A fully coupled element‐free Galerkin model for hydro‐mechanical analysis of advancement of fluid‐driven fractures in porous media

Abstract

SUMMARYHydraulic fracturing (HF) of underground formations has widely been used in different fields of engineering. Despite the technological advances in techniques of in situ HF, the industry uses semi-analytical tools to design HF treatment. This is due to the complex interaction among various mechanisms involved in this process, so that for thorough simulations of HF operations a fully coupled numerical model is required.In this study, using element-free Galerkin (EFG) mesh-less method, a new formulation for numerical modeling of hydraulic fracture propagation in porous media is developed. This numerical approach, which is based on the simultaneous solution of equilibrium and continuity equations, considers the hydromechanical coupling between the crack and its surrounding porous medium. Therefore, the developed EFG model is capable of simulating fluid leak-off and fluid lag phenomena.To create the discrete equation system, the Galerkin technique is applied, and the essential boundary conditions are imposed via penalty method. Then, the resultant constrained integral equations are discretized in space using EFG shape functions. For temporal discretization, a fully implicit scheme is employed. The final set of algebraic equations that forms a non-linear equation system is solved using the direct iterative procedure.Modeling of cracks is performed on the basis of linear elastic fracture mechanics, and for this purpose, the so-called diffraction method is employed. For verification of the model, a number of problems are solved. According to the obtained results, the developed EFG computer program can successfully be applied for simulating the complex process of hydraulic fracture propagation in porous media.

Numerical methods for hydraulic fracture propagation: A review of recent trends

“…The reasons for its limited success are mostly related to integration procedures (underlying mesh), data structure, and weight functions for handling fracture propagation in a simple and accurate manner. Recently, Samimi and Pak (2016) have proposed a algorithm based on EFG and an implicit time stepping scheme for the propagation of a hydraulic fracture in a porous material under plane strain conditions. The fracture propagation appears to be performed in an explicit way, using a computation of the stress intensity factor to set a predefined new fracture increment.…”

Numerical analysis of the hydrofracturing behaviour of heterogeneous glutenite considering hydro‐mechanical coupling effects based on bonded particle models

“…For conventional numerical techniques, the simulated morphologies of hydraulic fracturing are quite different from the actual phenomenon, in which one of the challenging and vital effects is fluid‐solid coupling, which remains a focus of disagreement regarding the reliability and accuracy of simulated results in hydraulic fracturing. Samimi and Pak developed a fully coupled element‐free Galerkin mesh‐less method considering fluid‐solid coupling for numerical modelling of hydraulic fracture propagation in porous media . A fully coupled finite element and finite volume approach is proposed, which is capable of modelling large‐scale problems involving hydraulically driven fractures in 3D models .…”

Numerical analysis of the effect of natural microcracks on the supercritical CO2 fracturing crack network of shale rock based on bonded particle models

“…The research showed that the BPM approach can generally capture the brittle failure process of anisotropic rock under uniaxial compression. Samimi and Pak developed an element‐free Galerkin mesh‐less method for the numerical modeling of hydraulic fracture propagation . Settgast et al proposed a fully coupled finite element/finite volume approach, which is capable of modeling large‐scale problems that involve hydraulically driven fractures in 3 dimensions …”

“…Samimi and Pak developed an element-free Galerkin mesh-less method for the numerical modeling of hydraulic fracture propagation. 25 Settgast et al proposed a fully coupled finite element/finite volume approach, which is capable of modeling large-scale problems that involve hydraulically driven fractures in 3 dimensions. 26 The overall material response of rock is very complicated, and its anisotropy is governed mainly by micromechanisms such as the formation, growth, and eventual interaction of microcracks.…”