Modelagem numérica de fraturamento hidráulico via método dos elementos finitos estendido

Abstract

This research develops a numerical analysis of hydraulic fracturing using Extended Finite Element Method (XFEM). This method intend to simulate the initiation mechanism and propagation of cracks induced from the tip of an initial fracture. The main objective of this work is to improve the understanding of hydraulic fracturing phenomenon guided by an initial notch. It is understood that the hydraulic fracturing problem is a phenomenon that combines various physical process, including the fluid flow, the rock matrix deformation and the fracture propagation, however simplifications are essential. The XFEM is used to perform spatial discretization of the models. This method is considered to be a robust tool to solve numerical discontinuities problems. XFEM is the basis of the Finite Element Method (FEM), adding degrees of freedom and enrichment functions to describe the local discontinuities of the model. Through XFEM, the geometry of the fracture becomes independent of the mesh, it allows to move freely through the area without a step to adapt the mesh to the discontinuity. The validation of XFEM was performed using two classical tests of Fracture Mechanics: a single edge notched beam (SEN(B)) and the disk shaped compact tension test (CDT). Additionally, a hydraulic fracturing model is used to study the influence of various parameters of the material and geometry of the initial fracture. The simulation of hydraulic fracturing is accomplished by a two-dimensional numerical model, wherein the porous medium is idealized as linear elastic and the propagation criterion is based on the energy released rate and the stress intensity factors (SIF). The solutions provided by the numerical model based on XFEM are compared with experimental data and analytical formulations, giving it very good agreement. It has been shown the capability of the XFEM to solve complex fracture propagation problems.