Study on Numerical Calculation Model of Hydraulic Fracture for Heterogeneous Rock Materials Based on PHF⁃SFM

Based on the permeability-based hydraulic fracture (PHF) model, a statistical fracture model (SFM) is introduced to capture the influence of the micro non-uniform distribution of rock materials on the macroscale characteristics of hydraulic fracture. The Weibull probability model is adopted to account for the discreteness of characteristics of these characteristics. By assuming that the permeability of rock material is a function of the mean effective stress, the PHF-SFM model is proposed based on the Biot consolidation theory. The model incorporates the Mohr-Coulomb elastoplastic constitutive model and Darcy’ s law to represent mechanical behaviors for the solid and liquid phase of rock material in pre- and post-failure part. The verification is carried out by comparing the simulated results with those of the KGD model. Breakdown pressure, equivalent fracture height and fracture width were studied by varying the Weibull modulus and scale parameters in the SFM model and material properties of rock. The simulation results indicate that including the SFM model does not affect the breakdown pressure, but does vary the fracture geometry. When the Weibull modulus decreases or the scale parameter increases, the discreteness of fracture geometry features increases.