Viscosity-dominated hydraulic fractures

Using scaling arguments, this paper first demonstrates that most hydraulic fracturing treatments are in the viscosity-dominated regime; i.e., the evolution of the fracture during fluid injection does not depend on the rock toughness, a material parameter quantifying the energy required to break the rock. In the viscosity-dominated regime, the aperture in the crack tip region (viewed at the fracture scale) is no longer characterized by the classical square root behavior predicted by linear elastic fracture mechanics, since other asymptotic behaviors prevail. For example, under conditions of large efficiency and small fluid lag, the asymptotic tip aperture that reflects the predominance of viscous dissipation is of the form w ∼ s^2/3 (where s is the distance from the tip). The physical reality of the viscosity-dominated regime is confirmed by results of laboratory experiments where radial hydraulic fractures were propagated by injecting aqueous solutions of glycerin or glucose along an epoxy-bonded interface between two Polymethyl Methacrylate (PMMA) blocks. Agreement to within 10 percent is demonstrated between the experimental results for the location of the fracture front and the full-field fracture opening (measured using a novel optical technique), and the semi-analytical solution of a radial hydraulic fracture propagating in a zero toughness impermeable elastic material. Finally, we demonstrate that provided the appropriate tip behavior is embedded in the algorithm, a planar hydraulic fracture simulator with a rather coarse mesh is able to accurately reproduce the semi-analytical solution for a radial hydraulic fracture propagating in the viscosity-dominated regime.