Modeling method for a rock matrix with inclusions distributed and hydraulic fracturing characteristics

A permeability-based hydraulic fracturing (PHF) model based on a smeared approach is presented in this paper to study fracture propagation. This model is based on the elasto-plastic behavior of a rock-fluid system. The coefficient for the permeability modification of the rock is assumed to be a function of the mean effective stress via a hyperbolic tangent function. Level set method (LSM) is used to track the material interfaces between inclusions and matrix. The transition of interfaces between matrix and inclusions can be described by mathematical functions such as a jump function, linear function and hyperbolic tangent function. Numerical cases are carried out to study the influence of mesh of the traditional finite element method (FEM) and method using the LSM. Results show that coupling the LSM to the FEM is a good way for keeping the mesh unchanged for various rock samples. The propagation characteristics in a rock matrix with regularly distributed inclusions are classified according to the relative position when the fracture tip reaches the inclusions. We observe that the fracture propagation features in a rock matrix with inclusions randomly distributed can be well simulated via the PHF model combined with the LSM. Finally, fracture zone development, fracture opening, and the pore pressure of the observation points in a rock sample with irregularly distributed inclusions are studied by using the presented method.