A Hybrid Finite Volume and Extended Finite Element Method for Hydraulic Fracturing with Cohesive Crack Propagation in Quasi-Brittle Materials

Abstract

High-pressure hydraulic fractures are often reported in real engineering applications, which occur due to the existence of discontinuities such as cracks, faults, or shear bands. In this paper, a hybrid finite volume and extended finite element method (FVM-XFEM) is developed for simulating hydro-fracture propagation in quasi-brittle materials, in which the coupling between fluids and deformation is considered. Flow within the fracture is modelled using lubrication theory for a one-dimensional laminar flow that obeys the cubic law. The solid deformation is governed by the linear momentum balance equation under quasi-static conditions. The cohesive crack model is used to analyze the non-linear fracture process zone ahead of the crack tip. The discretization of the pressure field is implemented by employing the FVM, while the discretization of the displacement field is accomplished through the use of the XFEM. The final governing equations of a fully coupled hydro-mechanical problem is solved using the Picard iteration method. Finally, the validity of the proposed method is demonstrated through three examples. Moreover, the fluid pressure distribution along the fracture, the fracture mouth width, and the pattern of the fracture are investigated. It is shown that the numerical results correlated well with the theoretical solutions and experimental results.

RETRACTED: Application of Symmetry Law in Numerical Modeling of Hydraulic Fracturing by Finite Element Method

“…Different types of numerical methods in rock engineering are schematically depicted in Figure 1. Liu et al [30] proposed a numerical model based on the extended finite element method and hybrid finite volume to simulate the propagation of hydraulic fracturing. It is coupled with the fluid flow and rock deformation behavior as the one-dimensional flow for the laminar condition.…”

“…It is coupled with the fluid flow and rock deformation behavior as the one-dimensional flow for the laminar condition. To analyze the nonlinear fractures, the cohesive crack model was used as it is more adapted with the reservoir characteristics in the real condition [30]. Zhang et al [31] proposed a developed discrete element method coupled with a synthetic rock mass method to model the fluid-driven fracture Liu et al [30] proposed a numerical model based on the extended finite element method and hybrid finite volume to simulate the propagation of hydraulic fracturing.…”

Calculation Methods for the Permeability Coefficient of Concrete Face Rockfill Dam with Cracks

“…Some scholars have used the equivalent continuum method (ECM) and the discrete medium method to solve the problem of fissured flow through CFRD cracks [8,9,10]. For instance, Lomize [11] applied a parallel-face seepage experiment to prove the cubic relationship between the seepage flow and unit width of cracks (denoted as the cubic law).…”

Discrete Element Simulation of Interaction between Hydraulic Fracturing and a Single Natural Fracture

“…Liu et al [21] presented a fully coupled finite-element method (FEM)-based hydraulic-geomechanical fracture model accommodating gas sorption and damage to better understand the interaction between hydraulic fracture and oriented perforation. Liu et al [22] developed a hybrid finite volume and XFEM for simulating hydro-fracture propagation in quasi-brittle materials. Han et al [23] adopted a modified fluid-mechanically coupled algorithm in the Particle Flow Code (PFC 2D ) to study the influence of grain size heterogeneity and in situ stress on hydraulic fracturing behavior.…”

“…In order to understand the interaction mechanism and the importance of each parameter, it is necessary These interaction modes depend on the in situ stresses, the orientation of induced fracture with respect to the NF, mechanical properties of the rock, properties of NF, and the HF treatment parameters, including fracturing fluid properties and injection rate. In this regard, several works have been published in three categories of experimental [5][6][7][8][9][10][11][12], analytical [13][14][15][16], and numerical methods [17][18][19][20][21][22][23].…”