Propagation regimes of fluid-driven fractures in impermeable rocks

This paper reviews recent results of a research program aimed at developing a theoretical framework to understand and predict the different modes of propagation of a fluid-driven fracture. The research effort involves constructing detailed solutions of the crack tip region, developing global models of hydraulic fractures for plane strain and radial geometry, and identifying the parameters controlling the fracture growth. The paper focuses on the propagation of hydraulic fractures in impermeable rocks. The controlling parameters are identified from scaling laws that recognize the existence of two dissipative processes: fracturing of the rock (toughness) and dissipation in the fracturing fluid (viscosity). It is shown that the two limit solutions (corresponding to zero toughness and zero viscosity) are characterized by a power law dependence on time and that the transition between these two asymptotic solutions depends on a single number, which can be chosen to be either a dimensionless toughness or a dimensionless viscosity. The viscosity- and toughness-dominated regime of crack propagation are then identified by comparing the general solutions with the asymptotic solutions. This analysis yields the ranges of the dimensionless parameter for which the solution can be approximated for all practical purposes either by the zero toughness or by the zero viscosity solution.