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 viscositydominated 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 ~ s2/3 (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.
Fluid-driven fractures represent a particular class of tensile fractures that propagate in solid media, typically under preexisting compressive stresses, as a result of internal pressurization by an injected viscous fluid. Hydraulic fractures are most commonly engineered for the stimulation of hydrocarbon-bearing rock strata to increase production of oil and gas wells (Economides & Nolte 2000), but there are other industrial applications such as remediation projects in contaminated soils (Murdoch 2002), waste disposal (Abou-Sayed 1994), preconditioning and cave inducement in mining (Jeffrey & Mills 2000).