Showing papers on "Fracture (geology) published in 1983"

A Local Criterion for Cleavage Fracture of a Nuclear Pressure Vessel Steel

Abstract: Experiments were performed on three heats of A508 class 3 steel in order to determine the mechanical conditions for cleavage fracture. These tests were carried out on various geometries including 4-point bend specimens and axisymmetric notched tensile bars with different notch radii which have been modelized using the finite element method. In one heat, the temperature range investigated was from 77 K to 233 K. It is shown that the cleavage resistance is increased by tensile straining. Moreover, the probability of fracture obeys the Weibull statistical distribution. All the results can be accounted for in terms of a local criterion based on Weibull theory and which takes into account the effect of plastic strain. In this criterion, the parameters which were experimentally determined are found to be temperature independent over the range 77 K to 170 K. The applicability of the approach proposed for cleavage fracture at the crack tip is also examined. It is shown that the experimental results published in the literature giving the variation of fracture toughness with temperature can be explained by the proposed criterion which predicts reasonably well both the scatter in the experimental results and theKICtemperature dependence.

Improvements in Simulation of Naturally Fractured Reservoirs

Abstract: Simulation of multiphase flow in heterogeneous two-porosity reservoirs such as naturally fractured systems is a difficult problem. In the last several years much progress has been made in this area. This paper focuses on the practical aspects of that technology. It describes a stable, flexible, fully implicit, finite-difference simulator in heterogeneous, two-porosity reservoirs. Flow rates and wellbore pressures are solved simultaneously along with fracture and matrix fluid saturations and pressures at all grid points. Hydrodynamic pressure gradient is maintained at formation perforations in the wellbore. The simulator is accurate enough to match analytical solutions to single-phase problems. The equations have been extended to include polymer flooding and tracer transport with nine-point connection for determining severe local channeling and directional tendencies. It is shown that the two-porosity model presented in this paper will produce essentially the same answers as the common single-porosity model of a highly heterogeneous system but with a substantial reduction of computing time. In addition, this paper describes in detail several two-porosity parameters not fully discussed in previous publications.

A Stochastic Analysis of Macroscopic Dispersion in Fractured Media

Abstract: A stochastic modeling technique has been developed to investigate mass transport in a network of discrete fractures. The model is based on the repetitive generation of realizations of a fracture network from probability distributions, describing the fracture geometry, and on a solution for mass transport within each network, using a particle-tracking technique. The system we work with consists of two orthogonal fracture sets of finite length, oriented at various angles with respect to the direction of the mean hydraulic gradient. Emphasis is placed on describing the character of dispersion, which develops as a consequence of fracture interconnectivity, and on testing the validity of the conventional diffusion-based model of dispersion in describing transport in fractured media. Results show that mass distributions have a complex form. Marked longitudinal dispersion can develop even a short distance from a source. The distribution of mass in the direction of flow has a consistent negative skew. This pattern of dispersion arises from the limited number of pathways for mass to migrate through the network. Controlling factors in the transport process are the orientation of the fracture sets with respect to the mean hydraulic gradient, the difference in the mean flow velocity in the two fracture sets, and the standard deviation in velocity for fracture set 1. Transport patterns can change greatly as the orientation of the hydraulic gradient changes with respect to the two fracture sets. A conventional diffusion-based model of dispersion cannot characterize transport in these fracture networks. A skewed spatial distribution of mass is observed much more frequently than a Gaussian distribution. When the mean velocities in the two fracture sets are not equal, the form of mass spreading is described by a more general, skewed distribution that accounts for the bias in the probability of mass moving along one fracture set over another. There is a tendency for mass to form a more symmetric distribution as the orientation of the two fracture sets is rotated toward a 45° angle with respect to the direction of the mean hydraulic gradient. Furthermore, constant dispersivity values or simple dispersivity functions are not definable because of the sensitivity of transport to the local velocity field in the fracture network.

Simulation of Naturally Fractured Reservoirs

Abstract: A three-dimensional, three-phase reservoir simulator was developed to study the behavior of fully or partially fractured reservoirs It is also demonstrated, that when a fractured reservoir is subject to a relatively large rate of pressure drop and/or it composed of relatively large blocks, the pseudo steady-state pressure concept gives large errors as compared with transient fromulation In addition, when gravity drainage and imbibitum processes, which is the most important mechanism in the fractured reservoirs, are represented by a ''lumped parameter'' even larger errors can be produced in exchange flow between matrix and fractures For these reasons, the matrix blocks are gridded and the transfer between matrix and fractures are calculated using pressure and diffusion transient concept In this way the gravity drainage is also calculated accurately As the matrix-fracture exchange flow depends on the location of each matrix grid relative to the GOC and/or WOC in fracture, the exchange flow equation are derived and given for each possible case The differential equation describing the flow of water, oil, and gas within the matrix and fracture system, each of which may contain six unknowns, are presented The two sets of equations are solved implicitly for pressure water, and gas stauration inmore » both matrix and fractures The first twenty two years of the history of Haft Kel field was successfully matched with this model and the results are included« less

In Situ Studies of Velocity in Fractured Crystalline Rocks

Abstract: A study of the effects of macroscopic fractures on P and S wave velocities has been conducted in four wells drilled in granitic rock to depths between 0.6 and 1.2 km. The effect of macroscopic fractures is to decrease both Vp and Vs and increase Vp/Vs. In wells with a relatively low density of macroscopic fractures, the in situ velocity is similar to that of saturated core samples under confining pressure in the laboratory, and there is a clear correlation between zones with macroscopic fractures and anomalously low velocities. In wells with numerous macroscopic fractures, the in situ velocity is lower than that of intact samples under pressure, and there is a correlation between the rate at which in situ velocity increases with depth and the rate at which the velocity of laboratory samples increases with pressure. Differences in in situ P wave velocity between wells cannot be explained solely by differences in the degree of macroscopic fracturing, thus emphasizing the importance of composition and microcracks on velocity. In one highly fractured well the in situ P wave velocity is essentially the same for frequencies ranging from 10 Hz to 20 kHz; this suggests that the macrofractures affect velocity similarly over a broad frequency range. Chemical alteration of rock adjacent to macroscopic fractures appears to play an important role in reducing in situ velocities. Synthetic reflection seismograms generated from the velocity logs suggest that fracture zones are one possible source of deep-crustal reflectors observed on seismic reflection profiles.

The dependence of fracture mechanical and fluid flow properties on fracture roughness and sample size

Abstract: A parameter study has been carried out to investigate the interdependence of mechanical and fluid flow properties of fractures with fracture roughness and sample size. A rough fracture can be defined mathematically in terms of its aperture density distribution. Correlations were found between the shapes of the aperture density distribution function and the specific fractures of the stress-strain behavior and fluid flow characteristics. Well-matched fractures had peaked aperture distributions that resulted in very nonlinear stress-strain behavior. With an increasing degree of mismatching between the top and bottom of a fracture, the aperture density distribution broadened and the nonlinearity of the stress-strain behavior became less accentuated. The different aperture density distributions also gave rise to qualitatively different fluid flow behavior. Findings from this investigation make it possible to estimate the stress-strain and fluid flow behavior when the roughness characteristics of the fracture are known and, conversely, to estimate the fracture roughness from an examination of the hydraulic and mechanical data. Results from this study showed that both the mechanical and hydraulic properties of the fracture are controlled by the large-scale roughness of the joint surface. This suggests that when the stress-flow behavior of a fracture is being investigated, the size ofmore » the rock sample should be larger than the typical wave length of the roughness undulations.« less

Finite element techniques for modeling groundwater flow in fractured aquifers

Abstract: A mathematical description of groundwater flow in fractured aquifers is presented. Four alternative conceptual models are considered. The first three are based on the dual-porosity approach with different representations of fluid interactions between the fractures and porous matrix blocks, and the fourth is based on the discrete fracture approach. Two numerical solution techniques are presented for solving the governing equations associated with the dual-porosity flow models. In the first technique the Galerkin finite element method is used to approximate the equation of flow in the fracture domain and a convolution integral is used to describe the leakage flux between the fractures and porous matrix blocks. In the second the Galerkin finite element approximation is used in conjunction with a one-dimensional finite difference approximation to handle flow in the fractures and matrix blocks, respectively. Both numerical techniques are shown to be readily amendable to the governing equations of the discrete fracture flow model. To verify the proposed numerical techniques and compare various conceptual models, four simulations of a problem involving flow to a well fully penetrating a fractured confined aquifer were performed. Each simulation corresponded to one of the four conceptual models. For the three simulated cases, where analytical solutions are available, the numerical and the analytical solutions were compared. It was found that both solution techniques yielded good results with relative coarse spatial and temporal discretizations. Greater accuracy was achieved by the combined finite element-convolution integral technique for early time values at which steep hydraulic gradients occurring near the fracture-matrix interface could not be accommodated by the linear finite difference approximation. Finally, the results obtained from the four simulations are compared and a discussion is presented on practical implications of these results and the utility of various flow models.

New pressure transient analysis methods for naturally fractured reservoirs

Abstract: This paper presents new methods for analyzing pressure drawdown and buildup data obtained at wells producing naturally fractured reservoirs. The model used in this study assumes unsteady-state fluid transfer from the matrix system to the fracture system. A new flow regime is identified. The discovery of this flow regime explains field behavior that has been considered unusual. The probability of obtaining data reflecting this flow regime in a field test is higher than that of obtaining the classical responses given in the literature. The identification of this new flow regime provides methods for preparing a complete analysis of pressure data obtained from naturally fractured reservoirs. Applications to field data are discussed.

Energy Principle of Elastic-Plastic Fracture and Its Application to the Fracture Mechanics of a Polycrystalline Graphite

Abstract: Utilizing loading-unloading procedures on the basis of nonlinear energy principles, an empirical method for evaluating the nonlinear fracture mechanics parameters, i.e. the nonlinear energy toughness Gc, the crack growth resistance R, the Jc value, and the plastic energy dissipation rate φp, was established. These parameters were experimentally determined for an isotropic polycrystalline graphite enabling the elastic-plastic fracture mechanics of graphite to he addressed. The graphite exhibits a typical elastic-plastic fracture with ×38% of the total fracture energy consumed as plastic energy. It was concluded that the widely used assumption of the applicability of linear elastic fracture mechanics to polycrystalline graphites can lead to erroneous results if the fracture tests are conducted with the usual specimen size. The proposed experimental method for evaluating elastic-plastic fracture parameters is potentially very effective for studying various nonlinear fractures in other ceramic materials.

Microcrack connectivity in rocks: A renormalization group approach to the critical phenomena of conduction and failure in crystalline rocks

Abstract: A study is made of the critical phenomena associated with the onset of conductivity and the onset of failure in a rock with a random distribution of microcracks using a renormalization group theory approach. The interaction between different length scales is an important element in the theory, which is a departure from the results of equivalent media theory. The crack parameter that determines if the rock can conduct or is to fail is the crack count per unit area times the square of the crack length. The parameter space is divided up into regions or phases. These phases are those of no conduction and no failure, conduction and no failure, and conduction and failure. The predictions of the model agree well with SEM data on the microcrack populations of stressed and unstressed rock samples. The crack densities seen in unstressed Westerly granite fall in the range that predicts conduction but no failure, but only a 50% increase in density is needed to reach the failure criteria. A sample stressed to 65% of the failure stress has greatly increased conduction connectivity but seems no closer to failure. The sample stressed to failure shows an appropriate crack density increase.

Statistical Analysis of Bending Strengths for Brittle Solids: A Multiaxial Fracture Problem

Abstract: A general approach for the statistical analysis of brittle fracture under tensile multiaxial stress states was evaluated for a fracture criterion based on recent concepts of noncoplanar crack extension. The resultant failure expressions were applied to bend tests and used to interpret experimental results obtained with porcelain cylinders. Implications for the interpretation of bending tests and some important trends in the failiire strength with specimen size are discussed.

Overview of Current Hydraulic Fracturing Design and Treatment Technology--Part 1

Abstract: This paper focuses primarily on fractures that are oriented more or less in the vertical plane, and propagate outward in opposite directions from a wellbore (e.g. vertical fractures). Economics and optimization, general design aspects, potential reservoir response, fracture propagation, and some rock mechanics aspects of fracture propagation are discussed. The design difficulties and high cost of MHF have promoted a strong awareness of the need to enhance fracture design and treatment capabilities.

A practical numerical simulator for three-dimensional fracture propagation in heterogeneous media

Abstract: A numerical simulator capable of predicting fracture geometries during propagation in both height and length directions has been developed. The simulator is capable of handling random spatial variations in elastic properties, confining stress, pore pressure, and rock strength. Fracture fluid pressures, fracture widths, and net stresses are calculated at uniformly spaced points over the entire fracture face. The solution of the problem combines a finite difference formulation for calculation of fluid flow within the crack with an integral equation for fracture width. The fracture width equation is based on the work of I. N. Sneddon, but eliminates some of the simplifying assumptions he introduced. Results of simulation of laboratory fractures under various stress conditions are presented. The effects of varying rock properties and stresses on fracture containment are shown. The general nature of the formulation, with its flexibility in handling any number of randomly arranged rock formations, is ideal for application of the simulator to the prediction of hydraulic fracture geometries under field conditions. Input and output of the model are easily comprehensible and convenient to the user.

Mechanisms of Deformation and Fracture

Abstract: Publisher Summary This chapter provides an overview of mechanisms of deformation and fracture. Crystalline solids deform plastically by a number of alternative (and often competing) mechanisms: Low-temperature plasticity, twinning, power-law creep, diffusional flow, and so forth. Each has certain characteristics: A rate that depends strongly on temperature, for instance, or on grain size, or which is influenced by a dispersion of a second phase. These characteristics are summarized by the constitutive law for that mechanism and each has a characteristic regime of dominance, that is, a range of stresses, temperatures, and strain rates over which it is the primary mechanism. Fracture, too, can occur by any one of a number of alternative micromechanisms: Cleavage, ductile fracture, rupture intergranular creep fracture, and so forth. Each has certain characteristics: Negligible ductility, for instance, or a ductility that depends on inclusion density or grain size; and, for given stress states-simple tension, for example—each has a characteristic regime of dominance, that is, a range of stresses and temperatures over which it is the primary mechanism. This chapter describes the mechanisms of plasticity and fracture and develops ways of displaying their ranges of dominance and certain of their characteristics.

Strength and Fracture of Engineering Solids

Abstract: An undergraduated-level text providing an update on theories of strength and practical developments of stronger materials. Attention is also paid to problems with high-performance composite materials, failure analysis, and brittle fracture. Some chapters with problems but no answers. Contents: traditional strength tests and mechanical processing, pure elements, single phases, martensites, fracture, irons, cermics and glasses, composites, index.

Microplane Model for Fracture Analysis of Concrete Structures

Abstract: : Dynamic fracture analysis of concrete structures necessitates a triaxial stress-strain relation that describes gradual strain-softening with reduction of tensile stress to zero. A new model which does that and is applicable under general loading, including rotating principal stress directions, is a proposed. It is based on accumulating stress relaxations due to microcracking from the planes of all orientation within the microstructure. Comparisons with tensile test data are given.

Bedrock fracture parameters from the interpretation of well tides

Abstract: This paper presents a theory to account for the main features of the tidal response of an isolated plane fracture as revealed by the water level in an intersecting open borehole. According to the theory the diurnal and semidiurnal tidal constituents (both amplitude and phase) of water level variations depend on the fracture aperture, the orientation (dip and strike) and the radial extent of the fracture, and the compressibility of the asperites. The theory is applied to water level observations made in six open boreholes located in crystalline rock at a test site at the Chalk River Nuclear Laboratories, Atomic Energy of Canada Limited, in Chalk River, Ontario, Canada. The boreholes were uncased and intersected many open fractures so that a definitive test of the theory could not be made. However, in four cases a fracture model could be found which fitted the observations within the experimental error.

Hydrogen Traps, Repellers, and Obstacles in Steel; Consequences on Hydrogen Diffusion, Solubility, and Embrittlement

Abstract: H20 emission were not observed, while the CH4 emission was always significant. The H2 emission was less pronounced than the CH4 emission. Typical results for the embrittled regions are shown in Figure I. The partial pressures vs time curves for CH4 and H2 are presented in Figure 1. Both curves are normalized to the pressure before fracture. The fracture occurred at time zero. The results for a sample taken from the region that was not embrittled are presented in Figure 2. If the fracture time is much less than the decay of the gas emission signal (less than 0.1 second), the area under the peaks can be used as a relative measure of the gas emission during fracture. Table II summarizes some typical results of the gas emission and SEM measurements. Sample numbers 1 to 3 were cut from the embrittled part of the tube while sample numbers 4 and 5 were taken from the part of the tube which was not embrittled. The methane emission for sample numbers 4 and 5 and the hydrogen emission for all samples (except number 3) are given to characterize the noise level of the system. It is clear from Table II that the samples studied can be divided into two groups: ductile samples (percentage of brittle fracture less than 15 pct) and brittle samples (percentage of brittle fracture is in the range of 70 to 80 pet). Thus, a function connection, reflecting the correlation, between the brittleness and methane emission could not be established. Table II, however, demonstrates clearly that only the brittle fracture is associated with methane emission; thus, we conclude that the formation of methane filled bubbles, cracks, etc. may be primarily responsible for the brittleness of these evaporator tubes. In summarizing, we conclude that this simple measurement technique is suitable to identify the gas content of the cracks, bubbles, etc. revealed by the fracture.