Phase-field method of crack branching during SC-CO2 fracturing: A new energy release rate criterion coupling pore pressure gradient

Abstract

The critical energy release rate of the crack is always set as an inherent material property (constant value) in the phase-field method (PFM) to depict the compression-shear and mixed-mode failures of the shale rock. However, the recent experimental results about supercritical carbon dioxide (SC-CO2) fracturing indicate that the degradation in strength of the porous medium is of significant importance because of the associated effect of fluid infiltration. To capture this tendency, a modified phase-field method is developed to fully consider the mixed-mode failure and shear strength degradation during the SC-CO2 fracturing (SCF) process. Precisely, the finite element method (FEM) is used to discretize the solution space and staggered scheme is employed to solve the system of non-linear equations derived from the proposed PFM. A new critical energy release rate criterion that considers the pore pressure gradient is generated and a distinction between two different failure modes (Mode-I and Mode-II) is made through the spectral decomposition of strain energy. The model is validated against experimental results and depicts the crack branching behavior with a wide range of fluid viscosities and injection rates. Tension and shear failure modes alternately dominate the behavior of branching, followed by periodic fluctuation of the crack tip velocity and equivalent driving term, which is quantitatively depicted by the phase diagram.