7 1999Jun 9 1999

Publication series

NameVail Rocks 1999 - 37th U.S. Symposium on Rock Mechanics (USRMS)

Other

Other37th U.S. Symposium on Rock Mechanics, Vail Rocks 1999
CountryUnited States
CityVail
Period6/7/996/9/99

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