Numerical simulation of hydraulic fracturing in the viscosity-dominated regime

Most hydraulic fracturing treatments are in the viscosity-dominated regime. Hence, fracture growth does not depend on the rock toughness and it can be shown that the fracture aperture w near the fracture front, when viewed at the scale of the whole fracture, is not characterized by the classical square root behavior predicted by linear elastic fracture mechanics w ~∼s^1/2, where s is the distance from the tip. Instead, the asymptotic tip aperture that reflects the predominance of viscous dissipation is of the form w ∼ s ^2/3, under conditions of large efficiency and small fluid lag. After demonstrating the intimate connection between the tip aperture and the fracture propagation regime, we report the results of hydraulic fracturing laboratory experiments in PMMA and glass blocks that employ a novel optical technique to measure the fracture opening. These experiments provide incontrovertible evidence that the power law index, characterizing the fracture aperture near the tip, depends on the propagation regime in accordance with theoretical findings. Finally, we demonstrate that a coarsely-meshed planar hydraulic fracture simulator can produce accurate results relative to benchmark solutions provided that the appropriate tip behavior is embedded in the algorithm. Through theoretical, experimental, and computational considerations, these results make it clear that advances in the accuracy and efficiency of fracture simulators critically depend on a sophisticated treatment of the near-tip aperture that goes beyond basic linear elastic fracture considerations.