Self-Similar Propagation of a Hydraulic Fracture in a Poroelastic Medium

This paper considers the plane strain problem of a hydraulic fracture propagating in a poroelastic medium, as a result of injection of fluid from a well. It describes an asymptotic solution that is applicable provided that four conditions are met: (i) the material toughness is negligible; (ii) the viscosity of the injected fluid is similar to that of the native pore-fluid; (iii) the medium has a large permeability relative to the fracture conductivity; and (iv) the injection rate is small enough that the fracture propagates inside the growing region around the well, where the pore pressure field is quasi-stationary. If these conditions are met, the fracture propagates stably in a self-similar manner, with its length and aperture growing as square root of time. Because the fracture remains in the quasi steady-state region, poroelastic effects are fully developed and significantly impact crack growth.