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Title:A generalized finite element method for the simulation of non-planar three-dimensional hydraulic fracture propagation
Author(s):Gupta, Piyush
Director of Research:Duarte, Carlos Armando
Doctoral Committee Chair(s):Duarte, Carlos Armando
Doctoral Committee Member(s):Valocchi, Albert J.; Masud, Arif; Elbanna, Ahmed E.; Gordon, Peter
Department / Program:Civil & Environmental Eng
Discipline:Civil Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Hydraulic fracturing
Generalized Finite Element Method (GFEM)
Extended Finite Element Method (XFEM)
Coupled formulation
Hydro-mechanical coupling
Non-planar fracture propagation
Injection fracturing
Reynold’s lubrication theory
Fluid flow
Fluid-Driven fracturing
Abstract:Hydraulic fractures are a class of tensile fractures that occur in brittle and quasi-brittle materials due to the injection of a viscous fluid. Hydraulic fractures occur both naturally and created deliberately for engineering applications. In the oil and gas industry, it is a preferred method to enhance the recovery of hydrocarbons by creation of permeable pathways. A successful hydraulic fracturing treatment may increase the production tens of times, making the technique economically attractive. Yet, there are concerns about the environmental impact of the toxic fluids used in reservoir treatment. The potential of groundwater contamination from the hydraulic fracturing treatments has been one of the major roadblocks for its rapid development. One of the main reasons for this concern is the lack of a thorough understanding of induced hydraulic fracture propagation. With the advent of real-time monitoring techniques fully three-dimensional models that can be used to update treatment designs in real time as information is fed back into the models. Typically, hydraulic fracturing of low-permeability shale reservoirs involves modeling of three coupled processes: (i) the mechanical deformation of the rock induced by the applied fluid pressure on fracture faces; (ii) the flow of viscous fracturing fluid in the fracture; and (iii) the fracture propagation in the rock from the induced hydraulic loading. Additional difficulties in modeling of this already challenging problem are, for example, change in magnitude and/or orientation of the in-situ confining stresses, presence of a nearby natural fracture/fault, transport of suspended proppant particles within the fracture etc. In this work, we develop a fully-coupled system of equations for modeling non-planar three-dimensional hydraulic fracture propagation with a Generalized/Extended Finite Element Method (G/XFEM). This method greatly facilitates the discretization of complex 3-D fractures since the finite element mesh is not required to fit the crack surface(s). Adaptive surface triangulations are used to represent complex 3-D fracture surfaces. Such explicit surface representation retains the finer and complex details of the fracture, thus providing a high fidelity numerical simulation. The proposed coupled formulation does not make any assumptions about the geometry of the solid domain or the fracture surface except that the fracture geometry is such that the fluid flow in the fracture can be modeled using the Reynolds lubrication equation. A modified Newton – Raphson algorithm to solve the nonlinear system of coupled equations is also developed. The stress and pressure singularities of the solution of hydraulic fracturing problems require adaptive mesh refinement for efficient discretization error control. Dealing with adaptive mesh refinement in time-dependent problems is challenging for any method. This is typically handled through mappings of solutions at every time step. In this work, we avoid volume mappings by taking advantage of the explicit representation of the crack surface geometry adopted in the GFEM. This allows the use of completely different meshes at every time step and is much less computationally demanding than volume mappings. One of the main challenges in hydraulic fracture propagation is satisfying the Irwin’s criterion for fracture propagation. In this work, we propose a new fracture propagation model, named GD model, based on a regularization of Irwin’s criterion for brittle materials. Utilizing the proposed fracture model, a fully automated adaptive non-linear solution algorithm using the coupled hydro–mechanical formulation for hydraulic fracture propagation is also presented. The proposed algorithm is computationally efficient by automatically computing the time step increment at each fracture propagation step using the solution history. An energy based predictor-corrector algorithm for the fully automatic simulation of the fracture growth in three-dimensional linear elastic fracture mechanics (LEFM) problems is also proposed. The effects of dominant in-situ stresses, orientation of wellbore, rock toughness on fracture propagation, and interaction of hydraulic fracture with wellbore are studied in detail in this work. The proposed GFEM is also utilized to study the effects of wellbore modeling, near-wellbore tortuosity and interaction of multiple hydraulic fractures. The accuracy and the efficiency of the proposed coupled formulation and algorithms is accessed on various representative, large-scale examples.
Issue Date:2016-04-14
Rights Information:Copypright 2016 by Piyush Gupta. All rights reserved.
Date Available in IDEALS:2016-07-07
Date Deposited:2016-05

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