One of the tests used to assess the possible dependence of the fracture toughness on stress relies on injecting fluid into a slotted borehole within a cylindrical rock sample subject to confining pressure and interpreting the toughness from the observed breakdown pressure. There is a wealth of experimental evidence that the so-measured toughness indeed increases with the confining stress. However, the interpretation of the observed breakdown pressure relies critically on assuming that the fluid pressure in the slots and the cracks ahead is uniform and on identifying the peak (breakdown) pressure with the fracture initiation pressure. The model described in this paper challenges these assumptions by considering the existence of a fluid lag at the tip of the hydraulic fracture and by incorporating the hydraulic compliance of the injection system. Numerical simulations indicate that there is an episode of stable crack growth, which is reflected by a continuous increase of the injection pressure after fracture initiation until the fracture becomes unstable. This model suggests that the actual toughness is generally overestimated, when it is interpreted from the breakdown pressure under the assumption of a uniform fluid pressure in the crack. Furthermore, this interpretation results in an artificial dependence of the toughness on the confining pressure. The overestimation depends essentially on two numbers, a scaled toughness and a scaled confining stress.
Bibliographical noteFunding Information:
Support for this research was provided by the T.W. Bennett Chair in Mining Engineering and Rock Mechanics. This support is gratefully acknowledged. The motivation for constructing a model of laboratory injection experiment to measure toughness arose during the course of a research contract with BP Petroleum. The authors acknowledge valuable discussions about this experimental set-up and observations with Robert Eve and Robert Heller at BP Petroleum, Ion Ispas formerly at BP Petroleum and now at Texas Tech University, and John McLennan at the University of Utah.
- Fluid injection experiment
- Fluid lag
- Fracture toughness measurement
- Hydraulic fracture
- Singular integral equations