Compartmentalization analysis using discrete fracture network models
Energy Technology Data Exchange (ETDEWEB)
La Pointe, P.R.; Eiben, T.; Dershowitz, W. [Golder Associates, Redmond, VA (United States); Wadleigh, E. [Marathon Oil Co., Midland, TX (United States)
1997-08-01
This paper illustrates how Discrete Fracture Network (DFN) technology can serve as a basis for the calculation of reservoir engineering parameters for the development of fractured reservoirs. It describes the development of quantitative techniques for defining the geometry and volume of structurally controlled compartments. These techniques are based on a combination of stochastic geometry, computational geometry, and graph the theory. The parameters addressed are compartment size, matrix block size and tributary drainage volume. The concept of DFN models is explained and methodologies to compute these parameters are demonstrated.
Discrete fracture modelling for the Stripa tracer validation experiment predictions
International Nuclear Information System (INIS)
Dershowitz, W.; Wallmann, P.
1992-02-01
Groundwater flow and transport through three-dimensional networks of discrete fractures was modeled to predict the recovery of tracer from tracer injection experiments conducted during phase 3 of the Stripa site characterization and validation protect. Predictions were made on the basis of an updated version of the site scale discrete fracture conceptual model used for flow predictions and preliminary transport modelling. In this model, individual fractures were treated as stochastic features described by probability distributions of geometric and hydrologic properties. Fractures were divided into three populations: Fractures in fracture zones near the drift, non-fracture zone fractures within 31 m of the drift, and fractures in fracture zones over 31 meters from the drift axis. Fractures outside fracture zones are not modelled beyond 31 meters from the drift axis. Transport predictions were produced using the FracMan discrete fracture modelling package for each of five tracer experiments. Output was produced in the seven formats specified by the Stripa task force on fracture flow modelling. (au)
Discrete fracture modelling of the Finnsjoen rock mass: Phase 2
International Nuclear Information System (INIS)
Geier, J.E.; Axelsson, C.L.; Haessler, L.; Benabderrahmane, A.
1992-04-01
A discrete fracture network (DFN) model of the Finnsjoen site was derived from field data, and used to predict block-scale flow and transport properties. The DFN model was based on a compound Poisson process, with stochastic fracture zones, and individual fracture concentrated around the fracture zones. This formulation was used to represent the multitude of fracture zones at the site which could be observed on lineament maps and in boreholes, but were not the focus of detailed characterization efforts. Due to a shortage of data for fracture geometry at depth, distributions of fracture orientation and size were assumed to be uniform throughout the site. Transmissivity within individual fracture planes was assumed to vary according to a fractal model. Constant-head packer tests were simulated with the model, and the observed transient responses were compared with actual tests in terms of distributions of interpreted transmissivity and flow dimension, to partially validate the model. Both simulated and actual tests showed a range of flow dimension from sublinear to spherical, indicating local variations in the connectivity of the fracture population. A methodology was developed for estimation of an effective stochastic continuum from the DFN model, but this was only partly demonstrated. Directional conductivities for 40 m block were estimated using the DFN model. These show extremely poor correlation with results of multiple packer tests in the same blocks, indicating possible limitation of small-scale packer tests for predicting block-scale properties. Estimates are given of effective flow porosity and flow wetted surface, based on the block-scale flow fields calculated by the DFN model, and probabilistic models for the relationships among local fracture transmissivity, void space, and specific surface. The database for constructing these models is extremely limited. A review is given of the existing database for single fracture hydrologic properties. (127 refs
El-Amin, Mohamed F.; Kou, Jisheng; Sun, Shuyu
2017-01-01
Recently, applications of nanoparticles have been considered in many branches of petroleum engineering, especially, enhanced oil recovery. The current paper is devoted to investigate the problem of nanoparticles transport in fractured porous media, numerically. We employed the discrete-fracture model (DFM) to represent the flow and transport in the fractured formations. The system of the governing equations consists of the mass conservation law, Darcy's law, nanoparticles concentration in water, deposited nanoparticles concentration on the pore-wall, and entrapped nanoparticles concentration in the pore-throat. The variation of porosity and permeability due to the nanoparticles deposition/entrapment on/in the pores is also considered. We employ the multiscale time-splitting strategy to control different time-step sizes for different physics, such as pressure and concentration. The cell-centered finite difference (CCFD) method is used for the spatial discretization. Numerical examples are provided to demonstrate the efficiency of the proposed multiscale time splitting approach.
El-Amin, Mohamed F.
2017-06-06
Recently, applications of nanoparticles have been considered in many branches of petroleum engineering, especially, enhanced oil recovery. The current paper is devoted to investigate the problem of nanoparticles transport in fractured porous media, numerically. We employed the discrete-fracture model (DFM) to represent the flow and transport in the fractured formations. The system of the governing equations consists of the mass conservation law, Darcy\\'s law, nanoparticles concentration in water, deposited nanoparticles concentration on the pore-wall, and entrapped nanoparticles concentration in the pore-throat. The variation of porosity and permeability due to the nanoparticles deposition/entrapment on/in the pores is also considered. We employ the multiscale time-splitting strategy to control different time-step sizes for different physics, such as pressure and concentration. The cell-centered finite difference (CCFD) method is used for the spatial discretization. Numerical examples are provided to demonstrate the efficiency of the proposed multiscale time splitting approach.
Directory of Open Access Journals (Sweden)
Wang Yueying
2017-08-01
Full Text Available Isolated fractures usually exist in fractured media systems, where the capillary pressure in the fracture is lower than that of the matrix, causing the discrepancy in oil recoveries between fractured and non-fractured porous media. Experiments, analytical solutions and conventional simulation methods based on the continuum model approach are incompetent or insufficient in describing media containing isolated fractures. In this paper, the simulation of the counter-current imbibition in fractured media is based on the discrete-fracture model (DFM. The interlocking or arrangement of matrix and fracture system within the model resembles the traditional discrete fracture network model and the hybrid-mixed-finite-element method is employed to solve the associated equations. The Behbahani experimental data validates our simulation solution for consistency. The simulation results of the fractured media show that the isolated-fractures affect the imbibition in the matrix block. Moreover, the isolated fracture parameters such as fracture length and fracture location influence the trend of the recovery curves. Thus, the counter-current imbibition behavior of media with isolated fractures can be predicted using this method based on the discrete-fracture model.
An efficient hydro-mechanical model for coupled multi-porosity and discrete fracture porous media
Yan, Xia; Huang, Zhaoqin; Yao, Jun; Li, Yang; Fan, Dongyan; Zhang, Kai
2018-02-01
In this paper, a numerical model is developed for coupled analysis of deforming fractured porous media with multiscale fractures. In this model, the macro-fractures are modeled explicitly by the embedded discrete fracture model, and the supporting effects of fluid and fillings in these fractures are represented explicitly in the geomechanics model. On the other hand, matrix and micro-fractures are modeled by a multi-porosity model, which aims to accurately describe the transient matrix-fracture fluid exchange process. A stabilized extended finite element method scheme is developed based on the polynomial pressure projection technique to address the displacement oscillation along macro-fracture boundaries. After that, the mixed space discretization and modified fixed stress sequential implicit methods based on non-matching grids are applied to solve the coupling model. Finally, we demonstrate the accuracy and application of the proposed method to capture the coupled hydro-mechanical impacts of multiscale fractures on fractured porous media.
A new computer code for discrete fracture network modelling
Xu, Chaoshui; Dowd, Peter
2010-03-01
The authors describe a comprehensive software package for two- and three-dimensional stochastic rock fracture simulation using marked point processes. Fracture locations can be modelled by a Poisson, a non-homogeneous, a cluster or a Cox point process; fracture geometries and properties are modelled by their respective probability distributions. Virtual sampling tools such as plane, window and scanline sampling are included in the software together with a comprehensive set of statistical tools including histogram analysis, probability plots, rose diagrams and hemispherical projections. The paper describes in detail the theoretical basis of the implementation and provides a case study in rock fracture modelling to demonstrate the application of the software.
Donado-Garzon, L. D.; Pardo, Y.
2013-12-01
Fractured media are very heterogeneous systems where occur complex physical and chemical processes to model. One of the possible approaches to conceptualize this type of massifs is the Discrete Fracture Network (DFN). Donado et al., modeled flow and transport in a granitic batholith based on this approach and found good fitting with hydraulic and tracer tests, but the computational cost was excessive due to a gigantic amount of elements to model. We present in this work a methodology based on percolation theory for reducing the number of elements and in consequence, to reduce the bandwidth of the conductance matrix and the execution time of each network. DFN poses as an excellent representation of all the set of fractures of the media, but not all the fractures of the media are part of the conductive network. Percolation theory is used to identify which nodes or fractures are not conductive, based on the occupation probability or percolation threshold. In a fractured system, connectivity determines the flow pattern in the fractured rock mass. This volume of fluid is driven through connection paths formed by the fractures, when the permeability of the rock is negligible compared to the fractures. In a population of distributed fractures, each of this that has no intersection with any connected fracture do not contribute to generate a flow field. This algorithm also permits us to erase these elements however they are water conducting and hence, refine even more the backbone of the network. We used 100 different generations of DFN that were optimized in this study using percolation theory. In each of the networks calibrate hydrodynamic parameters as hydraulic conductivity and specific storage coefficient, for each of the five families of fractures, yielding a total of 10 parameters to estimate, at each generation. Since the effects of the distribution of fault orientation changes the value of the percolation threshold, but not the universal laws of classical
Yushi, Zou; Xinfang, Ma; Tong, Zhou; Ning, Li; Ming, Chen; Sihai, Li; Yinuo, Zhang; Han, Li
2017-09-01
Hydraulic fracture (HF) height containment tends to occur in layered formations, and it significantly influences the entire HF geometry or the stimulated reservoir volume. This study aims to explore the influence of preexisting bedding planes (BPs) on the HF height growth in layered formations. Laboratory fracturing experiments were performed to confirm the occurrence of HF height containment in natural shale that contains multiple weak and high-permeability BPs under triaxial stresses. Numerical simulations were then conducted to further illustrate the manner in which vertical stress, BP permeability, BP density(or spacing), pump rate, and fluid viscosity control HF height growth using a 3D discrete element method-based fracturing model. In this model, the rock matrix was considered transversely isotropic and multiple BPs can be explicitly represented. Experimental and numerical results show that the vertically growing HF tends to be limited by multi-high-permeability BPs, even under higher vertical stress. When the vertically growing HF intersects with the multi-high-permeability BPs, the injection pressure will be sharply reduced. If a low pumping rate or a low-viscosity fluid is used, the excess fracturing fluid leak-off into the BPs obviously decreases the rate of pressure build up, which will then limit the growth of HF. Otherwise, a higher pumping rate and/or a higher viscosity will reduce the leak-off time and fluid volume, but increase the injection pressure to drive the HF to grow and to penetrate through the BPs.
Numerical simulation on ferrofluid flow in fractured porous media based on discrete-fracture model
Huang, Tao; Yao, Jun; Huang, Zhaoqin; Yin, Xiaolong; Xie, Haojun; Zhang, Jianguang
2017-06-01
Water flooding is an efficient approach to maintain reservoir pressure and has been widely used to enhance oil recovery. However, preferential water pathways such as fractures can significantly decrease the sweep efficiency. Therefore, the utilization ratio of injected water is seriously affected. How to develop new flooding technology to further improve the oil recovery in this situation is a pressing problem. For the past few years, controllable ferrofluid has caused the extensive concern in oil industry as a new functional material. In the presence of a gradient in the magnetic field strength, a magnetic body force is produced on the ferrofluid so that the attractive magnetic forces allow the ferrofluid to be manipulated to flow in any desired direction through the control of the external magnetic field. In view of these properties, the potential application of using the ferrofluid as a new kind of displacing fluid for flooding in fractured porous media is been studied in this paper for the first time. Considering the physical process of the mobilization of ferrofluid through porous media by arrangement of strong external magnetic fields, the magnetic body force was introduced into the Darcy equation and deals with fractures based on the discrete-fracture model. The fully implicit finite volume method is used to solve mathematical model and the validity and accuracy of numerical simulation, which is demonstrated through an experiment with ferrofluid flowing in a single fractured oil-saturated sand in a 2-D horizontal cell. At last, the water flooding and ferrofluid flooding in a complex fractured porous media have been studied. The results showed that the ferrofluid can be manipulated to flow in desired direction through control of the external magnetic field, so that using ferrofluid for flooding can raise the scope of the whole displacement. As a consequence, the oil recovery has been greatly improved in comparison to water flooding. Thus, the ferrofluid
Discrete fracture modelling of the Finnsjoen rock mass. Phase 1: Feasibility study
International Nuclear Information System (INIS)
Geier, J.E.; Axelsson, C.L.
1991-03-01
The geometry and properties of discrete fractures are expected to control local heterogeneity in flow and solute transport within crystalline rock in the Finnsjoen area. The present report describes the first phase of a discrete-fracture modelling study, the goal of which is to develop stochastic-continuum and hydrologic properties. In the first phase of this study, the FracMan discrete fracture modelling package was used to analyse discrete fracture geometrical and hyrological data. Constant-pressure packer tests were analysed using fractional dimensional methods to estimate effective transmissivities and flow dimension for the packer test intervals. Discrete fracture data on orientation, size, shape, and location were combined with hydrologic data to develop a preliminary conceptual model for the conductive fractures at the site. The variability of fracture properties was expressed in the model by probability distributions. The preliminary conceptual model was used to simulate three-dimensional populations of conductive fractures in 25 m and 50 m cubes of rock. Transient packer tests were simulated in these fracture populations, and the simulated results were used to validate the preliminary conceptual model. The calibrated model was used to estimate the components of effective conductivity tensors for the rock by simulating steady-state groundwater flow through the cubes in three orthogonal directions. Monte Carlo stochastic simulations were performed for alternative realizations of the conceptual model. The number of simulations was insufficient to give a quantitative prediction of the effective conductivity heterogeneity and anisotropy on the scales of the cubes. However, the results give preliminary, rough estimates of these properties, and provide a demonstration of how the discrete-fracture network concept can be applied to derive data that is necessary for stochastic continuum and channel network modelling. (authors)
International Nuclear Information System (INIS)
Geier, J.E.; Thomas, A.L.
1996-08-01
This report describes the statistical derivation and partial validation of discrete-fracture network (DFN) models for the rock beneath the island of Aespoe in southeastern Sweden. The purpose was to develop DFN representations of the rock mass within a hypothetical, spent-fuel repository, located under Aespoe. Analyses are presented for four major lithologic types, with separate analyses of the rock within fracture zones, the rock excluding fracture zones, and all rock. Complete DFN models are proposed as descriptions of the rock mass in the near field. The procedure for validation, by comparison between actual and simulated packer tests, was found to be useful for discriminating among candidate DFN models. In particular, the validation approach was shown to be sensitive to a change in the fracture location (clustering) model, and to a change in the variance of single-fracture transmissivity. The proposed models are defined in terms of stochastic processes and statistical distributions, and thus are descriptive of the variability of the fracture system. This report includes discussion of the numerous sources of uncertainty in the models, including uncertainty that results from the variability of the natural system. 62 refs
Energy Technology Data Exchange (ETDEWEB)
Huang, Hai; Plummer, Mitchell; Podgorney, Robert
2013-02-01
Advancement of EGS requires improved prediction of fracture development and growth during reservoir stimulation and long-term operation. This, in turn, requires better understanding of the dynamics of the strongly coupled thermo-hydro-mechanical (THM) processes within fractured rocks. We have developed a physically based rock deformation and fracture propagation simulator by using a quasi-static discrete element model (DEM) to model mechanical rock deformation and fracture propagation induced by thermal stress and fluid pressure changes. We also developed a network model to simulate fluid flow and heat transport in both fractures and porous rock. In this paper, we describe results of simulations in which the DEM model and network flow & heat transport model are coupled together to provide realistic simulation of the changes of apertures and permeability of fractures and fracture networks induced by thermal cooling and fluid pressure changes within fractures. Various processes, such as Stokes flow in low velocity pores, convection-dominated heat transport in fractures, heat exchange between fluid-filled fractures and solid rock, heat conduction through low-permeability matrices and associated mechanical deformations are all incorporated into the coupled model. The effects of confining stresses, developing thermal stress and injection pressure on the permeability evolution of fracture and fracture networks are systematically investigated. Results are summarized in terms of implications for the development and evolution of fracture distribution during hydrofracturing and thermal stimulation for EGS.
International Nuclear Information System (INIS)
Dershowitz, B.; Eiben, T.; Follin, S.; Andersson, Johan
1999-08-01
As part of studies into the siting of a deep repository for nuclear waste, Swedish Nuclear Fuel and Waste Management Company (SKB) has commissioned the Alternative Models Project (AMP). The AMP is a comparison of three alternative modeling approaches for geosphere performance assessment for a single hypothetical site. The hypothetical site, arbitrarily named Aberg is based on parameters from the Aespoe Hard Rock Laboratory in southern Sweden. The Aberg model domain, boundary conditions and canister locations are defined as a common reference case to facilitate comparisons between approaches. This report presents the results of a discrete fracture pathways analysis of the Aberg site, within the context of the SR 97 performance assessment exercise. The Aberg discrete fracture network (DFN) site model is based on consensus Aberg parameters related to the Aespoe HRL site. Discrete fracture pathways are identified from canister locations in a prototype repository design to the surface of the island or to the sea bottom. The discrete fracture pathways analysis presented in this report is used to provide the following parameters for SKB's performance assessment transport codes FARF31 and COMP23: * F-factor: Flow wetted surface normalized with regards to flow rate (yields an appreciation of the contact area available for diffusion and sorption processes) [TL -1 ]. * Travel Time: Advective transport time from a canister location to the environmental discharge [T]. * Canister Flux: Darcy flux (flow rate per unit area) past a representative canister location [LT -1 ]. In addition to the above, the discrete fracture pathways analysis in this report also provides information about: additional pathway parameters such as pathway length, pathway width, transport aperture, reactive surface area and transmissivity, percentage of canister locations with pathways to the surface discharge, spatial pattern of pathways and pathway discharges, visualization of pathways, and statistical
Energy Technology Data Exchange (ETDEWEB)
Dershowitz, B.; Eiben, T. [Golder Associates Inc., Seattle (United States); Follin, S.; Andersson, Johan [Golder Grundteknik KB, Stockholm (Sweden)
1999-08-01
As part of studies into the siting of a deep repository for nuclear waste, Swedish Nuclear Fuel and Waste Management Company (SKB) has commissioned the Alternative Models Project (AMP). The AMP is a comparison of three alternative modeling approaches for geosphere performance assessment for a single hypothetical site. The hypothetical site, arbitrarily named Aberg is based on parameters from the Aespoe Hard Rock Laboratory in southern Sweden. The Aberg model domain, boundary conditions and canister locations are defined as a common reference case to facilitate comparisons between approaches. This report presents the results of a discrete fracture pathways analysis of the Aberg site, within the context of the SR 97 performance assessment exercise. The Aberg discrete fracture network (DFN) site model is based on consensus Aberg parameters related to the Aespoe HRL site. Discrete fracture pathways are identified from canister locations in a prototype repository design to the surface of the island or to the sea bottom. The discrete fracture pathways analysis presented in this report is used to provide the following parameters for SKB's performance assessment transport codes FARF31 and COMP23: * F-factor: Flow wetted surface normalized with regards to flow rate (yields an appreciation of the contact area available for diffusion and sorption processes) [TL{sup -1}]. * Travel Time: Advective transport time from a canister location to the environmental discharge [T]. * Canister Flux: Darcy flux (flow rate per unit area) past a representative canister location [LT{sup -1}]. In addition to the above, the discrete fracture pathways analysis in this report also provides information about: additional pathway parameters such as pathway length, pathway width, transport aperture, reactive surface area and transmissivity, percentage of canister locations with pathways to the surface discharge, spatial pattern of pathways and pathway discharges, visualization of pathways, and
Qin, Guan; Bi, Linfeng; Popov, Peter; Efendiev, Yalchin; Espedal, Magne
2010-01-01
, fractures and their interconnectivities in coarse-scale simulation models. In this paper, we present a procedure based on our previously proposed Stokes-Brinkman model (SPE 125593) and the discrete fracture network method for accurate and efficient upscaling
Energy Technology Data Exchange (ETDEWEB)
La Pointe, Paul; Fox, Aaron (Golder Associates Inc (United States)); Hermanson, Jan; Oehman, Johan (Golder Associates AB, Stockholm (Sweden))
2008-12-15
The Swedish Nuclear Fuel and Waste Management Company (SKB) is performing site characterization at two different locations, Forsmark and Laxemar, in order to locate a site for a final geologic repository for spent nuclear fuel. The program is built upon the development of Site Descriptive Models (SDMs) at specific timed data freezes. Each SDM is formed from discipline-specific reports from across the scientific spectrum. This report describes the methods, analyses, and conclusions of the modelling team in the production of the SDM-Site Laxemar geological discrete-fracture network (DFN) model. The DFN builds upon the work of other geological models, including the deformation zone and rock domain models. The geological DFN is a statistical model for stochastically simulating rock fractures and minor deformation zones at a scale of less than 1,000 m (the lower cut-off of the DZ models). The geological DFN is valid within six distinct fracture domains inside the Laxemar local model subarea: FSM{sub C}, FSM{sub E}W007, FSM{sub N}, FSM{sub N}E005, FSM{sub S}, and FSM{sub W}. The models are built using data from detailed surface outcrop maps, geophysical lineament maps, and the cored borehole record at Laxemar. The conceptual model for the SDM-Site Laxemar geological DFN model revolves around the identification of fracture domains based on relative fracture set intensities, orientation clustering, and the regional tectonic framework (including deformation zones). A single coupled fracture size/fracture intensity concept (the Base Model) based on a Pareto (power-law) distribution for fracture sizes was chosen as the recommended parameterisation. A slew of alternative size-intensity models were also carried through the fracture analyses and into the uncertainty and model verification analyses. Uncertainty is modelled by analysing the effects on fracture intensity (P32) that alternative model cases can have. Uncertainty is parameterised as a ratio between the P32 of the
International Nuclear Information System (INIS)
La Pointe, Paul; Fox, Aaron; Hermanson, Jan; Oehman, Johan
2008-10-01
The Swedish Nuclear Fuel and Waste Management Company (SKB) is performing site characterization at two different locations, Forsmark and Laxemar, in order to locate a site for a final geologic repository for spent nuclear fuel. The program is built upon the development of Site Descriptive Models (SDMs) at specific timed data freezes. Each SDM is formed from discipline-specific reports from across the scientific spectrum. This report describes the methods, analyses, and conclusions of the modelling team in the production of the SDM-Site Laxemar geological discrete-fracture network (DFN) model. The DFN builds upon the work of other geological models, including the deformation zone and rock domain models. The geological DFN is a statistical model for stochastically simulating rock fractures and minor deformation zones at a scale of less than 1,000 m (the lower cut-off of the DZ models). The geological DFN is valid within six distinct fracture domains inside the Laxemar local model subarea: FSM C , FSM E W007, FSM N , FSM N E005, FSM S , and FSM W . The models are built using data from detailed surface outcrop maps, geophysical lineament maps, and the cored borehole record at Laxemar. The conceptual model for the SDM-Site Laxemar geological DFN model revolves around the identification of fracture domains based on relative fracture set intensities, orientation clustering, and the regional tectonic framework (including deformation zones). A single coupled fracture size/fracture intensity concept (the Base Model) based on a Pareto (power-law) distribution for fracture sizes was chosen as the recommended parameterisation. A slew of alternative size-intensity models were also carried through the fracture analyses and into the uncertainty and model verification analyses. Uncertainty is modelled by analysing the effects on fracture intensity (P32) that alternative model cases can have. Uncertainty is parameterised as a ratio between the P32 of the alternative model and the P
International Nuclear Information System (INIS)
Hartley, Lee; Roberts, David
2013-04-01
The Swedish Nuclear Fuel and Waste Management Company (SKB) is responsible for the development of a deep geological repository for spent nuclear fuel. The permitting of such a repository is informed by assessment studies to estimate the risks of the disposal method. One of the potential risks involves the transport of radionuclides in groundwater from defective canisters in the repository to the accessible environment. The Swedish programme for geological disposal of spent nuclear fuel has involved undertaking detailed surface-based site characterisation studies at two different sites, Forsmark and Laxemar-Simpevarp. A key component of the hydrogeological modelling of these two sites has been the development of Discrete Fracture Network (DFN) concepts of groundwater flow through the fractures in the crystalline rocks present. A discrete fracture network model represents some of the characteristics of fractures explicitly, such as their, orientation, intensity, size, spatial distribution, shape and transmissivity. This report summarises how the discrete fracture network methodology has been applied to model groundwater flow and transport at Forsmark and Laxemar. The account has involved summarising reports previously published by SKB between 2001 and 2011. The report describes the conceptual framework and assumptions used in interpreting site data, and in particular how data has been used to calibrate the various parameters that define the discrete fracture network representation of bedrock hydrogeology against borehole geologic and hydraulic data. Steps taken to confirm whether the developed discrete fracture network models provide a description of regional-scale groundwater flow and solute transport consistent with wider hydraulic tests hydrochemical data from Forsmark and Laxemar are discussed. It illustrates the use of derived hydrogeological DFN models in the simulations of the temperate period hydrogeology that provided input to radionuclide transport
Energy Technology Data Exchange (ETDEWEB)
Hartley, Lee; Roberts, David
2013-04-15
The Swedish Nuclear Fuel and Waste Management Company (SKB) is responsible for the development of a deep geological repository for spent nuclear fuel. The permitting of such a repository is informed by assessment studies to estimate the risks of the disposal method. One of the potential risks involves the transport of radionuclides in groundwater from defective canisters in the repository to the accessible environment. The Swedish programme for geological disposal of spent nuclear fuel has involved undertaking detailed surface-based site characterisation studies at two different sites, Forsmark and Laxemar-Simpevarp. A key component of the hydrogeological modelling of these two sites has been the development of Discrete Fracture Network (DFN) concepts of groundwater flow through the fractures in the crystalline rocks present. A discrete fracture network model represents some of the characteristics of fractures explicitly, such as their, orientation, intensity, size, spatial distribution, shape and transmissivity. This report summarises how the discrete fracture network methodology has been applied to model groundwater flow and transport at Forsmark and Laxemar. The account has involved summarising reports previously published by SKB between 2001 and 2011. The report describes the conceptual framework and assumptions used in interpreting site data, and in particular how data has been used to calibrate the various parameters that define the discrete fracture network representation of bedrock hydrogeology against borehole geologic and hydraulic data. Steps taken to confirm whether the developed discrete fracture network models provide a description of regional-scale groundwater flow and solute transport consistent with wider hydraulic tests hydrochemical data from Forsmark and Laxemar are discussed. It illustrates the use of derived hydrogeological DFN models in the simulations of the temperate period hydrogeology that provided input to radionuclide transport
Prediction of Fracture Behavior in Rock and Rock-like Materials Using Discrete Element Models
Katsaga, T.; Young, P.
2009-05-01
The study of fracture initiation and propagation in heterogeneous materials such as rock and rock-like materials are of principal interest in the field of rock mechanics and rock engineering. It is crucial to study and investigate failure prediction and safety measures in civil and mining structures. Our work offers a practical approach to predict fracture behaviour using discrete element models. In this approach, the microstructures of materials are presented through the combination of clusters of bonded particles with different inter-cluster particle and bond properties, and intra-cluster bond properties. The geometry of clusters is transferred from information available from thin sections, computed tomography (CT) images and other visual presentation of the modeled material using customized AutoCAD built-in dialog- based Visual Basic Application. Exact microstructures of the tested sample, including fractures, faults, inclusions and void spaces can be duplicated in the discrete element models. Although the microstructural fabrics of rocks and rock-like structures may have different scale, fracture formation and propagation through these materials are alike and will follow similar mechanics. Synthetic material provides an excellent condition for validating the modelling approaches, as fracture behaviours are known with the well-defined composite's properties. Calibration of the macro-properties of matrix material and inclusions (aggregates), were followed with the overall mechanical material responses calibration by adjusting the interfacial properties. The discrete element model predicted similar fracture propagation features and path as that of the real sample material. The path of the fractures and matrix-inclusion interaction was compared using computed tomography images. Initiation and fracture formation in the model and real material were compared using Acoustic Emission data. Analysing the temporal and spatial evolution of AE events, collected during the
International Nuclear Information System (INIS)
Dershowitz, W.S.
1994-01-01
The Stripa project has played a major role in developing discrete fracture analysis from a theoretical research topic to a practical repository evaluation tool. The Site Characterization and Validation (SCV) program positively answered questions regarding: (1) the validation of discrete fracture models, (2) the feasibility of collecting data for discrete fracture models, (3) the ability of discrete fracture models to simulate flow in a rock volume of approximately 10 6 cubic meters using modest computing resources, and (4) the ability to model transport in discrete fractures. The SCV program also made progress on such continuing issues as the importance of in-plane fracture heterogeneity and coupled effects. (author). 16 refs., 2 tabs., 6 figs
Investigation of discrete-fracture network conceptual model uncertainty at Forsmark
International Nuclear Information System (INIS)
Geier, Joel
2011-04-01
In the present work a discrete fracture model has been further developed and implemented using the latest SKB site investigation data. The model can be used for analysing the fracture network and to model flow through the rock in Forsmark. The aim has been to study uncertainties in the hydrological discrete fracture network (DFN) for the repository model. More specifically the objective has been to study to which extent available data limits uncertainties in the DFN model and how data that can be obtained in future underground work can further limit these uncertainties. Moreover, the effects on deposition hole utilisation and placement have been investigated as well as the effects on the flow to deposition holes
Discrete Dual Porosity Modeling of Electrical Current Flow in Fractured Media
Roubinet, D.; Irving, J.
2013-12-01
The study of fractured rocks is highly important in a variety of research fields and applications such as hydrogeology, geothermal energy, hydrocarbon extraction, and the long-term storage of toxic waste. Fractured media are characterized by a large contrast in permeability between the fractures and the rock matrix. For hydrocarbon extraction, the presence of highly conductive fractures is an advantage as they allow for quick and easy access to the resource. For toxic waste storage, however, the fractures represent a significant drawback as there is an increased risk of leakage and migration of pollutants deep into the subsurface. In both cases, the identification of fracture network characteristics is a critical, challenging, and required step. A number of previous studies have indicated that the presence of fractures in geological materials can have a significant impact on geophysical electrical resistivity measurements. It thus appears that, in some cases, geoelectrical surveys might be used to obtain useful information regarding fracture network characteristics. However, existing geoelectrical modeling tools and inversion methods are not properly adapted to deal with the specific challenges of fractured media. This prevents us from fully exploring the potential of the method to characterize fracture network properties. We thus require, as a first step, the development of accurate and efficient numerical modeling tools specifically designed for fractured domains. Building on the discrete fracture network (DFN) approach that has been widely used for modeling groundwater flow in fractured rocks, we have developed a discrete dual-porosity model for electrical current flow in fractured media. Our novel approach combines an explicit representation of the fractures with fracture-matrix electrical flow exchange at the block-scale. Tests in two dimensions show the ability of our method to deal with highly heterogeneous fracture networks in a highly computationally
A Discrete Fracture Network Model with Stress-Driven Nucleation and Growth
Lavoine, E.; Darcel, C.; Munier, R.; Davy, P.
2017-12-01
The realism of Discrete Fracture Network (DFN) models, beyond the bulk statistical properties, relies on the spatial organization of fractures, which is not issued by purely stochastic DFN models. The realism can be improved by injecting prior information in DFN from a better knowledge of the geological fracturing processes. We first develop a model using simple kinematic rules for mimicking the growth of fractures from nucleation to arrest, in order to evaluate the consequences of the DFN structure on the network connectivity and flow properties. The model generates fracture networks with power-law scaling distributions and a percentage of T-intersections that are consistent with field observations. Nevertheless, a larger complexity relying on the spatial variability of natural fractures positions cannot be explained by the random nucleation process. We propose to introduce a stress-driven nucleation in the timewise process of this kinematic model to study the correlations between nucleation, growth and existing fracture patterns. The method uses the stress field generated by existing fractures and remote stress as an input for a Monte-Carlo sampling of nuclei centers at each time step. Networks so generated are found to have correlations over a large range of scales, with a correlation dimension that varies with time and with the function that relates the nucleation probability to stress. A sensibility analysis of input parameters has been performed in 3D to quantify the influence of fractures and remote stress field orientations.
Geological discrete-fracture network model (version 1) for the Olkiluoto site, Finland
International Nuclear Information System (INIS)
Fox, A.; Buoro, A.; Dahlbo, K.; Wiren, L.
2009-10-01
This report describes the methods, analyses, and conclusions of the modelling team in the production of a discrete-fracture network (DFN) model for the Olkiluoto Site in Finland. The geological DFN is a statistical model for stochastically simulating rock fractures and minor faults at a scale ranging from approximately 0.05 m to approximately 500 m; an upper scale limit is not expressly defined, but the DFN model explicitly excludes structures at deformation-zone scales (∼ 500 m) and larger. The DFN model is presented as a series of tables summarizing probability distributions for several parameters necessary for fracture modelling: fracture orientation, fracture size, fracture intensity, and associated spatial constraints. The geological DFN is built from data collected during site characterization (SC) activities at Olkiluoto, which is currently planned to function as a final deep geological repository for spent fuel and nuclear waste from the Finnish nuclear power program. Data used in the DFN analyses include fracture maps from surface outcrops and trenches (as of July 2007), geological and structural data from cored boreholes (as of July 2007), and fracture information collected during the construction of the main tunnels and shafts at the ONKALO laboratory (January 2008). The modelling results suggest that the rock volume at Olkiluoto surrounding the ONKALO tunnel can be separated into three distinct volumes (fracture domains): an upper block, an intermediate block, and a lower block. The three fracture domains are bounded horizontally and vertically by large deformation zones. Fracture properties, such as fracture orientation and relative orientation set intensity, vary between fracture domains. The rock volume at Olkiluoto is dominated by three distinct fracture sets: subhorizontally-dipping fractures striking north-northeast and dipping to the east, a subvertically-dipping fracture set striking roughly north-south, and a subverticallydipping fracture set
A discrete-element model for viscoelastic deformation and fracture of glacial ice
Riikilä, T. I.; Tallinen, T.; Åström, J.; Timonen, J.
2015-10-01
A discrete-element model was developed to study the behavior of viscoelastic materials that are allowed to fracture. Applicable to many materials, the main objective of this analysis was to develop a model specifically for ice dynamics. A realistic model of glacial ice must include elasticity, brittle fracture and slow viscous deformations. Here the model is described in detail and tested with several benchmark simulations. The model was used to simulate various ice-specific applications with resulting flow rates that were compatible with Glen's law, and produced under fragmentation fragment-size distributions that agreed with the known analytical and experimental results.
Visualization and Hierarchical Analysis of Flow in Discrete Fracture Network Models
Aldrich, G. A.; Gable, C. W.; Painter, S. L.; Makedonska, N.; Hamann, B.; Woodring, J.
2013-12-01
Flow and transport in low permeability fractured rock is primary in interconnected fracture networks. Prediction and characterization of flow and transport in fractured rock has important implications in underground repositories for hazardous materials (eg. nuclear and chemical waste), contaminant migration and remediation, groundwater resource management, and hydrocarbon extraction. We have developed methods to explicitly model flow in discrete fracture networks and track flow paths using passive particle tracking algorithms. Visualization and analysis of particle trajectory through the fracture network is important to understanding fracture connectivity, flow patterns, potential contaminant pathways and fast paths through the network. However, occlusion due to the large number of highly tessellated and intersecting fracture polygons preclude the effective use of traditional visualization methods. We would also like quantitative analysis methods to characterize the trajectory of a large number of particle paths. We have solved these problems by defining a hierarchal flow network representing the topology of particle flow through the fracture network. This approach allows us to analyses the flow and the dynamics of the system as a whole. We are able to easily query the flow network, and use paint-and-link style framework to filter the fracture geometry and particle traces based on the flow analytics. This allows us to greatly reduce occlusion while emphasizing salient features such as the principal transport pathways. Examples are shown that demonstrate the methodology and highlight how use of this new method allows quantitative analysis and characterization of flow and transport in a number of representative fracture networks.
International Nuclear Information System (INIS)
Tanaka, Tatsuya; Ando, Kenichi; Hashimoto, Shuuji; Saegusa, Hiromitsu; Takeuchi, Shinji; Amano, Kenji
2007-01-01
This study aims to establish comprehensive techniques for site descriptive modelling considering the hydraulic heterogeneity due to the Water Conducting Features in fractured rocks. The WCFs was defined by the interpretation and integration of geological and hydrogeological data obtained from the deep borehole investigation campaign in the Mizunami URL project and Regional Hydrogeological Study. As a result of surface based investigation phase, the block-scale hydrogeological descriptive model was generated using hydraulic discrete fracture networks. Uncertainties and remaining issues associated with the assumption in interpreting the data and its modelling were addressed in a systematic way. (author)
Directory of Open Access Journals (Sweden)
Yongbin Zhang
2015-06-01
Full Text Available In this study, a 3D multicomponent multiphase simulator with a new fracture characterization technique is developed to simulate the enhanced recovery of coalbed methane. In this new model, the diffusion source from the matrix is calculated using the traditional dual-continuum approach, while in the Darcy flow scale, the Discrete Fracture Model (DFM is introduced to explicitly represent the flow interaction between cleats and large-scale fractures. For this purpose, a general formulation is proposed to model the multicomponent multiphase flow through the fractured coal media. The S&D model and a revised P&M model are incorporated to represent the geomechanical effects. Then a finite volume based discretization and solution strategies are constructed to solve the general ECBM equations. The prismatic meshing algorism is used to construct the grids for 3D reservoirs with complex fracture geometry. The simulator is validated with a benchmark case in which the results show close agreement with GEM. Finally, simulation of a synthetic heterogeneous 3D coal reservoir modified from a published literature is performed to evaluate the production performance and the effects of injected gas composition, well pattern and gas buoyancy.
Frampton, A.; Hyman, J.; Zou, L.
2017-12-01
Analysing flow and transport in sparsely fractured media is important for understanding how crystalline bedrock environments function as barriers to transport of contaminants, with important applications towards subsurface repositories for storage of spent nuclear fuel. Crystalline bedrocks are particularly favourable due to their geological stability, low advective flow and strong hydrogeochemical retention properties, which can delay transport of radionuclides, allowing decay to limit release to the biosphere. There are however many challenges involved in quantifying and modelling subsurface flow and transport in fractured media, largely due to geological complexity and heterogeneity, where the interplay between advective and dispersive flow strongly impacts both inert and reactive transport. A key to modelling transport in a Lagrangian framework involves quantifying pathway travel times and the hydrodynamic control of retention, and both these quantities strongly depend on heterogeneity of the fracture network at different scales. In this contribution, we present recent analysis of flow and transport considering fracture networks with single-fracture heterogeneity described by different multivariate normal distributions. A coherent triad of fields with identical correlation length and variance are created but which greatly differ in structure, corresponding to textures with well-connected low, medium and high permeability structures. Through numerical modelling of multiple scales in a stochastic setting we quantify the relative impact of texture type and correlation length against network topological measures, and identify key thresholds for cases where flow dispersion is controlled by single-fracture heterogeneity versus network-scale heterogeneity. This is achieved by using a recently developed novel numerical discrete fracture network model. Furthermore, we highlight enhanced flow channelling for cases where correlation structure continues across
Geological discrete fracture network model for the Olkiluoto site, Eurajoki, Finland. Version 2.0
International Nuclear Information System (INIS)
Fox, A.; Forchhammer, K.; Pettersson, A.; La Pointe, P.; Lim, D-H.
2012-06-01
This report describes the methods, analyses, and conclusions of the modeling team in the production of the 2010 revision to the geological discrete fracture network (DFN) model for the Olkiluoto Site in Finland. The geological DFN is a statistical model for stochastically simulating rock fractures and minor faults at a scale ranging from approximately 0.05 m to approximately 565m; deformation zones are expressly excluded from the DFN model. The DFN model is presented as a series of tables summarizing probability distributions for several parameters necessary for fracture modeling: fracture orientation, fracture size, fracture intensity, and associated spatial constraints. The geological DFN is built from data collected during site characterization (SC) activities at Olkiluoto, which is selected to function as a final deep geological repository for spent fuel and nuclear waste from the Finnish nuclear power program. Data used in the DFN analyses include fracture maps from surface outcrops and trenches, geological and structural data from cored drillholes, and fracture information collected during the construction of the main tunnels and shafts at the ONKALO laboratory. Unlike the initial geological DFN, which was focused on the vicinity of the ONKALO tunnel, the 2010 revisions present a model parameterization for the entire island. Fracture domains are based on the tectonic subdivisions at the site (northern, central, and southern tectonic units) presented in the Geological Site Model (GSM), and are further subdivided along the intersection of major brittle-ductile zones. The rock volume at Olkiluoto is dominated by three distinct fracture sets: subhorizontally-dipping fractures striking north-northeast and dipping to the east that is subparallel to the mean bedrock foliation direction, a subvertically-dipping fracture set striking roughly north-south, and a subvertically-dipping fracture set striking approximately east-west. The subhorizontally-dipping fractures
Geological discrete fracture network model for the Olkiluoto site, Eurajoki, Finland. Version 2.0
Energy Technology Data Exchange (ETDEWEB)
Fox, A.; Forchhammer, K.; Pettersson, A. [Golder Associates AB, Stockholm (Sweden); La Pointe, P.; Lim, D-H. [Golder Associates Inc. (Finland)
2012-06-15
This report describes the methods, analyses, and conclusions of the modeling team in the production of the 2010 revision to the geological discrete fracture network (DFN) model for the Olkiluoto Site in Finland. The geological DFN is a statistical model for stochastically simulating rock fractures and minor faults at a scale ranging from approximately 0.05 m to approximately 565m; deformation zones are expressly excluded from the DFN model. The DFN model is presented as a series of tables summarizing probability distributions for several parameters necessary for fracture modeling: fracture orientation, fracture size, fracture intensity, and associated spatial constraints. The geological DFN is built from data collected during site characterization (SC) activities at Olkiluoto, which is selected to function as a final deep geological repository for spent fuel and nuclear waste from the Finnish nuclear power program. Data used in the DFN analyses include fracture maps from surface outcrops and trenches, geological and structural data from cored drillholes, and fracture information collected during the construction of the main tunnels and shafts at the ONKALO laboratory. Unlike the initial geological DFN, which was focused on the vicinity of the ONKALO tunnel, the 2010 revisions present a model parameterization for the entire island. Fracture domains are based on the tectonic subdivisions at the site (northern, central, and southern tectonic units) presented in the Geological Site Model (GSM), and are further subdivided along the intersection of major brittle-ductile zones. The rock volume at Olkiluoto is dominated by three distinct fracture sets: subhorizontally-dipping fractures striking north-northeast and dipping to the east that is subparallel to the mean bedrock foliation direction, a subvertically-dipping fracture set striking roughly north-south, and a subvertically-dipping fracture set striking approximately east-west. The subhorizontally-dipping fractures
Discrete Modeling of Early-Life Thermal Fracture in Ceramic Nuclear Fuel
Energy Technology Data Exchange (ETDEWEB)
Spencer, Benjamin W. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Huang, Hai [Idaho National Lab. (INL), Idaho Falls, ID (United States); Dolbow, John E. [Duke Univ., Durham, NC (United States); Hales, Jason D. [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2015-03-01
Fracturing of ceramic fuel pellets heavily influences performance of light water reactor (LWR) fuel. Early in the life of fuel, starting with the initial power ramp, large thermal gradients cause high tensile hoop and axial stresses in the outer region of the fuel pellets, resulting in the formation of radial and axial cracks. Circumferential cracks form due to thermal gradients that occur when the power is ramped down. These thermal cracks cause the fuel to expand radially, closing the pellet/cladding gap and enhancing the thermal conductance across that gap, while decreasing the effective conductivity of the fuel in directions normal to the cracking. At lower length scales, formation of microcracks is an important contributor to the decrease in bulk thermal conductivity that occurs over the life of the fuel as the burnup increases. Because of the important effects that fracture has on fuel performance, a realistic, physically based fracture modeling capability is essential to predict fuel behavior in a wide variety of normal and abnormal conditions. Modeling fracture within the context of the finite element method, which is based on continuous interpolations of solution variables, has always been challenging because fracture is an inherently discontinuous phenomenon. Work is underway at Idaho National Laboratory to apply two modeling techniques model fracture as a discrete displacement discontinuity to nuclear fuel: The extended finite element method (XFEM), and discrete element method (DEM). XFEM is based on the standard finite element method, but with enhancements to represent discontinuous behavior. DEM represents a solid as a network of particles connected by bonds, which can arbitrarily fail if a fracture criterion is reached. This paper presents initial results applying the aforementioned techniques to model fuel fracturing. This work has initially focused on early life behavior of ceramic LWR fuel. A coupled thermal-mechanical XFEM method that includes
International Nuclear Information System (INIS)
Darcel, C.; Davy, P.; Le Goc, R.; Dreuzy, J.R. de; Bour, O.
2009-11-01
the other, addresses the issue of the nature of the transition. We develop a new 'mechanistic' model that could help in modeling why and where this transition can occur. The transition between both regimes would occur for a fracture length of 1-10 m and even at a smaller scale for the few outcrops that follow the self-similar density model. A consequence for the disposal issue is that the model that is likely to apply in the 'blind' scale window between 10-100 m is the self-similar model as it is defined for large-scale lineaments. The self-similar model, as it is measured for some outcrops and most lineament maps, is definitely worth being investigated as a reference for scales above 1-10 m. In the rest of the report, we develop a methodology for incorporating uncertainty and variability into the DFN modeling. Fracturing properties arise from complex processes which produce an intrinsic variability; characterizing this variability as an admissible variation of model parameter or as the division of the site into subdomains with distinct DFN models is a critical point of the modeling effort. Moreover, the DFN model encompasses a part of uncertainty, due to data inherent uncertainties and sampling limits. Both effects must be quantified and incorporated into the DFN site model definition process. In that context, all available borehole data including recording of fracture intercept positions, pole orientation and relative uncertainties are used as the basis for the methodological development and further site model assessment. An elementary dataset contains a set of discrete fracture intercepts from which a parent orientation/density distribution can be computed. The elementary bricks of the site, from which these initial parent density distributions are computed, rely on the former Single Hole Interpretation division of the boreholes into sections whose local boundaries are expected to reflect - locally - geology and fracturing properties main characteristics. From that
Discrete Fracture Network Models for Risk Assessment of Carbon Sequestration in Coal
Energy Technology Data Exchange (ETDEWEB)
Jack Pashin; Guohai Jin; Chunmiao Zheng; Song Chen; Marcella McIntyre
2008-07-01
A software package called DFNModeler has been developed to assess the potential risks associated with carbon sequestration in coal. Natural fractures provide the principal conduits for fluid flow in coal-bearing strata, and these fractures present the most tangible risks for the leakage of injected carbon dioxide. The objectives of this study were to develop discrete fracture network (DFN) modeling tools for risk assessment and to use these tools to assess risks in the Black Warrior Basin of Alabama, where coal-bearing strata have high potential for carbon sequestration and enhanced coalbed methane recovery. DFNModeler provides a user-friendly interface for the construction, visualization, and analysis of DFN models. DFNModeler employs an OpenGL graphics engine that enables real-time manipulation of DFN models. Analytical capabilities in DFNModeler include display of structural and hydrologic parameters, compartmentalization analysis, and fluid pathways analysis. DFN models can be exported to third-party software packages for flow modeling. DFN models were constructed to simulate fracturing in coal-bearing strata of the upper Pottsville Formation in the Black Warrior Basin. Outcrops and wireline cores were used to characterize fracture systems, which include joint systems, cleat systems, and fault-related shear fractures. DFN models were constructed to simulate jointing, cleating, faulting, and hydraulic fracturing. Analysis of DFN models indicates that strata-bound jointing compartmentalizes the Pottsville hydrologic system and helps protect shallow aquifers from injection operations at reservoir depth. Analysis of fault zones, however, suggests that faulting can facilitate cross-formational flow. For this reason, faults should be avoided when siting injection wells. DFN-based flow models constructed in TOUGH2 indicate that fracture aperture and connectivity are critical variables affecting the leakage of injected CO{sub 2} from coal. Highly transmissive joints
Energy Technology Data Exchange (ETDEWEB)
Darcel, C. (Itasca Consultants SAS (France)); Davy, P.; Le Goc, R.; Dreuzy, J.R. de; Bour, O. (Geosciences Rennes, UMR 6118 CNRS, Univ. def Rennes, Rennes (France))
2009-11-15
the lineament scale (k{sub t} = 2) on the other, addresses the issue of the nature of the transition. We develop a new 'mechanistic' model that could help in modeling why and where this transition can occur. The transition between both regimes would occur for a fracture length of 1-10 m and even at a smaller scale for the few outcrops that follow the self-similar density model. A consequence for the disposal issue is that the model that is likely to apply in the 'blind' scale window between 10-100 m is the self-similar model as it is defined for large-scale lineaments. The self-similar model, as it is measured for some outcrops and most lineament maps, is definitely worth being investigated as a reference for scales above 1-10 m. In the rest of the report, we develop a methodology for incorporating uncertainty and variability into the DFN modeling. Fracturing properties arise from complex processes which produce an intrinsic variability; characterizing this variability as an admissible variation of model parameter or as the division of the site into subdomains with distinct DFN models is a critical point of the modeling effort. Moreover, the DFN model encompasses a part of uncertainty, due to data inherent uncertainties and sampling limits. Both effects must be quantified and incorporated into the DFN site model definition process. In that context, all available borehole data including recording of fracture intercept positions, pole orientation and relative uncertainties are used as the basis for the methodological development and further site model assessment. An elementary dataset contains a set of discrete fracture intercepts from which a parent orientation/density distribution can be computed. The elementary bricks of the site, from which these initial parent density distributions are computed, rely on the former Single Hole Interpretation division of the boreholes into sections whose local boundaries are expected to reflect - locally - geology
Discrete fracture network modelling of a KBS-3H repository at Olkiluoto
Energy Technology Data Exchange (ETDEWEB)
Lanyon, G.W. (Fracture Systems Ltd, St Ives (United Kingdom)); Marschall, P. (Nagra, Wettingen (Switzerland))
2008-06-15
This report presents Discrete Fracture Network (DFN) models of groundwater flow around a KBS-3H repository situated at Olkiluoto. The study was performed in support of the Safety Case for the KBS-3H Concept, being jointly studied by SKB and Posiva. As part of the preliminary assessment of long term safety of a KBS-3H repository, a Process Report and an Evolution Report (evolution of the disposal system from the emplacement of the first canister to the long term) are being produced. In the course of the task definition the project team identified the need for complementary modelling studies aimed at increasing insight into the hydrodynamic evolution of the disposal system after waste emplacement. In particular, the following issues were identified as requiring input from hydrodynamic models: Probability of high inflow points which may cause buffer erosion. Time transients of inflows after construction of deposition drifts. Interference between deposition drifts and transport tunnels. The DFN models represent the fault and fracture system in the planned repository volume at Olkiluoto. In particular, they represent the hydro geologically significant features. The types of hydrogeological features included in the models are: Major Fracture Zones (MFZs). Local Fracture Zones (LFZs) and associated water conducting features (LFZ-WCFs). Water Conducting Features in the background rock (BR-WCFs). These feature types are derived from the current geological and hydrogeological interpretations developed by Posiva. Several model variants were developed during the study and these variants were used for geometric simulations of the WCF network around the deposition drifts. A simple layout adaptation scheme has been applied to the network models to derive statistics for performance measures relating to the deposition drifts, compartments, plugs and super-containers. A single fracture transient flow model was developed to provide insight to transient flow behaviour around
Discrete fracture network modelling of a KBS-3H repository at Olkiluoto
International Nuclear Information System (INIS)
Lanyon, G.W.; Marschall, P.
2008-06-01
This report presents Discrete Fracture Network (DFN) models of groundwater flow around a KBS-3H repository situated at Olkiluoto. The study was performed in support of the Safety Case for the KBS-3H Concept, being jointly studied by SKB and Posiva. As part of the preliminary assessment of long term safety of a KBS-3H repository, a Process Report and an Evolution Report (evolution of the disposal system from the emplacement of the first canister to the long term) are being produced. In the course of the task definition the project team identified the need for complementary modelling studies aimed at increasing insight into the hydrodynamic evolution of the disposal system after waste emplacement. In particular, the following issues were identified as requiring input from hydrodynamic models: Probability of high inflow points which may cause buffer erosion. Time transients of inflows after construction of deposition drifts. Interference between deposition drifts and transport tunnels. The DFN models represent the fault and fracture system in the planned repository volume at Olkiluoto. In particular, they represent the hydro geologically significant features. The types of hydrogeological features included in the models are: Major Fracture Zones (MFZs). Local Fracture Zones (LFZs) and associated water conducting features (LFZ-WCFs). Water Conducting Features in the background rock (BR-WCFs). These feature types are derived from the current geological and hydrogeological interpretations developed by Posiva. Several model variants were developed during the study and these variants were used for geometric simulations of the WCF network around the deposition drifts. A simple layout adaptation scheme has been applied to the network models to derive statistics for performance measures relating to the deposition drifts, compartments, plugs and super-containers. A single fracture transient flow model was developed to provide insight to transient flow behaviour around
Directory of Open Access Journals (Sweden)
Arthur Coré
2017-01-01
Full Text Available This paper deals with the characterization and the numerical modelling of the collapse of composite hollow spherical structures developed to absorb energy during high velocity impacts. The structure is composed of hollow spheres (ϕ=2–30 mm made of epoxy resin and mineral powder. First of all, quasi-static and dynamic (v=5 mm·min−1 to v=2 m·s−1 compression tests are conducted at room temperature on a single sphere to study energy dissipation mechanisms. Fracture of the material appears to be predominant. A numerical model based on the discrete element method is investigated to simulate the single sphere crushing. The stress-strain-time relationship of the material based on the Ree-Eyring law is numerically implemented. The DEM modelling takes naturally into account the dynamic fracture and the crack path computed is close to the one observed experimentally in uniaxial compression. Eventually, high velocity impacts (v>100 m·s−1 of a hollow sphere on a rigid surface are conducted with an air cannon. The numerical results are in good agreement with the experimental data and demonstrate the ability of the present model to correctly describe the mechanical behavior of brittle materials at high strain rate.
Statistical geological discrete fracture network model. Forsmark modelling stage 2.2
International Nuclear Information System (INIS)
Fox, Aaron; La Pointe, Paul; Simeonov, Assen; Hermanson, Jan; Oehman, Johan
2007-11-01
The Swedish Nuclear Fuel and Waste Management Company (SKB) is performing site characterization at two different locations, Forsmark and Laxemar, in order to locate a site for a final geologic repository for spent nuclear fuel. The program is built upon the development of Site Descriptive Models (SDMs) at specific timed data freezes. Each SDM is formed from discipline-specific reports from across the scientific spectrum. This report describes the methods, analyses, and conclusions of the geological modeling team with respect to a geological and statistical model of fractures and minor deformation zones (henceforth referred to as the geological DFN), version 2.2, at the Forsmark site. The geological DFN builds upon the work of other geological modelers, including the deformation zone (DZ), rock domain (RD), and fracture domain (FD) models. The geological DFN is a statistical model for stochastically simulating rock fractures and minor deformation zones as a scale of less than 1,000 m (the lower cut-off of the DZ models). The geological DFN is valid within four specific fracture domains inside the local model region, and encompassing the candidate volume at Forsmark: FFM01, FFM02, FFM03, and FFM06. The models are build using data from detailed surface outcrop maps and the cored borehole record at Forsmark. The conceptual model for the Forsmark 2.2 geological revolves around the concept of orientation sets; for each fracture domain, other model parameters such as size and intensity are tied to the orientation sets. Two classes of orientation sets were described; Global sets, which are encountered everywhere in the model region, and Local sets, which represent highly localized stress environments. Orientation sets were described in terms of their general cardinal direction (NE, NW, etc). Two alternatives are presented for fracture size modeling: - the tectonic continuum approach (TCM, TCMF) described by coupled size-intensity scaling following power law distributions
Statistical geological discrete fracture network model. Forsmark modelling stage 2.2
Energy Technology Data Exchange (ETDEWEB)
Fox, Aaron; La Pointe, Paul [Golder Associates Inc (United States); Simeonov, Assen [Swedish Nuclear Fuel and Waste Management Co., Stockholm (Sweden); Hermanson, Jan; Oehman, Johan [Golder Associates AB, Stockholm (Sweden)
2007-11-15
The Swedish Nuclear Fuel and Waste Management Company (SKB) is performing site characterization at two different locations, Forsmark and Laxemar, in order to locate a site for a final geologic repository for spent nuclear fuel. The program is built upon the development of Site Descriptive Models (SDMs) at specific timed data freezes. Each SDM is formed from discipline-specific reports from across the scientific spectrum. This report describes the methods, analyses, and conclusions of the geological modeling team with respect to a geological and statistical model of fractures and minor deformation zones (henceforth referred to as the geological DFN), version 2.2, at the Forsmark site. The geological DFN builds upon the work of other geological modelers, including the deformation zone (DZ), rock domain (RD), and fracture domain (FD) models. The geological DFN is a statistical model for stochastically simulating rock fractures and minor deformation zones as a scale of less than 1,000 m (the lower cut-off of the DZ models). The geological DFN is valid within four specific fracture domains inside the local model region, and encompassing the candidate volume at Forsmark: FFM01, FFM02, FFM03, and FFM06. The models are build using data from detailed surface outcrop maps and the cored borehole record at Forsmark. The conceptual model for the Forsmark 2.2 geological revolves around the concept of orientation sets; for each fracture domain, other model parameters such as size and intensity are tied to the orientation sets. Two classes of orientation sets were described; Global sets, which are encountered everywhere in the model region, and Local sets, which represent highly localized stress environments. Orientation sets were described in terms of their general cardinal direction (NE, NW, etc). Two alternatives are presented for fracture size modeling: - the tectonic continuum approach (TCM, TCMF) described by coupled size-intensity scaling following power law distributions
International Nuclear Information System (INIS)
Sun, Zhi-xue; Zhang, Xu; Xu, Yi; Yao, Jun; Wang, Hao-xuan; Lv, Shuhuan; Sun, Zhi-lei; Huang, Yong; Cai, Ming-yu; Huang, Xiaoxue
2017-01-01
The Enhanced Geothermal System (EGS) creates an artificial geothermal reservoir by hydraulic fracturing which allows heat transmission through the fractures by the circulating fluids as they extract heat from Hot Dry Rock (HDR). The technique involves complex thermal–hydraulic–mechanical (THM) coupling process. A numerical approach is presented in this paper to simulate and analyze the heat extraction process in EGS. The reservoir is regarded as fractured porous media consisting of rock matrix blocks and discrete fracture networks. Based on thermal non-equilibrium theory, the mathematical model of THM coupling process in fractured rock mass is used. The proposed model is validated by comparing it with several analytical solutions. An EGS case from Cooper Basin, Australia is simulated with 2D stochastically generated fracture model to study the characteristics of fluid flow, heat transfer and mechanical response in geothermal reservoir. The main parameters controlling the outlet temperature of EGS are also studied by sensitivity analysis. The results shows the significance of taking into account the THM coupling effects when investigating the efficiency and performance of EGS. - Highlights: • EGS reservoir comprising discrete fracture networks and matrix rock is modeled. • A THM coupling model is proposed for simulating the heat extraction in EGS. • The numerical model is validated by comparing with several analytical solutions. • A case study is presented for understanding the main characteristics of EGS. • The THM coupling effects are shown to be significant factors to EGS's running performance.
Qin, Guan
2010-01-01
Naturally-fractured carbonate karst reservoirs are characterized by various-sized solution caves that are connected via fracture networks at multiple scales. These complex geologic features can not be fully resolved in reservoir simulations due to the underlying uncertainty in geologic models and the large computational resource requirement. They also bring in multiple flow physics which adds to the modeling difficulties. It is thus necessary to develop a method to accurately represent the effect of caves, fractures and their interconnectivities in coarse-scale simulation models. In this paper, we present a procedure based on our previously proposed Stokes-Brinkman model (SPE 125593) and the discrete fracture network method for accurate and efficient upscaling of naturally fractured carbonate karst reservoirs.
Statistical analysis of fracture data, adapted for modelling Discrete Fracture Networks-Version 2
Energy Technology Data Exchange (ETDEWEB)
Munier, Raymond
2004-04-01
The report describes the parameters which are necessary for DFN modelling, the way in which they can be extracted from the data base acquired during site investigations, and their assignment to geometrical objects in the geological model. The purpose here is to present a methodology for use in SKB modelling projects. Though the methodology is deliberately tuned to facilitate subsequent DFN modelling with other tools, some of the recommendations presented here are applicable to other aspects of geo-modelling as well. For instance, we here recommend a nomenclature to be used within SKB modelling projects, which are truly multidisciplinary, to ease communications between scientific disciplines and avoid misunderstanding of common concepts. This report originally occurred as an appendix to a strategy report for geological modelling (SKB-R--03-07). Strategy reports were intended to be successively updated to include experience gained during site investigations and site modelling. Rather than updating the entire strategy report, we choose to present the update of the appendix as a stand-alone document. This document thus replaces Appendix A2 in SKB-R--03-07. In short, the update consists of the following: The target audience has been broadened and as a consequence thereof, the purpose of the document. Correction of errors found in various formulae. All expressions have been rewritten. Inclusion of more worked examples in each section. A new section describing area normalisation. A new section on spatial correlation. A new section describing anisotropy. A new chapter describing the expected output from DFN modelling, within SKB projects.
Statistical analysis of fracture data, adapted for modelling Discrete Fracture Networks-Version 2
International Nuclear Information System (INIS)
Munier, Raymond
2004-04-01
The report describes the parameters which are necessary for DFN modelling, the way in which they can be extracted from the data base acquired during site investigations, and their assignment to geometrical objects in the geological model. The purpose here is to present a methodology for use in SKB modelling projects. Though the methodology is deliberately tuned to facilitate subsequent DFN modelling with other tools, some of the recommendations presented here are applicable to other aspects of geo-modelling as well. For instance, we here recommend a nomenclature to be used within SKB modelling projects, which are truly multidisciplinary, to ease communications between scientific disciplines and avoid misunderstanding of common concepts. This report originally occurred as an appendix to a strategy report for geological modelling (SKB-R--03-07). Strategy reports were intended to be successively updated to include experience gained during site investigations and site modelling. Rather than updating the entire strategy report, we choose to present the update of the appendix as a stand-alone document. This document thus replaces Appendix A2 in SKB-R--03-07. In short, the update consists of the following: The target audience has been broadened and as a consequence thereof, the purpose of the document. Correction of errors found in various formulae. All expressions have been rewritten. Inclusion of more worked examples in each section. A new section describing area normalisation. A new section on spatial correlation. A new section describing anisotropy. A new chapter describing the expected output from DFN modelling, within SKB projects
Directory of Open Access Journals (Sweden)
Yongliang Wang
2018-01-01
Full Text Available Hydrofracturing technology of perforated horizontal well has been widely used to stimulate the tight hydrocarbon reservoirs for gas production. To predict the hydraulic fracture propagation, the microseismicity can be used to infer hydraulic fractures state; by the effective numerical methods, microseismic events can be addressed from changes of the computed stresses. In numerical models, due to the challenges in accurately representing the complex structure of naturally fractured reservoir, the interaction between hydraulic and pre-existing fractures has not yet been considered and handled satisfactorily. To overcome these challenges, the adaptive finite element-discrete element method is used to refine mesh, effectively identify the fractures propagation, and investigate microseismic modelling. Numerical models are composed of hydraulic fractures, pre-existing fractures, and microscale pores, and the seepage analysis based on the Darcy’s law is used to determine fluid flow; then moment tensors in microseismicity are computed based on the computed stresses. Unfractured and naturally fractured models are compared to assess the influences of pre-existing fractures on hydrofracturing. The damaged and contact slip events were detected by the magnitudes, B-values, Hudson source type plots, and focal spheres.
Pyatkov, A. A.; Kosyakov, V. P.; Rodionov, S. P.; Botalov, A. Y.
2018-03-01
In this work was the study of the processes of isothermal and non-isothermal flow of high viscosity oil in a fractured-porous reservoir. The numerical experiment was done using our own reservoir simulator with the possibility of modeling of fluid motion in conditions of non-isothermal processes and long fractures in the formation.
A discrete element model for damage and fracture of geomaterials under fatigue loading
Gao, Xiaofeng; Koval, Georg; Chazallon, Cyrille
2017-06-01
Failure processes in geomaterials (concrete, asphalt concrete, masonry, etc.) under fatigue loading (repeated moving loads, cycles of temperature, etc.) are responsible for most of the dysfunctions in pavements, brick structures, etc. In the beginning of the lifetime of a structure, the material presents only inner defects (micro cracks, voids, etc.). Due to the effect of the cyclic loading, these small defects tend to grow in size and quantity which damage the material, reducing its stiffness. With a relatively high number of cycles, these growing micro cracks become large cracks, which characterizes the fracture behavior. From a theoretical point of view, both mechanisms are treated differently. Fracture is usually described locally, with the propagation of cracks defined by the energy release rate at the crack tip; damage is usually associated to non-local approaches. In the present work, damage and fracture mechanics are combined in a local discrete element approach.
El-Amin, Mohamed
2017-11-23
In this article, we consider a two-phase immiscible incompressible flow including nanoparticles transport in fractured heterogeneous porous media. The system of the governing equations consists of water saturation, Darcy’s law, nanoparticles concentration in water, deposited nanoparticles concentration on the pore-wall, and entrapped nanoparticles concentration in the pore-throat, as well as, porosity and permeability variation due to the nanoparticles deposition/entrapment on/in the pores. The discrete-fracture model (DFM) is used to describe the flow and transport in fractured porous media. Moreover, multiscale time-splitting strategy has been employed to manage different time-step sizes for different physics, such as saturation, concentration, etc. Numerical examples are provided to demonstrate the efficiency of the proposed multi-scale time splitting approach.
El-Amin, Mohamed; Kou, Jisheng; Sun, Shuyu
2017-01-01
In this article, we consider a two-phase immiscible incompressible flow including nanoparticles transport in fractured heterogeneous porous media. The system of the governing equations consists of water saturation, Darcy’s law, nanoparticles concentration in water, deposited nanoparticles concentration on the pore-wall, and entrapped nanoparticles concentration in the pore-throat, as well as, porosity and permeability variation due to the nanoparticles deposition/entrapment on/in the pores. The discrete-fracture model (DFM) is used to describe the flow and transport in fractured porous media. Moreover, multiscale time-splitting strategy has been employed to manage different time-step sizes for different physics, such as saturation, concentration, etc. Numerical examples are provided to demonstrate the efficiency of the proposed multi-scale time splitting approach.
Sensitivity analysis of a discrete fracture network model for performance assessment of Aberg
International Nuclear Information System (INIS)
Outters, N.; Shuttle, D.
2000-12-01
This report presents a sensitivity analysis of pathway simulations in a DFN model. The DFN model consists of two sets of stochastic fractures at different scales and the canister locations of a hypothetical repository layout. The hydrogeological base case model is defined by constant head boundary conditions on the edges of a 2000 x 2000 x 1000 m 3 block. The pathway analysis carried out by the program PAWorks provides pathway parameters (pathway length, pathway width, transport aperture, reactive surface area, pathway transmissivity), canister statistics (average number of pathways per canister, percentage of canister locations with pathways) and visualisation of pathways. The project provided the following results from the alternative cases: Case 1: Model with a 100 m thick fracture network at the repository scale instead of 50 m in the base case. The model is little sensitive to the increase of the thickness of the local fracture network. Case 2: Model including fracture networks where the mean size and size standard deviation is twice the ones used in the base case. The travel times to the biosphere is slightly shortened by increasing the fracture diameter. Case 3: Two models with alternative hydraulic boundary conditions: two different flux boundary conditions are tested instead of head boundary conditions in the base case. The advective travel time is shortened by changing the boundary conditions in both alternative cases; in some cases it is reduced to less than a year. Case 4: Study of alternative pathway search algorithms: the pathway search is here based on minimum travel time. The pathway search algorithm of PAWorks based on minimum travel time gives much more optimistic results than the base case where the maximum flow rate was used. The mean travel time is about 5000 years. Due to editorial reasons only a subset of all this information is treated in this report
International Nuclear Information System (INIS)
Bazr-Afkan, S.
2012-01-01
To simulate fluid flow in Naturally Fractured Reservoirs (NFRs), a new Descrete Fracture and Matrix (DFM) simulation technique is developed as a physically more realistic alternative to the dual continuum approach. This Finite-Element Centered Finite-Volume method (FECFVM) has the advantage over earlier FECFVM approaches that it honors saturation dicontinuities that can arise at material interfaces from the interplay of viscous, capillary and gravitational forces. By contrast with an earlier embedded-discontinuity DFEFVM method, the FECFVM achieves this without introducing additional degrees of freedom. It also allows to simulate capillary- and other fracture-matrix exchange processes using a lower dimensional representation of fractures, simplifying model construction and unstructured meshing as well as speeding up computations. A further step-up is obtained by solving the two-phase fluid-flow and saturation transport equations only on 'active elements'. This also diminishes round-off and truncation errors, reducing numerical diffusion during the solution of the transport equation. The FECFVM is verified by comparing IMPES operator-splitting sequential solutions with analytical ones, as well as benchmarking it against commercial reservoir simulators on simple geometries that these can represent. This testing confirms that my 2D FECFVM implementation simulates gravitational segregation, capillary redistribution, capillary barriers, and combinations thereof physically realistically, achieving (at least) first-order solution accuracy. Following this verification, the FECFVM is applied to study Gas-Oil Gravity Drainage (GOGD) process in cross-sectional models of layered NFRs. Here comparisons with dual continua simulations show that these do not capture a range of block-to-block effects, yielding over-optimistic drainage rates. Observations made on individual matrix blocks in the DFM simulations further reveal that their saturation evolution is at odds with the
Energy Technology Data Exchange (ETDEWEB)
Stafford, Paige L. [Univ. of Tennessee, Knoxville, TN (United States). Dept. of Geological Sciences
1996-05-01
Simulations of a tritium tracer experiment in fractured shale saprolite, conducted at the Oak Ridge National Laboratory, were performed using 1D and 2D equivalent porous medium (EPM) and discrete-fracture/matrix-diffusion (DFMD) models. The models successfully reproduced the general shape of the breakthrough curves in down-gradient monitoring wells which are characterized by rapid first arrival, a slow-moving center of mass, and a persistent ``tail`` of low concentration. In plan view, the plume shows a large degree of transverse spreading with the width almost as great as the length. EPM models were sensitive to dispersivity coefficient values which had to be large (relative to the 3.7m distance between the injection and monitoring wells) to fit the tail and transverse spreading. For example, to fit the tail a longitudinal dispersivity coefficient, α_{L}, of 0.8 meters for the 2D simulations was used. To fit the transverse spreading, a transverse dispersivity coefficient, α_{T}, of 0.8 to 0.08 meters was used indicating an α_{L}/α_{T} ratio between 10 and 1. Transverse spreading trends were also simulated using a 2D DFMD model using a few larger aperture fractures superimposed onto an EPM. Of the fracture networks studied, only those with truncated fractures caused transverse spreading. Simulated tritium levels in all of the cases were larger than observed values by a factor of approximately 100. Although this is partly due to input of too much tritium mass by the models it appears that dilution in the wells, which were not purged prior to sampling, is also a significant factor. The 1D and 2D EPM models were fitted to monitoring data from the first five years of the experiment and then used to predict future tritium concentrations.
International Nuclear Information System (INIS)
Stafford, P.L.
1996-05-01
Simulations of a tritium tracer experiment in fractured shale saprolite, conducted at the Oak Ridge National Laboratory, were performed using 1D and 2D equivalent porous medium (EPM) and discrete-fracture/matrix-diffusion (DFMD) models. The models successfully reproduced the general shape of the breakthrough curves in down-gradient monitoring wells which are characterized by rapid first arrival, a slow-moving center of mass, and a persistent ''tail'' of low concentration. In plan view, the plume shows a large degree of transverse spreading with the width almost as great as the length. EPM models were sensitive to dispersivity coefficient values which had to be large (relative to the 3.7m distance between the injection and monitoring wells) to fit the tail and transverse spreading. For example, to fit the tail a longitudinal dispersivity coefficient, α L , of 0.8 meters for the 2D simulations was used. To fit the transverse spreading, a transverse dispersivity coefficient, α T , of 0.8 to 0.08 meters was used indicating an α L /α T ratio between 10 and 1. Transverse spreading trends were also simulated using a 2D DFMD model using a few larger aperture fractures superimposed onto an EPM. Of the fracture networks studied, only those with truncated fractures caused transverse spreading. Simulated tritium levels in all of the cases were larger than observed values by a factor of approximately 100. Although this is partly due to input of too much tritium mass by the models it appears that dilution in the wells, which were not purged prior to sampling, is also a significant factor. The 1D and 2D EPM models were fitted to monitoring data from the first five years of the experiment and then used to predict future tritium concentrations
International Nuclear Information System (INIS)
Billaux, D.; Guerin, F.; Riss, J.; Dewiere, L.; Fillion, E.
2000-01-01
The sitting of a nuclear waste repository in a geological medium involves, among other aspects, predicting water inflows in the shafts and drifts, and evaluating possible geometries for the waste handling and storage galleries. In sedimentary host rocks, porous medium hydrogeology can be used easily to provide water inflow estimates, while geology will describe the geometry of the various layers, as well as the limited number of faults that may cut them. However, crystalline rocks such as the Vienne site, may be cut by numerous faults and fractures. To deal with such host rocks, we need new concepts - which have been under development during the last 15 years - in order to describe properly the spatial arrangement of discontinuities, its consequences in terms of the site hydrogeology, and in terms of the geometry of volumes available between faults for designing the underground storage cavities. A starting point is building a model of the fractures, using the statistical description of the investigated fracture field, including dips, dip directions, sizes, and intensities noted in boreholes or on outcrops. Such a model can then be used to compute flows. It is based on idealizing fractures as planar objects, often disks, with statistical geometrical properties inferred from available data. The model realism can be improved by conditioning the geometry on data, either directly observed - by fixing in space observed fractures - or indirectly inferred - by integrating the results of hydraulic, or even tracer tests. Discrete fracture models can then be used for many treatments, well beyond simple flow and transport computations. We illustrate this through two studies applied to the crystalline Vienne massif. First, image analysis techniques that were first developed for two dimensions, and have been recently extended to three dimensions, help with describing the space available between discontinuities, in order to define the sound rock blocks available for the waste
Preliminary - discrete fracture network modelling of tracer migration experiments at the SCV site
International Nuclear Information System (INIS)
Dershowitz, W.S.; Wallmann, P.; Geier, J.E.; Lee, G.
1991-09-01
This report describes a numerical modelling study of solute transport within the Site Characterization and Validation (SCV) block at the Stripa site. The study was carried out with the FracMan/MAFIC package, utilizing statistics from stages 3 and 4 of the Stripa phase 3 Site Characterization and Validation project. Simulations were carried out to calibrate fracture solute transport properties against observations in the first stage of saline injection radar experiments. These results were then used to predict the performance of planned tracer experiments, using both particle tracking network solute transport, and pathways analysis approaches. Simulations were also carried out to predict results of the second stage of saline injection radar experiments. (au) (34 refs.)
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Zhou, Jing [Idaho National Lab. (INL), Idaho Falls, ID (United States); Huang, Hai [Idaho National Lab. (INL), Idaho Falls, ID (United States); Mattson, Earl [Idaho National Lab. (INL), Idaho Falls, ID (United States); Wang, Herb F. [Univ. of Wisconsin, Madison, WI (United States); Haimson, Bezalel C. [Univ. of Wisconsin, Madison, WI (United States); Doe, Thomas W. [Golder Associates Inc., Redmond, VA (United States); Oldenburg, Curtis M. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Dobson, Patrick F. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2017-02-01
Aimed at supporting the design of hydraulic fracturing experiments at the kISMET site, ~1500 m below ground in a deep mine, we performed pre-experimental hydraulic fracturing simulations in order to estimate the breakdown pressure, propagation pressure, fracture geometry, and the magnitude of induced seismicity using a newly developed fully coupled three-dimensional (3D) network flow and quasi-static discrete element model (DEM). The quasi-static DEM model, which is constructed by Delaunay tessellation of the rock volume, considers rock fabric heterogeneities by using the “disordered” DEM mesh and adding random perturbations to the stiffness and tensile/shear strengths of individual DEM elements and the elastic beams between them. A conjugate 3D flow network based on the DEM lattice is constructed to calculate the fluid flow in both the fracture and porous matrix. One distinctive advantage of the model is that fracturing is naturally described by the breakage of elastic beams between DEM elements. It is also extremely convenient to introduce mechanical anisotropy into the model by simply assigning orientation-dependent tensile/shear strengths to the elastic beams. In this paper, the 3D hydraulic fracturing model was verified against the analytic solution for a penny-shaped crack model. We applied the model to simulate fracture propagation from a vertical open borehole based on initial estimates of rock mechanical properties and in-situ stress conditions. The breakdown pressure and propagation pressure are directly obtained from the simulation. In addition, the released elastic strain energies of individual fracturing events were calculated and used as a conservative estimate for the magnitudes of the potential induced seismic activities associated with fracturing. The comparisons between model predictions and experimental results are still ongoing.
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Fu, P; Johnson, S M; Hao, Y; Carrigan, C R
2011-01-18
The primary objective of our current research is to develop a computational test bed for evaluating borehole techniques to enhance fluid flow and heat transfer in enhanced geothermal systems (EGS). Simulating processes resulting in hydraulic fracturing and/or the remobilization of existing fractures, especially the interaction between propagating fractures and existing fractures, represents a critical goal of our project. To this end, we are continuing to develop a hydraulic fracturing simulation capability within the Livermore Distinct Element Code (LDEC), a combined FEM/DEM analysis code with explicit solid-fluid mechanics coupling. LDEC simulations start from an initial fracture distribution which can be stochastically generated or upscaled from the statistics of an actual fracture distribution. During the hydraulic stimulation process, LDEC tracks the propagation of fractures and other modifications to the fracture system. The output is transferred to the Non-isothermal Unsaturated Flow and Transport (NUFT) code to capture heat transfer and flow at the reservoir scale. This approach is intended to offer flexibility in the types of analyses we can perform, including evaluating the effects of different system heterogeneities on the heat extraction rate as well as seismicity associated with geothermal operations. This paper details the basic methodology of our approach. Two numerical examples showing the capability and effectiveness of our simulator are also presented.
Discrete fracture network code development
Energy Technology Data Exchange (ETDEWEB)
Dershowitz, W.; Doe, T.; Shuttle, D.; Eiben, T.; Fox, A.; Emsley, S.; Ahlstrom, E. [Golder Associates Inc., Redmond, Washington (United States)
1999-02-01
This report presents the results of fracture flow model development and application performed by Golder Associates Inc. during the fiscal year 1998. The primary objective of the Golder Associates work scope was to provide theoretical and modelling support to the JNC performance assessment effort in fiscal year 2000. In addition, Golder Associates provided technical support to JNC for the Aespoe project. Major efforts for performance assessment support included extensive flow and transport simulations, analysis of pathway simplification, research on excavation damage zone effects, software verification and cross-verification, and analysis of confidence bounds on Monte Carlo simulations. In addition, a Fickian diffusion algorithm was implemented for Laplace Transform Galerkin solute transport. Support for the Aespoe project included predictive modelling of sorbing tracer transport in the TRUE-1 rock block, analysis of 1 km geochemical transport pathways for Task 5', and data analysis and experimental design for the TRUE Block Scale experiment. Technical information about Golder Associates support to JNC is provided in the appendices to this report. (author)
DEFF Research Database (Denmark)
Bisdom, Kevin; Nick, Hamid; Bertotti, Giovanni
2017-01-01
stresssensitive fracture permeability and matrix flow to determine the full permeability tensor. The applicability of this workflow is illustrated using an outcropping carbonate pavement in the Potiguar basin in Brazil, from which 1082 fractures are digitised. The permeability tensor for a range of matrix...
Energy Technology Data Exchange (ETDEWEB)
Dershowitz, William S.; Einstein, Herbert H.; LaPoint, Paul R.; Eiben, Thorsten; Wadleigh, Eugene; Ivanova, Violeta
1998-12-01
This report summarizes research conducted for the Fractured Reservoir Discrete Feature Network Technologies Project. The five areas studied are development of hierarchical fracture models; fractured reservoir compartmentalization, block size, and tributary volume analysis; development and demonstration of fractured reservoir discrete feature data analysis tools; development of tools for data integration and reservoir simulation through application of discrete feature network technologies for tertiary oil production; quantitative evaluation of the economic value of this analysis approach.
Energy Technology Data Exchange (ETDEWEB)
Makedonska, Nataliia [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Kwicklis, Edward Michael [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Birdsell, Kay Hanson [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Harrod, Jeremy Ashcraft [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Karra, Satish [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-10-18
This progress report for fiscal year 2015 (FY15) describes the development of discrete fracture network (DFN) models for Pahute Mesa. DFN models will be used to upscale parameters for simulations of subsurface flow and transport in fractured media in Pahute Mesa. The research focuses on modeling of groundwater flow and contaminant transport using DFNs generated according to fracture characteristics observed in the Topopah Spring Aquifer (TSA) and the Lava Flow Aquifer (LFA). This work will improve the representation of radionuclide transport processes in large-scale, regulatory-focused models with a view to reduce pessimistic bounding approximations and provide more realistic contaminant boundary calculations that can be used to describe the future extent of contaminated groundwater. Our goal is to refine a modeling approach that can translate parameters to larger-scale models that account for local-scale flow and transport processes, which tend to attenuate migration.
International Nuclear Information System (INIS)
Normani, S.D.; Sykes, J.F.
2011-01-01
A high resolution three-dimensional sub-regional scale (104 km 2 ) density-dependent, discretely fractured groundwater flow model with hydro-mechanical coupling and pseudo-permafrost was developed from a larger 5734 km 2 regional-scale groundwater flow model of a Canadian Shield setting. The objective of the work is to determine the sensitivity of modelled groundwater system evolution to the hydro-mechanical parameters. The discrete fracture dual continuum numerical model FRAC3DVS-OPG was used for all simulations. A discrete fracture network model delineated from surface features was superimposed onto an approximate 790 000 element domain mesh with approximately 850 000 nodes. Orthogonal fracture faces (between adjacent finite element grid blocks) were used to best represent the irregular discrete fracture zone network. Interconnectivity of the permeable fracture zones is an important pathway for the possible migration and subsequent reduction in groundwater and contaminant residence times. The crystalline rock matrix between these structural discontinuities was assigned mechanical and flow properties characteristic of those reported for the Canadian Shield. The variation of total dissolved solids with depth was assigned using literature data for the Canadian Shield. Performance measures for the sensitivity analysis include equivalent freshwater heads, environmental heads, linear velocities, and depth of penetration by conservative non-decaying tracers released at the surface. A 121 000 year North American continental scale paleo-climate simulation was applied to the domain with ice-sheet histories estimated by the University of Toronto Glacial Systems Model (UofT GSM). Hydro-mechanical coupling between the rock matrix and the pore fluid, due to the ice sheet normal stress, was included in the simulations. The flow model included the influence of vertical strain and assumed that areal loads were homogeneous. Permafrost depth was applied as a permeability reduction
Quantifying Discrete Fracture Network Connectivity in Hydraulic Fracturing Stimulation
Urbancic, T.; Ardakani, E. P.; Baig, A.
2017-12-01
Hydraulic fracture stimulations generally result in microseismicity that is associated with the activation or extension of pre-existing microfractures and discontinuities. Microseismic events acquired under 3D downhole sensor coverage provide accurate event locations outlining hydraulic fracture growth. Combined with source characteristics, these events provide a high quality input for seismic moment tensor inversion and eventually constructing the representative discrete fracture network (DFN). In this study, we investigate the strain and stress state, identified fracture orientation, and DFN connectivity and performance for example stages in a multistage perf and plug completion in a North American shale play. We use topology, the familiar concept in many areas of structural geology, to further describe the relationships between the activated fractures and their effectiveness in enhancing permeability. We explore how local perturbations of stress state lead to the activation of different fractures sets and how that effects the DFN interaction and complexity. In particular, we observe that a more heterogeneous stress state shows a higher percentage of sub-horizontal fractures or bedding plane slips. Based on topology, the fractures are evenly distributed from the injection point, with decreasing numbers of connections by distance. The dimensionless measure of connection per branch and connection per line are used for quantifying the DFN connectivity. In order to connect the concept of connectivity back to productive volume and stimulation efficiency, the connectivity is compared with the character of deformation in the reservoir as deduced from the collective behavior of microseismicity using robustly determined source parameters.
Discrete fracture network for the Forsmark site
Energy Technology Data Exchange (ETDEWEB)
Darcel, C. [Itasca Consultants, Ecully (France); Davy, P.; Bour, O.; Dreuzy, J.R. de [Geosciences, Rennes (France)
2006-08-15
In this report, we aim at defining a self-consistent method for analyzing the fracture patterns from boreholes, outcrops and lineaments. The objective was both to point out some variations in the fracture network parameters, and to define the global scaling fracture models that can encompass all the constraints brought by the different datasets. Although a full description of the DFN model variability is obviously fundamental for the future, we have put emphasis on the determination of mean parameters. The main parameters of the disc-shaped DFN model are the fracture size, orientations and spatial density distribution. The scaling model is defined as an extrapolation of existing i) observations at specific scales and ii) local fitting models to the whole range of scales. The range of possible models is restricted to the power-law scaling models. During the project we have put emphasize on the definition of the theory and methodology necessary to assess a sound comparison between data taken at different scales, with different techniques. Both 'local' and 'global' models have been investigated. Local models are linked exactly to the dataset they represent. Then, the global DFN models arise from the association of local models, different scales and different sample support shapes. Discrepancies between local and global model illustrate the variability associated to the DFN models. We define two possible Global Scaling Models (GSM). The first one is consistent with the scaling measured in the outcrops (Model A). Its scaling exponent is a{sub 3d}=3.5 (eq. to k{sub r}=2.5); it overestimates the fracture densities observed in the lineament maps. The second one assumes that both lineaments and outcrops belong to the same distribution model (Model B), which entails a scaling exponent a{sub 3d}=3.9 (eq. to k{sub r}=2.9). Both models have been tested by looking for the best consistency in the fracture density-dip relationships, between boreholes data at
Discrete fracture network for the Forsmark site
International Nuclear Information System (INIS)
Darcel, C.; Davy, P.; Bour, O.; Dreuzy, J.R. de
2006-08-01
In this report, we aim at defining a self-consistent method for analyzing the fracture patterns from boreholes, outcrops and lineaments. The objective was both to point out some variations in the fracture network parameters, and to define the global scaling fracture models that can encompass all the constraints brought by the different datasets. Although a full description of the DFN model variability is obviously fundamental for the future, we have put emphasis on the determination of mean parameters. The main parameters of the disc-shaped DFN model are the fracture size, orientations and spatial density distribution. The scaling model is defined as an extrapolation of existing i) observations at specific scales and ii) local fitting models to the whole range of scales. The range of possible models is restricted to the power-law scaling models. During the project we have put emphasize on the definition of the theory and methodology necessary to assess a sound comparison between data taken at different scales, with different techniques. Both 'local' and 'global' models have been investigated. Local models are linked exactly to the dataset they represent. Then, the global DFN models arise from the association of local models, different scales and different sample support shapes. Discrepancies between local and global model illustrate the variability associated to the DFN models. We define two possible Global Scaling Models (GSM). The first one is consistent with the scaling measured in the outcrops (Model A). Its scaling exponent is a 3d =3.5 (eq. to k r =2.5); it overestimates the fracture densities observed in the lineament maps. The second one assumes that both lineaments and outcrops belong to the same distribution model (Model B), which entails a scaling exponent a 3d =3.9 (eq. to k r =2.9). Both models have been tested by looking for the best consistency in the fracture density-dip relationships, between boreholes data at depth (based on boreholes KFM02A, KFM
Directory of Open Access Journals (Sweden)
Bingqing Lu
2018-01-01
Full Text Available Fractional calculus provides efficient physical models to quantify non-Fickian dynamics broadly observed within the Earth system. The potential advantages of using fractional partial differential equations (fPDEs for real-world problems are often limited by the current lack of understanding of how earth system properties influence observed non-Fickian dynamics. This study explores non-Fickian dynamics for pollutant transport in field-scale discrete fracture networks (DFNs, by investigating how fracture and rock matrix properties influence the leading and tailing edges of pollutant breakthrough curves (BTCs. Fractured reservoirs exhibit erratic internal structures and multi-scale heterogeneity, resulting in complex non-Fickian dynamics. A Monte Carlo approach is used to simulate pollutant transport through DFNs with a systematic variation of system properties, and the resultant non-Fickian transport is upscaled using a tempered-stable fractional in time advection–dispersion equation. Numerical results serve as a basis for determining both qualitative and quantitative relationships between BTC characteristics and model parameters, in addition to the impacts of fracture density, orientation, and rock matrix permeability on non-Fickian dynamics. The observed impacts of medium heterogeneity on tracer transport at late times tend to enhance the applicability of fPDEs that may be parameterized using measurable fracture–matrix characteristics.
Discrete fracture in quasi-brittle materials under compressive and tensile stress states
CSIR Research Space (South Africa)
Klerck, PA
2004-01-01
Full Text Available A method for modelling discrete fracture in geomaterials under tensile and compressive stress fields has been developed based on a Mohr-Coulomb failure surface in compression and three independent anisotropic rotating crack models in tension...
Electrical Conductivity Distributions in Discrete Fluid-Filled Fractures
James, S. C.; Ahmmed, B.; Knox, H. A.; Johnson, T.; Dunbar, J. A.
2017-12-01
It is commonly asserted that hydraulic fracturing enhances permeability by generating new fractures in the reservoir. Furthermore, it is assumed that in the fractured system predominant flow occurs in these newly formed and pre-existing fractures. Among the phenomenology that remains enigmatic are fluid distributions inside fractures. Therefore, determining fluid distribution and their associated temporal and spatial evolution in fractures is critical for safe and efficient hydraulic fracturing. Previous studies have used both forward modeling and inversion of electrical data to show that a geologic system consisting of fluid filled fractures has a conductivity distribution, where fractures act as electrically conductive bodies when the fluids are more conductive than the host material. We will use electrical inversion for estimating electrical conductivity distribution within multiple fractures from synthetic and measured data. Specifically, we will use data and well geometries from an experiment performed at Blue Canyon Dome in Socorro, NM, which was used as a study site for subsurface technology, engineering, and research (SubTER) funded by DOE. This project used a central borehole for energetically stimulating the system and four monitoring boreholes, emplaced in the cardinal directions. The electrical data taken during this project used 16 temporary electrodes deployed in the stimulation borehole and 64 permanent electrodes in the monitoring wells (16 each). We present results derived using E4D from scenarios with two discrete fractures, thereby discovering the electric potential response of both spatially and temporarily variant fluid distribution and the resolution of fluid and fracture boundaries. These two fractures have dimensions of 3m × 0.01m × 7m and are separated by 1m. These results can be used to develop stimulation and flow tests at the meso-scale that will be important for model validation. Sandia National Laboratories is a multi
Holton, D.; Frampton, A.; Cvetkovic, V.
2006-12-01
The Onkalo underground research facility for rock characterisation for nuclear waste disposal is located at Olkiluoto island, just off the Finnish coast in the Baltic Sea. Prior to the start of the excavation of the Onkalo facility, an extensive amount of hydraulic data has been collected during various pumping experiments from a large number of boreholes placed throughout an area of approximately 10 km2, reaching depths of 1000 meters below sea level. In particular, the hydraulic borehole data includes classical measurements of pressure, but also new measurements of flow rate and flow direction in boreholes (so called flow-logging). These measurements indicate large variations in heterogeneity and are a clear reflection of the discrete nature of the system. Here we present results from an ongoing project which aims to explore and asses the implications of these new flow-logging measurements to site descriptive modelling and modelling at performance assessment scales. The main challange of the first phase of this project is to obtain a greater understanding of a strongly heterogenious and anisotropic groundwater system in which open boreholes are located; that is, a system in which the observation boreholes themselves create new hydraulic conductive features of the groundwater system. The results presented are from recent hydraulic flow modelling simulations with a combined continuous porous media and discrete fracture network approach using a commercial finite-element software. An advantage of this approach is we may adapt a continuum mesh on the regional scale, were only a few conductive features are known, together with a local scale discrete fracture network approach, where detailed site-investigation has revealed a large amount of conductive features. Current findings indicate the system is sensitive to certain combinations of hydraulic features, and we quantify the significance of including these variations in terms of their implications for reduction of
Energy Technology Data Exchange (ETDEWEB)
Zhang, Boning [Univ. of Colorado, Boulder, CO (United States); Herbold, Eric B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Homel, Michael A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Regueiro, Richard A. [Univ. of Colorado, Boulder, CO (United States)
2015-12-01
An adaptive particle fracture model in poly-ellipsoidal Discrete Element Method is developed. The poly-ellipsoidal particle will break into several sub-poly-ellipsoids by Hoek-Brown fracture criterion based on continuum stress and the maximum tensile stress in contacts. Also Weibull theory is introduced to consider the statistics and size effects on particle strength. Finally, high strain-rate split Hopkinson pressure bar experiment of silica sand is simulated using this newly developed model. Comparisons with experiments show that our particle fracture model can capture the mechanical behavior of this experiment very well, both in stress-strain response and particle size redistribution. The effects of density and packings o the samples are also studied in numerical examples.
Selroos, J. O.; Appleyard, P.; Bym, T.; Follin, S.; Hartley, L.; Joyce, S.; Munier, R.
2015-12-01
In 2011 the Swedish Nuclear Fuel and Waste Management Company (SKB) applied for a license to start construction of a final repository for spent nuclear fuel at Forsmark in Northern Uppland, Sweden. The repository is to be built at approximately 500 m depth in crystalline rock. A stochastic, discrete fracture network (DFN) concept was chosen for interpreting the surface-based (incl. boreholes) data, and for assessing the safety of the repository in terms of groundwater flow and flow pathways to and from the repository. Once repository construction starts, also underground data such as tunnel pilot borehole and tunnel trace data will become available. It is deemed crucial that DFN models developed at this stage honors the mapped structures both in terms of location and geometry, and in terms of flow characteristics. The originally fully stochastic models will thus increase determinism towards the repository. Applying the adopted probabilistic framework, predictive modeling to support acceptance criteria for layout and disposal can be performed with the goal of minimizing risks associated with the repository. This presentation describes and illustrates various methodologies that have been developed to condition stochastic realizations of fracture networks around underground openings using borehole and tunnel trace data, as well as using hydraulic measurements of inflows or hydraulic interference tests. The methodologies, implemented in the numerical simulators ConnectFlow and FracMan/MAFIC, are described in some detail, and verification tests and realistic example cases are shown. Specifically, geometric and hydraulic data are obtained from numerical synthetic realities approximating Forsmark conditions, and are used to test the constraining power of the developed methodologies by conditioning unconditional DFN simulations following the same underlying fracture network statistics. Various metrics are developed to assess how well the conditional simulations compare to
Discrete Feature Model (DFM) User Documentation
International Nuclear Information System (INIS)
Geier, Joel
2008-06-01
This manual describes the Discrete-Feature Model (DFM) software package for modelling groundwater flow and solute transport in networks of discrete features. A discrete-feature conceptual model represents fractures and other water-conducting features around a repository as discrete conductors surrounded by a rock matrix which is usually treated as impermeable. This approximation may be valid for crystalline rocks such as granite or basalt, which have very low permeability if macroscopic fractures are excluded. A discrete feature is any entity that can conduct water and permit solute transport through bedrock, and can be reasonably represented as a piecewise-planar conductor. Examples of such entities may include individual natural fractures (joints or faults), fracture zones, and disturbed-zone features around tunnels (e.g. blasting-induced fractures or stress-concentration induced 'onion skin' fractures around underground openings). In a more abstract sense, the effectively discontinuous nature of pathways through fractured crystalline bedrock may be idealized as discrete, equivalent transmissive features that reproduce large-scale observations, even if the details of connective paths (and unconnected domains) are not precisely known. A discrete-feature model explicitly represents the fundamentally discontinuous and irregularly connected nature of systems of such systems, by constraining flow and transport to occur only within such features and their intersections. Pathways for flow and solute transport in this conceptualization are a consequence not just of the boundary conditions and hydrologic properties (as with continuum models), but also the irregularity of connections between conductive/transmissive features. The DFM software package described here is an extensible code for investigating problems of flow and transport in geological (natural or human-altered) systems that can be characterized effectively in terms of discrete features. With this software, the
Discrete Feature Model (DFM) User Documentation
Energy Technology Data Exchange (ETDEWEB)
Geier, Joel (Clearwater Hardrock Consulting, Corvallis, OR (United States))
2008-06-15
This manual describes the Discrete-Feature Model (DFM) software package for modelling groundwater flow and solute transport in networks of discrete features. A discrete-feature conceptual model represents fractures and other water-conducting features around a repository as discrete conductors surrounded by a rock matrix which is usually treated as impermeable. This approximation may be valid for crystalline rocks such as granite or basalt, which have very low permeability if macroscopic fractures are excluded. A discrete feature is any entity that can conduct water and permit solute transport through bedrock, and can be reasonably represented as a piecewise-planar conductor. Examples of such entities may include individual natural fractures (joints or faults), fracture zones, and disturbed-zone features around tunnels (e.g. blasting-induced fractures or stress-concentration induced 'onion skin' fractures around underground openings). In a more abstract sense, the effectively discontinuous nature of pathways through fractured crystalline bedrock may be idealized as discrete, equivalent transmissive features that reproduce large-scale observations, even if the details of connective paths (and unconnected domains) are not precisely known. A discrete-feature model explicitly represents the fundamentally discontinuous and irregularly connected nature of systems of such systems, by constraining flow and transport to occur only within such features and their intersections. Pathways for flow and solute transport in this conceptualization are a consequence not just of the boundary conditions and hydrologic properties (as with continuum models), but also the irregularity of connections between conductive/transmissive features. The DFM software package described here is an extensible code for investigating problems of flow and transport in geological (natural or human-altered) systems that can be characterized effectively in terms of discrete features. With this
Li, Mingchao; Han, Shuai; Zhou, Sibao; Zhang, Ye
2018-06-01
Based on a 3D model of a discrete fracture network (DFN) in a rock mass, an improved projective method for computing the 3D mechanical connectivity rate was proposed. The Monte Carlo simulation method, 2D Poisson process and 3D geological modeling technique were integrated into a polyhedral DFN modeling approach, and the simulation results were verified by numerical tests and graphical inspection. Next, the traditional projective approach for calculating the rock mass connectivity rate was improved using the 3D DFN models by (1) using the polyhedral model to replace the Baecher disk model; (2) taking the real cross section of the rock mass, rather than a part of the cross section, as the test plane; and (3) dynamically searching the joint connectivity rates using different dip directions and dip angles at different elevations to calculate the maximum, minimum and average values of the joint connectivity at each elevation. In a case study, the improved method and traditional method were used to compute the mechanical connectivity rate of the slope of a dam abutment. The results of the two methods were further used to compute the cohesive force of the rock masses. Finally, a comparison showed that the cohesive force derived from the traditional method had a higher error, whereas the cohesive force derived from the improved method was consistent with the suggested values. According to the comparison, the effectivity and validity of the improved method were verified indirectly.
Directory of Open Access Journals (Sweden)
Jae-Yeol Cheong
2017-12-01
Full Text Available In instances of damage to engineered barriers containing nuclear waste material, surrounding bedrock is a natural barrier that retards radionuclide movement by way of adsorption and delay due to groundwater flow through highly tortuous fractured rock pathways. At the Gyeongju nuclear waste disposal site, groundwater mainly flows through granitic and sedimentary rock fractures. Therefore, to understand the nuclide migration path, it is necessary to understand discrete fracture networks based on heterogeneous fracture orientations, densities, and size characteristics. In this study, detailed heterogeneous fracture distribution, including the density and orientation of the fractures, was considered for a region that has undergone long periods of change from various geological activities at and around the Gyeongju site. A site-scale discrete fracture network (DFN model was constructed taking into account: (i regional fracture heterogeneity constrained by a multiple linear regression analysis of fracture intensity on faults and electrical resistivity; and (ii the connectivity of conductive fractures having fracture hydraulic parameters, using transient flow simulation. Geometric and hydraulic heterogeneity of the DFN was upscaled into equivalent porous media for flow and transport simulation for a large-scale model.
New approach for simulating groundwater flow in discrete fracture network
Fang, H.; Zhu, J.
2017-12-01
In this study, we develop a new approach to calculate groundwater flowrate and hydraulic head distribution in two-dimensional discrete fracture network (DFN) where both laminar and turbulent flows co-exist in individual fractures. The cubic law is used to calculate hydraulic head distribution and flow behaviors in fractures where flow is laminar, while the Forchheimer's law is used to quantify turbulent flow behaviors. Reynolds number is used to distinguish flow characteristics in individual fractures. The combination of linear and non-linear equations is solved iteratively to determine flowrates in all fractures and hydraulic heads at all intersections. We examine potential errors in both flowrate and hydraulic head from the approach of uniform flow assumption. Applying the cubic law in all fractures regardless of actual flow conditions overestimates the flowrate when turbulent flow may exist while applying the Forchheimer's law indiscriminately underestimate the flowrate when laminar flows exist in the network. The contrast of apertures of large and small fractures in the DFN has significant impact on the potential errors of using only the cubic law or the Forchheimer's law. Both the cubic law and Forchheimer's law simulate similar hydraulic head distributions as the main difference between these two approaches lies in predicting different flowrates. Fracture irregularity does not significantly affect the potential errors from using only the cubic law or the Forchheimer's law if network configuration remains similar. Relative density of fractures does not significantly affect the relative performance of the cubic law and Forchheimer's law.
International Nuclear Information System (INIS)
Kanehiro, B.Y.; Lai, C.H.; Stow, S.H.
1987-05-01
Conceptual models for sedimentary rock settings that could be used in future evaluation and suitability studies are being examined through the DOE Repository Technology Program. One area of concern for the hydrologic aspects of these models is discrete fracture flow analysis as related to the estimation of the size of the representative elementary volume, evaluation of the appropriateness of continuum assumptions and estimation of the large-scale permeabilities of sedimentary rocks. A basis for preliminary analysis of flow in fracture systems of the types that might be expected to occur in low permeability sedimentary rocks is presented. The approach used involves numerical modeling of discrete fracture flow for the configuration of a large-scale hydrologic field test directed at estimation of the size of the representative elementary volume and large-scale permeability. Analysis of fracture data on the basis of this configuration is expected to provide a preliminary indication of the scale at which continuum assumptions can be made
Energy Technology Data Exchange (ETDEWEB)
Johnston, Henry [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Wang, Cong [Colorado School of Mines; Winterfeld, Philip [Colorado School of Mines; Wu, Yu-Shu [Colorado School of Mines
2018-02-14
An efficient modeling approach is described for incorporating arbitrary 3D, discrete fractures, such as hydraulic fractures or faults, into modeling fracture-dominated fluid flow and heat transfer in fractured geothermal reservoirs. This technique allows 3D discrete fractures to be discretized independently from surrounding rock volume and inserted explicitly into a primary fracture/matrix grid, generated without including 3D discrete fractures in prior. An effective computational algorithm is developed to discretize these 3D discrete fractures and construct local connections between 3D fractures and fracture/matrix grid blocks of representing the surrounding rock volume. The constructed gridding information on 3D fractures is then added to the primary grid. This embedded fracture modeling approach can be directly implemented into a developed geothermal reservoir simulator via the integral finite difference (IFD) method or with TOUGH2 technology This embedded fracture modeling approach is very promising and computationally efficient to handle realistic 3D discrete fractures with complicated geometries, connections, and spatial distributions. Compared with other fracture modeling approaches, it avoids cumbersome 3D unstructured, local refining procedures, and increases computational efficiency by simplifying Jacobian matrix size and sparsity, while keeps sufficient accuracy. Several numeral simulations are present to demonstrate the utility and robustness of the proposed technique. Our numerical experiments show that this approach captures all the key patterns about fluid flow and heat transfer dominated by fractures in these cases. Thus, this approach is readily available to simulation of fractured geothermal reservoirs with both artificial and natural fractures.
Energy Technology Data Exchange (ETDEWEB)
Morris, J; Johnson, S
2007-12-03
The Distinct Element Method (also frequently referred to as the Discrete Element Method) (DEM) is a Lagrangian numerical technique where the computational domain consists of discrete solid elements which interact via compliant contacts. This can be contrasted with Finite Element Methods where the computational domain is assumed to represent a continuum (although many modern implementations of the FEM can accommodate some Distinct Element capabilities). Often the terms Discrete Element Method and Distinct Element Method are used interchangeably in the literature, although Cundall and Hart (1992) suggested that Discrete Element Methods should be a more inclusive term covering Distinct Element Methods, Displacement Discontinuity Analysis and Modal Methods. In this work, DEM specifically refers to the Distinct Element Method, where the discrete elements interact via compliant contacts, in contrast with Displacement Discontinuity Analysis where the contacts are rigid and all compliance is taken up by the adjacent intact material.
An implicit finite element method for discrete dynamic fracture
Energy Technology Data Exchange (ETDEWEB)
Gerken, Jobie M. [Colorado State Univ., Fort Collins, CO (United States)
1999-12-01
A method for modeling the discrete fracture of two-dimensional linear elastic structures with a distribution of small cracks subject to dynamic conditions has been developed. The foundation for this numerical model is a plane element formulated from the Hu-Washizu energy principle. The distribution of small cracks is incorporated into the numerical model by including a small crack at each element interface. The additional strain field in an element adjacent to this crack is treated as an externally applied strain field in the Hu-Washizu energy principle. The resulting stiffness matrix is that of a standard plane element. The resulting load vector is that of a standard plane element with an additional term that includes the externally applied strain field. Except for the crack strain field equations, all terms of the stiffness matrix and load vector are integrated symbolically in Maple V so that fully integrated plane stress and plane strain elements are constructed. The crack strain field equations are integrated numerically. The modeling of dynamic behavior of simple structures was demonstrated within acceptable engineering accuracy. In the model of axial and transverse vibration of a beam and the breathing mode of vibration of a thin ring, the dynamic characteristics were shown to be within expected limits. The models dominated by tensile forces (the axially loaded beam and the pressurized ring) were within 0.5% of the theoretical values while the shear dominated model (the transversely loaded beam) is within 5% of the calculated theoretical value. The constant strain field of the tensile problems can be modeled exactly by the numerical model. The numerical results should therefore, be exact. The discrepancies can be accounted for by errors in the calculation of frequency from the numerical results. The linear strain field of the transverse model must be modeled by a series of constant strain elements. This is an approximation to the true strain field, so some
Energy Technology Data Exchange (ETDEWEB)
Dershowitz, W.S.; La Pointe, P.R.; Einstein, H.H.; Ivanova, V.
1998-01-01
This report describes progress on the project, {open_quotes}Fractured Reservoir Discrete Feature Network Technologies{close_quotes} during the period March 7, 1996 to February 28, 1997. The report presents summaries of technology development for the following research areas: (1) development of hierarchical fracture models, (2) fractured reservoir compartmentalization and tributary volume, (3) fractured reservoir data analysis, and (4) integration of fractured reservoir data and production technologies. In addition, the report provides information on project status, publications submitted, data collection activities, and technology transfer through the world wide web (WWW). Research on hierarchical fracture models included geological, mathematical, and computer code development. The project built a foundation of quantitative, geological and geometrical information about the regional geology of the Permian Basin, including detailed information on the lithology, stratigraphy, and fracturing of Permian rocks in the project study area (Tracts 17 and 49 in the Yates field). Based on the accumulated knowledge of regional and local geology, project team members started the interpretation of fracture genesis mechanisms and the conceptual modeling of the fracture system in the study area. Research on fractured reservoir compartmentalization included basic research, technology development, and application of compartmentalized reservoir analyses for the project study site. Procedures were developed to analyze compartmentalization, tributary drainage volume, and reservoir matrix block size. These algorithms were implemented as a Windows 95 compartmentalization code, FraCluster.
Directory of Open Access Journals (Sweden)
Z. M. Jaini
Full Text Available Abstract Numerical modeling of fracture failure is challenging due to various issues in the constitutive law and the transition of continuum to discrete bodies. Therefore, this study presents the application of the combined finite-discrete element method to investigate the fracture failure of reinforced concrete slabs subjected to blast loading. In numerical modeling, the interaction of non-uniform blast loading on the concrete slab was modeled using the incorporation of the finite element method with a crack rotating approach and the discrete element method to model crack, fracture onset and its post-failures. A time varying pressure-time history based on the mapping method was adopted to define blast loading. The Mohr-Coulomb with Rankine cut-off and von-Mises criteria were applied for concrete and steel reinforcement respectively. The results of scabbing, spalling and fracture show a reliable prediction of damage and fracture.
Simulation of water flow in fractured porous medium by using discretized virtual internal bond
Peng, Shujun; Zhang, Zhennan; Li, Chunfang; He, Guofu; Miao, Guoqing
2017-12-01
The discretized virtual internal bond (DVIB) is adopted to simulate the water flow in fractured porous medium. The intact porous medium is permeable because it contains numerous micro cracks and pores. These micro discontinuities construct a fluid channel network. The representative volume of this fluid channel network is modeled as a lattice bond cell with finite number of bonds in statistical sense. Each bond serves as a fluid channel. In fractured porous medium, many bond cells are cut by macro fractures. The conductivity of the fracture facet in a bond cell is taken over by the bonds parallel to the flow direction. The equivalent permeability and volumetric storage coefficient of a micro bond are calibrated based on the ideal bond cell conception, which makes it unnecessary to consider the detailed geometry of a specific element. Such parameter calibration method is flexible and applicable to any type of element. The accuracy check results suggest this method has a satisfying accuracy in both the steady and transient flow simulation. To simulate the massive fractures in rockmass, the bond cells intersected by fracture are assigned aperture values, which are assumed random numbers following a certain distribution law. By this method, any number of fractures can be implicitly incorporated into the background mesh, avoiding the setup of fracture element and mesh modification. The fracture aperture heterogeneity is well represented by this means. The simulation examples suggest that the present method is a feasible, simple and efficient approach to the numerical simulation of water flow in fractured porous medium.
Normani, S. D.; Sykes, J. F.; Jensen, M. R.
2009-04-01
A high resolution sub-regional scale (84 km2) density-dependent, fracture zone network groundwater flow model with hydromechanical coupling and pseudo-permafrost, was developed from a larger 5734 km2 regional scale groundwater flow model of a Canadian Shield setting in fractured crystalline rock. The objective of the work is to illustrate aspects of regional and sub-regional groundwater flow that are relevant to the long-term performance of a hypothetical nuclear fuel repository. The discrete fracture dual continuum numerical model FRAC3DVS-OPG was used for all simulations. A discrete fracture zone network model delineated from surface features was superimposed onto an 789887 element flow domain mesh. Orthogonal fracture faces (between adjacent finite element grid blocks) were used to best represent the irregular discrete fracture zone network. The crystalline rock between these structural discontinuities was assigned properties characteristic of those reported for the Canadian Shield at the Underground Research Laboratory at Pinawa, Manitoba. Interconnectivity of permeable fracture features is an important pathway for the possibly relatively rapid migration of average water particles and subsequent reduction in residence times. The multiple 121000 year North American continental scale paleoclimate simulations are provided by W.R. Peltier using the University of Toronto Glacial Systems Model (UofT GSM). Values of ice sheet normal stress, and proglacial lake depth from the UofT GSM are applied to the sub-regional model as surface boundary conditions, using a freshwater head equivalent to the normal stress imposed by the ice sheet at its base. Permafrost depth is applied as a permeability reduction to both three-dimensional grid blocks and fractures that lie within the time varying permafrost zone. Two different paleoclimate simulations are applied to the sub-regional model to investigate the effect on the depth of glacial meltwater migration into the subsurface. In
Numerical Experiments on Advective Transport in Large Three-Dimensional Discrete Fracture Networks
Makedonska, N.; Painter, S. L.; Karra, S.; Gable, C. W.
2013-12-01
Modeling of flow and solute transport in discrete fracture networks is an important approach for understanding the migration of contaminants in impermeable hard rocks such as granite, where fractures provide dominant flow and transport pathways. The discrete fracture network (DFN) model attempts to mimic discrete pathways for fluid flow through a fractured low-permeable rock mass, and may be combined with particle tracking simulations to address solute transport. However, experience has shown that it is challenging to obtain accurate transport results in three-dimensional DFNs because of the high computational burden and difficulty in constructing a high-quality unstructured computational mesh on simulated fractures. An integrated DFN meshing [1], flow, and particle tracking [2] simulation capability that enables accurate flow and particle tracking simulation on large DFNs has recently been developed. The new capability has been used in numerical experiments on advective transport in large DFNs with tens of thousands of fractures and millions of computational cells. The modeling procedure starts from the fracture network generation using a stochastic model derived from site data. A high-quality computational mesh is then generated [1]. Flow is then solved using the highly parallel PFLOTRAN [3] code. PFLOTRAN uses the finite volume approach, which is locally mass conserving and thus eliminates mass balance problems during particle tracking. The flow solver provides the scalar fluxes on each control volume face. From the obtained fluxes the Darcy velocity is reconstructed for each node in the network [4]. Velocities can then be continuously interpolated to any point in the domain of interest, thus enabling random walk particle tracking. In order to describe the flow field on fractures intersections, the control volume cells on intersections are split into four planar polygons, where each polygon corresponds to a piece of a fracture near the intersection line. Thus
Hyman, J.; Aldrich, G. A.; Viswanathan, H. S.; Makedonska, N.; Karra, S.
2016-12-01
We characterize how different fracture size-transmissivity relationships influence flow and transport simulations through sparse three-dimensional discrete fracture networks. Although it is generally accepted that there is a positive correlation between a fracture's size and its transmissivity/aperture, the functional form of that relationship remains a matter of debate. Relationships that assume perfect correlation, semi-correlation, and non-correlation between the two have been proposed. To study the impact that adopting one of these relationships has on transport properties, we generate multiple sparse fracture networks composed of circular fractures whose radii follow a truncated power law distribution. The distribution of transmissivities are selected so that the mean transmissivity of the fracture networks are the same and the distributions of aperture and transmissivity in models that include a stochastic term are also the same.We observe that adopting a correlation between a fracture size and its transmissivity leads to earlier breakthrough times and higher effective permeability when compared to networks where no correlation is used. While fracture network geometry plays the principal role in determining where transport occurs within the network, the relationship between size and transmissivity controls the flow speed. These observations indicate DFN modelers should be aware that breakthrough times and effective permeabilities can be strongly influenced by such a relationship in addition to fracture and network statistics.
Hydraulic fracture propagation modeling and data-based fracture identification
Zhou, Jing
Successful shale gas and tight oil production is enabled by the engineering innovation of horizontal drilling and hydraulic fracturing. Hydraulically induced fractures will most likely deviate from the bi-wing planar pattern and generate complex fracture networks due to mechanical interactions and reservoir heterogeneity, both of which render the conventional fracture simulators insufficient to characterize the fractured reservoir. Moreover, in reservoirs with ultra-low permeability, the natural fractures are widely distributed, which will result in hydraulic fractures branching and merging at the interface and consequently lead to the creation of more complex fracture networks. Thus, developing a reliable hydraulic fracturing simulator, including both mechanical interaction and fluid flow, is critical in maximizing hydrocarbon recovery and optimizing fracture/well design and completion strategy in multistage horizontal wells. A novel fully coupled reservoir flow and geomechanics model based on the dual-lattice system is developed to simulate multiple nonplanar fractures' propagation in both homogeneous and heterogeneous reservoirs with or without pre-existing natural fractures. Initiation, growth, and coalescence of the microcracks will lead to the generation of macroscopic fractures, which is explicitly mimicked by failure and removal of bonds between particles from the discrete element network. This physics-based modeling approach leads to realistic fracture patterns without using the empirical rock failure and fracture propagation criteria required in conventional continuum methods. Based on this model, a sensitivity study is performed to investigate the effects of perforation spacing, in-situ stress anisotropy, rock properties (Young's modulus, Poisson's ratio, and compressive strength), fluid properties, and natural fracture properties on hydraulic fracture propagation. In addition, since reservoirs are buried thousands of feet below the surface, the
Discrete modeling of multiple discontinuities in rock mass using XFEM
Das, Kamal C.; Ausas, Roberto Federico; Carol, Ignacio; Rodrigues, Eduardo; Sandeep, Sandra; Vargas, P. E.; Gonzalez, Nubia Aurora; Segura, Josep María; Lakshmikantha, Ramasesha Mookanahallipatna; Mello,, U.
2017-01-01
Modeling of discontinuities (fractures and fault surfaces) is of major importance to assess the geomechanical behavior of oil and gas reservoirs, especially for tight and unconventional reservoirs. Numerical analysis of discrete discontinuities traditionally has been studied using interface element concepts, however more recently there are attempts to use extended finite element method (XFEM). The development of an XFEM tool for geo-mechanical fractures/faults modeling has significant industr...
The Effect of Loading Rate on Hydraulic Fracturing in Synthetic Granite - a Discrete Element Study
Tomac, I.; Gutierrez, M.
2015-12-01
Hydraulic fracture initiation and propagation from a borehole in hard synthetic rock is modeled using the two dimensional Discrete Element Method (DEM). DEM uses previously established procedure for modeling the strength and deformation parameters of quasi-brittle rocks with the Bonded Particle Model (Itasca, 2004). A series of simulations of laboratory tests on granite in DEM serve as a reference for synthetic rock behavior. Fracturing is enabled by breaking parallel bonds between DEM particles as a result of the local stress state. Subsequent bond breakage induces fracture propagation during a time-stepping procedure. Hydraulic fracturing occurs when pressurized fluid induces hoop stresses around the wellbore which cause rock fracturing and serves for geo-reservoir permeability enhancement in oil, gas and geothermal industries. In DEM, a network of fluid pipes and reservoirs is used for mathematical calculation of fluid flow through narrow channels between DEM particles, where the hydro-mechanical coupling is fully enabled. The fluid flow calculation is superimposed with DEM stress-strain calculation at each time step. As a result, the fluid pressures during borehole pressurization in hydraulic fracturing, as well as, during the fracture propagation from the borehole, can be simulated. The objective of this study is to investigate numerically a hypothesis that fluid pressurization rate, or the fluid flow rate, influences upon character, shape and velocity of fracture propagation in rock. The second objective is to better understand and define constraints which are important for successful fracture propagation in quasi-brittle rock from the perspective of flow rate, fluid density, viscosity and compressibility relative to the rock physical properties. Results from this study indicate that not only too high fluid flow rates cause fracture arrest and multiple fracture branching from the borehole, but also that the relative compressibility of fracturing fluid and
Ahmed, Raheel; Edwards, Michael G.; Lamine, Sadok; Huisman, Bastiaan A. H.; Pal, Mayur
2017-11-01
Two novel control-volume methods are presented for flow in fractured media, and involve coupling the control-volume distributed multi-point flux approximation (CVD-MPFA) constructed with full pressure support (FPS), to two types of discrete fracture-matrix approximation for simulation on unstructured grids; (i) involving hybrid grids and (ii) a lower dimensional fracture model. Flow is governed by Darcy's law together with mass conservation both in the matrix and the fractures, where large discontinuities in permeability tensors can occur. Finite-volume FPS schemes are more robust than the earlier CVD-MPFA triangular pressure support (TPS) schemes for problems involving highly anisotropic homogeneous and heterogeneous full-tensor permeability fields. We use a cell-centred hybrid-grid method, where fractures are modelled by lower-dimensional interfaces between matrix cells in the physical mesh but expanded to equi-dimensional cells in the computational domain. We present a simple procedure to form a consistent hybrid-grid locally for a dual-cell. We also propose a novel hybrid-grid for intersecting fractures, for the FPS method, which reduces the condition number of the global linear system and leads to larger time steps for tracer transport. The transport equation for tracer flow is coupled with the pressure equation and provides flow parameter assessment of the fracture models. Transport results obtained via TPS and FPS hybrid-grid formulations are compared with the corresponding results of fine-scale explicit equi-dimensional formulations. The results show that the hybrid-grid FPS method applies to general full-tensor fields and provides improved robust approximations compared to the hybrid-grid TPS method for fractured domains, for both weakly anisotropic permeability fields and very strong anisotropic full-tensor permeability fields where the TPS scheme exhibits spurious oscillations. The hybrid-grid FPS formulation is extended to compressible flow and the
Shale Fracture Analysis using the Combined Finite-Discrete Element Method
Carey, J. W.; Lei, Z.; Rougier, E.; Knight, E. E.; Viswanathan, H.
2014-12-01
Hydraulic fracturing (hydrofrac) is a successful method used to extract oil and gas from highly carbonate rocks like shale. However, challenges exist for industry experts estimate that for a single $10 million dollar lateral wellbore fracking operation, only 10% of the hydrocarbons contained in the rock are extracted. To better understand how to improve hydrofrac recovery efficiencies and to lower its costs, LANL recently funded the Laboratory Directed Research and Development (LDRD) project: "Discovery Science of Hydraulic Fracturing: Innovative Working Fluids and Their Interactions with Rocks, Fractures, and Hydrocarbons". Under the support of this project, the LDRD modeling team is working with the experimental team to understand fracture initiation and propagation in shale rocks. LANL's hybrid hydro-mechanical (HM) tool, the Hybrid Optimization Software Suite (HOSS), is being used to simulate the complex fracture and fragment processes under a variety of different boundary conditions. HOSS is based on the combined finite-discrete element method (FDEM) and has been proven to be a superior computational tool for multi-fracturing problems. In this work, the comparison of HOSS simulation results to triaxial core flooding experiments will be presented.
Energy Technology Data Exchange (ETDEWEB)
Birkholzer, J.; Karasaki, K. [Lawrence Berkeley National Lab., CA (United States). Earth Sciences Div.
1996-07-01
Fracture network simulators have extensively been used in the past for obtaining a better understanding of flow and transport processes in fractured rock. However, most of these models do not account for fluid or solute exchange between the fractures and the porous matrix, although diffusion into the matrix pores can have a major impact on the spreading of contaminants. In the present paper a new finite element code TRIPOLY is introduced which combines a powerful fracture network simulator with an efficient method to account for the diffusive interaction between the fractures and the adjacent matrix blocks. The fracture network simulator used in TRIPOLY features a mixed Lagrangian-Eulerian solution scheme for the transport in fractures, combined with an adaptive gridding technique to account for sharp concentration fronts. The fracture-matrix interaction is calculated with an efficient method which has been successfully used in the past for dual-porosity models. Discrete fractures and matrix blocks are treated as two different systems, and the interaction is modeled by introducing sink/source terms in both systems. It is assumed that diffusive transport in the matrix can be approximated as a one-dimensional process, perpendicular to the adjacent fracture surfaces. A direct solution scheme is employed to solve the coupled fracture and matrix equations. The newly developed combination of the fracture network simulator and the fracture-matrix interaction module allows for detailed studies of spreading processes in fractured porous rock. The authors present a sample application which demonstrate the codes ability of handling large-scale fracture-matrix systems comprising individual fractures and matrix blocks of arbitrary size and shape.
Modeling discrete competitive facility location
Karakitsiou, Athanasia
2015-01-01
This book presents an up-to-date review of modeling and optimization approaches for location problems along with a new bi-level programming methodology which captures the effect of competition of both producers and customers on facility location decisions. While many optimization approaches simplify location problems by assuming decision making in isolation, this monograph focuses on models which take into account the competitive environment in which such decisions are made. New insights in modeling, algorithmic and theoretical possibilities are opened by this approach and new applications are possible. Competition on equal term plus competition between market leader and followers are considered in this study, consequently bi-level optimization methodology is emphasized and further developed. This book provides insights regarding modeling complexity and algorithmic approaches to discrete competitive location problems. In traditional location modeling, assignment of customer demands to supply sources are made ...
Riahi, A.; Damjanac, B.
2013-12-01
Viability of an enhanced or engineered geothermal reservoir is determined by the rate of produced fluid at production wells and the rate of temperature drawdown in the reservoir as well as that of the produced fluid. Meeting required targets demands sufficient permeability and flow circulation in a relatively large volume of rock mass. In-situ conditions such overall permeability of the bedrock formation, magnitude and orientation of stresses, and the characteristics of the existing Discrete Fracture Network (DFN) greatly affect sustainable heat production. Because much of the EGS resources are in formations with low permeability, different stimulation techniques are required prior to the production phase to enhance fluid circulation. Shear stimulation or hydro-shearing is the method of injecting a fluid into the reservoir with the aim of increasing the fluid pressure in the naturally fractured rock and inducing shear failure or slip events. This mechanism can enhance the system's permeability through permanent dilatational opening of the sheared fractures. Using a computational modeling approach, the correlation between heat production and DFN statistical characteristics, namely the fracture length distribution, fracture orientation, and also fracture density is studied in this paper. Numerical analyses were completed using two-dimensional distinct element code UDEC (Itasca, 2011), which represents rock masses as an assembly of interacting blocks separated by fractures. UDEC allows for simulation of fracture propagation along the predefined planes only (i.e., the trajectory of the hydraulic fracture is not part of the solution of the problem). Thus, the hydraulic fracture is assumed to be planar, aligned with the direction of the major principal stress. The pre-existing fractures were represented explicitly. They are discontinuities which deform elastically, but also can open and slip (Coulomb slip law) as a function of pressure and total stress changes. The fluid
Discrete modelling of drapery systems
Thoeni, Klaus; Giacomini, Anna
2016-04-01
Drapery systems are an efficient and cost-effective measure in preventing and controlling rockfall hazards on rock slopes. The simplest form consists of a row of ground anchors along the top of the slope connected to a horizontal support cable from which a wire mesh is suspended down the face of the slope. Such systems are generally referred to as simple or unsecured draperies (Badger and Duffy 2012). Variations such as secured draperies, where a pattern of ground anchors is incorporated within the field of the mesh, and hybrid systems, where the upper part of an unsecured drapery is elevated to intercept rockfalls originating upslope of the installation, are becoming more and more popular. This work presents a discrete element framework for simulation of unsecured drapery systems and its variations. The numerical model is based on the classical discrete element method (DEM) and implemented into the open-source framework YADE (Šmilauer et al., 2010). The model takes all relevant interactions between block, drapery and slope into account (Thoeni et al., 2014) and was calibrated and validated based on full-scale experiments (Giacomini et al., 2012).The block is modelled as a rigid clump made of spherical particles which allows any shape to be approximated. The drapery is represented by a set of spherical particle with remote interactions. The behaviour of the remote interactions is governed by the constitutive behaviour of the wire and generally corresponds to a piecewise linear stress-strain relation (Thoeni et al., 2013). The same concept is used to model wire ropes. The rock slope is represented by rigid triangular elements where material properties (e.g., normal coefficient of restitution, friction angle) are assigned to each triangle. The capabilities of the developed model to simulate drapery systems and estimate the residual hazard involved with such systems is shown. References Badger, T.C., Duffy, J.D. (2012) Drapery systems. In: Turner, A.K., Schuster R
Computer model for ductile fracture
International Nuclear Information System (INIS)
Moran, B.; Reaugh, J. E.
1979-01-01
A computer model is described for predicting ductile fracture initiation and propagation. The computer fracture model is calibrated by simple and notched round-bar tension tests and a precracked compact tension test. The model is used to predict fracture initiation and propagation in a Charpy specimen and compare the results with experiments. The calibrated model provides a correlation between Charpy V-notch (CVN) fracture energy and any measure of fracture toughness, such as J/sub Ic/. A second simpler empirical correlation was obtained using the energy to initiate fracture in the Charpy specimen rather than total energy CVN, and compared the results with the empirical correlation of Rolfe and Novak
International Nuclear Information System (INIS)
Ijiri, Yuji; Sawada, Atsushi; Uchida, Masahiro; Ishiguro, Katsuhiko; Umeki, Hiroyuki; Sakamoto, Kazuhiko; Ohnishi, Yuzo
2001-01-01
It is important to take into account scale effects on fracture geometry if the modeling scale is much larger than the in-situ observation scale. The scale effect on fracture trace length, which is the most scale dependent parameter, is investigated using fracture maps obtained at various scales in tunnel and dam sites. We found that the distribution of fracture trace length follows negative power law distribution in regardless of locations and rock types. The hydraulic characteristics of fractured rock is also investigated by numerical analysis of discrete fracture network (DFN) model where power law distribution of fracture radius is adopted. We found that as the exponent of power law distribution become larger, the hydraulic conductivity of DFN model increases and the travel time in DFN model decreases. (author)
International Nuclear Information System (INIS)
Senapati, Rajeev; Zhang Jianmei
2010-01-01
Advanced ceramic materials have been extensively applied in aerospace, automobile and other industries. However, the reliability of the advanced ceramics is a major concern because of the brittle nature of the materials. In this paper, combination of nondestructive testing and numerical modeling Discrete Element Method is proposed to identify the fracture origin in ceramics. The nondestructive testing--laser scattering technology is first performed on the ceramic components to reveal the machining-induced damage such as cracks and the material-inherent flaws such as voids, then followed by the four point bending test. Discrete Element software package PFC 2D is used to simulate the four point bending test and try to identify where the fractures start. The numerical representation of the ceramic materials is done by generating a densely packed particle system using the specimen genesis procedure and then applying the suitable microparameters to the particle system. Simulation of four point bending test is performed on materials having no defects, materials having manufacturing-induced defects like cracks, and materials having material-inherent flaws like voids. The initiation and propagation of defects is modeled and the mean contact force on the loading ball is also plotted. The simulation prediction results are well in accordance with the nondestructive testing results.
Amir, Sahar Z.
2017-06-09
A Hybrid Embedded Fracture (HEF) model was developed to reduce various computational costs while maintaining physical accuracy (Amir and Sun, 2016). HEF splits the computations into fine scale and coarse scale. Fine scale solves analytically for the matrix-fracture flux exchange parameter. Coarse scale solves for the properties of the entire system. In literature, fractures were assumed to be either vertical or horizontal for simplification (Warren and Root, 1963). Matrix-fracture flux exchange parameter was given few equations built on that assumption (Kazemi, 1968; Lemonnier and Bourbiaux, 2010). However, such simplified cases do not apply directly for actual random fracture shapes, directions, orientations …etc. This paper shows that the HEF fine scale analytic solution (Amir and Sun, 2016) generates the flux exchange parameter found in literature for vertical and horizontal fracture cases. For other fracture cases, the flux exchange parameter changes according to the angle, slop, direction, … etc. This conclusion rises from the analysis of both: the Discrete Fracture Network (DFN) and the HEF schemes. The behavior of both schemes is analyzed with exactly similar fracture conditions and the results are shown and discussed. Then, a generalization is illustrated for any slightly compressible single-phase fluid within fractured porous media and its results are discussed.
Amir, Sahar Z.; Chen, Huangxin; Sun, Shuyu
2017-01-01
A Hybrid Embedded Fracture (HEF) model was developed to reduce various computational costs while maintaining physical accuracy (Amir and Sun, 2016). HEF splits the computations into fine scale and coarse scale. Fine scale solves analytically for the matrix-fracture flux exchange parameter. Coarse scale solves for the properties of the entire system. In literature, fractures were assumed to be either vertical or horizontal for simplification (Warren and Root, 1963). Matrix-fracture flux exchange parameter was given few equations built on that assumption (Kazemi, 1968; Lemonnier and Bourbiaux, 2010). However, such simplified cases do not apply directly for actual random fracture shapes, directions, orientations …etc. This paper shows that the HEF fine scale analytic solution (Amir and Sun, 2016) generates the flux exchange parameter found in literature for vertical and horizontal fracture cases. For other fracture cases, the flux exchange parameter changes according to the angle, slop, direction, … etc. This conclusion rises from the analysis of both: the Discrete Fracture Network (DFN) and the HEF schemes. The behavior of both schemes is analyzed with exactly similar fracture conditions and the results are shown and discussed. Then, a generalization is illustrated for any slightly compressible single-phase fluid within fractured porous media and its results are discussed.
A Two-Scale Reduced Model for Darcy Flow in Fractured Porous Media
Chen, Huangxin; Sun, Shuyu
2016-01-01
scale, and the effect of fractures on each coarse scale grid cell intersecting with fractures is represented by the discrete fracture model (DFM) on the fine scale. In the DFM used on the fine scale, the matrix-fracture system are resolved
Handbook on modelling for discrete optimization
Pitsoulis, Leonidas; Williams, H
2006-01-01
The primary objective underlying the Handbook on Modelling for Discrete Optimization is to demonstrate and detail the pervasive nature of Discrete Optimization. While its applications cut across an incredibly wide range of activities, many of the applications are only known to specialists. It is the aim of this handbook to correct this. It has long been recognized that "modelling" is a critically important mathematical activity in designing algorithms for solving these discrete optimization problems. Nevertheless solving the resultant models is also often far from straightforward. In recent years it has become possible to solve many large-scale discrete optimization problems. However, some problems remain a challenge, even though advances in mathematical methods, hardware, and software technology have pushed the frontiers forward. This handbook couples the difficult, critical-thinking aspects of mathematical modeling with the hot area of discrete optimization. It will be done in an academic handbook treatment...
Comparing the Discrete and Continuous Logistic Models
Gordon, Sheldon P.
2008-01-01
The solutions of the discrete logistic growth model based on a difference equation and the continuous logistic growth model based on a differential equation are compared and contrasted. The investigation is conducted using a dynamic interactive spreadsheet. (Contains 5 figures.)
Mathematical modelling of fracture hydrology
International Nuclear Information System (INIS)
Herbert, A.W.; Hodgkinson, D.P.; Lever, D.A.; Robinson, P.C.; Rae, J.
1985-06-01
This report summarises the work performed between January 1983 and December 1984 for the CEC/DOE contract 'Mathematical Modelling of Fracture Hydrology', under the following headings: 1) Statistical fracture network modelling, 2) Continuum models of flow and transport, 3) Simplified models, 4) Analysis of laboratory experiments and 5) Analysis of field experiments. (author)
Current Density and Continuity in Discretized Models
Boykin, Timothy B.; Luisier, Mathieu; Klimeck, Gerhard
2010-01-01
Discrete approaches have long been used in numerical modelling of physical systems in both research and teaching. Discrete versions of the Schrodinger equation employing either one or several basis functions per mesh point are often used by senior undergraduates and beginning graduate students in computational physics projects. In studying…
Modeling contaminant plumes in fractured limestone aquifers
DEFF Research Database (Denmark)
Mosthaf, Klaus; Brauns, Bentje; Fjordbøge, Annika Sidelmann
Determining the fate and transport of contaminant plumes from contaminated sites in limestone aquifers is important because they are a major drinking water resource. This is challenging because they are often heavily fractured and contain chert layers and nodules, resulting in a complex transport...... model. The paper concludes with recommendations on how to identify and employ suitable models to advance the conceptual understanding and as decision support tools for risk assessment and the planning of remedial actions....... behavior. Improved conceptual models are needed for this type of site. Here conceptual models are developed by combining numerical models with field data. Several types of fracture flow and transport models are available for the modeling of contaminant transport in fractured media. These include...... the established approaches of the equivalent porous medium, discrete fracture and dual continuum models. However, these modeling concepts are not well tested for contaminant plume migration in limestone geologies. Our goal was to develop and evaluate approaches for modeling the transport of dissolved contaminant...
Modeling interfacial fracture in Sierra.
Energy Technology Data Exchange (ETDEWEB)
Brown, Arthur A.; Ohashi, Yuki; Lu, Wei-Yang; Nelson, Stacy A. C.; Foulk, James W.,; Reedy, Earl David,; Austin, Kevin N.; Margolis, Stephen B.
2013-09-01
This report summarizes computational efforts to model interfacial fracture using cohesive zone models in the SIERRA/SolidMechanics (SIERRA/SM) finite element code. Cohesive surface elements were used to model crack initiation and propagation along predefined paths. Mesh convergence was observed with SIERRA/SM for numerous geometries. As the funding for this project came from the Advanced Simulation and Computing Verification and Validation (ASC V&V) focus area, considerable effort was spent performing verification and validation. Code verification was performed to compare code predictions to analytical solutions for simple three-element simulations as well as a higher-fidelity simulation of a double-cantilever beam. Parameter identification was conducted with Dakota using experimental results on asymmetric double-cantilever beam (ADCB) and end-notched-flexure (ENF) experiments conducted under Campaign-6 funding. Discretization convergence studies were also performed with respect to mesh size and time step and an optimization study was completed for mode II delamination using the ENF geometry. Throughout this verification process, numerous SIERRA/SM bugs were found and reported, all of which have been fixed, leading to over a 10-fold increase in convergence rates. Finally, mixed-mode flexure experiments were performed for validation. One of the unexplained issues encountered was material property variability for ostensibly the same composite material. Since the variability is not fully understood, it is difficult to accurately assess uncertainty when performing predictions.
Local discrete symmetries from superstring derived models
International Nuclear Information System (INIS)
Faraggi, A.E.
1996-10-01
Discrete and global symmetries play an essential role in many extensions of the Standard Model, for example, to preserve the proton lifetime, to prevent flavor changing neutral currents, etc. An important question is how can such symmetries survive in a theory of quantum gravity, like superstring theory. In a specific string model the author illustrates how local discrete symmetries may arise in string models and play an important role in preventing fast proton decay and flavor changing neutral currents. The local discrete symmetry arises due to the breaking of the non-Abelian gauge symmetries by Wilson lines in the superstring models and forbids, for example dimension five operators which mediate rapid proton decay, to all orders of nonrenormalizable terms. In the context of models of unification of the gauge and gravitational interactions, it is precisely this type of local discrete symmetries that must be found in order to insure that a given model is not in conflict with experimental observations
A discrete control model of PLANT
Mitchell, C. M.
1985-01-01
A model of the PLANT system using the discrete control modeling techniques developed by Miller is described. Discrete control models attempt to represent in a mathematical form how a human operator might decompose a complex system into simpler parts and how the control actions and system configuration are coordinated so that acceptable overall system performance is achieved. Basic questions include knowledge representation, information flow, and decision making in complex systems. The structure of the model is a general hierarchical/heterarchical scheme which structurally accounts for coordination and dynamic focus of attention. Mathematically, the discrete control model is defined in terms of a network of finite state systems. Specifically, the discrete control model accounts for how specific control actions are selected from information about the controlled system, the environment, and the context of the situation. The objective is to provide a plausible and empirically testable accounting and, if possible, explanation of control behavior.
Quadratic Term Structure Models in Discrete Time
Marco Realdon
2006-01-01
This paper extends the results on quadratic term structure models in continuos time to the discrete time setting. The continuos time setting can be seen as a special case of the discrete time one. Recursive closed form solutions for zero coupon bonds are provided even in the presence of multiple correlated underlying factors. Pricing bond options requires simple integration. Model parameters may well be time dependent without scuppering such tractability. Model estimation does not require a r...
On discrete models of space-time
International Nuclear Information System (INIS)
Horzela, A.; Kempczynski, J.; Kapuscik, E.; Georgia Univ., Athens, GA; Uzes, Ch.
1992-02-01
Analyzing the Einstein radiolocation method we come to the conclusion that results of any measurement of space-time coordinates should be expressed in terms of rational numbers. We show that this property is Lorentz invariant and may be used in the construction of discrete models of space-time different from the models of the lattice type constructed in the process of discretization of continuous models. (author)
Discrete modeling considerations in multiphase fluid dynamics
International Nuclear Information System (INIS)
Ransom, V.H.; Ramshaw, J.D.
1988-01-01
The modeling of multiphase flows play a fundamental role in light water reactor safety. The main ingredients in our discrete modeling Weltanschauung are the following considerations: (1) Any physical model must be cast into discrete form for a digital computer. (2) The usual approach of formulating models in differential form and then discretizing them is potentially hazardous. It may be preferable to formulate the model in discrete terms from the outset. (3) Computer time and storage constraints limit the resolution that can be employed in practical calculations. These limits effectively define the physical phenomena, length scales, and time scales which cannot be directly represented in the calculation and therefore must be modeled. This information should be injected into the model formulation process at an early stage. (4) Practical resolution limits are generally so coarse that traditional convergence and truncation-error analyses become irrelevant. (5) A discrete model constitutes a reduced description of a physical system, from which fine-scale details are eliminated. This elimination creates a statistical closure problem. Methods from statistical physics may therefore be useful in the formulation of discrete models. In the present paper we elaborate on these themes and illustrate them with simple examples. 48 refs
Suppachoknirun, Theerapat; Tutuncu, Azra N.
2017-12-01
With increasing production from shale gas and tight oil reservoirs, horizontal drilling and multistage hydraulic fracturing processes have become a routine procedure in unconventional field development efforts. Natural fractures play a critical role in hydraulic fracture growth, subsequently affecting stimulated reservoir volume and the production efficiency. Moreover, the existing fractures can also contribute to the pressure-dependent fluid leak-off during the operations. Hence, a reliable identification of the discrete fracture network covering the zone of interest prior to the hydraulic fracturing design needs to be incorporated into the hydraulic fracturing and reservoir simulations for realistic representation of the in situ reservoir conditions. In this research study, an integrated 3-D fracture and fluid flow model have been developed using a new approach to simulate the fluid flow and deliver reliable production forecasting in naturally fractured and hydraulically stimulated tight reservoirs. The model was created with three key modules. A complex 3-D discrete fracture network model introduces realistic natural fracture geometry with the associated fractured reservoir characteristics. A hydraulic fracturing model is created utilizing the discrete fracture network for simulation of the hydraulic fracture and flow in the complex discrete fracture network. Finally, a reservoir model with the production grid system is used allowing the user to efficiently perform the fluid flow simulation in tight formations with complex fracture networks. The complex discrete natural fracture model, the integrated discrete fracture model for the hydraulic fracturing, the fluid flow model, and the input dataset have been validated against microseismic fracture mapping and commingled production data obtained from a well pad with three horizontal production wells located in the Eagle Ford oil window in south Texas. Two other fracturing geometries were also evaluated to optimize
Rich dynamics of discrete delay ecological models
International Nuclear Information System (INIS)
Peng Mingshu
2005-01-01
We study multiple bifurcations and chaotic behavior of a discrete delay ecological model. New form of chaos for the 2-D map is observed: the combination of potential period doubling and reverse period-doubling leads to cascading bubbles
Discrete approximations to vector spin models
Energy Technology Data Exchange (ETDEWEB)
Van Enter, Aernout C D [University of Groningen, Johann Bernoulli Institute of Mathematics and Computing Science, Postbus 407, 9700 AK Groningen (Netherlands); Kuelske, Christof [Ruhr-Universitaet Bochum, Fakultaet fuer Mathematik, D44801 Bochum (Germany); Opoku, Alex A, E-mail: A.C.D.v.Enter@math.rug.nl, E-mail: Christof.Kuelske@ruhr-uni-bochum.de, E-mail: opoku@math.leidenuniv.nl [Mathematisch Instituut, Universiteit Leiden, Postbus 9512, 2300 RA, Leiden (Netherlands)
2011-11-25
We strengthen a result from Kuelske and Opoku (2008 Electron. J. Probab. 13 1307-44) on the existence of effective interactions for discretized continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of discretizing continuous-spin models, and show that except for very low temperatures, they behave similarly in two dimensions. We also discuss some possibilities in higher dimensions. (paper)
Discrete approximations to vector spin models
International Nuclear Information System (INIS)
Van Enter, Aernout C D; Külske, Christof; Opoku, Alex A
2011-01-01
We strengthen a result from Külske and Opoku (2008 Electron. J. Probab. 13 1307–44) on the existence of effective interactions for discretized continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of discretizing continuous-spin models, and show that except for very low temperatures, they behave similarly in two dimensions. We also discuss some possibilities in higher dimensions. (paper)
Discrete Dislocation Plasticity Analysis of Cracks and Fracture
Giessen, Erik van der; Pippan, R; Gumbsch, P
2010-01-01
Fracture in plastically deforming crystals involves several length scales for cleavage-like crack growth. The relevant length scales range from that of the macroscale object to the atomic scale, including the various microstructural length scales in between that are associated with, for example,
Ongoing Model Development Analyzing Glass Fracture
DEFF Research Database (Denmark)
Molnar, G.; Bojtar, I.; Nielsen, Jens Henrik
2013-01-01
Present subject deals with an ongoing experimental and numerical analysis of inplane loaded glass plates. The main goal of the investigation is to develop a hybrid – discrete and finite element – model which could follow the fracture process in annealed and in tempered glass. Measurements of the ...... an overview of the structure of the research and a summary of current status archived so far.......Present subject deals with an ongoing experimental and numerical analysis of inplane loaded glass plates. The main goal of the investigation is to develop a hybrid – discrete and finite element – model which could follow the fracture process in annealed and in tempered glass. Measurements...... of the residual stress state before failure and high-speed camera recordings of the failure are being performed in order to verify the numerical model. The primary goal of this research is to follow the overall fracture of a structural element – e.g. beam – loaded inplane. Present paper would like to give...
Charles, Joanna M; Roberts, Jessica L; Din, Nafees Ud; Williams, Nefyn H; Yeo, Seow Tien; Edwards, Rhiannon T
2018-05-14
As part of a wider feasibility study, the feasibility of gaining older patients' views for hip fracture rehabilitation services was tested using a discrete choice experiment in a UK context. Discrete choice experiment is a method used for eliciting individuals' preferences about goods and services. The discrete choice experiment was administered to 41 participants who had experienced hip fracture (mean age 79.3 years; standard deviation (SD) 7.5 years), recruited from a larger feasibility study exploring a new multidisciplinary rehabilitation for hip fracture. Attributes and levels for this discrete choice experiment were identified from a systematic review and focus groups. The questionnaire was administered at the 3-month follow-up. Participants indicated a significant preference for a fully-qualified physiotherapist or occupational therapist to deliver the rehabilitation sessions (β = 0·605, 95% confidence interval (95% CI) 0.462-0.879), and for their rehabilitation session to last less than 90 min (β = -0.192, 95% CI -0.381 to -0.051). The design of the discrete choice experiment using attributes associated with service configuration could have the potential to inform service implementation, and assist rehabilitation service design that incorporates the preferences of patients.
Current density and continuity in discretized models
International Nuclear Information System (INIS)
Boykin, Timothy B; Luisier, Mathieu; Klimeck, Gerhard
2010-01-01
Discrete approaches have long been used in numerical modelling of physical systems in both research and teaching. Discrete versions of the Schroedinger equation employing either one or several basis functions per mesh point are often used by senior undergraduates and beginning graduate students in computational physics projects. In studying discrete models, students can encounter conceptual difficulties with the representation of the current and its divergence because different finite-difference expressions, all of which reduce to the current density in the continuous limit, measure different physical quantities. Understanding these different discrete currents is essential and requires a careful analysis of the current operator, the divergence of the current and the continuity equation. Here we develop point forms of the current and its divergence valid for an arbitrary mesh and basis. We show that in discrete models currents exist only along lines joining atomic sites (or mesh points). Using these results, we derive a discrete analogue of the divergence theorem and demonstrate probability conservation in a purely localized-basis approach.
Discrete-Feature Model Implementation of SDM-Site Forsmark
International Nuclear Information System (INIS)
Geier, Joel
2010-03-01
A discrete-feature model (DFM) was implemented for the Forsmark repository site based on the final site descriptive model from surface based investigations. The discrete-feature conceptual model represents deformation zones, individual fractures, and other water-conducting features around a repository as discrete conductors surrounded by a rock matrix which, in the present study, is treated as impermeable. This approximation is reasonable for sites in crystalline rock which has very low permeability, apart from that which results from macroscopic fracturing. Models are constructed based on the geological and hydrogeological description of the sites and engineering designs. Hydraulic heads and flows through the network of water-conducting features are calculated by the finite-element method, and are used in turn to simulate migration of non-reacting solute by a particle-tracking method, in order to estimate the properties of pathways by which radionuclides could be released to the biosphere. Stochastic simulation is used to evaluate portions of the model that can only be characterized in statistical terms, since many water-conducting features within the model volume cannot be characterized deterministically. Chapter 2 describes the methodology by which discrete features are derived to represent water-conducting features around the hypothetical repository at Forsmark (including both natural features and features that result from the disturbance of excavation), and then assembled to produce a discrete-feature network model for numerical simulation of flow and transport. Chapter 3 describes how site-specific data and repository design are adapted to produce the discrete-feature model. Chapter 4 presents results of the calculations. These include utilization factors for deposition tunnels based on the emplacement criteria that have been set forth by the implementers, flow distributions to the deposition holes, and calculated properties of discharge paths as well as
Discrete-Feature Model Implementation of SDM-Site Forsmark
Energy Technology Data Exchange (ETDEWEB)
Geier, Joel (Clearwater Hardrock Consulting, Corvallis, OR (United States))
2010-03-15
A discrete-feature model (DFM) was implemented for the Forsmark repository site based on the final site descriptive model from surface based investigations. The discrete-feature conceptual model represents deformation zones, individual fractures, and other water-conducting features around a repository as discrete conductors surrounded by a rock matrix which, in the present study, is treated as impermeable. This approximation is reasonable for sites in crystalline rock which has very low permeability, apart from that which results from macroscopic fracturing. Models are constructed based on the geological and hydrogeological description of the sites and engineering designs. Hydraulic heads and flows through the network of water-conducting features are calculated by the finite-element method, and are used in turn to simulate migration of non-reacting solute by a particle-tracking method, in order to estimate the properties of pathways by which radionuclides could be released to the biosphere. Stochastic simulation is used to evaluate portions of the model that can only be characterized in statistical terms, since many water-conducting features within the model volume cannot be characterized deterministically. Chapter 2 describes the methodology by which discrete features are derived to represent water-conducting features around the hypothetical repository at Forsmark (including both natural features and features that result from the disturbance of excavation), and then assembled to produce a discrete-feature network model for numerical simulation of flow and transport. Chapter 3 describes how site-specific data and repository design are adapted to produce the discrete-feature model. Chapter 4 presents results of the calculations. These include utilization factors for deposition tunnels based on the emplacement criteria that have been set forth by the implementers, flow distributions to the deposition holes, and calculated properties of discharge paths as well as
Discrete stochastic analogs of Erlang epidemic models.
Getz, Wayne M; Dougherty, Eric R
2018-12-01
Erlang differential equation models of epidemic processes provide more realistic disease-class transition dynamics from susceptible (S) to exposed (E) to infectious (I) and removed (R) categories than the ubiquitous SEIR model. The latter is itself is at one end of the spectrum of Erlang SE[Formula: see text]I[Formula: see text]R models with [Formula: see text] concatenated E compartments and [Formula: see text] concatenated I compartments. Discrete-time models, however, are computationally much simpler to simulate and fit to epidemic outbreak data than continuous-time differential equations, and are also much more readily extended to include demographic and other types of stochasticity. Here we formulate discrete-time deterministic analogs of the Erlang models, and their stochastic extension, based on a time-to-go distributional principle. Depending on which distributions are used (e.g. discretized Erlang, Gamma, Beta, or Uniform distributions), we demonstrate that our formulation represents both a discretization of Erlang epidemic models and generalizations thereof. We consider the challenges of fitting SE[Formula: see text]I[Formula: see text]R models and our discrete-time analog to data (the recent outbreak of Ebola in Liberia). We demonstrate that the latter performs much better than the former; although confining fits to strict SEIR formulations reduces the numerical challenges, but sacrifices best-fit likelihood scores by at least 7%.
Jiang, Yawen; Ni, Weiyi
2016-11-01
This work was undertaken to provide an estimation of expected lifetime numbers, risks, and burden of fractures for 50-year-old Chinese women. A discrete event simulation model was developed to simulate the lifetime fractures of 50-year-old Chinese women at average risk of osteoporotic fracture. Main events in the model included hip fracture, clinical vertebral fracture, wrist fracture, humerus fracture, and other fracture. Fracture risks were calculated using the FRAX ® tool. Simulations of 50-year-old Chinese women without fracture risks were also carried out as a comparison to determine the burden of fractures. A 50-year-old Chinese woman at average risk of fracture is expected to experience 0.135 (95 % CI: 0.134-0.137) hip fractures, 0.120 (95 % CI: 0.119-0.122) clinical vertebral fractures, 0.095 (95 % CI: 0.094-0.096) wrist fractures, 0.079 (95 % CI: 0.078-0.080) humerus fractures, and 0.407 (95 % CI: 0.404-0.410) other fractures over the remainder of her life. The residual lifetime risk of any fracture, hip fracture, clinical vertebral fracture, wrist fracture, humerus fracture, and other fracture for a 50-year-old Chinese woman is 37.36, 11.77, 10.47, 8.61, 7.30, and 27.80 %, respectively. The fracture-attributable excess quality-adjusted life year (QALY) loss and lifetime costs are estimated at 0.11 QALYs (95 % CI: 0.00-0.22 QALYs) and US $714.61 (95 % CI: US $709.20-720.02), totaling a net monetary benefit loss of US $1,104.43 (95 % CI: US $904.09-1,304.78). Chinese women 50 years of age are at high risk of osteoporotic fracture, and the expected economic and quality-of-life burden attributable to osteoporotic fractures among Chinese women is substantial.
The brush model - a new approach to numerical modeling of matrix diffusion in fractured clay stone
International Nuclear Information System (INIS)
Lege, T.; Shao, H.
1998-01-01
A special approach for numerical modeling of contaminant transport in fractured clay stone is presented. The rock matrix and the fractures are simulated with individual formulations for FE grids and transport, coupled into a single model. The capacity of the rock matrix to take up contaminants is taken into consideration with a discrete simulation of matrix diffusion. Thus, the natural process of retardation due to matrix diffusion can be better simulated than by a standard introduction of an empirical parameter into the transport equation. Transport in groundwater in fractured clay stone can be simulated using a model called a 'brush model'. The 'brush handle' is discretized by 2-D finite elements. Advective-dispersive transport in groundwater in the fractures is assumed. The contaminant diffuses into 1D finite elements perpendicular to the fractures, i.e., the 'bristles of the brush'. The conclusion is drawn that matrix diffusion is an important property of fractured clay stone for contaminant retardation. (author)
Discrete dispersion models and their Tweedie asymptotics
DEFF Research Database (Denmark)
Jørgensen, Bent; Kokonendji, Célestin C.
2016-01-01
The paper introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The equidispersed Poisson model has a special place in this ap......The paper introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The equidispersed Poisson model has a special place...... in this approach, whereas several overdispersed discrete distributions, such as the Neyman Type A, Pólya-Aeppli, negative binomial and Poisson-inverse Gaussian, turn out to be Poisson-Tweedie factorial dispersion models with power dispersion functions, analogous to ordinary Tweedie exponential dispersion models...... with power variance functions. Using the factorial cumulant generating function as tool, we introduce a dilation operation as a discrete analogue of scaling, generalizing binomial thinning. The Poisson-Tweedie factorial dispersion models are closed under dilation, which in turn leads to a Poisson...
Analysis hierarchical model for discrete event systems
Ciortea, E. M.
2015-11-01
The This paper presents the hierarchical model based on discrete event network for robotic systems. Based on the hierarchical approach, Petri network is analysed as a network of the highest conceptual level and the lowest level of local control. For modelling and control of complex robotic systems using extended Petri nets. Such a system is structured, controlled and analysed in this paper by using Visual Object Net ++ package that is relatively simple and easy to use, and the results are shown as representations easy to interpret. The hierarchical structure of the robotic system is implemented on computers analysed using specialized programs. Implementation of hierarchical model discrete event systems, as a real-time operating system on a computer network connected via a serial bus is possible, where each computer is dedicated to local and Petri model of a subsystem global robotic system. Since Petri models are simplified to apply general computers, analysis, modelling, complex manufacturing systems control can be achieved using Petri nets. Discrete event systems is a pragmatic tool for modelling industrial systems. For system modelling using Petri nets because we have our system where discrete event. To highlight the auxiliary time Petri model using transport stream divided into hierarchical levels and sections are analysed successively. Proposed robotic system simulation using timed Petri, offers the opportunity to view the robotic time. Application of goods or robotic and transmission times obtained by measuring spot is obtained graphics showing the average time for transport activity, using the parameters sets of finished products. individually.
Hydromechanical modeling of clay rock including fracture damage
Asahina, D.; Houseworth, J. E.; Birkholzer, J. T.
2012-12-01
Argillaceous rock typically acts as a flow barrier, but under certain conditions significant and potentially conductive fractures may be present. Fracture formation is well-known to occur in the vicinity of underground excavations in a region known as the excavation disturbed zone. Such problems are of particular importance for low-permeability, mechanically weak rock such as clays and shales because fractures can be relatively transient as a result of fracture self-sealing processes. Perhaps not as well appreciated is the fact that natural fractures can form in argillaceous rock as a result of hydraulic overpressure caused by phenomena such as disequlibrium compaction, changes in tectonic stress, and mineral dehydration. Overpressure conditions can cause hydraulic fracturing if the fluid pressure leads to tensile effective stresses that exceed the tensile strength of the material. Quantitative modeling of this type of process requires coupling between hydrogeologic processes and geomechanical processes including fracture initiation and propagation. Here we present a computational method for three-dimensional, hydromechanical coupled processes including fracture damage. Fractures are represented as discrete features in a fracture network that interact with a porous rock matrix. Fracture configurations are mapped onto an unstructured, three-dimensonal, Voronoi grid, which is based on a random set of spatial points. Discrete fracture networks (DFN) are represented by the connections of the edges of a Voronoi cells. This methodology has the advantage that fractures can be more easily introduced in response to coupled hydro-mechanical processes and generally eliminates several potential issues associated with the geometry of DFN and numerical gridding. A geomechanical and fracture-damage model is developed here using the Rigid-Body-Spring-Network (RBSN) numerical method. The hydrogelogic and geomechanical models share the same geometrical information from a 3D Voronoi
Model-Checking Discrete Duration Calculus
DEFF Research Database (Denmark)
Hansen, Michael Reichhardt
1994-01-01
can do model-checking. The subset we consider is expressive enough to formalize the requirements to the gas burner system given by A.P. Ravn (1993); but only for a discrete time domain. Model-checking is done by reducing the correctness problem ℳ|=𝒟 to the inclusion problem of regular...
Discrete choice models with multiplicative error terms
DEFF Research Database (Denmark)
Fosgerau, Mogens; Bierlaire, Michel
2009-01-01
The conditional indirect utility of many random utility maximization (RUM) discrete choice models is specified as a sum of an index V depending on observables and an independent random term ε. In general, the universe of RUM consistent models is much larger, even fixing some specification of V due...
A Discrete Dynamical Model of Signed Partitions
Directory of Open Access Journals (Sweden)
G. Chiaselotti
2013-01-01
Full Text Available We use a discrete dynamical model with three evolution rules in order to analyze the structure of a partially ordered set of signed integer partitions whose main properties are actually not known. This model is related to the study of some extremal combinatorial sum problems.
Discrete-time rewards model-checked
Larsen, K.G.; Andova, S.; Niebert, Peter; Hermanns, H.; Katoen, Joost P.
2003-01-01
This paper presents a model-checking approach for analyzing discrete-time Markov reward models. For this purpose, the temporal logic probabilistic CTL is extended with reward constraints. This allows to formulate complex measures – involving expected as well as accumulated rewards – in a precise and
PHASE CHAOS IN THE DISCRETE KURAMOTO MODEL
DEFF Research Database (Denmark)
Maistrenko, V.; Vasylenko, A.; Maistrenko, Y.
2010-01-01
The paper describes the appearance of a novel, high-dimensional chaotic regime, called phase chaos, in a time-discrete Kuramoto model of globally coupled phase oscillators. This type of chaos is observed at small and intermediate values of the coupling strength. It arises from the nonlinear...... interaction among the oscillators, while the individual oscillators behave periodically when left uncoupled. For the four-dimensional time-discrete Kuramoto model, we outline the region of phase chaos in the parameter plane and determine the regions where phase chaos coexists with different periodic...
Modeling and simulation of discrete event systems
Choi, Byoung Kyu
2013-01-01
Computer modeling and simulation (M&S) allows engineers to study and analyze complex systems. Discrete-event system (DES)-M&S is used in modern management, industrial engineering, computer science, and the military. As computer speeds and memory capacity increase, so DES-M&S tools become more powerful and more widely used in solving real-life problems. Based on over 20 years of evolution within a classroom environment, as well as on decades-long experience in developing simulation-based solutions for high-tech industries, Modeling and Simulation of Discrete-Event Systems is the only book on
International Nuclear Information System (INIS)
Andre, Damien; Iordanoff, Ivan; Charles, Jean-luc; Jebahi, Mohamed; Neauport, Jerome
2013-01-01
The mechanical behavior of materials is usually simulated by a continuous mechanics approach. However, non-continuous phenomena such as multi-fracturing cannot be accurately simulated using a continuous description. The discrete element method (DEM) naturally accounts for discontinuities and is therefore a good alternative to the continuum approach. This work uses a discrete element model based on interaction given by 3D beam model. This model has proved to correctly simulate the elastic properties at the macroscopic scale. The simulation of brittle cracks is now tackled. This goal is attained by computing a failure criterion based on an equivalent hydrostatic stress. This microscopic criterion is then calibrated to fit experimental values of the macroscopic failure stress. Then, the simulation results are compared to experimental results of indentation tests in which a spherical indenter is used to load a silica glass, which is considered to be a perfectly brittle elastic material. (authors)
Modeling of brittle-viscous flow using discrete particles
Thordén Haug, Øystein; Barabasch, Jessica; Virgo, Simon; Souche, Alban; Galland, Olivier; Mair, Karen; Abe, Steffen; Urai, Janos L.
2017-04-01
Many geological processes involve both viscous flow and brittle fractures, e.g. boudinage, folding and magmatic intrusions. Numerical modeling of such viscous-brittle materials poses challenges: one has to account for the discrete fracturing, the continuous viscous flow, the coupling between them, and potential pressure dependence of the flow. The Discrete Element Method (DEM) is a numerical technique, widely used for studying fracture of geomaterials. However, the implementation of viscous fluid flow in discrete element models is not trivial. In this study, we model quasi-viscous fluid flow behavior using Esys-Particle software (Abe et al., 2004). We build on the methodology of Abe and Urai (2012) where a combination of elastic repulsion and dashpot interactions between the discrete particles is implemented. Several benchmarks are presented to illustrate the material properties. Here, we present extensive, systematic material tests to characterize the rheology of quasi-viscous DEM particle packing. We present two tests: a simple shear test and a channel flow test, both in 2D and 3D. In the simple shear tests, simulations were performed in a box, where the upper wall is moved with a constant velocity in the x-direction, causing shear deformation of the particle assemblage. Here, the boundary conditions are periodic on the sides, with constant forces on the upper and lower walls. In the channel flow tests, a piston pushes a sample through a channel by Poisseuille flow. For both setups, we present the resulting stress-strain relationships over a range of material parameters, confining stress and strain rate. Results show power-law dependence between stress and strain rate, with a non-linear dependence on confining force. The material is strain softening under some conditions (which). Additionally, volumetric strain can be dilatant or compactant, depending on porosity, confining pressure and strain rate. Constitutive relations are implemented in a way that limits the
Modeling discrete time-to-event data
Tutz, Gerhard
2016-01-01
This book focuses on statistical methods for the analysis of discrete failure times. Failure time analysis is one of the most important fields in statistical research, with applications affecting a wide range of disciplines, in particular, demography, econometrics, epidemiology and clinical research. Although there are a large variety of statistical methods for failure time analysis, many techniques are designed for failure times that are measured on a continuous scale. In empirical studies, however, failure times are often discrete, either because they have been measured in intervals (e.g., quarterly or yearly) or because they have been rounded or grouped. The book covers well-established methods like life-table analysis and discrete hazard regression models, but also introduces state-of-the art techniques for model evaluation, nonparametric estimation and variable selection. Throughout, the methods are illustrated by real life applications, and relationships to survival analysis in continuous time are expla...
Failure diagnosis using discrete event models
International Nuclear Information System (INIS)
Sampath, M.; Sengupta, R.; Lafortune, S.; Teneketzis, D.; Sinnamohideen, K.
1994-01-01
We propose a Discrete Event Systems (DES) approach to the failure diagnosis problem. We present a methodology for modeling physical systems in a DES framework. We discuss the notion of diagnosability and present the construction procedure of the diagnoser. Finally, we illustrate our approach using a Heating, Ventilation and Air Conditioning (HVAC) system
Roubinet, D.; Linde, N.; Jougnot, D.; Irving, J.
2016-05-01
Numerous field experiments suggest that the self-potential (SP) geophysical method may allow for the detection of hydraulically active fractures and provide information about fracture properties. However, a lack of suitable numerical tools for modeling streaming potentials in fractured media prevents quantitative interpretation and limits our understanding of how the SP method can be used in this regard. To address this issue, we present a highly efficient two-dimensional discrete-dual-porosity approach for solving the fluid flow and associated self-potential problems in fractured rock. Our approach is specifically designed for complex fracture networks that cannot be investigated using standard numerical methods. We then simulate SP signals associated with pumping conditions for a number of examples to show that (i) accounting for matrix fluid flow is essential for accurate SP modeling and (ii) the sensitivity of SP to hydraulically active fractures is intimately linked with fracture-matrix fluid interactions. This implies that fractures associated with strong SP amplitudes are likely to be hydraulically conductive, attracting fluid flow from the surrounding matrix.
International Nuclear Information System (INIS)
Hawkins, I.; Swift, B.; Hoch, A.; Wendling, J.
2010-01-01
Document available in extended abstract form only. Andra is studying the Callovo-Oxfordian mud-stones, located at a depth of approximately 500 m beneath the borders of the Meuse and the Haute-Marne Departements, in order to assess the feasibility of constructing a repository for radioactive waste in this low-permeability geological formation. The construction of a repository will lead to the formation of a zone adjacent to the repository (the Excavation Damaged Zone, or EDZ) in which the rock suffers mechanical damage. In the EDZ, fractures and cracks will develop, and therefore the hydraulic properties (including the permeability) will be different from those of the undamaged rock. There are some experimental data which, despite significant uncertainties, allow a conceptual model of the fractures to be defined. The objectives of this study were: - To develop a Discrete Fracture Network (DFN) model of the EDZ; - To derive effective properties for both single continuum and Multiple Interacting Continua (MINC) models from the DFN model; and - To use the various models to simulate desaturation of the rock during the operational phase of the repository, and subsequent re-saturation of a tunnel post-closure (a period of thousands of years). The approaches to modelling flow and transport in fractured systems fall into two rough classes: DFN models; and continuum models. DFN models account explicitly for the effects of individual fractures on fluid flow and solute transport, and usually do not consider the interaction between the fractures and the rock matrix. Continuum models may be single continuum, double continuum or MINC. Single continuum models are applicable when the interaction between the fractures and the rock matrix is sufficient to establish a local equilibrium. Double continuum models account for the two interacting systems (i.e. fractures and rock matrix) by conceptualising each as a continuum occupying the entire domain. An exchange function describes mass
Discrete dynamic modeling of cellular signaling networks.
Albert, Réka; Wang, Rui-Sheng
2009-01-01
Understanding signal transduction in cellular systems is a central issue in systems biology. Numerous experiments from different laboratories generate an abundance of individual components and causal interactions mediating environmental and developmental signals. However, for many signal transduction systems there is insufficient information on the overall structure and the molecular mechanisms involved in the signaling network. Moreover, lack of kinetic and temporal information makes it difficult to construct quantitative models of signal transduction pathways. Discrete dynamic modeling, combined with network analysis, provides an effective way to integrate fragmentary knowledge of regulatory interactions into a predictive mathematical model which is able to describe the time evolution of the system without the requirement for kinetic parameters. This chapter introduces the fundamental concepts of discrete dynamic modeling, particularly focusing on Boolean dynamic models. We describe this method step-by-step in the context of cellular signaling networks. Several variants of Boolean dynamic models including threshold Boolean networks and piecewise linear systems are also covered, followed by two examples of successful application of discrete dynamic modeling in cell biology.
Oldenburg, C. M.; Zhou, Q.; Birkholzer, J. T.
2017-12-01
The injection of supercritical CO2 (scCO2) in fractured reservoirs has been conducted at several storage sites. However, no site-specific dual-continuum modeling for fractured reservoirs has been reported and modeling studies have generally underestimated the fracture-matrix interactions. We developed a conceptual model for enhanced CO2 storage to take into account global scCO2 migration in the fracture continuum, local storage of scCO2 and dissolved CO2 (dsCO2) in the matrix continuum, and driving forces for scCO2 invasion and dsCO2 diffusion from fractures. High-resolution discrete fracture-matrix models were developed for a column of idealized matrix blocks bounded by vertical and horizontal fractures and for a km-scale fractured reservoir. The column-scale simulation results show that equilibrium storage efficiency strongly depends on matrix entry capillary pressure and matrix-matrix connectivity while the time scale to reach equilibrium is sensitive to fracture spacing and matrix flow properties. The reservoir-scale modeling results shows that the preferential migration of scCO2 through fractures is coupled with bulk storage in the rock matrix that in turn retards the fracture scCO2 plume. We also developed unified-form diffusive flux equations to account for dsCO2 storage in brine-filled matrix blocks and found solubility trapping is significant in fractured reservoirs with low-permeability matrix.
International Nuclear Information System (INIS)
Ding Qing
2007-01-01
We prove that the integrable-nonintegrable discrete nonlinear Schroedinger equation (AL-DNLS) introduced by Cai, Bishop and Gronbech-Jensen (Phys. Rev. Lett. 72 591(1994)) is the discrete gauge equivalent to an integrable-nonintegrable discrete Heisenberg model from the geometric point of view. Then we study whether the transmission and bifurcation properties of the AL-DNLS equation are preserved under the action of discrete gauge transformations. Our results reveal that the transmission property of the AL-DNLS equation is completely preserved and the bifurcation property is conditionally preserved to those of the integrable-nonintegrable discrete Heisenberg model
Fischer, P.; Jardani, A.; Lecoq, N.
2018-02-01
In this paper, we present a novel inverse modeling method called Discrete Network Deterministic Inversion (DNDI) for mapping the geometry and property of the discrete network of conduits and fractures in the karstified aquifers. The DNDI algorithm is based on a coupled discrete-continuum concept to simulate numerically water flows in a model and a deterministic optimization algorithm to invert a set of observed piezometric data recorded during multiple pumping tests. In this method, the model is partioned in subspaces piloted by a set of parameters (matrix transmissivity, and geometry and equivalent transmissivity of the conduits) that are considered as unknown. In this way, the deterministic optimization process can iteratively correct the geometry of the network and the values of the properties, until it converges to a global network geometry in a solution model able to reproduce the set of data. An uncertainty analysis of this result can be performed from the maps of posterior uncertainties on the network geometry or on the property values. This method has been successfully tested for three different theoretical and simplified study cases with hydraulic responses data generated from hypothetical karstic models with an increasing complexity of the network geometry, and of the matrix heterogeneity.
Physical models on discrete space and time
International Nuclear Information System (INIS)
Lorente, M.
1986-01-01
The idea of space and time quantum operators with a discrete spectrum has been proposed frequently since the discovery that some physical quantities exhibit measured values that are multiples of fundamental units. This paper first reviews a number of these physical models. They are: the method of finite elements proposed by Bender et al; the quantum field theory model on discrete space-time proposed by Yamamoto; the finite dimensional quantum mechanics approach proposed by Santhanam et al; the idea of space-time as lattices of n-simplices proposed by Kaplunovsky et al; and the theory of elementary processes proposed by Weizsaecker and his colleagues. The paper then presents a model proposed by the authors and based on the (n+1)-dimensional space-time lattice where fundamental entities interact among themselves 1 to 2n in order to build up a n-dimensional cubic lattice as a ground field where the physical interactions take place. The space-time coordinates are nothing more than the labelling of the ground field and take only discrete values. 11 references
Mathematical modelling of fracture hydrology
International Nuclear Information System (INIS)
Herbert, A.W.; Hodgkindon, D.P.; Lever, D.A.; Robinson, P.C.; Rae, J.
1985-01-01
This report reviews work carried out between January 1983 and December 1984 for the CEC/DOE contract 'Mathematical Modelling of Fracture Hydrology' which forms part of the CEC Mirage project (CEC 1984. Come 1985. Bourke et. al. 1983). It describes the development and use of a variety of mathematical models for the flow of water and transport of radionuclides in flowing groundwater. These models have an important role to play in assessing the long-term safety of radioactive waste burial, and in the planning and interpretation of associated experiments. The work is reported under five headings, namely 1) Statistical fracture network modelling, 2) Continuum models of flow and transport, 3) Simplified models, 4) Analysis of laboratory experiments, 5) Analysis of field experiments
Mathematical modelling of fracture hydrology
International Nuclear Information System (INIS)
Rae, J.; Hodgkinson, D.P.; Robinson, P.C.; Herbert, A.W.
1984-04-01
This progress report contains notes on three aspects of hydrological modelling. Work on hydrodynamic dispersion in fractured media has been extended to transverse dispersion. Further work has been done on diffusion into the rock matrix and its effect on solute transport. The program NAMSOL has been used for the MIRAGE code comparison exercise being organised by Atkins R and D. (author)
Fracture mechanics model of fragmentation
International Nuclear Information System (INIS)
Glenn, L.A.; Gommerstadt, B.Y.; Chudnovsky, A.
1986-01-01
A model of the fragmentation process is developed, based on the theory of linear elastic fracture mechanics, which predicts the average fragment size as a function of strain rate and material properties. This approach permits a unification of previous results, yielding Griffith's solution in the low-strain-rate limit and Grady's solution at high strain rates
Jenkins, Paul J; McDonald, David A; Van Der Meer, Robert; Morton, Alec; Nugent, Margaret; Rymaszewski, Lech A
2017-01-01
Objective Healthcare faces the continual challenge of improving outcome while aiming to reduce cost. The aim of this study was to determine the micro cost differences of the Glasgow non-operative trauma virtual pathway in comparison to a traditional pathway. Design Discrete event simulation was used to model and analyse cost and resource utilisation with an activity-based costing approach. Data for a full comparison before the process change was unavailable so we used a modelling approach, comparing a virtual fracture clinic (VFC) with a simulated traditional fracture clinic (TFC). Setting The orthopaedic unit VFC pathway pioneered at Glasgow Royal Infirmary has attracted significant attention and interest and is the focus of this cost study. Outcome measures Our study focused exclusively on patients with non-operative trauma attending emergency department or the minor injuries unit and the subsequent step in the patient pathway. Retrospective studies of patient outcomes as a result of the protocol introductions for specific injuries are presented in association with activity costs from the models. Results Patients are satisfied with the new pathway, the information provided and the outcome of their injuries (Evidence Level IV). There was a 65% reduction in the number of first outpatient face-to-face (f2f) attendances in orthopaedics. In the VFC pathway, the resources required per day were significantly lower for all staff groups (p≤0.001). The overall cost per patient of the VFC pathway was £22.84 (95% CI 21.74 to 23.92) per patient compared with £36.81 (95% CI 35.65 to 37.97) for the TFC pathway. Conclusions Our results give a clearer picture of the cost comparison of the virtual pathway over a wholly traditional f2f clinic system. The use of simulation-based stochastic costings in healthcare economic analysis has been limited to date, but this study provides evidence for adoption of this method as a basis for its application in other healthcare settings
Anderson, Gillian H; Jenkins, Paul J; McDonald, David A; Van Der Meer, Robert; Morton, Alec; Nugent, Margaret; Rymaszewski, Lech A
2017-09-07
Healthcare faces the continual challenge of improving outcome while aiming to reduce cost. The aim of this study was to determine the micro cost differences of the Glasgow non-operative trauma virtual pathway in comparison to a traditional pathway. Discrete event simulation was used to model and analyse cost and resource utilisation with an activity-based costing approach. Data for a full comparison before the process change was unavailable so we used a modelling approach, comparing a virtual fracture clinic (VFC) with a simulated traditional fracture clinic (TFC). The orthopaedic unit VFC pathway pioneered at Glasgow Royal Infirmary has attracted significant attention and interest and is the focus of this cost study. Our study focused exclusively on patients with non-operative trauma attending emergency department or the minor injuries unit and the subsequent step in the patient pathway. Retrospective studies of patient outcomes as a result of the protocol introductions for specific injuries are presented in association with activity costs from the models. Patients are satisfied with the new pathway, the information provided and the outcome of their injuries (Evidence Level IV). There was a 65% reduction in the number of first outpatient face-to-face (f2f) attendances in orthopaedics. In the VFC pathway, the resources required per day were significantly lower for all staff groups (p≤0.001). The overall cost per patient of the VFC pathway was £22.84 (95% CI 21.74 to 23.92) per patient compared with £36.81 (95% CI 35.65 to 37.97) for the TFC pathway. Our results give a clearer picture of the cost comparison of the virtual pathway over a wholly traditional f2f clinic system. The use of simulation-based stochastic costings in healthcare economic analysis has been limited to date, but this study provides evidence for adoption of this method as a basis for its application in other healthcare settings. © Article author(s) (or their employer(s) unless otherwise
International Nuclear Information System (INIS)
Chan, T.; Scheier, N.W.; O'Connor, P.A.
1997-10-01
A numerical study has been conducted to investigate the effects of a discrete fracture and an excavation damage zone (EDZ) on groundwater mediated transport of I2 9 from a hypothetical nuclear fuel waste disposal vault through saturated, sparsely fractured plutonic rock to the biosphere. The reference disposal system simulated in the present work is based on the median value case of the postclosure assessment case study presented by AECL to support the Environmental Impact Statement (EIS) submitted to the Canadian Environmental Assessment Agency (CEAA). In particular, the reference geosphere is based mainly on hydrogeological characteristics at the site of AECL's Underground Research Laboratory in the Whiteshell Research Area, southeastern Manitoba. Several features not explicitly simulated in the EIS postclosure assessment case study are investigated in this study. These include the hypothetical possibility of a discrete fracture or a narrow fracture zone existing in the rock in the immediate vicinity of the disposal vault. This hypothetical fracture is modeled as a discrete fracture that connects or almost connects the vault to nearby fracture zone LD1. Simulations are performed using a combination of three-dimensional flow model and corresponding two-dimensional transport models, and the MOTIF finite-element code. It should be emphasized that the primary purpose of the present study it to investigate the relative importance of the various possible features in the rock in the immediate vicinity of the vault. Detailed numerical modelling of the effectiveness of various engineered barriers that could be used to mitigate any negative effects of such features is beyond the scope of this study
Jiang, Jiamin; Younis, Rami M.
2017-06-01
The first-order methods commonly employed in reservoir simulation for computing the convective fluxes introduce excessive numerical diffusion leading to severe smoothing of displacement fronts. We present a fully-implicit cell-centered finite-volume (CCFV) framework that can achieve second-order spatial accuracy on smooth solutions, while at the same time maintain robustness and nonlinear convergence performance. A novel multislope MUSCL method is proposed to construct the required values at edge centroids in a straightforward and effective way by taking advantage of the triangular mesh geometry. In contrast to the monoslope methods in which a unique limited gradient is used, the multislope concept constructs specific scalar slopes for the interpolations on each edge of a given element. Through the edge centroids, the numerical diffusion caused by mesh skewness is reduced, and optimal second order accuracy can be achieved. Moreover, an improved smooth flux-limiter is introduced to ensure monotonicity on non-uniform meshes. The flux-limiter provides high accuracy without degrading nonlinear convergence performance. The CCFV framework is adapted to accommodate a lower-dimensional discrete fracture-matrix (DFM) model. Several numerical tests with discrete fractured system are carried out to demonstrate the efficiency and robustness of the numerical model.
Discrete Symmetries and Models of Flavour Mixing
International Nuclear Information System (INIS)
King, Stephen F
2015-01-01
In this talk we shall give an overview of the role of discrete symmetries, including both CP and family symmetry, in constructing unified models of quark and lepton (including especially neutrino) masses and mixing. Various different approaches to model building will be described, denoted as direct, semi-direct and indirect, and the pros and cons of each approach discussed. Particular examples based on Δ(6n 2 ) will be discussed and an A to Z of Flavour with Pati-Salam will be presented. (paper)
A Discrete Model for Color Naming
Directory of Open Access Journals (Sweden)
J. M. Boi
2007-01-01
Full Text Available The ability to associate labels to colors is very natural for human beings. Though, this apparently simple task hides very complex and still unsolved problems, spreading over many different disciplines ranging from neurophysiology to psychology and imaging. In this paper, we propose a discrete model for computational color categorization and naming. Starting from the 424 color specimens of the OSA-UCS set, we propose a fuzzy partitioning of the color space. Each of the 11 basic color categories identified by Berlin and Kay is modeled as a fuzzy set whose membership function is implicitly defined by fitting the model to the results of an ad hoc psychophysical experiment (Experiment 1. Each OSA-UCS sample is represented by a feature vector whose components are the memberships to the different categories. The discrete model consists of a three-dimensional Delaunay triangulation of the CIELAB color space which associates each OSA-UCS sample to a vertex of a 3D tetrahedron. Linear interpolation is used to estimate the membership values of any other point in the color space. Model validation is performed both directly, through the comparison of the predicted membership values to the subjective counterparts, as evaluated via another psychophysical test (Experiment 2, and indirectly, through the investigation of its exploitability for image segmentation. The model has proved to be successful in both cases, providing an estimation of the membership values in good agreement with the subjective measures as well as a semantically meaningful color-based segmentation map.
A Discrete Model for Color Naming
Menegaz, G.; Le Troter, A.; Sequeira, J.; Boi, J. M.
2006-12-01
The ability to associate labels to colors is very natural for human beings. Though, this apparently simple task hides very complex and still unsolved problems, spreading over many different disciplines ranging from neurophysiology to psychology and imaging. In this paper, we propose a discrete model for computational color categorization and naming. Starting from the 424 color specimens of the OSA-UCS set, we propose a fuzzy partitioning of the color space. Each of the 11 basic color categories identified by Berlin and Kay is modeled as a fuzzy set whose membership function is implicitly defined by fitting the model to the results of an ad hoc psychophysical experiment (Experiment 1). Each OSA-UCS sample is represented by a feature vector whose components are the memberships to the different categories. The discrete model consists of a three-dimensional Delaunay triangulation of the CIELAB color space which associates each OSA-UCS sample to a vertex of a 3D tetrahedron. Linear interpolation is used to estimate the membership values of any other point in the color space. Model validation is performed both directly, through the comparison of the predicted membership values to the subjective counterparts, as evaluated via another psychophysical test (Experiment 2), and indirectly, through the investigation of its exploitability for image segmentation. The model has proved to be successful in both cases, providing an estimation of the membership values in good agreement with the subjective measures as well as a semantically meaningful color-based segmentation map.
Predictions of first passage times in sparse discrete fracture networks using graph-based reductions
Hyman, J.; Hagberg, A.; Srinivasan, G.; Mohd-Yusof, J.; Viswanathan, H. S.
2017-12-01
We present a graph-based methodology to reduce the computational cost of obtaining first passage times through sparse fracture networks. We derive graph representations of generic three-dimensional discrete fracture networks (DFNs) using the DFN topology and flow boundary conditions. Subgraphs corresponding to the union of the k shortest paths between the inflow and outflow boundaries are identified and transport on their equivalent subnetworks is compared to transport through the full network. The number of paths included in the subgraphs is based on the scaling behavior of the number of edges in the graph with the number of shortest paths. First passage times through the subnetworks are in good agreement with those obtained in the full network, both for individual realizations and in distribution. Accurate estimates of first passage times are obtained with an order of magnitude reduction of CPU time and mesh size using the proposed method.
Quantum mechanical Hamiltonian models of discrete processes
International Nuclear Information System (INIS)
Benioff, P.
1981-01-01
Here the results of other work on quantum mechanical Hamiltonian models of Turing machines are extended to include any discrete process T on a countably infinite set A. The models are constructed here by use of scattering phase shifts from successive scatterers to turn on successive step interactions. Also a locality requirement is imposed. The construction is done by first associating with each process T a model quantum system M with associated Hilbert space H/sub M/ and step operator U/sub T/. Since U/sub T/ is not unitary in general, M, H/sub M/, and U/sub T/ are extended into a (continuous time) Hamiltonian model on a larger space which satisfies the locality requirement. The construction is compared with the minimal unitary dilation of U/sub T/. It is seen that the model constructed here is larger than the minimal one. However, the minimal one does not satisfy the locality requirement
Xiong, Ziming; Wang, Mingyang; Shi, ShaoShuai; Xia, YuanPu; Lu, Hao; Bu, Lin
2017-12-01
The construction of tunnels and underground engineering in China has developed rapidly in recent years in both the number and the length of tunnels. However, with the development of tunnel construction technology, risk assessment of the tunnels has become increasingly important. Water inrush is one of the most important causes of engineering accidents worldwide, resulting in considerable economic and environmental losses. Accordingly, water inrush prediction is important for ensuring the safety of tunnel construction. Therefore, in this study, we constructed a three-dimensional discrete network fracture model using the Monte Carlo method first with the basic data from the engineering geological map of the Longmen Mountain area, the location of the Longmen Mountain tunnel. Subsequently, we transformed the discrete fracture networks into a pipe network model. Next, the DEM of the study area was analysed and a submerged analysis was conducted to determine the water storage area. Finally, we attempted to predict the water inrush along the Longmen Mountain tunnel based on the Darcy flow equation. Based on the contrast of water inrush between the proposed approach, groundwater dynamics and precipitation infiltration method, we conclude the following: the water inflow determined using the groundwater dynamics simulation results are basically consistent with those in the D2K91+020 to D2K110+150 mileage. Specifically, in the D2K91+020 to D2K94+060, D2K96+440 to D2K98+100 and other sections of the tunnel, the simulated and measured results are in close agreement and show that this method is effective. In general, we can predict the water inflow in the area of the Longmen Mountain tunnel based on the existing fracture joint parameters and the hydrogeological data of the Longmen Mountain area, providing a water inrush simulation and guiding the tunnel excavation and construction stages.
Discrete time modelization of human pilot behavior
Cavalli, D.; Soulatges, D.
1975-01-01
This modelization starts from the following hypotheses: pilot's behavior is a time discrete process, he can perform only one task at a time and his operating mode depends on the considered flight subphase. Pilot's behavior was observed using an electro oculometer and a simulator cockpit. A FORTRAN program has been elaborated using two strategies. The first one is a Markovian process in which the successive instrument readings are governed by a matrix of conditional probabilities. In the second one, strategy is an heuristic process and the concepts of mental load and performance are described. The results of the two aspects have been compared with simulation data.
Discrete ellipsoidal statistical BGK model and Burnett equations
Zhang, Yu-Dong; Xu, Ai-Guo; Zhang, Guang-Cai; Chen, Zhi-Hua; Wang, Pei
2018-06-01
A new discrete Boltzmann model, the discrete ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) model, is proposed to simulate nonequilibrium compressible flows. Compared with the original discrete BGK model, the discrete ES-BGK has a flexible Prandtl number. For the discrete ES-BGK model in the Burnett level, two kinds of discrete velocity model are introduced and the relations between nonequilibrium quantities and the viscous stress and heat flux in the Burnett level are established. The model is verified via four benchmark tests. In addition, a new idea is introduced to recover the actual distribution function through the macroscopic quantities and their space derivatives. The recovery scheme works not only for discrete Boltzmann simulation but also for hydrodynamic ones, for example, those based on the Navier-Stokes or the Burnett equations.
Coupled models in porous media: reactive transport and fractures
International Nuclear Information System (INIS)
Amir, L.
2008-12-01
This thesis deals with numerical simulation of coupled models for flow and transport in porous media. We present a new method for coupling chemical reactions and transport by using a Newton-Krylov method, and we also present a model of flow in fractured media, based on a domain decomposition method that takes into account the case of intersecting fractures. This study is composed of three parts: the first part contains an analysis, and implementation, of various numerical methods for discretizing advection-diffusion problems, in particular by using operator splitting methods. The second part is concerned with a fully coupled method for modeling transport and chemistry problems. The coupled transport-chemistry model is described, after discretization in time, by a system of nonlinear equations. The size of the system, namely the number of grid points times the number a chemical species, precludes a direct solution of the linear system. To alleviate this difficulty, we solve the system by a Newton-Krylov method, so as to avoid forming and factoring the Jacobian matrix. In the last part, we present a model of flow in 3D for intersecting fractures, by using a domain decomposition method. The fractures are treated as interfaces between sub-domains. We show existence and uniqueness of the solution, and we validate the model by numerical tests. (author)
Discrete-time modelling of musical instruments
International Nuclear Information System (INIS)
Vaelimaeki, Vesa; Pakarinen, Jyri; Erkut, Cumhur; Karjalainen, Matti
2006-01-01
This article describes physical modelling techniques that can be used for simulating musical instruments. The methods are closely related to digital signal processing. They discretize the system with respect to time, because the aim is to run the simulation using a computer. The physics-based modelling methods can be classified as mass-spring, modal, wave digital, finite difference, digital waveguide and source-filter models. We present the basic theory and a discussion on possible extensions for each modelling technique. For some methods, a simple model example is chosen from the existing literature demonstrating a typical use of the method. For instance, in the case of the digital waveguide modelling technique a vibrating string model is discussed, and in the case of the wave digital filter technique we present a classical piano hammer model. We tackle some nonlinear and time-varying models and include new results on the digital waveguide modelling of a nonlinear string. Current trends and future directions in physical modelling of musical instruments are discussed
Directory of Open Access Journals (Sweden)
Pooya Hamdi
2015-12-01
Full Text Available Heterogeneity is an inherent component of rock and may be present in different forms including mineral heterogeneity, geometrical heterogeneity, weak grain boundaries and micro-defects. Microcracks are usually observed in crystalline rocks in two forms: natural and stress-induced; the amount of stress-induced microcracking increases with depth and in-situ stress. Laboratory results indicate that the physical properties of rocks such as strength, deformability, P-wave velocity and permeability are influenced by increase in microcrack intensity. In this study, the finite-discrete element method (FDEM is used to model microcrack heterogeneity by introducing into a model sample sets of microcracks using the proposed micro discrete fracture network (μDFN approach. The characteristics of the microcracks required to create μDFN models are obtained through image analyses of thin sections of Lac du Bonnet granite adopted from published literature. A suite of two-dimensional laboratory tests including uniaxial, triaxial compression and Brazilian tests is simulated and the results are compared with laboratory data. The FDEM-μDFN models indicate that micro-heterogeneity has a profound influence on both the mechanical behavior and resultant fracture pattern. An increase in the microcrack intensity leads to a reduction in the strength of the sample and changes the character of the rock strength envelope. Spalling and axial splitting dominate the failure mode at low confinement while shear failure is the dominant failure mode at high confinement. Numerical results from simulated compression tests show that microcracking reduces the cohesive component of strength alone, and the frictional strength component remains unaffected. Results from simulated Brazilian tests show that the tensile strength is influenced by the presence of microcracks, with a reduction in tensile strength as microcrack intensity increases. The importance of microcrack heterogeneity in
Micromechanics modelling of ductile fracture
Chen, Zengtao
2013-01-01
This book summarizes research advances in micromechanics modelling of ductile fractures made in the past two decades. The ultimate goal of this book is to reach manufacturing frontline designers and materials engineers by providing a user-oriented, theoretical background of micromechanics modeling. Accordingly, the book is organized in a unique way and presents a vigorous damage percolation model developed by the authors over the last ten years. This model overcomes almost all difficulties of the existing models and can be used to completely accommodate ductile damage development within a single, measured microstructure frame. Related void damage criteria including nucleation, growth and coalescence are then discussed in detail: how they are improved, when and where they are used in the model, and how the model performs in comparison with the existing models. Sample forming simulations are provided to illustrate the model’s performance.
Numerical modelling of flow and transport in rough fractures
Directory of Open Access Journals (Sweden)
Scott Briggs
2014-12-01
Full Text Available Simulation of flow and transport through rough walled rock fractures is investigated using the lattice Boltzmann method (LBM and random walk (RW, respectively. The numerical implementation is developed and validated on general purpose graphic processing units (GPGPUs. Both the LBM and RW method are well suited to parallel implementation on GPGPUs because they require only next-neighbour communication and thus can reduce expenses. The LBM model is an order of magnitude faster on GPGPUs than published results for LBM simulations run on modern CPUs. The fluid model is verified for parallel plate flow, backward facing step and single fracture flow; and the RW model is verified for point-source diffusion, Taylor-Aris dispersion and breakthrough behaviour in a single fracture. Both algorithms place limitations on the discrete displacement of fluid or particle transport per time step to minimise the numerical error that must be considered during implementation.
Modeling flow and transport in fracture networks using graphs
Karra, S.; O'Malley, D.; Hyman, J. D.; Viswanathan, H. S.; Srinivasan, G.
2018-03-01
Fractures form the main pathways for flow in the subsurface within low-permeability rock. For this reason, accurately predicting flow and transport in fractured systems is vital for improving the performance of subsurface applications. Fracture sizes in these systems can range from millimeters to kilometers. Although modeling flow and transport using the discrete fracture network (DFN) approach is known to be more accurate due to incorporation of the detailed fracture network structure over continuum-based methods, capturing the flow and transport in such a wide range of scales is still computationally intractable. Furthermore, if one has to quantify uncertainty, hundreds of realizations of these DFN models have to be run. To reduce the computational burden, we solve flow and transport on a graph representation of a DFN. We study the accuracy of the graph approach by comparing breakthrough times and tracer particle statistical data between the graph-based and the high-fidelity DFN approaches, for fracture networks with varying number of fractures and degree of heterogeneity. Due to our recent developments in capabilities to perform DFN high-fidelity simulations on fracture networks with large number of fractures, we are in a unique position to perform such a comparison. We show that the graph approach shows a consistent bias with up to an order of magnitude slower breakthrough when compared to the DFN approach. We show that this is due to graph algorithm's underprediction of the pressure gradients across intersections on a given fracture, leading to slower tracer particle speeds between intersections and longer travel times. We present a bias correction methodology to the graph algorithm that reduces the discrepancy between the DFN and graph predictions. We show that with this bias correction, the graph algorithm predictions significantly improve and the results are very accurate. The good accuracy and the low computational cost, with O (104) times lower times than
Discrete element modeling of microstructure of nacre
Chandler, Mei Qiang; Cheng, Jing-Ru C.
2018-04-01
The microstructure of nacre consists of polygon-shaped aragonite mineral tablets bonded by very thin layers of organic materials and is organized in a brick-mortar morphology. In this research, the discrete element method was utilized to model this structure. The aragonite mineral tablets were modeled with three-dimensional polygon particles generated by the Voronoi tessellation method to represent the Voronoi-like patterns of mineral tablets assembly observed in experiments. The organic matrix was modeled with a group of spring elements. The constitutive relations of the spring elements were inspired from the experimental results of organic molecules from the literature. The mineral bridges were modeled with simple elastic bonds with the parameters based on experimental data from the literature. The bulk stress-strain responses from the models agreed well with experimental results. The model results show that the mineral bridges play important roles in providing the stiffness and yield strength for the nacre, while the organic matrix in providing the ductility for the nacre. This work demonstrated the suitability of particle methods for modeling microstructures of nacre.
Fracture network modeling and GoldSim simulation support
International Nuclear Information System (INIS)
Sugita, Kenichirou; Dershowitz, W.
2005-01-01
During Heisei-16, Golder Associates provided support for JNC Tokai through discrete fracture network data analysis and simulation of the Mizunami Underground Research Laboratory (MIU), participation in Task 6 of the AEspoe Task Force on Modeling of Groundwater Flow and Transport, and development of methodologies for analysis of repository site characterization strategies and safety assessment. MIU support during H-16 involved updating the H-15 FracMan discrete fracture network (DFN) models for the MIU shaft region, and developing improved simulation procedures. Updates to the conceptual model included incorporation of 'Step2' (2004) versions of the deterministic structures, and revision of background fractures to be consistent with conductive structure data from the DH-2 borehole. Golder developed improved simulation procedures for these models through the use of hybrid discrete fracture network (DFN), equivalent porous medium (EPM), and nested DFN/EPM approaches. For each of these models, procedures were documented for the entire modeling process including model implementation, MMP simulation, and shaft grouting simulation. Golder supported JNC participation in Task 6AB, 6D and 6E of the AEspoe Task Force on Modeling of Groundwater Flow and Transport during H-16. For Task 6AB, Golder developed a new technique to evaluate the role of grout in performance assessment time-scale transport. For Task 6D, Golder submitted a report of H-15 simulations to SKB. For Task 6E, Golder carried out safety assessment time-scale simulations at the block scale, using the Laplace Transform Galerkin method. During H-16, Golder supported JNC's Total System Performance Assessment (TSPA) strategy by developing technologies for the analysis of the use site characterization data in safety assessment. This approach will aid in the understanding of the use of site characterization to progressively reduce site characterization uncertainty. (author)
Assessing alternative conceptual models of fracture flow
International Nuclear Information System (INIS)
Ho, C.K.
1995-01-01
The numerical code TOUGH2 was used to assess alternative conceptual models of fracture flow. The models that were considered included the equivalent continuum model (ECM) and the dual permeability (DK) model. A one-dimensional, layered, unsaturated domain was studied with a saturated bottom boundary and a constant infiltration at the top boundary. Two different infiltration rates were used in the studies. In addition, the connection areas between the fracture and matrix elements in the dual permeability model were varied. Results showed that the two conceptual models of fracture flow produced different saturation and velocity profiles-even under steady-state conditions. The magnitudes of the discrepancies were sensitive to two parameters that affected the flux between the fractures and matrix in the dual permeability model: (1) the fracture-matrix connection areas and (2) the capillary pressure gradients between the fracture and matrix elements
Identification of parameters of discrete-continuous models
International Nuclear Information System (INIS)
Cekus, Dawid; Warys, Pawel
2015-01-01
In the paper, the parameters of a discrete-continuous model have been identified on the basis of experimental investigations and formulation of optimization problem. The discrete-continuous model represents a cantilever stepped Timoshenko beam. The mathematical model has been formulated and solved according to the Lagrange multiplier formalism. Optimization has been based on the genetic algorithm. The presented proceeding’s stages make the identification of any parameters of discrete-continuous systems possible
Identification of parameters of discrete-continuous models
Energy Technology Data Exchange (ETDEWEB)
Cekus, Dawid, E-mail: cekus@imipkm.pcz.pl; Warys, Pawel, E-mail: warys@imipkm.pcz.pl [Institute of Mechanics and Machine Design Foundations, Czestochowa University of Technology, Dabrowskiego 73, 42-201 Czestochowa (Poland)
2015-03-10
In the paper, the parameters of a discrete-continuous model have been identified on the basis of experimental investigations and formulation of optimization problem. The discrete-continuous model represents a cantilever stepped Timoshenko beam. The mathematical model has been formulated and solved according to the Lagrange multiplier formalism. Optimization has been based on the genetic algorithm. The presented proceeding’s stages make the identification of any parameters of discrete-continuous systems possible.
Model of T-Type Fracture in Coal Fracturing and Analysis of Influence Factors of Fracture Morphology
Directory of Open Access Journals (Sweden)
Yuwei Li
2018-05-01
Full Text Available Special T-type fractures can be formed when coal is hydraulically fractured and there is currently no relevant theoretical model to calculate and describe them. This paper first establishes the height calculation model of vertical fractures in multi-layered formations and deduces the stress intensity factor (SIF at the upper and lower sides of the fracture in the process of vertical fracture extension. Combined with the fracture tip stress analysis method of fracture mechanics theory, the horizontal bedding is taken into account for tensile and shear failure, and the critical mechanical conditions for the formation of horizontal fracture in coal are obtained. Finally, the model of T-type fracture in coal fracturing is established, and it is verified by fracturing simulation experiments. The model calculation result shows that the increase of vertical fracture height facilitates the increase of horizontal fracture length. The fracture toughness of coal has a significant influence on the length of horizontal fracture and there is a threshold. When the fracture toughness is less than the threshold, the length of horizontal fracture remains unchanged, otherwise, the length of horizontal fracture increases rapidly with the increase of fracture toughness. When the shear strength of the interface between the coalbed and the interlayer increases, the length of the horizontal fracture of the T-type fracture rapidly decreases.
Williams, T. R. N.; Baxter, S.; Hartley, L.; Appleyard, P.; Koskinen, L.; Vanhanarkaus, O.; Selroos, J. O.; Munier, R.
2017-12-01
Discrete fracture network (DFN) models provide a natural analysis framework for rock conditions where flow is predominately through a series of connected discrete features. Mechanistic models to predict the structural patterns of networks are generally intractable due to inherent uncertainties (e.g. deformation history) and as such fracture characterisation typically involves empirical descriptions of fracture statistics for location, intensity, orientation, size, aperture etc. from analyses of field data. These DFN models are used to make probabilistic predictions of likely flow or solute transport conditions for a range of applications in underground resource and construction projects. However, there are many instances when the volumes in which predictions are most valuable are close to data sources. For example, in the disposal of hazardous materials such as radioactive waste, accurate predictions of flow-rates and network connectivity around disposal areas are required for long-term safety evaluation. The problem at hand is thus: how can probabilistic predictions be conditioned on local-scale measurements? This presentation demonstrates conditioning of a DFN model based on the current structural and hydraulic characterisation of the Demonstration Area at the ONKALO underground research facility. The conditioned realisations honour (to a required level of similarity) the locations, orientations and trace lengths of fractures mapped on the surfaces of the nearby ONKALO tunnels and pilot drillholes. Other data used as constraints include measurements from hydraulic injection tests performed in pilot drillholes and inflows to the subsequently reamed experimental deposition holes. Numerical simulations using this suite of conditioned DFN models provides a series of prediction-outcome exercises detailing the reliability of the DFN model to make local-scale predictions of measured geometric and hydraulic properties of the fracture system; and provides an understanding
Calibration of discrete element model parameters: soybeans
Ghodki, Bhupendra M.; Patel, Manish; Namdeo, Rohit; Carpenter, Gopal
2018-05-01
Discrete element method (DEM) simulations are broadly used to get an insight of flow characteristics of granular materials in complex particulate systems. DEM input parameters for a model are the critical prerequisite for an efficient simulation. Thus, the present investigation aims to determine DEM input parameters for Hertz-Mindlin model using soybeans as a granular material. To achieve this aim, widely acceptable calibration approach was used having standard box-type apparatus. Further, qualitative and quantitative findings such as particle profile, height of kernels retaining the acrylic wall, and angle of repose of experiments and numerical simulations were compared to get the parameters. The calibrated set of DEM input parameters includes the following (a) material properties: particle geometric mean diameter (6.24 mm); spherical shape; particle density (1220 kg m^{-3} ), and (b) interaction parameters such as particle-particle: coefficient of restitution (0.17); coefficient of static friction (0.26); coefficient of rolling friction (0.08), and particle-wall: coefficient of restitution (0.35); coefficient of static friction (0.30); coefficient of rolling friction (0.08). The results may adequately be used to simulate particle scale mechanics (grain commingling, flow/motion, forces, etc) of soybeans in post-harvest machinery and devices.
Linking advanced fracture models to structural analysis
Energy Technology Data Exchange (ETDEWEB)
Chiesa, Matteo
2001-07-01
Shell structures with defects occur in many situations. The defects are usually introduced during the welding process necessary for joining different parts of the structure. Higher utilization of structural materials leads to a need for accurate numerical tools for reliable prediction of structural response. The direct discretization of the cracked shell structure with solid finite elements in order to perform an integrity assessment of the structure in question leads to large size problems, and makes such analysis infeasible in structural application. In this study a link between local material models and structural analysis is outlined. An ''ad hoc'' element formulation is used in order to connect complex material models to the finite element framework used for structural analysis. An improved elasto-plastic line spring finite element formulation, used in order to take cracks into account, is linked to shell elements which are further linked to beam elements. In this way one obtain a global model of the shell structure that also accounts for local flexibilities and fractures due to defects. An important advantage with such an approach is a direct fracture mechanics assessment e.g. via computed J-integral or CTOD. A recent development in this approach is the notion of two-parameter fracture assessment. This means that the crack tip stress tri-axiality (constraint) is employed in determining the corresponding fracture toughness, giving a much more realistic capacity of cracked structures. The present thesis is organized in six research articles and an introductory chapter that reviews important background literature related to this work. Paper I and II address the performance of shell and line spring finite elements as a cost effective tool for performing the numerical calculation needed to perform a fracture assessment. In Paper II a failure assessment, based on the testing of a constraint-corrected fracture mechanics specimen under tension, is
Directory of Open Access Journals (Sweden)
Qi Zhao
2014-12-01
Full Text Available Hydraulic fracturing (HF technique has been extensively used for the exploitation of unconventional oil and gas reservoirs. HF enhances the connectivity of less permeable oil and gas-bearing rock formations by fluid injection, which creates an interconnected fracture network and increases the hydrocarbon production. Meanwhile, microseismic (MS monitoring is one of the most effective approaches to evaluate such stimulation process. In this paper, the combined finite-discrete element method (FDEM is adopted to numerically simulate HF and associated MS. Several post-processing tools, including frequency-magnitude distribution (b-value, fractal dimension (D-value, and seismic events clustering, are utilized to interpret numerical results. A non-parametric clustering algorithm designed specifically for FDEM is used to reduce the mesh dependency and extract more realistic seismic information. Simulation results indicated that at the local scale, the HF process tends to propagate following the rock mass discontinuities; while at the reservoir scale, it tends to develop in the direction parallel to the maximum in-situ stress.
Directory of Open Access Journals (Sweden)
Rubén Graffe
2010-01-01
Full Text Available Este trabajo describe la formulación, implementación y aplicación de un modelo discreto de fisura cohesiva el cual permite simular el proceso de fractura en modo I de vigas de concreto simple cuya trayectoria de fisuración está definida. En el proceso de fractura se establece una relación entre el esfuerzo normal de cohesión y la apertura de una fisura, donde el material ubicado fuera de la zona de fractura conserva un comportamiento elástico lineal en carga o descarga, mientras que el material en el interior de la zona de fractura tiene un comportamiento inelástico con ablandamiento por deformación. En la malla se ubican parejas de nudos en la misma posición espacial sobre la trayectoria de la fisura, las cuales desligan a los elementos bidimensionales contiguos. Estos nudos duplicados están conectados entre sí por resortes elasto - plásticos que representan el proceso de fractura. Se simulan numéricamente tres vigas de concreto de diferentes dimensiones que soportan una carga en el centro de la luz. Cada simulación es un análisis no lineal estático con elementos finitos en condición plana de esfuerzos, considerando deformaciones infinitesimales y aplicando un desplazamiento vertical incremental sobre la cara superior de la mitad de la luz de la viga. Se obtuvieron resultados satisfactorios de la respuesta estructural de las vigas, en comparación con los ensayos experimentales y modelaciones numéricas desarrolladas por otros autores.This work describes the formulation, implementation and application of a cohesive crack discrete model, which can simulate the fracture process in mode I of simple concrete beams with defined cracking pattern. In the fracture process, a relationship between the cohesive normal stress and crack opening is established, where the material outside the fracture zone has a lineal elastic behavior in loading and unloading, whereas the material inside the fracture zone has an inelastic behavior with
Discrete and Continuous Models for Partitioning Problems
Lellmann, Jan; Lellmann, Bjö rn; Widmann, Florian; Schnö rr, Christoph
2013-01-01
-based techniques. This work is concerned with the sources of such artifacts. We discuss the importance of differentiating between artifacts caused by discretization and those caused by relaxation and provide supporting numerical examples. Moreover, we consider
Exact solutions for some discrete models of the Boltzmann equation
International Nuclear Information System (INIS)
Cabannes, H.; Hong Tiem, D.
1987-01-01
For the simplest of the discrete models of the Boltzmann equation: the Broadwell model, exact solutions have been obtained by Cornille in the form of bisolitons. In the present Note, we build exact solutions for more complex models [fr
Discrete element modelling of bedload transport
Loyer, A.; Frey, P.
2011-12-01
Discrete element modelling (DEM) has been widely used in solid mechanics and in granular physics. In this type of modelling, each individual particle is taken into account and intergranular interactions are modelled with simple laws (e.g. Coulomb friction). Gravity and contact forces permit to solve the dynamical behaviour of the system. DEM is interesting to model configurations and access to parameters not directly available in laboratory experimentation, hence the term "numerical experimentations" sometimes used to describe DEM. DEM was used to model bedload transport experiments performed at the particle scale with spherical glass beads in a steep and narrow flume. Bedload is the larger material that is transported on the bed on stream channels. It has a great geomorphic impact. Physical processes ruling bedload transport and more generally coarse-particle/fluid systems are poorly known, arguably because granular interactions have been somewhat neglected. An existing DEM code (PFC3D) already computing granular interactions was used. We implemented basic hydrodynamic forces to model the fluid interactions (buoyancy, drag, lift). The idea was to use the minimum number of ingredients to match the experimental results. Experiments were performed with one-size and two-size mixtures of coarse spherical glass beads entrained by a shallow turbulent and supercritical water flow down a steep channel with a mobile bed. The particle diameters were 4 and 6mm, the channel width 6.5mm (about the same width as the coarser particles) and the channel inclination was typically 10%. The water flow rate and the particle rate were kept constant at the upstream entrance and adjusted to obtain bedload transport equilibrium. Flows were filmed from the side by a high-speed camera. Using image processing algorithms made it possible to determine the position, velocity and trajectory of both smaller and coarser particles. Modelled and experimental particle velocity and concentration depth
A discrete-space urban model with environmental amenities
Liaila Tajibaeva; Robert G. Haight; Stephen Polasky
2008-01-01
This paper analyzes the effects of providing environmental amenities associated with open space in a discrete-space urban model and characterizes optimal provision of open space across a metropolitan area. The discrete-space model assumes distinct neighborhoods in which developable land is homogeneous within a neighborhood but heterogeneous across neighborhoods. Open...
Fracture network modeling and GoldSim simulation support
International Nuclear Information System (INIS)
Sugita, Kenichiro; Dershowitz, William
2004-01-01
During Heisei-15, Golder Associates provided support for JNC Tokai through discrete fracture network data analysis and simulation of the MIU Underground Rock Laboratory, participation in Task 6 of the Aespoe Task Force on Modelling of Groundwater Flow and Transport, and development of methodologies for analysis of repository site characterization strategies and safety assessment. MIU Underground Rock Laboratory support during H-15 involved development of new discrete fracture network (DFN) models for the MIU Shoba-sama Site, in the region of shaft development. Golder developed three DFN models for the site using discrete fracture network, equivalent porous medium (EPM), and nested DFN/EPM approaches. Each of these models were compared based upon criteria established for the multiple modeling project (MMP). Golder supported JNC participation in Task 6AB, 6D and 6E of the Aespoe Task Force on Modelling of Groundwater Flow and Transport during H-15. For Task 6AB, Golder implemented an updated microstructural model in GoldSim, and used this updated model to simulate the propagation of uncertainty from experimental to safety assessment time scales, for 5 m scale transport path lengths. Task 6D and 6E compared safety assessment (PA) and experimental time scale simulations in a 200 m scale discrete fracture network. For Task 6D, Golder implemented a DFN model using FracMan/PA Works, and determined the sensitivity of solute transport to a range of material property and geometric assumptions. For Task 6E, Golder carried out demonstration FracMan/PA Works transport calculations at a 1 million year time scale, to ensure that task specifications are realistic. The majority of work for Task 6E will be carried out during H-16. During H-15, Golder supported JNC's Total System Performance Assessment (TSPO) strategy by developing technologies for the analysis of precipitant concentration. These approaches were based on the GoldSim precipitant data management features, and were
Simulation of quasistatic deformations using discrete rod models
Linn, J.; Stephan, T.
2008-01-01
Recently we developed a discrete model of elastic rods with symmetric cross section suitable for a fast simulation of quasistatic deformations [33]. The model is based on Kirchhoff’s geometrically exact theory of rods. Unlike simple models of “mass & spring” type typically used in VR applications, our model provides a proper coupling of bending and torsion. The computational approach comprises a variational formulation combined with a finite difference discretization of the continuum model. A...
Models for the discrete berth allocation problem: A computational comparison
DEFF Research Database (Denmark)
Buhrkal, Katja Frederik; Zuglian, Sara; Røpke, Stefan
2011-01-01
In this paper we consider the problem of allocating arriving ships to discrete berth locations at container terminals. This problem is recognized as one of the most important processes for any container terminal. We review and describe three main models of the discrete dynamic berth allocation...
Models for the Discrete Berth Allocation Problem: A Computational Comparison
DEFF Research Database (Denmark)
Buhrkal, Katja; Zuglian, Sara; Røpke, Stefan
In this paper we consider the problem of allocating arriving ships to discrete berth locations at container terminals. This problem is recognized as one of the most important processes for any container terminal. We review and describe the three main models of the discrete dynamic berth allocation...
Discrete element modeling of subglacial sediment deformation
DEFF Research Database (Denmark)
Damsgaard, Anders; Egholm, David L.; Piotrowski, Jan A.
2013-01-01
The Discrete Element Method (DEM) is used in this study to explore the highly nonlinear dynamics of a granular bed when exposed to stress conditions comparable to those at the bed of warm-based glaciers. Complementary to analog experiments, the numerical approach allows a detailed analysis...
Discrete element modeling of subglacial sediment deformation
DEFF Research Database (Denmark)
Damsgaard, Anders; Egholm, David L.; Piotrowski, Jan A.
The Discrete Element Method (DEM) is used to explore the highly nonlinear dynamics of a granular bed when exposed to stress conditions comparable to those at the bed of warm-based glaciers. In the DEM, the material is simulated on a grain-by-grain basis, and defining the micromechanical properties...
Discrete dislocation modelling of submicron indentation
Widjaja, A; Van der Giessen, E; Needleman, A
2005-01-01
Indentation of a planar single crystal by a circular rigid indenter is analyzed using discrete dislocation plasticity. The crystal has three slip systems and is initially dislocation-free, but edge dislocations can nucleate from point sources inside the crystal. The lattice resistance to dislocation
A Two-Scale Reduced Model for Darcy Flow in Fractured Porous Media
Chen, Huangxin
2016-06-01
In this paper, we develop a two-scale reduced model for simulating the Darcy flow in two-dimensional porous media with conductive fractures. We apply the approach motivated by the embedded fracture model (EFM) to simulate the flow on the coarse scale, and the effect of fractures on each coarse scale grid cell intersecting with fractures is represented by the discrete fracture model (DFM) on the fine scale. In the DFM used on the fine scale, the matrix-fracture system are resolved on unstructured grid which represents the fractures accurately, while in the EFM used on the coarse scale, the flux interaction between fractures and matrix are dealt with as a source term, and the matrix-fracture system can be resolved on structured grid. The Raviart-Thomas mixed finite element methods are used for the solution of the coupled flows in the matrix and the fractures on both fine and coarse scales. Numerical results are presented to demonstrate the efficiency of the proposed model for simulation of flow in fractured porous media.
Multiphase flow models for hydraulic fracturing technology
Osiptsov, Andrei A.
2017-10-01
The technology of hydraulic fracturing of a hydrocarbon-bearing formation is based on pumping a fluid with particles into a well to create fractures in porous medium. After the end of pumping, the fractures filled with closely packed proppant particles create highly conductive channels for hydrocarbon flow from far-field reservoir to the well to surface. The design of the hydraulic fracturing treatment is carried out with a simulator. Those simulators are based on mathematical models, which need to be accurate and close to physical reality. The entire process of fracture placement and flowback/cleanup can be conventionally split into the following four stages: (i) quasi-steady state effectively single-phase suspension flow down the wellbore, (ii) particle transport in an open vertical fracture, (iii) displacement of fracturing fluid by hydrocarbons from the closed fracture filled with a random close pack of proppant particles, and, finally, (iv) highly transient gas-liquid flow in a well during cleanup. The stage (i) is relatively well described by the existing hydralics models, while the models for the other three stages of the process need revisiting and considerable improvement, which was the focus of the author’s research presented in this review paper. For stage (ii), we consider the derivation of a multi-fluid model for suspension flow in a narrow vertical hydraulic fracture at moderate Re on the scale of fracture height and length and also the migration of particles across the flow on the scale of fracture width. At the stage of fracture cleanaup (iii), a novel multi-continua model for suspension filtration is developed. To provide closure relationships for permeability of proppant packings to be used in this model, a 3D direct numerical simulation of single phase flow is carried out using the lattice-Boltzmann method. For wellbore cleanup (iv), we present a combined 1D model for highly-transient gas-liquid flow based on the combination of multi-fluid and
Modeling of 1D Anomalous Diffusion in Fractured Nanoporous Media
Directory of Open Access Journals (Sweden)
Albinali Ali
2016-07-01
Full Text Available Fractured nanoporous reservoirs include multi-scale and discontinuous fractures coupled with a complex nanoporous matrix. Such systems cannot be described by the conventional dual-porosity (or multi-porosity idealizations due to the presence of different flow mechanisms at multiple scales. More detailed modeling approaches, such as Discrete Fracture Network (DFN models, similarly suffer from the extensive data requirements dictated by the intricacy of the flow scales, which eventually deter the utility of these models. This paper discusses the utility and construction of 1D analytical and numerical anomalous diffusion models for heterogeneous, nanoporous media, which is commonly encountered in oil and gas production from tight, unconventional reservoirs with fractured horizontal wells. A fractional form of Darcy’s law, which incorporates the non-local and hereditary nature of flow, is coupled with the classical mass conservation equation to derive a fractional diffusion equation in space and time. Results show excellent agreement with established solutions under asymptotic conditions and are consistent with the physical intuitions.
Efendiev, Yalchin R.
2015-06-05
In this paper, we develop a multiscale finite element method for solving flows in fractured media. Our approach is based on generalized multiscale finite element method (GMsFEM), where we represent the fracture effects on a coarse grid via multiscale basis functions. These multiscale basis functions are constructed in the offline stage via local spectral problems following GMsFEM. To represent the fractures on the fine grid, we consider two approaches (1) discrete fracture model (DFM) (2) embedded fracture model (EFM) and their combination. In DFM, the fractures are resolved via the fine grid, while in EFM the fracture and the fine grid block interaction is represented as a source term. In the proposed multiscale method, additional multiscale basis functions are used to represent the long fractures, while short-size fractures are collectively represented by a single basis functions. The procedure is automatically done via local spectral problems. In this regard, our approach shares common concepts with several approaches proposed in the literature as we discuss. We would like to emphasize that our goal is not to compare DFM with EFM, but rather to develop GMsFEM framework which uses these (DFM or EFM) fine-grid discretization techniques. Numerical results are presented, where we demonstrate how one can adaptively add basis functions in the regions of interest based on error indicators. We also discuss the use of randomized snapshots (Calo et al. Randomized oversampling for generalized multiscale finite element methods, 2014), which reduces the offline computational cost.
Modeling of strongly heat-driven flow in partially saturated fractured porous media
International Nuclear Information System (INIS)
Pruess, K.; Tsang, Y.W.; Wang, J.S.Y.
1985-01-01
The authors have performed modeling studies on the simultaneous transport of heat, liquid water, vapor, and air in partially saturated fractured porous media, with particular emphasis on strongly heat-driven flow. The presence of fractures makes the transport problem very complex, both in terms of flow geometry and physics. The numerical simulator used for their flow calculations takes into account most of the physical effects which are important in multi-phase fluid and heat flow. It has provisions to handle the extreme non-linearities which arise in phase transitions, component disappearances, and capillary discontinuities at fracture faces. They model a region around an infinite linear string of nuclear waste canisters, taking into account both the discrete fractures and the porous matrix. From an analysis of the results obtained with explicit fractures, they develop equivalent continuum models which can reproduce the temperature, saturation, and pressure variation, and gas and liquid flow rates of the discrete fracture-porous matrix calculations. The equivalent continuum approach makes use of a generalized relative permeability concept to take into account the fracture effects. This results in a substantial simplification of the flow problem which makes larger scale modeling of complicated unsaturated fractured porous systems feasible. Potential applications for regional scale simulations and limitations of the continuum approach are discussed. 27 references, 13 figures, 2 tables
Modeling of strongly heat-driven flow in partially saturated fractured porous media
International Nuclear Information System (INIS)
Pruess, K.; Tsang, Y.W.; Wang, J.S.Y.
1984-10-01
We have performed modeling studies on the simultaneous transport of heat, liquid water, vapor, and air in partially saturated fractured porous media, with particular emphasis on strongly heat-driven flow. The presence of fractures makes the transport problem very complex, both in terms of flow geometry and physics. The numerical simulator used for our flow calculations takes into account most of the physical effects which are important in multi-phase fluid and heat flow. It has provisions to handle the extreme non-linearities which arise in phase transitions, component disappearances, and capillary discontinuities at fracture faces. We model a region around an infinite linear string of nuclear waste canisters, taking into account both the discrete fractures and the porous matrix. From an analysis of the results obtained with explicit fractures, we develop equivalent continuum models which can reproduce the temperature, saturation, and pressure variation, and gas and liquid flow rates of the discrete fracture-porous matrix calculations. The equivalent continuum approach makes use of a generalized relative permeability concept to take into account for fracture effects. This results in a substantial simplification of the flow problem which makes larger scale modeling of complicated unsaturated fractured porous systems feasible. Potential applications for regional scale simulations and limitations of the continuum approach are discussed. 27 references, 13 figures, 2 tables
Fourno, A.; Grenier, C.; Benabderrahmane, H.
2003-04-01
Modeling flow and transport in natural fractured media is a difficult issue due among others to the complexity of the system, the particularities of the geometrical features, the strong parameter value contrasts between the fracture zones (flow zones) and the matrix zones (no flow zones). This lead to the development of dedicated tools like for instance discrete fracture network models (DFN). We follow here another line applicable for classical continuous modeling codes. The fracture network is not meshed here but presence of fractures is taken into account by means of continuous heterogeneous fields (permeability, porosity, head, velocity, concentration ...). This line, followed by different authors, is referred as smeared fracture approach and presents the following advantages: the approach is very versatile because no dedicated spatial discretization effort is required (we use a basic regular mesh, simulations can be done on a rough mesh saving computer time). This makes this kind of approach very promising for taking heterogeneity of properties as well as uncertainties into account within a Monte Carlo framework for instance. Furthermore, the geometry of the matrix blocks where transfers proceed by diffusion is fully taken into account contrary to classical simplified 1D approach for instance. Nevertheless continuous heterogeneous field representation of a fractured medium requires a homogenization process at the scale of the mesh considered. Literature proves that this step of homogenization for transport is still a challenging task. Consequently, the level precision of the results has to be estimated. We precedently proposed a new approach dedicated to Mixed and Hybrid Finite Element approach. This numerical scheme is very interesting for such highly heterogeneous media and in particular guaranties exact conservation of mass flow for each mesh leading to good transport results. We developed a smeared fractures approach to model flow and transport limited to
Modelling of 3D fractured geological systems - technique and application
Cacace, M.; Scheck-Wenderoth, M.; Cherubini, Y.; Kaiser, B. O.; Bloecher, G.
2011-12-01
All rocks in the earth's crust are fractured to some extent. Faults and fractures are important in different scientific and industry fields comprising engineering, geotechnical and hydrogeological applications. Many petroleum, gas and geothermal and water supply reservoirs form in faulted and fractured geological systems. Additionally, faults and fractures may control the transport of chemical contaminants into and through the subsurface. Depending on their origin and orientation with respect to the recent and palaeo stress field as well as on the overall kinematics of chemical processes occurring within them, faults and fractures can act either as hydraulic conductors providing preferential pathways for fluid to flow or as barriers preventing flow across them. The main challenge in modelling processes occurring in fractured rocks is related to the way of describing the heterogeneities of such geological systems. Flow paths are controlled by the geometry of faults and their open void space. To correctly simulate these processes an adequate 3D mesh is a basic requirement. Unfortunately, the representation of realistic 3D geological environments is limited by the complexity of embedded fracture networks often resulting in oversimplified models of the natural system. A technical description of an improved method to integrate generic dipping structures (representing faults and fractures) into a 3D porous medium is out forward. The automated mesh generation algorithm is composed of various existing routines from computational geometry (e.g. 2D-3D projection, interpolation, intersection, convex hull calculation) and meshing (e.g. triangulation in 2D and tetrahedralization in 3D). All routines have been combined in an automated software framework and the robustness of the approach has been tested and verified. These techniques and methods can be applied for fractured porous media including fault systems and therefore found wide applications in different geo-energy related
Discretization model for nonlinear dynamic analysis of three dimensional structures
International Nuclear Information System (INIS)
Hayashi, Y.
1982-12-01
A discretization model for nonlinear dynamic analysis of three dimensional structures is presented. The discretization is achieved through a three dimensional spring-mass system and the dynamic response obtained by direct integration of the equations of motion using central diferences. First the viability of the model is verified through the analysis of homogeneous linear structures and then its performance in the analysis of structures subjected to impulsive or impact loads, taking into account both geometrical and physical nonlinearities is evaluated. (Author) [pt
International Nuclear Information System (INIS)
Vela, A.; Elorza, F.J.; Florez, F.; Paredes, C.; Mazadiego, L.; Llamas, J.F.; Perez, E.; Vives, L.; Carrera, J.; Munoz, A.; De Vicente, G.; Casquet, C.
1999-01-01
Safety analysis of radioactive waste storage systems require fractured rock studies. The performance assessment studies of this type of problems include the development of radionuclide flow and transport models to predict the evolution of possible contaminants released from the repository to the biosphere. The methodology developed in the HIDROBAP project and some results obtained with its application in El Berrocal granite batholith are presented. It integrates modern tools belonging to different disciplines. A Discrete Fracture Network model (DFT) was selected to simulate the fractured medium and a 3D finite element flow and transport model that includes the inverse problem techniques has been coupled to the DFT model to simulate the water movement trough the fracture network system. Preliminary results show that this integrated methodology can be very useful for the hydrogeological characterisation of rock fractured media. (author)
Computational models of the hydrodynamics of fractured-porous media
International Nuclear Information System (INIS)
Grandi, G.M.
1989-01-01
The prediction of the flow pattern in fractured-porous media has great importance in the assessment of the local thermohydrological effects of the siting of a nuclear waste repository, among many other technological applications. Computational models must be used due to the complexity of the different phenomena involved which restricts the use of analytical techniques. A new numerical method, based on the boundary-fitted finite-difference technique, is presented in this thesis. The boundaries are external (the boundary of the physical domain), and internal (which correspond to the fracture network). The inclusion of the discrete fracture representation in the volume that represents the porous medium is the difference between the usual approach and the present one. The numerical model has been used in the prediction of the flow pattern in several internationally recognized verification cases and to hypothetical problems of our interest. The results obtained proved that the numerical approach considered gives accurate and reliable predictions of the hydrodynamics of fractured-porous media, allowing its use for the above mentioned studies. (Author) [es
International Nuclear Information System (INIS)
Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.
2016-01-01
A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell’s equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell–Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell–Lorentz equations, we trace the development
Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.
2018-01-01
A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell’s equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell–Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell–Lorentz equations, we trace the development
Energy Technology Data Exchange (ETDEWEB)
Mishchenko, Michael I., E-mail: michael.i.mishchenko@nasa.gov [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Dlugach, Janna M. [Main Astronomical Observatory of the National Academy of Sciences of Ukraine, 27 Zabolotny Str., 03680, Kyiv (Ukraine); Yurkin, Maxim A. [Voevodsky Institute of Chemical Kinetics and Combustion, SB RAS, Institutskaya str. 3, 630090 Novosibirsk (Russian Federation); Novosibirsk State University, Pirogova 2, 630090 Novosibirsk (Russian Federation); Bi, Lei [Department of Atmospheric Sciences, Texas A& M University, College Station, TX 77843 (United States); Cairns, Brian [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Liu, Li [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Columbia University, 2880 Broadway, New York, NY 10025 (United States); Panetta, R. Lee [Department of Atmospheric Sciences, Texas A& M University, College Station, TX 77843 (United States); Travis, Larry D. [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Yang, Ping [Department of Atmospheric Sciences, Texas A& M University, College Station, TX 77843 (United States); Zakharova, Nadezhda T. [Trinnovim LLC, 2880 Broadway, New York, NY 10025 (United States)
2016-05-16
A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell’s equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell–Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell–Lorentz equations, we trace the development
Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.
2016-01-01
A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell's equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell- Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of
Galerkin v. discrete-optimal projection in nonlinear model reduction
Energy Technology Data Exchange (ETDEWEB)
Carlberg, Kevin Thomas [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Barone, Matthew Franklin [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Antil, Harbir [George Mason Univ., Fairfax, VA (United States)
2015-04-01
Discrete-optimal model-reduction techniques such as the Gauss{Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible ow problems where standard Galerkin techniques have failed. However, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform projection at the time-continuous level, while discrete-optimal techniques do so at the time-discrete level. This work provides a detailed theoretical and experimental comparison of the two techniques for two common classes of time integrators: linear multistep schemes and Runge{Kutta schemes. We present a number of new ndings, including conditions under which the discrete-optimal ROM has a time-continuous representation, conditions under which the two techniques are equivalent, and time-discrete error bounds for the two approaches. Perhaps most surprisingly, we demonstrate both theoretically and experimentally that decreasing the time step does not necessarily decrease the error for the discrete-optimal ROM; instead, the time step should be `matched' to the spectral content of the reduced basis. In numerical experiments carried out on a turbulent compressible- ow problem with over one million unknowns, we show that increasing the time step to an intermediate value decreases both the error and the simulation time of the discrete-optimal reduced-order model by an order of magnitude.
Methodology for characterizing modeling and discretization uncertainties in computational simulation
Energy Technology Data Exchange (ETDEWEB)
ALVIN,KENNETH F.; OBERKAMPF,WILLIAM L.; RUTHERFORD,BRIAN M.; DIEGERT,KATHLEEN V.
2000-03-01
This research effort focuses on methodology for quantifying the effects of model uncertainty and discretization error on computational modeling and simulation. The work is directed towards developing methodologies which treat model form assumptions within an overall framework for uncertainty quantification, for the purpose of developing estimates of total prediction uncertainty. The present effort consists of work in three areas: framework development for sources of uncertainty and error in the modeling and simulation process which impact model structure; model uncertainty assessment and propagation through Bayesian inference methods; and discretization error estimation within the context of non-deterministic analysis.
Discrete event simulation: Modeling simultaneous complications and outcomes
Quik, E.H.; Feenstra, T.L.; Krabbe, P.F.M.
2012-01-01
OBJECTIVES: To present an effective and elegant model approach to deal with specific characteristics of complex modeling. METHODS: A discrete event simulation (DES) model with multiple complications and multiple outcomes that each can occur simultaneously was developed. In this DES model parameters,
Inclusion-initiated fracture model for ceramics
International Nuclear Information System (INIS)
Sung, J.; Nicholson, P.S.
1990-01-01
The fracture of ceramics initiating from a typical inclusion is analyzed. The inclusion is considered to have a thermal expansion coefficient and fracture toughness lower than those of the matrix and a Young's modulus higher than that of the matrix. Inclusion-initiated fracture is modeled for a spherical inclusion using a weight function method to compute the residual stress intensity factor for a part-through elliptical crack. The results are applied to an α-Al 2 O 3 inclusion embedded in a tetragonal ZrO 2 ceramic. The strength predictions agree well with experimental data
Discrete and Continuous Models for Partitioning Problems
Lellmann, Jan
2013-04-11
Recently, variational relaxation techniques for approximating solutions of partitioning problems on continuous image domains have received considerable attention, since they introduce significantly less artifacts than established graph cut-based techniques. This work is concerned with the sources of such artifacts. We discuss the importance of differentiating between artifacts caused by discretization and those caused by relaxation and provide supporting numerical examples. Moreover, we consider in depth the consequences of a recent theoretical result concerning the optimality of solutions obtained using a particular relaxation method. Since the employed regularizer is quite tight, the considered relaxation generally involves a large computational cost. We propose a method to significantly reduce these costs in a fully automatic way for a large class of metrics including tree metrics, thus generalizing a method recently proposed by Strekalovskiy and Cremers (IEEE conference on computer vision and pattern recognition, pp. 1905-1911, 2011). © 2013 Springer Science+Business Media New York.
A discrete dislocation–transformation model for austenitic single crystals
International Nuclear Information System (INIS)
Shi, J; Turteltaub, S; Remmers, J J C; Van der Giessen, E
2008-01-01
A discrete model for analyzing the interaction between plastic flow and martensitic phase transformations is developed. The model is intended for simulating the microstructure evolution in a single crystal of austenite that transforms non-homogeneously into martensite. The plastic flow in the untransformed austenite is simulated using a plane-strain discrete dislocation model. The phase transformation is modeled via the nucleation and growth of discrete martensitic regions embedded in the austenitic single crystal. At each instant during loading, the coupled elasto-plasto-transformation problem is solved using the superposition of analytical solutions for the discrete dislocations and discrete transformation regions embedded in an infinite homogeneous medium and the numerical solution of a complementary problem used to enforce the actual boundary conditions and the heterogeneities in the medium. In order to describe the nucleation and growth of martensitic regions, a nucleation criterion and a kinetic law suitable for discrete regions are specified. The constitutive rules used in discrete dislocation simulations are supplemented with additional evolution rules to account for the phase transformation. To illustrate the basic features of the model, simulations of specimens under plane-strain uniaxial extension and contraction are analyzed. The simulations indicate that plastic flow reduces the average stress at which transformation begins, but it also reduces the transformation rate when compared with benchmark simulations without plasticity. Furthermore, due to local stress fluctuations caused by dislocations, martensitic systems can be activated even though transformation would not appear to be favorable based on the average stress. Conversely, the simulations indicate that the plastic hardening behavior is influenced by the reduction in the effective austenitic grain size due to the evolution of transformation. During cyclic simulations, the coupled plasticity
Discretization-dependent model for weakly connected excitable media
Arroyo, Pedro André; Alonso, Sergio; Weber dos Santos, Rodrigo
2018-03-01
Pattern formation has been widely observed in extended chemical and biological processes. Although the biochemical systems are highly heterogeneous, homogenized continuum approaches formed by partial differential equations have been employed frequently. Such approaches are usually justified by the difference of scales between the heterogeneities and the characteristic spatial size of the patterns. Under different conditions, for example, under weak coupling, discrete models are more adequate. However, discrete models may be less manageable, for instance, in terms of numerical implementation and mesh generation, than the associated continuum models. Here we study a model to approach discreteness which permits the computer implementation on general unstructured meshes. The model is cast as a partial differential equation but with a parameter that depends not only on heterogeneities sizes, as in the case of quasicontinuum models, but also on the discretization mesh. Therefore, we refer to it as a discretization-dependent model. We validate the approach in a generic excitable media that simulates three different phenomena: the propagation of action membrane potential in cardiac tissue, in myelinated axons of neurons, and concentration waves in chemical microemulsions.
DEFF Research Database (Denmark)
Bisdom, Kevin; Bertotti, Giovanni; Nick, Hamid
2016-01-01
networks, digitized from outcropping pavements. These networks cover a wide range of possible geometries and spatial distributions. The geometrically based method predicts the average hydraulic aperture and equivalent permeability of fractured porous media with error margins of less than 5%....
RECENT ADVANCES IN NATURALLY FRACTURED RESERVOIR MODELING
ORDOÑEZ, A; PEÑUELA, G; IDROBO, E. A; MEDINA, C. E
2001-01-01
Large amounts of oil reserves are contained in naturally fractured reservoirs. Most of these hydrocarbon volumes have been left behind because of the poor knowledge and/or description methodology of those reservoirs. This lack of knowledge has lead to the nonexistence of good quantitative models for this complicated type of reservoirs. The complexity of naturally fractured reservoirs causes the need for integration of all existing information at all scales (drilling, well logging, seismic, we...
Symmetries and discretizations of the O(3) nonlinear sigma model
Energy Technology Data Exchange (ETDEWEB)
Flore, Raphael [TPI, Universitaet Jena (Germany)
2011-07-01
Nonlinear sigma models possess many interesting properties like asymptotic freedom, confinement or dynamical mass generation, and hence serve as toy models for QCD and other theories. We derive a formulation of the N=2 supersymmetric extension of the O(3) nonlinear sigma model in terms of constrained field variables. Starting from this formulation, it is discussed how the model can be discretized in a way that maintains as many symmetries of the theory as possible. Finally, recent numerical results related to these discretizations are presented.
Discrete time duration models with group-level heterogeneity
DEFF Research Database (Denmark)
Frederiksen, Anders; Honoré, Bo; Hu, Loujia
2007-01-01
Dynamic discrete choice panel data models have received a great deal of attention. In those models, the dynamics is usually handled by including the lagged outcome as an explanatory variable. In this paper we consider an alternative model in which the dynamics is handled by using the duration...
Compensatory neurofuzzy model for discrete data classification in biomedical
Ceylan, Rahime
2015-03-01
Biomedical data is separated to two main sections: signals and discrete data. So, studies in this area are about biomedical signal classification or biomedical discrete data classification. There are artificial intelligence models which are relevant to classification of ECG, EMG or EEG signals. In same way, in literature, many models exist for classification of discrete data taken as value of samples which can be results of blood analysis or biopsy in medical process. Each algorithm could not achieve high accuracy rate on classification of signal and discrete data. In this study, compensatory neurofuzzy network model is presented for classification of discrete data in biomedical pattern recognition area. The compensatory neurofuzzy network has a hybrid and binary classifier. In this system, the parameters of fuzzy systems are updated by backpropagation algorithm. The realized classifier model is conducted to two benchmark datasets (Wisconsin Breast Cancer dataset and Pima Indian Diabetes dataset). Experimental studies show that compensatory neurofuzzy network model achieved 96.11% accuracy rate in classification of breast cancer dataset and 69.08% accuracy rate was obtained in experiments made on diabetes dataset with only 10 iterations.
Mosthaf, K.; Rosenberg, L.; Balbarini, N.; Broholm, M. M.; Bjerg, P. L.; Binning, P. J.
2014-12-01
It is important to understand the fate and transport of contaminants in limestone aquifers because they are a major drinking water resource. This is challenging because they are highly heterogeneous; with micro-porous grains, flint inclusions, and being heavily fractured. Several modeling approaches have been developed to describe contaminant transport in fractured media, such as the discrete fracture (with various fracture geometries), equivalent porous media (with and without anisotropy), and dual porosity models. However, these modeling concepts are not well tested for limestone geologies. Given available field data and model purpose, this paper therefore aims to develop, examine and compare modeling approaches for transport of contaminants in fractured limestone aquifers. The model comparison was conducted for a contaminated site in Denmark, where a plume of a dissolved contaminant (PCE) has migrated through a fractured limestone aquifer. Multilevel monitoring wells have been installed at the site and available data includes information on spill history, extent of contamination, geology and hydrogeology. To describe the geology and fracture network, data from borehole logs was combined with an analysis of heterogeneities and fractures from a nearby excavation (analog site). Methods for translating the geological information and fracture mapping into each of the model concepts were examined. Each model was compared with available field data, considering both model fit and measures of model suitability. An analysis of model parameter identifiability and sensitivity is presented. Results show that there is considerable difference between modeling approaches, and that it is important to identify the right one for the actual scale and model purpose. A challenge in the use of field data is the determination of relevant hydraulic properties and interpretation of aqueous and solid phase contaminant concentration sampling data. Traditional water sampling has a bias
Discrete Model Reference Adaptive Control System for Automatic Profiling Machine
Directory of Open Access Journals (Sweden)
Peng Song
2012-01-01
Full Text Available Automatic profiling machine is a movement system that has a high degree of parameter variation and high frequency of transient process, and it requires an accurate control in time. In this paper, the discrete model reference adaptive control system of automatic profiling machine is discussed. Firstly, the model of automatic profiling machine is presented according to the parameters of DC motor. Then the design of the discrete model reference adaptive control is proposed, and the control rules are proven. The results of simulation show that adaptive control system has favorable dynamic performances.
International Nuclear Information System (INIS)
Tien, N.-C.; Li Shihhai
2002-01-01
Many physical and chemical processes dominate the transport of radionuclides in groundwater. Among these processes, the decay chain process of radionuclides was frequently disregarded in previous research. However, the daughter products may travel much farther than their parents along the fracture. Therefore, some models neglecting the effect of the decay chain may underestimate the transport radionuclide concentration in geological media. The transport of radionuclides in groundwater is also controlled by colloidal particles. The radionuclides may be enhanced or retarded by the colloids, according to the mobility of these colloidal particles. This work describes a novel model of the transport of a two-member decay chain of radionuclides through a discrete fracture in a porous rock matrix in the presence of colloids. The model addresses the following processes: (a) advective transport in the fracture, (b) mechanical dispersion and molecular diffusion along the fracture, (c) molecular diffusion from the fracture to the rock matrix, (d) adsorption onto the fracture wall, (e) adsorption in the rock matrix, and (f) radioactive decay. Furthermore, colloids are assumed to be excluded from the matrix pores because of their size. A fully developed concentration profile system with nonreactive colloids is used to understand the effect of colloidal sizes by using hydrodynamic chromatography. The external forces acting on the colloid surface, such as the inertial, the van der Waals attractive force, the double layer force, and the gravitational force are accounted for. The parameters, the average velocity of the colloid, the dispersion coefficient of the colloid, and the distribution coefficient of radionuclides with colloids are modified according to the colloidal size. The transport equations for the parent radionuclides are solved analytically using the Laplace transformation and inversion method. However, for the transformed solution of the daughter products along the
Energy Technology Data Exchange (ETDEWEB)
Geier, J.E. [Golder Associates AB, Uppsala (Sweden)
1996-12-01
A 3-dimensional, discrete-feature hydrological model is developed. The model integrates structural and hydrologic data for the Aespoe site, on scales ranging from semi regional fracture zones to individual fractures in the vicinity of the nuclear waste canisters. Hydrologic properties of the large-scale structures are initially estimated from cross-hole hydrologic test data, and automatically calibrated by numerical simulation of network flow, and comparison with undisturbed heads and observed drawdown in selected cross-hole tests. The calibrated model is combined with a separately derived fracture network model, to yield the integrated model. This model is partly validated by simulation of transient responses to a long-term pumping test and a convergent tracer test, based on the LPT2 experiment at Aespoe. The integrated model predicts that discharge from the SITE-94 repository is predominantly via fracture zones along the eastern shore of Aespoe. Similar discharge loci are produced by numerous model variants that explore uncertainty with regard to effective semi regional boundary conditions, hydrologic properties of the site-scale structures, and alternative structural/hydrological interpretations. 32 refs.
International Nuclear Information System (INIS)
Geier, J.E.
1996-12-01
A 3-dimensional, discrete-feature hydrological model is developed. The model integrates structural and hydrologic data for the Aespoe site, on scales ranging from semi regional fracture zones to individual fractures in the vicinity of the nuclear waste canisters. Hydrologic properties of the large-scale structures are initially estimated from cross-hole hydrologic test data, and automatically calibrated by numerical simulation of network flow, and comparison with undisturbed heads and observed drawdown in selected cross-hole tests. The calibrated model is combined with a separately derived fracture network model, to yield the integrated model. This model is partly validated by simulation of transient responses to a long-term pumping test and a convergent tracer test, based on the LPT2 experiment at Aespoe. The integrated model predicts that discharge from the SITE-94 repository is predominantly via fracture zones along the eastern shore of Aespoe. Similar discharge loci are produced by numerous model variants that explore uncertainty with regard to effective semi regional boundary conditions, hydrologic properties of the site-scale structures, and alternative structural/hydrological interpretations. 32 refs
Ivanova, Violeta M.; Sousa, Rita; Murrihy, Brian; Einstein, Herbert H.
2014-06-01
This paper presents results from research conducted at MIT during 2010-2012 on modeling of natural rock fracture systems with the GEOFRAC three-dimensional stochastic model. Following a background summary of discrete fracture network models and a brief introduction of GEOFRAC, the paper provides a thorough description of the newly developed mathematical and computer algorithms for fracture intensity, aperture, and intersection representation, which have been implemented in MATLAB. The new methods optimize, in particular, the representation of fracture intensity in terms of cumulative fracture area per unit volume, P32, via the Poisson-Voronoi Tessellation of planes into polygonal fracture shapes. In addition, fracture apertures now can be represented probabilistically or deterministically whereas the newly implemented intersection algorithms allow for computing discrete pathways of interconnected fractures. In conclusion, results from a statistical parametric study, which was conducted with the enhanced GEOFRAC model and the new MATLAB-based Monte Carlo simulation program FRACSIM, demonstrate how fracture intensity, size, and orientations influence fracture connectivity.
Fracture Mechanical Markov Chain Crack Growth Model
DEFF Research Database (Denmark)
Gansted, L.; Brincker, Rune; Hansen, Lars Pilegaard
1991-01-01
propagation process can be described by a discrete space Markov theory. The model is applicable to deterministic as well as to random loading. Once the model parameters for a given material have been determined, the results can be used for any structure as soon as the geometrical function is known....
International Nuclear Information System (INIS)
Herbert, A.; Gale, J.; MacLeod, R.; Lanyon, G.
1991-12-01
We present our approach to predicting flow through a fractured rock site; the site characterization and validation region in the Stripa mine. Our approach is based on discrete fracture network modelling using the NAPSAC computer code. We describe the conceptual models and assumptions that we have used to interpret the geometry and flow properties of the fracture networks, from measurements at the site. These are used to investigate large scale properties of the network and we show that for flows on scales larger than about 10 m, porous medium approximation should be used. The porous medium groundwater flow code CFEST is used to predict the large scale flows through the mine and the SCV region. This, in turn, is used to provide boundary conditions for more detailed models, which predict the details of flow, using a discrete fracture network model, on scales of less than 10 m. We conclude that a fracture network approach is feasible and that it provides a better understanding of details of flow than conventional porous medium approaches and a quantification of the uncertainty associated with predictive flow modelling characterised from field measurement in fractured rock. (au)
Introduction to numerical modeling of thermohydrologic flow in fractured rock masses
International Nuclear Information System (INIS)
Wang, J.S.Y.
1980-01-01
More attention is being given to the possibility of nuclear waste isolation in hard rock formations. The waste will generate heat which raises the temperature of the surrounding fractured rock masses and induces buoyancy flow and pressure change in the fluid. These effects introduce the potential hazard of radionuclides being carried to the biosphere, and affect the structure of a repository by stress changes in the rock formation. The thermohydrological and thermomechanical responses are determined by the fractures as well as the intact rock blocks. The capability of modeling fractured rock masses is essential to site characterization and repository evaluation. The fractures can be modeled either as a discrete system, taking into account the detailed fracture distributions, or as a continuum representing the spatial average of the fractures. A numerical model is characterized by the governing equations, the numerical methods, the computer codes, the validations, and the applications. These elements of the thermohydrological models are discussed. Along with the general review, some of the considerations in modeling fractures are also discussed. Some remarks on the research needs in modeling fractured rock mass conclude the paper
Modelling and real-time simulation of continuous-discrete systems in mechatronics
Energy Technology Data Exchange (ETDEWEB)
Lindow, H. [Rostocker, Magdeburg (Germany)
1996-12-31
This work presents a methodology for simulation and modelling of systems with continuous - discrete dynamics. It derives hybrid discrete event models from Lagrange`s equations of motion. This method combines continuous mechanical, electrical and thermodynamical submodels on one hand with discrete event models an the other hand into a hybrid discrete event model. This straight forward software development avoids numeric overhead.
Phase Chaos and Multistability in the Discrete Kuramoto Model
DEFF Research Database (Denmark)
Maistrenko, V. L.; Vasylenko, A. A.; Maistrenko, Y. L.
2008-01-01
The paper describes the appearance of a novel high-dimensional chaotic regime, called phase chaos, in the discrete Kuramoto model of globally coupled phase oscillators. This type of chaos is observed at small and intermediate values of the coupling strength. It is caused by the nonlinear interact......The paper describes the appearance of a novel high-dimensional chaotic regime, called phase chaos, in the discrete Kuramoto model of globally coupled phase oscillators. This type of chaos is observed at small and intermediate values of the coupling strength. It is caused by the nonlinear...... interaction of the oscillators, while the individual oscillators behave periodically when left uncoupled. For the four-dimensional discrete Kuramoto model, we outline the region of phase chaos in the parameter plane, distinguish the region where the phase chaos coexists with other periodic attractors...
Stability analysis of the Euler discretization for SIR epidemic model
International Nuclear Information System (INIS)
Suryanto, Agus
2014-01-01
In this paper we consider a discrete SIR epidemic model obtained by the Euler method. For that discrete model, existence of disease free equilibrium and endemic equilibrium is established. Sufficient conditions on the local asymptotical stability of both disease free equilibrium and endemic equilibrium are also derived. It is found that the local asymptotical stability of the existing equilibrium is achieved only for a small time step size h. If h is further increased and passes the critical value, then both equilibriums will lose their stability. Our numerical simulations show that a complex dynamical behavior such as bifurcation or chaos phenomenon will appear for relatively large h. Both analytical and numerical results show that the discrete SIR model has a richer dynamical behavior than its continuous counterpart
A Discrete Model for HIV Infection with Distributed Delay
Directory of Open Access Journals (Sweden)
Brahim EL Boukari
2014-01-01
Full Text Available We give a consistent discretization of a continuous model of HIV infection, with distributed time delays to express the lag between the times when the virus enters a cell and when the cell becomes infected. The global stability of the steady states of the model is determined and numerical simulations are presented to illustrate our theoretical results.
Powering stochastic reliability models by discrete event simulation
DEFF Research Database (Denmark)
Kozine, Igor; Wang, Xiaoyun
2012-01-01
it difficult to find a solution to the problem. The power of modern computers and recent developments in discrete-event simulation (DES) software enable to diminish some of the drawbacks of stochastic models. In this paper we describe the insights we have gained based on using both Markov and DES models...
Discrete choice models for commuting interactions
DEFF Research Database (Denmark)
Rouwendal, Jan; Mulalic, Ismir; Levkovich, Or
An emerging quantitative spatial economics literature models commuting interactions by a gravity equation that is mathematically equivalent to a multinomial logit model. This model is widely viewed as restrictive because of the independence of irrelevant alternatives (IIA) property that links sub...
Discrete symmetry breaking beyond the standard model
Dekens, Wouter Gerard
2015-01-01
The current knowledge of elementary particles and their interactions is summarized in the Standard Model of particle physics. Practically all the predictions of this model, that have been tested, were confirmed experimentally. Nonetheless, there are phenomena which the model cannot explain. For
Optimization of Operations Resources via Discrete Event Simulation Modeling
Joshi, B.; Morris, D.; White, N.; Unal, R.
1996-01-01
The resource levels required for operation and support of reusable launch vehicles are typically defined through discrete event simulation modeling. Minimizing these resources constitutes an optimization problem involving discrete variables and simulation. Conventional approaches to solve such optimization problems involving integer valued decision variables are the pattern search and statistical methods. However, in a simulation environment that is characterized by search spaces of unknown topology and stochastic measures, these optimization approaches often prove inadequate. In this paper, we have explored the applicability of genetic algorithms to the simulation domain. Genetic algorithms provide a robust search strategy that does not require continuity and differentiability of the problem domain. The genetic algorithm successfully minimized the operation and support activities for a space vehicle, through a discrete event simulation model. The practical issues associated with simulation optimization, such as stochastic variables and constraints, were also taken into consideration.
Discrete gradient methods for solving variational image regularisation models
International Nuclear Information System (INIS)
Grimm, V; McLachlan, Robert I; McLaren, David I; Quispel, G R W; Schönlieb, C-B
2017-01-01
Discrete gradient methods are well-known methods of geometric numerical integration, which preserve the dissipation of gradient systems. In this paper we show that this property of discrete gradient methods can be interesting in the context of variational models for image processing, that is where the processed image is computed as a minimiser of an energy functional. Numerical schemes for computing minimisers of such energies are desired to inherit the dissipative property of the gradient system associated to the energy and consequently guarantee a monotonic decrease of the energy along iterations, avoiding situations in which more computational work might lead to less optimal solutions. Under appropriate smoothness assumptions on the energy functional we prove that discrete gradient methods guarantee a monotonic decrease of the energy towards stationary states, and we promote their use in image processing by exhibiting experiments with convex and non-convex variational models for image deblurring, denoising, and inpainting. (paper)
Aggregation patterns from nonlocal interactions: Discrete stochastic and continuum modeling
Hackett-Jones, Emily J.
2012-04-17
Conservation equations governed by a nonlocal interaction potential generate aggregates from an initial uniform distribution of particles. We address the evolution and formation of these aggregating steady states when the interaction potential has both attractive and repulsive singularities. Currently, no existence theory for such potentials is available. We develop and compare two complementary solution methods, a continuous pseudoinverse method and a discrete stochastic lattice approach, and formally show a connection between the two. Interesting aggregation patterns involving multiple peaks for a simple doubly singular attractive-repulsive potential are determined. For a swarming Morse potential, characteristic slow-fast dynamics in the scaled inverse energy is observed in the evolution to steady state in both the continuous and discrete approaches. The discrete approach is found to be remarkably robust to modifications in movement rules, related to the potential function. The comparable evolution dynamics and steady states of the discrete model with the continuum model suggest that the discrete stochastic approach is a promising way of probing aggregation patterns arising from two- and three-dimensional nonlocal interaction conservation equations. © 2012 American Physical Society.
PREFACE: Continuum Models and Discrete Systems Symposia (CMDS-12)
Chakrabarti, Bikas K.
2011-09-01
of interest were: Thermodynamics, transport theory and statistical mechanics in the context of continuum modeling discrete systems; Statistical mechanics and dynamics of fluid flows; Continuum mechanics of complex fluids and deformable solids with microstructure; Fundamentals of fracture, defect dynamics, fatigue, and fracture dynamics; Statics and dynamics of dislocations, dislocation mediated phase transitions and plasticity; Granular materials: statics and dynamics; Physics and mechanics of earthquakes; Transport in composite materials; and Continuum theory of soft matter systems of biological motivation and living structures. The scientific program consisted of General Lectures and Research Communications. The four General Lectures (40 min + 5 min) introduced the most recent ideas and advances in the fields covered. The 25 Research Communications reported new results and methods in these fields and were presented orally (30 min + 5 min). In addition there were 15 posters which also presented interesting results and five of these posters were selected by a special committee chaired by David J Bergman to contribute to this proceedings. The selected five posters were presented by Moutushi D Choudhury, Morten Grova, Arya Paul, Arnab Saha and Amartya Sarkar. We were happy to note that 32 scientists from ten countries and a large number of students (both from India and other countries) participated in this symposium. The talks and poster sessions generated a lot of discussions, arguments and collaborations. The articles that appear in this proceedings are based on the invited talks and selected poster presentations. We would like to thank the Journal of Physics Conference Series (IOP Publishing) for publishing the proceedings of the conference. We would also like to thank all the contributors to this proceedings for their kind co-operation and the referees for their prompt and active support. A number of invited participants (Amit Acharya, Alexander Altland, Kamal K
Modeling of flow in faulted and fractured media
Energy Technology Data Exchange (ETDEWEB)
Oeian, Erlend
2004-03-01
The work on this thesis has been done as part of a collaborative and inter disciplinary effort to improve the understanding of oil recovery mechanisms in fractured reservoirs. This project has been organized as a Strategic University Program (SUP) at the University of Bergen, Norway. The complex geometries of fractured reservoirs combined with flow of several fluid phases lead to difficult mathematical and numerical problems. In an effort to try to decrease the gap between the geological description and numerical modeling capabilities, new techniques are required. Thus, the main objective has been to improve the ATHENA flow simulator and utilize it within a fault modeling context. Specifically, an implicit treatment of the advection dominated mass transport equations within a domain decomposition based local grid refinement framework has been implemented. Since large computational tasks may arise, the implicit formulation has also been included in a parallel version of the code. Within the current limits of the simulator, appropriate up scaling techniques has also been considered. Part I of this thesis includes background material covering the basic geology of fractured porous media, the mathematical model behind the in-house flow simulator ATHENA and the additions implemented to approach simulation of flow through fractured and faulted porous media. In Part II, a set of research papers stemming from Part I is presented. A brief outline of the thesis follows below. In Chapt. 1 important aspects of the geological description and physical parameters of fractured and faulted porous media is presented. Based on this the scope of this thesis is specified having numerical issues and consequences in mind. Then, in Chapt. 2, the mathematical model and discretizations in the flow simulator is given followed by the derivation of the implicit mass transport formulation. In order to be fairly self-contained, most of the papers in Part II also includes the mathematical model
Modeling of flow in faulted and fractured media
Energy Technology Data Exchange (ETDEWEB)
Oeian, Erlend
2004-03-01
The work on this thesis has been done as part of a collaborative and inter disciplinary effort to improve the understanding of oil recovery mechanisms in fractured reservoirs. This project has been organized as a Strategic University Program (SUP) at the University of Bergen, Norway. The complex geometries of fractured reservoirs combined with flow of several fluid phases lead to difficult mathematical and numerical problems. In an effort to try to decrease the gap between the geological description and numerical modeling capabilities, new techniques are required. Thus, the main objective has been to improve the ATHENA flow simulator and utilize it within a fault modeling context. Specifically, an implicit treatment of the advection dominated mass transport equations within a domain decomposition based local grid refinement framework has been implemented. Since large computational tasks may arise, the implicit formulation has also been included in a parallel version of the code. Within the current limits of the simulator, appropriate up scaling techniques has also been considered. Part I of this thesis includes background material covering the basic geology of fractured porous media, the mathematical model behind the in-house flow simulator ATHENA and the additions implemented to approach simulation of flow through fractured and faulted porous media. In Part II, a set of research papers stemming from Part I is presented. A brief outline of the thesis follows below. In Chapt. 1 important aspects of the geological description and physical parameters of fractured and faulted porous media is presented. Based on this the scope of this thesis is specified having numerical issues and consequences in mind. Then, in Chapt. 2, the mathematical model and discretizations in the flow simulator is given followed by the derivation of the implicit mass transport formulation. In order to be fairly self-contained, most of the papers in Part II also includes the mathematical model
Thermal modelling using discrete vasculature for thermal therapy: a review
Kok, H.P.; Gellermann, J.; van den Berg, C.A.T.; Stauffer, P.R.; Hand, J.W.; Crezee, J.
2013-01-01
Reliable temperature information during clinical hyperthermia and thermal ablation is essential for adequate treatment control, but conventional temperature measurements do not provide 3D temperature information. Treatment planning is a very useful tool to improve treatment quality and substantial progress has been made over the last decade. Thermal modelling is a very important and challenging aspect of hyperthermia treatment planning. Various thermal models have been developed for this purpose, with varying complexity. Since blood perfusion is such an important factor in thermal redistribution of energy in in vivo tissue, thermal simulations are most accurately performed by modelling discrete vasculature. This review describes the progress in thermal modelling with discrete vasculature for the purpose of hyperthermia treatment planning and thermal ablation. There has been significant progress in thermal modelling with discrete vasculature. Recent developments have made real-time simulations possible, which can provide feedback during treatment for improved therapy. Future clinical application of thermal modelling with discrete vasculature in hyperthermia treatment planning is expected to further improve treatment quality. PMID:23738700
Energy Technology Data Exchange (ETDEWEB)
Deluzarche, R
2004-12-15
In this study, a discrete numerical model for rock-fill is built up and validated. This model is based upon the definition of bidimensional clusters that can break in different ways. The resistance of the inner bonds of the clusters are calibrated by reproducing the size-dependant resistance of rock blocks submitted to crushing tests. Numerical simulations of laboratory tests are performed on samples made of the different clusters. Tests on crushable clusters emphasize the utmost importance of particle crushing on the behaviour. A dam is modelled. The role of the placed-rock face on the stabilisation is underlined. The deformation of the dam during reservoir filling, as well as its good seismic behaviour is well reproduced by the model. The model makes it possible to show the influence of particle breakage on the settlements. (author)
Modeling discrete and rhythmic movements through motor primitives: a review.
Degallier, Sarah; Ijspeert, Auke
2010-10-01
Rhythmic and discrete movements are frequently considered separately in motor control, probably because different techniques are commonly used to study and model them. Yet the increasing interest in finding a comprehensive model for movement generation requires bridging the different perspectives arising from the study of those two types of movements. In this article, we consider discrete and rhythmic movements within the framework of motor primitives, i.e., of modular generation of movements. In this way we hope to gain an insight into the functional relationships between discrete and rhythmic movements and thus into a suitable representation for both of them. Within this framework we can define four possible categories of modeling for discrete and rhythmic movements depending on the required command signals and on the spinal processes involved in the generation of the movements. These categories are first discussed in terms of biological concepts such as force fields and central pattern generators and then illustrated by several mathematical models based on dynamical system theory. A discussion on the plausibility of theses models concludes the work.
Stochastic Spectral Descent for Discrete Graphical Models
International Nuclear Information System (INIS)
Carlson, David; Hsieh, Ya-Ping; Collins, Edo; Carin, Lawrence; Cevher, Volkan
2015-01-01
Interest in deep probabilistic graphical models has in-creased in recent years, due to their state-of-the-art performance on many machine learning applications. Such models are typically trained with the stochastic gradient method, which can take a significant number of iterations to converge. Since the computational cost of gradient estimation is prohibitive even for modestly sized models, training becomes slow and practically usable models are kept small. In this paper we propose a new, largely tuning-free algorithm to address this problem. Our approach derives novel majorization bounds based on the Schatten- norm. Intriguingly, the minimizers of these bounds can be interpreted as gradient methods in a non-Euclidean space. We thus propose using a stochastic gradient method in non-Euclidean space. We both provide simple conditions under which our algorithm is guaranteed to converge, and demonstrate empirically that our algorithm leads to dramatically faster training and improved predictive ability compared to stochastic gradient descent for both directed and undirected graphical models.
Discrete element weld model, phase 2
Prakash, C.; Samonds, M.; Singhal, A. K.
1987-01-01
A numerical method was developed for analyzing the tungsten inert gas (TIG) welding process. The phenomena being modeled include melting under the arc and the flow in the melt under the action of buoyancy, surface tension, and electromagnetic forces. The latter entails the calculation of the electric potential and the computation of electric current and magnetic field therefrom. Melting may occur at a single temperature or over a temperature range, and the electrical and thermal conductivities can be a function of temperature. Results of sample calculations are presented and discussed at length. A major research contribution has been the development of numerical methodology for the calculation of phase change problems in a fixed grid framework. The model has been implemented on CHAM's general purpose computer code PHOENICS. The inputs to the computer model include: geometric parameters, material properties, and weld process parameters.
Discrete Variational Approach for Modeling Laser-Plasma Interactions
Reyes, J. Paxon; Shadwick, B. A.
2014-10-01
The traditional approach for fluid models of laser-plasma interactions begins by approximating fields and derivatives on a grid in space and time, leading to difference equations that are manipulated to create a time-advance algorithm. In contrast, by introducing the spatial discretization at the level of the action, the resulting Euler-Lagrange equations have particular differencing approximations that will exactly satisfy discrete versions of the relevant conservation laws. For example, applying a spatial discretization in the Lagrangian density leads to continuous-time, discrete-space equations and exact energy conservation regardless of the spatial grid resolution. We compare the results of two discrete variational methods using the variational principles from Chen and Sudan and Brizard. Since the fluid system conserves energy and momentum, the relative errors in these conserved quantities are well-motivated physically as figures of merit for a particular method. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY-1104683.
Modelling of Granular Materials Using the Discrete Element Method
DEFF Research Database (Denmark)
Ullidtz, Per
1997-01-01
With the Discrete Element Method it is possible to model materials that consists of individual particles where a particle may role or slide on other particles. This is interesting because most of the deformation in granular materials is due to rolling or sliding rather that compression of the gra...
Dynamics of breathers in discrete nonlinear Schrodinger models
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Johansson, Magnus; Aubry, Serge
1998-01-01
We review some recent results concerning the existence and stability of spatially localized and temporally quasiperiodic (non-stationary) excitations in discrete nonlinear Schrodinger (DNLS) models. In two dimensions, we show the existence of linearly stable, stationary and non-stationary localized...
Quasi-one-dimensional scattering in a discrete model
DEFF Research Database (Denmark)
Valiente, Manuel; Mølmer, Klaus
2011-01-01
We study quasi-one-dimensional scattering of one and two particles with short-range interactions on a discrete lattice model in two dimensions. One of the directions is tightly confined by an arbitrary trapping potential. We obtain the collisional properties of these systems both at finite and zero...
Discrete dislocation plasticity modeling of short cracks in single crystals
Deshpande, VS; Needleman, A; Van der Giessen, E
2003-01-01
The mode-I crack growth behavior of geometrically similar edge-cracked single crystal specimens of varying size subject to both monotonic and cyclic axial loading is analyzed using discrete dislocation dynamics. Plastic deformation is modeled through the motion of edge dislocations in an elastic
Nonparametric volatility density estimation for discrete time models
Es, van Bert; Spreij, P.J.C.; Zanten, van J.H.
2005-01-01
We consider discrete time models for asset prices with a stationary volatility process. We aim at estimating the multivariate density of this process at a set of consecutive time instants. A Fourier-type deconvolution kernel density estimator based on the logarithm of the squared process is proposed
Stable cycling in discrete-time genetic models.
Hastings, A
1981-01-01
Examples of stable cycling are discussed for two-locus, two-allele, deterministic, discrete-time models with constant fitnesses. The cases that cycle were found by using numerical techniques to search for stable Hopf bifurcations. One consequence of the results is that apparent cases of directional selection may be due to stable cycling.
Stable cycling in discrete-time genetic models.
Hastings, A
1981-11-01
Examples of stable cycling are discussed for two-locus, two-allele, deterministic, discrete-time models with constant fitnesses. The cases that cycle were found by using numerical techniques to search for stable Hopf bifurcations. One consequence of the results is that apparent cases of directional selection may be due to stable cycling.
Fracture network modeling and GoldSim simulation support
International Nuclear Information System (INIS)
Sugita, Kenichiro; Dershowitz, William
2003-01-01
During Heisei-14, Golder Associates provided support for JNC Tokai through data analysis and simulation of the MIU Underground Rock Laboratory, participation in Task 6 of the Aespoe Task Force on Modelling of Groundwater Flow and Transport, and analysis of repository safety assessment technologies including cell networks for evaluation of the disturbed rock zone (DRZ) and total systems performance assessment (TSPA). MIU Underground Rock Laboratory support during H-14 involved discrete fracture network (DFN) modelling in support of the Multiple Modelling Project (MMP) and the Long Term Pumping Test (LPT). Golder developed updated DFN models for the MIU site, reflecting updated analyses of fracture data. Golder also developed scripts to support JNC simulations of flow and transport pathways within the MMP. Golder supported JNC participation in Task 6 of the Aespoe Task Force on Modelling of Groundwater Flow and Transport during H-14. Task 6A and 6B compared safety assessment (PA) and experimental time scale simulations along a pipe transport pathway. Task 6B2 extended Task 6B simulations from 1-D to 2-D. For Task 6B2, Golder carried out single fracture transport simulations on a wide variety of generic heterogeneous 2D fractures using both experimental and safety assessment boundary conditions. The heterogeneous 2D fractures were implemented according to a variety of in plane heterogeneity patterns. Multiple immobile zones were considered including stagnant zones, infillings, altered wall rock, and intact rock. During H-14, JNC carried out extensive studies of the distributed rock zone (DRZ) surrounding repository tunnels and drifts. Golder supported this activity be evaluating the calculation time necessary for simulating a reference heterogeneous DRZ cell network for a range of computational strategies. To support the development of JNC's total system performance assessment (TSPA) strategy, Golder carried out a review of the US DOE Yucca Mountain Project TSPA. This
Challenges in Continuum Modelling of Intergranular Fracture
DEFF Research Database (Denmark)
Coffman, Valerie; Sethna, James P.; Ingraffea, A. R.
2011-01-01
of grain boundaries, but also in crucial ways on edges, corners and triple junctions of even greater geometrical complexity. To address the first two challenges, we explore the physical underpinnings for creating functional forms to capture the hierarchical commensurability structure in the grain boundary......Intergranular fracture in polycrystals is often simulated by finite elements coupled to a cohesive zone model for the interfaces, requiring cohesive laws for grain boundaries as a function of their geometry. We discuss three challenges in understanding intergranular fracture in polycrystals. First...... properties. To address the last challenge, we demonstrate a method for atomistically extracting the fracture properties of geometrically complex local regions on the fly from within a finite element simulation....
Kang, Peter K.; Dentz, Marco; Le Borgne, Tanguy; Lee, Seunghak; Juanes, Ruben
2017-08-01
We investigate tracer transport on random discrete fracture networks that are characterized by the statistics of the fracture geometry and hydraulic conductivity. While it is well known that tracer transport through fractured media can be anomalous and particle injection modes can have major impact on dispersion, the incorporation of injection modes into effective transport modeling has remained an open issue. The fundamental reason behind this challenge is that-even if the Eulerian fluid velocity is steady-the Lagrangian velocity distribution experienced by tracer particles evolves with time from its initial distribution, which is dictated by the injection mode, to a stationary velocity distribution. We quantify this evolution by a Markov model for particle velocities that are equidistantly sampled along trajectories. This stochastic approach allows for the systematic incorporation of the initial velocity distribution and quantifies the interplay between velocity distribution and spatial and temporal correlation. The proposed spatial Markov model is characterized by the initial velocity distribution, which is determined by the particle injection mode, the stationary Lagrangian velocity distribution, which is derived from the Eulerian velocity distribution, and the spatial velocity correlation length, which is related to the characteristic fracture length. This effective model leads to a time-domain random walk for the evolution of particle positions and velocities, whose joint distribution follows a Boltzmann equation. Finally, we demonstrate that the proposed model can successfully predict anomalous transport through discrete fracture networks with different levels of heterogeneity and arbitrary tracer injection modes.
Discrete/Finite Element Modelling of Rock Cutting with a TBM Disc Cutter
Labra, Carlos; Rojek, Jerzy; Oñate, Eugenio
2017-03-01
This paper presents advanced computer simulation of rock cutting process typical for excavation works in civil engineering. Theoretical formulation of the hybrid discrete/finite element model has been presented. The discrete and finite element methods have been used in different subdomains of a rock sample according to expected material behaviour, the part which is fractured and damaged during cutting is discretized with the discrete elements while the other part is treated as a continuous body and it is modelled using the finite element method. In this way, an optimum model is created, enabling a proper representation of the physical phenomena during cutting and efficient numerical computation. The model has been applied to simulation of the laboratory test of rock cutting with a single TBM (tunnel boring machine) disc cutter. The micromechanical parameters have been determined using the dimensionless relationships between micro- and macroscopic parameters. A number of numerical simulations of the LCM test in the unrelieved and relieved cutting modes have been performed. Numerical results have been compared with available data from in-situ measurements in a real TBM as well as with the theoretical predictions showing quite a good agreement. The numerical model has provided a new insight into the cutting mechanism enabling us to investigate the stress and pressure distribution at the tool-rock interaction. Sensitivity analysis of rock cutting performed for different parameters including disc geometry, cutting velocity, disc penetration and spacing has shown that the presented numerical model is a suitable tool for the design and optimization of rock cutting process.
Disease Extinction Versus Persistence in Discrete-Time Epidemic Models.
van den Driessche, P; Yakubu, Abdul-Aziz
2018-04-12
We focus on discrete-time infectious disease models in populations that are governed by constant, geometric, Beverton-Holt or Ricker demographic equations, and give a method for computing the basic reproduction number, [Formula: see text]. When [Formula: see text] and the demographic population dynamics are asymptotically constant or under geometric growth (non-oscillatory), we prove global asymptotic stability of the disease-free equilibrium of the disease models. Under the same demographic assumption, when [Formula: see text], we prove uniform persistence of the disease. We apply our theoretical results to specific discrete-time epidemic models that are formulated for SEIR infections, cholera in humans and anthrax in animals. Our simulations show that a unique endemic equilibrium of each of the three specific disease models is asymptotically stable whenever [Formula: see text].
Ayatollahy Tafti, Tayeb
We develop a new method for integrating information and data from different sources. We also construct a comprehensive workflow for characterizing and modeling a fracture network in unconventional reservoirs, using microseismic data. The methodology is based on combination of several mathematical and artificial intelligent techniques, including geostatistics, fractal analysis, fuzzy logic, and neural networks. The study contributes to scholarly knowledge base on the characterization and modeling fractured reservoirs in several ways; including a versatile workflow with a novel objective functions. Some the characteristics of the methods are listed below: 1. The new method is an effective fracture characterization procedure estimates different fracture properties. Unlike the existing methods, the new approach is not dependent on the location of events. It is able to integrate all multi-scaled and diverse fracture information from different methodologies. 2. It offers an improved procedure to create compressional and shear velocity models as a preamble for delineating anomalies and map structures of interest and to correlate velocity anomalies with fracture swarms and other reservoir properties of interest. 3. It offers an effective way to obtain the fractal dimension of microseismic events and identify the pattern complexity, connectivity, and mechanism of the created fracture network. 4. It offers an innovative method for monitoring the fracture movement in different stages of stimulation that can be used to optimize the process. 5. Our newly developed MDFN approach allows to create a discrete fracture network model using only microseismic data with potential cost reduction. It also imposes fractal dimension as a constraint on other fracture modeling approaches, which increases the visual similarity between the modeled networks and the real network over the simulated volume.
An XFEM Model for Hydraulic Fracturing in Partially Saturated Rocks
Directory of Open Access Journals (Sweden)
Salimzadeh Saeed
2016-01-01
Full Text Available Hydraulic fracturing is a complex multi-physics phenomenon. Numerous analytical and numerical models of hydraulic fracturing processes have been proposed. Analytical solutions commonly are able to model the growth of a single hydraulic fracture into an initially intact, homogeneous rock mass. Numerical models are able to analyse complex problems such as multiple hydraulic fractures and fracturing in heterogeneous media. However, majority of available models are restricted to single-phase flow through fracture and permeable porous rock. This is not compatible with actual field conditions where the injected fluid does not have similar properties as the host fluid. In this study we present a fully coupled hydro-poroelastic model which incorporates two fluids i.e. fracturing fluid and host fluid. Flow through fracture is defined based on lubrication assumption, while flow through matrix is defined as Darcy flow. The fracture discontinuity in the mechanical model is captured using eXtended Finite Element Method (XFEM while the fracture propagation criterion is defined through cohesive fracture model. The discontinuous matrix fluid velocity across fracture is modelled using leak-off loading which couples fracture flow and matrix flow. The proposed model has been discretised using standard Galerkin method, implemented in Matlab and verified against several published solutions. Multiple hydraulic fracturing simulations are performed to show the model robustness and to illustrate how problem parameters such as injection rate and rock permeability affect the hydraulic fracturing variables i.e. injection pressure, fracture aperture and fracture length. The results show the impact of partial saturation on leak-off and the fact that single-phase models may underestimate the leak-off.
Discrete Discriminant analysis based on tree-structured graphical models
DEFF Research Database (Denmark)
Perez de la Cruz, Gonzalo; Eslava, Guillermina
The purpose of this paper is to illustrate the potential use of discriminant analysis based on tree{structured graphical models for discrete variables. This is done by comparing its empirical performance using estimated error rates for real and simulated data. The results show that discriminant a...... analysis based on tree{structured graphical models is a simple nonlinear method competitive with, and sometimes superior to, other well{known linear methods like those assuming mutual independence between variables and linear logistic regression.......The purpose of this paper is to illustrate the potential use of discriminant analysis based on tree{structured graphical models for discrete variables. This is done by comparing its empirical performance using estimated error rates for real and simulated data. The results show that discriminant...
Discrete Model for the Structure and Strength of Cementitious Materials
Balopoulos, Victor D.; Archontas, Nikolaos; Pantazopoulou, Stavroula J.
2017-12-01
Cementitious materials are characterized by brittle behavior in direct tension and by transverse dilatation (due to microcracking) under compression. Microcracking causes increasingly larger transverse strains and a phenomenological Poisson's ratio that gradually increases to about ν =0.5 and beyond, at the limit point in compression. This behavior is due to the underlying structure of cementitious pastes which is simulated here with a discrete physical model. The computational model is generic, assembled from a statistically generated, continuous network of flaky dendrites consisting of cement hydrates that emanate from partially hydrated cement grains. In the actual amorphous material, the dendrites constitute the solid phase of the cement gel and interconnect to provide the strength and stiffness against load. The idealized dendrite solid is loaded in compression and tension to compute values for strength and Poisson's effects. Parametric studies are conducted, to calibrate the statistical parameters of the discrete model with the physical and mechanical characteristics of the material, so that the familiar experimental trends may be reproduced. The model provides a framework for the study of the mechanical behavior of the material under various states of stress and strain and can be used to model the effects of additives (e.g., fibers) that may be explicitly simulated in the discrete structure.
Xing, F.; Masson, R.; Lopez, S.
2017-09-01
This paper introduces a new discrete fracture model accounting for non-isothermal compositional multiphase Darcy flows and complex networks of fractures with intersecting, immersed and non-immersed fractures. The so called hybrid-dimensional model using a 2D model in the fractures coupled with a 3D model in the matrix is first derived rigorously starting from the equi-dimensional matrix fracture model. Then, it is discretized using a fully implicit time integration combined with the Vertex Approximate Gradient (VAG) finite volume scheme which is adapted to polyhedral meshes and anisotropic heterogeneous media. The fully coupled systems are assembled and solved in parallel using the Single Program Multiple Data (SPMD) paradigm with one layer of ghost cells. This strategy allows for a local assembly of the discrete systems. An efficient preconditioner is implemented to solve the linear systems at each time step and each Newton type iteration of the simulation. The numerical efficiency of our approach is assessed on different meshes, fracture networks, and physical settings in terms of parallel scalability, nonlinear convergence and linear convergence.
a Fractal Network Model for Fractured Porous Media
Xu, Peng; Li, Cuihong; Qiu, Shuxia; Sasmito, Agus Pulung
2016-04-01
The transport properties and mechanisms of fractured porous media are very important for oil and gas reservoir engineering, hydraulics, environmental science, chemical engineering, etc. In this paper, a fractal dual-porosity model is developed to estimate the equivalent hydraulic properties of fractured porous media, where a fractal tree-like network model is used to characterize the fracture system according to its fractal scaling laws and topological structures. The analytical expressions for the effective permeability of fracture system and fractured porous media, tortuosity, fracture density and fraction are derived. The proposed fractal model has been validated by comparisons with available experimental data and numerical simulation. It has been shown that fractal dimensions for fracture length and aperture have significant effect on the equivalent hydraulic properties of fractured porous media. The effective permeability of fracture system can be increased with the increase of fractal dimensions for fracture length and aperture, while it can be remarkably lowered by introducing tortuosity at large branching angle. Also, a scaling law between the fracture density and fractal dimension for fracture length has been found, where the scaling exponent depends on the fracture number. The present fractal dual-porosity model may shed light on the transport physics of fractured porous media and provide theoretical basis for oil and gas exploitation, underground water, nuclear waste disposal and geothermal energy extraction as well as chemical engineering, etc.
Townsend, Kevin C; Thomas-Aitken, Holly D; Rudert, M James; Kern, Andrew M; Willey, Michael C; Anderson, Donald D; Goetz, Jessica E
2018-01-23
Evaluation of abnormalities in joint contact stress that develop after inaccurate reduction of an acetabular fracture may provide a potential means for predicting the risk of developing post-traumatic osteoarthritis. Discrete element analysis (DEA) is a computational technique for calculating intra-articular contact stress distributions in a fraction of the time required to obtain the same information using the more commonly employed finite element analysis technique. The goal of this work was to validate the accuracy of DEA-computed contact stress against physical measurements of contact stress made in cadaveric hips using Tekscan sensors. Four static loading tests in a variety of poses from heel-strike to toe-off were performed in two different cadaveric hip specimens with the acetabulum intact and again with an intentionally malreduced posterior wall acetabular fracture. DEA-computed contact stress was compared on a point-by-point basis to stress measured from the physical experiments. There was good agreement between computed and measured contact stress over the entire contact area (correlation coefficients ranged from 0.88 to 0.99). DEA-computed peak contact stress was within an average of 0.5 MPa (range 0.2-0.8 MPa) of the Tekscan peak stress for intact hips, and within an average of 0.6 MPa (range 0-1.6 MPa) for fractured cases. DEA-computed contact areas were within an average of 33% of the Tekscan-measured areas (range: 1.4-60%). These results indicate that the DEA methodology is a valid method for accurately estimating contact stress in both intact and fractured hips. Copyright © 2017 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Geier, J.E.
1996-12-01
A 3-dimensional, discrete-feature hydrological model is developed. The model integrates structural and hydrologic data for the Aespoe site, on scales ranging from semi regional fracture zones to individual fractures in the vicinity of the nuclear waste canisters. Predicted parameters for the near field include fracture spacing, fracture aperture, and Darcy velocity at each of forty canister deposition holes. Parameters for the far field include discharge location, Darcy velocity, effective longitudinal dispersion coefficient and head gradient, flow porosity, and flow wetted surface, for each canister source that discharges to the biosphere. Results are presented in the form of statistical summaries for a total of 42 calculation cases, which treat a set of 25 model variants in various combinations. The variants for the SITE-94 Reference Case model address conceptual and parametric uncertainty related to the site-scale hydrogeologic model and its properties, the fracture network within the repository, effective semi regional boundary conditions for the model, and the disturbed-rock zone around the repository tunnels and shafts. Two calculation cases simulate hydrologic conditions that are predicted to occur during future glacial episodes. 30 refs
A discrete model for compressible flows in heterogeneous media
International Nuclear Information System (INIS)
Le Metayer, O.; Massol, A.; Favrie, N.; Hank, S.
2011-01-01
This work deals with the building of a discrete model able to describe and to predict the evolution of complex gas flows in heterogeneous media. In many physical applications, large scales numerical simulation is no longer possible because of a lack of computing resources. Indeed the medium topology may be complex due to the presence of many obstacles (walls, pipes, equipments, geometric singularities etc.). Aircraft powerplant compartments are examples where topology is complex due to the presence of pipes, ducts, coolers and other equipment. Other important examples are gas explosions and large scale dispersion of hazardous materials in urban places, cities or underground involving obstacles such as buildings and various infrastructures. In all cases efficient safety responses are required. Then a new discrete model is built and solved in reasonable execution times for large cells volumes including such obstacles. Quantitative comparisons between experimental and numerical results are shown for different significant test cases, showing excellent agreement.
Modeling reservoir geomechanics using discrete element method : Application to reservoir monitoring
Energy Technology Data Exchange (ETDEWEB)
Alassi, Haitham Tayseer
2008-09-15
Understanding reservoir geomechanical behavior is becoming more and more important for the petroleum industry. Reservoir compaction, which may result in surface subsidence and fault reactivation, occurs during reservoir depletion. Stress changes and possible fracture development inside and outside a depleting reservoir can be monitored using time-lapse (so-called '4D') seismic and/or passive seismic, and this can give valuable information about the conditions of a given reservoir during production. In this study we will focus on using the (particle-based) Discrete Element Method (DEM) to model reservoir geomechanical behavior during depletion and fluid injection. We show in this study that DEM can be used in modeling reservoir geomechanical behavior by comparing results obtained from DEM to those obtained from analytical solutions. The match of the displacement field between DEM and the analytical solution is good, however there is mismatch of the stress field which is related to the way stress is measured in DEM. A good match is however obtained by measuring the stress field carefully. We also use DEM to model reservoir geomechanical behavior beyond the elasticity limit where fractures can develop and faults can reactivate. A general technique has been developed to relate DEM parameters to rock properties. This is necessary in order to use correct reservoir geomechanical properties during modeling. For any type of particle packing there is a limitation that the maximum ratio between P- and S-wave velocity Vp/Vs that can be modeled is 3 . The static behavior for a loose packing is different from the dynamic behavior. Empirical relations are needed for the static behavior based on numerical test observations. The dynamic behavior for both dense and loose packing can be given by analytical relations. Cosserat continuum theory is needed to derive relations for Vp and Vs. It is shown that by constraining the particle rotation, the S-wave velocity can be
Energy Technology Data Exchange (ETDEWEB)
La Pointe, Paul R.; Hermanson, Jan
2002-09-09
The goal of this project is to improve the recovery of oil from the Circle Ridge Oilfield, located on the Wind River Reservation in Wyoming, through an innovative integration of matrix characterization, structural reconstruction, and the characterization of the fracturing in the reservoir through the use of discrete fracture network models.
RESEARCH PROGRAM ON FRACTURED PETROLEUM RESERVOIRS
Energy Technology Data Exchange (ETDEWEB)
Abbas Firoozabadi
2002-04-12
Numerical simulation of water injection in discrete fractured media with capillary pressure is a challenge. Dual-porosity models in view of their strength and simplicity can be mainly used for sugar-cube representation of fractured media. In such a representation, the transfer function between the fracture and the matrix block can be readily calculated for water-wet media. For a mixed-wet system, the evaluation of the transfer function becomes complicated due to the effect of gravity. In this work, they use a discrete-fracture model in which the fractures are discretized as one dimensional entities to account for fracture thickness by an integral form of the flow equations. This simple step greatly improves the numerical solution. Then the discrete-fracture model is implemented using a Galerkin finite element method. The robustness and the accuracy of the approach are shown through several examples. First they consider a single fracture in a rock matrix and compare the results of the discrete-fracture model with a single-porosity model. Then, they use the discrete-fracture model in more complex configurations. Numerical simulations are carried out in water-wet media as well as in mixed-wet media to study the effect of matrix and fracture capillary pressures.
Energy Technology Data Exchange (ETDEWEB)
Stigsson, Martin
2009-12-15
The objectives of this report is to investigate the frequency of fractures assumed to be water conductive, i.e. open or partly open and directly or indirectly connected to a source. Also the distribution of total transmissivity in 100 m and 20 m horizontal sections and 8 m vertical sections is calculated. The report is only intended to serve as input to the SER, Site Engineering Report, at Laxemar and Forsmark. The input data for the analyses is taken, as is, from the Discrete Fracture Network sections in published reports. No evaluation that the model parameters are appropriate for the task or sensitivity analysis is performed. The tunnels and deposition holes are modelled as scanlines which is a very coarse approximation, but it may give some rough estimation of the frequency of the water bearing features, especially for the larger ones, and the total transmissivity in a section
International Nuclear Information System (INIS)
Stigsson, Martin
2009-12-01
The objectives of this report is to investigate the frequency of fractures assumed to be water conductive, i.e. open or partly open and directly or indirectly connected to a source. Also the distribution of total transmissivity in 100 m and 20 m horizontal sections and 8 m vertical sections is calculated. The report is only intended to serve as input to the SER, Site Engineering Report, at Laxemar and Forsmark. The input data for the analyses is taken, as is, from the Discrete Fracture Network sections in published reports. No evaluation that the model parameters are appropriate for the task or sensitivity analysis is performed. The tunnels and deposition holes are modelled as scanlines which is a very coarse approximation, but it may give some rough estimation of the frequency of the water bearing features, especially for the larger ones, and the total transmissivity in a section
On discrete symmetries for a whole Abelian model
International Nuclear Information System (INIS)
Chauca, J.; Doria, R.
2012-01-01
Considering the whole concept applied to gauge theory a nonlinear abelian model is derived. A next step is to understand on the model properties. At this work, it will be devoted to discrete symmetries. For this, we will work based in two fields reference systems. This whole gauge symmetry allows to be analyzed through different sets which are the constructor basis {D μ ,X i μ } and the physical basis {G μI }. Taking as fields reference system the diagonalized spin-1 sector, P, C, T and PCT symmetries are analyzed. They show that under this systemic model there are conservation laws driven for the parts and for the whole. It develops the meaning of whole-parity, field-parity and so on. However it is the whole symmetry that rules. This means that usually forbidden particles as pseudovector photons can be introduced through such whole abelian system. As result, one notices that the fields whole {G μI } manifest a quanta diversity. It involves particles with different spins, masses and discrete quantum numbers under a same gauge symmetry. It says that without violating PCT symmetry different possibilities on discrete symmetries can be accommodated.
Fracture modelling of a high performance armour steel
Skoglund, P.; Nilsson, M.; Tjernberg, A.
2006-08-01
The fracture characteristics of the high performance armour steel Armox 500T is investigated. Tensile mechanical experiments using samples with different notch geometries are used to investigate the effect of multi-axial stress states on the strain to fracture. The experiments are numerically simulated and from the simulation the stress at the point of fracture initiation is determined as a function of strain and these data are then used to extract parameters for fracture models. A fracture model based on quasi-static experiments is suggested and the model is tested against independent experiments done at both static and dynamic loading. The result show that the fracture model give reasonable good agreement between simulations and experiments at both static and dynamic loading condition. This indicates that multi-axial loading is more important to the strain to fracture than the deformation rate in the investigated loading range. However on-going work will further characterise the fracture behaviour of Armox 500T.
Cohesive fracture model for functionally graded fiber reinforced concrete
International Nuclear Information System (INIS)
Park, Kyoungsoo; Paulino, Glaucio H.; Roesler, Jeffery
2010-01-01
A simple, effective, and practical constitutive model for cohesive fracture of fiber reinforced concrete is proposed by differentiating the aggregate bridging zone and the fiber bridging zone. The aggregate bridging zone is related to the total fracture energy of plain concrete, while the fiber bridging zone is associated with the difference between the total fracture energy of fiber reinforced concrete and the total fracture energy of plain concrete. The cohesive fracture model is defined by experimental fracture parameters, which are obtained through three-point bending and split tensile tests. As expected, the model describes fracture behavior of plain concrete beams. In addition, it predicts the fracture behavior of either fiber reinforced concrete beams or a combination of plain and fiber reinforced concrete functionally layered in a single beam specimen. The validated model is also applied to investigate continuously, functionally graded fiber reinforced concrete composites.
Discrete dynamic modeling of T cell survival signaling networks
Zhang, Ranran
2009-03-01
Biochemistry-based frameworks are often not applicable for the modeling of heterogeneous regulatory systems that are sparsely documented in terms of quantitative information. As an alternative, qualitative models assuming a small set of discrete states are gaining acceptance. This talk will present a discrete dynamic model of the signaling network responsible for the survival and long-term competence of cytotoxic T cells in the blood cancer T-LGL leukemia. We integrated the signaling pathways involved in normal T cell activation and the known deregulations of survival signaling in leukemic T-LGL, and formulated the regulation of each network element as a Boolean (logic) rule. Our model suggests that the persistence of two signals is sufficient to reproduce all known deregulations in leukemic T-LGL. It also indicates the nodes whose inactivity is necessary and sufficient for the reversal of the T-LGL state. We have experimentally validated several model predictions, including: (i) Inhibiting PDGF signaling induces apoptosis in leukemic T-LGL. (ii) Sphingosine kinase 1 and NFκB are essential for the long-term survival of T cells in T-LGL leukemia. (iii) T box expressed in T cells (T-bet) is constitutively activated in the T-LGL state. The model has identified potential therapeutic targets for T-LGL leukemia and can be used for generating long-term competent CTL necessary for tumor and cancer vaccine development. The success of this model, and of other discrete dynamic models, suggests that the organization of signaling networks has an determining role in their dynamics. Reference: R. Zhang, M. V. Shah, J. Yang, S. B. Nyland, X. Liu, J. K. Yun, R. Albert, T. P. Loughran, Jr., Network Model of Survival Signaling in LGL Leukemia, PNAS 105, 16308-16313 (2008).
Colloid transport in model fracture filling materials
Wold, S.; Garcia-Garcia, S.; Jonsson, M.
2010-12-01
Colloid transport in model fracture filling materials Susanna Wold*, Sandra García-García and Mats Jonsson KTH Chemical Science and Engineering Royal Institute of Technology, SE-100 44 Stockholm, Sweden *Corresponding author: E-mail: wold@kth.se Phone: +46 8 790 6295 In colloid transport in water-bearing fractures, the retardation depends on interactions with the fracture surface by sorption or filtration. These mechanisms are difficult to separate. A rougher surface will give a larger area available for sorption, and also when a particle is physically hindered, it approaches the surface and enables further sorption. Sorption can be explained by electrostatics were the strongest sorption on minerals always is observed at pH below pHpzc (Filby et al., 2008). The adhesion of colloids to mineral surfaces is related to the surface roughness according to a recent study (Darbha et al., 2010). There is a large variation in the characteristics of water-bearing fractures in bedrock in terms of aperture distribution, flow velocity, surface roughness, mineral distributions, presence of fracture filling material, and biological and organic material, which is hard to implement in modeling. The aim of this work was to study the transport of negatively charged colloids in model fracture filling material in relation to flow, porosity, mineral type, colloid size, and surface charge distribution. In addition, the impact on transport of colloids of mixing model fracture filling materials with different retention and immobilization capacities, determined by batch sorption experiments, was investigated. The transport of Na-montmorillonite colloids and well-defined negatively charged latex microspheres of 50, 100, and 200 nm diameter were studied in either columns containing quartz or quartz mixed with biotite. The ionic strength in the solution was exclusively 0.001 and pH 6 or 8.5. The flow rates used were 0.002, 0.03, and 0.6 mL min-1. Sorption of the colloids on the model fracture
Polynomial algebra of discrete models in systems biology.
Veliz-Cuba, Alan; Jarrah, Abdul Salam; Laubenbacher, Reinhard
2010-07-01
An increasing number of discrete mathematical models are being published in Systems Biology, ranging from Boolean network models to logical models and Petri nets. They are used to model a variety of biochemical networks, such as metabolic networks, gene regulatory networks and signal transduction networks. There is increasing evidence that such models can capture key dynamic features of biological networks and can be used successfully for hypothesis generation. This article provides a unified framework that can aid the mathematical analysis of Boolean network models, logical models and Petri nets. They can be represented as polynomial dynamical systems, which allows the use of a variety of mathematical tools from computer algebra for their analysis. Algorithms are presented for the translation into polynomial dynamical systems. Examples are given of how polynomial algebra can be used for the model analysis. alanavc@vt.edu Supplementary data are available at Bioinformatics online.
AN ACTIVE FRACTURE MODEL FOR UNSATURATED FLOW AND TRANSPORT
International Nuclear Information System (INIS)
HUI-HAI LIU, GUDMUNDUR S. BODVARSSON AND CHRISTINE DOUGHTY
1999-01-01
Fracture/matrix (F/M) interaction is a key factor affecting flow and transport in unsaturated fractured rocks. In classic continuum approaches (Warren and Root, 1963), it is assumed that flow occurs through all the connected fractures and is uniformly distributed over the entire fracture area, which generally gives a relatively large F/M interaction. However, fractures seem to have limited interaction with the surrounding matrix at Yucca Mountain, Nevada, as suggested by geochemical nonequilibrium between the perched water (resulting mainly from fracture flow) and pore water in the rock matrix. Because of the importance of the F/M interaction and related issues, there is a critical need to develop new approaches to accurately consider the interaction reduction inferred from field data at the Yucca Mountain site. Motivated by this consideration, they have developed an active fracture model based on the hypothesis that not all connected fractures actively conduct water in unsaturated fractured rocks
XFEM modeling of hydraulic fracture in porous rocks with natural fractures
Wang, Tao; Liu, ZhanLi; Zeng, QingLei; Gao, Yue; Zhuang, Zhuo
2017-08-01
Hydraulic fracture (HF) in porous rocks is a complex multi-physics coupling process which involves fluid flow, diffusion and solid deformation. In this paper, the extended finite element method (XFEM) coupling with Biot theory is developed to study the HF in permeable rocks with natural fractures (NFs). In the recent XFEM based computational HF models, the fluid flow in fractures and interstitials of the porous media are mostly solved separately, which brings difficulties in dealing with complex fracture morphology. In our new model the fluid flow is solved in a unified framework by considering the fractures as a kind of special porous media and introducing Poiseuille-type flow inside them instead of Darcy-type flow. The most advantage is that it is very convenient to deal with fluid flow inside the complex fracture network, which is important in shale gas extraction. The weak formulation for the new coupled model is derived based on virtual work principle, which includes the XFEM formulation for multiple fractures and fractures intersection in porous media and finite element formulation for the unified fluid flow. Then the plane strain Kristianovic-Geertsma-de Klerk (KGD) model and the fluid flow inside the fracture network are simulated to validate the accuracy and applicability of this method. The numerical results show that large injection rate, low rock permeability and isotropic in-situ stresses tend to lead to a more uniform and productive fracture network.
Energy Technology Data Exchange (ETDEWEB)
Geier, J E [Golder Associates AB, Uppsala (Sweden)
1996-12-01
Specific procedures and source data are described for the construction and application of discrete-feature hydrological models for the vicinity of Aespoe. Documentation is given for all major phases of the work, including: Statistical analyses to develop and validate discrete-fracture network models, Preliminary evaluation, construction, and calibration of the site-scale model based on the SITE-94 structural model of Aespoe, Simulation of multiple realizations of the integrated model, and variations, to predict groundwater flow, and Evaluation of near-field and far-field parameters for performance assessment calculations. Procedures are documented in terms of the computer batch files and executable scripts that were used to perform the main steps in these analyses, to provide for traceability of results that are used in the SITE-94 performance assessment calculations. 43 refs.
International Nuclear Information System (INIS)
Geier, J.E.
1996-12-01
Specific procedures and source data are described for the construction and application of discrete-feature hydrological models for the vicinity of Aespoe. Documentation is given for all major phases of the work, including: Statistical analyses to develop and validate discrete-fracture network models, Preliminary evaluation, construction, and calibration of the site-scale model based on the SITE-94 structural model of Aespoe, Simulation of multiple realizations of the integrated model, and variations, to predict groundwater flow, and Evaluation of near-field and far-field parameters for performance assessment calculations. Procedures are documented in terms of the computer batch files and executable scripts that were used to perform the main steps in these analyses, to provide for traceability of results that are used in the SITE-94 performance assessment calculations. 43 refs
International Nuclear Information System (INIS)
Rousseau, J.
2009-07-01
That study focuses on concrete structures submitted to impact loading and is aimed at predicting local damage in the vicinity of an impact zone as well as the global response of the structure. The Discrete Element Method (DEM) seems particularly well suited in this context for modeling fractures. An identification process of DEM material parameters from macroscopic data (Young's modulus, compressive and tensile strength, fracture energy, etc.) will first be presented for the purpose of enhancing reproducibility and reliability of the simulation results with DE samples of various sizes. Then, a particular interaction, between concrete and steel elements, was developed for the simulation of reinforced concrete. The discrete elements method was validated on quasi-static and dynamic tests carried out on small samples of concrete and reinforced concrete. Finally, discrete elements were used to simulate impacts on reinforced concrete slabs in order to confront the results with experimental tests. The modeling of a large structure by means of DEM may lead to prohibitive computation times. A refined discretization becomes required in the vicinity of the impact, while the structure may be modeled using a coarse FE mesh further from the impact area, where the material behaves elastically. A coupled discrete-finite element approach is thus proposed: the impact zone is modeled by means of DE and elastic FE are used on the rest of the structure. An existing method for 3D finite elements was extended to shells. This new method was then validated on many quasi-static and dynamic tests. The proposed approach is then applied to an impact on a concrete structure in order to validate the coupled method and compare computation times. (author)
Fixed Points in Discrete Models for Regulatory Genetic Networks
Directory of Open Access Journals (Sweden)
Orozco Edusmildo
2007-01-01
Full Text Available It is desirable to have efficient mathematical methods to extract information about regulatory iterations between genes from repeated measurements of gene transcript concentrations. One piece of information is of interest when the dynamics reaches a steady state. In this paper we develop tools that enable the detection of steady states that are modeled by fixed points in discrete finite dynamical systems. We discuss two algebraic models, a univariate model and a multivariate model. We show that these two models are equivalent and that one can be converted to the other by means of a discrete Fourier transform. We give a new, more general definition of a linear finite dynamical system and we give a necessary and sufficient condition for such a system to be a fixed point system, that is, all cycles are of length one. We show how this result for generalized linear systems can be used to determine when certain nonlinear systems (monomial dynamical systems over finite fields are fixed point systems. We also show how it is possible to determine in polynomial time when an ordinary linear system (defined over a finite field is a fixed point system. We conclude with a necessary condition for a univariate finite dynamical system to be a fixed point system.
International Nuclear Information System (INIS)
Seol, Yongkoo; Kneafsey, Timothy J.; Ito, Kazumasa
2003-01-01
Numerical simulation is an effective and economical tool for optimally designing laboratory experiments and deriving practical experimental conditions. We executed a detailed numerical simulation study to examine the active fracture concept (AFC, Liu et al., 1998) using a cubic meter-sized block model. The numerical simulations for this study were performed by applying various experimental conditions, including different bottom flow boundaries, varying injection rates, and different fracture-matrix interaction (by increasing absolute matrix permeability at the fracture matrix boundary) for a larger fracture interaction under transient or balanced-state flow regimes. Two conceptual block models were developed based on different numerical approaches: a two-dimensional discrete-fracture-network model (DFNM) and a one-dimensional dual continuum model (DCM). The DFNM was used as a surrogate for a natural block to produce synthetic breakthrough curves of water and tracer concentration under transient or balanced-state conditions. The DCM is the approach typically used for the Yucca Mountain Project because of its computational efficiency. The AFC was incorporated into the DCM to capture heterogeneous flow patterns that occur in unsaturated fractured rocks. The simulation results from the DCM were compared with the results from the DFNM to determine whether the DCM could predict the water flow and tracer transport observed in the DFNM at the scale of the experiment. It was found that implementing the AFC in the DCM improved the prediction of unsaturated flow and that the flow and transport experiments with low injection rates in the DFNM were compared better with the AFC implemented DCM at the meter scale. However, the estimated AFC parameter varied from 0.38 to 1.0 with different flow conditions, suggesting that the AFC parameter was not a sufficient to fully capture the complexity of the flow processes in a one meter sized discrete fracture network
a Discrete Mathematical Model to Simulate Malware Spreading
Del Rey, A. Martin; Sánchez, G. Rodriguez
2012-10-01
With the advent and worldwide development of Internet, the study and control of malware spreading has become very important. In this sense, some mathematical models to simulate malware propagation have been proposed in the scientific literature, and usually they are based on differential equations exploiting the similarities with mathematical epidemiology. The great majority of these models study the behavior of a particular type of malware called computer worms; indeed, to the best of our knowledge, no model has been proposed to simulate the spreading of a computer virus (the traditional type of malware which differs from computer worms in several aspects). In this sense, the purpose of this work is to introduce a new mathematical model not based on continuous mathematics tools but on discrete ones, to analyze and study the epidemic behavior of computer virus. Specifically, cellular automata are used in order to design such model.
Model-based Quantile Regression for Discrete Data
Padellini, Tullia
2018-04-10
Quantile regression is a class of methods voted to the modelling of conditional quantiles. In a Bayesian framework quantile regression has typically been carried out exploiting the Asymmetric Laplace Distribution as a working likelihood. Despite the fact that this leads to a proper posterior for the regression coefficients, the resulting posterior variance is however affected by an unidentifiable parameter, hence any inferential procedure beside point estimation is unreliable. We propose a model-based approach for quantile regression that considers quantiles of the generating distribution directly, and thus allows for a proper uncertainty quantification. We then create a link between quantile regression and generalised linear models by mapping the quantiles to the parameter of the response variable, and we exploit it to fit the model with R-INLA. We extend it also in the case of discrete responses, where there is no 1-to-1 relationship between quantiles and distribution\\'s parameter, by introducing continuous generalisations of the most common discrete variables (Poisson, Binomial and Negative Binomial) to be exploited in the fitting.
Synthesis of industrial applications of local approach to fracture models
International Nuclear Information System (INIS)
Eripret, C.
1993-03-01
This report gathers different applications of local approach to fracture models to various industrial configurations, such as nuclear pressure vessel steel, cast duplex stainless steels, or primary circuit welds such as bimetallic welds. As soon as models are developed on the basis of microstructural observations, damage mechanisms analyses, and fracture process, the local approach to fracture proves to solve problems where classical fracture mechanics concepts fail. Therefore, local approach appears to be a powerful tool, which completes the standard fracture criteria used in nuclear industry by exhibiting where and why those classical concepts become unvalid. (author). 1 tab., 18 figs., 25 refs
An application of a discrete fixed point theorem to the Cournot model
Sato, Junichi
2008-01-01
In this paper, we apply a discrete fixed point theorem of [7] to the Cournot model [1]. Then we can deal with the Cournot model where the production of the enterprises is discrete. To handle it, we define a discrete Cournot-Nash equilibrium, and prove its existence.
Modeling biological tissue growth: discrete to continuum representations.
Hywood, Jack D; Hackett-Jones, Emily J; Landman, Kerry A
2013-09-01
There is much interest in building deterministic continuum models from discrete agent-based models governed by local stochastic rules where an agent represents a biological cell. In developmental biology, cells are able to move and undergo cell division on and within growing tissues. A growing tissue is itself made up of cells which undergo cell division, thereby providing a significant transport mechanism for other cells within it. We develop a discrete agent-based model where domain agents represent tissue cells. Each agent has the ability to undergo a proliferation event whereby an additional domain agent is incorporated into the lattice. If a probability distribution describes the waiting times between proliferation events for an individual agent, then the total length of the domain is a random variable. The average behavior of these stochastically proliferating agents defining the growing lattice is determined in terms of a Fokker-Planck equation, with an advection and diffusion term. The diffusion term differs from the one obtained Landman and Binder [J. Theor. Biol. 259, 541 (2009)] when the rate of growth of the domain is specified, but the choice of agents is random. This discrepancy is reconciled by determining a discrete-time master equation for this process and an associated asymmetric nonexclusion random walk, together with consideration of synchronous and asynchronous updating schemes. All theoretical results are confirmed with numerical simulations. This study furthers our understanding of the relationship between agent-based rules, their implementation, and their associated partial differential equations. Since tissue growth is a significant cellular transport mechanism during embryonic growth, it is important to use the correct partial differential equation description when combining with other cellular functions.
Modelling of Local Necking and Fracture in Aluminium Alloys
International Nuclear Information System (INIS)
Achani, D.; Eriksson, M.; Hopperstad, O. S.; Lademo, O.-G.
2007-01-01
Non-linear Finite Element simulations are extensively used in forming and crashworthiness studies of automotive components and structures in which fracture need to be controlled. For thin-walled ductile materials, the fracture-related phenomena that must be properly represented are thinning instability, ductile fracture and through-thickness shear instability. Proper representation of the fracture process relies on the accuracy of constitutive and fracture models and their parameters that need to be calibrated through well defined experiments. The present study focuses on local necking and fracture which is of high industrial importance, and uses a phenomenological criterion for modelling fracture in aluminium alloys. As an accurate description of plastic anisotropy is important, advanced phenomenological constitutive equations based on the yield criterion YLD2000/YLD2003 are used. Uniaxial tensile tests and disc compression tests are performed for identification of the constitutive model parameters. Ductile fracture is described by the Cockcroft-Latham fracture criterion and an in-plane shear tests is performed to identify the fracture parameter. The reason is that in a well designed in-plane shear test no thinning instability should occur and it thus gives more direct information about the phenomenon of ductile fracture. Numerical simulations have been performed using a user-defined material model implemented in the general-purpose non-linear FE code LS-DYNA. The applicability of the model is demonstrated by correlating the predicted and experimental response in the in-plane shear tests and additional plane strain tension tests
Discrete Element Modeling (DEM) of Triboelectrically Charged Particles: Revised Experiments
Hogue, Michael D.; Calle, Carlos I.; Curry, D. R.; Weitzman, P. S.
2008-01-01
In a previous work, the addition of basic screened Coulombic electrostatic forces to an existing commercial discrete element modeling (DEM) software was reported. Triboelectric experiments were performed to charge glass spheres rolling on inclined planes of various materials. Charge generation constants and the Q/m ratios for the test materials were calculated from the experimental data and compared to the simulation output of the DEM software. In this paper, we will discuss new values of the charge generation constants calculated from improved experimental procedures and data. Also, planned work to include dielectrophoretic, Van der Waals forces, and advanced mechanical forces into the software will be discussed.
Experiments of reconstructing discrete atmospheric dynamic models from data (I)
Lin, Zhenshan; Zhu, Yanyu; Deng, Ziwang
1995-03-01
In this paper, we give some experimental results of our study in reconstructing discrete atmospheric dynamic models from data. After a great deal of numerical experiments, we found that the logistic map, x n + 1 = 1- μx {2/n}, could be used in monthly mean temperature prediction when it was approaching the chaotic region, and its predictive results were in reverse states to the practical data. This means that the nonlinear developing behavior of the monthly mean temperature system is bifurcating back into the critical chaotic states from the chaotic ones.
Control of discrete event systems modeled as hierarchical state machines
Brave, Y.; Heymann, M.
1991-01-01
The authors examine a class of discrete event systems (DESs) modeled as asynchronous hierarchical state machines (AHSMs). For this class of DESs, they provide an efficient method for testing reachability, which is an essential step in many control synthesis procedures. This method utilizes the asynchronous nature and hierarchical structure of AHSMs, thereby illustrating the advantage of the AHSM representation as compared with its equivalent (flat) state machine representation. An application of the method is presented where an online minimally restrictive solution is proposed for the problem of maintaining a controlled AHSM within prescribed legal bounds.
International Nuclear Information System (INIS)
St John, C.; Krug, A.; Key, S.; Monsees, J.
1983-05-01
Generalized computer codes capable of forming the basis for numerical models of fractured rock masses are being used within the NWTS program. Little additional development of these codes is considered justifiable, except in the area of representation of discrete fractures. On the other hand, model preparation requires definition of medium-specific constitutive descriptions and site characteristics and is therefore legitimately conducted by each of the media-oriented projects within the National Waste Terminal Storage program. However, it is essential that a uniform approach to the role of numerical modeling be adopted, including agreement upon the contribution of modeling to the design and licensing process and the need for, and means of, model qualification for particular purposes. This report discusses the role of numerical modeling, reviews the capabilities of several computer codes that are being used to support design or performance assessment, and proposes a framework for future numerical modeling activities within the NWTS program
Hybrid discrete choice models: Gained insights versus increasing effort
International Nuclear Information System (INIS)
Mariel, Petr; Meyerhoff, Jürgen
2016-01-01
Hybrid choice models expand the standard models in discrete choice modelling by incorporating psychological factors as latent variables. They could therefore provide further insights into choice processes and underlying taste heterogeneity but the costs of estimating these models often significantly increase. This paper aims at comparing the results from a hybrid choice model and a classical random parameter logit. Point of departure for this analysis is whether researchers and practitioners should add hybrid choice models to their suite of models routinely estimated. Our comparison reveals, in line with the few prior studies, that hybrid models gain in efficiency by the inclusion of additional information. The use of one of the two proposed approaches, however, depends on the objective of the analysis. If disentangling preference heterogeneity is most important, hybrid model seems to be preferable. If the focus is on predictive power, a standard random parameter logit model might be the better choice. Finally, we give recommendations for an adequate use of hybrid choice models based on known principles of elementary scientific inference. - Highlights: • The paper compares performance of a Hybrid Choice Model (HCM) and a classical Random Parameter Logit (RPL) model. • The HCM indeed provides insights regarding preference heterogeneity not gained from the RPL. • The RPL has similar predictive power as the HCM in our data. • The costs of estimating HCM seem to be justified when learning more on taste heterogeneity is a major study objective.
Hybrid discrete choice models: Gained insights versus increasing effort
Energy Technology Data Exchange (ETDEWEB)
Mariel, Petr, E-mail: petr.mariel@ehu.es [UPV/EHU, Economía Aplicada III, Avda. Lehendakari Aguire, 83, 48015 Bilbao (Spain); Meyerhoff, Jürgen [Institute for Landscape Architecture and Environmental Planning, Technical University of Berlin, D-10623 Berlin, Germany and The Kiel Institute for the World Economy, Duesternbrooker Weg 120, 24105 Kiel (Germany)
2016-10-15
Hybrid choice models expand the standard models in discrete choice modelling by incorporating psychological factors as latent variables. They could therefore provide further insights into choice processes and underlying taste heterogeneity but the costs of estimating these models often significantly increase. This paper aims at comparing the results from a hybrid choice model and a classical random parameter logit. Point of departure for this analysis is whether researchers and practitioners should add hybrid choice models to their suite of models routinely estimated. Our comparison reveals, in line with the few prior studies, that hybrid models gain in efficiency by the inclusion of additional information. The use of one of the two proposed approaches, however, depends on the objective of the analysis. If disentangling preference heterogeneity is most important, hybrid model seems to be preferable. If the focus is on predictive power, a standard random parameter logit model might be the better choice. Finally, we give recommendations for an adequate use of hybrid choice models based on known principles of elementary scientific inference. - Highlights: • The paper compares performance of a Hybrid Choice Model (HCM) and a classical Random Parameter Logit (RPL) model. • The HCM indeed provides insights regarding preference heterogeneity not gained from the RPL. • The RPL has similar predictive power as the HCM in our data. • The costs of estimating HCM seem to be justified when learning more on taste heterogeneity is a major study objective.
Numerical modelling in non linear fracture mechanics
Directory of Open Access Journals (Sweden)
Viggo Tvergaard
2007-07-01
Full Text Available Some numerical studies of crack propagation are based on using constitutive models that accountfor damage evolution in the material. When a critical damage value has been reached in a materialpoint, it is natural to assume that this point has no more carrying capacity, as is done numerically in the elementvanish technique. In the present review this procedure is illustrated for micromechanically based materialmodels, such as a ductile failure model that accounts for the nucleation and growth of voids to coalescence, and a model for intergranular creep failure with diffusive growth of grain boundary cavities leading to micro-crack formation. The procedure is also illustrated for low cycle fatigue, based on continuum damage mechanics. In addition, the possibility of crack growth predictions for elastic-plastic solids using cohesive zone models to represent the fracture process is discussed.
Modelling machine ensembles with discrete event dynamical system theory
Hunter, Dan
1990-01-01
Discrete Event Dynamical System (DEDS) theory can be utilized as a control strategy for future complex machine ensembles that will be required for in-space construction. The control strategy involves orchestrating a set of interactive submachines to perform a set of tasks for a given set of constraints such as minimum time, minimum energy, or maximum machine utilization. Machine ensembles can be hierarchically modeled as a global model that combines the operations of the individual submachines. These submachines are represented in the global model as local models. Local models, from the perspective of DEDS theory , are described by the following: a set of system and transition states, an event alphabet that portrays actions that takes a submachine from one state to another, an initial system state, a partial function that maps the current state and event alphabet to the next state, and the time required for the event to occur. Each submachine in the machine ensemble is presented by a unique local model. The global model combines the local models such that the local models can operate in parallel under the additional logistic and physical constraints due to submachine interactions. The global model is constructed from the states, events, event functions, and timing requirements of the local models. Supervisory control can be implemented in the global model by various methods such as task scheduling (open-loop control) or implementing a feedback DEDS controller (closed-loop control).
Sample selection and taste correlation in discrete choice transport modelling
DEFF Research Database (Denmark)
Mabit, Stefan Lindhard
2008-01-01
explain counterintuitive results in value of travel time estimation. However, the results also point at the difficulty of finding suitable instruments for the selection mechanism. Taste heterogeneity is another important aspect of discrete choice modelling. Mixed logit models are designed to capture...... the question for a broader class of models. It is shown that the original result may be somewhat generalised. Another question investigated is whether mode choice operates as a self-selection mechanism in the estimation of the value of travel time. The results show that self-selection can at least partly...... of taste correlation in willingness-to-pay estimation are presented. The first contribution addresses how to incorporate taste correlation in the estimation of the value of travel time for public transport. Given a limited dataset the approach taken is to use theory on the value of travel time as guidance...
Discrete persistent-chain model for protein binding on DNA.
Lam, Pui-Man; Zhen, Yi
2011-04-01
We describe and solve a discrete persistent-chain model of protein binding on DNA, involving an extra σ(i) at a site i of the DNA. This variable takes the value 1 or 0, depending on whether or not the site is occupied by a protein. In addition, if the site is occupied by a protein, there is an extra energy cost ɛ. For a small force, we obtain analytic expressions for the force-extension curve and the fraction of bound protein on the DNA. For higher forces, the model can be solved numerically to obtain force-extension curves and the average fraction of bound proteins as a function of applied force. Our model can be used to analyze experimental force-extension curves of protein binding on DNA, and hence deduce the number of bound proteins in the case of nonspecific binding. ©2011 American Physical Society
Modelling deformation and fracture in confectionery wafers
Energy Technology Data Exchange (ETDEWEB)
Mohammed, Idris K.; Charalambides, Maria N.; Williams, J. Gordon; Rasburn, John [Mechanical Engineering Department, Imperial College London, South Kensington, London, SW7 2AZ, United Kingdom and Nestec York Ltd., Nestlé Product Technology Centre, Haxby Road, PO Box 204, York YO91 1XY (United Kingdom)
2015-01-22
The aim of this research is to model the deformation and fracture behaviour of brittle wafers often used in chocolate confectionary products. Three point bending and compression experiments were performed on beam and circular disc samples respectively to determine the 'apparent' stress-strain curves in bending and compression. The deformation of the wafer for both these testing types was observed in-situ within an SEM. The wafer is modeled analytically and numerically as a composite material with a core which is more porous than the skins. X-ray tomography was used to generate a three dimensional volume of the wafer microstructure which was then meshed and used for quantitative analysis. A linear elastic material model, with a damage function and element deletion, was used and the XMT generated architecture was loaded in compression. The output from the FE simulations correlates closely to the load-deflection deformation observed experimentally.
Discrete modelling of front propagation in backward piping erosion
Tran, Duc-Kien; Prime, Noémie; Froiio, Francesco; Callari, Carlo; Vincens, Eric
2017-06-01
A preliminary discrete numerical model of a REV at the front region of an erosion pipe in a cohesive granular soil is briefly presented. The results reported herein refer to a simulation carried out by coupling the Discrete Element Method (DEM) with the Lattice Boltzmann Method (LBM) for the representation of the granular and fluid phases, respectively. The numerical specimen, consisiting of bonded grains, is tested under fully-saturated conditions and increasing pressure difference between the inlet (confined) and the outlet (unconfined) flow regions. The key role of compression arches of force chains that transversely cross the sample and carry most part of the hydrodynamic actions is pointed out. These arches partition the REV into an upstream region that remains almost intact and a downstream region that gradually degrades and is subsequently eroded in the form of a cluster. Eventually, the collapse of the compression arches causes the upstream region to be also eroded, abruptly, as a whole. A complete presentation of the numerical model and of the results of the simulation can be found in [12].
Discrete choice modeling of season choice for Minnesota turkey hunters
Schroeder, Susan A.; Fulton, David C.; Cornicelli, Louis; Merchant, Steven S.
2018-01-01
Recreational turkey hunting exemplifies the interdisciplinary nature of modern wildlife management. Turkey populations in Minnesota have reached social or biological carrying capacities in many areas, and changes to turkey hunting regulations have been proposed by stakeholders and wildlife managers. This study employed discrete stated choice modeling to enhance understanding of turkey hunter preferences about regulatory alternatives. We distributed mail surveys to 2,500 resident turkey hunters. Results suggest that, compared to season structure and lotteries, additional permits and level of potential interference from other hunters most influenced hunter preferences for regulatory alternatives. Low hunter interference was preferred to moderate or high interference. A second permit issued only to unsuccessful hunters was preferred to no second permit or permits for all hunters. Results suggest that utility is not strictly defined by harvest or an individual's material gain but can involve preference for other outcomes that on the surface do not materially benefit an individual. Discrete stated choice modeling offers wildlife managers an effective way to assess constituent preferences related to new regulations before implementing them.
Interfacial properties in a discrete model for tumor growth
Moglia, Belén; Guisoni, Nara; Albano, Ezequiel V.
2013-03-01
We propose and study, by means of Monte Carlo numerical simulations, a minimal discrete model for avascular tumor growth, which can also be applied for the description of cell cultures in vitro. The interface of the tumor is self-affine and its width can be characterized by the following exponents: (i) the growth exponent β=0.32(2) that governs the early time regime, (ii) the roughness exponent α=0.49(2) related to the fluctuations in the stationary regime, and (iii) the dynamic exponent z=α/β≃1.49(2), which measures the propagation of correlations in the direction parallel to the interface, e.g., ξ∝t1/z, where ξ is the parallel correlation length. Therefore, the interface belongs to the Kardar-Parisi-Zhang universality class, in agreement with recent experiments of cell cultures in vitro. Furthermore, density profiles of the growing cells are rationalized in terms of traveling waves that are solutions of the Fisher-Kolmogorov equation. In this way, we achieved excellent agreement between the simulation results of the discrete model and the continuous description of the growth front of the culture or tumor.
Mittag-Leffler function for discrete fractional modelling
Directory of Open Access Journals (Sweden)
Guo-Cheng Wu
2016-01-01
Full Text Available From the difference equations on discrete time scales, this paper numerically investigates one discrete fractional difference equation in the Caputo delta’s sense which has an explicit solution in form of the discrete Mittag-Leffler function. The exact numerical values of the solutions are given in comparison with the truncated Mittag-Leffler function.
On a discrete version of the CP 1 sigma model and surfaces immersed in R3
International Nuclear Information System (INIS)
Grundland, A M; Levi, D; Martina, L
2003-01-01
We present a discretization of the CP 1 sigma model. We show that the discrete CP 1 sigma model is described by a nonlinear partial second-order difference equation with rational nonlinearity. To derive discrete surfaces immersed in three-dimensional Euclidean space a 'complex' lattice is introduced. The so-obtained surfaces are characterized in terms of the quadrilateral cross-ratio of four surface points. In this way we prove that all surfaces associated with the discrete CP 1 sigma model are of constant mean curvature. An explicit example of such discrete surfaces is constructed
Sensitivity of using blunt and sharp crack models in elastic-plastic fracture mechanics
International Nuclear Information System (INIS)
Pan, Y.C.; Kennedy, J.M.; Marchertas, A.H.
1985-01-01
J-integral values are calculated for both the blunt (smeared) crack and the sharp (discrete) crack models in elastic-plastic fracture mechanics problems involving metallic materials. A sensitivity study is performed to show the relative strengths and weaknesses of the two cracking models. It is concluded that the blunt crack model is less dependent on the orientation of the mesh. For the mesh which is in line with the crack direction, however, the sharp crack model is less sensitive to the mesh size. Both models yield reasonable results for a properly discretized finite-element mesh. A subcycling technique is used in this study in the explicit integration scheme so that large time steps can be used for the coarse elements away from the crack tip. The savings of computation time by this technique are reported. 6 refs., 9 figs
Fault diagnosis for discrete event systems: Modelling and verification
International Nuclear Information System (INIS)
Simeu-Abazi, Zineb; Di Mascolo, Maria; Knotek, Michal
2010-01-01
This paper proposes an effective way for diagnosis of discrete-event systems using a timed-automaton. It is based on the model-checking technique, thanks to time analysis of the timed model. The paper proposes a method to construct all the timed models and details the different steps used to obtain the diagnosis path. A dynamic model with temporal transitions is proposed in order to model the system. By 'dynamical model', we mean an extension of timed automata for which the faulty states are identified. The model of the studied system contains the faultless functioning states and all the faulty states. Our method is based on the backward exploitation of the dynamic model, where all possible reverse paths are searched. The reverse path is the connection of the faulty state to the initial state. The diagnosis method is based on the coherence between the faulty occurrence time and the reverse path length. A real-world batch process is used to demonstrate the modelling steps and the proposed backward time analysis method to reach the diagnosis results.
Specimen-specific modeling of hip fracture pattern and repair.
Ali, Azhar A; Cristofolini, Luca; Schileo, Enrico; Hu, Haixiang; Taddei, Fulvia; Kim, Raymond H; Rullkoetter, Paul J; Laz, Peter J
2014-01-22
Hip fracture remains a major health problem for the elderly. Clinical studies have assessed fracture risk based on bone quality in the aging population and cadaveric testing has quantified bone strength and fracture loads. Prior modeling has primarily focused on quantifying the strain distribution in bone as an indicator of fracture risk. Recent advances in the extended finite element method (XFEM) enable prediction of the initiation and propagation of cracks without requiring a priori knowledge of the crack path. Accordingly, the objectives of this study were to predict femoral fracture in specimen-specific models using the XFEM approach, to perform one-to-one comparisons of predicted and in vitro fracture patterns, and to develop a framework to assess the mechanics and load transfer in the fractured femur when it is repaired with an osteosynthesis implant. Five specimen-specific femur models were developed from in vitro experiments under a simulated stance loading condition. Predicted fracture patterns closely matched the in vitro patterns; however, predictions of fracture load differed by approximately 50% due to sensitivity to local material properties. Specimen-specific intertrochanteric fractures were induced by subjecting the femur models to a sideways fall and repaired with a contemporary implant. Under a post-surgical stance loading, model-predicted load sharing between the implant and bone across the fracture surface varied from 59%:41% to 89%:11%, underscoring the importance of considering anatomic and fracture variability in the evaluation of implants. XFEM modeling shows potential as a macro-level analysis enabling fracture investigations of clinical cohorts, including at-risk groups, and the design of robust implants. © 2013 Published by Elsevier Ltd.
Performance analysis of chi models using discrete-time probabilistic reward graphs
Trcka, N.; Georgievska, S.; Markovski, J.; Andova, S.; Vink, de E.P.
2008-01-01
We propose the model of discrete-time probabilistic reward graphs (DTPRGs) for performance analysis of systems exhibiting discrete deterministic time delays and probabilistic behavior, via their interpretation as discrete-time Markov reward chains, full-fledged platform for qualitative and
On the relationship of steady states of continuous and discrete models arising from biology.
Veliz-Cuba, Alan; Arthur, Joseph; Hochstetler, Laura; Klomps, Victoria; Korpi, Erikka
2012-12-01
For many biological systems that have been modeled using continuous and discrete models, it has been shown that such models have similar dynamical properties. In this paper, we prove that this happens in more general cases. We show that under some conditions there is a bijection between the steady states of continuous and discrete models arising from biological systems. Our results also provide a novel method to analyze certain classes of nonlinear models using discrete mathematics.
Integrable discretizations for the short-wave model of the Camassa-Holm equation
International Nuclear Information System (INIS)
Feng Baofeng; Maruno, Ken-ichi; Ohta, Yasuhiro
2010-01-01
The link between the short-wave model of the Camassa-Holm equation (SCHE) and bilinear equations of the two-dimensional Toda lattice equation is clarified. The parametric form of the N-cuspon solution of the SCHE in Casorati determinant is then given. Based on the above finding, integrable semi-discrete and full-discrete analogues of the SCHE are constructed. The determinant solutions of both semi-discrete and fully discrete analogues of the SCHE are also presented.
Modeling energy market dynamics using discrete event system simulation
International Nuclear Information System (INIS)
Gutierrez-Alcaraz, G.; Sheble, G.B.
2009-01-01
This paper proposes the use of Discrete Event System Simulation to study the interactions among fuel and electricity markets and consumers, and the decision-making processes of fuel companies (FUELCOs), generation companies (GENCOs), and consumers in a simple artificial energy market. In reality, since markets can reach a stable equilibrium or fail, it is important to observe how they behave in a dynamic framework. We consider a Nash-Cournot model in which marketers are depicted as Nash-Cournot players that determine supply to meet end-use consumption. Detailed engineering considerations such as transportation network flows are omitted, because the focus is upon the selection and use of appropriate market models to provide answers to policy questions. (author)
Discrete element modeling of calcium-silicate-hydrate
International Nuclear Information System (INIS)
Chandler, Mei Qiang; Peters, John F; Pelessone, Daniele
2013-01-01
The discrete element method (DEM) was used to model calcium-silicate-hydrate (C-S-H) at the nanoscale. The C-S-H nanoparticles were modeled as spherical particles with diameters of approximately 5 nm. Interparticle forces included traditional mechanical contact forces, van der Waals forces and ionic correlation forces due to negatively charged C-S-H nanoparticles and ion species in the nanopores. Previous work by the authors demonstrated the DEM method was feasible in studying the properties of the C-S-H nanostructures. In this work, the simulations were performed to look into the effects of nanoparticle packing, nanoparticle morphology, interparticle forces and nanoparticle properties on the deformation mechanisms and mechanical properties of the C-S-H matrix. This work will provide insights into possible ways to improve the properties of the C-S-H matrix. (paper)
Stochastic cluster algorithms for discrete Gaussian (SOS) models
International Nuclear Information System (INIS)
Evertz, H.G.; Hamburg Univ.; Hasenbusch, M.; Marcu, M.; Tel Aviv Univ.; Pinn, K.; Muenster Univ.; Solomon, S.
1990-10-01
We present new Monte Carlo cluster algorithms which eliminate critical slowing down in the simulation of solid-on-solid models. In this letter we focus on the two-dimensional discrete Gaussian model. The algorithms are based on reflecting the integer valued spin variables with respect to appropriately chosen reflection planes. The proper choice of the reflection plane turns out to be crucial in order to obtain a small dynamical exponent z. Actually, the successful versions of our algorithm are a mixture of two different procedures for choosing the reflection plane, one of them ergodic but slow, the other one non-ergodic and also slow when combined with a Metropolis algorithm. (orig.)
A practical guide for operational validation of discrete simulation models
Directory of Open Access Journals (Sweden)
Fabiano Leal
2011-04-01
Full Text Available As the number of simulation experiments increases, the necessity for validation and verification of these models demands special attention on the part of the simulation practitioners. By analyzing the current scientific literature, it is observed that the operational validation description presented in many papers does not agree on the importance designated to this process and about its applied techniques, subjective or objective. With the expectation of orienting professionals, researchers and students in simulation, this article aims to elaborate a practical guide through the compilation of statistical techniques in the operational validation of discrete simulation models. Finally, the guide's applicability was evaluated by using two study objects, which represent two manufacturing cells, one from the automobile industry and the other from a Brazilian tech company. For each application, the guide identified distinct steps, due to the different aspects that characterize the analyzed distributions
Directory of Open Access Journals (Sweden)
Chong Shi
2017-10-01
Full Text Available Fractured seepage is an important factor affecting the interface stability of rock mass. It is closely related to fracture properties and hydraulic conditions. In this study, the law of seepage in a single fracture surface based on modified cubic law is described, and the three-dimensional discrete element method is used to simulate the dam foundation structure of the Capulin San Pablo (Costa Rica hydropower station. The effect of construction joints and developed structure on dam stability is studied, and its permeability law and sliding stability are also evaluated. It is found that the hydraulic-mechanical coupling with strength reduction method in DEM is more appropriate to use to study the seepage-related problems of fractured rock mass, which considers practical conditions, such as the roughness of and the width of fracture. The strength reduction method provides a more accurate safety factor of dam when considering the deformation coordination with bedrocks. It is an important method with which to study the stability of seepage conditions in complex structures. The discrete method also provided an effective and reasonable way of determining seepage control measures.
Strong Local-Nonlocal Coupling for Integrated Fracture Modeling
Energy Technology Data Exchange (ETDEWEB)
Littlewood, David John [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Silling, Stewart A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Mitchell, John A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Seleson, Pablo D. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Bond, Stephen D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Parks, Michael L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Turner, Daniel Z. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Burnett, Damon J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ostien, Jakob [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Gunzburger, Max [Florida State Univ., Tallahassee, FL (United States)
2015-09-01
Peridynamics, a nonlocal extension of continuum mechanics, is unique in its ability to capture pervasive material failure. Its use in the majority of system-level analyses carried out at Sandia, however, is severely limited, due in large part to computational expense and the challenge posed by the imposition of nonlocal boundary conditions. Combined analyses in which peridynamics is em- ployed only in regions susceptible to material failure are therefore highly desirable, yet available coupling strategies have remained severely limited. This report is a summary of the Laboratory Directed Research and Development (LDRD) project "Strong Local-Nonlocal Coupling for Inte- grated Fracture Modeling," completed within the Computing and Information Sciences (CIS) In- vestment Area at Sandia National Laboratories. A number of challenges inherent to coupling local and nonlocal models are addressed. A primary result is the extension of peridynamics to facilitate a variable nonlocal length scale. This approach, termed the peridynamic partial stress, can greatly reduce the mathematical incompatibility between local and nonlocal equations through reduction of the peridynamic horizon in the vicinity of a model interface. A second result is the formulation of a blending-based coupling approach that may be applied either as the primary coupling strategy, or in combination with the peridynamic partial stress. This blending-based approach is distinct from general blending methods, such as the Arlequin approach, in that it is specific to the coupling of peridynamics and classical continuum mechanics. Facilitating the coupling of peridynamics and classical continuum mechanics has also required innovations aimed directly at peridynamic models. Specifically, the properties of peridynamic constitutive models near domain boundaries and shortcomings in available discretization strategies have been addressed. The results are a class of position-aware peridynamic constitutive laws for
Discrete modelling of the electrochemical performance of SOFC electrodes
International Nuclear Information System (INIS)
Schneider, L.C.R.; Martin, C.L.; Bultel, Y.; Bouvard, D.; Siebert, E.
2006-01-01
The composite anode and cathode of solid oxide fuel cells (SOFC) are modelled as sintered mixtures of electrolyte and electrocatalyst particles. A particle packing is first created numerically by the discrete element method (DEM) from a loose packing of 40 000 spherical, monosized, homogeneously mixed, and randomly positioned particles. Once the microstructure is sintered numerically, the effective electrode conductivity is determined by discretization of the particle packing into a resistance network. Each particle contact is characteristic of a bond resistance that depends on contact geometry and particle properties. The network, which typically consists of 120 000 bond resistances in total, is solved using Kirchhoff's current law. Distributions of local current densities and particle potentials are then performed. We investigate how electrode performance depends on parameters such as electrode composition, thickness, density and intrinsic material conductivities that are temperature dependent. The simulations show that the best electrode performance is obtained for compositions close to the percolation threshold of the electronic conductor. Depending on particle conductivities, the electrode performance is a function of its thickness. Additionally, DEM simulations generate useful microstructural information such as: coordination numbers, triple phase boundary length and percolation thresholds
Modeling discrete and continuous entities with fractions and decimals.
Rapp, Monica; Bassok, Miriam; DeWolf, Melissa; Holyoak, Keith J
2015-03-01
When people use mathematics to model real-life situations, their use of mathematical expressions is often mediated by semantic alignment (Bassok, Chase, & Martin, 1998): The entities in a problem situation evoke semantic relations (e.g., tulips and vases evoke the functionally asymmetric "contain" relation), which people align with analogous mathematical relations (e.g., the noncommutative division operation, tulips/vases). Here we investigate the possibility that semantic alignment is also involved in the comprehension and use of rational numbers (fractions and decimals). A textbook analysis and results from two experiments revealed that both mathematic educators and college students tend to align the discreteness versus continuity of the entities in word problems (e.g., marbles vs. distance) with distinct symbolic representations of rational numbers--fractions versus decimals, respectively. In addition, fractions and decimals tend to be used with nonmetric units and metric units, respectively. We discuss the importance of the ontological distinction between continuous and discrete entities to mathematical cognition, the role of symbolic notations, and possible implications of our findings for the teaching of rational numbers. PsycINFO Database Record (c) 2015 APA, all rights reserved.
Directory of Open Access Journals (Sweden)
Ingrid Tomac
2017-02-01
Full Text Available This paper presents an improved understanding of coupled hydro-thermo-mechanical (HTM hydraulic fracturing of quasi-brittle rock using the bonded particle model (BPM within the discrete element method (DEM. BPM has been recently extended by the authors to account for coupled convective–conductive heat flow and transport, and to enable full hydro-thermal fluid–solid coupled modeling. The application of the work is on enhanced geothermal systems (EGSs, and hydraulic fracturing of hot dry rock (HDR is studied in terms of the impact of temperature difference between rock and a flowing fracturing fluid. Micro-mechanical investigation of temperature and fracturing fluid effects on hydraulic fracturing damage in rocks is presented. It was found that fracture is shorter with pronounced secondary microcracking along the main fracture for the case when the convective–conductive thermal heat exchange is considered. First, the convection heat exchange during low-viscosity fluid infiltration in permeable rock around the wellbore causes significant rock cooling, where a finger-like fluid infiltration was observed. Second, fluid infiltration inhibits pressure rise during pumping and delays fracture initiation and propagation. Additionally, thermal damage occurs in the whole area around the wellbore due to rock cooling and cold fluid infiltration. The size of a damaged area around the wellbore increases with decreasing fluid dynamic viscosity. Fluid and rock compressibility ratio was found to have significant effect on the fracture propagation velocity.
Modeling of flow through fractured tuff at Fran Ridge
International Nuclear Information System (INIS)
Eaton, R.R.; Ho, C.K.; Glass, R.J.; Nicholl, M.J.; Arnold, B.W.
1996-01-01
Numerical studies have modeled an infiltration experiment at Fran Ridge, using the TOUGH2 code, to aid in the selection of computational models for waste repository performance assessment. This study investigates the capabilities of TOUGH2 to simulate transient flows through highly fractured tuff, and provides a possible means of calibrating hydrologic parameters such as effective fracture aperture and fracture-matrix connectivity. Two distinctly different conceptual models were used in the TOUGH2 code, the dual permeability model and the equivalent continuum model. The field experiments involved the infiltration of dyed ponded water in highly fractured tuff. The infiltration observed in the experiment was subsequently modeled using Fran Ridge fracture frequencies, obtained during post-experiment site excavation. Comparison of the TOUGH2 results obtained using the two conceptual models gives insight into their relative strengths and weaknesses
Directory of Open Access Journals (Sweden)
Spyridon Liakas
2017-08-01
Full Text Available The particulate discrete element method (DEM can be employed to capture the response of rock, provided that appropriate bonding models are used to cement the particles to each other. Simulations of laboratory tests are important to establish the extent to which those models can capture realistic rock behaviors. Hitherto the focus in such comparison studies has either been on homogeneous specimens or use of two-dimensional (2D models. In situ rock formations are often heterogeneous, thus exploring the ability of this type of models to capture heterogeneous material behavior is important to facilitate their use in design analysis. In situ stress states are basically three-dimensional (3D, and therefore it is important to develop 3D models for this purpose. This paper revisits an earlier experimental study on heterogeneous specimens, of which the relative proportions of weaker material (siltstone and stronger, harder material (sandstone were varied in a controlled manner. Using a 3D DEM model with the parallel bond model, virtual heterogeneous specimens were created. The overall responses in terms of variations in strength and stiffness with different percentages of weaker material (siltstone were shown to agree with the experimental observations. There was also a good qualitative agreement in the failure patterns observed in the experiments and the simulations, suggesting that the DEM data enabled analysis of the initiation of localizations and micro fractures in the specimens.
Discrete Event Simulation Model of the Polaris 2.1 Gamma Ray Imaging Radiation Detection Device
2016-06-01
release; distribution is unlimited DISCRETE EVENT SIMULATION MODEL OF THE POLARIS 2.1 GAMMA RAY IMAGING RADIATION DETECTION DEVICE by Andres T...ONLY (Leave blank) 2. REPORT DATE June 2016 3. REPORT TYPE AND DATES COVERED Master’s thesis 4. TITLE AND SUBTITLE DISCRETE EVENT SIMULATION MODEL...modeled. The platform, Simkit, was utilized to create a discrete event simulation (DES) model of the Polaris. After carefully constructing the DES
The Fracture Mechanical Markov Chain Fatigue Model Compared with Empirical Data
DEFF Research Database (Denmark)
Gansted, L.; Brincker, Rune; Hansen, Lars Pilegaard
The applicability of the FMF-model (Fracture Mechanical Markov Chain Fatigue Model) introduced in Gansted, L., R. Brincker and L. Pilegaard Hansen (1991) is tested by simulations and compared with empirical data. Two sets of data have been used, the Virkler data (aluminium alloy) and data...... established at the Laboratory of Structural Engineering at Aalborg University, the AUC-data, (mild steel). The model, which is based on the assumption, that the crack propagation process can be described by a discrete Space Markov theory, is applicable to constant as well as random loading. It is shown...
Discrete competing risk model with application to modeling bus-motor failure data
International Nuclear Information System (INIS)
Jiang, R.
2010-01-01
Failure data are often modeled using continuous distributions. However, a discrete distribution can be appropriate for modeling interval or grouped data. When failure data come from a complex system, a simple discrete model can be inappropriate for modeling such data. This paper presents two types of discrete distributions. One is formed by exponentiating an underlying distribution, and the other is a two-fold competing risk model. The paper focuses on two special distributions: (a) exponentiated Poisson distribution and (b) competing risk model involving a geometric distribution and an exponentiated Poisson distribution. The competing risk model has a decreasing-followed-by-unimodal mass function and a bathtub-shaped failure rate. Five classical data sets on bus-motor failures can be simultaneously and appropriately fitted by a general 5-parameter competing risk model with the parameters being functions of the number of successive failures. The lifetime and aging characteristics of the fitted distribution are analyzed.
Determining Trajectory of Triboelectrically Charged Particles, Using Discrete Element Modeling
2008-01-01
The Kennedy Space Center (KSC) Electrostatics and Surface Physics Laboratory is participating in an Innovative Partnership Program (IPP) project with an industry partner to modify a commercial off-the-shelf simulation software product to treat the electrodynamics of particulate systems. Discrete element modeling (DEM) is a numerical technique that can track the dynamics of particle systems. This technique, which was introduced in 1979 for analysis of rock mechanics, was recently refined to include the contact force interaction of particles with arbitrary surfaces and moving machinery. In our work, we endeavor to incorporate electrostatic forces into the DEM calculations to enhance the fidelity of the software and its applicability to (1) particle processes, such as electrophotography, that are greatly affected by electrostatic forces, (2) grain and dust transport, and (3) the study of lunar and Martian regoliths.
Hopf Bifurcation in a Cobweb Model with Discrete Time Delays
Directory of Open Access Journals (Sweden)
Luca Gori
2014-01-01
Full Text Available We develop a cobweb model with discrete time delays that characterise the length of production cycle. We assume a market comprised of homogeneous producers that operate as adapters by taking the (expected profit-maximising quantity as a target to adjust production and consumers with a marginal willingness to pay captured by an isoelastic demand. The dynamics of the economy is characterised by a one-dimensional delay differential equation. In this context, we show that (1 if the elasticity of market demand is sufficiently high, the steady-state equilibrium is locally asymptotically stable and (2 if the elasticity of market demand is sufficiently low, quasiperiodic oscillations emerge when the time lag (that represents the length of production cycle is high enough.
Nuclear facility safeguards systems modeling using discrete event simulation
International Nuclear Information System (INIS)
Engi, D.
1977-01-01
The threat of theft or dispersal of special nuclear material at a nuclear facility is treated by studying the temporal relationships between adversaries having authorized access to the facility (insiders) and safeguards system events by using a GASP IV discrete event simulation. The safeguards system events--detection, assessment, delay, communications, and neutralization--are modeled for the general insider adversary strategy which includes degradation of the safeguards system elements followed by an attempt to steal or disperse special nuclear material. The performance measure used in the analysis is the estimated probability of safeguards system success in countering the adversary based upon a predetermined set of adversary actions. An exemplary problem which includes generated results is presented for a hypothetical nuclear facility. The results illustrate representative information that could be utilized by safeguards decision-makers
Multistability and complex dynamics in a simple discrete economic model
International Nuclear Information System (INIS)
Peng Mingshu; Jiang Zhonghao; Jiang Xiaoxia; Hu Jiping; Qu Youli
2009-01-01
In this paper, we will propose a generalized Cournot duopoly model with Z 2 symmetry. We demonstrate that cost functions incorporating an interfirm externality lead to a system of couple one-dimensional maps. In the situation where agents take turns, we find in an analytic way that there coexist multiple unstable/stable period-2 cycles or synchronized/asynchronized periodic orbits. Coupling one-dimension chaos can be observed. In a more general situation, where agents move simultaneously, a closer analysis reveals some well-known local bifurcations and global bifurcations which typically occur in two-parameter families of two-dimensional discrete time dynamical systems, including codimension-one (fold-, flip-, Neimark-Sacker-) bifurcations, codimension-two (fold/flip, 1:2 resonance, 1:3 resonance and 1:4 resonance) bifurcations, and hetero-clinic, homo-clinic bifurcations, etc. Multistability, including the coexistence of synchronized/asynchronized solutions are also discussed.
Navier-Stokes Dynamics by a Discrete Boltzmann Model
Rubinstein, Robet
2010-01-01
This work investigates the possibility of particle-based algorithms for the Navier-Stokes equations and higher order continuum approximations of the Boltzmann equation; such algorithms would generalize the well-known Pullin scheme for the Euler equations. One such method is proposed in the context of a discrete velocity model of the Boltzmann equation. Preliminary results on shock structure are consistent with the expectation that the shock should be much broader than the near discontinuity predicted by the Pullin scheme, yet narrower than the prediction of the Boltzmann equation. We discuss the extension of this essentially deterministic method to a stochastic particle method that, like DSMC, samples the distribution function rather than resolving it completely.
Modeling Dynamic Fracture of Cryogenic Pellets
Energy Technology Data Exchange (ETDEWEB)
Parks, Paul [General Atomics, San Diego, CA (United States)
2016-06-30
This work is part of an investigation with the long-range objective of predicting the size distribution function and velocity dispersion of shattered pellet fragments after a large cryogenic pellet impacts a solid surface at high velocity. The study is vitally important for the shattered pellet injection (SPI) technique, one of the leading technologies being implemented at ORNL for the mitigation of disruption damage on current tokamaks and ITER. The report contains three parts that are somewhat interwoven. In Part I we formulated a self-similar model for the expansion dynamics and velocity dispersion of the debris cloud following pellet impact against a thick (rigid) target plate. Also presented in Part I is an analytical fracture model that predicts the nominal or mean size of the fragments in the debris cloud and agrees well with known SPI data. The aim of Part II is to gain an understanding of the pellet fracturing process when a pellet is shattered inside a miter tube with a sharp bend. Because miter tubes have a thin stainless steel (SS) wall a permanent deformation (dishing) of the wall is produced at the site of the impact. A review of the literature indicates that most projectile impact on thin plates are those for which the target is deformed and the projectile is perfectly rigid. Such impacts result in “projectile embedding” where the projectile speed is reduced to zero during the interaction so that all the kinetic energy (KE) of the projectile goes into the energy stored in plastic deformation. Much of the literature deals with perforation of the target. The problem here is quite different; the softer pellet easily undergoes complete material failure causing only a small transfer of KE to stored energy of wall deformation. For the real miter tube, we derived a strain energy function for the wall deflection using a non-linear (plastic) stress-strain relation for 304 SS. Using a dishing profile identical to the linear Kirchkoff-Love profile (for lack
Cai, Zuansi; Merly, Corrine; Thomson, Neil R.; Wilson, Ryan D.; Lerner, David N.
2007-08-01
Technical developments have now made it possible to emplace granular zero-valent iron (Fe 0) in fractured media to create a Fe 0 fracture reactive barrier (Fe 0 FRB) for the treatment of contaminated groundwater. To evaluate this concept, we conducted a laboratory experiment in which trichloroethylene (TCE) contaminated water was flushed through a single uniform fracture created between two sandstone blocks. This fracture was partly filled with what was intended to be a uniform thickness of iron. Partial treatment of TCE by iron demonstrated that the concept of a Fe 0 FRB is practical, but was less than anticipated for an iron layer of uniform thickness. When the experiment was disassembled, evidence of discrete channelised flow was noted and attributed to imperfect placement of the iron. To evaluate the effect of the channel flow, an explicit Channel Model was developed that simplifies this complex flow regime into a conceptualised set of uniform and parallel channels. The mathematical representation of this conceptualisation directly accounts for (i) flow channels and immobile fluid arising from the non-uniform iron placement, (ii) mass transfer from the open fracture to iron and immobile fluid regions, and (iii) degradation in the iron regions. A favourable comparison between laboratory data and the results from the developed mathematical model suggests that the model is capable of representing TCE degradation in fractures with non-uniform iron placement. In order to apply this Channel Model concept to a Fe 0 FRB system, a simplified, or implicit, Lumped Channel Model was developed where the physical and chemical processes in the iron layer and immobile fluid regions are captured by a first-order lumped rate parameter. The performance of this Lumped Channel Model was compared to laboratory data, and benchmarked against the Channel Model. The advantages of the Lumped Channel Model are that the degradation of TCE in the system is represented by a first
Sahoo, Debasis; Deck, Caroline; Yoganandan, Narayan; Willinger, Rémy
2013-12-01
A composite material model for skull, taking into account damage is implemented in the Strasbourg University finite element head model (SUFEHM) in order to enhance the existing skull mechanical constitutive law. The skull behavior is validated in terms of fracture patterns and contact forces by reconstructing 15 experimental cases. The new SUFEHM skull model is capable of reproducing skull fracture precisely. The composite skull model is validated not only for maximum forces, but also for lateral impact against actual force time curves from PMHS for the first time. Skull strain energy is found to be a pertinent parameter to predict the skull fracture and based on statistical (binary logistical regression) analysis it is observed that 50% risk of skull fracture occurred at skull strain energy of 544.0mJ. © 2013 Elsevier Ltd. All rights reserved.
A fractal model for intergranular fractures in nanocrystals
International Nuclear Information System (INIS)
Lung, C.W.; Xiong, L.Y.; Zhou, X.Z.
1993-09-01
A fractal model for intergranular fractures in nanocrystals is proposed to explain the dependence of fracture toughness with grain size in this range of scale. Based on positron annihilation and internal friction experimental results, we point out that the assumption of a constant grain boundary thickness in previous models is too simplified to be true. (author). 7 refs, 6 figs
A discrete model to study reaction-diffusion-mechanics systems.
Weise, Louis D; Nash, Martyn P; Panfilov, Alexander V
2011-01-01
This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.
A discrete model to study reaction-diffusion-mechanics systems.
Directory of Open Access Journals (Sweden)
Louis D Weise
Full Text Available This article introduces a discrete reaction-diffusion-mechanics (dRDM model to study the effects of deformation on reaction-diffusion (RD processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material. Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.
Jougnot, D.; Roubinet, D.; Linde, N.; Irving, J.
2016-12-01
Quantifying fluid flow in fractured media is a critical challenge in a wide variety of research fields and applications. To this end, geophysics offers a variety of tools that can provide important information on subsurface physical properties in a noninvasive manner. Most geophysical techniques infer fluid flow by data or model differencing in time or space (i.e., they are not directly sensitive to flow occurring at the time of the measurements). An exception is the self-potential (SP) method. When water flows in the subsurface, an excess of charge in the pore water that counterbalances electric charges at the mineral-pore water interface gives rise to a streaming current and an associated streaming potential. The latter can be measured with the SP technique, meaning that the method is directly sensitive to fluid flow. Whereas numerous field experiments suggest that the SP method may allow for the detection of hydraulically active fractures, suitable tools for numerically modeling streaming potentials in fractured media do not exist. Here, we present a highly efficient two-dimensional discrete-dual-porosity approach for solving the fluid-flow and associated self-potential problems in fractured domains. Our approach is specifically designed for complex fracture networks that cannot be investigated using standard numerical methods due to computational limitations. We then simulate SP signals associated with pumping conditions for a number of examples to show that (i) accounting for matrix fluid flow is essential for accurate SP modeling and (ii) the sensitivity of SP to hydraulically active fractures is intimately linked with fracture-matrix fluid interactions. This implies that fractures associated with strong SP amplitudes are likely to be hydraulically conductive, attracting fluid flow from the surrounding matrix.
Doe, T.; McLaren, R.; Finilla, A.
2017-12-01
An enduring legacy of Paul Witherspoon and his students and colleagues has been both the development of geothermal energy and the bases of modern fractured-rock hydrogeology. One of the seminal contributions to the geothermal field was Gringarten, Witherspoon, and Ohnishi's analytical models for enhanced geothermal systems. Although discrete fracture network (DFN) modeling developed somewhat independently in the late 1970s, Paul Witherspoon's foresight in promoting underground in situ testing at the Stripa Mine in Sweden was a major driver in Lawrence Berkeley Laboratory's contributions to its development.This presentation looks extensions of Gringarten's analytical model into discrete fracture network modeling as a basis for providing further insights into the challenges and opportunities of engineered geothermal systems. The analytical solution itself has many insightful applications beyond those presented in the original paper. The definition of dimensionless time by itself shows that thermal breakthrough has a second power dependence on surface area and on flow rate. The fracture intensity also plays a strong role, as it both increases the surface area and decrease his flow rate per fracture. The improvement of EGS performance with fracture intensity reaches a limit where thermal depletion of the rock lags only slightly behind the thermal breakthrough of cold water in the fracture network.Simple network models, which couple a DFN generator (FracMan) with a hydrothermally coupled flow solver (HydroGeoSphere) expand on Gringarten's concepts to show that realistic heterogeneity of spacing and transmissivity significantly degrades EGS performance. EGS production in networks of stimulated fractures initially follows Gringarten's type curves, with a later deviation is the smaller rock blocks thermally deplete and the entire stimulated volume acts as a single sink. Three-dimensional models of EGS performance show the critical importance of the relative magnitudes of
Bauer, Daniel J.; Curran, Patrick J.
2004-01-01
Structural equation mixture modeling (SEMM) integrates continuous and discrete latent variable models. Drawing on prior research on the relationships between continuous and discrete latent variable models, the authors identify 3 conditions that may lead to the estimation of spurious latent classes in SEMM: misspecification of the structural model,…
Lean business model and implementation of a geriatric fracture center.
Kates, Stephen L
2014-05-01
Geriatric hip fracture is a common event associated with high costs of care and often with suboptimal outcomes for the patients. Ideally, a new care model to manage geriatric hip fractures would address both quality and safety of patient care as well as the need for reduced costs of care. The geriatric fracture center model of care is one such model reported to improve both outcomes and quality of care. It is a lean business model applied to medicine. This article describes basic lean business concepts applied to geriatric fracture care and information needed to successfully implement a geriatric fracture center. It is written to assist physicians and surgeons in their efforts to implement an improved care model for their patients. Copyright © 2014 Elsevier Inc. All rights reserved.
Nonparametric Identification and Estimation of Finite Mixture Models of Dynamic Discrete Choices
Hiroyuki Kasahara; Katsumi Shimotsu
2006-01-01
In dynamic discrete choice analysis, controlling for unobserved heterogeneity is an important issue, and finite mixture models provide flexible ways to account for unobserved heterogeneity. This paper studies nonparametric identifiability of type probabilities and type-specific component distributions in finite mixture models of dynamic discrete choices. We derive sufficient conditions for nonparametric identification for various finite mixture models of dynamic discrete choices used in appli...
Bayesian inference for hybrid discrete-continuous stochastic kinetic models
International Nuclear Information System (INIS)
Sherlock, Chris; Golightly, Andrew; Gillespie, Colin S
2014-01-01
We consider the problem of efficiently performing simulation and inference for stochastic kinetic models. Whilst it is possible to work directly with the resulting Markov jump process (MJP), computational cost can be prohibitive for networks of realistic size and complexity. In this paper, we consider an inference scheme based on a novel hybrid simulator that classifies reactions as either ‘fast’ or ‘slow’ with fast reactions evolving as a continuous Markov process whilst the remaining slow reaction occurrences are modelled through a MJP with time-dependent hazards. A linear noise approximation (LNA) of fast reaction dynamics is employed and slow reaction events are captured by exploiting the ability to solve the stochastic differential equation driving the LNA. This simulation procedure is used as a proposal mechanism inside a particle MCMC scheme, thus allowing Bayesian inference for the model parameters. We apply the scheme to a simple application and compare the output with an existing hybrid approach and also a scheme for performing inference for the underlying discrete stochastic model. (paper)
A stochastic discrete optimization model for designing container terminal facilities
Zukhruf, Febri; Frazila, Russ Bona; Burhani, Jzolanda Tsavalista
2017-11-01
As uncertainty essentially affect the total transportation cost, it remains important in the container terminal that incorporates several modes and transshipments process. This paper then presents a stochastic discrete optimization model for designing the container terminal, which involves the decision of facilities improvement action. The container terminal operation model is constructed by accounting the variation of demand and facilities performance. In addition, for illustrating the conflicting issue that practically raises in the terminal operation, the model also takes into account the possible increment delay of facilities due to the increasing number of equipment, especially the container truck. Those variations expectantly reflect the uncertainty issue in the container terminal operation. A Monte Carlo simulation is invoked to propagate the variations by following the observed distribution. The problem is constructed within the framework of the combinatorial optimization problem for investigating the optimal decision of facilities improvement. A new variant of glow-worm swarm optimization (GSO) is thus proposed for solving the optimization, which is rarely explored in the transportation field. The model applicability is tested by considering the actual characteristics of the container terminal.
Tuning Fractures With Dynamic Data
Yao, Mengbi; Chang, Haibin; Li, Xiang; Zhang, Dongxiao
2018-02-01
Flow in fractured porous media is crucial for production of oil/gas reservoirs and exploitation of geothermal energy. Flow behaviors in such media are mainly dictated by the distribution of fractures. Measuring and inferring the distribution of fractures is subject to large uncertainty, which, in turn, leads to great uncertainty in the prediction of flow behaviors. Inverse modeling with dynamic data may assist to constrain fracture distributions, thus reducing the uncertainty of flow prediction. However, inverse modeling for flow in fractured reservoirs is challenging, owing to the discrete and non-Gaussian distribution of fractures, as well as strong nonlinearity in the relationship between flow responses and model parameters. In this work, building upon a series of recent advances, an inverse modeling approach is proposed to efficiently update the flow model to match the dynamic data while retaining geological realism in the distribution of fractures. In the approach, the Hough-transform method is employed to parameterize non-Gaussian fracture fields with continuous parameter fields, thus rendering desirable properties required by many inverse modeling methods. In addition, a recently developed forward simulation method, the embedded discrete fracture method (EDFM), is utilized to model the fractures. The EDFM maintains computational efficiency while preserving the ability to capture the geometrical details of fractures because the matrix is discretized as structured grid, while the fractures being handled as planes are inserted into the matrix grids. The combination of Hough representation of fractures with the EDFM makes it possible to tune the fractures (through updating their existence, location, orientation, length, and other properties) without requiring either unstructured grids or regridding during updating. Such a treatment is amenable to numerous inverse modeling approaches, such as the iterative inverse modeling method employed in this study, which is
Modelling Laccoliths: Fluid-Driven Fracturing in the Lab
Ball, T. V.; Neufeld, J. A.
2017-12-01
Current modelling of the formation of laccoliths neglects the necessity to fracture rock layers for propagation to occur [1]. In magmatic intrusions at depth the idea of fracture toughness is used to characterise fracturing, however an analogue for near surface intrusions has yet to be explored [2]. We propose an analytical model for laccolith emplacement that accounts for the energy required to fracture at the tip of an intrusion. For realistic physical parameters we find that a lag region exists between the fluid magma front and the crack tip where large negative pressures in the tip cause volatiles to exsolve from the magma. Crucially, the dynamics of this tip region controls the spreading due to the competition between viscous forces and fracture energy. We conduct a series of complementary experiments to investigate fluid-driven fracturing of adhered layers and confirm the existence of two regimes: viscosity dominant spreading, controlled by the pressure in the lag region, and fracture energy dominant spreading, controlled by the energy required to fracture layers. Our experiments provide the first observations, and evolution, of a vapour tip. These experiments and our simplified model provide insight into the key physical processes in near surface magmatic intrusions with applications to fluid-driven fracturing more generally. Michaut J. Geophys. Res. 116(B5), B05205. Bunger & Cruden J. Geophys. Res. 116(B2), B02203.
Bioremediation in fractured rock: 1. Modeling to inform design, monitoring, and expectations
Tiedeman, Claire; Shapiro, Allen M.; Hsieh, Paul A.; Imbrigiotta, Thomas; Goode, Daniel J.; Lacombe, Pierre; DeFlaun, Mary F.; Drew, Scott R.; Johnson, Carole D.; Williams, John H.; Curtis, Gary P.
2018-01-01
Field characterization of a trichloroethene (TCE) source area in fractured mudstones produced a detailed understanding of the geology, contaminant distribution in fractures and the rock matrix, and hydraulic and transport properties. Groundwater flow and chemical transport modeling that synthesized the field characterization information proved critical for designing bioremediation of the source area. The planned bioremediation involved injecting emulsified vegetable oil and bacteria to enhance the naturally occurring biodegradation of TCE. The flow and transport modeling showed that injection will spread amendments widely over a zone of lower‐permeability fractures, with long residence times expected because of small velocities after injection and sorption of emulsified vegetable oil onto solids. Amendments transported out of this zone will be diluted by groundwater flux from other areas, limiting bioremediation effectiveness downgradient. At nearby pumping wells, further dilution is expected to make bioremediation effects undetectable in the pumped water. The results emphasize that in fracture‐dominated flow regimes, the extent of injected amendments cannot be conceptualized using simple homogeneous models of groundwater flow commonly adopted to design injections in unconsolidated porous media (e.g., radial diverging or dipole flow regimes). Instead, it is important to synthesize site characterization information using a groundwater flow model that includes discrete features representing high‐ and low‐permeability fractures. This type of model accounts for the highly heterogeneous hydraulic conductivity and groundwater fluxes in fractured‐rock aquifers, and facilitates designing injection strategies that target specific volumes of the aquifer and maximize the distribution of amendments over these volumes.
Thermo-hydro-mechanical modelling of fractured rock masses application to radioactive wastes storage
International Nuclear Information System (INIS)
Vuillod, E.
1995-01-01
This work belongs to the Decovalex project (international cooperative project for the development of coupled models and their validation against experiments in nuclear waste isolation) of thermo-hydro-mechanical (THM) modeling of fractured rock massifs inside which high level radioactive waste disposal sites are simulated. The mathematical laws controlling the behaviour of the environment are resolved analytically in the case of a continuous environment (definition of an equivalent environment) and numerically if the environment is discontinuous (modeling of joints behaviour). The coupled THM models strongly influence the behaviour of a model. Modeling performed with the UDEC code shows the importance of HM couplings depending on whether the calculations are made in permanent or transient regime, and the influence of the loading path in the case of TM modeling. The geometry of fractures also influences the behaviour of the model. Studying the connexity of a fractures network allows to determine its degree of homogeneity. The comparison between two methods, continuous environment and discontinuous environment, has been carried out by determining the permeability tensor and the stress-deformation relations on fractured test-samples. It shows the differences in behaviour between an homogenized environment and a discrete environment. Finally two exercises of THM modeling of radioactive waste disposal sites illustrate the researches carried out. A far field model has permitted to compare the results obtained with calculation codes using different logics. The second model, a near field one, focusses more on the importance played by fracturing on the behaviour of the massif. The high density of the reference network has required some mathematical developments, in order to determine the representative equivalent volume (continuous approaches), and some mathematical analyses, to correctly simplify the environment (discontinuous approaches). These methods and analyses are
Modelling of discrete TDS-spectrum of hydrogen desorption
Rodchenkova, Natalia I.; Zaika, Yury V.
2015-12-01
High concentration of hydrogen in metal leads to hydrogen embrittlement. One of the methods to evaluate the hydrogen content is the method of thermal desorption spectroscopy (TDS). As the sample is heated under vacuumization, atomic hydrogen diffuses inside the bulk and is desorbed from the surface in the molecular form. The extraction curve (measured by a mass-spectrometric analyzer) is recorded. In experiments with monotonous external heating it is observed that background hydrogen fluxes from the extractor walls and fluxes from the sample cannot be reliably distinguished. Thus, the extraction curve is doubtful. Therefore, in this case experimenters use discrete TDS-spectrum: the sample is removed from the analytical part of the device for the specified time interval, and external temperature is then increased stepwise. The paper is devoted to the mathematical modelling and simulation of experimental studies. In the corresponding boundary-value problem with nonlinear dynamic boundary conditions physical- chemical processes in the bulk and on the surface are taken into account: heating of the sample, diffusion in the bulk, hydrogen capture by defects, penetration from the bulk to the surface and desorption. The model aimed to analyze the dynamics of hydrogen concentrations without preliminary artificial sample saturation. Numerical modelling allows to choose the point on the extraction curve that corresponds to the initial quantity of the surface hydrogen, to estimate the values of the activation energies of diffusion, desorption, parameters of reversible capture and hydride phase decomposition.
Modelling of discrete TDS-spectrum of hydrogen desorption
International Nuclear Information System (INIS)
Rodchenkova, Natalia I; Zaika, Yury V
2015-01-01
High concentration of hydrogen in metal leads to hydrogen embrittlement. One of the methods to evaluate the hydrogen content is the method of thermal desorption spectroscopy (TDS). As the sample is heated under vacuumization, atomic hydrogen diffuses inside the bulk and is desorbed from the surface in the molecular form. The extraction curve (measured by a mass-spectrometric analyzer) is recorded. In experiments with monotonous external heating it is observed that background hydrogen fluxes from the extractor walls and fluxes from the sample cannot be reliably distinguished. Thus, the extraction curve is doubtful. Therefore, in this case experimenters use discrete TDS-spectrum: the sample is removed from the analytical part of the device for the specified time interval, and external temperature is then increased stepwise. The paper is devoted to the mathematical modelling and simulation of experimental studies. In the corresponding boundary-value problem with nonlinear dynamic boundary conditions physical- chemical processes in the bulk and on the surface are taken into account: heating of the sample, diffusion in the bulk, hydrogen capture by defects, penetration from the bulk to the surface and desorption. The model aimed to analyze the dynamics of hydrogen concentrations without preliminary artificial sample saturation. Numerical modelling allows to choose the point on the extraction curve that corresponds to the initial quantity of the surface hydrogen, to estimate the values of the activation energies of diffusion, desorption, parameters of reversible capture and hydride phase decomposition. (paper)
A modified discrete element model for sea ice dynamics
Institute of Scientific and Technical Information of China (English)
LI Baohui; LI Hai; LIU Yu; WANG Anliang; JI Shunying
2014-01-01
Considering the discontinuous characteristics of sea ice on various scales, a modified discrete element mod-el (DEM) for sea ice dynamics is developed based on the granular material rheology. In this modified DEM, a soft sea ice particle element is introduced as a self-adjustive particle size function. Each ice particle can be treated as an assembly of ice floes, with its concentration and thickness changing to variable sizes un-der the conservation of mass. In this model, the contact forces among ice particles are calculated using a viscous-elastic-plastic model, while the maximum shear forces are described with the Mohr-Coulomb fric-tion law. With this modified DEM, the ice flow dynamics is simulated under the drags of wind and current in a channel of various widths. The thicknesses, concentrations and velocities of ice particles are obtained, and then reasonable dynamic process is analyzed. The sea ice dynamic process is also simulated in a vortex wind field. Taking the influence of thermodynamics into account, this modified DEM will be improved in the future work.
From discrete-time models to continuous-time, asynchronous modeling of financial markets
Boer, Katalin; Kaymak, Uzay; Spiering, Jaap
2007-01-01
Most agent-based simulation models of financial markets are discrete-time in nature. In this paper, we investigate to what degree such models are extensible to continuous-time, asynchronous modeling of financial markets. We study the behavior of a learning market maker in a market with information
From Discrete-Time Models to Continuous-Time, Asynchronous Models of Financial Markets
K. Boer-Sorban (Katalin); U. Kaymak (Uzay); J. Spiering (Jaap)
2006-01-01
textabstractMost agent-based simulation models of financial markets are discrete-time in nature. In this paper, we investigate to what degree such models are extensible to continuous-time, asynchronous modelling of financial markets. We study the behaviour of a learning market maker in a market with
Energy Technology Data Exchange (ETDEWEB)
Follin, Sven (SF GeoLogic AB, Taeby (SE)); Leven, Jakob (Swedish Nuclear Fuel and Waste Management Co., Stockholm (SE)); Hartley, Lee; Jackson, Peter; Joyce, Steve; Roberts, David; Swift, Ben (Serco Assurance, Harwell (GB))
2007-09-15
based on about 120-150 m of borehole data. It is proposed that fracture domains FFM04 and FFM05 are assumed to have the same properties as FFM03. Finally, comments and recommendations are made in the report as a guidance for several aspects in forthcoming hydrogeological discrete fracture network and groundwater flow models. The comments and recommendations address the following matters: fracture set definitions reflecting observations made for all boreholes in modelling stage 2.2, i.e. the geological DFN results reported for modelling stage 2.2, semi-deterministic DFN modelling of so called possible deformation zones below the elevation -400 m RHB 70 in the potential target volume, and fracture domains outside the candidate area where there are no cored boreholes. For the conclusions drawn in the work reported here these three matters are of minor importance
Modelling of ductile and cleavage fracture by local approach
International Nuclear Information System (INIS)
Samal, M.K.; Dutta, B.K.; Kushwaha, H.S.
2000-08-01
This report describes the modelling of ductile and cleavage fracture processes by local approach. It is now well known that the conventional fracture mechanics method based on single parameter criteria is not adequate to model the fracture processes. It is because of the existence of effect of size and geometry of flaw, loading type and rate on the fracture resistance behaviour of any structure. Hence, it is questionable to use same fracture resistance curves as determined from standard tests in the analysis of real life components because of existence of all the above effects. So, there is need to have a method in which the parameters used for the analysis will be true material properties, i.e. independent of geometry and size. One of the solutions to the above problem is the use of local approaches. These approaches have been extensively studied and applied to different materials (including SA33 Gr.6) in this report. Each method has been studied and reported in a separate section. This report has been divided into five sections. Section-I gives a brief review of the fundamentals of fracture process. Section-II deals with modelling of ductile fracture by locally uncoupled type of models. In this section, the critical cavity growth parameters of the different models have been determined for the primary heat transport (PHT) piping material of Indian pressurised heavy water reactor (PHWR). A comparative study has been done among different models. The dependency of the critical parameters on stress triaxiality factor has also been studied. It is observed that Rice and Tracey's model is the most suitable one. But, its parameters are not fully independent of triaxiality factor. For this purpose, a modification to Rice and Tracery's model is suggested in Section-III. Section-IV deals with modelling of ductile fracture process by locally coupled type of models. Section-V deals with the modelling of cleavage fracture process by Beremins model, which is based on Weibulls
Analysis of stochastic effects in Kaldor-type business cycle discrete model
Bashkirtseva, Irina; Ryashko, Lev; Sysolyatina, Anna
2016-07-01
We study nonlinear stochastic phenomena in the discrete Kaldor model of business cycles. A numerical parametric analysis of stochastically forced attractors (equilibria, closed invariant curves, discrete cycles) of this model is performed using the stochastic sensitivity functions technique. A spatial arrangement of random states in stochastic attractors is modeled by confidence domains. The phenomenon of noise-induced transitions ;chaos-order; is discussed.
Directory of Open Access Journals (Sweden)
S. Psakhie
2013-04-01
Full Text Available A general approach to realization of models of elasticity, plasticity and fracture of heterogeneous materials within the framework of particle-based numerical methods is proposed in the paper. It is based on building many-body forces of particle interaction, which provide response of particle ensemble correctly conforming to the response (including elastic-plastic behavior and fracture of simulated solids. Implementation of proposed approach within particle-based methods is demonstrated by the example of the movable cellular automaton (MCA method, which integrates the possibilities of particle-based discrete element method (DEM and cellular automaton methods. Emergent advantages of the developed approach to formulation of many-body interaction are discussed. Main of them are its applicability to various realizations of the concept of discrete elements and a possibility to realize various rheological models (including elastic-plastic or visco-elastic-plastic and models of fracture to study deformation and fracture of solid-phase materials and media. Capabilities of particle-based modeling of heterogeneous solids are demonstrated by the problem of simulation of deformation and fracture of particle-reinforced metal-ceramic composites.
Energy Technology Data Exchange (ETDEWEB)
Wiggins, Michael L.; Brown, Raymon L.; Civan, Frauk; Hughes, Richard G.
2001-08-15
Research continues on characterizing and modeling the behavior of naturally fractured reservoir systems. Work has progressed on developing techniques for estimating fracture properties from seismic and well log data, developing naturally fractured wellbore models, and developing a model to characterize the transfer of fluid from the matrix to the fracture system for use in the naturally fractured reservoir simulator.
A discrete stress-strength interference model based on universal generating function
International Nuclear Information System (INIS)
An Zongwen; Huang Hongzhong; Liu Yu
2008-01-01
Continuous stress-strength interference (SSI) model regards stress and strength as continuous random variables with known probability density function. This, to some extent, results in a limitation of its application. In this paper, stress and strength are treated as discrete random variables, and a discrete SSI model is presented by using the universal generating function (UGF) method. Finally, case studies demonstrate the validity of the discrete model in a variety of circumstances, in which stress and strength can be represented by continuous random variables, discrete random variables, or two groups of experimental data
Three-Dimensional Modeling of Fracture Clusters in Geothermal Reservoirs
Energy Technology Data Exchange (ETDEWEB)
Ghassemi, Ahmad [Univ. of Oklahoma, Norman, OK (United States)
2017-08-11
The objective of this is to develop a 3-D numerical model for simulating mode I, II, and III (tensile, shear, and out-of-plane) propagation of multiple fractures and fracture clusters to accurately predict geothermal reservoir stimulation using the virtual multi-dimensional internal bond (VMIB). Effective development of enhanced geothermal systems can significantly benefit from improved modeling of hydraulic fracturing. In geothermal reservoirs, where the temperature can reach or exceed 350oC, thermal and poro-mechanical processes play an important role in fracture initiation and propagation. In this project hydraulic fracturing of hot subsurface rock mass will be numerically modeled by extending the virtual multiple internal bond theory and implementing it in a finite element code, WARP3D, a three-dimensional finite element code for solid mechanics. The new constitutive model along with the poro-thermoelastic computational algorithms will allow modeling the initiation and propagation of clusters of fractures, and extension of pre-existing fractures. The work will enable the industry to realistically model stimulation of geothermal reservoirs. The project addresses the Geothermal Technologies Office objective of accurately predicting geothermal reservoir stimulation (GTO technology priority item). The project goal will be attained by: (i) development of the VMIB method for application to 3D analysis of fracture clusters; (ii) development of poro- and thermoelastic material sub-routines for use in 3D finite element code WARP3D; (iii) implementation of VMIB and the new material routines in WARP3D to enable simulation of clusters of fractures while accounting for the effects of the pore pressure, thermal stress and inelastic deformation; (iv) simulation of 3D fracture propagation and coalescence and formation of clusters, and comparison with laboratory compression tests; and (v) application of the model to interpretation of injection experiments (planned by our
Discrete random walk models for space-time fractional diffusion
International Nuclear Information System (INIS)
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo
2002-01-01
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order α is part of (0,2] and skewness θ (moduleθ≤{α,2-α}), and the first-order time derivative with a Caputo derivative of order β is part of (0,1]. Such evolution equation implies for the flux a fractional Fick's law which accounts for spatial and temporal non-locality. The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process that we view as a generalized diffusion process. By adopting appropriate finite-difference schemes of solution, we generate models of random walk discrete in space and time suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation
Discrete Velocity Models for Polyatomic Molecules Without Nonphysical Collision Invariants
Bernhoff, Niclas
2018-05-01
An important aspect of constructing discrete velocity models (DVMs) for the Boltzmann equation is to obtain the right number of collision invariants. Unlike for the Boltzmann equation, for DVMs there can appear extra collision invariants, so called spurious collision invariants, in plus to the physical ones. A DVM with only physical collision invariants, and hence, without spurious ones, is called normal. The construction of such normal DVMs has been studied a lot in the literature for single species, but also for binary mixtures and recently extensively for multicomponent mixtures. In this paper, we address ways of constructing normal DVMs for polyatomic molecules (here represented by that each molecule has an internal energy, to account for non-translational energies, which can change during collisions), under the assumption that the set of allowed internal energies are finite. We present general algorithms for constructing such models, but we also give concrete examples of such constructions. This approach can also be combined with similar constructions of multicomponent mixtures to obtain multicomponent mixtures with polyatomic molecules, which is also briefly outlined. Then also, chemical reactions can be added.
Discrete bivariate population balance modelling of heteroaggregation processes.
Rollié, Sascha; Briesen, Heiko; Sundmacher, Kai
2009-08-15
Heteroaggregation in binary particle mixtures was simulated with a discrete population balance model in terms of two internal coordinates describing the particle properties. The considered particle species are of different size and zeta-potential. Property space is reduced with a semi-heuristic approach to enable an efficient solution. Aggregation rates are based on deterministic models for Brownian motion and stability, under consideration of DLVO interaction potentials. A charge-balance kernel is presented, relating the electrostatic surface potential to the property space by a simple charge balance. Parameter sensitivity with respect to the fractal dimension, aggregate size, hydrodynamic correction, ionic strength and absolute particle concentration was assessed. Results were compared to simulations with the literature kernel based on geometric coverage effects for clusters with heterogeneous surface properties. In both cases electrostatic phenomena, which dominate the aggregation process, show identical trends: impeded cluster-cluster aggregation at low particle mixing ratio (1:1), restabilisation at high mixing ratios (100:1) and formation of complex clusters for intermediate ratios (10:1). The particle mixing ratio controls the surface coverage extent of the larger particle species. Simulation results are compared to experimental flow cytometric data and show very satisfactory agreement.
Simulating discrete models of pattern formation by ion beam sputtering
International Nuclear Information System (INIS)
Hartmann, Alexander K; Kree, Reiner; Yasseri, Taha
2009-01-01
A class of simple, (2+1)-dimensional, discrete models is reviewed, which allow us to study the evolution of surface patterns on solid substrates during ion beam sputtering (IBS). The models are based on the same assumptions about the erosion process as the existing continuum theories. Several distinct physical mechanisms of surface diffusion are added, which allow us to study the interplay of erosion-driven and diffusion-driven pattern formation. We present results from our own work on evolution scenarios of ripple patterns, especially for longer timescales, where nonlinear effects become important. Furthermore we review kinetic phase diagrams, both with and without sample rotation, which depict the systematic dependence of surface patterns on the shape of energy depositing collision cascades after ion impact. Finally, we discuss some results from more recent work on surface diffusion with Ehrlich-Schwoebel barriers as the driving force for pattern formation during IBS and on Monte Carlo simulations of IBS with codeposition of surfactant atoms.
Discrete Element Modeling Results of Proppant Rearrangement in the Cooke Conductivity Cell
Energy Technology Data Exchange (ETDEWEB)
Earl Mattson; Hai Huang; Michael Conway; Lisa O' Connell
2014-02-01
The study of propped fracture conductivity began in earnest with the development of the Cooke cell which later became part of the initial API standard. Subsequent developments included a patented multicell design to conduct 4 tests in a press at the same time. Other modifications have been used by various investigators. Recent studies by the Stim-Lab proppant consortium have indicated that the flow field across a Cooke proppant conductivity testing cell may not be uniform as initially believed which resulted is significantly different conductivity results. Post test analysis of low temperature metal alloy injections at the termination of proppant testing prior to the release of the applied stress suggest that higher flow is to be expected along the sides and top of the proppant pack than compared to the middle of the pack. To evaluate these experimental findings, a physics-based two-dimensional (2-D) discrete element model (DEM) was developed and applied to simulate proppant rearrangement during stress loading in the Cooke conductivity cell and the resulting porosity field. Analysis of these simulations are critical to understanding the impact of modification to the testing cell as well as understanding key proppant conductivity issues such as how these effects are manifested in proppant concentration testing results. The 2-D DEM model was constructed to represent a realistic cross section of the Cooke cell with a distribution of four material properties, three that represented the Cooke cell (steel, sandstone,square rings), and one representing the proppant. In principle, Cooke cell materials can be approximated as assemblies of independent discrete elements (particles) of various sizes and material properties that interact via cohesive interactions, repulsive forces, and frictional forces. The macroscopic behavior can then be modeled as the collective behavior of many interacting discrete elements. This DEM model is particularly suitable for modeling proppant
Directory of Open Access Journals (Sweden)
Jian Zhou
2016-09-01
Full Text Available Hydraulic fracturing is a useful tool for enhancing rock mass permeability for shale gas development, enhanced geothermal systems, and geological carbon sequestration by the high-pressure injection of a fracturing fluid into tight reservoir rocks. Although significant advances have been made in hydraulic fracturing theory, experiments, and numerical modeling, when it comes to the complexity of geological conditions knowledge is still limited. Mechanisms of fluid injection-induced fracture initiation and propagation should be better understood to take full advantage of hydraulic fracturing. This paper presents the development and application of discrete particle modeling based on two-dimensional particle flow code (PFC2D. Firstly, it is shown that the modeled value of the breakdown pressure for the hydraulic fracturing process is approximately equal to analytically calculated values under varied in situ stress conditions. Furthermore, a series of simulations for hydraulic fracturing in competent rock was performed to examine the influence of the in situ stress ratio, fluid injection rate, and fluid viscosity on the borehole pressure history, the geometry of hydraulic fractures, and the pore-pressure field, respectively. It was found that the hydraulic fractures in an isotropic medium always propagate parallel to the orientation of the maximum principal stress. When a high fluid injection rate is used, higher breakdown pressure is needed for fracture propagation and complex geometries of fractures can develop. When a low viscosity fluid is used, fluid can more easily penetrate from the borehole into the surrounding rock, which causes a reduction of the effective stress and leads to a lower breakdown pressure. Moreover, the geometry of the fractures is not particularly sensitive to the fluid viscosity in the approximate isotropic model.
Connectivity, flow and transport in network models of fractured media
International Nuclear Information System (INIS)
Robinson, P.C.
1984-10-01
In order to evaluate the safety of radioactive waste disposal underground it is important to understand the way in which radioactive material is transported through the rock to the surface. If the rock is fractured the usual models may not be applicable. In this work we look at three aspects of fracture networks: connectivity, flow and transport. These are studied numerically by generating fracture networks in a computer and modelling the processes which occur. Connectivity relates to percolation theory, and critical densities for fracture systems are found in two and three dimensions. The permeability of two-dimensional networks is studied. The way that permeability depends on fracture density, network size and spread of fracture length can be predicted using a cut lattice model. Transport through the fracture network by convection through the fractures and mixing at the intersections is studied. The Fickian dispersion equation does not describe the resulting hydrodynamic dispersion. Extensions to the techniques to three dimensions and to include other processes are discussed. (author)
Aggregation patterns from nonlocal interactions: Discrete stochastic and continuum modeling
Hackett-Jones, Emily J.; Landman, Kerry A.; Fellner, Klemens
2012-01-01
both attractive and repulsive singularities. Currently, no existence theory for such potentials is available. We develop and compare two complementary solution methods, a continuous pseudoinverse method and a discrete stochastic lattice approach
Fluid coupling in a discrete model of cochlear mechanics.
Elliott, Stephen J; Lineton, Ben; Ni, Guangjian
2011-09-01
A discrete model of cochlear mechanics is introduced that includes a full, three-dimensional, description of fluid coupling. This formulation allows the fluid coupling and basilar membrane dynamics to be analyzed separately and then coupled together with a simple piece of linear algebra. The fluid coupling is initially analyzed using a wavenumber formulation and is separated into one component due to one-dimensional fluid coupling and one comprising all the other contributions. Using the theory of acoustic waves in a duct, however, these two components of the pressure can also be associated with a far field, due to the plane wave, and a near field, due to the evanescent, higher order, modes. The near field components are then seen as one of a number of sources of additional longitudinal coupling in the cochlea. The effects of non-uniformity and asymmetry in the fluid chamber areas can also be taken into account, to predict both the pressure difference between the chambers and the mean pressure. This allows the calculation, for example, of the effect of a short cochlear implant on the coupled response of the cochlea. © 2011 Acoustical Society of America
Model of the discrete destruction process of a solid body
Glagolev, V. V.; Markin, A. A.
2018-03-01
Destruction is considered as a discrete thermomechanical process, in which the deformation of a solid body is achieved by changing the boundary stresses acting on the part of the volume being destroyed with the external load unchanged. On the basis of the proposed concept, a model for adhesive stratification of a composite material is constructed. When adhesive stratification is used, the stress state of one or two boundaries of the adhesive layer changes to zero if the bonds with the joined body are broken. As a result of the stratification, the interaction between the part of the composite, which may include an adhesive layer and the rest of the body stops. When solving the elastoplastic problem of cohesive stratification, the region in which the destruction criterion is achieved is identified. With the help of a repeated solution of the problem of subcritical deformation with the known law of motion of the boundary of the region, the distribution of the load (nodal forces) acting from the region to the body is located. The next step considers the change in the stress–strain state of the body in the process of destruction of the selected area. The elastoplastic problem is solved with a simple unloading of the formed surface of the body and preservation of the external load corresponding to the beginning of the process of destruction.
Company Value with Ruin Constraint in a Discrete Model
Directory of Open Access Journals (Sweden)
Christian Hipp
2018-01-01
Full Text Available Optimal dividend payment under a ruin constraint is a two objective control problem which—in simple models—can be solved numerically by three essentially different methods. One is based on a modified Bellman equation and the policy improvement method (see Hipp (2003. In this paper we use explicit formulas for running allowed ruin probabilities which avoid a complete search and speed up and simplify the computation. The second is also a policy improvement method, but without the use of a dynamic equation (see Hipp (2016. It is based on closed formulas for first entry probabilities and discount factors for the time until first entry. Third a new, faster and more intuitive method which uses appropriately chosen barrier levels and a closed formula for the corresponding dividend value. Using the running allowed ruin probabilities, a simple test for admissibility—concerning the ruin constraint—is given. All these methods work for the discrete De Finetti model and are applied in a numerical example. The non stationary Lagrange multiplier method suggested in Hipp (2016, Section 2.2.2, also yields optimal dividend strategies which differ from those in all other methods, and Lagrange gaps are present here.
Discrete kinetic models from funneled energy landscape simulations.
Directory of Open Access Journals (Sweden)
Nicholas P Schafer
Full Text Available A general method for facilitating the interpretation of computer simulations of protein folding with minimally frustrated energy landscapes is detailed and applied to a designed ankyrin repeat protein (4ANK. In the method, groups of residues are assigned to foldons and these foldons are used to map the conformational space of the protein onto a set of discrete macrobasins. The free energies of the individual macrobasins are then calculated, informing practical kinetic analysis. Two simple assumptions about the universality of the rate for downhill transitions between macrobasins and the natural local connectivity between macrobasins lead to a scheme for predicting overall folding and unfolding rates, generating chevron plots under varying thermodynamic conditions, and inferring dominant kinetic folding pathways. To illustrate the approach, free energies of macrobasins were calculated from biased simulations of a non-additive structure-based model using two structurally motivated foldon definitions at the full and half ankyrin repeat resolutions. The calculated chevrons have features consistent with those measured in stopped flow chemical denaturation experiments. The dominant inferred folding pathway has an "inside-out", nucleation-propagation like character.
Boundary Layer Effect on Behavior of Discrete Models.
Eliáš, Jan
2017-02-10
The paper studies systems of rigid bodies with randomly generated geometry interconnected by normal and tangential bonds. The stiffness of these bonds determines the macroscopic elastic modulus while the macroscopic Poisson's ratio of the system is determined solely by the normal/tangential stiffness ratio. Discrete models with no directional bias have the same probability of element orientation for any direction and therefore the same mechanical properties in a statistical sense at any point and direction. However, the layers of elements in the vicinity of the boundary exhibit biased orientation, preferring elements parallel with the boundary. As a consequence, when strain occurs in this direction, the boundary layer becomes stiffer than the interior for the normal/tangential stiffness ratio larger than one, and vice versa. Nonlinear constitutive laws are typically such that the straining of an element in shear results in higher strength and ductility than straining in tension. Since the boundary layer tends, due to the bias in the elemental orientation, to involve more tension than shear at the contacts, it also becomes weaker and less ductile. The paper documents these observations and compares them to the results of theoretical analysis.
A discrete dislocation dynamics model of creeping single crystals
Rajaguru, M.; Keralavarma, S. M.
2018-04-01
Failure by creep is a design limiting issue for metallic materials used in several high temperature applications. Current theoretical models of creep are phenomenological with little connection to the underlying microscopic mechanisms. In this paper, a bottom-up simulation framework based on the discrete dislocation dynamics method is presented for dislocation creep aided by the diffusion of vacancies, known to be the rate controlling mechanism at high temperature and stress levels. The time evolution of the creep strain and the dislocation microstructure in a periodic unit cell of a nominally infinite single crystal is simulated using the kinetic Monte Carlo method, together with approximate constitutive laws formulated for the rates of thermal activation of dislocations over local pinning obstacles. The deformation of the crystal due to dislocation glide between individual thermal activation events is simulated using a standard dislocation dynamics algorithm, extended to account for constant stress periodic boundary conditions. Steady state creep conditions are obtained in the simulations with the predicted creep rates as a function of stress and temperature in good agreement with experimentally reported values. Arrhenius scaling of the creep rates as a function of temperature and power-law scaling with the applied stress are also reproduced, with the values of the power-law exponents in the high stress regime in good agreement with experiments.
Integrating Continuous-Time and Discrete-Event Concepts in Process Modelling, Simulation and Control
Beek, van D.A.; Gordijn, S.H.F.; Rooda, J.E.; Ertas, A.
1995-01-01
Currently, modelling of systems in the process industry requires the use of different specification languages for the specification of the discrete-event and continuous-time subsystems. In this way, models are restricted to individual subsystems of either a continuous-time or discrete-event nature.
Energy Technology Data Exchange (ETDEWEB)
Kadiri, I
2002-10-15
The hydro-mechanical modeling of the fractured media is quite complex. Simplifications are necessary for the modeling of such media, but, not always justified, Only permeable fractures are often considered. The rest of the network is approximated by an equivalent continuous medium. Even if we suppose that this approach is validated, the hydraulic and mechanical properties of the fractures and of the continuous medium are seldom known. Calibrations are necessary for the determination of these properties. Until now, one does not know very well the nature of measurements which must be carried out in order to carry on a modeling in discontinuous medium, nor elements of enough robust validation for this kind of modeling. For a better understanding of the hydro-mechanical phenomena in fractured media, two different sites have been selected for the work. The first is the site of Grimsel in Switzerland in which an underground laboratory is located at approximately 400 m of depth. The FEBEX experiment aims at the in-situ study of the consecutive phenomena due to the installation of a heat source representative of radioactive waste in the last 17 meters of the FEBEX tunnel in the laboratory of Grimsel. Only, the modeling of the hydro-mechanical of the excavation was model. The modeling of the Febex enabled us to establish a methodology of calibration of the hydraulic properties in the discontinuous media. However, this kind of study on such complex sites does not make possible to answer all the questions which arise on the hydro-mechanical behavior of the fractured media. We thus carried out modeling on an other site, smaller than the fist one and more accessible. The experimental site of Coaraze, in the Maritime Alps, is mainly constituted of limestone and fractures. Then the variation of water pressure along fractures is governed by the opening/closure sequence of a water gate. Normal displacement as well as the pore pressure along these fractures are recorded, and then
Dynamic modeling method for infrared smoke based on enhanced discrete phase model
Zhang, Zhendong; Yang, Chunling; Zhang, Yan; Zhu, Hongbo
2018-03-01
The dynamic modeling of infrared (IR) smoke plays an important role in IR scene simulation systems and its accuracy directly influences the system veracity. However, current IR smoke models cannot provide high veracity, because certain physical characteristics are frequently ignored in fluid simulation; simplifying the discrete phase as a continuous phase and ignoring the IR decoy missile-body spinning. To address this defect, this paper proposes a dynamic modeling method for IR smoke, based on an enhanced discrete phase model (DPM). A mathematical simulation model based on an enhanced DPM is built and a dynamic computing fluid mesh is generated. The dynamic model of IR smoke is then established using an extended equivalent-blackbody-molecule model. Experiments demonstrate that this model realizes a dynamic method for modeling IR smoke with higher veracity.
Finite-difference modelling of anisotropic wave scattering in discrete ...
Indian Academy of Sciences (India)
A M Ekanem
2018-04-05
Apr 5, 2018 ... scattering characteristics in fractured media and thus, validate the practical utility of using anisotropic .... to fluid flow. ... account the porosity of the host rock and assumes .... The free surface boundary conditions generally.
International Nuclear Information System (INIS)
Morice, Erwan
2014-01-01
Fracture in quasi-brittle materials, such as ceramics or concrete, can be represented schematically by series of events of nucleation and coalescence of micro-cracks. Modeling this process is an important challenge for the reliability and life prediction of concrete structures, in particular the prediction of the permeability of damaged structures. A multi-scale approach is proposed. The global behavior is modeled within the fracture mechanics framework and the local behavior is modeled by the discrete element method. An approach was developed to condense the non linear behavior of the mortar. A model reduction technic is used to extract the relevant information from the discrete elements method. To do so, the velocity field is partitioned into mode I, II, linear and non-linear components, each component being characterized by an intensity factor and a fixed spatial distribution. The response of the material is hence condensed in the evolution of the intensity factors, used as non-local variables. A model was also proposed to predict the behavior of the crack for proportional and non-proportional mixed mode I+II loadings. An experimental campaign was finally conducted to characterize the fatigue and fracture behavior of mortar. The results show that fatigue crack growth can be of significant importance. The experimental velocity field determined, in the crack tip region, by DIC, were analyzed using the same technic as that used for analyzing the fields obtained by the discrete element method showing consistent results. (author)
Discrete Bogomolny equations for the nonlinear O(3) σ model in 2+1 dimensions
International Nuclear Information System (INIS)
Leese, R.
1989-01-01
Discrete analogues of the topological charge and of the Bogomolny equations are constructed for the nonlinear O(3) σ model in 2+1 dimensions, subject to the restriction that the energy density be radially symmetric. These are then incorporated into a discretized version of the evolution equations. Using the discrete Bogomolny relations to construct the initial data for numerical simulations removes the ''lattice wobble'' sometimes observed at low kinetic energies. This feature is very important for the delicate question of instanton stability
Energy Technology Data Exchange (ETDEWEB)
Hermanson, Jan; Forssberg, Ola [Golder Associates AB, Stockholm (Sweden); Fox, Aaron; La Pointe, Paul [Golder Associates Inc., Redmond, WA (United States)
2005-10-15
The goal of this summary report is to document the data sources, software tools, experimental methods, assumptions, and model parameters in the discrete-fracture network (DFN) model for the local model volume in Laxemar, version 1.2. The model parameters presented herein are intended for use by other project modeling teams. Individual modeling teams may elect to simplify or use only a portion of the DFN model, depending on their needs. This model is not intended to be a flow model or a mechanical model; as such, only the geometrical characterization is presented. The derivations of the hydraulic or mechanical properties of the fractures or their subsurface connectivities are not within the scope of this report. This model represents analyses carried out on particular data sets. If additional data are obtained, or values for existing data are changed or excluded, the conclusions reached in this report, and the parameter values calculated, may change as well. The model volume is divided into two subareas; one located on the Simpevarp peninsula adjacent to the power plant (Simpevarp), and one further to the west (Laxemar). The DFN parameters described in this report were determined by analysis of data collected within the local model volume. As such, the final DFN model is only valid within this local model volume and the modeling subareas (Laxemar and Simpevarp) within.
Ni, W; Jiang, Y
2017-02-01
This study used a simulation model to determine the cost-effective threshold of fracture risk to treat osteoporosis among elderly Chinese women. Osteoporosis treatment is cost-effective among average-risk women who are at least 75 years old and above-average-risk women who are younger than 75 years old. Aging of the Chinese population is imposing increasing economic burden of osteoporosis. This study evaluated the cost-effectiveness of osteoporosis treatment among the senior Chinese women population. A discrete event simulation model using age-specific probabilities of hip fracture, clinical vertebral fracture, wrist fracture, humerus fracture, and other fracture; costs (2015 US dollars); and quality-adjusted life years (QALYs) was used to assess the cost-effectiveness of osteoporosis treatment. Incremental cost-effectiveness ratio (ICER) was calculated. The willingness to pay (WTP) for a QALY in China was compared with the calculated ICER to decide the cost-effectiveness. To determine the absolute 10-year hip fracture probability at which the osteoporosis treatment became cost-effective, average age-specific probabilities for all fractures were multiplied by a relative risk (RR) that was systematically varied from 0 to 10 until the WTP threshold was observed for treatment relative to no intervention. Sensitivity analyses were also performed to evaluate the impacts from WTP and annual treatment costs. In baseline analysis, simulated ICERs were higher than the WTP threshold among Chinese women younger than 75, but much lower than the WTP among the older population. Sensitivity analyses indicated that cost-effectiveness could vary due to a higher WTP threshold or a lower annual treatment cost. A 30 % increase in WTP or a 30 % reduction in annual treatment costs will make osteoporosis treatment cost-effective for Chinese women population from 55 to 85. The current study provides evidence that osteoporosis treatment is cost-effective among a subpopulation of
The discretized Schroedinger equation and simple models for semiconductor quantum wells
International Nuclear Information System (INIS)
Boykin, Timothy B; Klimeck, Gerhard
2004-01-01
The discretized Schroedinger equation is one of the most commonly employed methods for solving one-dimensional quantum mechanics problems on the computer, yet many of its characteristics remain poorly understood. The differences with the continuous Schroedinger equation are generally viewed as shortcomings of the discrete model and are typically described in purely mathematical terms. This is unfortunate since the discretized equation is more productively viewed from the perspective of solid-state physics, which naturally links the discrete model to realistic semiconductor quantum wells and nanoelectronic devices. While the relationship between the discrete model and a one-dimensional tight-binding model has been known for some time, the fact that the discrete Schroedinger equation admits analytic solutions for quantum wells has gone unnoted. Here we present a solution to this new analytically solvable problem. We show that the differences between the discrete and continuous models are due to their fundamentally different bandstructures, and present evidence for our belief that the discrete model is the more physically reasonable one
International Nuclear Information System (INIS)
Woerman, Anders; Shulan Xu
2003-10-01
Field data of physical properties in heterogeneous crystalline bedrock, like fracture zones, fracture connectivity, matrix porosity and fracture aperture, is associated with uncertainty that can have a significant impact on the analysis of solute transport in fractured rock. The purpose of this study is to develop a performance assessment (PA) model for analyses of radionuclide transport in the geosphere, in which the model takes into account both the effect of heterogeneities of hydrological and geochemical rock properties. By using a travel time description of radionuclide transport in rock fractures, we decompose the transport problem into a one-dimensional mass transfer problem along a distribution of transport pathways and a multi-dimensional flow problem in the fractured bedrock. The hydraulic/flow problem is solved based on a statistical discrete-fracture model (DFM) that represents the network of fractures around the repository and in the surrounding geosphere. A Monte Carlo technique reflects the fact that the representation of the fracture network is uncertain. If the flow residence time PDF exhibits multiple peaks or in another way shows a more erratic hydraulic response on the network scale, the three-dimensional travel time approach is superior to a one-dimensional transport modeling. Examples taken from SITE 94, a study performed by the Swedish Nuclear Power Inspectorate, showed that such cases can be found in safety assessments based on site data. The solute transport is formulated based on partial, differential equations and perturbations (random spatial variability in bedrock properties) are introduced in the coefficients to reflect an uncertainty of the exact appearance of the bedrock associated with the discrete data collection. The combined approach for water flow and solute transport, thereby, recognises an uncertainty in our knowledge in both 1) bedrock properties along individual pathways and 2) the distribution of pathways. Solutions to the
Investigation on the Productivity Behaviour in Deformable Heterogeneous Fractured Reservoirs
DEFF Research Database (Denmark)
Kadeethum, Teeratorn; Salimzadeh, Saeed; Nick, Hamid
reasons for this reduction. Discrete fracture and matrix (DFM) modelling is selected in this investigation because of its ability to represent fracture behaviours more realistically. Moreover, it has become a preferential method for modelling flow in fractured formations for the past decade (Bisdom et al...
Jones, Brendon R; Brouwers, Luke B; Van Tonder, Warren D; Dippenaar, Matthys A
2017-05-01
The vadose zone typically comprises soil underlain by fractured rock. Often, surface water and groundwater parameters are readily available, but variably saturated flow through soil and rock are oversimplified or estimated as input for hydrological models. In this paper, a series of geotechnical centrifuge experiments are conducted to contribute to the knowledge gaps in: (i) variably saturated flow and dispersion in soil and (ii) variably saturated flow in discrete vertical and horizontal fractures. Findings from the research show that the hydraulic gradient, and not the hydraulic conductivity, is scaled for seepage flow in the geotechnical centrifuge. Furthermore, geotechnical centrifuge modelling has been proven as a viable experimental tool for the modelling of hydrodynamic dispersion as well as the replication of similar flow mechanisms for unsaturated fracture flow, as previously observed in literature. Despite the imminent challenges of modelling variable saturation in the vadose zone, the geotechnical centrifuge offers a powerful experimental tool to physically model and observe variably saturated flow. This can be used to give valuable insight into mechanisms associated with solid-fluid interaction problems under these conditions. Findings from future research can be used to validate current numerical modelling techniques and address the subsequent influence on aquifer recharge and vulnerability, contaminant transport, waste disposal, dam construction, slope stability and seepage into subsurface excavations.
Gong, J.; Rossen, W.R.
2014-01-01
Fracture network connectivity and aperture (or conductivity) distribution are two crucial features controlling the flow behavior of fractured formations. The effect of connectivity on flow properties is well documented. We focus here on the influence of fracture aperture distribution. We model a
Measuring and Modeling Flow in Welded Fractured Tuffs
International Nuclear Information System (INIS)
R. Salve; C. Doughty; J.S. Wang
2001-01-01
We have carried out a series of in situ liquid-release experiments in conjunction with a numerical modeling study to examine the effect of the rock matrix on liquid flow and transport occurring primarily through the fracture network. Field experiments were conducted in the highly fractured Topopah Spring welded tuff at a site accessed from the Exploratory Studies Facility (ESFS), an underground laboratory in the unsaturated zone at Yucca Mountain, Nevada. During the experiment, wetting-front movement, flow-field evolution, and drainage of fracture flow paths were evaluated. Modeling was used to aid in experimental design, predict experimental results, and study the physical processes accompanying liquid flow through unsaturated fractured welded tuff. Field experiments and modeling suggest that it may not be sufficient to conceptualize the fractured tuff as consisting of a single network of high-permeability fractures embedded in a low-permeability matrix. The need to include a secondary fracture network is demonstrated by comparison to the liquid flow observed in the field
Modelling microwave heating of discrete samples of oil palm kernels
International Nuclear Information System (INIS)
Law, M.C.; Liew, E.L.; Chang, S.L.; Chan, Y.S.; Leo, C.P.
2016-01-01
Highlights: • Microwave (MW) drying of oil palm kernels is experimentally determined and modelled. • MW heating of discrete samples of oil palm kernels (OPKs) is simulated. • OPK heating is due to contact effect, MW interference and heat transfer mechanisms. • Electric field vectors circulate within OPKs sample. • Loosely-packed arrangement improves temperature uniformity of OPKs. - Abstract: Recently, microwave (MW) pre-treatment of fresh palm fruits has showed to be environmentally friendly compared to the existing oil palm milling process as it eliminates the condensate production of palm oil mill effluent (POME) in the sterilization process. Moreover, MW-treated oil palm fruits (OPF) also possess better oil quality. In this work, the MW drying kinetic of the oil palm kernels (OPK) was determined experimentally. Microwave heating/drying of oil palm kernels was modelled and validated. The simulation results show that temperature of an OPK is not the same over the entire surface due to constructive and destructive interferences of MW irradiance. The volume-averaged temperature of an OPK is higher than its surface temperature by 3–7 °C, depending on the MW input power. This implies that point measurement of temperature reading is inadequate to determine the temperature history of the OPK during the microwave heating process. The simulation results also show that arrangement of OPKs in a MW cavity affects the kernel temperature profile. The heating of OPKs were identified to be affected by factors such as local electric field intensity due to MW absorption, refraction, interference, the contact effect between kernels and also heat transfer mechanisms. The thermal gradient patterns of OPKs change as the heating continues. The cracking of OPKs is expected to occur first in the core of the kernel and then it propagates to the kernel surface. The model indicates that drying of OPKs is a much slower process compared to its MW heating. The model is useful
Adaptive Multiscale Modeling of Geochemical Impacts on Fracture Evolution
Molins, S.; Trebotich, D.; Steefel, C. I.; Deng, H.
2016-12-01
Understanding fracture evolution is essential for many subsurface energy applications, including subsurface storage, shale gas production, fracking, CO2 sequestration, and geothermal energy extraction. Geochemical processes in particular play a significant role in the evolution of fractures through dissolution-driven widening, fines migration, and/or fracture sealing due to precipitation. One obstacle to understanding and exploiting geochemical fracture evolution is that it is a multiscale process. However, current geochemical modeling of fractures cannot capture this multi-scale nature of geochemical and mechanical impacts on fracture evolution, and is limited to either a continuum or pore-scale representation. Conventional continuum-scale models treat fractures as preferential flow paths, with their permeability evolving as a function (often, a cubic law) of the fracture aperture. This approach has the limitation that it oversimplifies flow within the fracture in its omission of pore scale effects while also assuming well-mixed conditions. More recently, pore-scale models along with advanced characterization techniques have allowed for accurate simulations of flow and reactive transport within the pore space (Molins et al., 2014, 2015). However, these models, even with high performance computing, are currently limited in their ability to treat tractable domain sizes (Steefel et al., 2013). Thus, there is a critical need to develop an adaptive modeling capability that can account for separate properties and processes, emergent and otherwise, in the fracture and the rock matrix at different spatial scales. Here we present an adaptive modeling capability that treats geochemical impacts on fracture evolution within a single multiscale framework. Model development makes use of the high performance simulation capability, Chombo-Crunch, leveraged by high resolution characterization and experiments. The modeling framework is based on the adaptive capability in Chombo
Makedonska, N.; Sparks, D. W.; Aharonov, E.
2012-12-01
Pressure solution (also termed chemical compaction) is considered the most important ductile deformation mechanism operating in the Earth's upper crust. This mechanism is a major player in a variety of geological processes, including evolution of sedimentary basins, hydrocarbon reservoirs, aquifers, earthquake recurrence cycles, and fault healing. Pressure solution in massive rocks often localizes into solution seams or stylolites. Field observations of stylolites often show elastic/brittle interactions in regions between pressure solution features, including and shear fractures, veins and pull-apart features. To understand these interactions, we use a grain-scale model based on the Discrete Element Method that allows granular dissolution at stressed contacts between grains. The new model captures both the slow chemical compaction process and the more abrupt brittle fracturing and sliding between grains. We simulate a sample of rock as a collection of particles, each representing either a grain or a unit of rock, bonded to each other with breakable cement. We apply external stresses to this sample, and calculate elastic and frictional interactions between the grains. Dissolution is modeled by an irreversible penetration of contacting grains into each other at a rate that depends on the contact stress and an adjustable rate constant. Experiments have shown that dissolution rates at grain contacts are greatly enhanced when there is a mineralogical contrast. Therefore, we dissolution rate constant can be increased to account for an amount of impurities (e.g. clay in a quartz or calcite sandstone) that can accumulate on dissolving contacts. This approach allows large compaction and shear strains within the rock, while allowing examination of local grain-scale heterogeneity. For example, we will describe the effect of pressure solution on the distribution of contact forces magnitudes and orientations. Contact forces in elastic granular packings are inherently
Radon transport in fractured soil. Laboratory experiments and modelling
International Nuclear Information System (INIS)
Hoff, A.
1997-10-01
Radon (Rn-222) transport in fractured soil has been investigated by laboratory experiments and by modelling. Radon transport experiments have been performed with two sand columns (homogeneous and inhomogeneous) and one undisturbed clayey till column containing a net of preferential flow paths (root holes). A numerical model (the finite-element model FRACTRAN) and an analytic model (a pinhole model) have been applied in simulations if soil gas and radon transport in fractured soil. Experiments and model calculations are included in a discussion of radon entry rates into houses placed on fractured soil. The main conclusion is, that fractures does not in general alter transport of internally generated radon out of soil, when the pressure and flow conditions in the soil is comparable to the conditions prevailing under a house. This indicates the important result, that fractures in soil have no impact on radon entry into a house beyond that of an increased gas permeability, but a more thorough investigation of this subject is needed. Only in the case where the soil is exposed to large pressure gradients, relative to gradients induced by a house, may it be possible to observe effects of radon exchange between fractures and matrix. (au) 52 tabs., 60 ill., 5 refs
Radon transport in fractured soil. Laboratory experiments and modelling
Energy Technology Data Exchange (ETDEWEB)
Hoff, A
1997-10-01
Radon (Rn-222) transport in fractured soil has been investigated by laboratory experiments and by modelling. Radon transport experiments have been performed with two sand columns (homogeneous and inhomogeneous) and one undisturbed clayey till column containing a net of preferential flow paths (root holes). A numerical model (the finite-element model FRACTRAN) and an analytic model (a pinhole model) have been applied in simulations if soil gas and radon transport in fractured soil. Experiments and model calculations are included in a discussion of radon entry rates into houses placed on fractured soil. The main conclusion is, that fractures does not in general alter transport of internally generated radon out of soil, when the pressure and flow conditions in the soil is comparable to the conditions prevailing under a house. This indicates the important result, that fractures in soil have no impact on radon entry into a house beyond that of an increased gas permeability, but a more thorough investigation of this subject is needed. Only in the case where the soil is exposed to large pressure gradients, relative to gradients induced by a house, may it be possible to observe effects of radon exchange between fractures and matrix. (au) 52 tabs., 60 ill., 5 refs.
Modelling tracer transport in fractured rock at Stripa
International Nuclear Information System (INIS)
Herbert, A.
1992-01-01
We present the results of a modelling study, making predictions for tracer transport experiments carried out within the H-zone feature in the Stripa mine. We use a direct fracture network approach to represent the system of interconnected flow-conducting fractures comprising this zone. It is a highly fractured granite, and our fracture-network models include up to 60000 fractures. We have had to develop efficient algorithms to calculate the flow and transport through these networks; these techniques are described and justified. The first stage of modelling addressed two saline injection experiments. The results of these were known to us and so in addition to 'predicting' the results of these experiments, we used them to calibrate a flow model of the experimental site. This model was then used to make true 'blind' predictions for a set of tracer experiments carried out in the natural head-field, caused by an open drift. Where our flow model was good, our predictions were found to be very accurate, explaining the dispersion in the tracer breakthrough in terms of the fracture network geometry. Discrepancies for experiments in less well characterised regions of the H-zone are presented, and we suggest that the errors in these predictions are a consequence of the inaccuracies of the flow-field. We have demonstrated the use of large-scale fracture network modelling. It has proved very successful, and made very accurate predictions of field experiments carried out at the Stripa mine. The measured dispersion of tracers can be accounted for by the geometry of the fracture network flow system. (14 refs.) (au)
Discrete element modeling of deformable particles in YADE
Directory of Open Access Journals (Sweden)
Martin Haustein
2017-01-01
Full Text Available In this paper we describe the open-source discrete element framework YADE and the implementation of a new deformation engine. YADE is a highly expandable software package that allows the simulation of current industrial problems in the field of granular materials using particle-based numerical methods. The description of the compaction of powders and granular material like metal pellets is now possible with a pure and simple discrete element approach in a modern DEM-framework. The deformation is realized by expanding the radius of the spherical particles, depending on their overlap, so that the volume of the material is kept constant.
A new spatial multiple discrete-continuous modeling approach to land use change analysis.
2013-09-01
This report formulates a multiple discrete-continuous probit (MDCP) land-use model within a : spatially explicit economic structural framework for land-use change decisions. The spatial : MDCP model is capable of predicting both the type and intensit...
Slug flow model for infiltration into fractured porous media
International Nuclear Information System (INIS)
Martinez, M.J.
1999-01-01
A model for transient infiltration into a periodically fractured porous layer is presented. The fracture is treated as a permeable-walled slot and the moisture distribution is in the form of a slug being an advancing meniscus. The wicking of moisture from the fracture to the unsaturated porous matrix is a nonlinear diffusion process and is approximately by self-similar solutions. The resulting model is a nonlinear Volterra integral equation with a weakly singular kernel. Numerical analysis provides solutions over a wide range of the parameter space and reveals the asymptotic forms of the penetration of this slug in terms of dimensionless variables arising in the model. The numerical solutions corroborate asymptotic results given earlier by Nitao and Buscheck (1991), and by Martinez (1988). Some implications for the transport of liquid in fractured rock are discussed
Application of coalescence and breakup models in a discrete bubble model for bubble columns
van den Hengel, E.I.V.; Deen, N.G.; Kuipers, J.A.M.
2005-01-01
In this work, a discrete bubble model (DBM) is used to investigate the hydrodynamics, coalescence, and breakup occurring in a bubble column. The DBM, originally developed by Delnoij et al. (Chem. Eng. Sci. 1997, 52, 1429-1458; Chem. Eng. Sci. 1999, 54, 2217-2226),1,2 was extended to incorporate
Zhu, Xiaoshu
2013-01-01
The current study introduced a general modeling framework, multilevel mixture IRT (MMIRT) which detects and describes characteristics of population heterogeneity, while accommodating the hierarchical data structure. In addition to introducing both continuous and discrete approaches to MMIRT, the main focus of the current study was to distinguish…
Particle models for discrete element modeling of bulk grain properties of wheat kernels
Recent research has shown the potential of discrete element method (DEM) in simulating grain flow in bulk handling systems. Research has also revealed that simulation of grain flow with DEM requires establishment of appropriate particle models for each grain type. This research completes the three-p...
ADAM: analysis of discrete models of biological systems using computer algebra.
Hinkelmann, Franziska; Brandon, Madison; Guang, Bonny; McNeill, Rustin; Blekherman, Grigoriy; Veliz-Cuba, Alan; Laubenbacher, Reinhard
2011-07-20
Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed. We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second. Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on mathematical algorithms as a web
DEFF Research Database (Denmark)
Iskhakov, Fedor; Jørgensen, Thomas H.; Rust, John
2017-01-01
We present a fast and accurate computational method for solving and estimating a class of dynamic programming models with discrete and continuous choice variables. The solution method we develop for structural estimation extends the endogenous grid-point method (EGM) to discrete-continuous (DC) p...
Teeuwen, P.A.; Kleinman, C.S.; Snijder, H.H.
2012-01-01
This paper presents a mechanical model for a structure comprising of steel frames with discretely connected precast concrete infill panels having window openings, termed semi-integral infilled frames. The discrete panel-to-frame connections are realized by structural bolts acting under compression.
A discrete finite element modelling and measurements for powder compaction
International Nuclear Information System (INIS)
Choi, J L; Gethin, D T
2009-01-01
An experimental investigation into friction between powder and a target surface together with numerical modelling of compaction and friction processes at a micro-scale are presented in this paper. The experimental work explores friction mechanisms by using an extended sliding plate apparatus operating at low load while sliding over a long distance. Tests were conducted for copper and 316 steel with variation in loads, surface finish and its orientation. The behaviours of the static and dynamic friction were identified highlighting the important influence of particle size, particle shape, material response and surface topography. The results also highlighted that under light loading the friction coefficient remains at a level lower than that derived from experiments on equipment having a wider dynamic range and this is attributed to the enhanced sensitivity of the measurement equipment. The results also suggest that friction variation with sliding distance is a consequence of damage, rather than presentation of an uncontaminated target sliding surface. The complete experimental cycle was modelled numerically using a combined discrete and finite element scheme enabling exploration of mechanisms that are defined at the particle level. Using compaction as the starting point, a number of simulation factors and process parameters were investigated. Comparisons were made with previously published work, showing reasonable agreement and the simulations were then used to explore the process response to the range of particle scale factors. Models comprising regular packing of round particles exhibited stiff response with high initial density. Models with random packing were explored and were found to reflect trends that are more closely aligned with experimental observation, including rearrangement, followed by compaction under a regime of elastic then plastic deformation. Numerical modelling of the compaction stage was extended to account for the shearing stage of the
Fictitious Crack Model of Concrete Fracture
DEFF Research Database (Denmark)
Brincker, Rune; Dahl, H.
1989-01-01
The substructure method introduced by Petersson is reformulated for the three-point bending specimen in order to obtain complete load-displacement relations without significant truncation. The problem of instability caused by the linearization of the softening in the fracture zone is discussed, a...
A new scripting library for modeling flow and transport in fractured rock with channel networks
Dessirier, Benoît; Tsang, Chin-Fu; Niemi, Auli
2018-02-01
Deep crystalline bedrock formations are targeted to host spent nuclear fuel owing to their overall low permeability. They are however highly heterogeneous and only a few preferential paths pertaining to a small set of dominant rock fractures usually carry most of the flow or mass fluxes, a behavior known as channeling that needs to be accounted for in the performance assessment of repositories. Channel network models have been developed and used to investigate the effect of channeling. They are usually simpler than discrete fracture networks based on rock fracture mappings and rely on idealized full or sparsely populated lattices of channels. This study reexamines the fundamental parameter structure required to describe a channel network in terms of groundwater flow and solute transport, leading to an extended description suitable for unstructured arbitrary networks of channels. An implementation of this formalism in a Python scripting library is presented and released along with this article. A new algebraic multigrid preconditioner delivers a significant speedup in the flow solution step compared to previous channel network codes. 3D visualization is readily available for verification and interpretation of the results by exporting the results to an open and free dedicated software. The new code is applied to three example cases to verify its results on full uncorrelated lattices of channels, sparsely populated percolation lattices and to exemplify the use of unstructured networks to accommodate knowledge on local rock fractures.
Hybrid modelling in discrete-event control system design
Beek, van D.A.; Rooda, J.E.; Gordijn, S.H.F.; Borne, P.
1996-01-01
Simulation-based testing of discrete-event control systems can be advantageous. There is, however, a considerable difference between languages for real-time control and simulation languages. The Chi language, presented in this paper, is suited to specification and simulation of real-time control
Discrete vessel heat transfer in perfused tissue - model comparison
Stanczyk, M.; Leeuwen, van G.M.J.; Steenhoven, van A.A.
2007-01-01
The aim of this paper is to compare two methods of calculating heat transfer in perfused biological tissue using a discrete vessel description. The methods differ in two important aspects: the representation of the vascular system and the algorithm for calculating the heat flux between tissue and
Groundwater degassing in fractured rock: Modelling and data comparison
Energy Technology Data Exchange (ETDEWEB)
Jarsjoe, J.; Destouni, G. [Royal Inst. of Tech., Stockholm (Sweden). Water Resources Engineering
1998-11-01
Dissolved gas may be released from deep groundwater in the vicinity of open boreholes and drifts, where the water pressures are relatively low. Degassing of groundwater may influence observations of hydraulic conditions made in drifts, interpretation of experiments performed close to drifts, and buffer mass and backfill performance, particularly during emplacement and repository closure. Under certain conditions, considerable fracture inflow and transmissivity reductions have been observed during degassing experiments in the field and in the laboratory; such reductions affect the outcome and interpretation of both hydraulic and tracer tests. We develop models for the estimation of the resulting degree of fracture gas saturation and the associated transmissivity reduction due to groundwater degassing in fractured rock. Derived expressions for bubble trapping probability show that fracture aperture variability and correlation length influence the conditions for capillary bubble trapping and gas accumulation. The laboratory observations of bubble trapping in an Aespoe fracture replica are consistent with the prediction of a relatively high probability of bubble trapping in this fracture. The prediction was based on the measured aperture distribution of the Aespoe fracture and the applied hydraulic gradient. Results also show that the conceptualisation of gas and water occupancy in a fracture greatly influences model predictions of gas saturation and relative transmissivity. Images from laboratory degassing experiments indicate that tight apertures are completely filled with water, whereas both gas and water exist in wider apertures under degassing conditions; implementation of this relation in our model resulted in the best agreement between predictions and laboratory observations. Model predictions for conditions similar to those prevailing in field for single fractures at great depths indicate that degassing effects in boreholes should generally be small, unless the
International Nuclear Information System (INIS)
Capilla, J. E.; Rodrigo, J.; Gomez Hernandez, J. J.
2003-01-01
Characterizing the uncertainty of flow and mass transport models requires the definition of stochastic models to describe hydrodynamic parameters. Porosity and hydraulic conductivity (K) are two of these parameters that exhibit a high degree of spatial variability. K is usually the parameter whose variability influence to a more extended degree solutes movement. In fracture media, it is critical to properly characterize K in the most altered zones where flow and solutes migration tends to be concentrated. However, K measurements use to be scarce and sparse. This fact calls to consider stochastic models that allow quantifying the uncertainty of flow and mass transport predictions. This paper presents a convective transport problem solved in a 3D block of fractured crystalline rock. the case study is defined based on data from a real geological formation. As the scarcity of K data in fractures does not allow supporting classical multi Gaussian assumptions for K in fractures, the non multi Gaussian hypothesis has been explored, comparing mass transport results for alternative Gaussian and non-Gaussian assumptions. The latter hypothesis allows reproducing high spatial connectivity for extreme values of K. This feature is present in nature, might lead to reproduce faster solute pathways, and therefore should be modeled in order to obtain reasonably safe prediction of contaminants migration in a geological formation. The results obtained for the two alternative hypotheses show a remarkable impact of the K random function model in solutes movement. (Author) 9 refs
Relating Cohesive Zone Model to Linear Elastic Fracture Mechanics
Wang, John T.
2010-01-01
The conditions required for a cohesive zone model (CZM) to predict a failure load of a cracked structure similar to that obtained by a linear elastic fracture mechanics (LEFM) analysis are investigated in this paper. This study clarifies why many different phenomenological cohesive laws can produce similar fracture predictions. Analytical results for five cohesive zone models are obtained, using five different cohesive laws that have the same cohesive work rate (CWR-area under the traction-separation curve) but different maximum tractions. The effect of the maximum traction on the predicted cohesive zone length and the remote applied load at fracture is presented. Similar to the small scale yielding condition for an LEFM analysis to be valid. the cohesive zone length also needs to be much smaller than the crack length. This is a necessary condition for a CZM to obtain a fracture prediction equivalent to an LEFM result.
Modeling biogechemical reactive transport in a fracture zone
Energy Technology Data Exchange (ETDEWEB)
Molinero, Jorge; Samper, Javier; Yang, Chan Bing, and Zhang, Guoxiang; Guoxiang, Zhang
2005-01-14
A coupled model of groundwater flow, reactive solute transport and microbial processes for a fracture zone of the Aspo site at Sweden is presented. This is the model of the so-called Redox Zone Experiment aimed at evaluating the effects of tunnel construction on the geochemical conditions prevailing in a fracture granite. It is found that a model accounting for microbially-mediated geochemical processes is able to reproduce the unexpected measured increasing trends of dissolved sulfate and bicarbonate. The model is also useful for testing hypotheses regarding the role of microbial processes and evaluating the sensitivity of model results to changes in biochemical parameters.
Modeling biogeochemical reactive transport in a fracture zone
International Nuclear Information System (INIS)
Molinero, Jorge; Samper, Javier; Yang, Chan Bing; Zhang, Guoxiang; Guoxiang, Zhang
2005-01-01
A coupled model of groundwater flow, reactive solute transport and microbial processes for a fracture zone of the Aspo site at Sweden is presented. This is the model of the so-called Redox Zone Experiment aimed at evaluating the effects of tunnel construction on the geochemical conditions prevailing in a fracture granite. It is found that a model accounting for microbially-mediated geochemical processes is able to reproduce the unexpected measured increasing trends of dissolved sulfate and bicarbonate. The model is also useful for testing hypotheses regarding the role of microbial processes and evaluating the sensitivity of model results to changes in biochemical parameters
Liao, Bolin; Zhang, Yunong; Jin, Long
2016-02-01
In this paper, a new Taylor-type numerical differentiation formula is first presented to discretize the continuous-time Zhang neural network (ZNN), and obtain higher computational accuracy. Based on the Taylor-type formula, two Taylor-type discrete-time ZNN models (termed Taylor-type discrete-time ZNNK and Taylor-type discrete-time ZNNU models) are then proposed and discussed to perform online dynamic equality-constrained quadratic programming. For comparison, Euler-type discrete-time ZNN models (called Euler-type discrete-time ZNNK and Euler-type discrete-time ZNNU models) and Newton iteration, with interesting links being found, are also presented. It is proved herein that the steady-state residual errors of the proposed Taylor-type discrete-time ZNN models, Euler-type discrete-time ZNN models, and Newton iteration have the patterns of O(h(3)), O(h(2)), and O(h), respectively, with h denoting the sampling gap. Numerical experiments, including the application examples, are carried out, of which the results further substantiate the theoretical findings and the efficacy of Taylor-type discrete-time ZNN models. Finally, the comparisons with Taylor-type discrete-time derivative model and other Lagrange-type discrete-time ZNN models for dynamic equality-constrained quadratic programming substantiate the superiority of the proposed Taylor-type discrete-time ZNN models once again.
Investigating Some Technical Issues on Cohesive Zone Modeling of Fracture
Wang, John T.
2011-01-01
This study investigates some technical issues related to the use of cohesive zone models (CZMs) in modeling fracture processes. These issues include: why cohesive laws of different shapes can produce similar fracture predictions; under what conditions CZM predictions have a high degree of agreement with linear elastic fracture mechanics (LEFM) analysis results; when the shape of cohesive laws becomes important in the fracture predictions; and why the opening profile along the cohesive zone length needs to be accurately predicted. Two cohesive models were used in this study to address these technical issues. They are the linear softening cohesive model and the Dugdale perfectly plastic cohesive model. Each cohesive model constitutes five cohesive laws of different maximum tractions. All cohesive laws have the same cohesive work rate (CWR) which is defined by the area under the traction-separation curve. The effects of the maximum traction on the cohesive zone length and the critical remote applied stress are investigated for both models. For a CZM to predict a fracture load similar to that obtained by an LEFM analysis, the cohesive zone length needs to be much smaller than the crack length, which reflects the small scale yielding condition requirement for LEFM analysis to be valid. For large-scale cohesive zone cases, the predicted critical remote applied stresses depend on the shape of cohesive models used and can significantly deviate from LEFM results. Furthermore, this study also reveals the importance of accurately predicting the cohesive zone profile in determining the critical remote applied load.
Video modeling to train staff to implement discrete-trial instruction.
Catania, Cynthia N; Almeida, Daniel; Liu-Constant, Brian; DiGennaro Reed, Florence D
2009-01-01
Three new direct-service staff participated in a program that used a video model to train target skills needed to conduct a discrete-trial session. Percentage accuracy in completing a discrete-trial teaching session was evaluated using a multiple baseline design across participants. During baseline, performances ranged from a mean of 12% to 63% accuracy. During video modeling, there was an immediate increase in accuracy to a mean of 98%, 85%, and 94% for each participant. Performance during maintenance and generalization probes remained at high levels. Results suggest that video modeling can be an effective technique to train staff to conduct discrete-trial sessions.
Sensitivity Analysis of the Bone Fracture Risk Model
Lewandowski, Beth; Myers, Jerry; Sibonga, Jean Diane
2017-01-01
Introduction: The probability of bone fracture during and after spaceflight is quantified to aid in mission planning, to determine required astronaut fitness standards and training requirements and to inform countermeasure research and design. Probability is quantified with a probabilistic modeling approach where distributions of model parameter values, instead of single deterministic values, capture the parameter variability within the astronaut population and fracture predictions are probability distributions with a mean value and an associated uncertainty. Because of this uncertainty, the model in its current state cannot discern an effect of countermeasures on fracture probability, for example between use and non-use of bisphosphonates or between spaceflight exercise performed with the Advanced Resistive Exercise Device (ARED) or on devices prior to installation of ARED on the International Space Station. This is thought to be due to the inability to measure key contributors to bone strength, for example, geometry and volumetric distributions of bone mass, with areal bone mineral density (BMD) measurement techniques. To further the applicability of model, we performed a parameter sensitivity study aimed at identifying those parameter uncertainties that most effect the model forecasts in order to determine what areas of the model needed enhancements for reducing uncertainty. Methods: The bone fracture risk model (BFxRM), originally published in (Nelson et al) is a probabilistic model that can assess the risk of astronaut bone fracture. This is accomplished by utilizing biomechanical models to assess the applied loads; utilizing models of spaceflight BMD loss in at-risk skeletal locations; quantifying bone strength through a relationship between areal BMD and bone failure load; and relating fracture risk index (FRI), the ratio of applied load to bone strength, to fracture probability. There are many factors associated with these calculations including
Directory of Open Access Journals (Sweden)
Fernando Gómez-Salas
2015-01-01
Full Text Available This work proposes a discrete-time nonlinear rational approximate model for the unstable magnetic levitation system. Based on this model and as an application of the input-output linearization technique, a discrete-time tracking control design will be derived using the corresponding classical state space representation of the model. A simulation example illustrates the efficiency of the proposed methodology.
Disaster Response Modeling Through Discrete-Event Simulation
Wang, Jeffrey; Gilmer, Graham
2012-01-01
Organizations today are required to plan against a rapidly changing, high-cost environment. This is especially true for first responders to disasters and other incidents, where critical decisions must be made in a timely manner to save lives and resources. Discrete-event simulations enable organizations to make better decisions by visualizing complex processes and the impact of proposed changes before they are implemented. A discrete-event simulation using Simio software has been developed to effectively analyze and quantify the imagery capabilities of domestic aviation resources conducting relief missions. This approach has helped synthesize large amounts of data to better visualize process flows, manage resources, and pinpoint capability gaps and shortfalls in disaster response scenarios. Simulation outputs and results have supported decision makers in the understanding of high risk locations, key resource placement, and the effectiveness of proposed improvements.
Discrete Charge Effects on an Infinitely Long Cylindrical Rod Model
Agung, Ahmad A. J; Jesudason, Christopher G.
2011-01-01
Two methods for determining the potential (\\psi) around a discretely charged rod have been devised. The methods utilize the potential around the continuously charged rod (\\bar{\\psi}) as the reference where \\bar{\\psi} isdetermined by the Poisson-Boltzmann equation. The potential data are used to determine the theoretical radial distribution function (RDF) which is compared with MD simulation data. It is shown that the magnitude of the charge and size parameters very strongly affects the shape ...
Convergence of discrete Aubry–Mather model in the continuous limit
Su, Xifeng; Thieullen, Philippe
2018-05-01
We develop two approximation schemes for solving the cell equation and the discounted cell equation using Aubry–Mather–Fathi theory. The Hamiltonian is supposed to be Tonelli, time-independent and periodic in space. By Legendre transform it is equivalent to find a fixed point of some nonlinear operator, called Lax-Oleinik operator, which may be discounted or not. By discretizing in time, we are led to solve an additive eigenvalue problem involving a discrete Lax–Oleinik operator. We show how to approximate the effective Hamiltonian and some weak KAM solutions by letting the time step in the discrete model tend to zero. We also obtain a selected discrete weak KAM solution as in Davini et al (2016 Invent. Math. 206 29–55), and show that it converges to a particular solution of the cell equation. In order to unify the two settings, continuous and discrete, we develop a more general formalism of the short-range interactions.
The hydro-mechanical modeling of the fractured media
International Nuclear Information System (INIS)
Kadiri, I.
2002-10-01
The hydro-mechanical modeling of the fractured media is quite complex. Simplifications are necessary for the modeling of such media, but, not always justified, Only permeable fractures are often considered. The rest of the network is approximated by an equivalent continuous medium. Even if we suppose that this approach is validated, the hydraulic and mechanical properties of the fractures and of the continuous medium are seldom known. Calibrations are necessary for the determination of these properties. Until now, one does not know very well the nature of measurements which must be carried out in order to carry on a modeling in discontinuous medium, nor elements of enough robust validation for this kind of modeling. For a better understanding of the hydro-mechanical phenomena in fractured media, two different sites have been selected for the work. The first is the site of Grimsel in Switzerland in which an underground laboratory is located at approximately 400 m of depth. The FEBEX experiment aims at the in-situ study of the consecutive phenomena due to the installation of a heat source representative of radioactive waste in the last 17 meters of the FEBEX tunnel in the laboratory of Grimsel. Only, the modeling of the hydro-mechanical of the excavation was model. The modeling of the Febex enabled us to establish a methodology of calibration of the hydraulic properties in the discontinuous media. However, this kind of study on such complex sites does not make possible to answer all the questions which arise on the hydro-mechanical behavior of the fractured media. We thus carried out modeling on an other site, smaller than the fist one and more accessible. The experimental site of Coaraze, in the Maritime Alps, is mainly constituted of limestone and fractures. Then the variation of water pressure along fractures is governed by the opening/closure sequence of a water gate. Normal displacement as well as the pore pressure along these fractures are recorded, and then
Li, Zejing
2012-01-01
This dissertation is mainly devoted to the research of two problems - the continuous-time portfolio optimization in different Wishart models and the effects of discrete rebalancing on portfolio wealth distribution and optimal portfolio strategy.
Modeling the Fracture of Ice Sheets on Parallel Computers
Energy Technology Data Exchange (ETDEWEB)
Waisman, Haim [Columbia Univ., New York, NY (United States); Tuminaro, Ray [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2013-10-10
The objective of this project was to investigate the complex fracture of ice and understand its role within larger ice sheet simulations and global climate change. This objective was achieved by developing novel physics based models for ice, novel numerical tools to enable the modeling of the physics and by collaboration with the ice community experts. At the present time, ice fracture is not explicitly considered within ice sheet models due in part to large computational costs associated with the accurate modeling of this complex phenomena. However, fracture not only plays an extremely important role in regional behavior but also influences ice dynamics over much larger zones in ways that are currently not well understood. To this end, our research findings through this project offers significant advancement to the field and closes a large gap of knowledge in understanding and modeling the fracture of ice sheets in the polar regions. Thus, we believe that our objective has been achieved and our research accomplishments are significant. This is corroborated through a set of published papers, posters and presentations at technical conferences in the field. In particular significant progress has been made in the mechanics of ice, fracture of ice sheets and ice shelves in polar regions and sophisticated numerical methods that enable the solution of the physics in an efficient way.
Transport modeling of sorbing tracers in artificial fractures
International Nuclear Information System (INIS)
Keum, Dong Kwon; Baik, Min Hoon; Park, Chung Kyun; Cho, Young Hwan; Hahn, Phil Soo.
1998-02-01
This study was performed as part of a fifty-man year attachment program between AECL (Atomic Energy Canada Limited) and KAERI. Three kinds of computer code, HDD, POMKAP and VAMKAP, were developed to predict transport of contaminants in fractured rock. MDDM was to calculate the mass transport of contaminants in a single fracture using a simple hydrodynamic dispersion diffusion model. POMKAP was to predict the mass transport of contaminants by a two-dimensional variable aperture model. In parallel with modeling, the validation of models was also performed through the analysis of the migration experimental data obtained in acrylic plastic and granite artificial fracture system at the Whiteshell laboratories, AECL, Canada. (author). 34 refs., 11 tabs., 76 figs
Transport modeling of sorbing tracers in artificial fractures
Energy Technology Data Exchange (ETDEWEB)
Keum, Dong Kwon; Baik, Min Hoon; Park, Chung Kyun; Cho, Young Hwan; Hahn, Phil Soo
1998-02-01
This study was performed as part of a fifty-man year attachment program between AECL (Atomic Energy Canada Limited) and KAERI. Three kinds of computer code, HDD, POMKAP and VAMKAP, were developed to predict transport of contaminants in fractured rock. MDDM was to calculate the mass transport of contaminants in a single fracture using a simple hydrodynamic dispersion diffusion model. POMKAP was to predict the mass transport of contaminants by a two-dimensional variable aperture model. In parallel with modeling, the validation of models was also performed through the analysis of the migration experimental data obtained in acrylic plastic and granite artificial fracture system at the Whiteshell laboratories, AECL, Canada. (author). 34 refs., 11 tabs., 76 figs.
Continuum equivalent model for the fractured EDZ around underground galleries in clay-stone
International Nuclear Information System (INIS)
Pouya, A.; Bourgeois, E.; Larbi, B.; Poutrel, A.
2010-01-01
, parallel and equidistant fractures perpendicular to n, the vector normal to the local fractures surface. This behaviour has thus the axial symmetry around the axis n. We have studied this problem first for a linear elastic behaviour of the intact rock and of fractures and then extended it to more complex behaviours. In this case, the local elastic behaviour of the CEM is defined by a tensor which has the transversal isotropy around n. Because of the finite size of the studied domain, the assumption of uniform stress or uniform strain at the boundary leads to different CEM models called 1 and 2 in the following. To validate the 'homogenization' procedure, we compare the displacement and stress fields calculated around the galleries with two approaches: the first one uses a discrete model (with individual representation of the fractures) and the other one relies on the CEM model of the EDZ. Both models assume the same geometry with axial symmetry. In the first case, fractures are represented numerically by the Goodman (1966) 'joint elements' implemented in the finite element code CESAR, and in the second case, the special anisotropic and position depending elastic model (1) implemented in CESAR is used. The total displacement at the wall obtained by the first method and the two CEM models given by the procedure described above is shown. Except for the beginning of the gallery where boundary effects are dominant, CEM models give nearly the same displacements that the discontinuous model. The comparison between the stresses leads also to a good agreement between the results. This approach was extended to the elastoplastic behaviour of the rock and of the fractures with also taking into account the curvature of the fractures. A good agreement between the discontinuous and CEM models could be obtained for these cases also. This shows the possibility of replacing effectively in the numerical models the fractured EDZ by a CEM determined by homogenization
ON DISCRETE STRUCTURE OF GEOLOGIC MEDIUM AND CONTINUAL APPROACH TO MODELING ITS MOVEMENTS
Directory of Open Access Journals (Sweden)
Sh. A. Mukhamediev
2016-01-01
Full Text Available This paper discusses the structure of a geologic medium represented by accessible lithified rocks and provides an overview of methods used to describe its movements. Two basic opinions are considered in the framework of the discussion: (1 an initially homogeneous and continuous geologic medium acquires the structure composed of blocks in the process of the geologic medium’s deformation/destruction/degradation, and (2 a geologic medium is composed of blocks (and often has hierarchic, active, energy-saturated features, and the continuity model is thus not valid for describing the geologic medium’s deformation. Proponents of the first point of view actively apply the standard or modified continuum model of a solid deformed body (SDB in estimations of the stress-strain state, but the input parameters of this model do not contain any information on discreteness in principle. Authors who support the second opinion, either explicitly or implicitly assume that the block structure of the geologic medium, which is detectable by geological methods, makes a direct and unambiguous impact on all other mechanical properties of the geologic medium and, above all, on the nature of its movements.Based on results obtained by interpreting the data collected in our long-term field studies of rock fracturing, mathematical processing of GPS-measurements, and theoretical models, we agree with the concept of the geologic medium’s block structure, but argue that the geologic block-structure property is not acquired but congenital. Regarding sedimentary rocks, it means that the discrete structure has been already embodied in the rock before sediment lithification, regardless of the intensity of macroscopic deformations. A discrete structure is the form of the geologic medium existence and a cause of the congenital anisotropy of the geologic medium’s strength characteristics. Due to subsequent deformation of the geologic medium, some elements of the structure can
An approach to ductile fracture resistance modelling in pipeline steels
Energy Technology Data Exchange (ETDEWEB)
Pussegoda, L.N.; Fredj, A. [BMT Fleet Technology Ltd., Kanata (Canada)
2009-07-01
Ductile fracture resistance studies of high grade steels in the pipeline industry often included analyses of the crack tip opening angle (CTOA) parameter using 3-point bend steel specimens. The CTOA is a function of specimen ligament size in high grade materials. Other resistance measurements may include steady state fracture propagation energy, critical fracture strain, and the adoption of damage mechanisms. Modelling approaches for crack propagation were discussed in this abstract. Tension tests were used to calibrate damage model parameters. Results from the tests were then applied to the crack propagation in a 3-point bend specimen using modern 1980 vintage steels. Limitations and approaches to overcome the difficulties associated with crack propagation modelling were discussed.
Modeling of Hydrodynamic Chromatography for Colloid Migration in Fractured Rock
International Nuclear Information System (INIS)
Li Shihhai; Jen, C.-P.
2001-01-01
The role of colloids in the migration of radionuclides in the geosphere has been emphasized in the performance assessment of high-level radioactive waste disposal. The literature indicates that the colloid velocity may not be equal to the velocity of groundwater owing to hydrodynamic chromatography. A theoretical model for hydrodynamic chromatography of colloid migration in the fracture is proposed in the present work. In this model, the colloids are treated as nonreactive and the external forces acting on colloidal particles are considered including the inertial force, the van der Waals attractive force, and the electrical double-layer repulsive force, as well as the gravitational force. A fully developed concentration profile for colloids is obtained to elucidate migration behavior for colloids in the fracture. The effects of parameters governing these forces and the aperture of the fracture are determined using a theoretical model
Multiscale model reduction for shale gas transport in fractured media
Akkutlu, I. Y.
2016-05-18
In this paper, we develop a multiscale model reduction technique that describes shale gas transport in fractured media. Due to the pore-scale heterogeneities and processes, we use upscaled models to describe the matrix. We follow our previous work (Akkutlu et al. Transp. Porous Media 107(1), 235–260, 2015), where we derived an upscaled model in the form of generalized nonlinear diffusion model to describe the effects of kerogen. To model the interaction between the matrix and the fractures, we use Generalized Multiscale Finite Element Method (Efendiev et al. J. Comput. Phys. 251, 116–135, 2013, 2015). In this approach, the matrix and the fracture interaction is modeled via local multiscale basis functions. In Efendiev et al. (2015), we developed the GMsFEM and applied for linear flows with horizontal or vertical fracture orientations aligned with a Cartesian fine grid. The approach in Efendiev et al. (2015) does not allow handling arbitrary fracture distributions. In this paper, we (1) consider arbitrary fracture distributions on an unstructured grid; (2) develop GMsFEM for nonlinear flows; and (3) develop online basis function strategies to adaptively improve the convergence. The number of multiscale basis functions in each coarse region represents the degrees of freedom needed to achieve a certain error threshold. Our approach is adaptive in a sense that the multiscale basis functions can be added in the regions of interest. Numerical results for two-dimensional problem are presented to demonstrate the efficiency of proposed approach. © 2016 Springer International Publishing Switzerland
Simulating Dynamic Fracture in Oxide Fuel Pellets Using Cohesive Zone Models
Energy Technology Data Exchange (ETDEWEB)
R. L. Williamson
2009-08-01
It is well known that oxide fuels crack during the first rise to power, with continued fracture occurring during steady operation and especially during power ramps or accidental transients. Fractures have a very strong influence on the stress state in the fuel which, in turn, drives critical phenomena such as fission gas release, fuel creep, and eventual fuel/clad mechanical interaction. Recently, interest has been expressed in discrete fracture methods, such as the cohesive zone approach. Such models are attractive from a mechanistic and physical standpoint, since they reflect the localized nature of cracking. The precise locations where fractures initiate, as well as the crack evolution characteristics, are determined as part of the solution. This paper explores the use of finite element cohesive zone concepts to predict dynamic crack behavior in oxide fuel pellets during power-up, steady operation, and power ramping. The aim of this work is first to provide an assessment of cohesive zone models for application to fuel cracking and explore important numerical issues associated with this fracture approach. A further objective is to provide basic insight into where and when cracks form, how they interact, and how cracking effects the stress field in a fuel pellet. The ABAQUS commercial finite element code, which includes powerful cohesive zone capabilities, was used for this study. Fully-coupled thermo-mechanical behavior is employed, including the effects of thermal expansion, swelling due to solid and gaseous fission products, and thermal creep. Crack initiation is determined by a temperature-dependent maximum stress criterion, based on measured fracture strengths for UO2. Damage evolution is governed by a traction-separation relation, calibrated to data from temperature and burn-up dependent fracture toughness measurements. Numerical models are first developed in 2D based on both axisymmetric (to explore axial cracking) and plane strain (to explore radial
Directory of Open Access Journals (Sweden)
Youwei He
2018-02-01
Full Text Available Although technical advances in hydraulically fracturing and drilling enable commercial production from tight reservoirs, oil/gas recovery remains at a low level. Due to the technical and economic limitations of well-testing operations in tight reservoirs, rate-transient analysis (RTA has become a more attractive option. However, current RTA models hardly consider the effect of the non-uniform production on rate decline behaviors. In fact, PLT results demonstrate that production profile is non-uniform. To fill this gap, this paper presents an improved RTA model of multi-fractured horizontal wells (MFHWs to investigate the effects of non-uniform properties of hydraulic fractures (production of fractures, fracture half-length, number of fractures, fracture conductivity, and vertical permeability on rate transient behaviors through the diagnostic type curves. Results indicate obvious differences on the rate decline curves among the type curves of uniform properties of fractures (UPF and non-uniform properties of fractures (NPF. The use of dimensionless production integral derivative curve magnifies the differences so that we can diagnose the phenomenon of non-uniform production. Therefore, it’s significant to incorporate the effects of NPF into the RDA models of MFHWs, and the model proposed in this paper enables us to better evaluate well performance based on long-term production data.
Equilibrium and nonequilibrium attractors for a discrete, selection-migration model
James F. Selgrade; James H. Roberds
2003-01-01
This study presents a discrete-time model for the effects of selection and immigration on the demographic and genetic compositions of a population. Under biologically reasonable conditions, it is shown that the model always has an equilibrium. Although equilibria for similar models without migration must have real eigenvalues, for this selection-migration model we...
Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System
Directory of Open Access Journals (Sweden)
Zhenhua Hu
2013-01-01
Full Text Available We propose a new nonlinear economic system with fractional derivative. According to the Jumarie’s definition of fractional derivative, we obtain a discrete fractional nonlinear economic system. Three variables, the gross domestic production, inflation, and unemployment rate, are considered by this nonlinear system. Based on the concrete macroeconomic data of USA, the coefficients of this nonlinear system are estimated by the method of least squares. The application of discrete fractional economic model with linear and nonlinear structure is shown to illustrate the efficiency of modeling the macroeconomic data with discrete fractional dynamical system. The empirical study suggests that the nonlinear discrete fractional dynamical system can describe the actual economic data accurately and predict the future behavior more reasonably than the linear dynamic system. The method proposed in this paper can be applied to investigate other macroeconomic variables of more states.
Fracture flow modelling. Proof of evidence
International Nuclear Information System (INIS)
Hencher, S.R.
1996-01-01
Proof of Evidence by an expert witness is presented in support of the case by Friends of the Earth (FOE) against the proposed construction by UK Nirex Ltd of an underground Rock Characterisation Facility (RCF) at a site in the Sellafield area. The RCF is part of an investigation by Nirex into a suitable site for an underground repository for the disposal of radioactive waste. The objections were raised at a Planning Inquiry in 1995. The evidence points out that current understanding of the factors which control flow through a network of interconnecting fractures, such as that at the Sellafield site, is at a very early stage of development. Neither are the methods of investigation and analysis required for a post-closure performance assessment (PCPA) for a repository well developed. These issues are being investigated in international underground research laboratories but the proposed RCF is intended to be confirmatory rather than experimental. (23 references). (UK)
A Lateral Tensile Fracturing Model for Listric Fault
Qiu, Z.
2007-12-01
The new discovery of a major seismic fault of the great 1976 Tangshan earthquake suggests a lateral tensile fracturing process at the seismic source. The fault is in listric shape but can not be explained with the prevailing model of listric fault. A double-couple of forces without moment is demonstrated to be applicable to simulate the source mechanism. Based on fracture mechanics, laboratory experiments as well as numerical simulations, the model is against the assumption of stick-slip on existing fault as the cause of the earthquake but not in conflict with seismological observations. Global statistics of CMT solutions of great earthquakes raises significant support to the idea that lateral tensile fracturing might account for not only the Tangshan earthquake but also others.
Bi, Linfeng
2009-01-01
The main challenges in modeling fluid flow through naturally-fractured carbonate karst reservoirs are how to address various flow physics in complex geological architectures due to the presence of vugs and caves which are connected via fracture networks at multiple scales. In this paper, we present a unified multi-physics model that adapts to the complex flow regime through naturally-fractured carbonate karst reservoirs. This approach generalizes Stokes-Brinkman model (Popov et al. 2007). The fracture networks provide the essential connection between the caves in carbonate karst reservoirs. It is thus very important to resolve the flow in fracture network and the interaction between fractures and caves to better understand the complex flow behavior. The idea is to use Stokes-Brinkman model to represent flow through rock matrix, void caves as well as intermediate flows in very high permeability regions and to use an idea similar to discrete fracture network model to represent flow in fracture network. Consequently, various numerical solution strategies can be efficiently applied to greatly improve the computational efficiency in flow simulations. We have applied this unified multi-physics model as a fine-scale flow solver in scale-up computations. Both local and global scale-up are considered. It is found that global scale-up has much more accurate than local scale-up. Global scale-up requires the solution of global flow problems on fine grid, which generally is computationally expensive. The proposed model has the ability to deal with large number of fractures and caves, which facilitate the application of Stokes-Brinkman model in global scale-up computation. The proposed model flexibly adapts to the different flow physics in naturally-fractured carbonate karst reservoirs in a simple and effective way. It certainly extends modeling and predicting capability in efficient development of this important type of reservoir.
Numerical modeling of thermal conductive heating in fractured bedrock.
Baston, Daniel P; Falta, Ronald W; Kueper, Bernard H
2010-01-01
Numerical modeling was employed to study the performance of thermal conductive heating (TCH) in fractured shale under a variety of hydrogeological conditions. Model results show that groundwater flow in fractures does not significantly affect the minimum treatment zone temperature, except near the beginning of heating or when groundwater influx is high. However, fracture and rock matrix properties can significantly influence the time necessary to remove all liquid water (i.e., reach superheated steam conditions) in the treatment area. Low matrix permeability, high matrix porosity, and wide fracture spacing can contribute to boiling point elevation in the rock matrix. Consequently, knowledge of these properties is important for the estimation of treatment times. Because of the variability in boiling point throughout a fractured rock treatment zone and the absence of a well-defined constant temperature boiling plateau in the rock matrix, it may be difficult to monitor the progress of thermal treatment using temperature measurements alone. Copyright © 2010 The Author(s). Journal compilation © 2010 National Ground Water Association.
Modelling road accident blackspots data with the discrete generalized Pareto distribution.
Prieto, Faustino; Gómez-Déniz, Emilio; Sarabia, José María
2014-10-01
This study shows how road traffic networks events, in particular road accidents on blackspots, can be modelled with simple probabilistic distributions. We considered the number of crashes and the number of fatalities on Spanish blackspots in the period 2003-2007, from Spanish General Directorate of Traffic (DGT). We modelled those datasets, respectively, with the discrete generalized Pareto distribution (a discrete parametric model with three parameters) and with the discrete Lomax distribution (a discrete parametric model with two parameters, and particular case of the previous model). For that, we analyzed the basic properties of both parametric models: cumulative distribution, survival, probability mass, quantile and hazard functions, genesis and rth-order moments; applied two estimation methods of their parameters: the μ and (μ+1) frequency method and the maximum likelihood method; used two goodness-of-fit tests: Chi-square test and discrete Kolmogorov-Smirnov test based on bootstrap resampling; and compared them with the classical negative binomial distribution in terms of absolute probabilities and in models including covariates. We found that those probabilistic models can be useful to describe the road accident blackspots datasets analyzed. Copyright © 2014 Elsevier Ltd. All rights reserved.
Modeling Anti-Air Warfare With Discrete Event Simulation and Analyzing Naval Convoy Operations
2016-06-01
W., & Scheaffer, R. L. (2008). Mathematical statistics with applications . Belmont, CA: Cengage Learning. 118 THIS PAGE INTENTIONALLY LEFT BLANK...WARFARE WITH DISCRETE EVENT SIMULATION AND ANALYZING NAVAL CONVOY OPERATIONS by Ali E. Opcin June 2016 Thesis Advisor: Arnold H. Buss Co...REPORT DATE June 2016 3. REPORT TYPE AND DATES COVERED Master’s thesis 4. TITLE AND SUBTITLE MODELING ANTI-AIR WARFARE WITH DISCRETE EVENT
Safety Discrete Event Models for Holonic Cyclic Manufacturing Systems
Ciufudean, Calin; Filote, Constantin
In this paper the expression “holonic cyclic manufacturing systems” refers to complex assembly/disassembly systems or fork/join systems, kanban systems, and in general, to any discrete event system that transforms raw material and/or components into products. Such a system is said to be cyclic if it provides the same sequence of products indefinitely. This paper considers the scheduling of holonic cyclic manufacturing systems and describes a new approach using Petri nets formalism. We propose an approach to frame the optimum schedule of holonic cyclic manufacturing systems in order to maximize the throughput while minimize the work in process. We also propose an algorithm to verify the optimum schedule.
Nonaligned shocks for discrete velocity models of the Boltzmann equation
Directory of Open Access Journals (Sweden)
J. M. Greenberg
1991-05-01
Full Text Available At the conclusion of I. Bonzani's presentation on the existence of structured shock solutions to the six-velocity, planar, discrete Boltzmann equation (with binary and triple collisions, Greenberg asked whether such solutions were possible in directions e(α=(cosα ,sinα when α was not one of the particle flow directions. This question generated a spirited discussion but the question was still open at the conclusion of the conference. In this note the author will provide a partial resolution to the question raised above. Using formal perturbation arguments he will produce approximate solutions to the equation considered by Bonzani which represent traveling waves propagating in any direction e(α=(cosα ,sinα.
Discrete gradients in discrete classical mechanics
International Nuclear Information System (INIS)
Renna, L.
1987-01-01
A simple model of discrete classical mechanics is given where, starting from the continuous Hamilton equations, discrete equations of motion are established together with a proper discrete gradient definition. The conservation laws of the total discrete momentum, angular momentum, and energy are demonstrated
Fracture initiation associated with chemical degradation: observation and modeling
Energy Technology Data Exchange (ETDEWEB)
Byoungho Choi; Zhenwen Zhou; Chudnovsky, Alexander [Illinois Univ., Dept. of Civil and Materials Engineering (M/C 246), Chicago, IL (United States); Stivala, Salvatore S. [Stevens Inst. of Technology, Dept. of Chemistry and Chemical Biology, Hoboken, NJ (United States); Sehanobish, Kalyan; Bosnyak, Clive P. [Dow Chemical Co., Freeport, TX (United States)
2005-01-01
The fracture initiation in engineering thermoplastics resulting from chemical degradation is usually observed in the form of a microcrack network within a surface layer of degraded polymer exposed to a combined action of mechanical stresses and chemically aggressive environment. Degradation of polymers is usually manifested in a reduction of molecular weight, increase of crystallinity in semi crystalline polymers, increase of material density, a subtle increase in yield strength, and a dramatic reduction in toughness. An increase in material density, i.e., shrinkage of the degraded layer is constrained by adjacent unchanged material results in a buildup of tensile stress within the degraded layer and compressive stress in the adjacent unchanged material due to increasing incompatibility between the two. These stresses are an addition to preexisting manufacturing and service stresses. At a certain level of degradation, a combination of toughness reduction and increase of tensile stress result in fracture initiation. A quantitative model of the described above processes is presented in these work. For specificity, the internally pressurized plastic pipes that transport a fluid containing a chemically aggressive (oxidizing) agent is used as the model of fracture initiation. Experimental observations of material density and toughness dependence on degradation reported elsewhere are employed in the model. An equation for determination of a critical level of degradation corresponding to the offset of fracture is constructed. The critical level of degradation for fracture initiation depends on the rates of toughness deterioration and build-up of the degradation related stresses as well as on the manufacturing and service stresses. A method for evaluation of the time interval prior to fracture initiation is also formulated. (Author)
Mineral Precipitation in Fractures: Multiscale Imaging and Geochemical Modeling
Hajirezaie, S.; Peters, C. A.; Swift, A.; Sheets, J. M.; Cole, D. R.; Crandall, D.; Cheshire, M.; Stack, A. G.; Anovitz, L. M.
2017-12-01
For subsurface energy technologies such as geologic carbon sequestration, fractures are potential pathways for fluid migration from target formations. Highly permeable fractures may become sealed by mineral precipitation. In this study, we examined shale specimens with existing cemented fractures as natural analogues, using an array of imaging methods to characterize mineralogy and porosity at several spatial scales. In addition, we used reactive transport modeling to investigate geochemical conditions that can lead to extensive mineral precipitation and to simulate the impacts on fracture hydraulic properties. The naturally-cemented fractured rock specimens were from the Upper Wolfcamp formation in Texas, at 10,000 ft depth. The specimens were scanned using x-ray computed tomography (xCT) at resolution of 13 microns. The xCT images revealed an original fracture aperture of 1.9 mm filled with several distinct mineral phases and vuggy void regions, and the mineral phase volumes and surface areas were quantified and mapped in 3D. Specimens were thin-sectioned and examined at micron- and submicron-scales using petrographic microscopy (PM), scanning electron microscopy (SEM), energy dispersive X-ray spectroscopy (EDX), and small angle X-ray scattering (SAXS). Collectively these methods revealed crystals of dolomite as large as 900 microns in length overlain with a heterogeneous mixture of carbonate minerals including calcite, dolomite, and Fe-rich dolomite, interspersed at spatial scales as small as 5 microns. In addition, secondary precipitation of SiO2 was found to fill some of the void space. This multiscale imaging was used to inform the reactive transport modeling employed to examine the conditions that can cause the observed mineral precipitation in fractures at a larger scale. Two brines containing solutions that when mixed would lead to precipitation of various carbonate minerals were simulated as injectants into a fracture domain. In particular, the competing
Modelling Dowel Action of Discrete Reinforcing Bars in Cracked Concrete Structures
International Nuclear Information System (INIS)
Kwan, A. K. H.; Ng, P. L.; Lam, J. Y. K.
2010-01-01
Dowel action is one of the component actions for shear force transfer in cracked reinforced concrete. In finite element analysis of concrete structures, the use of discrete representation of reinforcing bars is considered advantageous over the smeared representation due to the relative ease of modelling the bond-slip behaviour. However, there is very limited research on how to simulate the dowel action of discrete reinforcing bars. Herein, a numerical model for dowel action of discrete reinforcing bars crossing cracks in concrete is developed. The model features the derivation of dowel stiffness matrix based on beam-on-elastic-foundation theory and the direct assemblage of dowel stiffness into the concrete element stiffness matrices. The dowel action model is incorporated in a nonlinear finite element programme with secant stiffness formulation. Deep beams tested in the literature are analysed and it is found that the incorporation of dowel action model improves the accuracy of analysis.
Modelling a reliability system governed by discrete phase-type distributions
International Nuclear Information System (INIS)
Ruiz-Castro, Juan Eloy; Perez-Ocon, Rafael; Fernandez-Villodre, Gemma
2008-01-01
We present an n-system with one online unit and the others in cold standby. There is a repairman. When the online fails it goes to repair, and instantaneously a standby unit becomes the online one. The operational and repair times follow discrete phase-type distributions. Given that any discrete distribution defined on the positive integers is a discrete phase-type distribution, the system can be considered a general one. A model with unlimited number of units is considered for approximating a system with a great number of units. We show that the process that governs the system is a quasi-birth-and-death process. For this system, performance reliability measures; the up and down periods, and the involved costs are calculated in a matrix and algorithmic form. We show that the discrete case is not a trivial case of the continuous one. The results given in this paper have been implemented computationally with Matlab
Modelling a reliability system governed by discrete phase-type distributions
Energy Technology Data Exchange (ETDEWEB)
Ruiz-Castro, Juan Eloy [Departamento de Estadistica e Investigacion Operativa, Universidad de Granada, 18071 Granada (Spain)], E-mail: jeloy@ugr.es; Perez-Ocon, Rafael [Departamento de Estadistica e Investigacion Operativa, Universidad de Granada, 18071 Granada (Spain)], E-mail: rperezo@ugr.es; Fernandez-Villodre, Gemma [Departamento de Estadistica e Investigacion Operativa, Universidad de Granada, 18071 Granada (Spain)
2008-11-15
We present an n-system with one online unit and the others in cold standby. There is a repairman. When the online fails it goes to repair, and instantaneously a standby unit becomes the online one. The operational and repair times follow discrete phase-type distributions. Given that any discrete distribution defined on the positive integers is a discrete phase-type distribution, the system can be considered a general one. A model with unlimited number of units is considered for approximating a system with a great number of units. We show that the process that governs the system is a quasi-birth-and-death process. For this system, performance reliability measures; the up and down periods, and the involved costs are calculated in a matrix and algorithmic form. We show that the discrete case is not a trivial case of the continuous one. The results given in this paper have been implemented computationally with Matlab.
Stabilization of multiple rib fractures in a canine model.
Huang, Ke-Nan; Xu, Zhi-Fei; Sun, Ju-Xian; Ding, Xin-Yu; Wu, Bin; Li, Wei; Qin, Xiong; Tang, Hua
2014-12-01
Operative stabilization is frequently used in the clinical treatment of multiple rib fractures (MRF); however, no ideal material exists for use in this fixation. This study investigates a newly developed biodegradable plate system for the stabilization of MRF. Silk fiber-reinforced polycaprolactone (SF/PCL) plates were developed for rib fracture stabilization and studied using a canine flail chest model. Adult mongrel dogs were divided into three groups: one group received the SF/PCL plates, one group received standard clinical steel plates, and the final group did not undergo operative fracture stabilization (n = 6 for each group). Radiographic, mechanical, and histologic examination was performed to evaluate the effectiveness of the biodegradable material for the stabilization of the rib fractures. No nonunion and no infections were found when using SF-PCL plates. The fracture sites collapsed in the untreated control group, leading to obvious chest wall deformity not encountered in the two groups that underwent operative stabilization. Our experimental study shows that the SF/PCL plate has the biocompatibility and mechanical strength suitable for fixation of MRF and is potentially ideal for the treatment of these injuries. Copyright © 2014 Elsevier Inc. All rights reserved.
Numerical modeling of ductile tearing effects on cleavage fracture toughness
International Nuclear Information System (INIS)
Dodds, R.H. Jr.; Tang, M.; Anderson, T.L.
1994-05-01
Experimental studies demonstrate a significant effect of specimen size, a/W ratio and prior ductile tearing on cleavage fracture toughness values (J c ) measured in the ductile-to-brittle transition region of ferritic materials. In the lower-transition region, cleavage fracture often occurs under conditions of large-scale yielding but without prior ductile crack extension. The increased toughness develops when plastic zones formed at the crack tip interact with nearby specimen surfaces which relaxes crack-tip constraint (stress triaxiality). In the mid-to-upper transition region, small amounts of ductile crack extension (often c -values. Previous work by the authors described a micromechanics fracture model to correct measured J c -values for the mechanistic effects of large-scale yielding. This new work extends the model to also include the influence of ductile crack extension prior to cleavage. The paper explores development of the new model, provides necessary graphs and procedures for its application and demonstrates the effects of the model on fracture data sets for two pressure vessel steels (A533B and A515)
2016-04-01
AND ROTORCRAFT FROM DISCRETE -POINT LINEAR MODELS Eric L. Tobias and Mark B. Tischler Aviation Development Directorate Aviation and Missile...Stitching Architecture for Continuous Full Flight-Envelope Simulation of Fixed-Wing Aircraft and Rotorcraft from Discrete -Point Linear Models 5...of discrete -point linear models and trim data. The model stitching simulation architecture is applicable to any aircraft configuration readily
Directory of Open Access Journals (Sweden)
Hideki Katagiri
2017-10-01
Full Text Available This paper considers linear programming problems (LPPs where the objective functions involve discrete fuzzy random variables (fuzzy set-valued discrete random variables. New decision making models, which are useful in fuzzy stochastic environments, are proposed based on both possibility theory and probability theory. In multi-objective cases, Pareto optimal solutions of the proposed models are newly defined. Computational algorithms for obtaining the Pareto optimal solutions of the proposed models are provided. It is shown that problems involving discrete fuzzy random variables can be transformed into deterministic nonlinear mathematical programming problems which can be solved through a conventional mathematical programming solver under practically reasonable assumptions. A numerical example of agriculture production problems is given to demonstrate the applicability of the proposed models to real-world problems in fuzzy stochastic environments.
Modeling of the fracture behavior of spot welds using advanced micro-mechanical damage models
International Nuclear Information System (INIS)
Sommer, Silke
2010-01-01
This paper presents the modeling of deformation and fracture behavior of resistance spot welded joints in DP600 steel sheets. Spot welding is still the most commonly used joining technique in automotive engineering. In overloading situations like crash joints are often the weakest link in a structure. For those reasons, crash simulations need reliable and applicable tools to predict the load bearing capacity of spot welded components. Two series of component tests with different spot weld diameters have shown that the diameter of the weld nugget is the main influencing factor affecting fracture mode (interfacial or pull-out fracture), load bearing capacity and energy absorption. In order to find a correlation between nugget diameter, load bearing capacity and fracture mode, the spot welds are simulated with detailed finite element models containing base metal, heat affected zone and weld metal in lap-shear loading conditions. The change in fracture mode from interfacial to pull-out or peel-out fracture with growing nugget diameter under lap-shear loading was successfully modeled using the Gologanu-Leblond model in combination with the fracture criteria of Thomason and Embury. A small nugget diameter is identified to be the main cause for interfacial fracture. In good agreement with experimental observations, the calculated pull-out fracture initiates in the base metal at the boundary to the heat affected zone.
Li, Kewei; Ogden, Ray W; Holzapfel, Gerhard A
2018-01-01
Recently, micro-sphere-based methods derived from the angular integration approach have been used for excluding fibres under compression in the modelling of soft biological tissues. However, recent studies have revealed that many of the widely used numerical integration schemes over the unit sphere are inaccurate for large deformation problems even without excluding fibres under compression. Thus, in this study, we propose a discrete fibre dispersion model based on a systematic method for discretizing a unit hemisphere into a finite number of elementary areas, such as spherical triangles. Over each elementary area, we define a representative fibre direction and a discrete fibre density. Then, the strain energy of all the fibres distributed over each elementary area is approximated based on the deformation of the representative fibre direction weighted by the corresponding discrete fibre density. A summation of fibre contributions over all elementary areas then yields the resultant fibre strain energy. This treatment allows us to exclude fibres under compression in a discrete manner by evaluating the tension-compression status of the representative fibre directions only. We have implemented this model in a finite-element programme and illustrate it with three representative examples, including simple tension and simple shear of a unit cube, and non-homogeneous uniaxial extension of a rectangular strip. The results of all three examples are consistent and accurate compared with the previously developed continuous fibre dispersion model, and that is achieved with a substantial reduction of computational cost. © 2018 The Author(s).
Modulational instability and discrete breathers in a nonlinear helicoidal lattice model
Ding, Jinmin; Wu, Tianle; Chang, Xia; Tang, Bing
2018-06-01
We investigate the problem on the discrete modulation instability of plane waves and discrete breather modes in a nonlinear helicoidal lattice model, which is described by a discrete nonlinear Schrödinger equation with the first-, second-, and third-neighbor coupling. By means of the linear stability analysis, we present an analytical expression of the instability growth rate and identify the regions of modulational instability of plane waves. It is shown that the introduction of the third-neighbor coupling will affect the shape of the areas of modulational instability significantly. Based on the results obtained by the modulational instability analysis, we predict the existence conditions for the stationary breather modes. Otherwise, by making use of the semidiscrete multiple-scale method, we obtain analytical solutions of discrete breather modes and analyze their properties for different types of nonlinearities. Our results show that the discrete breathers obtained are stable for a long time only when the system exhibits the repulsive nonlinearity. In addition, it is found that the existence of the stable bright discrete breather closely relates to the presence of the third-neighbor coupling.
Pipe fracture evaluations for leak-rate detection: Probabilistic models
International Nuclear Information System (INIS)
Rahman, S.; Wilkowski, G.; Ghadiali, N.
1993-01-01
This is the second in series of three papers generated from studies on nuclear pipe fracture evaluations for leak-rate detection. This paper focuses on the development of novel probabilistic models for stochastic performance evaluation of degraded nuclear piping systems. It was accomplished here in three distinct stages. First, a statistical analysis was conducted to characterize various input variables for thermo-hydraulic analysis and elastic-plastic fracture mechanics, such as material properties of pipe, crack morphology variables, and location of cracks found in nuclear piping. Second, a new stochastic model was developed to evaluate performance of degraded piping systems. It is based on accurate deterministic models for thermo-hydraulic and fracture mechanics analyses described in the first paper, statistical characterization of various input variables, and state-of-the-art methods of modem structural reliability theory. From this model. the conditional probability of failure as a function of leak-rate detection capability of the piping systems can be predicted. Third, a numerical example was presented to illustrate the proposed model for piping reliability analyses. Results clearly showed that the model provides satisfactory estimates of conditional failure probability with much less computational effort when compared with those obtained from Monte Carlo simulation. The probabilistic model developed in this paper will be applied to various piping in boiling water reactor and pressurized water reactor plants for leak-rate detection applications
Directory of Open Access Journals (Sweden)
Chellaboina Vijaysekhar
2005-01-01
Full Text Available We develop thermodynamic models for discrete-time large-scale dynamical systems. Specifically, using compartmental dynamical system theory, we develop energy flow models possessing energy conservation, energy equipartition, temperature equipartition, and entropy nonconservation principles for discrete-time, large-scale dynamical systems. Furthermore, we introduce a new and dual notion to entropy; namely, ectropy, as a measure of the tendency of a dynamical system to do useful work and grow more organized, and show that conservation of energy in an isolated thermodynamic system necessarily leads to nonconservation of ectropy and entropy. In addition, using the system ectropy as a Lyapunov function candidate, we show that our discrete-time, large-scale thermodynamic energy flow model has convergent trajectories to Lyapunov stable equilibria determined by the system initial subsystem energies.
Ductile fracture theories for pressurised pipes and containers
Erdogan, F.
1976-01-01
Two mechanisms of fracture are distinguished. Plane strain fractures occur in materials which do not undergo large-scale plastic deformations prior to and during a possible fracture deformation. Plane stress or high energy fractures are generally accompanied by large inelastic deformations. Theories for analyzing plane stress are based on the concepts of critical crack opening stretch, K(R) characterization, J-integral, and plastic instability. This last is considered in some detail. The ductile fracture process involves fracture initiation followed by a stable crack growth and the onset of unstable fracture propagation. The ductile fracture propagation process may be characterized by either a multiparameter (discrete) model, or some type of a resistance curve which may be considered as a continuous model expressed graphically. These models are studied and an alternative model is also proposed for ductile fractures which cannot be modeled as progressive crack growth phenomena.
Bounded Model Checking and Inductive Verification of Hybrid Discrete-Continuous Systems
DEFF Research Database (Denmark)
Becker, Bernd; Behle, Markus; Eisenbrand, Fritz
2004-01-01
We present a concept to signicantly advance the state of the art for bounded model checking (BMC) and inductive verication (IV) of hybrid discrete-continuous systems. Our approach combines the expertise of partners coming from dierent domains, like hybrid systems modeling and digital circuit veri...
A discrete-choice model with social interactions : With an application to high school teen behavior
Soetevent, Adriaan R.; Kooreman, Peter
2007-01-01
We develop an empirical discrete-choice interaction model with a finite number of agents. We characterize its equilibrium properties-in particular the correspondence between interaction strength, number of agents, and the set of equilibria-and propose to estimate the model by means of simulation
Kemp, Steven; Madden, Gary; Simpson, Michael
1998-01-01
Isolates factors influencing choice of Australia as a preferred destination for international students in emerging regional markets. Uses data obtained from a survey of students in Indonesia and Taiwan to estimate a U.S./Australia and rest-of-world/Australia discrete destination-choice model. This model identifies key factors determining country…
The problem with time in mixed continuous/discrete time modelling
Rovers, K.C.; Kuper, Jan; Smit, Gerardus Johannes Maria
The design of cyber-physical systems requires the use of mixed continuous time and discrete time models. Current modelling tools have problems with time transformations (such as a time delay) or multi-rate systems. We will present a novel approach that implements signals as functions of time,
Kellen, David; Klauer, Karl Christoph
2014-01-01
A classic discussion in the recognition-memory literature concerns the question of whether recognition judgments are better described by continuous or discrete processes. These two hypotheses are instantiated by the signal detection theory model (SDT) and the 2-high-threshold model, respectively. Their comparison has almost invariably relied on…
Achievement Goals and Discrete Achievement Emotions: A Theoretical Model and Prospective Test
Pekrun, Reinhard; Elliot, Andrew J.; Maier, Markus A.
2006-01-01
A theoretical model linking achievement goals to discrete achievement emotions is proposed. The model posits relations between the goals of the trichotomous achievement goal framework and 8 commonly experienced achievement emotions organized in a 2 (activity/outcome focus) x 2 (positive/negative valence) taxonomy. Two prospective studies tested…
A discrete choice model with social interactions; with an application to high school teen behavior
Soetevent, Adriaan R.; Kooreman, Peter
2004-01-01
We develop an empirical discrete choice interaction model with a finite number of agents. We characterize its equilibrium properties - in particular the correspondence between the interaction strength, the number of agents, and the set of equilibria - and propose to estimate the model by means of
A discrete choice model with social interactions; with an application to high school teen behavior
Soetevent, A.R.; Kooreman, P.
2007-01-01
We develop an empirical discrete-choice interaction model with a finite number of agents. We characterize its equilibrium properties - in particular the correspondence between interaction strength, number of agents, and the set of equilibria - and propose to estimate the model by means of simulation
Modarres, Reza; Ouarda, Taha B. M. J.; Vanasse, Alain; Orzanco, Maria Gabriela; Gosselin, Pierre
2014-07-01
Changes in extreme meteorological variables and the demographic shift towards an older population have made it important to investigate the association of climate variables and hip fracture by advanced methods in order to determine the climate variables that most affect hip fracture incidence. The nonlinear autoregressive moving average with exogenous variable-generalized autoregressive conditional heteroscedasticity (ARMA X-GARCH) and multivariate GARCH (MGARCH) time series approaches were applied to investigate the nonlinear association between hip fracture rate in female and male patients aged 40-74 and 75+ years and climate variables in the period of 1993-2004, in Montreal, Canada. The models describe 50-56 % of daily variation in hip fracture rate and identify snow depth, air temperature, day length and air pressure as the influencing variables on the time-varying mean and variance of the hip fracture rate. The conditional covariance between climate variables and hip fracture rate is increasing exponentially, showing that the effect of climate variables on hip fracture rate is most acute when rates are high and climate conditions are at their worst. In Montreal, climate variables, particularly snow depth and air temperature, appear to be important predictors of hip fracture incidence. The association of climate variables and hip fracture does not seem to change linearly with time, but increases exponentially under harsh climate conditions. The results of this study can be used to provide an adaptive climate-related public health program and ti guide allocation of services for avoiding hip fracture risk.
Using outcrop data for geological well test modelling in fractured reservoirs
Aljuboori, F.; Corbett, P.; Bisdom, K.; Bertotti, G.; Geiger, S.
2015-01-01
Outcrop fracture data sets can now be acquired with ever more accuracy using drone technology augmented by field observations. These models can be used to form realistic, deterministic models of fractured reservoirs. Fractured well test models are traditionally seen to be finite or infinite