Phase field modelling of a single horizontal fluid-driven fracture propagation in spatially variable rock mass

Hydraulic fracture propagation directly affects the recovery rate of resources when hydraulic fracturing techniques are applied to exploiting unconventional oil and gas resources. Rock mass is the main engineering medium of hydraulic fractures and is generally considered to be of considerable spatial variability in physical and mechanical properties. Understanding the irregular propagation mechanism of hydraulic fracture in spatial heterogeneity rock mass is essential and beneficial to assess the recovery rate of oil or gas resources. This work develops a random phase-field method (RPFM) to simulate the irregular propagation of hydraulic fracture in spatially variable rock mass. The spatial variability of elastic modulus is characterized by the random field theory. Utilizing the advantages in modeling complex crack patterns and crack kinematics, the phase-field method (PFM) is used to predict the fracture propagation. Various anisotropic random fields of elastic modulus with different coefficients of variance and scales of fluctuation are generated via the Cholesky decomposition method. The random fields are subsequently implemented into COMSOL Multiphysics and combined with the PFM to investigate the hydraulic fracture propagation. This study investigates the influence of spatial variability of elastic modulus on the peak fluid pressure, fracture length, fracture area and fracture shape. It reveals that the spatial variability of elastic modulus has a significant influence on the propagation of hydraulic fractures, and the results provide a preliminary reference for hydraulic fracturing design with consideration of spatial variability of rock mass.