An enhancedJ‐integral for hydraulic fracture mechanics

Abstract

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.

A consistent linearization scheme for KGD problems using fracture tip asymptotic solutions

“…Multiple numerical techniques are developed in literature to model fracture propagation in solid media, including the modified 𝐽-integral method, 8 the cohesive zone model, [9][10][11][12] the (generalized) extended finite element method (G/XFEM), [13][14][15][16][17][18][19] the embedded discontinuity method, [20][21][22][23][24] to name a few. Most recently, a multi-resolution method is developed to combine the embedded discontinuity approach at the coarse scale with the phase-field approach at the fine scale to model hydraulic fracture propagation.…”

Prior with Far-Field Stress Approximation for Ensemble-Based Data Assimilation in Naturally Fractured Reservoirs

“…Toolkits with geomechanical capabilities such as ABAQUS (Smith, 2009;Agheshlui et al, 2018), COMSOL (Multiphysics, 2013), DARTS (Y. Wang et al, 2020;Boersma et al, 2021), ICGT (Thomas et al, 2020;, MRST (Ucar et al, 2018;Lie & Møyner, 2021), OpenCSMP (Pezzulli et al, 2022a(Pezzulli et al, , 2022b, or XFVM (Deb & Jenny, 2017a, 2017b can been used to calculate shear displacement and fracture apertures for this scenario. However, it might be computationally expensive to generate a whole ensemble of realisations that are needed as priors for a DA framework, especially when considering a decent number of fractures.…”