Magistral and fractal regimes of the hydro-fracturing

摘要

The paper describes the specific difference between two fracture growth regimes, when it forms the radial fracture network (fractal regime) and when it forms one big fracture in certain direction (magistral regime). A continuum model is used, which represents the fracture network in the media with the permeability tensor, rapidly increasing with the fracture appearance. The fracture front instability is shown, linked with the Saffman-Taylor instability, even in isotropic case. By analogy with Saffman-Taylor instability in porous media, the fractal nature of the fracture network is derived. The dimensionless parameters of fracture front speed and anisotropy are found, which would help to numerical and experimental modeling of the reservoir.