An enhanced J-integral for hydraulic fracture mechanics

This article revisits the formulation of the J-integral in the context of hydraulic fracture mechanics. We demonstrate that the use of the classical J-integral in finite element models overestimates the length of hydraulic fractures in the viscosity-dominated regime of propagation. A finite element analysis shows that the inaccurate numerical solution for fluid pressure is responsible for the loss in accuracy of the J-integral. With this understanding, two novel contributions are presented. The first contribution consists of two variations of the J-integral, termed the JHFM$J_{HFM}$ and JHFMA$J_{HFM}<^>A$-integral, that demonstrate an enhanced ability to predict viscosity-dominated propagation. In particular, such JHFM$J_{HFM}$-integrals accurately extract stress intensity factors in both viscosity and toughness-dominated regimes of propagation. The second contribution consists of a methodology to extract the propagation velocity from the energy release rate applicable throughout the toughness-viscous propagation regimes. Both techniques are combined to form an implicit front-tracking JHFM$J_{HFM}$-algorithm capable of quickly converging on the location of the fracture front independently to the toughness-viscous regime of propagation. The JHFM$J_{HFM}$-algorithm represents an energy-based alternative to the aperture-based methods frequently used with the Implicit Level Set Algorithm to simulate hydraulic fracturing. Simulations conducted at various resolutions of the fracture suggest that the new approach is suitable for hydro-mechanical finite element simulations at the reservoir scale.