The crack tip region in hydraulic fracturing

Abstract

We present analytical tip region solutions for fracture width and pressure when a power law fluid drives a plane strain fracture in an impermeable linear elastic solid. Our main result is an intermediate asymptotic solution in which the tip region stress is dominated by a singularity which is particular to the hydraulic fracturing problem. Moreover this singularity is weaker than the inverse square root singularity of linear elastic fracture mechanics. We also show how the solution for a semi-infinite crack may be exploited to obtain a useful approximation for the finite case.

Numerical methods for hydraulic fracture propagation: A review of recent trends

“…Hence, the solution near the tip of a propagating finite hydraulic fracture is captured by a stationary solution for a semi-finite crack moving at a constant velocity Va solution akin to a traveling wave solution. For more details, we refer to the contributions of Desroches et al (1994) for the zero toughness / zero leak-off case (viscosity asymptote), Lenoach (1995) for the leak-off dominated case and Garagash et al (2011) for the complete solution with toughness, leak-off and viscosity in the limiting case of a vanishing lag.…”

A finite element approach to the simulation of hydraulic fractures with lag

“…USA tE-mail: lewa@stanford.edu direction out of the plane [7,8]. For this geometry, the nature of the hydraulic fracture problem in the region of the crack tip has been analyzed by considering a crack propagating at a constant velocity in a semi-infinite medium [9][10][11]. For a crack of finite size with constant inlet flow rate, asymptotic solutions have been obtained in the limit of large viscosity [12,13] and large toughness [14].…”

Injection of solids to lift coastal areas

“…The coupling effects have been described by Spence & Sharp (1985), Lister (1990), Desroches et al (1994), Detournay (2004), Adachi et al (2007), Mitchell et al (2007) and Garagash (2009) among others. It appears that processes taking place near the fracture front and the corresponding scales control the response of the entire fracture.…”