Very often this phenomenon occurs at the damfoundation joint and is driven also by the. The amended crack propagation criterion, under remote mode i loading conditions, was. 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. The problem of a fluiddriven fracture propagating in rock arises in hydraulic. Experimental study on pennyshaped fluiddriven cracks in an. Therefore, classical biot poroelasticity theory is applied in the porous medium while arbitrary crack growth is naturally captured by the phase field model. Fluiddriven fracture is a common yet complex multifield physics problem. This paper presents an analysis of the propagation of a pennyshaped hydraulic fracture in an impermeable elastic rock. International journal for numerical and analytical methods in geomechanics 43. Linear elastic fracture mechanics in anisotropic solids.
We investigate this type of fracture both theoretically and experimentally. A twostep analysis is performed, and crack propagation is simulated. Modeling and analysis of fluid driven fracture propagation. Fluid driven fracturing is also encountered in nature when studying magma. 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. Specifically, our numerical findings confirm differences with test cases using the linear biot equations. 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. Experimental validation of the tip asymptotics for a fluid. As for the third one, it is based on griffiths energetic theory. 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. A statebased nonlocal peridynamic formulation is presented for simulating fluid driven fractures in an arbitrary heterogeneous poroelastic medium.
The issue of whether to include viscous fluid flow into the analysis or not is resolved. In this paper, we present a swelling driven fracture model for. Theory of propagation of elastic waves in a fluidsaturated porous solid. 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.
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. Coupled flow network and discrete element modeling of. Redirection of a crack driven by viscous fluid sciencedirect. Propagation analysis of fluiddriven fracture using the discrete crack. Fluid driven and mechanically induced fracture propagation. Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. Similarity solutions describe an overpressured source with no buoyancy and travellingwave solutions a buoyancydriven flow with no overpressure, but the combination of buoyancy and. As an application, the fluiddriven crack problem is addressed.
Experimental exploration of fluiddriven cracks in brittle hydrogels. The resisting forces during crack propagation include the viscous forces of the flow. A hybrid femmphase field method for fluiddriven fracture propagation in three dimension. In this study, we focus on a crack driven by an incompressible newtonian fluid, injected at a constant rate into an elastic matrix. The propagation of cracks driven by a pressurized fluid emerges in several areas of engineering, including structural, geotechnical, and petroleum engineering. 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. 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 dem network coupling model in pfc is modified to capture the evolution of fracture geometry. A phasefield method for propagating fluidfilled fractures coupled to a surrounding porous medium.
Fluid leakoff is included by the assumption that an incompressible filtrate produces a pistonlike displacement of. Crack propagation in concrete dams driven by internal. Theory and applications detournay, emmanuel, adachi, jose i. The injected fluid creates a radial fracture that propagates along a plane. Numerical investigation of fluiddriven crack propagation. We present a numerical analysis on injectioninduced crack propagation and coalescence in brittle rock. Initially, a theory was developed for hydraulic fractures in an infinite. Experimental validation of the tip asymptotics for a fluiddriven crack. Fluidthermal analysis of steamdriven fracture propagation. Crack propagation is described using fracture mechanics theory and would.
First, we formulate the governing equations for a semiinfinite fluiddriven fracture propagating steadily in an impermeable linear elastic medium. Fluiddriven cracks in an elastic matrix in the toughnessdominated. The tip region of a fluiddriven fracture in an elastic medium. This study numerically investigates the fluiddriven crack propagation process in rock specimen possessing two preexisting flaws using a fluid coupled discrete element method. The models describe the coupled process of fluid injection into a fluid saturated solid and mechanical deformation of the solid due to the internal fluid pressure. The parameters used for calculation are listed in table 4. A hybrid finite volume and extended finite element method.
A monolithic phasefield model of a fluiddriven fracture. Fluid driven cohesive crack propagation in quasibrittle. Capturing the twoway hydromechanical coupling effect on. We introduce the concept of crackshape adaptability. 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. Fracture mechanics is a field of continuum mechanics with the objective to predict how cracks initiate and propagate in solids. Fluiddriven fracturing is also encountered in nature when studying magma. A numerical procedure for simulation of hydraulicallydriven fracture propagation in poroelastic 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. Indeed, in accordance with lubrication theory, the shear stress acting on the crack faces can be. The next step represents the hydraulic fracture stage where the main volume of fluid is being injected into the well. Then, since the pressure in the lag zone is known, we suggest a new inversion of the integral equation from elasticity theory to. 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 in modern materials science, fracture mechanics is an important tool used to improve the. 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. The fracture is driven by injection of an incompressible newtonian fluid at a constant rate. For the fluid flow in the crack, lubrication theory can be applied due to the.
A numerical procedure for simulation of hydraulically. Beginning with a motivation for studying crack propagation in materials with complex microstructures in section 1. Swelling and crack propagation in ionized hydrogels plays an important role in industry application of personal care and biotechnology. Fluiddriven multiple fracture growth from a permeable. Other gelatin experiments on fluiddriven crack propagation were inspired by magma propagation problems, where buoyancy is the driving force 3,4,15. Fluid and solid singularities at the tip of a fluiddriven fracture. On the theory and numerical simulation of cohesive crack. The dynamics of fluiddriven cracks in an elastic matrix is studied experimentally. The fracture is driven by an incompressible newtonian fluid injected from a source at the center of the fracture. Crack propagation and lifetime estimation in ansys mechanical apdl 2 duration. It is shown that the scaled equations contain only one parameter, a dimensionless toughness, which controls the regimes of fracture propagation.
Crack propagation an overview sciencedirect topics. 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. Crack propagation has been simulated with one method, the discrete crack approach. A geostatic step is performed where equilibrium is achieved after applying the initial pore pressure to the formation and the initial insitu stresses. Swelling driven crack propagation in large deformation in. The fluiddriven crack is always contained in the middle part of the vertical joint. 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.
Fluid driven cohesive crack propagation in quasibrittle materials f. 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. Pak, a fully coupled elementfree galerkin model for hydromechanical analysis of advancement of fluiddriven fractures in porous media. Other gelatin experiments on fluiddriven crack propagation were. In order to remain the pathindependence for fluiddriven cracks, jintegral is revised. First, exact separationofvariable solutions have been obtained for a gasdriven. Computational results are provided that demonstrate the effectiveness of this approach in treating fluiddriven fracture propagation.
Propagation regimes of fluiddriven fractures in impermeable. Hence, a good understanding of the propagation and coalescence of fluiddriven cracks is important to improve the oil and gas exploitation efficiency. A phase field model for fluiddriven dynamic crack propagation in poroelastic media is proposed. 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. Fluid flow behavior along the opening discontinuity is assumed to follow the cubic law. Barenblatt, the mathematical theory of equilibrium cracks in brittle fracture. 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.
Experimental study on pennyshaped fluiddriven cracks in. Pdf 3773experimental investigation of crack opening. Pdf planestrain propagation of a fluiddriven crack in a. Using this medium, we examine the rate of radial crack growth, fracture. The tip region of a fluiddriven fracture in an elastic. A solution has been obtained for steady propagation of a twodimensional fluid fracture driven by buoyancy in an elastic medium. 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. Propagation of a pennyshaped fluiddriven fracture in an. 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. Mathematical modeling of a fluiddriven fracture has attracted numerous contributions. Numerical investigation into the simultaneous growth of. Propagation of hydraulically driven fracture using xfem. T1 experimental validation of the tip asymptotics for a fluiddriven crack. 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.
We listed the physical mechanisms during crack propagation for. A fully coupled porous flow and geomechanics model for. 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. The propagation behavior of hydraulic fracture in rock. A basic theory of twodimensional 2d fracture propagation has been developed with a lagrangian formulation combined with a virtual work analysis. Phasefield modeling of fluiddriven dynamic cracking in. Numerical examples are fully implemented to investigate the competition in the growth of two closely spaced fluiddriven fractures at different initial. Experimental exploration of fluiddriven cracks in brittle. Propagation analysis of fluiddriven fracture using the.
A solution to the problem of a planestrain fluiddriven crack propagation in elastic permeable rock with. Unlike nonionized hydrogel, ionized hydrogel swells up to strain of many s %. And the vertical joint is divided into 3 parts by two cutters. Since the joint is the weakest point in the structure, this evolutionary process. 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. In fluiddriven cracks, before the cracks reach propagation criteria, fluid.
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