Effects of the Correlation Length on the Hydraulic Parameters of a Fracture Network

We consider the influences of correlation length and aperture variability on the REV, the equivalent permeability of a fracture network, and the uncertainty in the equivalent permeability using a two-dimensional orthogonal bond percolation model. The percolation threshold, correlation length, effective conductivity, and coefficient of variation of the effective conductivity are investigated over statistically representative multiple realizations with Monte Carlo simulations in 2D fracture networks that have log-normally distributed individual fracture permeabilities. We show that although the aperture variability is large, the REV and the correlation length are similar near the percolation threshold. In contrast, when the fracture density is much larger than the percolation threshold they diverge as the aperture variability increases. We characterize the effects of correlation length and aperture variability on effective conductivity with a simple function. From the coefficient of variation analysis, the correlation length can be a criterion for evaluating which conceptual model is appropriate for describing the flow system for a given fracture network when aperture variability is sufficiently small. However, discrete fracture network models are recommended for flow simulation models because of the difficulty of REV estimation and the uncertainty in equivalent hydraulic parameters when aperture variability is large.     

A Study on the Evaluation of the Fracture Process Zone in CCNBD Rock Samples

The safety of many civil and mining concrete and rock structures including pre-existing crack networks is fundamentally affected by the mechanical behaviour of the material under static and cyclic loading. In cyclic loading case, cracks can grow at a lower load level compared to the monotonic case. This phenomenon is called fatigue due to subcritical crack propagation and depends on the behaviour of the fracture process zone (FPZ). This study presents the results of laboratory diametrical compression tests performed on Brisbane tuff disc specimens to investigate their mode-I (tensile) fracture toughness response to static and cyclic loading and relevant FPZ. The FPZ and fracture toughness response to cyclic loading was found to be different from that under static loading in terms of the ultimate load and the damage mechanisms in front of the chevron crack. A maximum reduction of the static fracture toughness (K _IC ) of 42 % was obtained for the highest amplitude increasing cyclic loading test. Detailed scanning electron microscope (SEM) examinations were performed on the surfaces of the tips of the chevron notch cracks, revealing that both loading methods cause FPZ development in the CCNBD specimens. When compared with monotonic FPZ development, the main difference with the cyclically loaded specimens was that intergranular cracks were formed due to particle breakage under cyclic loading, while smooth and bright cracks along cleavage planes were formed under static loading. Further, the SEM images showed that fatigue damage in Brisbane tuff is strongly influenced by the failure of the matrix because of both intergranular and transgranular subcritical fracturing.     

成型充填过程的ALE有限元模拟

在ALE框架中提出了一个用于成型充填过程有限元数值模拟的模型。应用ALE参考构形及ALE参考粒子速度描写充填过程中的熔体质量运动。摒弃了Hele-Shaw近似假定,因而所提出的模型能用于非薄壁型腔中高分子材料充填过程的数值模拟。应用基于时域分步算法的Taylor-Galerkin方法,对控制成型充填过程的守恒方程建立了弱形式。对移动自由面附近的充填材料区构造了网格生成算法与网格重划分方案。给出了在几种不同形状的典型腔体中充填过程的数值模拟结果,表明了所提出的ALE有限元模型模拟充填过程的有效性。     

Investigating ground effects on mixing and afterburning during a TNT explosion

In this paper, the unconfined and semi-confined condensed phase explosions of TNT will be studied using large eddy simulations based on the unsteady, compressible, reacting, multi-species Navier–Stokes equations to gain further understanding of the physical processes involved in a condensed phase explosion and the effect of confinement on the physical processes involved. The analysis of the mixing and afterburning of TNT explosions in free air (unconfined) and near the ground (semi-confined) indicates that the combustion region of detonation products and air is determined by the vorticity patterns, which are induced by the Richtmeyer–Meshkov instabilities that arise during the explosion. When the explosive is detonated in the vicinity of a surface, the surface affects the shock propagation by creating complex shock systems, thereby changing the orientation of the vorticity, giving the afterburning a mushroom shape, and increasing performance of an explosive charge by prolonging the existence of the mixing layer and thereby the afterburning.     

Effects of Fracture Boundary Conditions on Matrix-fracture Transfer Shape Factor

The matrix-fracture transfer shape factor is one of the important parameters in modeling naturally fractured reservoirs. Four decades after Warren and Root (1963, SPEJ, 245–255.) introduced the double porosity concept and suggested a relation for it, this parameter is still not completely understood. Even for a single-phase flow problem, investigators report different shape factors. This study shows that for a single-phase flow in a particular matrix block, the shape factor that Warren and Root defined is not unique and depends on the pressure in the fracture and how it changes with time. We use the Laplace domain analytical solutions of the diffusivity equation for different geometries and different boundary conditions to show that the shape factor depends on the fracture pressure change with time. In particular, by imposing a constant fracture pressure as it is typically done, one obtains the shape factor that Lim and Aziz (1995, J. Petrolean Sci. Eng. 13, 169.) calculated. However, other shape factors, similar to those reported in other studies are obtained, when other boundary conditions are chosen. Although, the time variability of the boundary conditions can be accounted for by the Duhamel’s theorem, in practice using large time-steps in numerical simulations can potentially introduce large errors in simulation results. However, numerical simulation models make use of a stepwise approximation of this theorem. It is shown in this paper that this approximation could lead to large errors in matrix-fracture transfer rate if large time-steps are chosen.     

Estimating the Hydraulic Conductivity of Two-Dimensional Fracture Networks Using Network Geometric Properties

Based on a modified Darcy–Brinkman–Maxwell model, a linear stability analysis of a Maxwell fluid in a horizontal porous layer heated from below by a constant flux is carried out. The non-oscillatory instability and oscillatory instability with different hydrodynamic boundaries such as rigid and free surfaces at the bottom are studied. Compared with the rigid surface cases, onset of fluid motion due to non-oscillatory instability and oscillatory instability is found to occur both more easily for the system with a free bottom surface. The critical Rayleigh number for onset of fluid motion due to non-oscillatory instability is lower with a constant flux heating bottom than with an isothermal heating bottom, but the result due to oscillatory instability is in contrast. The effects of the Darcy number, the relaxation time, and the Prandtl number on the critical Rayleigh number are also discussed.     

Effects of Gas Trapping on Foam Mobility in a Model Fracture

Transport in Porous Media - In enhanced oil recovery, foam can effectively mitigate conformance problems and maintain a stable displacement front, by trapping gas and reducing its relative...     

Effects of Heterogeneous Fracture Aperture on Multiphase Production from Shale Reservoirs

Production simulation from fractured shale reservoirs is often performed by simplifying the hydraulic fractures as rectangular planes with homogeneous aperture. This study investigates the effects of heterogeneous fracture aperture and proppant distribution in realistic, non-rectangular fractures on the multi-phase production from shales. The heterogeneous hydraulic fractures are generated with the GEOS multiphysics simulator under realistic 3D stress field. These fractures are embedded into the TOUGH+ multi-phase flow simulator for production simulation. The results emphasize the importance of flow barriers within the hydraulic fractures, due both to low-aperture regions caused by the stress-shadow effect and the settling of proppant. The production rate is particularly sensitive to aperture heterogeneity if the flow barriers are close to the wellbore such that a great portion of fracture volume is isolated from the well. A stage-to-stage comparison reveals that production from different stages could vary significantly because the local stress field leads to different fracture area and aperture. The use of proppant prevents fracture closure, but if the propped regions are far from the well, they do not enhance production because flow barriers between these regions and the well act as bottlenecks. The present study highlights the importance of incorporating aperture heterogeneity into production simulation, provides insights on the relationship between flow barriers, proppant concentration, and well production, and proposes a practical method to mitigate numerical difficulties when modeling heterogeneous fractures.

     

混凝土断裂过程区的虚拟裂纹粘聚力奇异性

混凝土断裂过程区视为具有粘聚阻力作用的虚拟裂纹，其非线性断裂和尺寸效应特性是与该虚拟裂纹粘聚力分布规律密切相关的。通过得到的粘聚应力分布函数解析结果，对该粘聚力分布特征的分析得知，在基于断裂过程区之外用线弹性场的力学模型上，该粘聚力随距离虚拟裂纹尖点的靠近，仍具有平方根奇异性。从而本文提出一个能够反映裂纹发展状态的粘聚应力奇异性强度参数，它是无粘聚力的线弹性裂纹应力强度因子和表征裂纹张开位移分布多项式参数的函数；因此，该参数可以作为混凝土非线性断裂的一个参量。文中就已有断裂试验测试结果进行了算例分析和相应的讨论。     

Buoyancy Effects on Upward Brine Displacement Caused by CO2 Injection

Upward displacement of brine from deep reservoirs driven by pressure increases resulting from CO₂ injection for geologic carbon sequestration may occur through improperly sealed abandoned wells, through permeable faults, or through permeable channels between pinch-outs of shale formations. The concern about upward brine flow is that, upon intrusion into aquifers containing groundwater resources, the brine may degrade groundwater. Because both salinity and temperature increase with depth in sedimentary basins, upward displacement of brine involves lifting fluid that is saline but also warm into shallower regions that contain fresher, cooler water. We have carried out dynamic simulations using TOUGH2/EOS7 of upward displacement of warm, salty water into cooler, fresher aquifers in a highly idealized two-dimensional model consisting of a vertical conduit (representing a well or permeable fault) connecting a deep and a shallow reservoir. Our simulations show that for small pressure increases and/or high-salinity-gradient cases, brine is pushed up the conduit to a new static steady-state equilibrium. On the other hand, if the pressure rise is large enough that brine is pushed up the conduit and into the overlying upper aquifer, flow may be sustained if the dense brine is allowed to spread laterally. In this scenario, dense brine only contacts the lower-most region of the upper aquifer. In a hypothetical case in which strong cooling of the dense brine occurs in the upper reservoir, the brine becomes sufficiently dense that it flows back down into the deeper reservoir from where it came. The brine then heats again in the lower aquifer and moves back up the conduit to repeat the cycle. Parameter studies delineate steady-state (static) and oscillatory solutions and reveal the character and period of oscillatory solutions. Such oscillatory solutions are mostly a curiosity rather than an expected natural phenomenon because in nature the geothermal gradient prevents the cooling in the upper aquifer that occurs in the model. The expected effect of upward brine displacement is either establishment of a new hydrostatic equilibrium or sustained upward flux into the bottom-most region of the upper aquifer.     

Evaluation of Irradiation Effects on Fracture Strength of Silicon Carbide using Micropillar Compression Tests

Micro-scale material testing techniques (e.g., nanoindentation, micropillar compression, etc.) have been developed and applied for the evaluation of radiation effects on the mechanical properties of nuclear reactor materials. These techniques can measure the mechanical properties from small volumes, which can be beneficial in the investigation of both neutron and ion-irradiated materials. In this study, we evaluated the compressive fracture strength of ion-irradiated silicon carbide (SiC) using micropillar compression tests. SiC and SiC-based composites are considered as candidate materials for micro electronics, sensors, and various components in next-generation reactors. Micropillars with a nominal diameter of 0.65 μm were fabricated on a monolithic polycrystalline cubic SiC plate using a lithography and plasma etching technique. Half of the total micropillars were irradiated with Si²⁺ ions. The SiC micropillars were uniaxially compressed using a flat diamond punch. A finite element model was used to compute the elastic stress state of the pillar. The results showed irradiation-induced strengthening, which is consistent with other investigations. In addition, plastic deformation of SiC at room temperature was observed. A slip was found to occur on {111} planes from a cross-sectional transmission electron microscopy observation. The micropillar tests are expected to significantly contribute to the study of irradiation and size effect on the mechanical properties of ceramic materials to be used in a radiation environment.     

Effects of Convection and Fracture Boundary Conditions on Heat Transfer Shape Factor in Fractured Geothermal Reservoirs

The yield stress fluids porosimetry method (YSM) was recently presented as a simple and non-toxic potential alternative to the extensively used mercury intrusion porosimetry (MIP). The success of YSM heavily relies on the choice of an appropriate yield stress fluid to be injected through the investigated porous medium. In previous works, xanthan gum aqueous solutions were used due to their ability to exhibit a pseudo-yield stress without substantial levels of unwanted thixotropy or viscoelasticity. Given that YSM is based on the existence of a yield stress, the accuracy of the obtained pore size distribution (PSD) crucially depends on the capacity of the injected fluid to emulate the shear rheology of a yield stress fluid. However, this capacity has still not been fully assessed in the case of xanthan gum solutions. Neither has the robustness of YSM with regard to errors in the determination of the shear-rheology parameters of the injected fluid been analysed. The shear viscosity of polymer solutions is known to be deeply influenced by polymer concentration. For these reasons, a first objective of this work is to evaluate the effect of polymer concentration on the accuracy of PSDs obtained by YSM when using xanthan gum solutions as injected fluids in laboratory experiments. To do so, xanthan gum solutions with different polymer concentrations were injected through analogous samples of a sintered silicate and the obtained PSDs were compared to the results of standard MIP. Moreover, the sensitivity of YSM to errors in the experimental determination of the shear-rheology parameters was also investigated through numerical experiments. The results of the present work permitted to gain further insight into the viability of YSM as an efficient alternative to MIP.     

Process validation of the normalized rheological function behavior during polymer crystallization

The film casting process of an isotactic polypropylene was adopted as the source of data to evaluate the behavior of a crystallizing polymer. The increase in viscosity due to the crystallization was quantified, and a model was proposed to estimate the normalized rheological function (NRF) during the process. The estimation was based also on the availability of rich sets of data, i.e., the polymer temperature and crystallinity, the film velocity and width distribution along the draw direction, gathered during the process. The quasi-experimental NRF evolutions were compared with just two of the very numerous hardening models proposed in literature, and the main result is that the process is coherent with the choice of an NRF model which predicts the increase in viscosity only for substantial crystallinity amount.     

Influence of Fracture Connectivity and Characterization Level on the Uncertainty of the Equivalent Permeability in Statistically Conceptualized Fracture Networks

A statistically conceptualized fracture network is generally used in modeling flow and transport in the discrete fracture network (DFN) approach. To quantify the influence of the fracture connectivity and characterization level on the uncertainty from a statistical conceptualization of fractures, the ensemble mean and variability of the equivalent permeability for stochastically generated fracture networks is analyzed with various percolation parameters (p) for different structures following power law size distributions. The results of Monte Carlo analyses show that statistics of a fracture network can be used to estimate its hydraulic properties with an acceptable level of uncertainty when p is greater than the specific percolation parameter (p _s) where the domain size is expected to become equal to the correlation length of a given fracture network. However, when p is smaller than the p _s, the uncertainty of the hydraulic properties induced from statistical characteristics of fractures is large, thus statistical conceptualization is not recommended. Conditional simulations support them: although we have deterministic information on a significant amount of fractures in the domain, a small number of stochastically generated fractures still produce significant uncertainty in the estimated system properties when p is smaller than p _s. These results suggest that the p _s and correlation length of a fracture network can be criteria to evaluate the applicability of the statistical conceptualization for modeling flow in a given fractured rock.     

Investigating the stabilizing effect of stochastic excitation on a chaotic dynamical system

The response of an interactive Mathieu–Duffing system in R ⁴, subjected to a harmonic excitation is investigated. For a deterministic circular frequency, chaotic behavior is observed. Subsequently it is shown that when the excitation becomes stochastic, chaos is subsided and trajectories tend to a diffused attracting set. The stabilizing effect of stochastic excitation is verified by finding the largest Lyapunov exponent for the two cases.     

Use of Scanning Electron Microscope and the Non-local Isotropic Damage Model to Investigate Fracture Process Zone in Notched Concrete Beams

In this study, a Scanning Electron Microscope (SEM) is used to understand the micro level aspect of the Fracture Process Zone (FPZ) in a concrete beam. It is mainly based on the preparation and analyzing samples which are considered as being a very important part of SEM (poor preparation techniques can lead to erroneous diagnosis of the concrete study). Numerically, the fracture of concrete requires the consideration of progressive damage, which is usually modeled by a constitutive law. This latest relies on numerical methods to obtain adequate solutions. It is shown herein that by using the Object Oriented Finite Element Method (OOFEM), obtained results agreed more or less with those of others researchers. On the other side, experimental results compromise those obtained by the use of the non-local isotropic damage model. It is finally proven throughout this study that the FPZ is defined by two parameters: the length and the width.     

On Publications on the Brittle Fracture Mechanics of Prestressed Materials

The paper analyzes new publications on the brittle fracture mechanics of prestressed materials. It is found out that new scientific results published in the International Journal of Solids and Structures in 2002 are a particular case of the results obtained at the Institute of Mechanics 20 years ago     

Fracture criteria based on local properties of the Eshelby tensor

Local failure criteria based on components of the Eshelby tensor are introduced and discussed. The application of the proposed criteria is demonstrated for a plane crack under mixed-mode loading conditions. Experiments have to show, if the criteria are also suitable to assess structures with distributed defects and are, thus, applicable to damage mechanics.