Unlike nonionized hydrogel, ionized hydrogel swells up to strain of many s %. Crack propagation has been simulated with one method, the discrete crack approach. Fluid and solid singularities at the tip of a fluiddriven fracture. Fracture mechanics is a field of continuum mechanics with the objective to predict how cracks initiate and propagate in solids. Propagation analysis of fluiddriven fracture using the.
Crack propagation is described using fracture mechanics theory and would therefore have its place in the mechanical compaction section. Then, since the pressure in the lag zone is known, we suggest a new inversion of the integral equation from elasticity theory to. The fluiddriven crack is always contained in the middle part of the vertical joint. The parameters used for calculation are listed in table 4. A presentation of detailed theory and computer programs which can be used for stress analysis.
We first use uniform q4 elements to discretize all the fields with the element size h 2. The propagation of cracks driven by a pressurized fluid emerges in several areas of engineering, including structural, geotechnical, and petroleum engineering. A solution has been obtained for steady propagation of a twodimensional fluid fracture driven by buoyancy in an elastic medium. During propagation of such cracks, energy is dissipated not only by breaking of material bonds ahead of the tip but also by flow of viscous fluid.
Numerical investigation into the simultaneous growth of. Swelling and crack propagation in ionized hydrogels plays an important role in industry application of personal care and biotechnology. In fluiddriven cracks, before the cracks reach propagation criteria, fluid. We present a numerical analysis on injectioninduced crack propagation and coalescence in brittle rock. Furthermore, a universal tip asymptotic solution, reflecting the unique multiscale tip behavior for fluiddriven fractures, is adopted as a propagation criterion to locate the fracture front. Fluiddriven fracturing is also encountered in nature when studying magma.
An extended jintegral for evaluating fluiddriven cracks in hydraulic. We introduce the concept of crackshape adaptability. In this simulation, the and are set with the same angle. A recently developed peridynamic formulation of porous flow has been coupled with the existing peridynamic formulation of solid and fracture mechanics resulting in a peridynamic model that for the first time simulates poroelasticity and fluiddriven fracture propagation. Fluidthermal analysis of steamdriven fracture propagation. A hybrid finite volume and extended finite element method. A numerical procedure for simulation of hydraulically. Numerical investigation of fluiddriven crack propagation. Therefore, classical biot poroelasticity theory is applied in the porous medium while arbitrary crack growth is naturally captured by the phase field model.
Mathematical modeling of a fluiddriven fracture has attracted numerous contributions. However, as it will be presented here, slow crack propagation in rocks is affected by the environment and the fluid chemistry and can be seen as mechanical phenomenon. Pdf 3773experimental investigation of crack opening. Phasefield modeling of fluiddriven dynamic cracking in. Since the joint is the weakest point in the structure, this evolutionary process.
This is achieved by applying biot theory for the behavior of porous solids,38,39 where the total stress in the. This study numerically investigates the fluiddriven crack propagation process in rock specimen possessing two preexisting flaws using a fluid coupled discrete element method. In this paper, we present a swelling driven fracture model for. Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. As for the third one, it is based on griffiths energetic theory. The fracture is driven by injection of an incompressible newtonian fluid at a constant rate. The next step represents the hydraulic fracture stage where the main volume of fluid is being injected into the well. Fluid driven and mechanically induced fracture propagation. Barenblatt, the mathematical theory of equilibrium cracks in brittle fracture. Experimental validation of the tip asymptotics for a fluid. The fluid flow is modeled according to lubrication theory, while the elastic response is governed by a singular integral equation relating the crack opening and the. Crack propagation in concrete dams driven by internal.
International journal for numerical and analytical methods in geomechanics 43. Capturing the twoway hydromechanical coupling effect on. A twostep analysis is performed, and crack propagation is simulated. The amended crack propagation criterion, under remote mode i loading conditions, was. A solution to the problem of a planestrain fluiddriven crack propagation in elastic permeable rock with. Initially, a theory was developed for hydraulic fractures in an infinite. Then, since the pressure in the lag zone is known, we suggest a new inversion of the integral equation from elasticity theory to express the opening in terms of the pressure. A monolithic phasefield model of a fluiddriven fracture. First, exact separationofvariable solutions have been obtained for a gasdriven. The dem network coupling model in pfc is modified to capture the evolution of fracture geometry. Hence, a good understanding of the propagation and coalescence of fluiddriven cracks is important to improve the oil and gas exploitation efficiency. Beginning with a motivation for studying crack propagation in materials with complex microstructures in section 1. Biot shell development concpany, rca buddirg, new york, new york received september 1, 1955 a theory is developed for the propagation of stress waves in. Other gelatin experiments on fluiddriven crack propagation were inspired by magma propagation problems, where buoyancy is the driving force 3,4,15.
Crack propagation and lifetime estimation in ansys mechanical apdl 2 duration. First, we formulate the governing equations for a semiinfinite fluiddriven fracture propagating steadily in an impermeable linear elastic medium. The resisting forces during crack propagation include the viscous forces of the flow. Fluid driven cohesive crack propagation in quasibrittle. Hydraulic fracturing is a procedure by which a fracture is initiated and propagates due to pressure hydraulic loading applied by a fluid introduced inside the fracture. It is shown that the classical tools of the isotropic fluiddriven crack model remain valid in anisotropy, provided the appropriate elastic constants are used. The injected fluid creates a radial fracture that propagates along a plane. Experimental study on pennyshaped fluiddriven cracks in an. An improved fluid flow model for fractured porous media is proposed and coupled with a bondbased dem model to simulate the interactions among cracks induced by injecting fluid in two nearby. Experimental validation of the tip asymptotics for a fluiddriven crack. To date, there has been little experimental attention given to the time dependence of the crack growth and shape. A fully coupled porous flow and geomechanics model for. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the materials resistance to fracture. A phase field model for fluiddriven dynamic crack propagation in poroelastic media is proposed.
A statebased nonlocal peridynamic formulation is presented for simulating fluid driven fractures in an arbitrary heterogeneous poroelastic medium. Fluid leakoff is included by the assumption that an incompressible filtrate produces a pistonlike displacement of. Indeed, in accordance with lubrication theory, the shear stress acting on the crack faces can be. Fluiddriven cracks in an elastic matrix in the toughnessdominated.
Fluid flow behavior along the opening discontinuity is assumed to follow the cubic law. Theory and applications detournay, emmanuel, adachi, jose i. Fluiddriven fracture in poroelastic medium a dissertation submitted to the faculty of the graduate school of the university of minnesota by yevhen kovalyshen in partial fulfillment of the requirements for the degree of doctor of philosophy february, 2010. Coupled flow network and discrete element modeling of. Crack propagation is described using fracture mechanics theory and would. Similarity solutions describe an overpressured source with no buoyancy and travellingwave solutions a buoyancydriven flow with no overpressure, but the combination of buoyancy and. Propagation analysis of fluiddriven fracture using the discrete crack. In this study, we focus on a crack driven by an incompressible newtonian fluid, injected at a constant rate into an elastic matrix. Experimental exploration of fluiddriven cracks in brittle.
Using this medium, we examine the rate of radial crack growth, fracture. Experimental exploration of fluiddriven cracks in brittle hydrogels. Similarity solutions describe an overpressured source with no buoyancy and travellingwave solutions a buoyancydriven flow with no overpressure, but the combination of buoyancy and overpressure gives finitetime blowup. T1 experimental validation of the tip asymptotics for a fluiddriven crack. In order to remain the pathindependence for fluiddriven cracks, jintegral is revised. On the theory and numerical simulation of cohesive crack. We analyse fluiddriven crack propagation using lubrication theory to describe the flow and elastostatics to describe the deformation of the crack walls by the flowinduced pressure distribution. The tip region of a fluiddriven fracture in an elastic medium. Propagation of a pennyshaped fluiddriven fracture in an. This paper presents an analysis of the propagation of a pennyshaped hydraulic fracture in an impermeable elastic rock. And the vertical joint is divided into 3 parts by two cutters. A basic theory of twodimensional 2d fracture propagation has been developed with a lagrangian formulation combined with a virtual work analysis.
Abstract this paper provides experimental confirmation of the opening asymptotes that have been predicted to develop at the tip of fluiddriven cracks propagating in impermeable brittle elastic media. However, as it will be presented here, slow crack propagation in rocks is affected by the environment and the fluid chemistry and can be seen as mechanical phenomenon facilitated by chemical effects. A phasefield method for propagating fluidfilled fractures coupled to a surrounding porous medium. The fracture is driven by an incompressible newtonian fluid injected from a source at the center of the fracture. Swelling driven crack propagation in large deformation in. When highpressure fluids such as water enter into an existing crack, the fracture propagation criterion is met ahead of the fracture tip, which leads to fluiddriven fracture initiation and propagation 1. Fluid driven fracturing is also encountered in nature when studying magma. A hybrid femmphase field method for fluiddriven fracture propagation in three dimension.
The problem is formulated in terms of an integrodifferential equation governing the elastic deformation, coupled with the differential equation of lubrication theory for viscous flow in the crack. The issue of whether to include viscous fluid flow into the analysis or not is resolved. It is shown that the scaled equations contain only one parameter, a dimensionless toughness, which controls the regimes of fracture propagation. Specifically, our numerical findings confirm differences with test cases using the linear biot equations.
Linear elastic fracture mechanics in anisotropic solids. The problem of a fluiddriven fracture propagating in rock arises in hydraulic. The tip region of a fluiddriven fracture in an elastic. The propagation behavior of hydraulic fracture in rock. Other gelatin experiments on fluiddriven crack propagation were. A recently developed peridynamic formulation of porous flow has been coupled with the existing peridynamic formulation of solid and fracture mechanics resulting in a peridynamic model that for the first time simulates poroelasticity and fluid. Redirection of a crack driven by viscous fluid sciencedirect. Fluiddriven multiple fracture growth from a permeable. For the fluid flow in the crack, lubrication theory can be applied due to the. As an application, the fluiddriven crack problem is addressed. Experimental study on pennyshaped fluiddriven cracks in. Pdf planestrain propagation of a fluiddriven crack in a.
Fluid driven cohesive crack propagation in quasibrittle materials f. Very often this phenomenon occurs at the damfoundation joint and is driven also by the. Propagation of hydraulically driven fracture using xfem. We listed the physical mechanisms during crack propagation for. The finite element formulations are developed through easytofollow derivations for the analysis of plane stress or strain and axisymmetric solid, platebending, three dimensional solid and shell problems. Fluiddriven fracture is a common yet complex multifield physics problem. Modeling and analysis of fluid driven fracture propagation. The process of fracture propagation driven by the pressure of the fluid flow between the fracture surfaces has been of considerable interest for understanding natural geological phenomena such as the formation of volcanic dikes and developing hydraulic fracturing technologies for industrial applications.
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