Unstable crack growth in hydraulic fracturing: The combined effects of pressure and shear stress for a power-law fluid

The underlying mechanisms of hydraulic fracturing remain elusive, and the optimization of the related processes for rocks of low permeability is challenging. There exists local crack closure induced by shear stress, which is one of the crack instabilities for a straight crack. In this study, we develop a full-stress model, which includes the combined effects of hydrodynamic pressure and shear stress on the crack surfaces. The hydrodynamic pressure is a driving force, while the shear stress is a resistance force. A novel criterion for crack propagation is derived based on the asymptotic solution of shear stress. The asymptotic solution, which is derived using perturbation analysis in the toughness-dominant regime, reveals the existence of the crack-closure phenomenon and shear-stress-dominant regime. The necessary condition for the crack closure is obtained according to numerical calculations. An energy analysis is conducted to discuss the difference between the shear-stress-dominant and the viscosity-dominant regimes. The existence of the crack closure is shown to be independent of two assumptions, lubrication theory and no-fluid-lag zone. The results presented in this study are useful for the simulation and design of hydraulic fracturing.