Modeling method for rock heterogeneities and multiple hydraulic fractures propagation based on homogenization approach and PHF-LSM

Hydraulic fracturing is an important technique to enhance the production rate of oil and gas. We extend the functions of Permeability-based Hydraulic Fracture, Level Set Method (PHF-LSM) by including homogenization approaches to take into account the influence of the heterogeneities of rock media at both mesoscale and macroscale during hydraulic fracture propagation. The center position pattern of mesoscale heterogeneities is generated by introducing the Fast Poisson Disk (FPD) approach with an inherent parameter controlling the randomly distributed inclusions, and we developed an algorithm to detect inclusion collision by binary image matrix calculation. The level set function is used to describe the distributed joints at the macroscale. Both numerical and theoretical homogenization approaches are applied to study the characteristics of the material properties of rock matrices with randomly distributed hard inclusions at the mesoscale. Based on these results, we adopt the Mori–Tanaka (MT) and the Halpin–Tsai (HT) methods to homogenize the elasticity parameters (elastic modulus and Poisson’s ratio) and the hydraulic conductivity of the rock material, respectively. The Voigt upper bound is applied to estimate the tensile strength of the rock material at the integration points. A series of numerical simulations first indicated that the proposed method can model multi-scale heterogeneous rock that contains both the influences of macro-heterogeneities, e.g., distributed joints, and meso-heterogeneities, e.g., randomly distributed inclusions. Second, the development of pore pressure and stress path varied at the injection point, on the fracture path and on a joint. Finally, both the macro- and meso- heterogeneities influenced the propagation of multiple hydraulic fractures with joints significantly influenced the propagation path of the fractures, and increased injection number N p enhanced the height of the equivalent fracture zone when N p < 5 .