Compartmentalization analysis using discrete fracture network models
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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.
Hydrofracture Modeling Using Discrete Fracture Network in Barnett Shale
Yaghoubi, A.; Zoback, M. D.
2012-12-01
Shale gas has become an important source of unconventional reservoir in the united state over the past decade. Since the shale gas formations are impermeable, hydraulic fracturing from vertical and horizontal well are commonly approach to extract natural gas deposit from these unconventional sources. Hydraulic fracturing has been a successful and relatively inexpensive stimulation method for stimulation and enhances hydrocarbon recovery. Multistage hydro fracturing treatments in horizontal well creates a large stimulated reservoir volume. However, modeling hydraulic fracturing requires to prior knowledge of natural fracture network. This problem can be deal with Discrete Fracture network modeling. The objective of this study is first to model discrete fracture network and then simulate hydro-fracturing in five horizontal well of a case study in Barnett shale gas reservoir. In the case study, five horizontal wells have been drilled in Barnett shale gas reservoir in which each of them has 10 stages of hydro-fracturing stimulation. Of all five wells, just well C has a full comprehensive logging data. Fracture date detected using FMI image log of well C for building DFN model are associated with different sources of uncertainty; orientation, density and length. After building reservoir geomechanics model and detecting natural fracture form image log from well C, DFN model has built based on fracture parameters, orientation, intensity, shape size and permeability detected from image log and core data. Modeling hydrofractuing in five wells are consistent with critically stressed-fracture and micro-seismic events.
An analytical thermohydraulic model for discretely fractured geothermal reservoirs
Fox, Don B.; Koch, Donald L.; Tester, Jefferson W.
2016-09-01
In discretely fractured reservoirs such as those found in Enhanced/Engineered Geothermal Systems (EGS), knowledge of the fracture network is important in understanding the thermal hydraulics, i.e., how the fluid flows and the resulting temporal evolution of the subsurface temperature. The purpose of this study was to develop an analytical model of the fluid flow and heat transport in a discretely fractured network that can be used for a wide range of modeling applications and serve as an alternative analysis tool to more computationally intensive numerical codes. Given the connectivity and structure of a fracture network, the flow in the system was solved using a linear system of algebraic equations for the pressure at the nodes of the network. With the flow determined, the temperature in the fracture was solved by coupling convective heat transport in the fracture with one-dimensional heat conduction perpendicular to the fracture, employing the Green's function derived solution for a single discrete fracture. The predicted temperatures along the fracture surfaces from the analytical solution were compared to numerical simulations using the TOUGH2 reservoir code. Through two case studies, we showed the capabilities of the analytical model and explored the effect of uncertainty in the fracture apertures and network structure on thermal performance. While both sources of uncertainty independently produce large variations in production temperature, uncertainty in the network structure, whenever present, had a predominant influence on thermal performance.
Hydraulic fracturing model based on the discrete fracture model and the generalized J integral
Liu, Z. Q.; Liu, Z. F.; Wang, X. H.; Zeng, B.
2016-08-01
The hydraulic fracturing technique is an effective stimulation for low permeability reservoirs. In fracturing models, one key point is to accurately calculate the flux across the fracture surface and the stress intensity factor. To achieve high precision, the discrete fracture model is recommended to calculate the flux. Using the generalized J integral, the present work obtains an accurate simulation of the stress intensity factor. Based on the above factors, an alternative hydraulic fracturing model is presented. Examples are included to demonstrate the reliability of the proposed model and its ability to model the fracture propagation. Subsequently, the model is used to describe the relationship between the geometry of the fracture and the fracturing equipment parameters. The numerical results indicate that the working pressure and the pump power will significantly influence the fracturing process.
Directory of Open Access Journals (Sweden)
Junling Fang
2017-02-01
Full Text Available This paper presents an integrated approach of discrete fracture network modelling for a naturally fractured buried-hill carbonate reservoir in the Jingbei Oilfield by using a 3D seismic survey, conventional well logs, and core data. The ant tracking attribute, extracted from 3D seismic data, is used to detect the faults and large-scale fractures. Fracture density and dip angle are evaluated by observing drilling cores of seven wells. The fracture density distribution in spatiality was predicted in four steps; firstly, the ant tracking attribute was extracted as a geophysical log; then an artificial neural network model was built by relating the fracture density with logs, e.g., acoustic, gamma ray, compensated neutron, density, and ant tracking; then 3D distribution models of acoustic, gamma ray, compensated neutron and density were generated by using a Gaussian random function simulation; and, finally, the fracture density distribution in 3D was predicted by using the generated artificial neural network model. Then, different methods were used to build the discrete fracture network model for different types of fractures of which large-scale fractures were modelled deterministically and small-scale fractures were modelled stochastically. The results show that the workflow presented in this study is effective for building discrete fracture network models for naturally fractured reservoirs.
Discrete modeling of hydraulic fracturing processes in a complex pre-existing fracture network
Kim, K.; Rutqvist, J.; Nakagawa, S.; Houseworth, J. E.; Birkholzer, J. T.
2015-12-01
Hydraulic fracturing and stimulation of fracture networks are widely used by the energy industry (e.g., shale gas extraction, enhanced geothermal systems) to increase permeability of geological formations. Numerous analytical and numerical models have been developed to help understand and predict the behavior of hydraulically induced fractures. However, many existing models assume simple fracturing scenarios with highly idealized fracture geometries (e.g., propagation of a single fracture with assumed shapes in a homogeneous medium). Modeling hydraulic fracture propagation in the presence of natural fractures and homogeneities can be very challenging because of the complex interactions between fluid, rock matrix, and rock interfaces, as well as the interactions between propagating fractures and pre-existing natural fractures. In this study, the TOUGH-RBSN code for coupled hydro-mechanical modeling is utilized to simulate hydraulic fracture propagation and its interaction with pre-existing fracture networks. The simulation tool combines TOUGH2, a simulator of subsurface multiphase flow and mass transport based on the finite volume approach, with the implementation of a lattice modeling approach for geomechanical and fracture-damage behavior, named Rigid-Body-Spring Network (RBSN). The discrete fracture network (DFN) approach is facilitated in the Voronoi discretization via a fully automated modeling procedure. The numerical program is verified through a simple simulation for single fracture propagation, in which the resulting fracture geometry is compared to an analytical solution for given fracture length and aperture. Subsequently, predictive simulations are conducted for planned laboratory experiments using rock-analogue (soda-lime glass) samples containing a designed, pre-existing fracture network. The results of a preliminary simulation demonstrate selective fracturing and fluid infiltration along the pre-existing fractures, with additional fracturing in part
Hao, Y.; Settgast, R. R.; Fu, P.; Tompson, A. F. B.; Morris, J.; Ryerson, F. J.
2016-12-01
It has long been recognized that multiphase flow and transport in fractured porous media is very important for various subsurface applications. Hydrocarbon fluid flow and production from hydraulically fractured shale reservoirs is an important and complicated example of multiphase flow in fractured formations. The combination of horizontal drilling and hydraulic fracturing is able to create extensive fracture networks in low permeability shale rocks, leading to increased formation permeability and enhanced hydrocarbon production. However, unconventional wells experience a much faster production decline than conventional hydrocarbon recovery. Maintaining sustainable and economically viable shale gas/oil production requires additional wells and re-fracturing. Excessive fracturing fluid loss during hydraulic fracturing operations may also drive up operation costs and raise potential environmental concerns. Understanding and modeling processes that contribute to decreasing productivity and fracturing fluid loss represent a critical component for unconventional hydrocarbon recovery analysis. Towards this effort we develop a discrete fracture model (DFM) in GEOS (LLNL multi-physics computational code) to simulate multiphase flow and transfer in hydraulically fractured reservoirs. The DFM model is able to explicitly account for both individual fractures and their surrounding rocks, therefore allowing for an accurate prediction of impacts of fracture-matrix interactions on hydrocarbon production. We apply the DFM model to simulate three-phase (water, oil, and gas) flow behaviors in fractured shale rocks as a result of different hydraulic stimulation scenarios. Numerical results show that multiphase flow behaviors at the fracture-matrix interface play a major role in controlling both hydrocarbon production and fracturing fluid recovery rates. The DFM model developed in this study will be coupled with the existing hydro-fracture model to provide a fully integrated
Characterization of fracture processes by continuum and discrete modelling
Kaliske, M.; Dal, H.; Fleischhauer, R.; Jenkel, C.; Netzker, C.
2012-09-01
A large number of methods to describe fracture mechanical features of structures on basis of computational algorithms have been developed in the past due to the importance of the topic. In this paper, current and promising numerical approaches for the characterization of fracture processes are presented. A fracture phenomenon can either be depicted by a continuum formulation or a discrete notch. Thus, starting point of the description is a micromechanically motivated formulation for the development of a local failure situation. A current, generalized method without any restriction to material modelling and loading situation in order to describe an existing crack in a structure is available through the material force approach. One possible strategy to simulate arbitrary crack growth is based on an adaptive implementation of cohesive elements in combination with the standard discretization of the body. In this case, crack growth criteria and the determination of the crack propagation direction in combination with the modification of the finite element mesh are required. The nonlinear structural behaviour of a fibre reinforced composite material is based on the heterogeneous microstructure. A two-scale simulation is therefore an appropriate and effective way to take into account the scale differences of macroscopic structures with microscopic elements. In addition, fracture mechanical structural properties are far from being sharp and deterministic. Moreover, a wide range of uncertainties influence the ultimate load bearing behaviour. Therefore, it is evident that the deterministic modelling has to be expanded by a characterization of the uncertainty in order to achieve a reliable and realistic simulation result. The employed methods are illustrated by numerical examples.
Application of Discrete Fracture Modeling and Upscaling Techniques to Complex Fractured Reservoirs
Karimi-Fard, M.; Lapene, A.; Pauget, L.
2012-12-01
During the last decade, an important effort has been made to improve data acquisition (seismic and borehole imaging) and workflow for reservoir characterization which has greatly benefited the description of fractured reservoirs. However, the geological models resulting from the interpretations need to be validated or calibrated against dynamic data. Flow modeling in fractured reservoirs remains a challenge due to the difficulty of representing mass transfers at different heterogeneity scales. The majority of the existing approaches are based on dual continuum representation where the fracture network and the matrix are represented separately and their interactions are modeled using transfer functions. These models are usually based on idealized representation of the fracture distribution which makes the integration of real data difficult. In recent years, due to increases in computer power, discrete fracture modeling techniques (DFM) are becoming popular. In these techniques the fractures are represented explicitly allowing the direct use of data. In this work we consider the DFM technique developed by Karimi-Fard et al. [1] which is based on an unstructured finite-volume discretization. The mass flux between two adjacent control-volumes is evaluated using an optimized two-point flux approximation. The result of the discretization is a list of control-volumes with the associated pore-volumes and positions, and a list of connections with the associated transmissibilities. Fracture intersections are simplified using a connectivity transformation which contributes considerably to the efficiency of the methodology. In addition, the method is designed for general purpose simulators and any connectivity based simulator can be used for flow simulations. The DFM technique is either used standalone or as part of an upscaling technique. The upscaling techniques are required for large reservoirs where the explicit representation of all fractures and faults is not possible
On adaptive refinements in discrete probabilistic fracture models
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J. Eliáš
2017-01-01
Full Text Available The possibility to adaptively change discretization density is a well acknowledged and used feature of many continuum models. It is employed to save computational time and increase solution accuracy. Recently, adaptivity has been introduced also for discrete particle models. This contribution applies adaptive technique in probabilistic discrete modelling where material properties are varying in space according to a random field. The random field discretization is adaptively refined hand in hand with the model geometry.
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.
Discrete Fracture Networks Groundwater Modelling at Bedding Control Fractured Sedimentary Rock mass
Pin, Yeh; Yuan-Chieh, Wu
2017-04-01
Groundwater flow modelling in fractured rock mass is an important challenging work in predicting the transport of contamination. So far as we know about the numerical analysis method was consider for crystalline rock, which means discontinuous are treated as stochastic distribution in homogeneous rock mass. Based on the understanding of geology in Taiwan in past few decades, we know that the hydraulic conductivities of Quaternary and Tertiary system rock mass are strongly controlled by development of sedimentary structures (bedding plane). The main purpose of this study is to understand how Discrete Fracture Networks (DFN) affects numerical results in terms of hydraulic behavior using different DFN generation methods. Base on surface geology investigation and core drilling work (3 boreholes with a total length of 120m), small scale fracture properties with in Cho-lan formation (muddy sandstone) are defined, including gently dip of bedding and 2 sub-vertical joint sets. Two FracMan/MAFIC numerical modellings are conducted, using ECPM approach (Equivalent Continuum Porous Media); case A considered all fracture were Power law distribution with Poisson fracture center; case B considered all bedding plans penetrate into modelling region, and remove the bedding count to recalculate joint fracture parameters. Modelling results show that Case B gives stronger groundwater pathways than Case A and have impact on flow field. This preliminary modelling result implicates the groundwater flow modelling work in some fractured sedimentary rock mass, might be considerate to rock sedimentary structure development itself, discontinuous maybe not follow the same stochastic DFN parameter.
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
Blessent, Daniela; Jørgensen, Peter R; Therrien, René
2014-01-01
We used the FRAC3Dvs numerical model (Therrien and Sudicky 1996) to compare the dual-porosity (DP), equivalent porous medium (EPM), and discrete fracture matrix diffusion (DFMD) conceptual models to predict field-scale contaminant transport in a fractured clayey till aquitard. The simulations show that the DP, EPM, and DFMD models could be equally well calibrated to reproduce contaminant breakthrough in the till aquitard for a base case. In contrast, when groundwater velocity and degradation rates are modified with respect to the base case, the DP method simulated contaminant concentrations up to three orders of magnitude different from those calculated by the DFMD model. In previous simulations of well-characterized column experiments, the DFMD method reproduced observed changes in solute transport for a range of flow and transport conditions comparable to those of the field-scale simulations, while the DP and EPM models required extensive recalibration to avoid high magnitude errors in predicted mass transport. The lack of robustness with respect to variable flow and transport conditions suggests that DP models and effective porosity EPM models have limitations for predicting cause-effect relationships in environmental planning. The study underlines the importance of obtaining well-characterized experimental data for further studies and evaluation of model key process descriptions and model suitability. © 2013, National Groundwater Association.
Discrete fracture network modeling of hydraulic stimulation coupling flow and geomechanics
McClure, Mark
2013-01-01
Discrete Fracture Network Modeling of Hydraulic Stimulation describes the development and testing of a model that couples fluid-flow, deformation, friction weakening, and permeability evolution in large, complex two-dimensional discrete fracture networks. The model can be used to explore the behavior of hydraulic stimulation in settings where matrix permeability is low and preexisting fractures play an important role, such as Enhanced Geothermal Systems and gas shale. Used also to describe pure shear stimulation, mixed-mechanism stimulation, or pure opening-mode stimulation. A variety of nov
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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.
Carbonate fracture stratigraphy: An integrated outcrop and 2D discrete element modelling study
Spence, Guy; Finch, Emma
2013-04-01
Constraining fracture stratigraphy is important as natural fractures control primary fluid flow in low matrix permeability naturally fractured carbonate hydrocarbon reservoirs. Away from the influence of folds and faults, stratigraphic controls are known to be the major control on fracture networks. The fracture stratigraphy of carbonate nodular-chert rhythmite successions are investigated using a Discrete Element Modelling (DEM) technique and validated against observations from outcrops. Comparisons are made to the naturally fractured carbonates of the Eocene Thebes Formation exposed in the west central Sinai of Egypt, which form reservoir rocks in the nearby East Ras Budran Field. DEM allows mechanical stratigraphy to be defined as the starting conditions from which forward numerical modelling can generate fracture stratigraphy. DEM can incorporate both stratigraphic and lateral heterogeneity, and enable mechanical and fracture stratigraphy to be characterised separately. Stratally bound stratified chert nodules below bedding surfaces generate closely spaced lateral heterogeneity in physical properties at stratigraphic mechanical interfaces. This generates extra complexity in natural fracture networks in addition to that caused by bed thickness and lithological physical properties. A series of representative geologically appropriate synthetic mechanical stratigraphic models were tested. Fracture networks generated in 15 DEM experiments designed to isolate and constrain the effects of nodular chert rhythmites on carbonate fracture stratigraphy are presented. The discrete element media used to model the elastic strengths of rocks contain 72,866 individual elements. Mechanical stratigraphies and the fracture networks generated are placed in a sequence stratigraphic framework. Nodular chert rhythmite successions are shown to be a distinct type of naturally fractured carbonate reservoir. Qualitative stratigraphic rules for predicting the distribution, lengths, spacing
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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
Directory of Open Access Journals (Sweden)
Qingdong Zeng
2015-10-01
Full Text Available Fluid-solid coupling is ubiquitous in the process of fluid flow underground and has a significant influence on the development of oil and gas reservoirs. To investigate these phenomena, the coupled mathematical model of solid deformation and fluid flow in fractured porous media is established. In this study, the discrete fracture model (DFM is applied to capture fluid flow in the fractured porous media, which represents fractures explicitly and avoids calculating shape factor for cross flow. In addition, the extended finite element method (XFEM is applied to capture solid deformation due to the discontinuity caused by fractures. More importantly, this model captures the change of fractures aperture during the simulation, and then adjusts fluid flow in the fractures. The final linear equation set is derived and solved for a 2D plane strain problem. Results show that the combination of discrete fracture model and extended finite element method is suited for simulating coupled deformation and fluid flow in fractured porous media.
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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
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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
A review of discrete modeling techniques for fracturing processes in discontinuous rock masses
Institute of Scientific and Technical Information of China (English)
A.Lisjak; G.Grasselli
2014-01-01
The goal of this review paper is to provide a summary of selected discrete element and hybrid finitee discrete element modeling techniques that have emerged in the field of rock mechanics as simulation tools for fracturing processes in rocks and rock masses. The fundamental principles of each computer code are illustrated with particular emphasis on the approach specifically adopted to simulate fracture nucleation and propagation and to account for the presence of rock mass discontinuities. This description is accom-panied by a brief review of application studies focusing on laboratory-scale models of rock failure processes and on the simulation of damage development around underground excavations.
A review of discrete modeling techniques for fracturing processes in discontinuous rock masses
Directory of Open Access Journals (Sweden)
A. Lisjak
2014-08-01
Full Text Available The goal of this review paper is to provide a summary of selected discrete element and hybrid finite–discrete element modeling techniques that have emerged in the field of rock mechanics as simulation tools for fracturing processes in rocks and rock masses. The fundamental principles of each computer code are illustrated with particular emphasis on the approach specifically adopted to simulate fracture nucleation and propagation and to account for the presence of rock mass discontinuities. This description is accompanied by a brief review of application studies focusing on laboratory-scale models of rock failure processes and on the simulation of damage development around underground excavations.
Discrete fracture modeling of hydro-mechanical damage processes in geological systems
Kim, K.; Rutqvist, J.; Houseworth, J. E.; Birkholzer, J. T.
2014-12-01
This study presents a modeling approach for investigating coupled thermal-hydrological-mechanical (THM) behavior, including fracture development, within geomaterials and structures. In the model, the coupling procedure consists of an effective linkage between two codes: TOUGH2, a simulator of subsurface multiphase flow and mass transport based on the finite volume approach; and an implementation of the rigid-body-spring network (RBSN) method, a discrete (lattice) modeling approach to represent geomechanical behavior. One main advantage of linking these two codes is that they share the same geometrical mesh structure based on the Voronoi discretization, so that a straightforward representation of discrete fracture networks (DFN) is available for fluid flow processes. The capabilities of the TOUGH-RBSN model are demonstrated through simulations of hydraulic fracturing, where fluid pressure-induced fracturing and damage-assisted flow are well represented. The TOUGH-RBSN modeling methodology has been extended to enable treatment of geomaterials exhibiting anisotropic characteristics. In the RBSN approach, elastic spring coefficients and strength parameters are systematically formulated based on the principal bedding direction, which facilitate a straightforward representation of anisotropy. Uniaxial compression tests are simulated for a transversely isotropic material to validate the new modeling scheme. The model is also used to simulate excavation fracture damage for the HG-A microtunnel in the Opalinus Clay rock, located at the Mont Terri underground research laboratory (URL) near Saint-Ursanne, Switzerland. The Opalinus Clay has transversely isotropic material properties caused by natural features such as bedding, foliation, and flow structures. Preferential fracturing and tunnel breakouts were observed following excavation, which are believed to be strongly influenced by the mechanical anisotropy of the rock material. The simulation results are qualitatively
Mendoza-Torres, F.; Diaz-Viera, M. A.
2015-12-01
In many natural fractured porous media, such as aquifers, soils, oil and geothermal reservoirs, fractures play a crucial role in their flow and transport properties. An approach that has recently gained popularity for modeling fracture systems is the Discrete Fracture Network (DFN) model. This approach consists in applying a stochastic boolean simulation method, also known as object simulation method, where fractures are represented as simplified geometric objects (line segments in 2D and polygons in 3D). One of the shortcomings of this approach is that it usually does not consider the dependency relationships that may exist between the geometric properties of fractures (direction, length, aperture, etc), that is, each property is simulated independently. In this work a method for modeling such dependencies by copula theory is introduced. In particular, a nonparametric model using Bernstein copulas for direction-length fracture dependency in 2D is presented. The application of this method is illustrated in a case study for a fractured rock sample from a carbonate reservoir outcrop.
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.
Geological discrete fracture network model for the Olkiluoto site, Eurajoki, Finland. Version 2.0
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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
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Zhou, Jing [Universiyt of Utah; Huang, Hai [Idaho National Lab. (INL), Idaho Falls, ID (United States); Deo, Milind
2015-10-01
The interaction between hydraulic fractures (HF) and natural fractures (NF) will lead to complex fracture networks due to the branching and merging of natural and hydraulic fractures in unconventional reservoirs. In this paper, a newly developed hydraulic fracturing simulator based on discrete element method is used to predict the generation of complex fracture network in the presence of pre-existing natural fractures. By coupling geomechanics and reservoir flow within a dual lattice system, this simulator can effectively capture the poro-elastic effects and fluid leakoff into the formation. When HFs are intercepting single or multiple NFs, complex mechanisms such as direct crossing, arresting, dilating and branching can be simulated. Based on the model, the effects of injected fluid rate and viscosity, the orientation and permeability of NFs and stress anisotropy on the HF-NF interaction process are investigated. Combined impacts from multiple parameters are also examined in the paper. The numerical results show that large values of stress anisotropy, intercepting angle, injection rate and viscosity will impede the opening of NFs.
Directory of Open Access Journals (Sweden)
Enan Chi
2015-06-01
Full Text Available The fracture and fragmentation of rock materials are basic and important problem in geomechanics and blasting engineering. An approach, which can simulate the process of fracture and fragmentation of rock materials, is introduced in this work. A beam–particle model is first introduced in the frame of the discrete element method. In the beam–particle model, the neighboring elements are connected by beams. Consequently, a beam network is formed in the particle system. The strength characteristics of rock materials are reflected by the beam network. The strength criterion was then built to verify whether a beam exists or not. The process of rock fracture and fragmentation is described by the gradual disappearance of beams. Finally, two cases were presented to indicate the validity of the method proposed in this work.
Discrete Modeling of Early-Life Thermal Fracture in Ceramic Nuclear Fuel
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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
Hu, Mengsu; Rutqvist, Jonny; Wang, Yuan
2017-04-01
In this study, a numerical manifold method (NMM) model was developed for fully coupled analysis of hydro-mechanical (HM) processes in porous rock masses with discrete fractures. Using an NMM two-cover-mesh system of mathematical and physical covers, fractures are conveniently discretized by dividing the mathematical cover along fracture traces to physical cover, resulting in a discontinuous model on a non-conforming mesh. In this model, discrete fracture deformation (e.g. open and slip) and fracture fluid flow within a permeable and deformable porous rock matrix are rigorously considered. For porous rock, direct pore-volume coupling was modeled based on an energy-work scheme. For mechanical analysis of fractures, a fracture constitutive model for mechanically open states was introduced. For fluid flow in fractures, both along-fracture and normal-to-fracture fluid flow are modeled without introducing additional degrees of freedom. When the mechanical aperture of a fracture is changing, its hydraulic aperture and hydraulic conductivity is updated. At the same time, under the effect of coupled deformation and fluid flow, the contact state may dynamically change, and the corresponding contact constraint is updated each time step. Therefore, indirect coupling is realized under stringent considerations of coupled HM effects and fracture constitutive behavior transfer dynamically. To verify the new model, examples involving deformable porous media containing a single and two sets of fractures were designed, showing good accuracy. Last, the model was applied to analyze coupled HM behavior of fractured porous rock domains with complex fracture networks under effects of loading and injection.
Discrete Fracture Network Models for Risk Assessment of Carbon Sequestration in Coal
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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
Lambert, Cédric; Thoeni, Klaus; Giacomini, Anna; Casagrande, Davide; Sloan, Scott
2012-09-01
Developing an accurate representation of the rock mass fabric is a key element in rock fall hazard analysis. The orientation, persistence and density of fractures control the volume and shape of unstable blocks or compartments. In this study, the discrete fracture modelling technique and digital photogrammetry were used to accurately depict the fabric. A volume distribution of unstable blocks was derived combining polyhedral modelling and kinematic analyses. For each block size, probabilities of failure and probabilities of propagation were calculated. A complete energy distribution was obtained by considering, for each block size, its occurrence in the rock mass, its probability of falling, its probability to reach a given location, and the resulting distribution of energies at each location. This distribution was then used with an energy-frequency diagram to assess the hazard.
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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
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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
Hu, Mengsu; Rutqvist, Jonny; Wang, Yuan
2016-11-01
In this study, a numerical manifold method (NMM) model is developed to analyze flow in porous media with discrete fractures in a non-conforming mesh. This new model is based on a two-cover-mesh system with a uniform triangular mathematical mesh and boundary/fracture-divided physical covers, where local independent cover functions are defined. The overlapping parts of the physical covers are elements where the global approximation is defined by the weighted average of the physical cover functions. The mesh is generated by a tree-cutting algorithm. A new model that does not introduce additional degrees of freedom (DOF) for fractures was developed for fluid flow in fractures. The fracture surfaces that belong to different physical covers are used to represent fracture flow in the direction of the fractures. In the direction normal to the fractures, the fracture surfaces are regarded as Dirichlet boundaries to exchange fluxes with the rock matrix. Furthermore, fractures that intersect with Dirichlet or Neumann boundaries are considered. Simulation examples are designed to verify the efficiency of the tree-cutting algorithm, the calculation's independency from the mesh orientation, and accuracy when modeling porous media that contain fractures with multiple intersections and different orientations. The simulation results show good agreement with available analytical solutions. Finally, the model is applied to cases that involve nine intersecting fractures and a complex network of 100 fractures, both of which achieve reasonable results. The new model is very practical for modeling flow in fractured porous media, even for a geometrically complex fracture network with large hydraulic conductivity contrasts between fractures and the matrix.
Statistical geological discrete fracture network model. Forsmark modelling stage 2.2
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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
Keralavarma, Shyam Mohan
behavior of a large number of nano and micro scale defects such as dislocations, vacancies and grain boundaries. Continuum models relate macroscopically observable quantities such as stress and strain by coarse graining the discrete defect microstructure. While continuum models provide a good approximation for the effective behavior of bulk materials, several deviations have been observed in experiments at small scales such as an intrinsic size dependence of the material strength. Discrete dislocation dynamics (DD) is a mesoscale method for obtaining the mechanical response of a material by direct simulation of the motion and interactions of dislocations. The model incorporates an intrinsic length scale in the dislocation Burgers vector and potentially allows for size dependent mechanical behavior to emerge naturally from the dynamics of the dislocation ensemble. In the second part of this dissertation, a simplified twodimensional DD model is employed to study several phenomena of practical interest such as strain hardening under homogeneous deformation, growth of microvoids in a crystalline matrix and creep of single crystals at elevated temperatures. These studies have been enabled by several recent enhancements to the existing two-dimensional DD framework described in Chapter V. The main contributions from this research are: (i) development of a fully anisotropic continuum model of void growth for use in ductile fracture simulations and (ii) enhancing the capabilities of an existing two-dimensional DD framework for large scale simulations in complex domains and at elevated temperatures.
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
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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.
Lei, Qinghua; Latham, John-Paul; Xiang, Jiansheng
2016-12-01
An empirical joint constitutive model (JCM) that captures the rough wall interaction behaviour of individual fractures associated with roughness characteristics observed in laboratory experiments is combined with the solid mechanical model of the finite-discrete element method (FEMDEM). The combined JCM-FEMDEM formulation gives realistic fracture behaviour with respect to shear strength, normal closure, and shear dilatancy and includes the recognition of fracture length influence as seen in experiments. The validity of the numerical model is demonstrated by a comparison with the experimentally established empirical solutions. A 2D plane strain geomechanical simulation is conducted using an outcrop-based naturally fractured rock model with far-field stresses loaded in two consecutive phases, i.e. take-up of isotropic stresses and imposition of two deviatoric stress conditions. The modelled behaviour of natural fractures in response to various stress conditions illustrates a range of realistic behaviour including closure, opening, shearing, dilatancy, and new crack propagation. With the increase in stress ratio, significant deformation enhancement occurs in the vicinity of fracture tips, intersections, and bends, where large apertures can be generated. The JCM-FEMDEM model is also compared with conventional approaches that neglect the scale dependency of joint properties or the roughness-induced additional frictional resistance. The results of this paper have important implications for understanding the geomechanical behaviour of fractured rocks in various engineering activities.
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Ito, Kazumasa; Yongkoo, Seol
2003-04-09
Water fluxes in unsaturated, fractured rock involve the physical processes occurring at fracture-matrix interfaces within fracture networks. Modeling these water fluxes using a discrete fracture network model is a complicated effort. Existing preprocessors for TOUGH2 are not suitable to generate grids for fracture networks with various orientations and inclinations. There are several 3-D discrete-fracture-network simulators for flow and transport, but most of them do not capture fracture-matrix interaction. We have developed a new 3-D discrete-fracture-network mesh generator, FRACMESH, to provide TOUGH2 with information about the fracture network configuration and fracture-matrix interactions. FRACMESH transforms a discrete fracture network into a 3 dimensional uniform mesh, in which fractures are considered as elements with unique rock material properties and connected to surrounding matrix elements. Using FRACMESH, individual fractures may have uniform or random aperture distributions to consider heterogeneity. Fracture element volumes and interfacial areas are calculated from fracture geometry within individual elements. By using FRACMESH and TOUGH2, fractures with various inclinations and orientations, and fracture-matrix interaction, can be incorporated. In this paper, results of flow and transport simulations in a fractured rock block utilizing FRACMESH are presented.
Profit, Matthew; Dutko, Martin; Yu, Jianguo; Cole, Sarah; Angus, Doug; Baird, Alan
2016-04-01
This paper presents a novel approach to predict the propagation of hydraulic fractures in tight shale reservoirs. Many hydraulic fracture modelling schemes assume that the fracture direction is pre-seeded in the problem domain discretisation. This is a severe limitation as the reservoir often contains large numbers of pre-existing fractures that strongly influence the direction of the propagating fracture. To circumvent these shortcomings, a new fracture modelling treatment is proposed where the introduction of discrete fracture surfaces is based on new and dynamically updated geometrical entities rather than the topology of the underlying spatial discretisation. Hydraulic fracturing is an inherently coupled engineering problem with interactions between fluid flow and fracturing when the stress state of the reservoir rock attains a failure criterion. This work follows a staggered hydro-mechanical coupled finite/discrete element approach to capture the key interplay between fluid pressure and fracture growth. In field practice, the fracture growth is hidden from the design engineer and microseismicity is often used to infer hydraulic fracture lengths and directions. Microseismic output can also be computed from changes of the effective stress in the geomechanical model and compared against field microseismicity. A number of hydraulic fracture numerical examples are presented to illustrate the new technology.
Cil, Mehmet B.; Alshibli, Khalid A.
2015-02-01
The constitutive behavior and deformation characteristics of uncemented granular materials are to a large extent derived from the fabric or geometry of the particle structure and the interparticle friction resulting from normal forces acting on particles or groups of particles. Granular materials consist of discrete particles with a fabric (microstructure) that changes under loading. Synchrotron micro-computed tomography (SMT) has emerged as a powerful non-destructive 3D scanning technique to study geomaterials. In this paper, SMT was used to acquire in situ scans of the oedometry test of a column of three silica sand particles. The sand is known as ASTM 20-30 Ottawa sand, and has a grain size between US sieves #20 (0.841 mm) and #30 (0.595 mm). The characteristics and evolution of particle fracture in sand were examined using SMT images, and a 3D discrete element method (DEM) was used to model the fracture behavior of sand particles. It adopts the bonded particle model to generate a crushable agglomerate that consists of a large number of small spherical sub-particles. The agglomerate shape matches the 3D physical shape of the tested sand particles by mapping the particle morphology from the SMT images. The paper investigates and discusses the influence of agglomerate packing (i.e., the number and size distribution of spherical sub-particles that constitute the agglomerate) and agglomerate shape on the fracture behavior of crushable particles.
Smart, Kevin J.; Wyrick, Danielle Y.; Ferrill, David A.
2011-04-01
Pit craters, circular to elliptical depressions that lack a raised rim or ejecta deposits, are common on the surface of Mars. Similar structures are also found on Earth, Venus, the Moon, and smaller planetary bodies, including some asteroids. While it is generally accepted that these pits form in response to material drainage into a subsurface void space, the primary mechanism(s) responsible for creating the void is a subject of debate. Previously proposed mechanisms include collapse into lave tubes, dike injection, extensional fracturing, and dilational normal faulting. In this study, we employ two-dimensional discrete element models to assess both extensional fracturing and dilational normal faulting as mechanisms for forming pit craters. We also examine the effect of mechanical stratigraphy (alternating strong and weak layers) and variation in regolith thickness on pit morphology. Our simulations indicate that both extensional fracturing and dilational normal faulting are viable mechanisms. Both mechanisms lead to generally convex (steepening downward) slope profiles; extensional fracturing results in generally symmetric pits, whereas dilational normal faulting produces strongly asymmetric geometries. Pit width is established early, whereas pit depth increases later in the deformation history. Inclusion of mechanical stratigraphy results in wider and deeper pits, particularly for the dilational normal faulting, and the presence of strong near-surface layers leads to pits with distinct edges as observed on Mars. The modeling results suggest that a thicker regolith leads to wider but shallower pits that are less distinct and may be more difficult to detect in areas of thick regolith.
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Hoch, A
1998-05-01
Groundwater flow in many low permeability rocks is believed to occur within discrete fractures. Radionuclides in solution can diffuse away from the fractures into immobile water in the rock matrix. This process (rock-matrix diffusion) is important in determining the performance of a repository situated in fractured rock because it retards the transport of radionuclides that might otherwise return more rapidly towards the biosphere. NAPSAC is a computer program used to model groundwater flow and radionuclide transport in fractured rock. This report describes the implementation of a rock-matrix diffusion model in NAPSAC. (author)
Gable, C. W.; Hyman, J.; Karra, S.; Makedonska, N.; Painter, S. L.; Viswanathan, H. S.
2015-12-01
dfnWorks generates discrete fracture networks (DFN) of planar polygons, creates a high quality conforming Delaunay triangulation of the intersecting DFN polygons, assigns properties (aperture, permeability) using geostatistics, sets boundary and initial conditions, solves pressure/flow in single or multi-phase fluids (water, air, CO2) using the parallel PFLOTRAN or serial FEHM, and solves for transport using Lagrangian particle tracking. We outline the dfnWorks workflow and present applications from a range of fractured rock systems. dfnWorks (http://www.lanl.gov/expertise/teams/view/dfnworks) is composed of three main components, all of which are freely available. dfnGen generates a distribution of fracture polygons from site characterization data (statistics or deterministic fractures) and utilizes the FRAM (Feature Rejection Algorithm for Meshing) to guarantee the mesh generation package LaGriT (lagrit.lanl.gov) will generate a high quality conforming Delaunay triangular mesh. dfnWorks links the mesh to either PFLOTRAN (pflotran.org) or FEHM (fehm.lanl.gov) for solving flow and transport. The various physics options available in FEHM and PFLOTRAN such as single and multi-phase flow and reactive transport are all available with appropriate initial and boundary conditions and material property models. dfnTrans utilizes explicit Lagrangian particle tracking on the DFN using a velocity field reconstructed from the steady state pressure/flow field solution obtained in PFLOTRAN or FEHM. Applications are demonstrated for nuclear waste repository in fractured granite, CO2 sequestration and extraction of unconventional hydrocarbon resources.
Discrete fracture network code development
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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)
Energy Technology Data Exchange (ETDEWEB)
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.
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...
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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.
Hodgetts, David; Seers, Thomas
2015-04-01
-deterministic, outcrop constrained discrete fracture network modeling code to derive volumetric fault intensity measures (fault area per unit volume / fault volume per unit volume). Producing per-vertex measures of volumetric intensity; our method captures the spatial variability in 3D fault density across a surveyed outcrop, enabling first order controls to be probed. We demonstrate our approach on pervasively faulted exposures of a Permian aged reservoir analogue from the Vale of Eden Basin, UK.
Three-phase flow simulations in discrete fracture networks
Geiger, S.; Niessner, J.; Matthai, S. K.; Helmig, R.
2006-12-01
Fractures are often the key conduits for fluid flow in otherwise low permeability rocks. Their presence in hydrocarbon reservoirs leads to complex production histories, unpredictable coupling of wells, rapidly changing flow rates, possibly early water breakthrough, and low final recovery. Recently, it has been demonstrated that a combination of finite volume and finite element discretization is well suited to model incompressible, immiscible two-phase flow in 3D discrete fracture networks (DFN) representing complexly fractured rocks. Such an approach has been commercialized in Golder Associates' FracMan Reservoir Edition software. For realistic reservoir simulations, however, it would be desirable if a third compressible gas phase can be included which is often present at reservoir conditions. Here we present the extension of an existing node-centred finite volume - finite element (FEFV) discretization for the efficient and accurate simulations of three-component - three-phase flow in geologically realistic representations of fractured porous media. Two possible types of fracture networks can be used: In 2D, they are detailed geometrical representations of fractured rock masses mapped in field studies. In 3D, they are geologically constrained, stochastically generated discrete fracture networks. Flow and transport can be simulated for fractures only or for fractures and matrix combined. The governing equations are solved decoupled using an implicit-pressure, explicit-saturation (IMPES) approach. Flux and concentration terms can be treated with higher-order accuracy in the finite volume scheme to preserve shock fronts. The method is locally mass conservative and works on unstructured, spatially refined grids. Flash calculations are carried out by a new description of the Black-Oil model. Capillary and gravity effects are included in this formulation. The robustness and accuracy of this formulation is shown in several applications. First, grid convergence is
Wang, Peitao; Cai, Meifeng; Ren, Fenhua; Li, Changhong; Yang, Tianhong
2017-07-01
This paper develops a numerical approach to determine the mechanical behavior of discrete fractures network (DFN) models based on digital image processing technique and particle flow code (PFC2D). A series of direct shear tests of jointed rocks were numerically performed to study the effect of normal stress, friction coefficient and joint bond strength on the mechanical behavior of joint rock and evaluate the influence of micro-parameters on the shear properties of jointed rocks using the proposed approach. The complete shear stress-displacement curve of the DFN model under direct shear tests was presented to evaluate the failure processes of jointed rock. The results show that the peak and residual strength are sensitive to normal stress. A higher normal stress has a greater effect on the initiation and propagation of cracks. Additionally, an increase in the bond strength ratio results in an increase in the number of both shear and normal cracks. The friction coefficient was also found to have a significant influence on the shear strength and shear cracks. Increasing in the friction coefficient resulted in the decreasing in the initiation of normal cracks. The unique contribution of this paper is the proposed modeling technique to simulate the mechanical behavior of jointed rock mass based on particle mechanics approaches.
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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.
Follin, Sven; Hartley, Lee; Rhén, Ingvar; Jackson, Peter; Joyce, Steven; Roberts, David; Swift, Ben
2014-03-01
The large-scale geological structure of the crystalline rock at the proposed high-level nuclear waste repository site at Forsmark, Sweden, has been classified in terms of deformation zones of elevated fracture frequency. The rock between deformation zones was divided into fracture domains according to fracture frequency. A methodology to constrain the geometric and hydraulic parameters that define a discrete fracture network (DFN) model for each fracture domain is presented. The methodology is based on flow logging and down-hole imaging in cored boreholes in combination with DFN realizations, fracture connectivity analysis and pumping test simulations. The simulations suggest that a good match could be obtained for a power law size distribution where the value of the location parameter equals the borehole radius but with different values for the shape parameter, depending on fracture domain and fracture set. Fractures around 10-100 m in size are the ones that typically form the connected network, giving inflows in the simulations. The report also addresses the issue of up-scaling of DFN properties to equivalent continuous porous medium (ECPM) bulk flow properties. Comparisons with double-packer injection tests provide confidence that the derived DFN formulation of detailed flows within individual fractures is also suited to simulating mean bulk flow properties and their spatial variability.
Discrete fracture network for the Forsmark site
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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 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...
Towards effective flow simulations in realistic discrete fracture networks
Berrone, Stefano; Pieraccini, Sandra; Scialò, Stefano
2016-04-01
We focus on the simulation of underground flow in fractured media, modeled by means of Discrete Fracture Networks. Focusing on a new recent numerical approach proposed by the authors for tackling the problem avoiding mesh generation problems, we further improve the new family of methods making a step further towards effective simulations of large, multi-scale, heterogeneous networks. Namely, we tackle the imposition of Dirichlet boundary conditions in weak form, in such a way that geometrical complexity of the DFN is not an issue; we effectively solve DFN problems with fracture transmissivities spanning many orders of magnitude and approaching zero; furthermore, we address several numerical issues for improving the numerical solution also in quite challenging networks.
Jia, Pin; Cheng, Linsong; Huang, Shijun; Xu, Zhongyi; Xue, Yongchao; Cao, Renyi; Ding, Guanyang
2017-08-01
This paper provides a comprehensive model for the flow behavior of a two-zone system with discrete fracture network. The discrete fracture network within the inner zone is represented explicitly by fracture segments. The Laplace-transform finite-difference method is used to numerically model discrete fracture network flow, with sufficient flexibility to consider arbitrary fracture geometries and conductivity distributions. Boundary-element method and line-source functions in the Laplace domain are employed to derive a semi-analytical flow solution for the two-zone system. By imposing the continuity of flux and pressure on discrete fracture surfaces, the semi-analytical two-zone system flow model and the numerical fracture flow model are coupled dynamically. The main advantage of the approach occurring in the Laplace domain is that simulation can be done with nodes only for discrete fractures and elements for boundaries and at predetermined, discrete times. Thus, stability and convergence problems caused by time discretization are avoided and the burden of gridding and computation is decreased without loss of important fracture characteristics. The model is validated by comparison with the results from an analytical solution and a fully numerical solution. Flow regime analysis shows that a two-zone system with discrete fracture network may develop six flow regimes: fracture linear flow, bilinear flow, inner zone linear flow, inner zone pseudosteady-state flow, outer zone pseudoradial flow and outer zone boundary-dominated flow. Especially, local solutions for the inner-zone linear flow have the same form with that of a finite conductivity planar fracture and can be correlated with the total length of discrete fractures and an intercept term. In the inner zone pseudosteady-state flow period, the discrete fractures, along with the boundary of the inner zone, will act as virtual closed boundaries, due to the pressure interference caused by fracture network and the
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.
Energy Technology Data Exchange (ETDEWEB)
McKoy, M.L., Sams, W.N.
1997-10-01
The US Department of Energy, Federal Energy Technology Center, has sponsored a project to simulate the behavior of tight, fractured, strata-bound gas reservoirs that arise from irregular discontinuous, or clustered networks of fractures. New FORTRAN codes have been developed to generate fracture networks, or simulate reservoir drainage/recharge, and to plot the fracture networks and reservoirs pressures. Ancillary codes assist with raw data analysis.
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
Salinelli, Ernesto
2014-01-01
This book provides an introduction to the analysis of discrete dynamical systems. The content is presented by an unitary approach that blends the perspective of mathematical modeling together with the ones of several discipline as Mathematical Analysis, Linear Algebra, Numerical Analysis, Systems Theory and Probability. After a preliminary discussion of several models, the main tools for the study of linear and non-linear scalar dynamical systems are presented, paying particular attention to the stability analysis. Linear difference equations are studied in detail and an elementary introduction of Z and Discrete Fourier Transform is presented. A whole chapter is devoted to the study of bifurcations and chaotic dynamics. One-step vector-valued dynamical systems are the subject of three chapters, where the reader can find the applications to positive systems, Markov chains, networks and search engines. The book is addressed mainly to students in Mathematics, Engineering, Physics, Chemistry, Biology and Economic...
Brauer, Fred; Feng, Zhilan; Castillo-Chavez, Carlos
2010-01-01
The mathematical theory of single outbreak epidemic models really began with the work of Kermack and Mackendrick about decades ago. This gave a simple answer to the long-standing question of why epidemics woould appear suddenly and then disappear just as suddenly without having infected an entire population. Therefore it seemed natural to expect that theoreticians would immediately proceed to expand this mathematical framework both because the need to handle recurrent single infectious disease outbreaks has always been a priority for public health officials and because theoreticians often try to push the limits of exiting theories. However, the expansion of the theory via the inclusion of refined epidemiological classifications or through the incorporation of categories that are essential for the evaluation of intervention strategies, in the context of ongoing epidemic outbreaks, did not materialize. It was the global threat posed by SARS in that caused theoreticians to expand the Kermack-McKendrick single-outbreak framework. Most recently, efforts to connect theoretical work to data have exploded as attempts to deal with the threat of emergent and re-emergent diseases including the most recent H1N1 influenza pandemic, have marched to the forefront of our global priorities. Since data are collected and/or reported over discrete units of time, developing single outbreak models that fit collected data naturally is relevant. In this note, we introduce a discrete-epidemic framework and highlight, through our analyses, the similarities between single-outbreak comparable classical continuous-time epidemic models and the discrete-time models introduced in this note. The emphasis is on comparisons driven by expressions for the final epidemic size.
Makedonska, Nataliia; Hyman, Jeffrey D.; Karra, Satish; Painter, Scott L.; Gable, Carl W.; Viswanathan, Hari S.
2016-08-01
The apertures of natural fractures in fractured rock are highly heterogeneous. However, in-fracture aperture variability is often neglected in flow and transport modeling and individual fractures are assumed to have uniform aperture distribution. The relative importance of in-fracture variability in flow and transport modeling within kilometer-scale field-scale fracture networks has been under a matter of debate for a long time because the flow in each single fracture is controlled not only by in-fracture variability but also by boundary conditions. Computational limitations have previously prohibited researchers from investigating the relative importance of in-fracture variability in flow and transport modeling within large-scale fracture networks. We address this question by incorporating internal heterogeneity of individual fractures into flow simulations within kilometer scale three-dimensional fracture networks, where fracture intensity, P32 (ratio between total fracture area and domain volume) is between 0.027 and 0.031 [1/m]. A recently developed discrete fracture network (DFN) simulation capability, dfnWorks, is used to generate DFNs that include in-fracture aperture variability represented by a stationary log-normal stochastic field with various correlation lengths and variances. The Lagrangian transport parameters, non-reacting travel time and cumulative retention, are calculated along particles streamlines. It is observed that due to local flow channeling early particle travel times are more sensitive to in-fracture variability than the tails of travel time distributions, where no significant effect of the in-fracture transmissivity variations and spatial correlation length is observed.
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.
Hadgu, Teklu; Karra, Satish; Kalinina, Elena; Makedonska, Nataliia; Hyman, Jeffrey D.; Klise, Katherine; Viswanathan, Hari S.; Wang, Yifeng
2017-10-01
One of the major challenges of simulating flow and transport in the far field of a geologic repository in crystalline host rock is related to reproducing the properties of the fracture network over the large volume of rock with sparse fracture characterization data. Various approaches have been developed to simulate flow and transport through the fractured rock. The approaches can be broadly divided into Discrete Fracture Network (DFN) and Equivalent Continuum Model (ECM). The DFN explicitly represents individual fractures, while the ECM uses fracture properties to determine equivalent continuum parameters. We compare DFN and ECM in terms of upscaled observed transport properties through generic fracture networks. The major effort was directed on making the DFN and ECM approaches similar in their conceptual representations. This allows for separating differences related to the interpretation of the test conditions and parameters from the differences between the DFN and ECM approaches. The two models are compared using a benchmark test problem that is constructed to represent the far field (1 × 1 × 1 km3) of a hypothetical repository in fractured crystalline rock. The test problem setting uses generic fracture properties that can be expected in crystalline rocks. The models are compared in terms of the: 1) effective permeability of the domain, and 2) nonreactive solute breakthrough curves through the domain. The principal differences between the models are mesh size, network connectivity, matrix diffusion and anisotropy. We demonstrate how these differences affect the flow and transport. We identify the factors that should be taken in consideration when selecting an approach most suitable for the site-specific conditions.
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.
Latham, J.P.; Xiang, J.; Belayneh, M.; Nick, H.M.; Tsang, C.F.; Blunt, M.J.
2013-01-01
The influence of in-situ stresses on flow processes in fractured rock is investigated using a novel modelling approach. The combined finite-discrete element method (FEMDEM) is used to model the deformation of a fractured rock mass. The fracture wall displacements and aperture changes are modelled in
Follin, S.; Stigsson, M.; Levén, J.
2006-12-01
Difference flow logging is a relatively new hydraulic test method. It offers a superior geometrical resolution compared to the classic double-packer injection test method. Other significant features of the difference flow logging method are the long duration of the test period and the line source flow regime. These three features are vital for the characterization and the modeling of the conductive fracture frequency in crystalline rocks. Further, combining difference flow logging with core mapping and in situ borehole wall image logging (BIPS) allows for an enhanced geological cross correlation and structural interpretation. The data and analyses presented here come from the ongoing site investigations for a high-level nuclear waste repository in Forsmark managed by the Swedish Nuclear Fuel and Waste Management Co. First, we demonstrate the statistical properties of the fracture transmissivities acquired by difference flow logging for a number of one-kilometer-long cored boreholes. Secondly, we make a hydraulic comparison between these data and the transmissivities acquired by double-packer injection tests. Thirdly, we present a method for investigating the geometrical connectivity of open fractures in fracture network simulations and how this connectivity can be cross correlated to the fracture transmissivity distribution acquired by difference flow logging. Finally, we discuss the geometrical properties of flowing fractures as acquired by BIPS data and the correlation to the current stress situation in Forsmark. The geometrical anisotropy observed in the transmissivity data suggests that the current stress situation is very important for the flow field in Forsmark. This puts constraints on the collection and use of geological/structural data for hydrogeological discrete fracture network modeling.
Simulation of Hydraulic and Natural Fracture Interaction Using a Coupled DFN-DEM Model
Energy Technology Data Exchange (ETDEWEB)
J. Zhou; H. Huang; M. Deo
2016-03-01
The presence of natural fractures will usually result in a complex fracture network due to the interactions between hydraulic and natural fracture. The reactivation of natural fractures can generally provide additional flow paths from formation to wellbore which play a crucial role in improving the hydrocarbon recovery in these ultra-low permeability reservoir. Thus, accurate description of the geometry of discrete fractures and bedding is highly desired for accurate flow and production predictions. Compared to conventional continuum models that implicitly represent the discrete feature, Discrete Fracture Network (DFN) models could realistically model the connectivity of discontinuities at both reservoir scale and well scale. In this work, a new hybrid numerical model that couples Discrete Fracture Network (DFN) and Dual-Lattice Discrete Element Method (DL-DEM) is proposed to investigate the interaction between hydraulic fracture and natural fractures. Based on the proposed model, the effects of natural fracture orientation, density and injection properties on hydraulic-natural fractures interaction are investigated.
Ezzedine, S. M.
2010-12-01
Fractures and fracture networks are the principle pathways for migration of water, heat and mass in enhanced geothermal systems, oil and gas reservoirs, CO2 leakage from saline aquifers, and radioactive and toxic industrial wastes from underground storage repositories. A major issue to overcome when characterizing a fractured reservoir is that of data limitation due to accessibility and affordability. Moreover, the ability to map discontinuities in the rock with available geological and geophysical tools tends to decrease particularly as the scale of the discontinuity goes down. Geological characterization data include measurements of fracture density, orientation, extent, and aperture, and are based on analysis of outcrops, borehole optical and acoustic televiewer logs, aerial photographs, and core samples among others. All of these measurements are taken at the field scale through a very sparse limited number of deep boreholes. These types of data are often reduced to probability distributions function for predictive modeling and simulation in a stochastic framework such as stochastic discrete fracture network. Stochastic discrete fracture network models enable, through Monte Carlo realizations and simulations, for probabilistic assessment of flow and transport phenomena that are not adequately captured using continuum models. Despite the fundamental uncertainties inherited within the probabilistic reduction of the sparse data collected, very little work has been conducted on quantifying uncertainty on the reduced probabilistic distribution functions. In the current study, using nested Monte Carlo simulations, we present the impact of parameter uncertainties of the distribution functions that characterize discrete fracture networks on the flow, heat and mass transport. Numerical results of first, second and third moments, normalized to a base case scenario, are presented and compared to theoretical results extended from percolation theory.
Merrien-Soukatchoff, V.; Korini, T.; Thoraval, A.
2012-03-01
The paper presents the Discrete Fracture Network code RESOBLOK, which couples geometrical block system construction and a quick iterative stability analysis in the same package. The deterministic or stochastic geometry of a fractured rock mass can be represented and interactively displayed in 3D using two different fracture generators: one mainly used for hydraulic purposes and another designed to allow block stability evaluation. RESOBLOK has downstream modules that can quickly compute stability (based on limit equilibrium or energy-based analysis), display geometric information and create links to other discrete software. The advantage of the code is that it couples stochastic geometrical representation and a quick iterative stability analysis to allow risk-analysis with or without reinforcement and, for the worst cases, more accurate analysis using stress-strain analysis computer codes. These different aspects are detailed for embankment and underground works.
Xiang, G.L.; Vire, A.; Pavlidis, D.; Pain, C.
2015-01-01
A three-dimensional fracture model developed in the context of the combined finite-discrete element method is incorporated into a two-way fluid-solid coupling model. The fracture model is capable of simulating the whole fracturing process. It includes pre-peak hardening deformation, post-peak strain
Ezzedine, S. M.
2009-12-01
Fractures and fracture networks are the principal pathways for transport of water and contaminants in groundwater systems, enhanced geothermal system fluids, migration of oil and gas, carbon dioxide leakage from carbon sequestration sites, and of radioactive and toxic industrial wastes from underground storage repositories. A major issue to overcome when characterizing a fractured reservoir is that of data limitation due to accessibility and affordability. Moreover, the ability to map discontinuities in the rock with available geological and geophysical tools tends to decrease particularly as the scale of the discontinuity goes down. Geological characterization data include measurements of fracture density, orientation, extent, and aperture, and are based on analysis of outcrops, borehole optical and acoustic televiewer logs, aerial photographs, and core samples, among other techniques. All of these measurements are taken at the field scale through a very sparse limited number of deep boreholes. These types of data are often reduced to probability distribution functions for predictive modeling and simulation in a stochastic framework such as a stochastic discrete fracture network. Stochastic discrete fracture network models enable, through Monte Carlo realizations and simulations, probabilistic assessment of flow and transport phenomena that are not adequately captured using continuum models. Despite the fundamental uncertainties inherited within the probabilistic reduction of the sparse data collected, very little work has been conducted on quantifying uncertainty on the reduced probabilistic distribution functions. In the current study, using nested Monte Carlo simulations, we present the impact of parameter uncertainties of the distribution functions of fracture density, orientation, aperture and size on the flow and transport using topological measures such as fracture connectivity, physical characteristics such as effective hydraulic conductivity tensors, and
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
Minisuperspace models of discrete systems
Baytaş, Bekir
2016-01-01
A discrete quantum spin system is presented in which several modern methods of canonical quantum gravity can be tested with promising results. In particular, features of interacting dynamics are analyzed with an emphasis on homogeneous configurations and the dynamical building-up and stability of long-range correlations. Different types of homogeneous minisuperspace models are introduced for the system, including one based on condensate states, and shown to capture different aspects of the discrete system. They are evaluated with effective methods and by means of continuum limits, showing good agreement with operator calculations whenever the latter are available. As a possibly quite general result, it is concluded that an analysis of the building-up of long-range correlations in discrete systems requires non-perturbative solutions of the dynamical equations. Some questions related to stability can be analyzed perturbatively, but suggest that matter couplings may be relevant for this question in the context o...
Modelling Mobility: A Discrete Revolution
Clementi, Andrea; Silvestri, Riccardo
2010-01-01
We introduce a new approach to model and analyze \\emph{Mobility}. It is fully based on discrete mathematics and yields a class of mobility models, called the \\emph{Markov Trace} Model. This model can be seen as the discrete version of the \\emph{Random Trip} Model including all variants of the \\emph{Random Way-Point} Model \\cite{L06}. We derive fundamental properties and \\emph{explicit} analytical formulas for the \\emph{stationary distributions} yielded by the Markov Trace Model. Such results can be exploited to compute formulas and properties for concrete cases of the Markov Trace Model by just applying counting arguments. We apply the above general results to the discrete version of the \\emph{Manhattan Random Way-Point} over a square of bounded size. We get formulas for the total stationary distribution and for two important \\emph{conditional} ones: the agent spatial and destination distributions. Our method makes the analysis of complex mobile systems a feasible task. As a further evidence of this important...
Discretization of Preisach hysteresis model
Institute of Scientific and Technical Information of China (English)
安凯; 蔡国平
2015-01-01
In order to reduce the partial derivative errors in Preisach hysteresis model caused by inaccurate experimental data, the concept and correlative method of discretization of Preisach hysteresis model are proposed, the essential of which is to centralize the distribution density of Preisach hysteresis model in local region as an integral, which is defined as the weight of a certain point in that region. For the input composed of an ascending segment and a descending segment, a method to determine the initial weights together with an additional method to determine present weights is given according to the number of input ascending segments. If the number of input ascending segments increases, the weights of the corresponding points in updating rectangle are updated by adding the initial weights of corresponding points. A prominent advantage of discrete Preisach hysteresis model is its memory efficiency. Another advantage of discrete Preisach hysteresis model is that there is no function in the model, and thus, it can be expediently operated using a computer. By generalizing the above updating rectangle method to the continuous Preisach hysteresis model, identification method of distribution density can be given as well.
Karimi-Fard, M.; Durlofsky, L. J.
2016-10-01
A comprehensive framework for modeling flow in porous media containing thin, discrete features, which could be high-permeability fractures or low-permeability deformation bands, is presented. The key steps of the methodology are mesh generation, fine-grid discretization, upscaling, and coarse-grid discretization. Our specialized gridding technique combines a set of intersecting triangulated surfaces by constructing approximate intersections using existing edges. This procedure creates a conforming mesh of all surfaces, which defines the internal boundaries for the volumetric mesh. The flow equations are discretized on this conforming fine mesh using an optimized two-point flux finite-volume approximation. The resulting discrete model is represented by a list of control-volumes with associated positions and pore-volumes, and a list of cell-to-cell connections with associated transmissibilities. Coarse models are then constructed by the aggregation of fine-grid cells, and the transmissibilities between adjacent coarse cells are obtained using flow-based upscaling procedures. Through appropriate computation of fracture-matrix transmissibilities, a dual-continuum representation is obtained on the coarse scale in regions with connected fracture networks. The fine and coarse discrete models generated within the framework are compatible with any connectivity-based simulator. The applicability of the methodology is illustrated for several two- and three-dimensional examples. In particular, we consider gas production from naturally fractured low-permeability formations, and transport through complex fracture networks. In all cases, highly accurate solutions are obtained with significant model reduction.
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...
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...... an overview of the structure of the research and a summary of current status archived so far....
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 ...
Fadakar Alghalandis, Younes
2017-05-01
Rapidly growing topic, the discrete fracture network engineering (DFNE), has already attracted many talents from diverse disciplines in academia and industry around the world to challenge difficult problems related to mining, geothermal, civil, oil and gas, water and many other projects. Although, there are few commercial software capable of providing some useful functionalities fundamental for DFNE, their costs, closed code (black box) distributions and hence limited programmability and tractability encouraged us to respond to this rising demand with a new solution. This paper introduces an open source comprehensive software package for stochastic modeling of fracture networks in two- and three-dimension in discrete formulation. Functionalities included are geometric modeling (e.g., complex polygonal fracture faces, and utilizing directional statistics), simulations, characterizations (e.g., intersection, clustering and connectivity analyses) and applications (e.g., fluid flow). The package is completely written in Matlab scripting language. Significant efforts have been made to bring maximum flexibility to the functions in order to solve problems in both two- and three-dimensions in an easy and united way that is suitable for beginners, advanced and experienced users.
Energy Technology Data Exchange (ETDEWEB)
Crichlow, H.B.; Crichlow, H.B. (ed.)
1980-02-07
A design tool is discussed whereby the various components that enter the design process of a hydraulic fracturing job are combined to provide a realistic appraisal of a stimulation job in the field. An interactive computer model is used to solve the problem numerically to obtain the effects of various parameters on the overall behavior of the system.
Ely, Gregory
2013-01-01
In this work we propose a novel algorithm for multiple-event localization for Hydraulic Fracture Monitoring (HFM) through the exploitation of the sparsity of the observed seismic signal when represented in a basis consisting of space time propagators. We provide explicit construction of these propagators using a forward model for wave propagation which depends non-linearly on the problem parameters - the unknown source location and mechanism of fracture, time and extent of event, and the locations of the receivers. Under fairly general assumptions and an appropriate discretization of these parameters we first build an over-complete dictionary of generalized Radon propagators and assume that the data is well represented as a linear superposition of these propagators. Exploiting this structure we propose sparsity penalized algorithms and workflow for super-resolution extraction of time overlapping multiple seismic events from single well data.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The continuum approach in fluid flow modeling is generally applied to porous geological media,but has limitel applicability to fractured rocks. With the presence of a discrete fracture network relatively sparsely distributed in the matrix, it may be difficult or erroneous to use a porous medium fluid flow model with continuum assumptions to describe the fluid flow in fractured rocks at small or even large field scales. A discrete fracture fluid flow approach incorporating a stochastic fracture network with numerical fluid flow simulations could have the capability of capturing fluid flow behaviors such as inhomogeneity and anisotropy while reflecting the changes of hydraulic features at different scales.Moreover, this approach can be implemented to estimate the size of the representative elementary volume (REV) in order to find out the scales at which a porous medium flow model could be applied, and then to determine the hydraulic conductivity tensor for fractured rocks. The following topics are focused on in this study: (a) conceptual discrete fracture fluid flow modeling incorporating a stochastic fracture network with numerical flow simulations; (b) estimation of REVand hydraulic conductivity tensor for fractured rocks utilizing a stochastic fracture network with numerical fluid flow simulations; (c) investigation of the effect of fracture orientation and density on the hydraulic conductivity and REV by implementing a stochastic fracture network with numerical fluid flow simulations, and (d) fluid flow conceptual models accounting for major and minor fractures in the 2-D or 3-D flow fields incorporating a stochastic fracture network with numerical fluid flow simulations.``
Certain Discrete Element Methods in Problems of Fracture Mechanics
Directory of Open Access Journals (Sweden)
P. P. Procházka
2002-01-01
Full Text Available In this paper two discrete element methods (DEM are discussed. The free hexagon element method is considered a powerful discrete element method, which is broadly used in mechanics of granular media. It substitutes the methods for solving continuum problems. The great disadvantage of classical DEM, such as the particle flow code (material properties are characterized by spring stiffness, is that they have to be fed with material properties provided from laboratory tests (Young's modulus, Poisson's ratio, etc.. The problem consists in the fact that the material properties of continuum methods (FEM, BEM are not mutually consistent with DEM. This is why we utilize the principal idea of DEM, but cover the continuum by hexagonal elastic, or elastic-plastic, elements. In order to complete the study, another one DEM is discussed. The second method starts with the classical particle flow code (PFC - which uses dynamic equilibrium, but applies static equilibrium. The second method is called the static particle flow code (SPFC. The numerical experience and comparison numerical with experimental results from scaled models are discussed in forthcoming paper by both authors.
New discrete element models for elastoplastic problems
Institute of Scientific and Technical Information of China (English)
Ming Cheng; Weifu Liu; Kaixin Liu
2009-01-01
The discrete element method (DEM) has attractive features for problems with severe damages, but lack of theoretical basis for continua behavior especially for nonlinear behavior has seriously restricted its application, The present study proposes a new approach to developing the DEM as a general and robust technique for modeling the elastoplastic behavior of solid materials. New types of connective links between elements are proposed, the inter-element parameters are theoretically determined based on the principle of energy equivalence and a yield criterion and a flow rule for DEM are given for describing nonlinear behavior of materials. Moreover, a numerical scheme, which can be applied to modeling the behavior of a continuum as well as the transformation from a continuum to a discontinuum, is obtained by introducing a fracture criterion and a contact model into the DEM. The elastoplastic stress wave propagations and the tensile failure process of a steel plate are simulated, and the numerical results agree well with those obtained from the finite element method (FEM) and corresponding experiment, and thus the accuracy and efficiency of the DEM scheme are demonstrated.
New discrete element models for elastoplastic problems
Cheng, Ming; Liu, Weifu; Liu, Kaixin
2009-10-01
The discrete element method (DEM) has attractive features for problems with severe damages, but lack of theoretical basis for continua behavior especially for nonlinear behavior has seriously restricted its application. The present study proposes a new approach to developing the DEM as a general and robust technique for modeling the elastoplastic behavior of solid materials. New types of connective links between elements are proposed, the inter-element parameters are theoretically determined based on the principle of energy equivalence and a yield criterion and a flow rule for DEM are given for describing nonlinear behavior of materials. Moreover, a numerical scheme, which can be applied to modeling the behavior of a continuum as well as the transformation from a continuum to a discontinuum, is obtained by introducing a fracture criterion and a contact model into the DEM. The elastoplastic stress wave propagations and the tensile failure process of a steel plate are simulated, and the numerical results agree well with those obtained from the finite element method (FEM) and corresponding experiment, and thus the accuracy and efficiency of the DEM scheme are demonstrated.
Generalized exponential function and discrete growth models
Souto Martinez, Alexandre; Silva González, Rodrigo; Lauri Espíndola, Aquino
2009-07-01
Here we show that a particular one-parameter generalization of the exponential function is suitable to unify most of the popular one-species discrete population dynamic models into a simple formula. A physical interpretation is given to this new introduced parameter in the context of the continuous Richards model, which remains valid for the discrete case. From the discretization of the continuous Richards’ model (generalization of the Gompertz and Verhulst models), one obtains a generalized logistic map and we briefly study its properties. Notice, however that the physical interpretation for the introduced parameter persists valid for the discrete case. Next, we generalize the (scramble competition) θ-Ricker discrete model and analytically calculate the fixed points as well as their stabilities. In contrast to previous generalizations, from the generalized θ-Ricker model one is able to retrieve either scramble or contest models.
Roubinet, D; Jougnot, D; Irving, J
2016-01-01
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 interaction...
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.
Developing fracture density models using terrestrial laser scan data
Pollyea, R.; Fairley, J. P.; Podgorney, R. K.; McLing, T. L.
2010-12-01
Characterizing fracture heterogeneity for subsurface flow and transport modeling has been of interest to the hydrogeologic community for many years. Currently, stochastic continuum and discrete fracture representations have come to be accepted as two of the most commonly used tools for incorporating fracture heterogeneity into subsurface flow and transport models. In this research, ground-based lidar data are used to model the surface roughness of vertical basalt exposures in the East Snake River Plain, Idaho (ESRP) as a surrogate for fracture density. The surface roughness is modeled by discretizing the dataset over a regular grid and fitting a regression plane to each gridblock. The standard deviation of distance from the block data to the regression plane is then assumed to represent a measure of roughness for each gridblock. Two-dimensional plots of surface roughness from ESRP exposures indicate discrete fractures can be quantitatively differentiated from unfractured rock at 0.25- meter resolution. This methodology may have broad applications for characterizing fracture heterogeneity. One application, demonstrated here, is to capture high resolution (low noise) covariance statistics for building stochastic property sets to be used in large scale flow simulations. Additional applications may include using surface roughness datasets as training images for multiple-point geostatistics analysis and for constraining discrete fracture models.
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.)
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.)
Colloid facilitated transport of lanthanides through discrete fractures in chalk
Tran, Emily; Klein Ben-David, Ofra; Teutsch, Nadya; Weisbrod, Noam
2015-04-01
transport rates and calculation of overall tracer recovery. Preliminary results suggest that mobility of Ce as a solute is negligible, and in experiments conducted without bentonite colloids, the 2% of the Ce that was recovered during the experiments travelled as "intrinsic" colloids in the form of Ce2(CO3)3-6H2O precipitate. However, the total recovery of the Ce increased to 9% when it was injected into the core in the presence of bentonite colloids and 13% when both bentonite and the carbonate precipitate colloids were injected. In addition, the maximum relative concentration (C/C0) of the Ce in the samples from the experiments conducted without bentonite colloids is about 0.002, whereas that of the experiments conducted in the presence of bentonite colloids reaches almost 0.2. This indicates that colloid presence does indeed markedly increase the mobility of radionuclides through fractured chalk matrices and should therefore be considered in models representing transport of radionuclide waste originating from nuclear repositories.
Modeling contaminant plumes in fractured limestone aquifers
DEFF Research Database (Denmark)
Mosthaf, Klaus; Brauns, Bentje; Fjordbøge, Annika Sidelmann
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...... in the planning of field tests and to update the conceptual model in an iterative process. Field data includes information on spill history, distribution of the contaminant (multilevel sampling), geology and hydrogeology. To describe the geology and fracture system, data from borehole logs, packer tests, optical...... distribution in the aquifer. Different models were used for the planning and interpretation of the pump and tracer test. The models were evaluated by examining their ability to describe collected field data. The comparison with data showed that the models have substantially different representations...
Gui, Y. L.; Zhao, Z. Y.; Zhou, H. Y.; Wu, W.
2016-10-01
In this paper, a cohesive fracture model is applied to model P-wave propagation through fractured rock mass using hybrid continuum-discrete element method, i.e. Universal Distinct Element Code (UDEC). First, a cohesive fracture model together with the background of UDEC is presented. The cohesive fracture model considers progressive failure of rock fracture rather than an abrupt damage through simultaneously taking into account the elastic, plastic and damage mechanisms as well as a modified failure function. Then, a series of laboratory tests from the literature on P-wave propagation through rock mass containing single fracture and two parallel fractures are introduced and the numerical models used to simulate these laboratory tests are described. After that, all the laboratory tests are simulated and presented. The results show that the proposed model, particularly the cohesive fracture model, can capture very well the wave propagation characteristics in rock mass with non-welded and welded fractures with and without filling materials. In the meantime, in order to identify the significance of fracture on wave propagation, filling materials with different particle sizes and the fracture thickness are discussed. Both factors are found to be crucial for wave attenuation. The simulations also show that the frequency of transmission wave is lowered after propagating through fractures. In addition, the developed numerical scheme is applied to two-dimensional wave propagation in the rock mass.
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…
Modelling of Specimen Fracture
2013-09-23
the plate center. An end load of 1.0 MPa was applied. 1 2 3 Modelling of Specimen Fracture – Final Report 11 TR-13-47 Figure 2.5: Crack Geometry Figure...Christopher Bayley DRDC Atlantic Dockyard Laboratory Pacific CFB Esquimalt, Building 199 PO Box 17000, Station Forces Victoria, British Columbia Canada...q The weighting function, q , can be any arbitrary function within the J-integral domain, and must be zero on the domain boundary . An easy function
Local discrete symmetries from superstring derived models
Energy Technology Data Exchange (ETDEWEB)
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.
Local discrete symmetries from superstring derived models
Faraggi, Alon E.
1997-02-01
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 I illustrate 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.
Local discrete symmetries from superstring derived models
Faraggi, A E
1996-01-01
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 I illustrate 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.
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.
Discrete Surface Modelling Using Partial Differential Equations.
Xu, Guoliang; Pan, Qing; Bajaj, Chandrajit L
2006-02-01
We use various nonlinear partial differential equations to efficiently solve several surface modelling problems, including surface blending, N-sided hole filling and free-form surface fitting. The nonlinear equations used include two second order flows, two fourth order flows and two sixth order flows. These nonlinear equations are discretized based on discrete differential geometry operators. The proposed approach is simple, efficient and gives very desirable results, for a range of surface models, possibly having sharp creases and corners.
A hybrid mortar virtual element method for discrete fracture network simulations
Benedetto, Matías Fernando; Berrone, Stefano; Borio, Andrea; Pieraccini, Sandra; Scialò, Stefano
2016-02-01
The most challenging issue in performing underground flow simulations in Discrete Fracture Networks (DFN) is to effectively tackle the geometrical difficulties of the problem. In this work we put forward a new application of the Virtual Element Method combined with the Mortar method for domain decomposition: we exploit the flexibility of the VEM in handling polygonal meshes in order to easily construct meshes conforming to the traces on each fracture, and we resort to the mortar approach in order to "weakly" impose continuity of the solution on intersecting fractures. The resulting method replaces the need for matching grids between fractures, so that the meshing process can be performed independently for each fracture. Numerical results show optimal convergence and robustness in handling very complex geometries.
Kavousi Ghahfarokhi, Payam
The Tensleep oil reservoir at Teapot Dome, Wyoming, USA, is a naturally fractured tight sandstone reservoir that has been considered for carbon-dioxide enhanced oil recovery (CO2-EOR) and sequestration. CO2-EOR analysis requires a thorough understanding of the Tensleep fracture network. Wireline image logs from the field suggest that the reservoir fracture network is dominated by early formed structural hinge oblique fractures with interconnectivity enhanced by hinge parallel and hinge perpendicular fracture sets. Available post stack 3D seismic data are used to generate a seismic fracture intensity attribute for the reservoir fracture network. The resulting seismic fracture intensity is qualitatively correlated to the field production history. Wells located on hinge-oblique discontinuities are more productive than other wells in the field. We use Oda's method to upscale the fracture permeabilities in the discrete fracture network for use in a dual porosity fluid flow simulator. We analytically show that Oda's method is sensitive to the grid orientation relative to fracture set strike. Results show that the calculated permeability tensors have maximum geometric mean for the non-zero permeability components (kxx,kyy,kzz,kxy) when the dominant fracture set cuts diagonally through the grid cell at 45° relative to the grid cell principal directions (i,j). The geometric mean of the permeability tensor components falls to a minimum when the dominant fracture set is parallel to either grid wall (i or j principal directions). The latter case has off-diagonal permeability terms close to zero. We oriented the Tensleep reservoir grid to N72°W to minimize the off-diagonal permeability terms. The seismic fracture intensity attribute is then used to generate a realization of the reservoir fracture network. Subsequently, fracture properties are upscaled to the reservoir grid scale for a fully compositional flow simulation. We implemented a PVT analysis using CO2 swelling test
Institute of Scientific and Technical Information of China (English)
王培涛; 杨天鸿; 于庆磊; 刘洪磊; 夏冬; 张鹏海
2013-01-01
节理岩体几何结构非常复杂，研究其渗流特性对于指导含水岩层稳定性分析具有重要价值。应用离散裂隙网络模型DFN方法，基于VC++6.0软件平台，建立了平面渗流分析方法，分析了节理岩体不同几何分布情况下的渗透率张量特征，通过定义渗流定向性系数对岩体渗流的定向性特征进行了定量分析。结果表明：单组节理岩体渗流具有明显的各向异性特征，渗流定向性随着节理角度变化显著；节理随着节理贯通性增加，节理渗透率呈现对数增加趋势；两组节理情况下，各向异性特征随着节理组间夹角变化；两组节理岩体渗流特征研究中，正交分布下，岩体仍存在各向异性，但渗流定向性系数较低；当节理倾角服从正态分布时，随着节理倾角标准差增大，渗透率增加；两组节理夹角不同时，节理渗透主方向倾角随着夹角增大而相应增大，基本沿两组节理夹角方向的角平分线方向。%Joint systems in rock masses are geometrically complex; and investigation of the hydraulic properties is important for understanding the hydraulic behavior of jointed rock masses and stability analysis of rock engineering. A discrete fracture network (DFN) model was designed using C++language based on VC++6.0 platform to realize a fracture network for seepage analysis. The permeability coefficients, possibility of equivalent permeability tensors of the jointed rock masses were examined by simulating flow through DFN models of varying joint properties. A directionality coefficient was defined to quantitatively assess the principal flow direction in jointed rock masses. The results show that the permeability coefficients are anisotropic according to permeability tensor analysis for rock masses with only one set of joints. The degree of obliquities of joint plane affects obviously the principal direction of permeability. The permeability coefficients
Analysis and Visualization of Discrete Fracture Networks Using a Flow Topology Graph.
Aldrich, Garrett; Hyman, Jeffrey; Karra, Satish; Gable, Carl; Makedonska, Nataliia; Viswanathan, Hari; Woodring, Jonathan; Hamann, Bernd
2016-06-20
We present an analysis and visualization prototype using the concept of a flow topology graph (FTG) for characterization of flow in constrained networks, with a focus on discrete fracture networks (DFN), developed collaboratively by geoscientists and visualization scientists. Our method allows users to understand and evaluate flow and transport in DFN simulations by computing statistical distributions, segment paths of interest, and cluster particles based on their paths. The new approach enables domain scientists to evaluate the accuracy of the simulations, visualize features of interest, and compare multiple realizations over a specific domain of interest. Geoscientists can simulate complex transport phenomena modeling large sites for networks consisting of several thousand fractures without compromising the geometry of the network. However, few tools exist for performing higher-level analysis and visualization of simulated DFN data. The prototype system we present addresses this need. We demonstrate its effectiveness for increasingly complex examples of DFNs, covering two distinct use cases - hydrocarbon extraction from unconventional resources and transport of dissolved contaminant from a spent nuclear fuel repository.
Formalising the Continuous/Discrete Modeling Step
Directory of Open Access Journals (Sweden)
Wen Su
2011-06-01
Full Text Available Formally capturing the transition from a continuous model to a discrete model is investigated using model based refinement techniques. A very simple model for stopping (eg. of a train is developed in both the continuous and discrete domains. The difference between the two is quantified using generic results from ODE theory, and these estimates can be compared with the exact solutions. Such results do not fit well into a conventional model based refinement framework; however they can be accommodated into a model based retrenchment. The retrenchment is described, and the way it can interface to refinement development on both the continuous and discrete sides is outlined. The approach is compared to what can be achieved using hybrid systems techniques.
Formalising the Continuous/Discrete Modeling Step
Banach, Richard; Su, Wen; Huang, Runlei; 10.4204/EPTCS.55.8
2011-01-01
Formally capturing the transition from a continuous model to a discrete model is investigated using model based refinement techniques. A very simple model for stopping (eg. of a train) is developed in both the continuous and discrete domains. The difference between the two is quantified using generic results from ODE theory, and these estimates can be compared with the exact solutions. Such results do not fit well into a conventional model based refinement framework; however they can be accommodated into a model based retrenchment. The retrenchment is described, and the way it can interface to refinement development on both the continuous and discrete sides is outlined. The approach is compared to what can be achieved using hybrid systems techniques.
Modeling Electric Current Flow in 3D Fractured Media
Demirel, S.; Roubinet, D.; Irving, J.
2014-12-01
The study of fractured rocks is extremely important in a variety of research fields and applications such as hydrogeology, hydrocarbon extraction and long-term storage of toxic waste. As fractures are highly conductive structures in comparison to the surrounding rock, their presence can be either an advantage or a drawback. For hydrocarbon extraction, fractures allow for quick and easy access to the resource whereas for toxic waste storage their presence increases the risk of leakage and migration of pollutants. In both cases, the identification of fracture network characteristics is an essential step. Recently, we have developed an approach for modeling electric current flow in 2D fractured media. This approach is based on a discrete-dual-porosity model where fractures are represented explicitly, the matrix is coarsely discretized into blocks, and current flow exchange between the fractures and matrix is analytically evaluated at the fracture-scale and integrated at the block-scale [1]. Although this approach has shown much promise and has proven its efficiency for 2D simulations, its extension to 3D remains to be addressed. To this end, we assume that fractures can be represented as two-dimensional finite planes embedded in the surrounding matrix, and we express analytically the distribution of electric potential at the fracture scale. This fracture-scale expression takes into account the electric-current-flow exchange with the surrounding matrix and flow conservation is enforced at the fracture intersections. The fracture-matrix exchange is then integrated at the matrix-block scale where the electric current flow conservation at the block boundaries is formulated with a modified finite volume method. With the objective of providing a low-computational-cost modeling approach adapted to 3D simulations in fractured media, our model is (i) validated and compared to existing modeling approaches and, (ii) used to evaluate the impact of the presence of fractures on
Discrete dispersion models and their Tweedie asymptotics
DEFF Research Database (Denmark)
Jørgensen, Bent; Kokonendji, Célestin C.
2016-01-01
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.
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.
Models for neutrino mass with discrete symmetries
Morisi, S.
2011-08-01
Discrete non-abelian flavor symmetries give in a natural way tri-bimaximal (TBM) mixing as showed in a prototype model. However neutrino mass matrix pattern may be very different from the tri-bimaximal one if small deviations of TBM will be observed. We give the result of a model independent analysis for TBM neutrino mass pattern.
Models for neutrino mass with discrete symmetries
Morisi, S
2010-01-01
Discrete non-abelian flavor symmetries give in a natural way tri-bimaximal (TBM) mixing as showed in a prototype model. However neutrino mass matrix pattern may be very different from the tri-bimaximal one if small deviations of TBM will be observed. We give the result of a model independent analysis for TBM neutrino mass pattern.
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
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...
A Discrete Cell Migration Model
Energy Technology Data Exchange (ETDEWEB)
Nutaro, James J [ORNL; Kruse, Kara L [ORNL; Ward, Richard C [ORNL; O' Quinn, Elizabeth [Wofford College; Woerner, Matthew M [ORNL; Beckerman, Barbara G [ORNL
2007-01-01
Migration of vascular smooth muscle cells is a fundamental process in the development of intimal hyperplasia, a precursor to development of cardiovascular disease and a potential response to injury of an arterial wall. Boyden chamber experiments are used to quantify the motion of cell populations in response to a chemoattractant gradient (i.e., cell chemotaxis). We are developing a mathematical model of cell migration within the Boyden chamber, while simultaneously conducting experiments to obtain parameter values for the migration process. In the future, the model and parameters will be used as building blocks for a detailed model of the process that causes intimal hyperplasia. The cell migration model presented in this paper is based on the notion of a cell as a moving sensor that responds to an evolving chemoattractant gradient. We compare the results of our three-dimensional hybrid model with results from a one-dimensional continuum model. Some preliminary experimental data that is being used to refine the model is also presented.
DEFF Research Database (Denmark)
Mosthaf, Klaus; Rosenberg, L.; Balbarini, Nicola
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...... 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 towards fracture sampling, however concentrations in the limestone matrix are needed for assessing contaminant...
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 inter...
A discrete anisotropic model for Scheibe aggregates
Directory of Open Access Journals (Sweden)
O. Bang
1991-05-01
Full Text Available A discrete anisotropic nonlinear model for the dynamics of Scheibe aggregates is investigated. The collapse of the collective excitations found by Möbius and Kuhn is described as a shrinking ring wave, which is eventually absorbed by an acceptor molecule. An optimal acceptor loss is found.
Method for efficient simulation of radionuclide transport in discrete fracture networks
Painter, S. L.; Cvetkovic, V.; Mancillas, J. W.; Selroos, J.
2006-12-01
Limitations of the advection-dispersion equation for predicting transport in sparsely or moderately fractured rock are well known and have prompted many to consider discrete fracture network (DFN) simulation combined with particle tracking as an alternative. Although it is relatively straightforward to track particles moving only by advection through DFN-derived flow fields, more complex processes such as matrix diffusion, longitudinal dispersion, and decay/in-growth of radionuclides are more difficult and more computationally demanding. Moreover, the DFN simulations themselves are computationally intensive and are usually limited to relatively small volumes. A new time-domain particle method has been developed to efficiently simulate radionuclide transport in pathways derived from DFN simulations. The algorithm moves particles from node to node on a segmented pathway. The time to complete each segment is sampled from residence time distributions that include the effects of advection, longitudinal dispersion, and a variety of matrix retention processes. The method has been extended to include transport of decay chains and transient flow fields. The result of the simulation is a set of arrival times that can be post-processed with a log-normal kernel method to construct mass discharge (breakthrough) versus time. The approach can be used directly on pathways extracted from DFN models, or it may be combined with pathway simulation algorithms (Painter and Cvetkovic, Water Resources Research 41, 2005) that use information extracted from DFNs to construct realistic artificial pathways. The latter variant helps recover the effects of sub-grid velocity variability in flow fields constructed from continuum flow models. Thus, when combined with flow models based on upscaled permeability tensors, the result is a type of multiscale simulation that is applicable at large scales without making continuum-type assumptions about the transport processes. Verification tests show that
Virgo, Simon; Abe, Steffen; Urai, Janos L.
2016-03-01
We present the results of a comparative study of loading conditions on the interactions between extension fractures and veins. We model the fracture behavior of brittle discrete element materials each containing a tabular vein body of variable orientation and strength in two different loading conditions. The first is uniaxial tension, applied with servo-controlled sidewalls. The second is a boudinage boundary condition in which a tensile triaxial stress state is induced in the brittle model volume by quasi-viscous extensional deformation in the adjacent layers. Most of the fracture- vein interactions observed in uniaxial tension also exists in boudinage boundary conditions. However, the importance of each interaction mechanism for a given configuration of relative strength and misorientation of the vein may differ according to the loading mechanism. Nucleation and internal deflection is under both boundary conditions the dominating fracture-vein interaction style in weak veins. In uniaxial tension models, strong veins tend to alter the fracture path by external deflection, while under boudinage loading these veins are more likely overcome by the fracture step over mechanism. Dynamic bifurcation of fractures was observed in uniaxial tension models but never for boudinage boundary conditions. This is because the acceleration of fracture tips in these conditions is suppressed by interaction with distributed fractures as well as viscous damping by the neighboring layers.
Griffith, W. A.; Ghaffari, H.; Barber, T. J.; Borjas, C.
2015-12-01
The motions of Earth's tectonic plates are typically measured in millimeters to tens of centimeters per year, seemingly confirming the generally-held view that tectonic processes are slow, and have been throughout Earth's history. In line with this perspective, the vast majority of laboratory rock mechanics research focused on failure in the brittle regime has been limited to experiments utilizing slow loading rates. On the other hand, many natural processes that pose significant risk for humans (e.g., earthquakes and extraterrestrial impacts), as well as risks associated with human activities (blow-outs, explosions, mining and mine failures, projectile penetration), occur at rates that are hundreds to thousands of times faster than those typically simulated in the laboratory. Little experimental data exists to confirm or calibrate theoretical models explaining the connection between these dramatic events and the pulverized rocks found in fault zones, impacts, or explosions; however the experimental data that does exist is thought-provoking: At the earth's surface, the process of brittle fracture passes through a critical transition in rocks at high strain rates (101-103s-1) between regimes of discrete fracture and distributed fragmentation, accompanied by a dramatic increase in strength. Previous experimental works on this topic have focused on key thresholds (e.g., peak stress, peak strain, average strain rate) that define this transition, but more recent work suggests that this transition is more fundamentally dependent on characteristics (e.g., shape) of the loading pulse and related microcrack dynamics, perhaps explaining why for different lithologies different thresholds more effectively define the pulverization transition. In this presentation we summarize some of our work focused on this transition, including the evolution of individual defects at the microscopic, microsecond scale and the energy budget associated with the brittle fragmentation process as a
Proportional hazards models with discrete frailty.
Caroni, Chrys; Crowder, Martin; Kimber, Alan
2010-07-01
We extend proportional hazards frailty models for lifetime data to allow a negative binomial, Poisson, Geometric or other discrete distribution of the frailty variable. This might represent, for example, the unknown number of flaws in an item under test. Zero frailty corresponds to a limited failure model containing a proportion of units that never fail (long-term survivors). Ways of modifying the model to avoid this are discussed. The models are illustrated on a previously published set of data on failures of printed circuit boards and on new data on breaking strengths of samples of cord.
Jia, Pin; Cheng, Linsong; Huang, Shijun; Wu, Yonghui
2016-06-01
This paper presents a semi-analytical model for the flow behavior of naturally fractured formations with multi-scale fracture networks. The model dynamically couples an analytical dual-porosity model with a numerical discrete fracture model. The small-scale fractures with the matrix are idealized as a dual-porosity continuum and an analytical flow solution is derived based on source functions in Laplace domain. The large-scale fractures are represented explicitly as the major fluid conduits and the flow is numerically modeled, also in Laplace domain. This approach allows us to include finer details of the fracture network characteristics while keeping the computational work manageable. For example, the large-scale fracture network may have complex geometry and varying conductivity, and the computations can be done at predetermined, discrete times, without any grids in the dual-porosity continuum. The validation of the semi-analytical model is demonstrated in comparison to the solution of ECLIPSE reservoir simulator. The simulation is fast, gridless and enables rapid model setup. On the basis of the model, we provide detailed analysis of the flow behavior of a horizontal production well in fractured reservoir with multi-scale fracture networks. The study has shown that the system may exhibit six flow regimes: large-scale fracture network linear flow, bilinear flow, small-scale fracture network linear flow, pseudosteady-state flow, interporosity flow and pseudoradial flow. During the first four flow periods, the large-scale fracture network behaves as if it only drains in the small-scale fracture network; that is, the effect of the matrix is negligibly small. The characteristics of the bilinear flow and the small-scale fracture network linear flow are predominantly determined by the dimensionless large-scale fracture conductivity. And low dimensionless fracture conductivity will generate large pressure drops in the large-scale fractures surrounding the wellbore. With
Discrete and continuum modelling of soil cutting
Coetzee, C. J.
2014-12-01
Both continuum and discrete methods are used to investigate the soil cutting process. The Discrete Element Method ( dem) is used for the discrete modelling and the Material-Point Method ( mpm) is used for continuum modelling. M pmis a so-called particle method or meshless finite element method. Standard finite element methods have difficulty in modelling the entire cutting process due to large displacements and deformation of the mesh. The use of meshless methods overcomes this problem. M pm can model large deformations, frictional contact at the soil-tool interface, and dynamic effects (inertia forces). In granular materials the discreteness of the system is often important and rotational degrees of freedom are active, which might require enhanced theoretical approaches like polar continua. In polar continuum theories, the material points are considered to possess orientations. A material point has three degrees-of-freedom for rigid rotations, in addition to the three classic translational degrees-of-freedom. The Cosserat continuum is the most transparent and straightforward extension of the nonpolar (classic) continuum. Two-dimensional dem and mpm (polar and nonpolar) simulations of the cutting problem are compared to experiments. The drag force and flow patterns are compared using cohesionless corn grains as material. The corn macro (continuum) and micro ( dem) properties were obtained from shear and oedometer tests. Results show that the dilatancy angle plays a significant role in the flow of material but has less of an influence on the draft force. Nonpolar mpm is the most accurate in predicting blade forces, blade-soil interface stresses and the position and orientation of shear bands. Polar mpm fails in predicting the orientation of the shear band, but is less sensitive to mesh size and mesh orientation compared to nonpolar mpm. dem simulations show less material dilation than observed during experiments.
Online Learning in Discrete Hidden Markov Models
Alamino, Roberto C.; Caticha, Nestor
2007-01-01
We present and analyse three online algorithms for learning in discrete Hidden Markov Models (HMMs) and compare them with the Baldi-Chauvin Algorithm. Using the Kullback-Leibler divergence as a measure of generalisation error we draw learning curves in simplified situations. The performance for learning drifting concepts of one of the presented algorithms is analysed and compared with the Baldi-Chauvin algorithm in the same situations. A brief discussion about learning and symmetry breaking b...
Discrete Choice Models - Estimation of Passenger Traffic
DEFF Research Database (Denmark)
Sørensen, Majken Vildrik
2003-01-01
), which simultaneously finds optimal coefficients values (utility elements) and parameter values (distributed terms) in the utility function. The shape of the distributed terms is specified prior to the estimation; hence, the validity is not tested during the estimation. The proposed method, assesses...... for data, a literature review follows. Models applied for estimation of discrete choice models are described by properties and limitations, and relations between these are established. Model types are grouped into three classes, Hybrid choice models, Tree models and Latent class models. Relations between...... the shape of the distribution from data, by means of repetitive model estimation. In particular, one model was estimated for each sub-sample of data. The shape of distributions is assessed from between model comparisons. This is not to be regarded as an alternative to MSL estimation, rather...
Ţene, Matei; Al Kobaisi, Mohammed Saad; Hajibeygi, Hadi
2016-09-01
This paper introduces an Algebraic MultiScale method for simulation of flow in heterogeneous porous media with embedded discrete Fractures (F-AMS). First, multiscale coarse grids are independently constructed for both porous matrix and fracture networks. Then, a map between coarse- and fine-scale is obtained by algebraically computing basis functions with local support. In order to extend the localization assumption to the fractured media, four types of basis functions are investigated: (1) Decoupled-AMS, in which the two media are completely decoupled, (2) Frac-AMS and (3) Rock-AMS, which take into account only one-way transmissibilities, and (4) Coupled-AMS, in which the matrix and fracture interpolators are fully coupled. In order to ensure scalability, the F-AMS framework permits full flexibility in terms of the resolution of the fracture coarse grids. Numerical results are presented for two- and three-dimensional heterogeneous test cases. During these experiments, the performance of F-AMS, paired with ILU(0) as second-stage smoother in a convergent iterative procedure, is studied by monitoring CPU times and convergence rates. Finally, in order to investigate the scalability of the method, an extensive benchmark study is conducted, where a commercial algebraic multigrid solver is used as reference. The results show that, given an appropriate coarsening strategy, F-AMS is insensitive to severe fracture and matrix conductivity contrasts, as well as the length of the fracture networks. Its unique feature is that a fine-scale mass conservative flux field can be reconstructed after any iteration, providing efficient approximate solutions in time-dependent simulations.
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
Evaluation of modeling approaches to simulate contaminant transport in a fractured limestone aquifer
DEFF Research Database (Denmark)
Mosthaf, Klaus; Fjordbøge, Annika Sidelmann; Broholm, Mette Martina
contaminant transport in fractured media, such as discrete fracture, equivalent porous media, and dual continuum models. However, these modeling concepts are not well tested for real limestone geologies. Our goal is therefore to develop, evaluate and compare approaches for modeling transport of contaminants...... 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 towards fracture sampling; however, concentrations in the limestone matrix are needed for assessing contaminant rebound...
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.
Stochastic discrete model of karstic networks
Jaquet, O.; Siegel, P.; Klubertanz, G.; Benabderrhamane, H.
Karst aquifers are characterised by an extreme spatial heterogeneity that strongly influences their hydraulic behaviour and the transport of pollutants. These aquifers are particularly vulnerable to contamination because of their highly permeable networks of conduits. A stochastic model is proposed for the simulation of the geometry of karstic networks at a regional scale. The model integrates the relevant physical processes governing the formation of karstic networks. The discrete simulation of karstic networks is performed with a modified lattice-gas cellular automaton for a representative description of the karstic aquifer geometry. Consequently, more reliable modelling results can be obtained for the management and the protection of karst aquifers. The stochastic model was applied jointly with groundwater modelling techniques to a regional karst aquifer in France for the purpose of resolving surface pollution issues.
Discrete Deterministic Modelling of Autonomous Missiles Salvos
Directory of Open Access Journals (Sweden)
Momcilo Milinovic
2014-09-01
Full Text Available The paper deals with mathematical models of sequent salvos battle, of autonomous flight missiles (AFM organized in the groups of combatants. Tactical integration of AFM system distance-controlled weapon is considered by performances of simultaneous approaches on targets, and continual battle models of guerilla and direct fire, are redesigned to the discrete-continual mixed model, for checking missiles sudden, and further salvos, attack effects. Superiority parameters, as well as losses and strengths of full, or the part of salvo battle, for the missiles groups as technology sub-systems combatants’, is expressed by mathematical and simulation examples. Targets engagements capacities of the missiles battle unit, is conducted through designed scenarios and mathematically derived in the research. Model orientated on answers about employment of rapid reaction defending tactics, by distance missiles attacks.Defence Science Journal, Vol. 64, No. 5, September 2014, pp.471-476, DOI:http://dx.doi.org/10.14429/dsj.64.5791
DISCRETE AND CONTINUUM MODELLING OF GRANULAR FLOW
Institute of Scientific and Technical Information of China (English)
H. P. Zhu; Y. H. WU; A. B. Yu
2005-01-01
This paper analyses three popular methods simulating granular flow at different time and length scales:discrete element method (DEM), averaging method and viscous, elastic-plastic continuum model. The theoretical models of these methods and their applications to hopper flows are discussed. It is shown that DEM is an effective method to study the fundamentals of granular flow at a particle or microscopic scale. By use of the continuum approach, granular flow can also be described at a continuum or macroscopic scale. Macroscopic quantities such as velocity and stress can be obtained by use of such computational method as FEM. However, this approach depends on the constitutive relationship of materials and ignores the effect of microscopic structure of granular flow. The combined approach of DEM and averaging method can overcome this problem. The approach takes into account the discrete nature of granular materials and does not require any global assumption and thus allows a better understanding of the fundamental mechanisms of granular flow. However, it is difficult to adapt this approach to process modelling because of the limited number of particles which can be handled with the present computational capacity, and the difficulty in handling non-spherical particles.Further work is needed to develop an appropriate approach to overcome these problems.
Institute of Scientific and Technical Information of China (English)
Pooya Hamdi; Doug Stead; Davide Elmo
2015-01-01
abstract 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 (mDFN) approach. The characteristics of the microcracks required to create mDFN 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-mDFN models indicate that micro-heterogeneity has a profound influence on both the me-chanical 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 reproducing
Discrete-time modelling of musical instruments
Välimäki, 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.
Discrete-time modelling of musical instruments
Energy Technology Data Exchange (ETDEWEB)
Vaelimaeki, Vesa; Pakarinen, Jyri; Erkut, Cumhur; Karjalainen, Matti [Laboratory of Acoustics and Audio Signal Processing, Helsinki University of Technology, PO Box 3000, FI-02015 TKK, Espoo (Finland)
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.
Some discrete SI and SIS epidemic models
Institute of Scientific and Technical Information of China (English)
LI Jian-quan; LOU Jie; LOU Mei-zhi
2008-01-01
The probability is introduced to formulate the death of individuals, the recovery of the infected individuals and incidence of epidemic disease. Based on the assumption that the number of individuals in a population is a constant, discrete-time SI and SIS epidemic models with vital dynamics are established respectively corresponding to the case that the infectives can recover from the disease or not. For these two models, the results obtained in this paper show that there is the same dynamical behavior as their corresponding continuous ones, and the threshold determining its dynamical behavior is found. Below the threshold the epidemic disease dies out eventually, above the threshold the epidemic disease becomes an endemic eventually, and the number of the infectives approaches a positive constant.
Numerical modelling of flow and transport in rough fractures
Institute of Scientific and Technical Information of China (English)
Scott Briggs; Bryan W. Karney; Brent E. Sleep
2014-01-01
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.
Fractal modeling of natural fracture networks
Energy Technology Data Exchange (ETDEWEB)
Ferer, M.; Dean, B.; Mick, C.
1995-06-01
West Virginia University will implement procedures for a fractal analysis of fractures in reservoirs. This procedure will be applied to fracture networks in outcrops and to fractures intersecting horizontal boreholes. The parameters resulting from this analysis will be used to generate synthetic fracture networks with the same fractal characteristics as the real networks. Recovery from naturally fractured, tight-gas reservoirs is controlled by the fracture network. Reliable characterization of the actual fracture network in the reservoir is severely limited. The location and orientation of fractures intersecting the borehole can be determined, but the length of these fractures cannot be unambiguously determined. Because of the lack of detailed information about the actual fracture network, modeling methods must represent the porosity and permeability associated with the fracture network, as accurately as possible with very little a priori information. In the sections following, the authors will (1) present fractal analysis of the MWX site, using the box-counting procedure; (2) review evidence testing the fractal nature of fracture distributions and discuss the advantages of using the fractal analysis over a stochastic analysis; and (3) present an efficient algorithm for producing a self-similar fracture networks which mimic the real MWX outcrop fracture network.
Partially decoupled modeling of hydraulic fracturing processes
Energy Technology Data Exchange (ETDEWEB)
Settari, A.; Puchyr, P.J.; Bachman, R.C. (Simtech Consulting Services, Calgary (CA))
1990-02-01
A new method of partial decoupling of the problem of modeling a hydraulic fracture in a reservoir is described. According to the authors this approach has significant advantages over previous methods with fully coupled or completely uncoupled models. Better accuracy can be achieved in modeling the fracture propagation, and the new system is very efficient and versatile. Virtually any reservoir model can be used for predicting postfracture productivity. Examples of single- and multiphase applications for modeling fractured wells are discussed.
Tatomir, Alexandru Bogdan A. C.; Flemisch, Bernd; Class, Holger; Helmig, Rainer; Sauter, Martin
2017-04-01
Geological storage of CO2 represents one viable solution to reduce greenhouse gas emission in the atmosphere. Potential leakage of CO2 storage can occur through networks of interconnected fractures. The geometrical complexity of these networks is often very high involving fractures occurring at various scales and having hierarchical structures. Such multiphase flow systems are usually hard to solve with a discrete fracture modelling (DFM) approach. Therefore, continuum fracture models assuming average properties are usually preferred. The multiple interacting continua (MINC) model is an extension of the classic double porosity model (Warren and Root, 1963) which accounts for the non-linear behaviour of the matrix-fracture interactions. For CO2 storage applications the transient representation of the inter-porosity two phase flow plays an important role. This study tests the accuracy and computational efficiency of the MINC method complemented with the multiple sub-region (MSR) upscaling procedure versus the DFM. The two phase flow MINC simulator is implemented in the free-open source numerical toolbox DuMux (www.dumux.org). The MSR (Gong et al., 2009) determines the inter-porosity terms by solving simplified local single-phase flow problems. The DFM is considered as the reference solution. The numerical examples consider a quasi-1D reservoir with a quadratic fracture system , a five-spot radial symmetric reservoir, and a completely random generated fracture system. Keywords: MINC, upscaling, two-phase flow, fractured porous media, discrete fracture model, continuum fracture model
Discrete Element Modelling of Floating Debris
Mahaffey, Samantha; Liang, Qiuhua; Parkin, Geoff; Large, Andy; Rouainia, Mohamed
2016-04-01
Flash flooding is characterised by high velocity flows which impact vulnerable catchments with little warning time and as such, result in complex flow dynamics which are difficult to replicate through modelling. The impacts of flash flooding can be made yet more severe by the transport of both natural and anthropogenic debris, ranging from tree trunks to vehicles, wheelie bins and even storage containers, the effects of which have been clearly evident during recent UK flooding. This cargo of debris can have wide reaching effects and result in actual flood impacts which diverge from those predicted. A build-up of debris may lead to partial channel blockage and potential flow rerouting through urban centres. Build-up at bridges and river structures also leads to increased hydraulic loading which may result in damage and possible structural failure. Predicting the impacts of debris transport; however, is difficult as conventional hydrodynamic modelling schemes do not intrinsically include floating debris within their calculations. Subsequently a new tool has been developed using an emerging approach, which incorporates debris transport through the coupling of two existing modelling techniques. A 1D hydrodynamic modelling scheme has here been coupled with a 2D discrete element scheme to form a new modelling tool which predicts the motion and flow-interaction of floating debris. Hydraulic forces arising from flow around the object are applied to instigate its motion. Likewise, an equivalent opposing force is applied to fluid cells, enabling backwater effects to be simulated. Shock capturing capabilities make the tool applicable to predicting the complex flow dynamics associated with flash flooding. The modelling scheme has been applied to experimental case studies where cylindrical wooden dowels are transported by a dam-break wave. These case studies enable validation of the tool's shock capturing capabilities and the coupling technique applied between the two numerical
Odefy -- From discrete to continuous models
Directory of Open Access Journals (Sweden)
Wittmann Dominik M
2010-05-01
Full Text Available Abstract Background Phenomenological information about regulatory interactions is frequently available and can be readily converted to Boolean models. Fully quantitative models, on the other hand, provide detailed insights into the precise dynamics of the underlying system. In order to connect discrete and continuous modeling approaches, methods for the conversion of Boolean systems into systems of ordinary differential equations have been developed recently. As biological interaction networks have steadily grown in size and complexity, a fully automated framework for the conversion process is desirable. Results We present Odefy, a MATLAB- and Octave-compatible toolbox for the automated transformation of Boolean models into systems of ordinary differential equations. Models can be created from sets of Boolean equations or graph representations of Boolean networks. Alternatively, the user can import Boolean models from the CellNetAnalyzer toolbox, GINSim and the PBN toolbox. The Boolean models are transformed to systems of ordinary differential equations by multivariate polynomial interpolation and optional application of sigmoidal Hill functions. Our toolbox contains basic simulation and visualization functionalities for both, the Boolean as well as the continuous models. For further analyses, models can be exported to SQUAD, GNA, MATLAB script files, the SB toolbox, SBML and R script files. Odefy contains a user-friendly graphical user interface for convenient access to the simulation and exporting functionalities. We illustrate the validity of our transformation approach as well as the usage and benefit of the Odefy toolbox for two biological systems: a mutual inhibitory switch known from stem cell differentiation and a regulatory network giving rise to a specific spatial expression pattern at the mid-hindbrain boundary. Conclusions Odefy provides an easy-to-use toolbox for the automatic conversion of Boolean models to systems of ordinary
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.
Discrete Element Modeling for Mobility and Excavation
Knuth, M. A.; Hopkins, M. A.
2011-12-01
The planning and completion of mobility and excavation efforts on the moon requires a thorough understanding of the planetary regolith. In this work, a discrete element method (DEM) model is created to replicate those activities in the laboratory and for planning mission activities in the future. The crux of this work is developing a particle bed that best replicates the regolith tool/wheel interaction seen in the laboratory. To do this, a DEM geotechnical triaxial strength cell was created allowing for comparison of laboratory JSC-1a triaxial tests to DEM simulated soils. This model relies on a triangular lattice membrane covered triaxial cell for determining the macroscopic properties of the modeled granular material as well as a fast and efficient contact detection algorithm for a variety of grain shapes. Multiple grain shapes with increasing complexity (ellipsoid, poly-ellipsoid and polyhedra) have been developed and tested. This comparison gives us a basis to begin scaling DEM grain size and shape to practical values for mobility and excavation modeling. Next steps include development of a DEM scoop for percussive excavation testing as well as continued analysis of rover wheel interactions using a wide assortment of grain shape and size distributions.
Observational Equivalence of Discrete String Models and Market Models
Kerkhof, F.L.J.; Pelsser, A.
2002-01-01
In this paper we show that, contrary to the claim made in Longsta, Santa-Clara, and Schwartz (2001a) and Longsta, Santa-Clara, and Schwartz (2001b), discrete string models are not more parsimonious than market models.In fact, they are found to be observationally equivalent.We derive that, for the es
A priori discretization error metrics for distributed hydrologic modeling applications
Liu, Hongli; Tolson, Bryan A.; Craig, James R.; Shafii, Mahyar
2016-12-01
Watershed spatial discretization is an important step in developing a distributed hydrologic model. A key difficulty in the spatial discretization process is maintaining a balance between the aggregation-induced information loss and the increase in computational burden caused by the inclusion of additional computational units. Objective identification of an appropriate discretization scheme still remains a challenge, in part because of the lack of quantitative measures for assessing discretization quality, particularly prior to simulation. This study proposes a priori discretization error metrics to quantify the information loss of any candidate discretization scheme without having to run and calibrate a hydrologic model. These error metrics are applicable to multi-variable and multi-site discretization evaluation and provide directly interpretable information to the hydrologic modeler about discretization quality. The first metric, a subbasin error metric, quantifies the routing information loss from discretization, and the second, a hydrological response unit (HRU) error metric, improves upon existing a priori metrics by quantifying the information loss due to changes in land cover or soil type property aggregation. The metrics are straightforward to understand and easy to recode. Informed by the error metrics, a two-step discretization decision-making approach is proposed with the advantage of reducing extreme errors and meeting the user-specified discretization error targets. The metrics and decision-making approach are applied to the discretization of the Grand River watershed in Ontario, Canada. Results show that information loss increases as discretization gets coarser. Moreover, results help to explain the modeling difficulties associated with smaller upstream subbasins since the worst discretization errors and highest error variability appear in smaller upstream areas instead of larger downstream drainage areas. Hydrologic modeling experiments under
Institute of Scientific and Technical Information of China (English)
Qi Zhao; Andrea Lisjak; Omid Mahabadi; Qinya Liu; Giovanni Grasselli
2014-01-01
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 eval-uate 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)
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.
Zeeb, Conny; Frühwirt, Thomas; Konietzky, Heinz
2015-04-01
Key to a successful exploitation of deep geothermal reservoirs in a petrothermal environment is the hydraulic stimulation of the host rock to increase permeability. The presented research investigates the fracture propagation and interaction during hydraulic stimulation of multiple fractures in a highly anisotropic stress field. The presented work was conducted within the framework of the OPTIRISS project, which is a cooperation of industry partners and universities in Thuringia and Saxony (Federal States of Germany) and was funded by the European Fond for Regional Development. One objective was the design optimization of the subsurface geothermal heat exchanger (SGHE) by means of numerical simulations. The presented simulations were conducted applying 3DEC (Itasca™), a software tool based on the discrete element method. The simulation results indicate that the main direction of fracture propagation is towards lower stresses and thus towards the biosphere. Therefore, barriers might be necessary to limit fracture propagation to the designated geological formation. Moreover, the hydraulic stimulation significantly alters the stresses in the vicinity of newly created fractures. Especially the change of the minimum stress component affects the hydraulic stimulation of subsequent fractures, which are deflected away from the previously stimulated fractures. This fracture deflection can render it impossible to connect all fractures with a second borehole for the later production. The results of continuative simulations indicate that a fracture deflection cannot be avoided completely. Therefore, the stage alignment was modified to minimize fracture deflection by varying (1) the pauses between stages, (2) the spacing's between adjacent stages, and (3) the angle between stimulation borehole and minimum stress component. An optimum SGHE design, which implies that all stimulated fractures are connected to the production borehole, can be achieved by aligning the stimulation
Modeling fracture porosity evolution in dolostone
Gale, Julia F. W.; Lander, Robert H.; Reed, Robert M.; Laubach, Stephen E.
2010-09-01
Opening-mode fractures in dolostones buried to depths of ˜1-5 km contain synkinematic dolomite cement, the amount and internal structure of which has a systematic relationship to fracture size. Narrow fractures (cement or cement with a crack-seal texture that indicates multiple incremental openings. Wider fractures can preserve considerable effective porosity, but anomalously thick dolomite cement bridges are commonly present in fractures that are otherwise lined with a thin veneer of cement. Dolomite bridges resemble quartz bridges that are common in fractured sandstones. We developed a geometric crystal growth model for synkinematic dolomite fracture fill in fractured dolostones, where periodic incremental fracture-opening events are introduced with concurrent cement growth. We assumed constant temperature and supersaturation with respect to dolomite. A key assumption in the model is that rapid dolomite accumulation within bridges is governed by high cement-growth rates on repeatedly broken grain surfaces during the process of crack seal. Slower cement-growth rates occur on euhedral crystals. This assumption is made on the basis of a comparison with quartz cement growth in fractured sandstones. Simulations with different fracture-opening rates mimic bridge and lining cement morphologies, including characteristic rhombic shapes of dolomite bridges.
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
Discrete particle modelling of granular roll waves
Tsang, Jonathan; Dalziel, Stuart; Vriend, Nathalie
2016-11-01
A granular current flowing down an inclined chute or plane can undergo an instability that leads to the formation of surface waves, known as roll waves. Examples of roll waves are found in avalanches and debris flows in landslides, and in many industrial processes. Although related to the Kapitza instability of viscous fluid films, granular roll waves are not yet as well understood. Laboratory experiments typically measure the surface height and velocity of a current as functions of position and time, but they do not give insight into the processes below the surface: in particular, the possible formation of a boundary layer at the free surface as well as the base. To overcome this, we are running discrete particle model (DPM) simulations. Simulations are validated against our laboratory experiments, but they also allow us to examine a much larger range of parameters, such as material properties, chute geometry and particle size dispersity, than that which is possible in the lab. We shall present results from simulations in which we vary particle size and dispersity, and examine the implications on roll wave formation and propagation. Future work will include simulations in which the shape of the chute is varied, both cross-sectionally and in the downstream direction. EPSRC studentship (Tsang) and Royal Society Research Fellowship (Vriend).
Discrete element modeling of subglacial sediment deformation
Damsgaard, Anders; Egholm, David L.; Piotrowski, Jan A.; Tulaczyk, Slawek; Larsen, Nicolaj K.; Tylmann, Karol
2013-12-01
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 of the material dynamics and the shear zone development during progressive shear strain. The geometry of the heterogeneous stress network is visible in the form of force-carrying grain bridges and adjacent, volumetrically dominant, inactive zones. We demonstrate how the shear zone thickness and dilation depend on the level of normal (overburden) stress, and we show how high normal stress can mobilize material to great depths. The particle rotational axes tend to align with progressive shear strain, with rotations both along and reverse to the shear direction. The results from successive laboratory ring-shear experiments on simple granular materials are compared to results from similar numerical experiments. The simulated DEM material and all tested laboratory materials deform by an elastoplastic rheology under the applied effective normal stress. These results demonstrate that the DEM is a viable alternative to continuum models for small-scale analysis of sediment deformation. It can be used to simulate the macromechanical behavior of simple granular sediments, and it provides an opportunity to study how microstructures in subglacial sediments are formed during progressive shear strain.
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...
A priori discretization quality metrics for distributed hydrologic modeling applications
Liu, Hongli; Tolson, Bryan; Craig, James; Shafii, Mahyar; Basu, Nandita
2016-04-01
In distributed hydrologic modelling, a watershed is treated as a set of small homogeneous units that address the spatial heterogeneity of the watershed being simulated. The ability of models to reproduce observed spatial patterns firstly depends on the spatial discretization, which is the process of defining homogeneous units in the form of grid cells, subwatersheds, or hydrologic response units etc. It is common for hydrologic modelling studies to simply adopt a nominal or default discretization strategy without formally assessing alternative discretization levels. This approach lacks formal justifications and is thus problematic. More formalized discretization strategies are either a priori or a posteriori with respect to building and running a hydrologic simulation model. A posteriori approaches tend to be ad-hoc and compare model calibration and/or validation performance under various watershed discretizations. The construction and calibration of multiple versions of a distributed model can become a seriously limiting computational burden. Current a priori approaches are more formalized and compare overall heterogeneity statistics of dominant variables between candidate discretization schemes and input data or reference zones. While a priori approaches are efficient and do not require running a hydrologic model, they do not fully investigate the internal spatial pattern changes of variables of interest. Furthermore, the existing a priori approaches focus on landscape and soil data and do not assess impacts of discretization on stream channel definition even though its significance has been noted by numerous studies. The primary goals of this study are to (1) introduce new a priori discretization quality metrics considering the spatial pattern changes of model input data; (2) introduce a two-step discretization decision-making approach to compress extreme errors and meet user-specified discretization expectations through non-uniform discretization threshold
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...... problem, improve the performance of one model, and, through extensive numerical tests, compare all models from a computational perspective. The results indicate that a generalized setpartitioning model outperforms all other existing models....
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 pr...... problem, improve the performance of one model, and, through extensive numerical tests, compare all models from a computational perspective. The results indicate that a generalized set-partitioning model outperforms all other existing models....
3D mode discrete element method with the elastoplastic model
Institute of Scientific and Technical Information of China (English)
2012-01-01
The three-dimensional mode-deformable discrete element method (3MDEM) is an extended distinct element approach under the assumptions of small strain,finite displacement,and finite rotation of blocks.The deformation of blocks is expressed by the combination of the deformation modes in 3MDEM.In this paper,the elastoplastic constitutive relationship of blocks is implemented on the 3MDEM platform to simulate the integrated process from elasticity to plasticity and finally to fracture.To overcome the shortcomings of the conventional criterion for contact fracturing,a new criterion based on plastic strain is introduced.This approach is verified by two numerical examples.Finally,a cantilever beam is simulated as a comprehensive case study,which went through elastic,elastoplastic,and discontinuous fracture stages.
Discrete Element Modeling of Complex Granular Flows
Movshovitz, N.; Asphaug, E. I.
2010-12-01
Granular materials occur almost everywhere in nature, and are actively studied in many fields of research, from food industry to planetary science. One approach to the study of granular media, the continuum approach, attempts to find a constitutive law that determines the material's flow, or strain, under applied stress. The main difficulty with this approach is that granular systems exhibit different behavior under different conditions, behaving at times as an elastic solid (e.g. pile of sand), at times as a viscous fluid (e.g. when poured), or even as a gas (e.g. when shaken). Even if all these physics are accounted for, numerical implementation is made difficult by the wide and often discontinuous ranges in continuum density and sound speed. A different approach is Discrete Element Modeling (DEM). Here the goal is to directly model every grain in the system as a rigid body subject to various body and surface forces. The advantage of this method is that it treats all of the above regimes in the same way, and can easily deal with a system moving back and forth between regimes. But as a granular system typically contains a multitude of individual grains, the direct integration of the system can be very computationally expensive. For this reason most DEM codes are limited to spherical grains of uniform size. However, spherical grains often cannot replicate the behavior of real world granular systems. A simple pile of spherical grains, for example, relies on static friction alone to keep its shape, while in reality a pile of irregular grains can maintain a much steeper angle by interlocking force chains. In the present study we employ a commercial DEM, nVidia's PhysX Engine, originally designed for the game and animation industry, to simulate complex granular flows with irregular, non-spherical grains. This engine runs as a multi threaded process and can be GPU accelerated. We demonstrate the code's ability to physically model granular materials in the three regimes
Discrete model of dislocations in fractional nonlocal elasticity
National Research Council Canada - National Science Library
Tarasov, Vasily E
2016-01-01
Discrete models of dislocations in fractional nonlocal materials are suggested. The proposed models are based on fractional-order differences instead of finite differences of integer orders that are usually used...
A discrete model of energy-conserved wavefunction collapse
Gao, Shan
2013-01-01
Energy nonconservation is a serious problem of dynamical collapse theories. In this paper, we propose a discrete model of energy-conserved wavefunction collapse. It is shown that the model is consistent with existing experiments and our macroscopic experience.
Mixed continuous/discrete time modelling with exact time adjustments
Rovers, K.C.; Kuper, Jan; van de Burgwal, M.D.; Kokkeler, Andre B.J.; Smit, Gerardus Johannes Maria
2011-01-01
Many systems interact with their physical environment. Design of such systems need a modelling and simulation tool which can deal with both the continuous and discrete aspects. However, most current tools are not adequately able to do so, as they implement both continuous and discrete time signals
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 of the...
The Discrete Site Sticky Wall Model.
1986-05-27
TECHNICAL REPORT #23 THE DISCRETE SITE STICKY WALL tMDEL by J.P. Badiali Laboratoire Propre No 15 de CNRS Physique des Liquides et Electrochimie Tour 22, 5e...Liquides et Electrochimie NTIS CRA&I DTIC TAB 5 Tour 22, 5e Etage, 4 Place Jussieu U’annou;.ced . J ’ tificatlo rn
Directory of Open Access Journals (Sweden)
Yu Wang
2016-05-01
Full Text Available In this study, variable injection-rate technology was numerically investigated in a pre-existing discrete fracture network (DFN formation, the Tarim Basin in China. A flow-stress-damage (FSD coupling model has been used in an initial attempt towards how reservoir response to variable injection-rates at different hydraulic fracturing stages. The established numerical model simultaneously considered the macroscopic and microscopic heterogeneity characteristics. Eight numerical cases were studied. Four cases were used to study the variable injection-rate technology, and the other four cases were applied for a constant injection-rate in order to compare with the variable injection-rate technology. The simulation results show that the variable injection-rate technology is a potentially good method to a form complex fracturing networks. The hydraulic fracturing effectiveness when increasing the injection-rate at each stage is the best, also, the total injected fluid is at a minimum. At the initial stage, many under-fracturing points appear around the wellbore with a relatively low injection-rate; the sudden increase of injection rate drives the dynamic propagation of hydraulic fractures along many branching fracturing points. However, the case with decreasing injection rate is the worst. By comparing with constant injection-rate cases, the hydraulic fracturing effectiveness with variable flow rate technology is generally better than those with constant injection-rate technology. This work strongly links the production technology and hydraulic fracturing effectiveness evaluation and aids in the understanding and optimization of hydraulic fracturing simulations in naturally fractured reservoirs.
Discrete Element Method for Modeling Penetration
2006-07-01
toughness K,, increases as the rate of applied load is increased. Mindess et al. (1987) conducted experiments on single-edge 24 notched concrete beams loaded...547. Mindess , S., Banthia, N., and Yan, C., "The Fracture Toughness of Concrete under Impact Loading," Cement and Concrete Research, Vol. 17, 1987
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.
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.
Heterogeneous Speed Profiles in Discrete Models for Pedestrian Simulation
Bandini, Stefania; Crociani, Luca; Vizzari, Giuseppe
2014-01-01
Discrete pedestrian simulation models are viable alternatives to particle based approaches based on a continuous spatial representation. The effects of discretisation, however, also imply some difficulties in modelling certain phenomena that can be observed in reality. This paper focuses on the possibility to manage heterogeneity in the walking speed of the simulated population of pedestrians by modifying an existing multi-agent model extending the floor field approach. Whereas some discrete ...
Discrete Event Simulation Modeling and Analysis of Key Leader Engagements
2012-06-01
SIMULATION MODELING AND ANALYSIS OF KEY LEADER ENGAGEMENTS by Clifford C. Wakeman June 2012 Thesis Co-Advisors: Arnold H. Buss Susan...DATE June 2012 3. REPORT TYPE AND DATES COVERED Master’s Thesis 4. TITLE AND SUBTITLE Discrete Event Simulation Modeling and Analysis of Key...for public release; distribution is unlimited DISCRETE EVENT SIMULATION MODELING AND ANALYSIS OF KEY LEADER ENGAGEMENTS Clifford C. Wakeman
Discrete Modeling of the Worm Spread with Random Scanning
Uchida, Masato
In this paper, we derive a set of discrete time difference equations that models the spreading process of computer worms such as Code-Red and Slammer, which uses a common strategy called “random scanning” to spread through the Internet. We show that the derived set of discrete time difference equations has an exact relationship with the Kermack and McKendrick susceptible-infectious-removed (SIR) model, which is known as a standard continuous time model for worm spreading.
Hydraulic fracture model comparison study: Complete results
Energy Technology Data Exchange (ETDEWEB)
Warpinski, N.R. [Sandia National Labs., Albuquerque, NM (United States); Abou-Sayed, I.S. [Mobil Exploration and Production Services (United States); Moschovidis, Z. [Amoco Production Co. (US); Parker, C. [CONOCO (US)
1993-02-01
Large quantities of natural gas exist in low permeability reservoirs throughout the US. Characteristics of these reservoirs, however, make production difficult and often economic and stimulation is required. Because of the diversity of application, hydraulic fracture design models must be able to account for widely varying rock properties, reservoir properties, in situ stresses, fracturing fluids, and proppant loads. As a result, fracture simulation has emerged as a highly complex endeavor that must be able to describe many different physical processes. The objective of this study was to develop a comparative study of hydraulic-fracture simulators in order to provide stimulation engineers with the necessary information to make rational decisions on the type of models most suited for their needs. This report compares the fracture modeling results of twelve different simulators, some of them run in different modes for eight separate design cases. Comparisons of length, width, height, net pressure, maximum width at the wellbore, average width at the wellbore, and average width in the fracture have been made, both for the final geometry and as a function of time. For the models in this study, differences in fracture length, height and width are often greater than a factor of two. In addition, several comparisons of the same model with different options show a large variability in model output depending upon the options chosen. Two comparisons were made of the same model run by different companies; in both cases the agreement was good. 41 refs., 54 figs., 83 tabs.
Comparative study on mode split discrete choice models
Institute of Scientific and Technical Information of China (English)
Xianlong Chen; Xiaoqian Liu; Fazhi Li
2013-01-01
Discrete choice model acts as one of the most important tools for studies involving mode split in the context of transport demand forecast. As different types of discrete choice models display their merits and restrictions diversely, how to properly select the specific type among discrete choice models for realistic application still remains to be a tough problem. In this article, five typical discrete choice models for transport mode split are, respectively, discussed, which includes multinomial logit model, nested logit model (NL), heteroscedastic extreme value model, multinominal probit model and mixed multinomial logit model (MMNL). The theoretical basis and application attributes of these five models are especially analysed with great attention, and they are also applied to a realistic intercity case of mode split forecast, which results indi-cating that NL model does well in accommodating simi-larity and heterogeneity across alternatives, while MMNL model serves as the most effective method for mode choice prediction since it shows the highest reliability with the least significant prediction errors and even outperforms the other four models in solving the heterogeneity and similarity problems. This study indicates that conclusions derived from a single discrete choice model are not reli-able, and it is better to choose the proper model based on its characteristics.
Fracture model of radiation blistering
Energy Technology Data Exchange (ETDEWEB)
Kamada, K.; Higashida, Y.
1979-06-01
The formation process of blisters is interpreted by a fracture model on the basis of the stress fields around a lenticular bubble calculated in a previous paper. This model implicitly presumes a microcrack nucleated at a depth near the projected range of the ions. Two factors are separated theoretically to explain the blister formation: One is a geometrical factor which depends only on the ratio of size to depth, from a free surface, and the other factor is proportional to the square of the ratio between the internal gas pressure of the bubble to plastic yield stress of the target materials, depending entirely on the physical and chemical properties of the materials and gas atoms. The relation between the blister diameter and the cover thickness must be basically linear as expected from the first factor, but is modulated by the second factor, giving a slight departure from linearity as observed by experiment. The ratio of the gas pressure to the yield stress must be 0.02--0.2 in magnitude and depends on the ion energy and the target materials. This value leads to an estimation that the amount of gas atoms contained in the blister is about 10% of the injected ions. Griffith's criterion for the crack propagation in the subsurface layer with taking into account of ductility of the materials near the crack tip was derived, and showed that the estimated internal pressure of the blister is far smaller than the necessary pressure to satisfy the criterion. The objections against the gas-pressure model were criticized on the basis of the present model.
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
Dynamics of a discrete Lotka-Volterra model
National Research Council Canada - National Science Library
Din, Qamar
2013-01-01
In this paper, we study the equilibrium points, local asymptotic stability of equilibrium points, and global behavior of equilibrium points of a discrete Lotka-Volterra model given by where parameters...
Discrete Event Simulation Modeling of Radiation Medicine Delivery Methods
Energy Technology Data Exchange (ETDEWEB)
Paul M. Lewis; Dennis I. Serig; Rick Archer
1998-12-31
The primary objective of this work was to evaluate the feasibility of using discrete event simulation (DES) modeling to estimate the effects on system performance of changes in the human, hardware, and software elements of radiation medicine delivery methods.
DEFF Research Database (Denmark)
Bisdom, Kevin; Bertotti, Giovanni; Nick, Hamid
2016-01-01
on subsurface fracture aperture, which is essential for quantifying porosity and permeability. Apertures are difficult to obtain from either outcropping or subsurface data and are therefore often based on fracture size or scaling relationships, but these do not consider the orientation and spatial distribution...
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.
2016-05-01
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
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
Jørgensen, Jakob H; Pan, Xiaochuan
2011-01-01
Discrete-to-discrete imaging models for computed tomography (CT) are becoming increasingly ubiquitous as the interest in iterative image reconstruction algorithms has heightened. Despite this trend, all the intuition for algorithm and system design derives from analysis of continuous-to-continuous models such as the X-ray and Radon transform. While the similarity between these models justifies some crossover, questions such as what are sufficient sampling conditions can be quite different for the two models. This sampling issue is addressed extensively in the first half of the article using singular value decomposition analysis for determining sufficient number of views and detector bins. The question of full sampling for CT is particularly relevant to current attempts to adapt compressive sensing (CS) motivated methods to application in CT image reconstruction. The second half goes in depth on this subject and discusses the link between object sparsity and sufficient sampling for accurate reconstruction. Par...
Micromechanics Modeling of Fracture in Nanocrystalline Metals
Glaessgen, E. H.; Piascik, R. S.; Raju, I. S.; Harris, C. E.
2002-01-01
Nanocrystalline metals have very high theoretical strength, but suffer from a lack of ductility and toughness. Therefore, it is critical to understand the mechanisms of deformation and fracture of these materials before their full potential can be achieved. Because classical fracture mechanics is based on the comparison of computed fracture parameters, such as stress intlmsity factors, to their empirically determined critical values, it does not adequately describe the fundamental physics of fracture required to predict the behavior of nanocrystalline metals. Thus, micromechanics-based techniques must be considered to quanti@ the physical processes of deformation and fracture within nanocrystalline metals. This paper discusses hndamental physicsbased modeling strategies that may be useful for the prediction Iof deformation, crack formation and crack growth within nanocrystalline metals.
Discrete model of dislocations in fractional nonlocal elasticity
Directory of Open Access Journals (Sweden)
Vasily E. Tarasov
2016-01-01
Full Text Available Discrete models of dislocations in fractional nonlocal materials are suggested. The proposed models are based on fractional-order differences instead of finite differences of integer orders that are usually used. The fractional differences allow us to describe long-range interactions in materials. In continuous limit the suggested discrete models give continuum models of dislocations in nonlocal continua. Fractional generalization of the Frenkel–Kontorova model by using long-range interactions is suggested. We also propose a fractional generalization of interacting atomic chains (IAC model of dislocations by considering long-range interacting chains.
Discrete Element Simulation of Asphalt Mastics Based on Burgers Model
Institute of Scientific and Technical Information of China (English)
LIU Yu; FENG Shi-rong; HU Xia-guang
2007-01-01
In order to investigate the viscoelastic performance of asphalt mastics, a micro-mechanical model for asphalt mastics was built by applying Burgers model to discrete element simulation and constructing Burgers contact model. Then the numerical simulation of creep tests was conducted, and results from the simulation were compared with the analytical solution for Burgers model. The comparision snowed that the two results agreed well with each other, suggesting that discrete element model based on Burgers model could be employed in the numerical simulation for asphalt mastics.
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.
Modeling rammed earth wall using discrete element method
Bui, T.-T.; Bui, Q.-B.; Limam, A.; Morel, J.-C.
2016-03-01
Rammed earth is attracting renewed interest throughout the world thanks to its "green" characteristics in the context of sustainable development. Several research studies have thus recently been carried out to investigate this material. Some of them attempted to simulate the rammed earth's mechanical behavior by using analytical or numerical models. Most of these studies assumed that there was a perfect cohesion at the interface between earthen layers. This hypothesis proved to be acceptable for the case of vertical loading, but it could be questionable for horizontal loading. To address this problem, discrete element modeling seems to be relevant to simulate a rammed earth wall. To our knowledge, no research has been conducted thus far using discrete element modeling to study a rammed earth wall. This paper presents an assessment of the discrete element modeling's robustness for rammed earth walls. Firstly, a brief description of the discrete element modeling is presented. Then the parameters necessary for discrete element modeling of the material law of the earthen layers and their interfaces law following the Mohr-Coulomb model with a tension cut-off and post-peak softening were given. The relevance of the model and the material parameters were assessed by comparing them with experimental results from the literature. The results showed that, in the case of vertical loading, interfaces did not have an important effect. In the case of diagonal loading, model with interfaces produced better results. Interface characteristics can vary from 85 to 100% of the corresponding earthen layer's characteristics.
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,
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.
Conceptual Modeling for Discrete-Event Simulation
Robinson, Stewart
2010-01-01
What is a conceptual model? How is conceptual modeling performed in general and in specific modeling domains? What is the role of established approaches in conceptual modeling? This book addresses these issues
Model Adequacy Checks for Discrete Choice Dynamic Models
Kheifets, Igor
2012-01-01
This paper proposes new parametric model adequacy tests for possibly nonlinear and nonstationary time series models with noncontinuous data distribution, which is often the case in applied work. In particular, we consider the correct specification of parametric conditional distributions in dynamic discrete choice models, not only of some particular conditional characteristics such as moments or symmetry. Knowing the true distribution is important in many circumstances, in particular to apply efficient maximum likelihood methods, obtain consistent estimates of partial effects and appropriate predictions of the probability of future events. We propose a transformation of data which under the true conditional distribution leads to continuous uniform iid series. The uniformity and serial independence of the new series is then examined simultaneously. The transformation can be considered as an extension of the integral transform tool for noncontinuous data. We derive asymptotic properties of such tests taking into...
Bonded-cell model for particle fracture
Nguyen, Duc-Hanh; Azéma, Émilien; Sornay, Philippe; Radjaï, Farhang
2015-01-01
International audience; Particle degradation and fracture play an important role in natural granular flows and in many applications of granular materials. We analyze the fracture properties of two-dimensional disklike particles modeled as aggregates of rigid cells bonded along their sides by a cohesive Mohr-Coulomb law and simulated by the contact dynamics method. We show that the compressive strength scales with tensile strength between cells but depends also on the friction coefficient and ...
Cohesive mixed mode fracture modelling and experiments
DEFF Research Database (Denmark)
Walter, Rasmus; Olesen, John Forbes
2008-01-01
A nonlinear mixed mode model originally developed by Wernersson [Wernersson H. Fracture characterization of wood adhesive joints. Report TVSM-1006, Lund University, Division of Structural Mechanics; 1994], based on nonlinear fracture mechanics, is discussed and applied to model interfacial cracking...... in a steel–concrete interface. The model is based on the principles of Hillerborgs fictitious crack model, however, the Mode I softening description is modified taking into account the influence of shear. The model couples normal and shear stresses for a given combination of Mode I and II fracture...... curves, which may be interpreted using the nonlinear mixed mode model. The interpretation of test results is carried out in a two step inverse analysis applying numerical optimization tools. It is demonstrated how to perform the inverse analysis, which couples the assumed individual experimental load...
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.
Modeling of crack propagation in weak snowpack layers using the discrete element method
Directory of Open Access Journals (Sweden)
J. Gaume
2015-01-01
Full Text Available Dry-snow slab avalanches are generally caused by a sequence of fracture processes including (1 failure initiation in a weak snow layer underlying a cohesive slab, (2 crack propagation within the weak layer and (3 tensile fracture through the slab which leads to its detachment. During the past decades, theoretical and experimental work has gradually led to a better understanding of the fracture process in snow involving the collapse of the structure in the weak layer during fracture. This now allows us to better model failure initiation and the onset of crack propagation, i.e. to estimate the critical length required for crack propagation. On the other hand, our understanding of dynamic crack propagation and fracture arrest propensity is still very limited. For instance, it is not uncommon to perform field measurements with widespread crack propagation on one day, while a few days later, with very little changes to the snowpack, crack propagation does not occur anymore. Thus far, there is no clear theoretical framework to interpret such observations, and it is not clear how and which snowpack properties affect dynamic crack propagation. To shed more light on this issue, we performed numerical propagation saw test (PST experiments applying the discrete element (DE method and compared the numerical results with field measurements based on particle tracking. The goal is to investigate the influence of weak layer failure and the mechanical properties of the slab on crack propagation and fracture arrest propensity. Crack propagation speeds and distances before fracture arrest were derived from the DE simulations for different snowpack configurations and mechanical properties. Then, the relation between mechanical parameters of the snowpack was taken into account so as to compare numerical and experimental results, which were in good agreement, suggesting that the simulations can reproduce crack propagation in PSTs. Finally, an in-depth analysis of the
Parameter redundancy in discrete state‐space and integrated models
McCrea, Rachel S.
2016-01-01
Discrete state‐space models are used in ecology to describe the dynamics of wild animal populations, with parameters, such as the probability of survival, being of ecological interest. For a particular parametrization of a model it is not always clear which parameters can be estimated. This inability to estimate all parameters is known as parameter redundancy or a model is described as nonidentifiable. In this paper we develop methods that can be used to detect parameter redundancy in discrete state‐space models. An exhaustive summary is a combination of parameters that fully specify a model. To use general methods for detecting parameter redundancy a suitable exhaustive summary is required. This paper proposes two methods for the derivation of an exhaustive summary for discrete state‐space models using discrete analogues of methods for continuous state‐space models. We also demonstrate that combining multiple data sets, through the use of an integrated population model, may result in a model in which all parameters are estimable, even though models fitted to the separate data sets may be parameter redundant. PMID:27362826
Parameter redundancy in discrete state-space and integrated models.
Cole, Diana J; McCrea, Rachel S
2016-09-01
Discrete state-space models are used in ecology to describe the dynamics of wild animal populations, with parameters, such as the probability of survival, being of ecological interest. For a particular parametrization of a model it is not always clear which parameters can be estimated. This inability to estimate all parameters is known as parameter redundancy or a model is described as nonidentifiable. In this paper we develop methods that can be used to detect parameter redundancy in discrete state-space models. An exhaustive summary is a combination of parameters that fully specify a model. To use general methods for detecting parameter redundancy a suitable exhaustive summary is required. This paper proposes two methods for the derivation of an exhaustive summary for discrete state-space models using discrete analogues of methods for continuous state-space models. We also demonstrate that combining multiple data sets, through the use of an integrated population model, may result in a model in which all parameters are estimable, even though models fitted to the separate data sets may be parameter redundant. © 2016 The Author. Biometrical Journal published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Discrete holomorphicity and integrability in loop models with open boundaries
de Gier, Jan; Rasmussen, Jorgen
2012-01-01
We consider boundary conditions compatible with discrete holomorphicity for the dilute O(n) and C_2^(1) loop models. In each model, for a general set of boundary plaquettes, multiple types of loops can appear. A generalisation of Smirnov's parafermionic observable is therefore required in order to maintain the discrete holomorphicity property in the bulk. We show that there exist natural boundary conditions for this observable which are consistent with integrability, that is to say that, by imposing certain boundary conditions, we obtain a set of linear equations whose solutions also satisfy the corresponding reflection equation. In both loop models, several new sets of integrable weights are found using this approach.
Challenges in Continuum Modelling of Intergranular Fracture
DEFF Research Database (Denmark)
Coffman, Valerie; Sethna, James P.; Ingraffea, A. R.;
2011-01-01
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......, 3D grain boundary geometries comprise a five-dimensional space. Second, the energy and peak stress of grain boundaries have singularities for all commensurate grain boundaries, especially those with short repeat distances. Thirdly, fracture nucleation and growth depend not only upon the properties...... 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....
Universal asymptotic umbrella for hydraulic fracture modeling
Linkov, Aleksandr M
2014-01-01
The paper presents universal asymptotic solution needed for efficient modeling of hydraulic fractures. We show that when neglecting the lag, there is universal asymptotic equation for the near-front opening. It appears that apart from the mechanical properties of fluid and rock, the asymptotic opening depends merely on the local speed of fracture propagation. This implies that, on one hand, the global problem is ill-posed, when trying to solve it as a boundary value problem under a fixed position of the front. On the other hand, when properly used, the universal asymptotics drastically facilitates solving hydraulic fracture problems (both analytically and numerically). We derive simple universal asymptotics and comment on their employment for efficient numerical simulation of hydraulic fractures, in particular, by well-established Level Set and Fast Marching Methods.
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.
Ju, Yang; Zhang, Qingang; Zheng, Jiangtao; Chang, Chun; Xie, Heping
2017-02-01
The irregular morphology of single rock fracture significantly influences subsurface fluid flow and gives rise to a complex and unsteady flow state that typically cannot be appropriately described using simple laws. Yet the fluid flow in rough fractures of underground rock is poorly understood. Here we present a numerical method and experimental measurements to probe the effect of fracture roughness on the properties of fluid flow in fractured rock. We develop a series of fracture models with various degrees of roughness characterized by fractal dimensions that are based on the Weierstrass-Mandelbrot fractal function. The Lattice Boltzmann Method (LBM), a discrete numerical algorithm, is employed for characterizing the complex unsteady non-Darcy flow through the single rough fractures and validated by experimental observations under the same conditions. Comparison indicates that the LBM effectively characterizes the unsteady non-Darcy flow in single rough fractures. Our LBM model predicts experimental measurements of unsteady fluid flow through single rough fractures with great satisfactory, but significant deviation is obtained from the conventional cubic law, showing the superiority of LBM models of single rough fractures.
Fractal model and Lattice Boltzmann Method for Characterization of Non-Darcy Flow in Rough Fractures
Ju, Yang; Zhang, Qingang; Zheng, Jiangtao; Chang, Chun; Xie, Heping
2017-02-01
The irregular morphology of single rock fracture significantly influences subsurface fluid flow and gives rise to a complex and unsteady flow state that typically cannot be appropriately described using simple laws. Yet the fluid flow in rough fractures of underground rock is poorly understood. Here we present a numerical method and experimental measurements to probe the effect of fracture roughness on the properties of fluid flow in fractured rock. We develop a series of fracture models with various degrees of roughness characterized by fractal dimensions that are based on the Weierstrass-Mandelbrot fractal function. The Lattice Boltzmann Method (LBM), a discrete numerical algorithm, is employed for characterizing the complex unsteady non-Darcy flow through the single rough fractures and validated by experimental observations under the same conditions. Comparison indicates that the LBM effectively characterizes the unsteady non-Darcy flow in single rough fractures. Our LBM model predicts experimental measurements of unsteady fluid flow through single rough fractures with great satisfactory, but significant deviation is obtained from the conventional cubic law, showing the superiority of LBM models of single rough fractures.
Modeling of Immiscible, Two-Phase Flows in a Natural Rock Fracture
Energy Technology Data Exchange (ETDEWEB)
Crandall, Dustin; Ahmadi, Goodarz; Smith, Duane H
2009-01-01
One potential method of geologically sequestering carbon dioxide (CO2) is to inject the gas into brine-filled, subsurface formations. Within these low-permeability rocks, fractures exist that can act as natural fluid conduits. Understanding how a less viscous fluid moves when injected into an initially saturated rock fracture is important for the prediction of CO2 transport within fractured rocks. Our study examined experimentally and numerically the motion of immiscible fluids as they were transported through models of a fracture in Berea sandstone. The natural fracture geometry was initially scanned using micro-computerized tomography (CT) at a fine volume-pixel (voxel) resolution by Karpyn et al. [1]. This CT scanned fracture was converted into a numerical mesh for two-phase flow calculations using the finite-volume solver FLUENT® and the volume-of-fluid method. Additionally, a translucent experimental model was constructed using stereolithography. The numerical model was shown to agree well with experiments for the case of a constant rate injection of air into the initially water-saturated fracture. The invading air moved intermittently, quickly invading large-aperture regions of the fracture. Relative permeability curves were developed to describe the fluid motion. These permeability curves can be used in reservoir-scale discrete fracture models for predictions of fluid motion within fractured geological formations. The numerical model was then changed to better mimic the subsurface conditions at which CO2 will move into brine saturated fractures. The different fluid properties of the modeled subsurface fluids were shown to increase the amount of volume the less-viscous invading gas would occupy while traversing the fracture.
A New Physics-Based Modeling of Multiple Non-Planar Hydraulic Fractures Propagation
Energy Technology Data Exchange (ETDEWEB)
Zhou, Jing [University of Utah; Huang, Hai [Idaho National Lab. (INL), Idaho Falls, ID (United States); Deo, Milind [University of Utah; Jiang, Shu [Energy & Geoscience Institute
2015-10-01
Because of the low permeability in shale plays, closely spaced hydraulic fractures and multilateral horizontal wells are generally required to improve production. Therefore, understanding the potential fracture interaction and stress evolution is critical in optimizing fracture/well design and completion strategy in multi-stage horizontal wells. In this paper, a novel fully coupled reservoir flow and geomechanics model based on the dual-lattice system is developed to simulate multiple non-planar fractures propagation. The numerical model from Discrete Element Method (DEM) is used to simulate the mechanics of fracture propagations and interactions, while a conjugate irregular lattice network is generated to represent fluid flow in both fractures and formation. The fluid flow in the formation is controlled by Darcy’s law, but within fractures it is simulated by using cubic law for laminar flow through parallel plates. 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. We investigate the fracture propagation path in both homogeneous and heterogeneous reservoirs using the simulator developed. Stress shadow caused by the transverse fracture will change the orientation of principal stress in the fracture neighborhood, which may inhibit or alter the growth direction of nearby fracture clusters. However, the initial in-situ stress anisotropy often helps overcome this phenomenon. Under large in-situ stress anisotropy, the hydraulic fractures are more likely to propagate in a direction that is perpendicular to the minimum horizontal stress. Under small in-situ stress anisotropy, there is a greater chance for fractures from nearby clusters to merge with each other. Then, we examine the differences in fracture geometry caused by fracturing in cemented or uncemented wellbore. Moreover, the impact of
Stability analysis of the Euler discretization for SIR epidemic model
Energy Technology Data Exchange (ETDEWEB)
Suryanto, Agus [Department of Mathematics, Faculty of Sciences, Brawijaya University, Jl. Veteran Malang 65145 (Indonesia)
2014-06-19
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.
Discrete flavor symmetries in D-brane models
Marchesano, Fernando; Vázquez-Mercado, Liliana
2013-01-01
We study the presence of discrete flavor symmetries in D-brane models of particle physics. By analyzing the compact extra dimensions of these models one can determine when such symmetries exist both in the context of intersecting and magnetized D-brane constructions. Our approach allows to distinguish between approximate and exact discrete symmetries, and it can be applied to compactification manifolds with continuous isometries or to manifolds that only contain discrete isometries, like Calabi-Yau three-folds. We analyze in detail the class of rigid D-branes models based on a Z_2 x Z'_2 toroidal orientifold, for which the flavor symmetry group is either the dihedral group D_4 or tensor products of it. We construct explicit Pati-Salam examples in which families transform in non-Abelian representations of the flavor symmetry group, constraining Yukawa couplings beyond the effect of massive U(1) D-brane symmetries.
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
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.
Discrete element modelling of fluidised bed spray granulation
Goldschmidt, M.J.V.; Weijers, G.G.C.; Boerefijn, R.; Kuipers, J.A.M.
2003-01-01
A novel discrete element spray granulation model capturing the key features of fluidised bed hydrodynamics, liquid¿solid contacting and agglomeration is presented. The model computes the motion of every individual particle and droplet in the system, considering the gas phase as a continuum. Microsca
Discrete element modelling of fluidised bed spray granulation
Goldschmidt, M.J.V.; Weijers, G.G.C.; Boerefijn, R.; Kuipers, J.A.M.
2002-01-01
A novel discrete element spray granulation model capturing the key features of fluidised bed hydrodynamics, liquid-solid contacting and agglomeration is presented. The model computes the motion of every individual particle and droplet in the system, considering the gas phase as a continuum. Micro sc
Scaling limit of a discrete prion dynamics model
Doumic, Marie; Lepoutre, Thomas
2009-01-01
This paper investigates the connection between discrete and continuous models describing prion proliferation. The scaling parameters are interpreted on biological grounds and we establish rigorous convergence statements. We also discuss, based on the asymptotic analysis, relevant boundary conditions that can be used to complete the continuous model.
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...
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.
Model on surface borehole squeezing deformation fracture*
Institute of Scientific and Technical Information of China (English)
SUN Hai-tao; HU Qian-ting; HUANG Sheng-shu
2009-01-01
As a good method to solve the problem of high methane on the workface and in the goaf, drawing coal strata methane through a surface borehole is used. However, the excavation affected the overlying rock strata greatly. When the excavation face passed through the surface borehole position, the surface borehole fractures fast. This problem was seriously related to the unformed squeeze effect. Therefore, a squeezing deformation fracture model based on the rock strata squeezing effect was set up. At the same time, a 3DEC simulation model is presented to confirm the theory. The result shows that the mod-el is reliable and has a good engineering application value.
A Gaussian Mixed Model for Learning Discrete Bayesian Networks.
Balov, Nikolay
2011-02-01
In this paper we address the problem of learning discrete Bayesian networks from noisy data. Considered is a graphical model based on mixture of Gaussian distributions with categorical mixing structure coming from a discrete Bayesian network. The network learning is formulated as a Maximum Likelihood estimation problem and performed by employing an EM algorithm. The proposed approach is relevant to a variety of statistical problems for which Bayesian network models are suitable - from simple regression analysis to learning gene/protein regulatory networks from microarray data.
Analysis of mixed-mode fracture in concrete using interface elements and a cohesive crack model
Indian Academy of Sciences (India)
Víctor O García-Álvarez; Ravindra Gettu; Ignacio Carol
2012-02-01
The paper presents a model, based on nonlinear fracture mechanics, for analysing crack propagation in quasi-brittle materials, such as concrete. The work is limited to two-dimensions, and therefore, the fracture modes of interest are mode I (pure tension) and mode II (pure shear). The constitutive model has been implemented in the context of the ﬁnite element method using interface elements. The fracture is simulated through a discrete crack represented by the interface with a cohesive crack stress-separation relation derived from the model, which is based on a fracture criterion, together with a ﬂow rule and a softening law. The model is used for simulating results from an experimental study on beams with centric and eccentric notches of high and normal strength concretes, and explaining other test results available in the literature.
Discrete element modelling of granular materials
Van Baars, S.
1996-01-01
A new model is developed by the author, which does not use the equations of motion but the equations of equilibrium to describe granular materials. The numerical results show great similarities with reality and can generally be described by an advanced Mohr-Coulomb model. However, many contacts betw
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
A discrete element model for simulating saturated granular soil
Institute of Scientific and Technical Information of China (English)
Mahan Lamei; Ali Asghar Mirghasemi
2011-01-01
A numerical model is developed to simulate saturated granular soil,based on the discrete element method.Soil particles are represented by Lagrangian discrete elements,and pore fluid,by appropriate discrete elements which represent alternately Lagrangian mass of water and Eulerian volume of space.Macroscale behavior of the model is verified by simulating undrained biaxial compression tests.Micro-scale behavior is compared to previous literature through pore pressure pattern visualization during shear tests,it is demonstrated that dynamic pore pressure patterns are generated by superposed stress waves.These pore-pressure patterns travel much faster than average drainage rate of the pore fluid and may initiate soil fabric change,ultimately leading to liquefaction in loose sands.Thus,this work demonstrates a tool to roughly link dynamic stress wave patterns to initiation of liquefaction phenomena.
Discrete gradient methods for solving variational image regularisation models
Grimm, V.; McLachlan, Robert I.; McLaren, David I.; Quispel, G. R. W.; Schönlieb, C.-B.
2017-07-01
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.
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.
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.
A numerical approach for pressure transient analysis of a vertical well with complex fractures
Institute of Scientific and Technical Information of China (English)
Yizhao Wan; Yuewu Liu; Wenchao Liu; Guofeng Han; Congcong Niu
2016-01-01
A new well test model for a vertical fractured well is developed based on a discrete-fracture model in which the fractures are discretized as one dimensional (1-D) entities. The model overcomes the weakness of complex meshing, a large number of grids, and instability in conventional stripe-fracture models. Then, the discrete-fracture model is implemented using a hybrid element finite-element method. Triangular elements are used for matrix and line elements for the fractures. The finite element formulation is validated by comparing with the semi-analytical solution of a single ver-tical fractured well. The accuracy of the approach is shown through several examples with different fracture apertures, fracture conductivity, and fracture amount. Results from the discrete-fracture model agree reasonably well with the stripe-fracture model and the analytic solutions. The advantages of the discrete-fracture model are presented in mesh gen-eration, computational improvement, and abilities to handle complex fractures like wedge-shaped fractures and fractures with branches. Analytical results show that the number of grids in the discrete-fracture model is 10%less than stripe-fracture model, and computational efficiency increases by about 50%. The more fractures there are, the more the com-putational efficiency increases.
Applied mathematics: Models, Discretizations, and Solvers
Institute of Scientific and Technical Information of China (English)
D.E. Keyes
2007-01-01
@@ Computational plasma physicists inherit decades of developments in mathematical models, numerical algorithms, computer architecture, and software engineering, whose recent coming together marks the beginning of a new era of large-scale simulation.
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)
Particle Decision Making Processes in Fractured Media: The Battle Between Models
Sund, N. L.; Parashar, R.; Pham, H. V.
2016-12-01
During a random walk through a discrete fracture network, a particle moves at a constant velocity through a fracture segment and when it arrives at a fracture intersection it chooses a path, changes velocity, and repeats the process. The set of possible velocities the particle may choose depends on which intersection it is at, inducing a correlation between its current and next velocity. This process of traveling at a constant velocity then choosing a new velocity is also a good approximation to transport in (non-fractured) porous media.For times greater than the Taylor time scale (L^2/D, where L is the length scale over which a particle must travel to sample the full range of velocities in the system and D is the diffusion coefficient), the particle's decision making process can be neglected. In fractured and highly heterogeneous porous media, however, this length scale (and time scale consequently) can be prohibitively long. Even for field scale applications, it's possible that this decision making process may not be neglected. Several upscaled models have been developed that either explicitly or implicitly model this decision making process, including continuous time random walk with a coupled space and time step distribution, multi-rate mass transfer models, the spatial Markov model, and a hybrid approach based on the Boltzmann transport equation. We ask: how do these models perform in predicting transport at scales of interest? To answer this question, we upscale transport using a variety of models in simple 2D discrete fracture networks, where transport through each fracture is purely advective (no longitudinal diffusion), yet fully mixed (infinite transverse diffusion) and there is no mass exchange between the fracture network and the rock matrix it is embedded in. This simplified testing ground reveals whether the question of "how" to model the decision process is as important as "whether" to model it.
Mass Transport Modelling in low permeability Fractured Rock: Eulerian versus Lagrangian approaches.
Capilla, J. E.; Rodrigo, J.; Llopis, C.; Grisales, C.; Gomez-Hernandez, J. J.
2003-04-01
Modeling flow and mass transport in fractured rocks can not be always successfully addressed by means of discrete fracture models which can fail due to the difficulty to be calibrated to experimental measurements. This is due to the need of having an accurate knowledge of fractures geometry and of the bidimensional distribution of hydrodynamic parameters on them. Besides, these models tend to be too rigid in the sense of not being able to re-adapt themselves correcting deficiencies or errors in the fracture definition. An alternative approach is assuming a pseudo-continuum media in which fractures are represented by the introduction of discretization blocks of very high hydraulic conductivity (K). This kind of model has been successfully tested in some real cases where the stochastic inversion of the flow equation has been performed to obtain equally likely K fields. However, in this framework, Eulerian mass transport modeling yields numerical dispersion and oscillations that make very difficult the analysis of tracer tests and the inversion of concentration data to identify K fields. In this contribution we present flow and mass transport modelling results in a fractured medium approached by a pseudo-continuum. The case study considered is based on data from a low permeability formation and both Eulerian and Lagrangian approaches have been applied. K fields in fractures are modeled as realizations of a stochastic process conditional to piezometric head data. Both a MultiGaussian and a non-multiGaussian approches are evaluated. The final goal of this research is obtaining K fields able to reproduce field tracer tests. Results show the important numerical problems found when applying an Eurelian approach and the possibilities of avoiding them with a 3D implementation of the Lagrangian random walk method. Besides, we see how different can be mass transport predictions when Gaussian and non-Gaussian models are assumed for K fields in fractures.
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
Topological impact of constrained fracture growth
Directory of Open Access Journals (Sweden)
Sigmund Mongstad Hope
2015-09-01
Full Text Available The topology of two discrete fracture network models is compared to investigate the impact of constrained fracture growth. In the Poissonian discrete fracture network model the fractures are assigned length, position and orientation independent of all other fractures, while in the mechanical discrete fracture network model the fractures grow and the growth can be limited by the presence of other fractures. The topology is found to be impacted by both the choice of model, as well as the choice of rules for the mechanical model. A significant difference is the degree mixing. In two dimensions the Poissonian model results in assortative networks, while the mechanical model results in disassortative networks. In three dimensions both models produce disassortative networks, but the disassortative mixing is strongest for the mechanical model.
Discrete choice models with multiplicative error terms
DEFF Research Database (Denmark)
Fosgerau, Mogens; Bierlaire, Michel
2009-01-01
differences. We develop some properties of this type of model and show that in several cases the change from an additive to a multiplicative formulation, maintaining a specification of V, may lead to a large improvement in fit, sometimes larger than that gained from introducing random coefficients in V....
Modelling localised fracture of reinforced concrete structures
Liao, F; Huang, Z.
2015-01-01
This paper presents a robust finite element procedure for simulating the localised fracture of reinforced concrete members. In this new model the concrete member is modelled as an assembly of plain concrete, reinforcing steel bar and bond-link elements. The 4-node quadrilateral elements are used for 2D modelling of plain concrete elements, in which the extended finite element method is adopted to simulate the formation and growth of individual cracks. The reinforcing steel bars are modelled b...
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.
Discrete Flavor Symmetries and Models of Neutrino Mixing
Altarelli, Guido
2010-01-01
We review the application of non abelian discrete groups to the theory of neutrino masses and mixing, which is strongly suggested by the agreement of the Tri-Bimaximal mixing pattern with experiment. After summarizing the motivation and the formalism, we discuss specific models, based on A4, S4 and other finite groups, and their phenomenological implications, including lepton flavor violating processes, leptogenesis and the extension to quarks. In alternative to Tri-Bimaximal mixing the application of discrete flavor symmetries to quark-lepton complementarity and Bimaximal Mixing is also considered.
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...
Costly innovators versus cheap imitators: a discrete choice model
Hommes, C.; Zeppini, P.
2010-01-01
Two alternative ways to an innovative product or process are R&D investment or imitation of others’ innovation. In this article we propose a discrete choice model with costly innovators and free imitators and study the endogenous dynamics of price and demand in a market with many firms producing a h
Bayesian online algorithms for learning in discrete Hidden Markov Models
Alamino, Roberto C.; Caticha, Nestor
2008-01-01
We propose and analyze two different Bayesian online algorithms for learning in discrete Hidden Markov Models and compare their performance with the already known Baldi-Chauvin Algorithm. Using the Kullback-Leibler divergence as a measure of generalization we draw learning curves in simplified situations for these algorithms and compare their performances.
Fractured-basement reservoir modeling using continuous fracture modeling (CFM) method
Isniarny, Nadya; Haris, Abdul; Nurdin, Safrizal
2016-02-01
The challenge in oil and gas exploration has now shifted due to increasingly difficult to get back up economic value in a conventional reservoir. Explorationist are developing various drilling technology, optimizing conventional reserves and unconventional reserve in reservoirs. One of the unconventional reservoir that has been developed is the basement reservoir. This rock type has no primary porosity and the permeability of the rocks of this type are generally influenced by the naturally fracture networks. The purpose of this study is to map the fracture intensity distribution in the basement reservoir using Continuous Fracture Modeling (CFM) method. CFM method applies the basic concepts of neural network in finding a relationship between well data with seismic data in order to build a model of fracture intensity. The Formation Micro Imager (FMI) interpretation data is used to identify the presence of fracture along the well as dip angle and dip azimuth. This indicator will be laterally populated in 3D grid model. Several seismic attribute which are generated from seismic data is used as a guidance to populate fracture intensity in the model. The results from the model were validated with Drill Stem Test (DST) data. Zones of high fracture intensity on the model correlates positively with the presence of fluid in accordance with DST data.
Local Lagrangian Formalism and Discretization of the Heisenberg Magnet Model
Karpeev, D
2004-01-01
In this paper we develop the Lagrangian and multisymplectic structures of the Heisenberg magnet (HM) model which are then used as the basis for geometric discretizations of HM. Despite a topological obstruction to the existence of a global Lagrangian density, a local variational formulation allows one to derive local conservation laws using a version of N\\"other's theorem from the formal variational calculus of Gelfand-Dikii. Using the local Lagrangian form we extend the method of Marsden, Patrick and Schkoller to derive local multisymplectic discretizations directly from the variational principle. We employ a version of the finite element method to discretize the space of sections of the trivial magnetic spin bundle $N = M\\times S^2$ over an appropriate space-time $M$. Since sections do not form a vector space, the usual FEM bases can be used only locally with coordinate transformations intervening on element boundaries, and conservation properties are guaranteed only within an element. We discuss possible w...
Discrete-element model for the interaction between ocean waves and sea ice.
Xu, Zhijie; Tartakovsky, Alexandre M; Pan, Wenxiao
2012-01-01
We present a discrete-element method (DEM) model to simulate the mechanical behavior of sea ice in response to ocean waves. The interaction of ocean waves and sea ice potentially can lead to the fracture and fragmentation of sea ice depending on the wave amplitude and period. The fracture behavior of sea ice explicitly is modeled by a DEM method where sea ice is modeled by densely packed spherical particles with finite sizes. These particles are bonded together at their contact points through mechanical bonds that can sustain both tensile and compressive forces and moments. Fracturing naturally can be represented by the sequential breaking of mechanical bonds. For a given amplitude and period of incident ocean waves, the model provides information for the spatial distribution and time evolution of stress and microfractures and the fragment size distribution. We demonstrate that the fraction of broken bonds α increases with increasing wave amplitude. In contrast, the ice fragment size l decreases with increasing amplitude. This information is important for the understanding of the breakup of individual ice floes and floe fragment size.
On the Spectral Problems for the Discrete Boltzmann Models
Institute of Scientific and Technical Information of China (English)
Aq Kwang-Hua Chu; J. FANG Jing
2000-01-01
The discrete Boltzmann models are used to study the spectral problems related to the one-dimensional plane wave propaogation in monatomic gases which are fundamental in the nonequilibrium tatistical thermodynamics. The results show that the 8-velocity model can only describe the propagation of the diffusion mode (entropy wave) in the intermediate Knudsen number regime. The 4- and 6-velocity models, instead, can describe the propagation of sound modes quite well, after comparison with the continuum-mechanical results.
A Discrete Velocity Traffic Kinetic Model Including Desired Speed
Directory of Open Access Journals (Sweden)
Shoufeng Lu
2013-05-01
Full Text Available We introduce the desired speed variable into the table of games and formulate a new table of games and the corresponding discrete traffic kinetic model. We use the hybrid programming technique of VB and MATLAB to develop the program. Lastly, we compared the proposed model result and the detector data. The results show that the proposed model can describe the traffic flow evolution.
Piecewise Silence in Discrete Cosmological Models
Clifton, Timothy; Rosquist, Kjell
2014-01-01
We consider a family of cosmological models in which all mass is confined to a regular lattice of identical black holes. By exploiting the reflection symmetry about planes that bisect these lattices into identical halves, we are able to consider the evolution of a number of geometrically distinguished surfaces that exist within each of them. We show that gravitational waves are effectively trapped within small chambers for all time, and are not free to propagate throughout the space-time. Each chamber therefore evolves as if it were in isolation from the rest of the universe. We call this phenomenon "piecewise silence".
Discrete element modeling of subglacial sediment deformation
DEFF Research Database (Denmark)
Damsgaard, Anders; Egholm, David L.; Piotrowski, Jan A.
. The numerical approach allows for a detailed analysis of the material dynamics and shear zone development during progressive shear strain. We demonstrate how the shear zone thickness and dilation increase with the magnitude of the normal stress. The stresses are distributed heterogeneously through the granular...... of the inter-particle contacts parameterizes the model. For validating the numerical approach, the macromechanical behavior of the numerical material is compared to the results from successive laboratory ring-shear experiments. Overall, there is a good agreement between the geotechnical behavior of the real...... granular materials and the numerical results. The materials deform by an elasto-plastic rheology under the applied effective normal stress and horizontal shearing. The peak and ultimate shear strengths depend linearly on the magnitude of the normal stress by the Mohr-Coulomb constitutive relationship...
Discrete element modeling of subglacial sediment deformation
DEFF Research Database (Denmark)
Damsgaard, Anders; Egholm, David L.; Piotrowski, Jan A.
2013-01-01
-shear experiments on simple granular materials are compared to results from similar numerical experiments. The simulated DEM material and all tested laboratory materials deform by an elasto-plastic rheology under the applied effective normal stress. These results demonstrate that the DEM is a viable alternative...... on the level of normal (overburden) stress, and we show how high normal stress can mobilize material to great depths. The particle rotational axes tend to align with progressive shear strain, with rotations both along and reverse to the shear direction. The results from successive laboratory ring...... to continuum models for small-scale analysis of sediment deformation. It can be used to simulate the macromechanical behavior of simple granular sediments, and it provides an opportunity to study how microstructures in subglacial sediments are formed during progressive shear strain....
A Spatial Clustering Approach for Stochastic Fracture Network Modelling
Seifollahi, S.; Dowd, P. A.; Xu, C.; Fadakar, A. Y.
2014-07-01
Fracture network modelling plays an important role in many application areas in which the behaviour of a rock mass is of interest. These areas include mining, civil, petroleum, water and environmental engineering and geothermal systems modelling. The aim is to model the fractured rock to assess fluid flow or the stability of rock blocks. One important step in fracture network modelling is to estimate the number of fractures and the properties of individual fractures such as their size and orientation. Due to the lack of data and the complexity of the problem, there are significant uncertainties associated with fracture network modelling in practice. Our primary interest is the modelling of fracture networks in geothermal systems and, in this paper, we propose a general stochastic approach to fracture network modelling for this application. We focus on using the seismic point cloud detected during the fracture stimulation of a hot dry rock reservoir to create an enhanced geothermal system; these seismic points are the conditioning data in the modelling process. The seismic points can be used to estimate the geographical extent of the reservoir, the amount of fracturing and the detailed geometries of fractures within the reservoir. The objective is to determine a fracture model from the conditioning data by minimizing the sum of the distances of the points from the fitted fracture model. Fractures are represented as line segments connecting two points in two-dimensional applications or as ellipses in three-dimensional (3D) cases. The novelty of our model is twofold: (1) it comprises a comprehensive fracture modification scheme based on simulated annealing and (2) it introduces new spatial approaches, a goodness-of-fit measure for the fitted fracture model, a measure for fracture similarity and a clustering technique for proposing a locally optimal solution for fracture parameters. We use a simulated dataset to demonstrate the application of the proposed approach
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.
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.
Hsu, Shih-Meng; Ke, Chien-Chung; Lo, Hung-Chieh; Lin, Yen-Tsu; Huang, Chi-Chao
2016-04-01
On the basis of a relatively sparse data set, fractured aquifers are difficult to be characterized and modelled. The three-dimensional configuration of transmissive fractures and fracture zones is needed to be understood flow heterogeneity in the aquifer. Innovative technologies for the improved interpretation are necessary to facilitate the development of accurate predictive models of ground-water flow and solute transport or to precisely estimate groundwater potential. To this end, this paper presents a procedure for characterizing and modelling preferential flow path in the fractured rock aquifer carried out at Fractured Rock Hydrogeology Research Site in Shuangliou Forest Recreation Area, Pingtung County, Southern Taiwan. The Shuangliou well field is a 40 by 30-meter area consisting of 6 wells (one geological well, one pumping well and four hydrogeological testing wells). The bedrock at the site is mainly composed of slate and intercalated by meta-sandstone. The overburden consists of about 5.6 m of gravel deposits. Based on results of 100 m geological borehole with borehole televiewer logging, vertical flow logging and full-wave sonic logging, high transmissivity zones in the bedrock underlying the well field were identified. One of transmissivity zone (at the depths of 30~32 m) and its fracture orientation(N56/54) selected for devising a multiple well system with 4 boreholes (borehole depths :45m, 35m, 35m and 25m, respectively), which were utilized to perform cross-borehole flow velocity data under the ambient flow and pumped flow conditions to identify preferential flow paths. Results from the cross-borehole test show the preferential flow pathways are corresponding to the predicted ones. Subsequently, a 3-D discrete fracture network model based on outcrop data was generated by the FracMan code. A validation between observed and simulated data has proved that the present model can accurately predict the hydrogeological properties (e.g., number of fractures
Discrete echo signal modeling of ultrasound imaging systems
Chen, Ming; Zhang, Cishen
2008-03-01
In this paper, a discrete model representing the pulse-tissue interaction in the medical ultrasound scanning and imaging process is developed. The model is based on discretizing the acoustical wave equation and is in terms of convolution between the input ultrasound pulses and the tissue mass density variation. Such a model can provide a useful means for ultrasound echo signal processing and imaging. Most existing models used for ultrasound imaging are based on frequency domain transform. A disadvantage of the frequency domain transform is that it is only applicable to shift-invariant models. Thus it has ignored the shift-variant nature of the original acoustic wave equation where the tissue compressibility and mass density distributions are spatial-variant factors. The discretized frequency domain model also obscures the compressibility and mass density representations of the tissue, which may mislead the physical understanding and interpretation of the image obtained. Moreover, only the classical frequency domain filtering methods have been applied to the frequency domain model for acquiring some tissue information from the scattered echo signals. These methods are non-parametric and require a prior knowledge of frequency spectra of the transmitted pulses. Our proposed model technique will lead to discrete, multidimensional, shift-variant and parametric difference or convolution equations with the transmitted pulse pressure as the input, the measurement data of the echo signals as the output, and functions of the tissue compressibility and mass density distributions as shift-variant parameters that can be readily identified from input-output measurements. The proposed model represents the entire multiple scattering process, and hence overcomes the key limitation in the current ultrasound imaging methods.
Novel web service selection model based on discrete group search.
Zhai, Jie; Shao, Zhiqing; Guo, Yi; Zhang, Haiteng
2014-01-01
In our earlier work, we present a novel formal method for the semiautomatic verification of specifications and for describing web service composition components by using abstract concepts. After verification, the instantiations of components were selected to satisfy the complex service performance constraints. However, selecting an optimal instantiation, which comprises different candidate services for each generic service, from a large number of instantiations is difficult. Therefore, we present a new evolutionary approach on the basis of the discrete group search service (D-GSS) model. With regard to obtaining the optimal multiconstraint instantiation of the complex component, the D-GSS model has competitive performance compared with other service selection models in terms of accuracy, efficiency, and ability to solve high-dimensional service composition component problems. We propose the cost function and the discrete group search optimizer (D-GSO) algorithm and study the convergence of the D-GSS model through verification and test cases.
Numerical Fractional-Calculus Model for Two-Phase Flow in Fractured Media
Directory of Open Access Journals (Sweden)
Wenwen Zhong
2013-01-01
Full Text Available Numerical simulation of two-phase flow in fractured porous media is an important topic in the subsurface flow, environmental problems, and petroleum reservoir engineering. The conventional model does not work well in many cases since it lacks the memory property of fracture media. In this paper, we develop a new numerical formulation with fractional time derivative for two-phase flow in fractured porous media. In the proposed formulation, the different fractional time derivatives are applied to fracture and matrix regions since they have different memory properties. We further develop a two-level time discrete method, which uses a large time step for the pressure and a small time step size for the saturation. The pressure equation is solved implicitly in each large time step, while the saturation is updated by an explicit fractional time scheme in each time substep. Finally, the numerical tests are carried out to demonstrate the effectiveness of the proposed numerical model.
Defects in the discrete non-linear Schroedinger model
Energy Technology Data Exchange (ETDEWEB)
Doikou, Anastasia, E-mail: adoikou@upatras.gr [University of Patras, Department of Engineering Sciences, Physics Division, GR-26500 Patras (Greece)
2012-01-01
The discrete non-linear Schroedinger (NLS) model in the presence of an integrable defect is examined. The problem is viewed from a purely algebraic point of view, starting from the fundamental algebraic relations that rule the model. The first charges in involution are explicitly constructed, as well as the corresponding Lax pairs. These lead to sets of difference equations, which include particular terms corresponding to the impurity point. A first glimpse regarding the corresponding continuum limit is also provided.
Discrete Boltzmann model of shallow water equations with polynomial equilibria
Meng, Jianping; Emerson, David R; Peng, Yong; Zhang, Jianmin
2016-01-01
A hierarchy of discrete Boltzmann model is proposed for simulating shallow water flows. By using the Hermite expansion and Gauss-Hermite quadrature, the conservation laws are automatically satisfied without extra effort. Moreover, the expansion order and quadrature can be chosen flexibly according to the problem for striking the balance of accuracy and efficiency. The models are then tested using the classical one-dimensional dam-breaking problem, and successes are found for both supercritical and subcritical flows.
Social Networks and Choice Set Formation in Discrete Choice Models
Directory of Open Access Journals (Sweden)
Bruno Wichmann
2016-10-01
Full Text Available The discrete choice literature has evolved from the analysis of a choice of a single item from a fixed choice set to the incorporation of a vast array of more complex representations of preferences and choice set formation processes into choice models. Modern discrete choice models include rich specifications of heterogeneity, multi-stage processing for choice set determination, dynamics, and other elements. However, discrete choice models still largely represent socially isolated choice processes —individuals are not affected by the preferences of choices of other individuals. There is a developing literature on the impact of social networks on preferences or the utility function in a random utility model but little examination of such processes for choice set formation. There is also emerging evidence in the marketplace of the influence of friends on choice sets and choices. In this paper we develop discrete choice models that incorporate formal social network structures into the choice set formation process in a two-stage random utility framework. We assess models where peers may affect not only the alternatives that individuals consider or include in their choice sets, but also consumption choices. We explore the properties of our models and evaluate the extent of “errors” in assessment of preferences, economic welfare measures and market shares if network effects are present, but are not accounted for in the econometric model. Our results shed light on the importance of the evaluation of peer or network effects on inclusion/exclusion of alternatives in a random utility choice framework.
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...... 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....
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....
Mishchenko, Michael I; Yurkin, Maxim A; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R Lee; Travis, Larry D; Yang, Ping; Zakharova, Nadezhda T
2016-01-01
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 the first-principles formalism enabling accurate calculations of monochromatic and quasi-monochromatic scattering by static and randomly varying multiparticle groups. We illustrate how this general framework can be coupled with state-of-the-art computer solvers of the Maxwell equations and applied to direct modeling of electromagnetic scattering by representative random multi-particle groups with arbitrary packing densities. This first-principles modeling yields general physical insights unavailable with phenomenological approaches. We discuss how the first-order-scattering approximation, the radiative transfer theory, and the theory of weak localization of electromagnetic waves ...
LARGE SIGNAL DISCRETE-TIME MODEL FOR PARALLELED BUCK CONVERTERS
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
As a number of switch-combinations are involved in operation of multi-converter-system, conventional methods for obtaining discrete-time large signal model of these converter systems result in a very complex solution. A simple sampled-data technique for modeling distributed dc-dc PWM converters system (DCS) was proposed. The resulting model is nonlinear and can be linearized for analysis and design of DCS. These models are also suitable for fast simulation of these networks. As the input and output of dc-dc converters are slow varying, suitable model for DCS was obtained in terms of the finite order input/output approximation.
TESTING FOR VARYING DISPERSION IN DISCRETE EXPONENTIAL FAMILY NONLINEAR MODELS
Institute of Scientific and Technical Information of China (English)
LinJinguan; WeiBocheng; ZhangNansong
2003-01-01
It is necessary to test for varying dispersion in generalized nonlinear models. Wei ,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models. This type of problem in the framework of general discrete exponential family nonlinear models is discussed. Two types of varying dispersion, which are random coefficients model and random effects model, are proposed,and corresponding score test statistics are constructed and expressed in simple ,easy to use ,matrix formulas.
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.
New Discrete Element Models for Three-Dimensional Impact Problems
Institute of Scientific and Technical Information of China (English)
SHAN Li; CHENG Ming; LIU Kai-xin; LIU Wei-Fu; CHEN Shi-Yang
2009-01-01
Two 3-D numerical models of the discrete element method(DEM)for impact problems are proposed.The models can calculate not only the impact problems of continuum and non-continuum,but also the transient process from continuum to non-continuum.The stress wave propagation in a concrete block and a dynamic splitting process of a marble disc under impact loading are numerically simulated with the proposed models.By comparing the numerical results with the corresponding results obtained by the finite element method(FEM)and the experiments,it is proved that the models are reliable for three-dimensional impact problems.
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...... in the current state as a covariate. We propose estimators that allow for group-specific effect in parametric and semiparametric versions of the model. The proposed method is illustrated by an empirical analysis of job durations allowing for firm-level effects....
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.
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
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 grains. This is true even of the resilient (or reversible) deformations. It is also interesting because the Discrete Element Method models resilient and plastic deformations as well as failure in a single process.The paper describes two types of calculations. One on a small sample of angular elements...... subjected to a pulsating (repeated) biaxial loading and another of a larger sample of circular element subjected to a plate load. Both cases are two dimensional, i.e. plane strain.The repeated biaxial loading showed a large increase in plastic strain for the first load pulse at a given load level...
A discrete Lagrangian based direct approach to macroscopic modelling
Sarkar, Saikat; Nowruzpour, Mohsen; Reddy, J. N.; Srinivasa, A. R.
2017-01-01
A direct discrete Lagrangian based approach, designed at a length scale of interest, to characterize the response of a body is proposed. The main idea is to understand the dynamics of a deformable body via a Lagrangian corresponding to a coupled interaction of rigid particles in the reduced dimension. We argue that the usual practice of describing the laws of a deformable body in the continuum limit is redundant, because for most of the practical problems, analytical solutions are not available. Since continuum limit is not taken, the framework automatically relaxes the requirement of differentiability of field variables. The discrete Lagrangian based approach is illustrated by deriving an equivalent of the Euler-Bernoulli beam model. A few test examples are solved, which demonstrate that the derived non-local model predicts lower deflections in comparison to classical Euler-Bernoulli beam solutions. We have also included crack propagation in thin structures for isotropic and anisotropic cases using the Lagrangian based approach.
Choice-Based Conjoint Analysis: Classification vs. Discrete Choice Models
Giesen, Joachim; Mueller, Klaus; Taneva, Bilyana; Zolliker, Peter
Conjoint analysis is a family of techniques that originated in psychology and later became popular in market research. The main objective of conjoint analysis is to measure an individual's or a population's preferences on a class of options that can be described by parameters and their levels. We consider preference data obtained in choice-based conjoint analysis studies, where one observes test persons' choices on small subsets of the options. There are many ways to analyze choice-based conjoint analysis data. Here we discuss the intuition behind a classification based approach, and compare this approach to one based on statistical assumptions (discrete choice models) and to a regression approach. Our comparison on real and synthetic data indicates that the classification approach outperforms the discrete choice 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.
Numerical modeling of oil displacement by water injection in fractured chalk
Energy Technology Data Exchange (ETDEWEB)
Gudbjerg, J. [Environment and Resources - DTU (Denmark); Hoegh Jensen, K. [Univ. of Copenhagen, Geological Inst. (Denmark)
2003-08-01
Modeling of multiphase flow in fractured porous media is complex due to the extreme heterogeneity introduced by the fractures. In this report modeling is performed using the numerical code T2VOC, which has not previously been tested on petroleum reservoir processes. Over the years several conceptual models have been proposed to model fracture flow. This work focuses on the following approaches: discrete fracture, dual-porosity and equivalent porous medium. The basic difference in these models is the way they discretized the domain of interest and thus their applicability vary with the scale of the problem. Olsen et al. (2001)performed a displacement experiment on a small chalk plug with a single fracture and modeled it using the numerical code Eclipse. In this report the experiment has been modeled using various concepts and degrees of discretization using T2VOC. The results obtained with T2VOC are coherent with earlier results obtained with Eclipse. It was not possible to match the outflow curve, which could be explained by the presence of a secondary fracture system or a larger capillary drive not accounted for in the model. The effect of using a different capillary pressure function was analyzed. It was shown that the best results were obtained using upstream weighting of the relative permeability even if the non-physical value of the outlet chamber was used. In general the dual-porosity concept could not capture the transient effects arising due to non-equilibrium between fracture and matrix. When using a pseudo-capillary pressure curve the recovery could be perfectly matched with only six grid blocks. When the injection rate was below the matrix imbibition rate the fracture and matrix were almost at equilibrium and it was possible to use a dualporosity concept and an equivalent porous medium concept. It was shown that using only a larger intrinsic permeability as effective parameter in the equivalent porous medium approach gave an erroneous intermediate
Models of optimum discrete signals on the vector combinatorial configurations
Directory of Open Access Journals (Sweden)
V. V. Riznyk
2016-06-01
Full Text Available Method for construction of optimum discrete signals, based on a new conceptual combinatorial model of the systems - Ideal Ring Vector sequences (clusters of the IRV is proposed. IRV clusters are cyclic ordered sequences of t- integer sub-sequences of sequence, which form perfect relationships of t-dimensional partitions over a virtual t-dimensional lattice covered surface of a finite space interval. The sums of connected sub-sequences of an IRV enumerate the set of t- coordinates specified with respect to cyclic frame reference exactly R-times. This property makes IRVs useful in applications, which need to partition multidimensional objects with the smallest possible number of intersections. There are discover a great class of new two- and multidimensional combinatorial constructions, which being in excess classic models of discrete systems with respect to number and combinatorial varieties with theoretically non-limited values of upper boundaries on order of dimensionality –IRV. It shows that remarkable properties of IRVs encoded in fine structure of torus circular symmetry. There are regarded basic properties these models and made shortest comparative analysis of the models with classical models. Indicate that the IRVs to be in exceed of difference sets multiply, and set of the classical difference sets is subset of the IRVs. Some of useful examples for constructing of the optimum discrete signals, error-correcting codes, and ring monolithic optimum vector codes using IRVs are considered. The problem statement involves development the regular method for construction of the optimum discrete signals using two- and multidimensional IRVs. The favorable technical merits of IRVs sets named “Gloria to Ukraine Stars”, which remarkable properties hold for the same set of the IRVs in varieties permutations of its terms is demonstrated, and method for design of two- or multidimensional vector signals coded based on the optimum binary monolithic
Phase computations and phase models for discrete molecular oscillators
2012-01-01
Background Biochemical oscillators perform crucial functions in cells, e.g., they set up circadian clocks. The dynamical behavior of oscillators is best described and analyzed in terms of the scalar quantity, phase. A rigorous and useful definition for phase is based on the so-called isochrons of oscillators. Phase computation techniques for continuous oscillators that are based on isochrons have been used for characterizing the behavior of various types of oscillators under the influence of perturbations such as noise. Results In this article, we extend the applicability of these phase computation methods to biochemical oscillators as discrete molecular systems, upon the information obtained from a continuous-state approximation of such oscillators. In particular, we describe techniques for computing the instantaneous phase of discrete, molecular oscillators for stochastic simulation algorithm generated sample paths. We comment on the accuracies and derive certain measures for assessing the feasibilities of the proposed phase computation methods. Phase computation experiments on the sample paths of well-known biological oscillators validate our analyses. Conclusions The impact of noise that arises from the discrete and random nature of the mechanisms that make up molecular oscillators can be characterized based on the phase computation techniques proposed in this article. The concept of isochrons is the natural choice upon which the phase notion of oscillators can be founded. The isochron-theoretic phase computation methods that we propose can be applied to discrete molecular oscillators of any dimension, provided that the oscillatory behavior observed in discrete-state does not vanish in a continuous-state approximation. Analysis of the full versatility of phase noise phenomena in molecular oscillators will be possible if a proper phase model theory is developed, without resorting to such approximations. PMID:22687330
Phase Computations and Phase Models for Discrete Molecular Oscillators.
Demir, Alper; Şuvak, Önder
2012-01-01
RESEARCH Open Access Phase computations and phase models for discrete molecular oscillators Onder Suvak* and Alper Demir Abstract Background: Biochemical oscillators perform crucial functions in cells, e.g., they set up circadian clocks. The dynamical behavior of oscillators is best described and analyzed in terms of the scalar quantity, phase. A rigorous and useful definition for phase is based on the so-called isochrons of oscillators. Phase computation techniques for ...
A discrete latent factor model for smoking, cancer and mortality.
Howdon, D.; Jones, A
2013-01-01
This paper investigates the relationships between social circumstances, individual behaviours, and ill-health later in life, with a particular focus on the development of cancer. A discrete latent factor model incorporating individuals' smoking and health outcomes (lifespan and time-to-cancer) is jointly estimated, using the 1984/5 British Health and Lifestyle Survey (HALS) dataset and its July 2009 follow-up, allowing for unobservable factors to affect decisions regarding smoking behaviours ...
The origin of discrete symmetries in F-theory models
2015-01-01
While non-abelian groups are undoubtedly the cornerstone of Grand Unified Theories (GUTs), phenomenology shows that the role of abelian and discrete symmetries is equally important in model building. The latter are the appropriate tool to suppress undesired proton decay operators and various flavour violating interactions, to generate a hierarchical fermion mass spectrum, etc. In F-theory, GUT symmetries are linked to the singularities of the elliptically fibred K3 manifolds; they are of ADE ...
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.
COHESIVE ZONE FINITE ELEMENT-BASED MODELING OF HYDRAULIC FRACTURES
Institute of Scientific and Technical Information of China (English)
Zuorong Chen; A.P. Bunger; Xi Zhang; Robert G. Jeffrey
2009-01-01
Hydraulic fracturing is a powerful technology used to stimulate fluid production from reservoirs. The fully 3-D numerical simulation of the hydraulic fracturing process is of great importance to the efficient application of this technology, but is also a great challenge because of the strong nonlinear coupling between the viscous flow of fluid and fracture propagation. By taking advantage of a cohesive zone method to simulate the fracture process, a finite element model based on the existing pore pressure cohesive finite elements has been established to investigate the propagation of a penny-shaped hydraulic fracture in an infinite elastic medium. The effect of cohesive material parameters and fluid viscosity on the hydraulic fracture behaviour has been investigated. Excellent agreement between the finite element results and analytical solutions for the limiting case where the fracture process is dominated by rock fracture toughness demonstrates the ability of the cohesive zone finite element model in simulating the hydraulic fracture growth for this case.
Solvation of chromone using combined Discrete/SCRF models
Alemán, Carlos; Galembeck, Sergio E.
1998-06-01
The solvation of chromone has been investigated using three different combined Discrete/SCRF models. Four chromone-H 2O complexes and one chromone-4H 2O complex were obtained from geometry optimizations at the HF/6-31G(d) level. Three SCRF methods (PCM/6-31G(d), PCM/AM1 and SM2/AM1) were applied to such complexes in order to: (1) evaluate the reliability of the combined Discrete/SCRF models; (2) investigate the effects of the explicit water molecules on the free energy of solvation; and (3) analyze the characteristics of the different solvation sites of chromone. The results show that explicit solvent molecules exert a large influence on the free energy of solvation of a given molecular system providing some information about the solvation sites. Thus, the interaction of the carbonyl oxygen of chromone with the explicit water molecules is stronger than interaction provided by the ether oxygen, providing the complexes with the former interaction a more hydrophobic free energy of solvation than those with the latter. On the other hand, the comparison of the free energies of solvation for solutes with explicit water molecules in the first hydration shell and the free energies of solvation of the molecular system computed in an all-continuum approach reveals that the combined Discrete/SCRF models constitute a very reasonable strategy.
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).
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
Dynamic model of normal behavior of rock fractures
Institute of Scientific and Technical Information of China (English)
YANG Wen-yi; KONG Guang-ya; CAI Jun-gang
2005-01-01
Based on laboratory tests of artificial fractures in mortar material, established the dynamic constitutive model of normal behaviour of rock fracture,. The tests were systematically conducted under quasi-static and dynamic monotonic loading conditions. The fractures were of different numbers of asperities in contact and were subsequently of different initial contact areas, which imitated the natural rock fractures. The rate of compressive load applied normal to the fractures covers a wide range from 10-1 MPa/s (quasi-static) up to 103 MPa/s (highly dynamic). The normal stress-closure responses of fractures were measured for different loading rates. Based on the stress-closure relation curves measured, a nonlinear (hyperbolic) dynamic model of fracture, normal behaviour, termed as dynamic BB model, was proposed, which was modified from the existing BB model of static normal behaviour of fractures by taking into account the effect of loading rate.
Bonded-cell model for particle fracture.
Nguyen, Duc-Hanh; Azéma, Emilien; Sornay, Philippe; Radjai, Farhang
2015-02-01
Particle degradation and fracture play an important role in natural granular flows and in many applications of granular materials. We analyze the fracture properties of two-dimensional disklike particles modeled as aggregates of rigid cells bonded along their sides by a cohesive Mohr-Coulomb law and simulated by the contact dynamics method. We show that the compressive strength scales with tensile strength between cells but depends also on the friction coefficient and a parameter describing cell shape distribution. The statistical scatter of compressive strength is well described by the Weibull distribution function with a shape parameter varying from 6 to 10 depending on cell shape distribution. We show that this distribution may be understood in terms of percolating critical intercellular contacts. We propose a random-walk model of critical contacts that leads to particle size dependence of the compressive strength in good agreement with our simulation data.
Spectral Problems for the Orientation-Free Discrete Kinetic Models
Institute of Scientific and Technical Information of China (English)
朱光华; 金燕芳; 方竞
2002-01-01
We present computations using orientation-free discrete velocity models for the dispersion relationship of ultrasound propagation in monatomic hard-sphere gases (or a type of gas composed of a system of vortices).Comparisons with previous verified fixed-orientation results for the propagation of the sound mode in rarefied gases show that, if collective excitations are considered, an orientation-free eight-velocity model can capture more physical insights. We also demonstrate the symmetry property of the spectra using the orientation-free eight-velocity model.
Context-specific graphical models for discret longitudinal data
DEFF Research Database (Denmark)
Edwards, David; Anantharama Ankinakatte, Smitha
2015-01-01
Ron et al. (1998) introduced a rich family of models for discrete longitudinal data called acyclic probabilistic finite automata. These may be represented as directed graphs that embody context-specific conditional independence relations. Here, the approach is developed from a statistical...... perspective. It is shown here that likelihood ratio tests may be constructed using standard contingency table methods, a model selection procedure that minimizes a penalized likelihood criterion is described, and a way to extend the models to incorporate covariates is proposed. The methods are applied...
Complex Dynamics of Discrete SEIS Models with Simple Demography
Directory of Open Access Journals (Sweden)
Hui Cao
2011-01-01
Full Text Available We investigate bifurcations and dynamical behaviors of discrete SEIS models with exogenous reinfections and a variety of treatment strategies. Bifurcations identified from the models include period doubling, backward, forward-backward, and multiple backward bifurcations. Multiple attractors, such as bistability and tristability, are observed. We also estimate the ultimate boundary of the infected regardless of initial status. Our rigorously mathematical analysis together with numerical simulations show that epidemiological factors alone can generate complex dynamics, though demographic factors only support simple equilibrium dynamics. Our model analysis supports and urges to treat a fixed percentage of exposed individuals.
Modelling discrete longitudinal data using acyclic probabilistic finite automata
DEFF Research Database (Denmark)
Anantharama Ankinakatte, Smitha; Edwards, David
2015-01-01
Acyclic probabilistic finite automata (APFA) constitute a rich family of models for discrete longitudinal data. An APFA may be represented as a directed multigraph, and embodies a set of context-specific conditional independence relations that may be read off the graph. A model selection algorithm...... to minimize a penalized likelihood criterion such as AIC or BIC is described. This algorithm is compared to one implemented in Beagle, a widely used program for processing genomic data, both in terms of rate of convergence to the true model as the sample size increases, and a goodness-of-fit measure assessed...
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.
Gaussian estimation for discretely observed Cox-Ingersoll-Ross model
Wei, Chao; Shu, Huisheng; Liu, Yurong
2016-07-01
This paper is concerned with the parameter estimation problem for Cox-Ingersoll-Ross model based on discrete observation. First, a new discretized process is built based on the Euler-Maruyama scheme. Then, the parameter estimators are obtained by employing the maximum likelihood method and the explicit expressions of the error of estimation are given. Subsequently, the consistency property of all parameter estimators are proved by applying the law of large numbers for martingales, Holder's inequality, B-D-G inequality and Cauchy-Schwarz inequality. Finally, a numerical simulation example for estimators and the absolute error between estimators and true values is presented to demonstrate the effectiveness of the estimation approach used in this paper.
Discrete-event modeling for internet multi-robotics
Institute of Scientific and Technical Information of China (English)
赵杰; 高胜; 蔡鹤皋
2004-01-01
Intemet multi-robotics is a typical discrete-event system. In order to describe joint activities between multiple operators and multiple robots, a 4-level discrete-event model is proposed in this paper based on the controlled condition/event Petri nets (CCEP). On the first or mission level, the task splitting of the system is defined; on the second or multi-operator level, a precedence graph is introduced for every operator to plan his or her robotic actions; on the third or coordination level, the above precedence graphs are translated and integrated into the corresponding CCEPs in terms of specific rules; and on the last or multi-robot level, operators can select their control range by setting the corresponding control marks of the obtained CCEPs. As a consequence, a clear mechanism of operator-robot collaboration is obtained to conduct the development of the system.
Fracture development around deep underground excavations: Insights from FDEM modelling
Directory of Open Access Journals (Sweden)
Andrea Lisjak
2014-12-01
Full Text Available Over the past twenty years, there has been a growing interest in the development of numerical models that can realistically capture the progressive failure of rock masses. In particular, the investigation of damage development around underground excavations represents a key issue in several rock engineering applications, including tunnelling, mining, drilling, hydroelectric power generation, and the deep geological disposal of nuclear waste. The goal of this paper is to show the effectiveness of a hybrid finite-discrete element method (FDEM code to simulate the fracturing mechanisms associated with the excavation of underground openings in brittle rock formations. A brief review of the current state-of-the-art modelling approaches is initially provided, including the description of selecting continuum- and discontinuum-based techniques. Then, the influence of a number of factors, including mechanical and in situ stress anisotropy, as well as excavation geometry, on the simulated damage is analysed for three different geomechanical scenarios. Firstly, the fracture nucleation and growth process under isotropic rock mass conditions is simulated for a circular shaft. Secondly, the influence of mechanical anisotropy on the development of an excavation damaged zone (EDZ around a tunnel excavated in a layered rock formation is considered. Finally, the interaction mechanisms between two large caverns of an underground hydroelectric power station are investigated, with particular emphasis on the rock mass response sensitivity to the pillar width and excavation sequence. Overall, the numerical results indicate that FDEM simulations can provide unique geomechanical insights in cases where an explicit consideration of fracture and fragmentation processes is of paramount importance.
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.
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.
A Fracture Mechanical Model and a Cohesive Zone Model of Interface Fracture
DEFF Research Database (Denmark)
Jensen, Henrik Myhre
2006-01-01
A comparison between the prediction of crack propagation through an adhesive interface based on a fracture mechanics approach and a cohesive zone approach is presented. Attention is focussed on predicting the shape of the crack front and the critical stress required to propagate the crack under...... quasi-static conditions. The cohesive zone model has several advantages over the fracture mechanics based model. It is easier to generalise the cohesive zone model to take into account effects such as plastic deformation in the adherends, and to take into account effects of large local curvatures...... of the interface crack front. The comparison shows a convergence of the results based on the cohesive zone model towards the results based on a fracture mechanics approach in the limit where the size of the cohesive zone becomes smaller than other relevant geometrical lengths for the problem....
Continuous vs. discrete models for the quantum harmonic oscillator and the hydrogen atom
Lorente, M
2001-01-01
The Kravchuk and Meixner polynomials of discrete variable are introduced for the discrete models of the harmonic oscillator and hydrogen atom. Starting from Rodrigues formula we construct raising and lowering operators, commutation and anticommutation relations. The physical properties of discrete models are figured out through the equivalence with the continuous models obtained by limit process.
Continuous vs. discrete models for the quantum harmonic oscillator and the hydrogen atom
Lorente, Miguel
2001-07-01
The Kravchuk and Meixner polynomials of discrete variable are introduced for the discrete models of the harmonic oscillator and hydrogen atom. Starting from Rodrigues formula we construct raising and lowering operators, commutation and anticommutation relations. The physical properties of discrete models are figured out through the equivalence with the continuous models obtained by limit process.
Continuous vs. discrete models for the quantum harmonic oscillator and the hydrogen atom
Lorente, M.
2004-01-01
The Kravchuk and Meixner polynomials of discrete variable are introduced for the discrete models of the harmonic oscillator and hydrogen atom. Starting from Rodrigues formula we construct raising and lowering operators, commutation and anticommutation relations. The physical properties of discrete models are figured out through the equivalence with the continuous models obtained by limit process.
Fracture and Medium Modeling, by Analizing Hidraulic Fracturing Induced Microseismicity
Gomez Alba, S.; Vargas Jiménez, C. A.
2014-12-01
Hydraulic fracturing is an essential technology for most unconventional hydrocarbon resources and many conventional ones as well. The primary limitation on the improvement and optimization of the fracturing process is the minimal access to observe the behavior of the fracture in the subsurface. Without direct observational evidence, hypothetical mechanisms must be assumed and then tested for their validity with indirect information such as wellbore measurements, indirect production and pressure behavior. One of the most important sources of information today is the relation made between micro seismic source mechanisms and fracture behavior. Hydraulic fractures induce some level of micro seismicity when the stress conditions in the Earth are altered by changes in stress during the operations. The result is the sudden movement between rock elements and the radiation of both compressional and shear energy in a seismic range that can be detected and recorded with sensitive receivers. The objective of this work is to provide reasonable information when applying inversion methods in order to estimate the vertical and horizontal spatial heterogeneities in medium and energy radiation distribution of microseisms while fracking operations. The method consist in record microseisms at a previous lineal array of stations (triaxial accelerometers) which are located close to the source coordinates and cover the area of study. The analysis clarify some ideas about what information can be gained from the micro seismic source data and according to the obtained results, what kind of comparisons and associations might be done to evaluate the fracking performance operation. Non uniformities in medium such as faults would be revealed by interpreted scattering coefficients. Fracture properties like distance, velocity and orientation would be also determined by analyzing energy radiation.
On reevaluation rate in discrete time Hogg-Huberman model
Tanaka, Toshijiro; Shibata, Junko; Inoue, Masayoshi
2002-06-01
The discrete time Hogg-Huberman model is extended to a case with time-dependent reevaluation rate at which agents using one resource decide to evaluate their resource choice. In this paper the time dependence of the reevaluation rate is determined by states of the system. The dynamical behavior of the extended Hogg-Huberman model is discussed. It is found that the change of fraction of agents using resource 1 is suppressed to be smaller than that in the case of constant reevaluation rate.
A discourse on sensitivity analysis for discretely-modeled structures
Adelman, Howard M.; Haftka, Raphael T.
1991-01-01
A descriptive review is presented of the most recent methods for performing sensitivity analysis of the structural behavior of discretely-modeled systems. The methods are generally but not exclusively aimed at finite element modeled structures. Topics included are: selections of finite difference step sizes; special consideration for finite difference sensitivity of iteratively-solved response problems; first and second derivatives of static structural response; sensitivity of stresses; nonlinear static response sensitivity; eigenvalue and eigenvector sensitivities for both distinct and repeated eigenvalues; and sensitivity of transient response for both linear and nonlinear structural response.
Discrete state space modeling and control of nonlinear unknown systems.
Savran, Aydogan
2013-11-01
A novel procedure for integrating neural networks (NNs) with conventional techniques is proposed to design industrial modeling and control systems for nonlinear unknown systems. In the proposed approach, a new recurrent NN with a special architecture is constructed to obtain discrete-time state-space representations of nonlinear dynamical systems. It is referred as the discrete state-space neural network (DSSNN). In the DSSNN, the outputs of the hidden layer neurons of the DSSNN represent the system's (pseudo) state. The inputs are fed to output neurons and the delayed outputs of the hidden layer neurons are fed to their inputs via adjustable weights. The discrete state space model of the actual system is directly obtained by training the DSSNN with the input-output data. A training procedure based on the back-propagation through time (BPTT) algorithm is developed. The Levenberg-Marquardt (LM) method with a trust region approach is used to update the DSSNN weights. Linear state space models enable to use well developed conventional analysis and design techniques. Thus, building a linear model of a system has primary importance in industrial applications. Thus, a suitable linearization procedure is proposed to derive the linear state space model from the nonlinear DSSNN representation. The controllability, observability and stability properties are examined. The state feedback controllers are designed with both the linear quadratic regulator (LQR) and the pole placement techniques. The regulator and servo control problems are both addressed. A full order observer is also designed to estimate the state variables. The performance of the proposed procedure is demonstrated by applying for both single-input single-output (SISO) and multiple-input multiple-output (MIMO) nonlinear control problems. © 2013 ISA. Published by Elsevier Ltd. All rights reserved.
Continuous-time discrete-space models for animal movement
Hanks, Ephraim M.; Hooten, Mevin B.; Alldredge, Mat W.
2015-01-01
The processes influencing animal movement and resource selection are complex and varied. Past efforts to model behavioral changes over time used Bayesian statistical models with variable parameter space, such as reversible-jump Markov chain Monte Carlo approaches, which are computationally demanding and inaccessible to many practitioners. We present a continuous-time discrete-space (CTDS) model of animal movement that can be fit using standard generalized linear modeling (GLM) methods. This CTDS approach allows for the joint modeling of location-based as well as directional drivers of movement. Changing behavior over time is modeled using a varying-coefficient framework which maintains the computational simplicity of a GLM approach, and variable selection is accomplished using a group lasso penalty. We apply our approach to a study of two mountain lions (Puma concolor) in Colorado, USA.
Comte, J C; Marquié, P; Remoissenet, M
1999-12-01
We introduce a nonlinear Klein-Gordon lattice model with specific double-well on-site potential, additional constant external force and dissipation terms, which admits exact discrete kink or traveling wave fronts solutions. In the non-dissipative or conservative regime, our numerical simulations show that narrow kinks can propagate freely, and reveal that static or moving discrete breathers, with a finite but long lifetime, can emerge from kink-antikink collisions. In the general dissipative regime, the lifetime of these breathers depends on the importance of the dissipative effects. In the overdamped or diffusive regime, the general equation of motion reduces to a discrete reaction diffusion equation; our simulations show that, for a given potential shape, discrete wave fronts can travel without experiencing any propagation failure but their collisions are inelastic.
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
The drag force of water flow through single fracture and the coupling characteristics of seepage and stress in single fracture surface are analyzed,and a three dimensional model of coupled unsteady seepage and stress fields is proposed.This model is used to the analysis of foundation rock mass of a high dam.If the coupling effects are considered,the changes of boundary heads have less influence on the inner head of rock mass,and the strong permeability of main fractures appears.If the coupling effects are not considered,the fractures distribution affects the inner head more greatly.When the upstream water head declines,the inner head of dam foundation slightly declines and the hydraulic gradient distribution becomes smoother.A bigger upstream water level declining velocity has a stronger lag effect,meanwhile the values of stress components change more greatly.Therefore the upstream water level declining velocity directly affects the stability of rock mass in dam foundation and we should take into account the above factors to make sure the safety of the dam during reservoir level fluctuation period.
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.
A microcosmic discrete occupant evacuation model based on individual characteristics
Institute of Scientific and Technical Information of China (English)
YANG Lizhong; LI Jian; ZHAO Daoliang; FANG Weifeng; FAN Weicheng
2004-01-01
The research of occupant evacuation in an emergency is of great benefit to building design and evacuation guidance. In this paper a microcosmic discrete evacuation model based on Cellular Automata (CA) is presented, in which the occupants' individual characteristics are considered. Thus, our model has given a description of evacuation route choice with influencing factors, including: individual knowledge of the building,individual realization of the emergency development, and the attractive and repulsive force between occupants. This model differs somewhat from other models in the attention to the associative and separate effect of influencing factors, based on occupant's behaviors. In addition, the model could reveal the phenomenon of escape in fire, as those simulations involving a fire condition have shown.
A reservoir simulation approach for modeling of naturally fractured reservoirs
Directory of Open Access Journals (Sweden)
H. Mohammadi
2012-12-01
Full Text Available In this investigation, the Warren and Root model proposed for the simulation of naturally fractured reservoir was improved. A reservoir simulation approach was used to develop a 2D model of a synthetic oil reservoir. Main rock properties of each gridblock were defined for two different types of gridblocks called matrix and fracture gridblocks. These two gridblocks were different in porosity and permeability values which were higher for fracture gridblocks compared to the matrix gridblocks. This model was solved using the implicit finite difference method. Results showed an improvement in the Warren and Root model especially in region 2 of the semilog plot of pressure drop versus time, which indicated a linear transition zone with no inflection point as predicted by other investigators. Effects of fracture spacing, fracture permeability, fracture porosity, matrix permeability and matrix porosity on the behavior of a typical naturally fractured reservoir were also presented.
Calculus and design of discrete velocity models using computer algebra
Babovsky, Hans; Grabmeier, Johannes
2016-11-01
In [2, 3], a framework for a calculus with Discrete Velocity Models (DVM) has been derived. The rotatonal symmetry of the discrete velocities can be modelled algebraically by the action of the cyclic group C4 - or including reflections of the dihedral group D4. Taking this point of view, the linearized collision operator can be represented in a compact form as a matrix of elements in the group algebra. Or in other words, by choosing a special numbering it exhibits a certain block structure which lets it appear as a matrix with entries in a certain polynomial ring. A convenient way for approaching such a structure is the use of a computer algebra system able to treat these (predefined) algebraic structures. We used the computer algebra system FriCAS/AXIOM [4, 5] for the generation of the velocity and the collision sets and for the analysis of the structure of the collision operator. Concerning the fluid dynamic limit, the system provides the characterization of sets of collisions and their contribution to the flow parameters. It allows the design of rotationally invariant symmetric models for prescribed Prandtl numbers. The implementation in FriCAS/AXIOM is explained and its results for a 25-velocity model are presented.
Discrete element modelling of sediment falling in water.
Wang, Dong; Ho-Minh, Dao; Tan, Danielle S
2016-11-01
The Discrete Element Method (DEM) is a discrete, particle-based method commonly used in studies involving granular media, e.g. sediment transport, and geomechanics. It is heavily dependent on particle properties, and one important component is the force model, which relates the relative positions and velocities of the simulated particles to the forces they experience. In this paper we model a collection of lightly compacted granular material, released at a short distance above a flat base in a quiescent fluid --similar to the process whereby sediment tailings are released back into the sea during nodule harvesting. We employ different typical force models, and consider how their varying components affect the simulated outcome. The results are compared with a physical experiment of similar dimensions. We find that a realistic simulation is achieved when the force model considers the local solid fraction in the drag force, and incorporates the hydrodynamic effect of neighbouring particles. The added mass effect increases the accuracy of the outcome, but does not contribute significantly in a qualitative sense.
A discrete impulsive model for random heating and Brownian motion
Ramshaw, John D.
2010-01-01
The energy of a mechanical system subjected to a random force with zero mean increases irreversibly and diverges with time in the absence of friction or dissipation. This random heating effect is usually encountered in phenomenological theories formulated in terms of stochastic differential equations, the epitome of which is the Langevin equation of Brownian motion. We discuss a simple discrete impulsive model that captures the essence of random heating and Brownian motion. The model may be regarded as a discrete analog of the Langevin equation, although it is developed ab initio. Its analysis requires only simple algebraic manipulations and elementary averaging concepts, but no stochastic differential equations (or even calculus). The irreversibility in the model is shown to be a consequence of a natural causal stochastic condition that is closely analogous to Boltzmann's molecular chaos hypothesis in the kinetic theory of gases. The model provides a simple introduction to several ostensibly more advanced topics, including random heating, molecular chaos, irreversibility, Brownian motion, the Langevin equation, and fluctuation-dissipation theorems.
Shape Optimization of Hollow Concrete Blocks Using the Lattice Discrete Particle Model
Directory of Open Access Journals (Sweden)
Fatemeh Javidan
2013-01-01
Full Text Available Hollow concrete blocks are one of the widely used building elements of masonry structures in whichthey are normally loaded under combined action of shear and compression. Accordingly and due to theirstructural importance, the present study intends to numerically search for an optimum shape of such blocks.The optimality index is selected to be the ratio of block’s failure strength to its weight, a non-dimensionalparameter, which needs to be maximized. The nonlinear analysis has been done using a homemade code writtenbased on the recently developed Lattice Discrete Particle Model (LDPM for the meso-scale simulation ofconcrete. This numerical approach accounts for the different aspects of concrete’s complex behavior such astensile fracturing, cohesive and frictional shearing and also its nonlinear compressive response. The modelparameters were calibrated against previously reported experimental data. Various two-core configurations forthe hollow blocks are examined, compared and discussed.
Multiple Discrete Endogenous Variables in Weakly-Separable Triangular Models
Directory of Open Access Journals (Sweden)
Sung Jae Jun
2016-02-01
Full Text Available We consider a model in which an outcome depends on two discrete treatment variables, where one treatment is given before the other. We formulate a three-equation triangular system with weak separability conditions. Without assuming assignment is random, we establish the identification of an average structural function using two-step matching. We also consider decomposing the effect of the first treatment into direct and indirect effects, which are shown to be identified by the proposed methodology. We allow for both of the treatment variables to be non-binary and do not appeal to an identification-at-infinity argument.
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.
Feigenbaum Cascade of Discrete Breathers in a Model of DNA
Maniadis, P; Bishop, A R; Rasmussen, K \\O
2010-01-01
We demonstrate that period-doubled discrete breathers appear from the anti-continuum limit of the driven Peyrard-Bishop-Dauxois model of DNA. These novel breathers result from a stability overlap between sub-harmonic solutions of the driven Morse oscillator. Sub-harmonic breathers exist whenever a stability overlap is present within the Feigenbaum cascade to chaos and therefore an entire cascade of such breathers exists. This phenomenon is present in any driven lattice where the on-site potential admits sub-harmonic solutions. In DNA these breathers may have ramifications for cellular gene expression.
Discrete symmetries in the three-Higgs-doublet model
Ivanov, I P
2012-01-01
N-Higgs-doublet models (NHDM) are among the most popular examples of electroweak symmetry breaking mechanisms beyond the Standard Model. Discrete symmetries imposed on the NHDM scalar potential play a pivotal role in shaping the phenomenology of the model, and various symmetry groups have been studied so far. However, in spite of all efforts, the classification of finite Higgs-family symmetry groups realizable in NHDM for any N>2 is still missing. Here, we solve this problem for the three-Higgs-doublet model. Using recently found realizable abelian groups and applying Burnside's theorem and other group-theoretic tools, we find the full list of finite symmetry groups of Higgs-family transformations which are realizable in the scalar sector of 3HDM.
Adaptive model reduction for nonsmooth discrete element simulation
Servin, Martin
2015-01-01
A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies of the corresponding shape and mass distribution. The method also support particles merging with articulated multibody systems. A model approximation error is defined used for deriving and conditions for when and where to apply model reduction and refinement back into particles and smaller rigid bodies. Three methods for refinement are proposed and tested: prediction from contact events, trial solutions computed in the background and using split sensors. The computational performance can be increased by 5 - 50 times for model reduction level between 70 - 95 %.
Multiscale modeling of rapid granular flow with a hybrid discrete-continuum method
Chen, Xizhong; Li, Jinghai
2015-01-01
Both discrete and continuum models have been widely used to study rapid granular flow, discrete model is accurate but computationally expensive, whereas continuum model is computationally efficient but its accuracy is doubtful in many situations. Here we propose a hybrid discrete-continuum method to profit from the merits but discard the drawbacks of both discrete and continuum models. Continuum model is used in the regions where it is valid and discrete model is used in the regions where continuum description fails, they are coupled via dynamical exchange of parameters in the overlap regions. Simulation of granular channel flow demonstrates that the proposed hybrid discrete-continuum method is nearly as accurate as discrete model, with much less computational cost.
Energy Technology Data Exchange (ETDEWEB)
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.
Hadgu, T.; Kalinina, E.; Klise, K. A.; Wang, Y.
2015-12-01
Numerical modeling of disposal of nuclear waste in a deep geologic repository in fractured crystalline rock requires robust characterization of fractures. Various methods for fracture representation in granitic rocks exist. In this study we used the fracture continuum model (FCM) to characterize fractured rock for use in the simulation of flow and transport in the far field of a generic nuclear waste repository located at 500 m depth. The FCM approach is a stochastic method that maps the permeability of discrete fractures onto a regular grid. The method generates permeability fields using field observations of fracture sets. The original method described in McKenna and Reeves (2005) was designed for vertical fractures. The method has since then been extended to incorporate fully three-dimensional representations of anisotropic permeability, multiple independent fracture sets, and arbitrary fracture dips and orientations, and spatial correlation (Kalinina et al. 20012, 2014). For this study the numerical code PFLOTRAN (Lichtner et al., 2015) has been used to model flow and transport. PFLOTRAN solves a system of generally nonlinear partial differential equations describing multiphase, multicomponent and multiscale reactive flow and transport in porous materials. The code is designed to run on massively parallel computing architectures as well as workstations and laptops (e.g. Hammond et al., 2011). Benchmark tests were conducted to simulate flow and transport in a specified model domain. Distributions of fracture parameters were used to generate a selected number of realizations. For each realization, the FCM method was used to generate a permeability field of the fractured rock. The PFLOTRAN code was then used to simulate flow and transport in the domain. Simulation results and analysis are presented. The results indicate that the FCM approach is a viable method to model fractured crystalline rocks. The FCM is a computationally efficient way to generate realistic
Felici, Fabrizio; Alemanni, Annalisa; Bouacida, Djamil; de Montleau, Pierre
2016-10-01
Fault arrays and natural fractures distribution strongly influence subsurface fluids migration, trapping and production. It is critical to develop methodologies that can be used to accurately characterize reservoir volumes as present-day exploration and appraisal campaigns become increasingly focused on tight or low porosity reservoirs. A common method used to model the distribution and intensity of subsurface fracture sets is the Discrete Fracture Network (DFN) technique. Shortcomings of the DFN technique include the evaluation of fracture attributes, computational aspects in the case of large fields, and most importantly issues related to upscaling. Thus, the aim of this work is to present a simplified methodology for fractured reservoir characterization based on the distribution of fracture intensity as a continuous property. Fracture intensity was calculated from image well-logs data and then distributed in the reservoir according to specific fracture drivers. The case study is related to a large appraisal gas field located in the Illizi Basin, Southern Algeria, where Late Ordovician glacial deposits are the primary reservoir levels, in which the presence of faults and fractures strongly enhance well performances. The final fracture intensity model was obtained by implementing a workflow in a commonly used commercial geomodeling software and calibrated by means of well test data analysis. The implemented methodology is a useful tool for large fractured reservoir characterization when DFN technique is hardly applicable for computational reasons or the level of uncertainty does not support a performing discrete analysis.
Institute of Scientific and Technical Information of China (English)
Yucang Wang; Shimin Wang; Sheng Xue; Deepak Adhikary
2015-01-01
Understanding the characteristics of hydraulic fracture, porous flow and heat transfer in fractured rock is critical for geothermal power generation applications, and numerical simulation can provide a powerful approach for systematically and thoroughly investigating these problems. In this paper, we present a fully coupled solid-fluid code using discrete element method (DEM) and lattice Boltzmann method (LBM). The DEM with bonded particles is used to model the deformation and fracture in solid, while the LBM is used to model the fluid flow. The two methods are two-way coupled, i.e., the solid part provides a moving boundary condition and transfers momentum to fluid, while the fluid exerts a dragging force to the solid. Two widely used open source codes, the ESyS_Particle and the OpenLB, are integrated into one code and paralleled with Message Passing Interface (MPI) library. Some preliminary 2D simulations, including particles moving in a fluid and hydraulic fracturing in-duced by injection of fluid into a borehole, are carried out to validate the integrated code. The prelimi-nary results indicate that the new code is capable of reproducing the basic features of hydraulic frac-ture and thus offers a promising tool for multiscale simulation of porous flow and heat transfer in fractured rock.
Thrombin related peptide TP508 promoted fracture repair in a mouse high energy fracture model
Directory of Open Access Journals (Sweden)
Pan Xiao-Hua
2009-01-01
Full Text Available Abstract Background Thrombin related peptide (TP508 is a 23 amino-acid synthetic peptide that represents a portion of the receptor-binding domain of thrombin molecule. Previous studies have shown that TP508 can accelerate musculoskeletal tissue repair including fracture healing. Objectives The aim of this study was to investigate the effect of TP508 on fracture healing in a murine fracture model representing high energy fracture situation. Methods Eighty CD 1 mice underwent controlled quadriceps muscle crush and open transverse mid diaphyseal femoral fracture that was then fixed with an external fixator. Animals were randomised into four groups to receive an intra-operative dose of either 100 μg TP508 into the fracture gap; 100 μg TP508 into the surrounding damaged muscle tissues; 10 μg TP508 into the fracture gap, or control equal amount of saline into the fracture gap. Radiographic assessment was performed weekly for 5 weeks; histological analysis was at 3 and 5 weeks post fracture and biomechanical testing of the fractured bone was performed at 5 weeks post fracture. Results Mechanical testing data showed that the fracture stiffness was significantly higher in the group receiving 100 μg TP508 into the fracture gap than other groups. Histological and radiographic analysis revealed a trend of increase in bone formation in the 100 μg TP508 injected into the fracture gap group compared to the saline control group. It was noted that the scar tissues was significantly less in Group II comparing with the saline control group and there was increased blood vessel formation in the crushed muscles and fracture gap areas in the groups receiving TP508 comparing to the saline control group. Conclusion The results from this study demonstrated the use of thrombin related peptide TP508 in the situation of a high energy fracture can promote fracture healing and reduce the potential complications such as muscle fibrosis and fracture delayed or non-union.
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.
Discrete Model of Ideological Struggle Accounting for Migration
Vitanov, Nikolay K; Rotundo, Giulia
2012-01-01
A discrete in time model of ideological competition is formulated taking into account population migration. The model is based on interactions between global populations of non-believers and followers of different ideologies. The complex dynamics of the attracting manifolds is investigated. Conversion from one ideology to another by means of (i) mass media influence and (ii) interpersonal relations is considered. Moreover a different birth rate is assumed for different ideologies, the rate being assumed to be positive for the reference population, made of initially non-believers. Ideological competition can happen in one or several regions in space. In the latter case, migration of non-believers and adepts is allowed; this leads to an enrichment of the ideological dynamics. Finally, the current ideological situation in the Arab countries and China is commented upon from the point of view of the presently developed mathematical model. The massive forced conversion by Ottoman Turks in the Balkans is briefly dis...
Sample selection and taste correlation in discrete choice transport modelling
DEFF Research Database (Denmark)
Mabit, Stefan Lindhard
2008-01-01
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...... 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...... 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 dynamical models: combinatorics, statistics and continuum approximations
Kornyak, Vladimir V
2015-01-01
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical description of such models. We demonstrate that many concepts of continuous physics --- such as continuous symmetries, the principle of least action, Lagrangians, deterministic evolution equations --- can be obtained from combinatorial structures as a result of the large number approximation. We propose a constructive description of quantum behavior that provides, in particular, a natural explanation of appearance of complex numbers in the formalism of quantum mechanics. Some approaches to construction of discrete models of quantum evolution that involve gauge connections are discussed.
Discrete Surface Modeling Based on Google Earth: A Case Study
Mei, Gang; Xu, Nengxiong
2012-01-01
Google Earth (GE) has become a powerful tool for geological, geophysical and geographical modeling; yet GE can be accepted to acquire elevation data of terrain. In this paper, we present a real study case of building the discrete surface model (DSM) at Haut-Barr Castle in France based on the elevation data of terrain points extracted from GE using the COM API. We first locate the position of Haut-Barr Castle and determine the region of the study area, then extract elevation data of terrain at Haut-Barr, and thirdly create a planar triangular mesh that covers the study area and finally generate the desired DSM by calculating the elevation of vertices in the planar mesh via interpolating with Universal Kriging (UK) and Inverse Distance Weighting (IDW). The generated DSM can reflect the features of the ground surface at Haut-Barr well, and can be used for constructingthe Sealed Engineering Geological Model (SEGM) in further step.
Adaptive model reduction for nonsmooth discrete element simulation
Servin, Martin; Wang, Da
2016-03-01
A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies of the corresponding shape and mass distribution. The method also support particles merging with articulated multibody systems. A model approximation error is defined and used to derive conditions for when and where to apply reduction and refinement back into particles and smaller rigid bodies. Three methods for refinement are proposed and tested: prediction from contact events, trial solutions computed in the background and using split sensors. The computational performance can be increased by 5-50 times for model reduction level between 70-95 %.
Stochastic effects in a discretized kinetic model of economic exchange
Bertotti, M. L.; Chattopadhyay, A. K.; Modanese, G.
2017-04-01
Linear stochastic models and discretized kinetic theory are two complementary analytical techniques used for the investigation of complex systems of economic interactions. The former employ Langevin equations, with an emphasis on stock trade; the latter is based on systems of ordinary differential equations and is better suited for the description of binary interactions, taxation and welfare redistribution. We propose a new framework which establishes a connection between the two approaches by introducing random fluctuations into the kinetic model based on Langevin and Fokker-Planck formalisms. Numerical simulations of the resulting model indicate positive correlations between the Gini index and the total wealth, that suggest a growing inequality with increasing income. Further analysis shows, in the presence of a conserved total wealth, a simultaneous decrease in inequality as social mobility increases, in conformity with economic data.
Phase-field modeling of hydraulic fracture
Wilson, Zachary A.; Landis, Chad M.
2016-11-01
In this work a theoretical framework implementing the phase-field approach to fracture is used to couple the physics of flow through porous media and cracks with the mechanics of fracture. The main modeling challenge addressed in this work, which is a challenge for all diffuse crack representations, is on how to allow for the flow of fluid and the action of fluid pressure on the aggregate within the diffuse damage zone of the cracks. The theory is constructed by presenting the general physical balance laws and conducting a consistent thermodynamic analysis to constrain the constitutive relationships. Constitutive equations that reproduce the desired responses at the various limits of the phase-field parameter are proposed in order to capture Darcy-type flow in the intact porous medium and Stokes-type flow within open cracks. A finite element formulation for the solution of the governing model equations is presented and discussed. Finally, the theoretical and numerical model is shown to compare favorably to several important analytical solutions. More complex and interesting calculations are also presented to illustrate some of the advantageous features of the approach.
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.
DISCRETE MODELLING OF TWO-DIMENSIONAL LIQUID FOAMS
Institute of Scientific and Technical Information of China (English)
Qicheng Sun
2003-01-01
Liquid foam is a dense random packing of gas or liquid bubbles in a small amount of immiscible liquid containing surfactants. The liquid within the Plateau borders, although small in volume, causes considerable difficulties to the investigation of the spatial structure and physical properties of foams, and the situation becomes even more complicated as the fluid flows. To solve these problems, a discrete model of two-dimensional liquid foams on the bubble scale is proposed in this work. The bubble surface is represented with finite number of nodes, and the liquid within Plateau borders is discretized into lattice particles. The gas in bubbles is treated as ideal gas at constant temperatures. This model is tested by choosing an arbitrary shape bubble as the initial condition. This then automatically evolves into a circular shape, which indicates that the surface energy minimum routine is obeyed without calling external controlling conditions. Without inserting liquid particle among the bubble channels, periodic ordered and disordered dry foams are both simulated, and the fine foam structures are developed. Wet foams are also simulated by inserting fluid among bubble channels. The calculated coordination number, as a function of liquid fractions, agrees well with the standard values.
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.
Modeling of Fracture Toughness of Electroless Nickel (EN) Coatings
Institute of Scientific and Technical Information of China (English)
K. Zangeneh; S.M. Monir-vaghefi; F. Ashrafizadeh
2004-01-01
In the present reserch, a model has been proposed for estimate fracture toughness of Nickel-phosphorus (EN)layers. For this purpose, high phosphorus (9%) EN coatings with thicknesses of 6, 12, 24, 36 and 48 μm were applied on steel substrates and then treated as conventional process. Fracture toughness of coatings was obtained using Vickers indentation method. It is found that fracture toughness increses as coating thickness reduces. Effect of coating thickness on fracture toughness was exhibited by various models. Evaluation of models revealed good agreement between of proposed model (Kc=f(t,t2)) and experimental data.
Quinn, Patryk M.; Cherry, John A.; Parker, Beth L.
2016-11-01
A method is presented for obtaining depth-discrete values of specific storage (Ss) from single-hole hydraulic tests in fractured rock boreholes using straddle packers (1.5-17 m test intervals). Low flow constant head (CH) step tests analyzed using the Thiem method provide transmissivity (T) values free from non-Darcian error. Short-term, constant-rate pumping tests (0.5-2 h) analyzed using the Cooper-Jacob approximation of the Theis method provide S from the hydraulic diffusivity using the Darcian T value from the CH step test. This synergistic use of two types of hydraulic tests avoids the common source of error when pumping tests (injection or withdrawal) are conducted at higher flow rates and thereby induce non-Darcian flow resulting in the underestimation of T. Other errors, such as well bore storage and leakage, can also substantially influence S by causing a shift in the time axis of the Cooper-Jacob semi-log plot. In this approach, the Darcian T values from the CH step tests are used in the analysis of the transient pumping test data for calculating S throughout the pumping test using the Cooper-Jacob approximation to minimize all of the aforementioned errors, resulting in more representative S values. The effect of these non-idealities on the measured drawdown is illustrated using the Theis equation with the Darcian T and S values to calculate drawdown for comparison to measured data. The Ss values for tests in sandstone obtained from this approach are more consistent with confined aquifer conditions than values derived from the traditional Cooper-Jacob method, and are within the range of field and lab values presented from a compilation of literature values for fractured sandstone. (10-7-10-5 m-1) This method for obtaining Ss values from short-interval, straddle packer tests improves the estimation of both K and Ss and provides opportunity to study their spatial distribution in fractured rock.
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.
Modelling deformation and fracture in confectionery wafers
Mohammed, Idris K.; Charalambides, Maria N.; Williams, J. Gordon; Rasburn, John
2015-01-01
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.
The fracture network model of Shen 229 block buried hill:A case study from Liaohe Basin, China
Institute of Scientific and Technical Information of China (English)
XING Yu-zhong; FAN Tai-liang; ZHENG Li-hui
2006-01-01
High oil production from the Proterozoic formation of Shen 229 block in Damingtun Depression, Liaohe Basin, China,indicates the presence of natural fractured reservoir whose production potential is dominated by the structural fracture. A consistent structural model and good knowledge of the fracture systems are therefore of key importance in reducing risk in the development strategies. So data from cores and image logs have been collected to account for the basic characteristics of fracture, and then the analyzed results were integrated with the structural model in order to restrict the fracture network development during the structural evolvement. The structural evolution of the Proterozoic reservoir with time forms the basis for understanding the development of the 3D fracture system. Seismic interpretation and formation correlation were used to build a 3D geological model.The fault blocks that compose the Proterozoic formation reservoir were subsequently restored to their pre-deformation. From here,the structures were kinematically modeled to simulate the structural evolution of the reservoirs. At each time step, the dilatational and cumulative strain was calculated throughout the modelling history. The total strain which records the total spatial variation in the reservoir due to its structural history, together with core data, well data and the lithology distribution, was used to simulate geologically realistic discrete fracture networks. The benefit of this technique over traditional curvature analysis is that the structural evolution is taken into account, a factor that mostly dominates fracture formation.
Modeling energy market dynamics using discrete event system simulation
Energy Technology Data Exchange (ETDEWEB)
Gutierrez-Alcaraz, G. [Department of Electrical and Electronics Engineering, Instituto Tecnologico de Morelia, Av. Tecnologico 1500, Col. Lomas de Santiaguito 58120, Morelia Michoacan (Mexico); Sheble, G.B. [Department of Electrical and Computer Engineering, Portland State University, Portland, OR 97207-0751 (United States)
2009-10-15
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)
Identifying Training Images from Fracture Outcrops for MPS-based Modeling
Roy, A.; Mukerji, T.; Caers, J.
2014-12-01
Various MPS (multi-point geostatistics) based techniques have been successfully employed for modeling heterogeneous geologic features such as channel bodies. However, few studies exist on modeling fracture networks implementing MPS. Selecting a TI (training image) that is representative of the target subsurface fracture pattern is key to an effective implementation of any MPS algorithm. While recent research has employed equivalent continuum models created from Discrete Fracture Networks (DFN) to serve as TIs, the present research explores the direct usage of outcrop analogues of fracture networks for this purpose. A set of nested-fracture maps from the Devonian Sandstone of Hornelen basin created at multiple scales and resolutions is considered. These maps have been previously classified as belonging to a single fractal system characterized by a fractal dimension but having slightly different spatial organization at each scale. Our research implements unconditional image quilting in generating multiple realizations of fracture networks from these maps. This pattern-based algorithm requires a template-size to be chosen which is representative of the heterogeneity of the pattern of interest. Lacunarity is a technique that essentially quantifies the distribution of spaces or gaps in a pattern and can thus delineate scale-dependent heterogeneity. It is therefore investigated if this technique, in conjunction with Entropy (a measure for randomness), can be applied for choosing the template-size required for reproducing a desired pattern from a given TI. Finally, it will be tested if fracture networks generated from two or more TIs at different scales but belonging to the same fractal-fracture system, can capture similar ranges of uncertainty.
High order discretization schemes for stochastic volatility models
Jourdain, Benjamin
2009-01-01
In usual stochastic volatility models, the process driving the volatility of the asset price evolves according to an autonomous one-dimensional stochastic differential equation. We assume that the coefficients of this equation are smooth. Using It\\^o's formula, we get rid, in the asset price dynamics, of the stochastic integral with respect to the Brownian motion driving this SDE. Taking advantage of this structure, we propose - a scheme, based on the Milstein discretization of this SDE, with order one of weak trajectorial convergence for the asset price, - a scheme, based on the Ninomiya-Victoir discretization of this SDE, with order two of weak convergence for the asset price. We also propose a specific scheme with improved convergence properties when the volatility of the asset price is driven by an Orstein-Uhlenbeck process. We confirm the theoretical rates of convergence by numerical experiments and show that our schemes are well adapted to the multilevel Monte Carlo method introduced by Giles [2008a,b].
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.
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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.
Landmine detection using mixture of discrete hidden Markov models
Frigui, Hichem; Hamdi, Anis; Missaoui, Oualid; Gader, Paul
2009-05-01
We propose a landmine detection algorithm that uses a mixture of discrete hidden Markov models. We hypothesize that the data are generated by K models. These different models reflect the fact that mines and clutter objects have different characteristics depending on the mine type, soil and weather conditions, and burial depth. Model identification could be achieved through clustering in the parameters space or in the feature space. However, this approach is inappropriate as it is not trivial to define a meaningful distance metric for model parameters or sequence comparison. Our proposed approach is based on clustering in the log-likelihood space, and has two main steps. First, one HMM is fit to each of the R individual sequence. For each fitted model, we evaluate the log-likelihood of each sequence. This will result in an R×R log-likelihood distance matrix that will be partitioned into K groups using a hierarchical clustering algorithm. In the second step, we pool the sequences, according to which cluster they belong, into K groups, and we fit one HMM to each group. The mixture of these K HMMs would be used to build a descriptive model of the data. An artificial neural networks is then used to fuse the output of the K models. Results on large and diverse Ground Penetrating Radar data collections show that the proposed method can identify meaningful and coherent HMM models that describe different properties of the data. Each HMM models a group of alarm signatures that share common attributes such as clutter, mine type, and burial depth. Our initial experiments have also indicated that the proposed mixture model outperform the baseline HMM that uses one model for the mine and one model for the background.
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
A discrete epidemic model for bovine Babesiosis disease and tick populations
Aranda, Diego F.; Trejos, Deccy Y.; Valverde, Jose C.
2017-06-01
In this paper, we provide and study a discrete model for the transmission of Babesiosis disease in bovine and tick populations. This model supposes a discretization of the continuous-time model developed by us previously. The results, here obtained by discrete methods as opposed to continuous ones, show that similar conclusions can be obtained for the discrete model subject to the assumption of some parametric constraints which were not necessary in the continuous case. We prove that these parametric constraints are not artificial and, in fact, they can be deduced from the biological significance of the model. Finally, some numerical simulations are given to validate the model and verify our theoretical study.
Directory of Open Access Journals (Sweden)
Ilić Miloje
2011-01-01
Full Text Available In this paper, a discrete structural-morphological type of magnesite deposits in ultrabasites, i.e., in magnesite-bearing fracture zones, is presented. The most prominent occurrences of such zones in Serbia are in the Zlatibor ultrabasic massif and they are economically very significant because they contain large reserves of high-quality magnesite, as well as of the accompanying sepiolite.
On the discretization and control of an SEIR epidemic model with a periodic impulsive vaccination
Alonso-Quesada, S.; De la Sen, M.; Ibeas, A.
2017-01-01
This paper deals with the discretization and control of an SEIR epidemic model. Such a model describes the transmission of an infectious disease among a time-varying host population. The model assumes mortality from causes related to the disease. Our study proposes a discretization method including a free-design parameter to be adjusted for guaranteeing the positivity of the resulting discrete-time model. Such a method provides a discrete-time model close to the continuous-time one without the need for the sampling period to be as small as other commonly used discretization methods require. This fact makes possible the design of impulsive vaccination control strategies with less burden of measurements and related computations if one uses the proposed instead of other discretization methods. The proposed discretization method and the impulsive vaccination strategy designed on the resulting discretized model are the main novelties of the paper. The paper includes (i) the analysis of the positivity of the obtained discrete-time SEIR model, (ii) the study of stability of the disease-free equilibrium point of a normalized version of such a discrete-time model and (iii) the existence and the attractivity of a globally asymptotically stable disease-free periodic solution under a periodic impulsive vaccination. Concretely, the exposed and infectious subpopulations asymptotically converge to zero as time tends to infinity while the normalized subpopulations of susceptible and recovered by immunization individuals oscillate in the context of such a solution. Finally, a numerical example illustrates the theoretic results.
Phase Field Modeling of Directional Fracture in Anisotropic Polycrystals
2015-02-01
the Army position unless so designated by other authorized documents. Citation of manufacturer’s or trade names does not constitute an official...consider preferential fracture on cleavage planes of multiple discrete orientations requires introduction of additional order parameter(s) for...trends for elastically compliant grain boundary phases are in general agreement with experiment [6]. As will be examined in more detail in Section 4.2
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.
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.
Discrete symmetries and model-independent patterns of lepton mixing
Hernandez, D
2012-01-01
In the context of discrete flavor symmetries, we elaborate a method that allows one to obtain relations between the mixing parameters in a model-independent way. Under very general conditions, we show that flavor groups of the von Dyck type, that are not necessarily finite, determine the absolute values of the entries of one column of the mixing matrix. We apply our formalism to finite subgroups of the infinite von Dyck groups, such as the modular groups, and find cases that yield an excellent agreement with the best fit values for the mixing angles. We explore the Klein group as the residual symmetry of the neutrino sector and explain the permutation property that appears between the elements of the mixing matrix in this case.
Discrete symmetries and model-independent patterns of lepton mixing
Hernandez, D.; Smirnov, A. Yu.
2013-03-01
In the context of discrete flavor symmetries, we elaborate a method that allows one to obtain relations between the mixing parameters in a model-independent way. Under very general conditions, we show that flavor groups of the von Dyck type, that are not necessarily finite, determine the absolute values of the entries of one column of the mixing matrix. We apply our formalism to finite subgroups of the infinite von Dyck groups, such as the modular groups, and find cases that yield an excellent agreement with the best fit values for the mixing angles. We explore the Klein group as the residual symmetry of the neutrino sector and explain the permutation property that appears between the elements of the mixing matrix in this case.
Modelling Mixed Discrete-Continuous Domains for Planning
Fox, M; 10.1613/jair.2044
2011-01-01
In this paper we present pddl+, a planning domain description language for modelling mixed discrete-continuous planning domains. We describe the syntax and modelling style of pddl+, showing that the language makes convenient the modelling of complex time-dependent effects. We provide a formal semantics for pddl+ by mapping planning instances into constructs of hybrid automata. Using the syntax of HAs as our semantic model we construct a semantic mapping to labelled transition systems to complete the formal interpretation of pddl+ planning instances. An advantage of building a mapping from pddl+ to HA theory is that it forms a bridge between the Planning and Real Time Systems research communities. One consequence is that we can expect to make use of some of the theoretical properties of HAs. For example, for a restricted class of HAs the Reachability problem (which is equivalent to Plan Existence) is decidable. pddl+ provides an alternative to the continuous durative action model of pddl2.1, adding a more flex...
Landmine detection using discrete hidden Markov models with Gabor features
Frigui, Hichem; Missaoui, Oualid; Gader, Paul
2007-04-01
We propose a general method for detecting landmine signatures in vehicle mounted ground penetrating radar (GPR) using discrete hidden Markov models and Gabor wavelet features. Observation vectors are constructed based on the expansion of the signature's B-scan using a bank of scale and orientation selective Gabor filters. This expansion provides localized frequency description that gets encoded in the observation sequence. These observations do not impose an explicit structure on the mine model, and are used to naturally model the time-varying signatures produced by the interaction of the GPR and the landmines as the vehicle moves. The proposed method is evaluated on real data collected by a GPR mounted on a moving vehicle at three different geographical locations that include several lanes. The model parameters are optimized using the BaumWelch algorithm, and lane-based cross-validation, in which each mine lane is in turn treated as a test set with the rest of the lanes used for training, is used to train and test the model. Preliminary results show that observations encoded with Gabor wavelet features perform better than observation encoded with gradient-based edge features.
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.
Discrete and continuous models of protein sorting in the Golgi
Gong, Haijun; Schwartz, Russell
2009-03-01
The Golgi apparatus plays an important role in processing and sorting proteins and lipids. Golgi compartments constantly exchange material with each other and with other cellular components, allowing them to maintain and reform distinct identities despite dramatic changes in structure and size during cell division, development and osmotic stress. We have developed two minimal models of membrane and protein exchange in the Golgi --- a discrete, stochastic model [1] and a continuous ordinary differential equation (ODE) model --- both based on two fundamental mechanisms: vesicle-coat-mediated selective concentration of soluble N-ethylmaleimide-sensitive factor attachment protein receptor (SNARE) proteins during vesicle formation and SNARE-mediated selective fusion of vesicles. Both show similar ability to establish and maintain distinct identities over broad parameter ranges, but they diverge in extreme conditions where Golgi collapse and reassembly may be observed. By exploring where the models differ, we hope to better identify those features essential to minimal models of various Golgi behaviors. [1] H. Gong, D. Sengupta, A. D. Linstedt, R. Schwartz. Biophys J. 95: 1674-1688, 2008.
Discrete Element Model for Suppression of Coffee-Ring Effect
Xu, Ting; Lam, Miu Ling; Chen, Ting-Hsuan
2017-02-01
When a sessile droplet evaporates, coffee-ring effect drives the suspended particulate matters to the droplet edge, eventually forming a ring-shaped deposition. Because it causes a non-uniform distribution of solid contents, which is undesired in many applications, attempts have been made to eliminate the coffee-ring effect. Recent reports indicated that the coffee-ring effect can be suppressed by a mixture of spherical and non-spherical particles with enhanced particle-particle interaction at air-water interface. However, a model to comprehend the inter-particulate activities has been lacking. Here, we report a discrete element model (particle system) to investigate the phenomenon. The modeled dynamics included particle traveling following the capillary flow with Brownian motion, and its resultant 3D hexagonal close packing of particles along the contact line. For particles being adsorbed by air-water interface, we modeled cluster growth, cluster deformation, and cluster combination. We found that the suppression of coffee-ring effect does not require a circulatory flow driven by an inward Marangoni flow at air-water interface. Instead, the number of new cluster formation, which can be enhanced by increasing the ratio of non-spherical particles and the overall number of microspheres, is more dominant in the suppression process. Together, this model provides a useful platform elucidating insights for suppressing coffee-ring effect for practical applications in the future.
A Discrete Evolutionary Model for Chess Players' Ratings
Fenner, Trevor; Loizou, George
2011-01-01
The Elo system for rating chess players, also used in other games and sports, was adopted by the World Chess Federation over four decades ago. Although not without controversy, it is accepted as generally reliable and provides a method for assessing players' strengths and ranking them in official tournaments. It is generally accepted that the distribution of players' rating data is approximately normal but, to date, no stochastic model of how the distribution might have arisen has been proposed. We propose such an evolutionary stochastic model, which models the arrival of players into the rating pool, the games they play against each other, and how the results of these games affect their ratings. Using a continuous approximation to the discrete model, we derive the distribution for players' ratings at time $t$ as a normal distribution, where the variance increases in time as a logarithmic function of $t$. We validate the model using published rating data from 2007 to 2010, showing that the parameters obtained...
Energy Technology Data Exchange (ETDEWEB)
Rousseau, J.
2009-07-15
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)
Multiscale model reduction for shale gas transport in fractured media
Akkutlu, I Y; Vasilyeva, Maria
2015-01-01
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 \\cite{aes14}, 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. In this approach, the matrix and the fracture interaction is modeled via local multiscale basis functions. We developed the GMsFEM and applied for linear flows with horizontal or vertical fracture orientations on a Cartesian fine grid. In this paper, we consider arbitrary fracture orientations and use triangular fine grid and developed GMsFEM for nonlinear flows. Moreover, we develop online basis function strategies to adaptively improve the convergence. The number of multiscale basis functions in each coarse region ...
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
Nonlinear Maps for Design of Discrete-Time Models of Neuronal Network Dynamics
2016-03-31
responsive tiring patterns . We propose to use modern DSP ideas to develop new efficient approaches to the design of such discrete-time models for...2016 Performance/Technic~ 03-01-2016- 03-31-2016 4. TITLE AND SUBTITLE Sa. CONTRACT NUMBER Nonlinear Maps for Design of Discrete-Time Models of...simulations is to design a neuronal model in the form of difference equations that generates neuronal states in discrete moments of time. In this
A cubic matrix-fracture geometry model for radial tracer flow in naturally fractured reservoirs
Energy Technology Data Exchange (ETDEWEB)
Jetzabeth Ramirez-Sabag; Fernando Samaniego V.
1992-01-01
This study presents a general solution for the radial flow of tracers in naturally fractured reservoirs, with cubic blocks matrix-fracture geometry. Continuous and finite step injection of chemical and radioactive tracers are considered. The reservoir is treated as being composed of two regions: a mobile where dispersion and convection take place and a stagnant where only diffusion and adsorption are allowed. Radioactive decay is considered in both regions. The model of this study is thoroughly compared under proper simplified conditions to those previously presented in the literature. The coupled matrix to fracture solution in the Laplace space is numerically inverted by means of the Crump algorithm. A detailed validation of the model with respect to solutions previously presented and/or simplified physical conditions solutions (i.e., homogeneous case) or limit solutions (i.e., naturally fractured nearly homogeneous) was carried out. The influence of the three of the main dimensionless parameters that enter into the solution was carefully investigated. A comparison of results for three different naturally fractured systems, vertical fractures (linear flow), horizontal fractures (radial flow) and the cubic geometry model of this study, is presented.
Discrete Mesh Approach in Morphogenesis Modelling: the Example of Gastrulation.
Demongeot, J; Lontos, A; Promayon, E
2016-12-01
Morphogenesis is a general concept in biology including all the processes which generate tissue shapes and cellular organizations in a living organism. Many hybrid formalizations (i.e., with both discrete and continuous parts) have been proposed for modelling morphogenesis in embryonic or adult animals, like gastrulation. We propose first to study the ventral furrow invagination as the initial step of gastrulation, early stage of embryogenesis. We focus on the study of the connection between the apical constriction of the ventral cells and the initiation of the invagination. For that, we have created a 3D biomechanical model of the embryo of the Drosophila melanogaster based on the finite element method. Each cell is modelled by an elastic hexahedron contour and is firmly attached to its neighbouring cells. A uniform initial distribution of elastic and contractile forces is applied to cells along the model. Numerical simulations show that invagination starts at ventral curved extremities of the embryo and then propagates to the ventral medial layer. Then, this observation already made in some experiments can be attributed uniquely to the specific shape of the embryo and we provide mechanical evidence to support it. Results of the simulations of the "pill-shaped" geometry of the Drosophila melanogaster embryo are compared with those of a spherical geometry corresponding to the Xenopus lævis embryo. Eventually, we propose to study the influence of cell proliferation on the end of the process of invagination represented by the closure of the ventral furrow.
Discrete Element Crowd Model for Pedestrian Evacuation Through an Exit
Lin, Peng; Lo, Siuming
2016-01-01
A series of accidents caused by crowd within the last decades evoked a lot of scientific interest in modeling the movement of pedestrian crowds. Based on discrete element method, a granular dynamic model, in which human body is simplified as self-driven sphere, is proposed to simulate the characteristics of crowd flow through an exit. In this model, the repulsive force among people is considered to have an anisotropic feature, and the physical contact force due to body deformation is quantified by the Hertz contact model. The movement of human body is simulated by applying the second Newton's law. The crowd flow through an exit at different desired velocities is studied and simulation results indicated that crowd flow exhibits three distinct states, i.e., smooth state, transition state and phase separation state. In the simulation, clogging phenomenon occurs more easily when the velocity of desired is high and the exit may as a result be totally blocked at a desired velocity of 1.6m/s or above, leading to fas...
Discrete element crowd model for pedestrian evacuation through an exit
Peng, Lin; Jian, Ma; Siuming, Lo
2016-03-01
A series of accidents caused by crowds within the last decades evoked a lot of scientific interest in modeling the movement of pedestrian crowds. Based on the discrete element method, a granular dynamic model, in which the human body is simplified as a self-driven sphere, is proposed to simulate the characteristics of crowd flow through an exit. In this model, the repulsive force among people is considered to have an anisotropic feature, and the physical contact force due to body deformation is quantified by the Hertz contact model. The movement of the human body is simulated by applying the second Newton’s law. The crowd flow through an exit at different desired velocities is studied and simulation results indicated that crowd flow exhibits three distinct states, i.e., smooth state, transition state and phase separation state. In the simulation, the clogging phenomenon occurs more easily when the desired velocity is high and the exit may as a result be totally blocked at a desired velocity of 1.6 m/s or above, leading to faster-to-frozen effect. Project supported by the National Natural Science Foundation of China (Grant Nos. 71473207, 51178445, and 71103148), the Research Grant Council, Government of Hong Kong, China (Grant No. CityU119011), and the Fundamental Research Funds for the Central Universities, China (Grant Nos. 2682014CX103 and 2682014RC05).
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.
Poroelastic modeling of seismic boundary conditions across a fracture.
Nakagawa, Seiji; Schoenberg, Michael A
2007-08-01
Permeability of a fracture can affect how the fracture interacts with seismic waves. To examine this effect, a simple mathematical model that describes the poroelastic nature of wave-fracture interaction is useful. In this paper, a set of boundary conditions is presented which relate wave-induced particle velocity (or displacement) and stress including fluid pressure across a compliant, fluid-bearing fracture. These conditions are derived by modeling a fracture as a thin porous layer with increased compliance and finite permeability. Assuming a small layer thickness, the boundary conditions can be derived by integrating the governing equations of poroelastic wave propagation. A finite jump in the stress and velocity across a fracture is expressed as a function of the stress and velocity at the boundaries. Further simplification for a thin fracture yields a set of characteristic parameters that control the seismic response of single fractures with a wide range of mechanical and hydraulic properties. These boundary conditions have potential applications in simplifying numerical models such as finite-difference and finite-element methods to compute seismic wave scattering off nonplanar (e.g., curved and intersecting) fractures.
Patterns of mesenchymal condensation in a multiscale, discrete stochastic model.
Directory of Open Access Journals (Sweden)
Scott Christley
2007-04-01
Full Text Available Cells of the embryonic vertebrate limb in high-density culture undergo chondrogenic pattern formation, which results in the production of regularly spaced "islands" of cartilage similar to the cartilage primordia of the developing limb skeleton. The first step in this process, in vitro and in vivo, is the generation of "cell condensations," in which the precartilage cells become more tightly packed at the sites at which cartilage will form. In this paper we describe a discrete, stochastic model for the behavior of limb bud precartilage mesenchymal cells in vitro. The model uses a biologically motivated reaction-diffusion process and cell-matrix adhesion (haptotaxis as the bases of chondrogenic pattern formation, whereby the biochemically distinct condensing cells, as well as the size, number, and arrangement of the multicellular condensations, are generated in a self-organizing fashion. Improving on an earlier lattice-gas representation of the same process, it is multiscale (i.e., cell and molecular dynamics occur on distinct scales, and the cells are represented as spatially extended objects that can change their shape. The authors calibrate the model using experimental data and study sensitivity to changes in key parameters. The simulations have disclosed two distinct dynamic regimes for pattern self-organization involving transient or stationary inductive patterns of morphogens. The authors discuss these modes of pattern formation in relation to available experimental evidence for the in vitro system, as well as their implications for understanding limb skeletal patterning during embryonic development.
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 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
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
van Gestel, Aukje; Severens, Johan L.; Webers, Carroll A. B.; Beckers, Henny J. M.; Jansonius, Nomdo M.; Schouten, Jan S. A. G.
2010-01-01
Objective: Discrete event simulation (DES) modeling has several advantages over simpler modeling techniques in health economics, such as increased flexibility and the ability to model complex systems. Nevertheless, these benefits may come at the cost of reduced transparency, which may compromise the
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.
Effect of Natural Fractures on Hydraulic Fracturing
Ben, Y.; Wang, Y.; Shi, G.
2012-12-01
Hydraulic Fracturing has been used successfully in the oil and gas industry to enhance oil and gas production in the past few decades. Recent years have seen the great development of tight gas, coal bed methane and shale gas. Natural fractures are believed to play an important role in the hydraulic fracturing of such formations. Whether natural fractures can benefit the fracture propagation and enhance final production needs to be studied. Various methods have been used to study the effect of natural fractures on hydraulic fracturing. Discontinuous Deformation Analysis (DDA) is a numerical method which belongs to the family of discrete element methods. In this paper, DDA is coupled with a fluid pipe network model to simulate the pressure response in the formation during hydraulic fracturing. The focus is to study the effect of natural fractures on hydraulic fracturing. In particular, the effect of rock joint properties, joint orientations and rock properties on fracture initiation and propagation will be analyzed. The result shows that DDA is a promising tool to study such complex behavior of rocks. Finally, the advantages of disadvantages of our current model and future research directions will be discussed.
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.
Creep and fracture of a model yoghurt
Manneville, Sebastien; Leocmach, Mathieu; Perge, Christophe; Divoux, Thibaut
2014-11-01
Biomaterials such as protein or polysaccharide gels are known to behave qualitatively as soft solids and to rupture under an external load. Combining optical and ultrasonic imaging to shear rheology we show that the failure scenario of a model yoghurt, namely a casein gel, is reminiscent of brittle solids: after a primary creep regime characterized by a macroscopically homogeneous deformation and a power-law behavior which exponent is fully accounted for by linear viscoelasticity, fractures nucleate and grow logarithmically perpendicularly to shear, up to the sudden rupture of the gel. A single equation accounting for those two successive processes nicely captures the full rheological response. The failure time follows a decreasing power-law with the applied shear stress, similar to the Basquin law of fatigue for solids. These results are in excellent agreement with recent fiber-bundle models that include damage accumulation on elastic fibers and exemplify protein gels as model, brittle-like soft solids. Work funded by the European Research Council under Grant Agreement No. 258803.
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
Modeling Acoustically Driven Microbubbles by Macroscopic Discrete-Mechanical Analogues
Directory of Open Access Journals (Sweden)
Víctor Sánchez-Morcillo
2013-06-01
Full Text Available The dynamics of continuous systems that exhibit circular or spherical symmetry like drops, bubbles or some macromolecules, under the influence of some external excitation, develop surface patters that are hard to predict in most practical situations. In the particular case of acoustically driven microbubbles (ultrasound contrast agent, the study of the behavior of the bubble shell requires complex modeling even for describe the most simple oscillation patterns. Furthermore, due to the smallness of the spatio-temporal scale of the problem, an experimental approach requires expensive hardware setup. Despite the complexity of the particular physical problem, the basic dynamical features of some continuous physical systems can be captured by simple models of coupled oscillators. In this work we consider an analogy between a shelled-gas bubble cavitating under the action of an acoustic field and a discrete mechanical system. Thus, we present a theoretical and experimental study of the spatial instabilities of a circular ring of coupled pendulums parametrically driven by a vertical harmonic force. The system is capable of wave propagation and exhibit nonlinearities and dispersion, so manifest rich dynamics: normal oscillation modes (breathing, dipole, quadrupole... and localized patterns of different types (breathers and kinks witch are predicted by finite-differences numerical solutions and observed experimentally. On the basis of this analogy, the oscillation patterns and localized modes observed experimentally in acoustically driven bubbles are interpreted and discussed.
Fluctuation theorems for discrete kinetic models of molecular motors
Faggionato, Alessandra; Silvestri, Vittoria
2017-04-01
Motivated by discrete kinetic models for non-cooperative molecular motors on periodic tracks, we consider random walks (also not Markov) on quasi one dimensional (1d) lattices, obtained by gluing several copies of a fundamental graph in a linear fashion. We show that, for a suitable class of quasi-1d lattices, the large deviation rate function associated to the position of the walker satisfies a Gallavotti-Cohen symmetry for any choice of the dynamical parameters defining the stochastic walk. This class includes the linear model considered in Lacoste et al (2008 Phys. Rev. E 78 011915). We also derive fluctuation theorems for the time-integrated cycle currents and discuss how the matrix approach of Lacoste et al (2008 Phys. Rev. E 78 011915) can be extended to derive the above Gallavotti-Cohen symmetry for any Markov random walk on {Z} with periodic jump rates. Finally, we review in the present context some large deviation results of Faggionato and Silvestri (2017 Ann. Inst. Henri Poincaré 53 46-78) and give some specific examples with explicit computations.
Discrete random walk models for space-time fractional diffusion
Energy Technology Data Exchange (ETDEWEB)
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo
2002-11-01
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 {alpha} is part of (0,2] and skewness {theta} (module{theta}{<=}{l_brace}{alpha},2-{alpha}{r_brace}), and the first-order time derivative with a Caputo derivative of order {beta} 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.
Entrainment of coarse grains using a discrete particle model
Energy Technology Data Exchange (ETDEWEB)
Valyrakis, Manousos, E-mail: Manousos.Valyrakis@glasgow.ac.uk [Lecturer in Water and Environmental Engineering, Rankine 817b, University of Glasgow, Glasgow G12 8LT (United Kingdom); Arnold, Roger B. Jr. [Environmental Engineer, Arcadis, USA (formerly: research assistant Virginia Tech, USA) (United States)
2014-10-06
Conventional bedload transport models and incipient motion theories relying on a time-averaged boundary shear stress are incapable of accounting for the effects of fluctuating near-bed velocity in turbulent flow and are therefore prone to significant errors. Impulse, the product of an instantaneous force magnitude and its duration, has been recently proposed as an appropriate criterion for quantifying the effects of flow turbulence in removing coarse grains from the bed surface. Here, a discrete particle model (DPM) is used to examine the effects of impulse, representing a single idealized turbulent event, on particle entrainment. The results are classified according to the degree of grain movement into the following categories: motion prior to entrainment, initial dislodgement, and energetic displacement. The results indicate that in all three cases the degree of particle motion depends on both the force magnitude and the duration of its application and suggest that the effects of turbulence must be adequately accounted for in order to develop a more accurate method of determining incipient motion. DPM is capable of simulating the dynamics of grain entrainment and is an appropriate tool for further study of the fundamental mechanisms of sediment transport.
Quasi-one-dimensional scattering in a discrete model
Energy Technology Data Exchange (ETDEWEB)
Valiente, Manuel; Moelmer, Klaus [Lundbeck Foundation Theoretical Center for Quantum System Research, Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C (Denmark)
2011-11-15
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 Bloch quasimomenta, considering as well finite sizes and transversal traps that support a continuum of states. This is made straightforward by using the exact ansatz for the quasi-one-dimensional states from the beginning. In the more interesting case of genuine two-particle scattering, we find that more than one confinement-induced resonances appear due to the nonseparability of the center-of-mass and relative coordinates on the lattice. This is done by solving its corresponding Lippmann-Schwinger-like equation. We characterize the effective one-dimensional interaction and compare it with a model that includes only the effect of the dominant, broadest resonance, which amounts to a single-pole approximation for the interaction coupling constant.
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
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
Integrated hydrologic modeling: Effects of spatial scale, discretization and initialization
Seck, A.; Welty, C.; Maxwell, R. M.
2011-12-01
Groundwater discharge contributes significantly to the annual flows of Chesapeake Bay tributaries and is presumed to contribute to the observed lag time between the implementation of management actions and the environmental response in the Chesapeake Bay. To investigate groundwater fluxes and flow paths and interaction with surface flow, we have developed a fully distributed integrated hydrologic model of the Chesapeake Bay Watershed using ParFlow. Here we present a comparison of model spatial resolution and initialization methods. We have studied the effect of horizontal discretization on overland flow processes at a range of scales. Three nested model domains have been considered: the Monocacy watershed (5600 sq. km), the Potomac watershed (92000 sq. km) and the Chesapeake Bay watershed (400,000 sq. km). Models with homogeneous subsurface and topographically-derived slopes were evaluated at 500-m, 1000-m, 2000-m, and 4000-m grid resolutions. Land surface slopes were derived from resampled DEMs and corrected using stream networks. Simulation results show that the overland flow processes are reasonably well represented with a resolution up to 2000 m. We observe that the effects of horizontal resolution dissipate with larger scale models. Using a homogeneous model that includes subsurface and surface terrain characteristics, we have evaluated various initialization methods for the integrated Monocacy watershed model. This model used several options for water table depths and two rainfall forcing methods including (1) a synthetic rainfall-recession cycle corresponding to the region's average annual rainfall rate, and (2) an initial shut-off of rainfall forcing followed by a rainfall-recession cycling. Results show the dominance of groundwater generated runoff during a first phase of the simulation followed by a convergence towards more balanced runoff generation mechanisms. We observe that the influence of groundwater runoff increases in dissected relief areas
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.
Liver Disease Recognition: A Discrete Hidden Markov Model Approach
Directory of Open Access Journals (Sweden)
Farzan Madadizadeh
2016-03-01
Full Text Available The liver alongside the heart and the brain is the largest and the most vital organ within the human body whose absence leads to certain death. In addition, diagnosis of liver diseases takes a long time and requires sufficient expertise of physicians. To this end, statistical methods as automatic prediction systems can help specialists to diagnose liver diseases quickly and accurately. The Discrete Hidden Markov Model (DHMM is an intelligent and a strong statistical model used to predict the types of liver diseases in patients in this study. The data in this crosssectional study included information elicited from the records of 1143 patients with 5 different types of liver diseases including cirrhosis of the liver, liver cancer, acute hepatitis, chronic hepatitis, and fatty liver disease admitted to Afzalipour Hospital in the city of Kerman in the time period of 2006-2013. At first, the type of diseases for each patient was identified; however, it was assumed that the type of diseases is unknown and there were attempts to diagnose the type of the disease through the DHMM to examine its accuracy. Therefore, the DHMM was fitted to the data and its performance was evaluated by using the parameters of accuracy, sensitivity, and specificity. Such parameters of the model were separately calculated for the diagnosis of liver diseases. The highest levels of accuracy, sensitivity, and specificity were associated with the diagnosis of cirrhosis of the liver and equal to 0.77, 0.82, 0.96, respectively; and the lowest levels were related to the diagnosis of fatty liver disease with an accuracy level of 0.65 and a sensitivity level of 0.69. As well, the specificity level in the diagnosis of fatty liver disease was 0.94. The results of this study indicated the potential ability of the DHMM; thus, the use of this model in terms of diagnosing liver diseases was strongly recommended.
Physical model studies of dispersion in fracture systems
Energy Technology Data Exchange (ETDEWEB)
Hull, L.C.
1985-04-01
The purposes of the laboratory-scale fracture network experiments are to study mechanisms controlling solute transport under conditions of known fracture parameters, to evaluate injection-backflow test procedures under conditions of known reservoir parameters, and to acquire data for validation of numerical models. Validation of computer codes against laboratory data collected under controlled conditions provides reassurance that the codes deal with important processes in a realistic manner. Preliminary simulations of the dual-permeability physical model have been made using the FRACSL reservoir code. These simulations permit locating electrodes and piezometers in the most advantageous positions to record tracer migration and pressure response. Much of the physical modeling effort this year was oriented towards validating the particle tracking algorithm used in FRACSL, and developing a better theoretical understanding of transport processes in fractures. Experiments were conducted in single fractures and single fracture junctions, and data on tracer migration collected. The Prickett, Naymik, and Lonnquist Random Walk aquifer simulation program has been modfied to simulate flow in single fractures. The particle tracking algorithm was also used to simulate infinite parallel plates under conditions where analytical solutions to the transport equation could be derived. The first case is for zero diffusion in the fracture, and transport based on a parabolic velocity profile. The second case is for diffusion homogenizing the tracer solution across the fracture. The particle tracking algorithm matched both analytical solutions quite well, with the same grid for both simulations. 48 refs., 41 figs., 2 tabs.
Discrete element modelling of pebble packing in pebble bed reactors
Energy Technology Data Exchange (ETDEWEB)
Suikkanen, Heikki, E-mail: heikki.suikkanen@lut.fi; Ritvanen, Jouni, E-mail: jouni.ritvanen@lut.fi; Jalali, Payman, E-mail: payman.jalali@lut.fi; Kyrki-Rajamäki, Riitta, E-mail: riitta.kyrki-rajamaki@lut.fi
2014-07-01
Highlights: • A discrete element method code is developed for pebble bed reactor analyses. • Methods are established to extract packing information at various spatial scales. • Packing simulations inside annular core geometry are done varying input parameters. • The restitution coefficient has the strongest effect on the resulting packing density. • Detailed analyses reveal local densification especially near the walls. - Abstract: It is important to understand the packing characteristics and behaviour of the randomly packed pebble bed to further analyse the reactor physical and thermal-hydraulic behaviour and to design a safe and economically feasible pebble bed reactor. The objective of this work was to establish methods to model and analyse the pebble packing in detail to provide useful tools and data for further analyses. Discrete element method (DEM) is a well acknowledged method for analysing granular materials, such as the fuel pebbles in a pebble bed reactor. In this work, a DEM computer code was written specifically for pebble bed analyses. Analysis methods were established to extract data at various spatial scales from the pebble beds resulting from the DEM simulations. A comparison with available experimental data was performed to validate the DEM implementation. To test the code implementation in full-scale reactor calculations, DEM packing simulations were done in annular geometry with 450,000 pebbles. Effects of the initial packing configuration, friction and restitution coefficients and pebble size distribution to the resulting pebble bed were investigated. The packing simulations revealed that from the investigated parameters the restitution coefficient had the largest effect on the resulting average packing density while other parameters had smaller effects. Detailed local packing density analysis of pebble beds with different average densities revealed local variations especially strong in the regions near the walls. The implemented DEM
Fracture of granular materials composed of arbitrary grain shapes: A new cohesive interaction model
Neveu, A.; Artoni, R.; Richard, P.; Descantes, Y.
2016-10-01
Discrete Element Methods (DEM) are a useful tool to model the fracture of cohesive granular materials. For this kind of application, simple particle shapes (discs in 2D, spheres in 3D) are usually employed. However, dealing with more general particle shapes allows to account for the natural heterogeneity of grains inside real materials. We present a discrete model allowing to mimic cohesion between contacting or non-contacting particles whatever their shape in 2D and 3D. The cohesive interactions are made of cohesion points placed on interacting particles, with the aim of representing a cohesive phase lying between the grains. Contact situations are solved according to unilateral contact and Coulomb friction laws. In order to test the developed model, 2D unixial compression simulations are performed. Numerical results show the ability of the model to mimic the macroscopic behavior of an aggregate grain subject to axial compression, as well as fracture initiation and propagation. A study of the influence of model and sample parameters provides important information on the ability of the model to reproduce various behaviors.
Discrete Method of Images for 3D Radio Propagation Modeling
Novak, Roman
2016-09-01
Discretization by rasterization is introduced into the method of images (MI) in the context of 3D deterministic radio propagation modeling as a way to exploit spatial coherence of electromagnetic propagation for fine-grained parallelism. Traditional algebraic treatment of bounding regions and surfaces is replaced by computer graphics rendering of 3D reflections and double refractions while building the image tree. The visibility of reception points and surfaces is also resolved by shader programs. The proposed rasterization is shown to be of comparable run time to that of the fundamentally parallel shooting and bouncing rays. The rasterization does not affect the signal evaluation backtracking step, thus preserving its advantage over the brute force ray-tracing methods in terms of accuracy. Moreover, the rendering resolution may be scaled back for a given level of scenario detail with only marginal impact on the image tree size. This allows selection of scene optimized execution parameters for faster execution, giving the method a competitive edge. The proposed variant of MI can be run on any GPU that supports real-time 3D graphics.
Boundary Layer Effect on Behavior of Discrete Models
Directory of Open Access Journals (Sweden)
Jan Eliáš
2017-02-01
Full Text Available 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.
Revisiting Discrete Dark Matter Model:\\theta_{13}\
Hamada, Yuta; Ogasahara, Atsushi; Omura, Yuji; Takayama, Fumihiro; Yasuhara, Daiki
2014-01-01
We revisit the discrete dark matter model with $A_4$ flavor symmetry originally introduced by M.Hirsch {\\it et.al}. We show that radiative corrections can lead to non-zero $\\theta_{13}$ and non-zero mass for the lightest neutrino. We find an interesting relation among neutrino mixing parameters and it indicates the sizable deviation of $s_{23}$ from the maximal angle $s_{23}^2=1/2$ and the degenerate mass spectrum for neutrinos. Also we study the possibilities that the right-handed neutrino is a dark matter candidate. Assuming the thermal freeze-out explains observed dark matter abundance, TeV-scale right-handed neutrino and flavored scalar bosons are required. In such a case, flavor symmetry plays an important role for the suppression of lepton flavor violating processes as well as for the stability of dark matter. We show that this scenario can be viable against currently existing constraints from collider, low energy experiments and cosmological observations.
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.
Dynamic mesh refinement for discrete models of jet electro-hydrodynamics
Lauricella, Marco; Pisignano, Dario; Succi, Sauro
2015-01-01
Nowadays, several models of unidimensional fluid jets exploit discrete element methods. In some cases, as for models aiming at describing the electrospinning nanofabrication process of polymer fibers, discrete element methods suffer a non constant resolution of the jet representation. We develop a dynamic mesh-refinement method for the numerical study of the electro-hydrodynamic behavior of charged jets using discrete element methods. To this purpose, we import ideas and techniques from the string method originally developed in the framework of free-energy landscape simulations. The mesh-refined discrete element method is demonstrated for the case of electrospinning applications.
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
Fracture and ductile vs. brittle behavior -- Theory, modeling and experiment
Energy Technology Data Exchange (ETDEWEB)
Beltz, G.E. [ed.] [Univ. of California, Santa Barbara, CA (United States); Selinger, R.L.B. [ed.] [Catholic Univ., Washington, DC (United States); Kim, K.S. [ed.] [Brown Univ., Providence, RI (United States); Marder, M.P. [ed.] [Univ. of Texas, Austin, TX (United States)
1999-08-01
The symposium brought together the many communities that investigate the fundamentals of fracture, with special emphasis on the ductile/brittle transition across a broad spectrum of material classes, fracture at interfaces, and modelling fracture over various length scales. Theoretical techniques discussed ranged from first-principles electronic structure theory to atomistic simulation to mesoscale and continuum theories, along with studies of fractals and scaling in fracture. Experimental and theoretical talks were interspersed throughout all sessions, rather than being segregated. The contributions to this volume generally follow the topical outline upon which the symposium was organized. The first part, dealing with ductile vs. brittle behavior in metals, concerns itself with investigations of high-strength steel, magnesium alloys, ordered intermetallics, and Fe-Cr-Al alloys. The development of analytical methods based on micromechanical models, such as dislocation mechanics and cohesive/contact zone models, are covered in a follow-up section. Nonmetals, including silicon, are considered in Parts 3 and 4. Fractals, chaos, and scaling theories are taken up in Part 5, with a special emphasis on fracture in heterogeneous solids. Modelling based on large populations of dislocations has substantially progressed during the past three years; hence, a section devoted to crystal plasticity and mesoscale dislocation modelling appears next. Finally, the technologically significant area of interfacial fracture, with applications to composites and intergranular fracture, is taken up in Part 7. Separate abstracts were prepared for most of the papers in this book.
Numerical modeling of multiphase flow in rough and propped fractures
Dabrowski, Marcin; Dzikowski, Michał; Jasinski, Lukasz; Olkiewicz, Piotr
2017-04-01
crystalline rocks. The detailed pattern of flow paths and effective fracture conductivity are largely dependent on the level of confining stresses and fracture wall roughness, which both determine the shape and distribution of fracture apertures and contact areas. The distribution of proppant grains, which are used to maintain apertures of hydraulic fractures, is a key factor governing fracture flow in industrial applications. The flow of multiphase fluids in narrow apertures of rock fractures may substantially differ from the flow of a single-phase fluid. For example, multiphase flow effects play an important role during all stages of unconventional reservoir life cycle. Multiphase flow conditions are also expected to prevail in high temperature geothermal fields and during the transport of non aqueous phase liquid contaminants in groundwaters. We use direct numerical simulations to study single- and multiphase flow in rough and propped fractures. We compute the fluid flow using either the finite element or the lattice Boltzmann method. Body-fitting, unstructured computational meshes are used to improve the numerical accuracy. The fluid-fluid and fluid-solid interfaces are directly resolved and an implicit approach to surface tension is used to alleviate restrictions due to capillary CFL condition. In FEM simulations, the Beltrami-Laplace operator is integrated by parts to avoid interface curvature computation during evaluation of the surface tension term. We derive and validate an upscaled approach to Stokes flow in propped and rough fractures. Our upscaled 2.5D fracture flow model features a Brinkman term and is capable of treating no-slip boundary conditions on the rims of proppant grains and fracture wall contact areas. The Stokes-Brinkman fracture flow model provides an improvement over the Reynolds model, both in terms of the effective fracture permeability and the local flow pattern. We present numerical and analytical models for the propped fracture
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.
Investigation into discretization methods of the six-parameter Iwan model
Li, Yikun; Hao, Zhiming; Feng, Jiaquan; Zhang, Dingguo
2017-02-01
Iwan model is widely applied for the purpose of describing nonlinear mechanisms of jointed structures. In this paper, parameter identification procedures of the six-parameter Iwan model based on joint experiments with different preload techniques are performed. Four kinds of discretization methods deduced from stiffness equation of the six-parameter Iwan model are provided, which can be used to discretize the integral-form Iwan model into a sum of finite Jenkins elements. In finite element simulation, the influences of discretization methods and numbers of Jenkins elements on computing accuracy are discussed. Simulation results indicate that a higher accuracy can be obtained with larger numbers of Jenkins elements. It is also shown that compared with other three kinds of discretization methods, the geometric series discretization based on stiffness provides the highest computing accuracy.
Directory of Open Access Journals (Sweden)
J. E. Macías-Díaz
2017-01-01
Full Text Available We depart from the well-known one-dimensional Fisher’s equation from population dynamics and consider an extension of this model using Riesz fractional derivatives in space. Positive and bounded initial-boundary data are imposed on a closed and bounded domain, and a fully discrete form of this fractional initial-boundary-value problem is provided next using fractional centered differences. The fully discrete population model is implicit and linear, so a convenient vector representation is readily derived. Under suitable conditions, the matrix representing the implicit problem is an inverse-positive matrix. Using this fact, we establish that the discrete population model is capable of preserving the positivity and the boundedness of the discrete initial-boundary conditions. Moreover, the computational solubility of the discrete model is tackled in the closing remarks.
A Discrete SIRS Model with Kicked Loss of Immunity and Infection Probability
Paladini, F.; Renna, I.; Renna, L.
2011-03-01
A discrete-time deterministic epidemic model is proposed with the aim of reproducing the behaviour observed in the incidence of real infectious diseases, such as oscillations and irregularities. For this purpose we introduce, in a naïve discrete-time SIRS model, seasonal variability in the loss of immunity and in the infection probability, modelled by sequences of kicks. Restrictive assumptions are made on the parameters of the models, in order to guarantee that the transitions are determined by true probabilities, so that comparisons with stochastic discrete-time previsions can be also provided. Numerical simulations show that the characteristics of real infectious diseases can be adequately modeled.
A Discrete SIRS Model with Kicked Loss of Immunity and Infection Probability
Energy Technology Data Exchange (ETDEWEB)
Paladini, F; Renna, L [Dipartimento di Fisica dell' Universita del Salento, 73100 Lecce (Italy); Renna, I, E-mail: luigi.renna@le.infn.it [ISIR, Universite Pierre et Marie Curie/CNRS, F-75005 Paris (France)
2011-03-01
A discrete-time deterministic epidemic model is proposed with the aim of reproducing the behaviour observed in the incidence of real infectious diseases, such as oscillations and irregularities. For this purpose we introduce, in a naive discrete-time SIRS model, seasonal variability in the loss of immunity and in the infection probability, modelled by sequences of kicks. Restrictive assumptions are made on the parameters of the models, in order to guarantee that the transitions are determined by true probabilities, so that comparisons with stochastic discrete-time previsions can be also provided. Numerical simulations show that the characteristics of real infectious diseases can be adequately modeled.
Joint modeling of longitudinal data and discrete-time survival outcome.
Qiu, Feiyou; Stein, Catherine M; Elston, Robert C
2016-08-01
A predictive joint shared parameter model is proposed for discrete time-to-event and longitudinal data. A discrete survival model with frailty and a generalized linear mixed model for the longitudinal data are joined to predict the probability of events. This joint model focuses on predicting discrete time-to-event outcome, taking advantage of repeated measurements. We show that the probability of an event in a time window can be more precisely predicted by incorporating the longitudinal measurements. The model was investigated by comparison with a two-step model and a discrete-time survival model. Results from both a study on the occurrence of tuberculosis and simulated data show that the joint model is superior to the other models in discrimination ability, especially as the latent variables related to both survival times and the longitudinal measurements depart from 0.
Jones, Brendon R; Brouwers, Luke B; Van Tonder, Warren D; Dippenaar, Matthys A
2017-01-05
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.
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
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
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.
Discrete-time delayed standard neural network model and its application
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A novel neural network model, termed the discrete-time delayed standard neural network model (DDSNNM), and similar to the nominal model in linear robust control theory, is suggested to facilitate the stability analysis of discrete-time recurrent neural networks (RNNs) and to ease the synthesis of controllers for discrete-time nonlinear systems. The model is composed of a discrete-time linear dynamic system and a bounded static delayed (or non-delayed) nonlinear operator. By combining various Lyapunov functionals with the S-procedure, sufficient conditions for the global asymptotic stability and global exponential stability of the DDSNNM are derived, which are formulated as linear or nonlinear matrix inequalities. Most discrete-time delayed or non-delayed RNNs, or discrete-time neural-network-based nonlinear control systems can be transformed into the DDSNNMs for stability analysis and controller synthesis in a unified way. Two application examples are given where the DDSNNMs are employed to analyze the stability of the discrete-time cellular neural networks (CNNs) and to synthesize the neuro-controllers for the discrete-time nonlinear systems, respectively. Through these examples, it is demonstrated that the DDSNNM not only makes the stability analysis of the RNNs much easier, but also provides a new approach to the synthesis of the controllers for the nonlinear systems.
Universal fuzzy models and universal fuzzy controllers for discrete-time nonlinear systems.
Gao, Qing; Feng, Gang; Dong, Daoyi; Liu, Lu
2015-05-01
This paper investigates the problems of universal fuzzy model and universal fuzzy controller for discrete-time nonaffine nonlinear systems (NNSs). It is shown that a kind of generalized T-S fuzzy model is the universal fuzzy model for discrete-time NNSs satisfying a sufficient condition. The results on universal fuzzy controllers are presented for two classes of discrete-time stabilizable NNSs. Constructive procedures are provided to construct the model reference fuzzy controllers. The simulation example of an inverted pendulum is presented to illustrate the effectiveness and advantages of the proposed method. These results significantly extend the approach for potential applications in solving complex engineering problems.
DEFF Research Database (Denmark)
Jørgensen, John Bagterp; Jørgensen, Sten Bay
2007-01-01
model is realized from a continuous-discrete-time linear stochastic system specified using transfer functions with time-delays. It is argued that the prediction-error criterion should be selected such that it is compatible with the objective function of the predictive controller in which the model......A Prediction-error-method tailored for model based predictive control is presented. The prediction-error method studied are based on predictions using the Kalman filter and Kalman predictors for a linear discrete-time stochastic state space model. The linear discrete-time stochastic state space...
A Modeling Approach to Fiber Fracture in Melt Impregnation
Ren, Feng; Zhang, Cong; Yu, Yang; Xin, Chunling; Tang, Ke; He, Yadong
2017-02-01
The effect of process variables such as roving pulling speed, melt temperature and number of pins on the fiber fracture during the processing of thermoplastic based composites was investigated in this study. The melt impregnation was used in this process of continuous glass fiber reinforced thermoplastic composites. Previous investigators have suggested a variety of models for melt impregnation, while comparatively little effort has been spent on modeling the fiber fracture caused by the viscous resin. Herein, a mathematical model was developed for impregnation process to predict the fiber fracture rate and describe the experimental results with the Weibull intensity distribution function. The optimal parameters of this process were obtained by orthogonal experiment. The results suggest that the fiber fracture is caused by viscous shear stress on fiber bundle in melt impregnation mold when pulling the fiber bundle.
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......, and an alternative energy formulation is given so that it is possible to distinguish between stable and unstable situations. The reformulated substructure method is implemented on computer to give a multilinear stress crack opening displacement relation for the material in the fracture zone, and some qualitative...
Discrete and continuous Hamiltonian systems for wave modelling
Nurijanyan, S.
2013-01-01
The main focus of this thesis is to develop numerical discretisations for both compressible and incompressible inviscid flows that also preserve conservation laws at the discrete level. Two alternative approaches are discussed in detail: a semi-analytical solution; and, a fully numerical
Model Reduction of Linear Switched Systems by Restricting Discrete Dynamics
DEFF Research Database (Denmark)
Bastug, Mert; Petreczky, Mihaly; Wisniewski, Rafal
2014-01-01
We present a procedure for reducing the number of continuous states of discrete-time linear switched systems, such that the reduced system has the same behavior as the original system for a subset of switching sequences. The proposed method is expected to be useful for abstraction based control s...
Modeling elastic tensile fractures in snow using nonlocal damage mechanics
Borstad, C. P.; McClung, D. M.
2011-12-01
The initiation and propagation of tensile fractures in snow and ice are fundamental to numerous important physical processes in the cryosphere, from iceberg calving to ice shelf rift propagation to slab avalanche release. The heterogeneous nature of snow and ice, their proximity to the melting temperature, and the varied governing timescales typically lead to nonlinear fracture behavior which does not follow the predictions of Linear Elastic Fracture Mechanics (LEFM). Furthermore, traditional fracture mechanics is formally inapplicable for predicting crack initiation in the absence of a pre-existing flaw or stress concentration. An alternative to fracture mechanics is continuum damage mechanics, which accounts for the material degradation associated with cracking in a numerically efficient framework. However, damage models which are formulated locally (e.g. stress and strain are defined as point properties) suffer from mesh-sensitive crack trajectories, spurious localization of damage and improper fracture energy dissipation with mesh refinement. Nonlocal formulations of damage, which smear the effects of the material heterogeneity over an intrinsic length scale related to the material microstructure, overcome these difficulties and lead to numerically efficient and mesh-objective simulations of the tensile failure of heterogeneous materials. We present the results of numerical simulations of tensile fracture initiation and propagation in cohesive snow using a nonlocal damage model. Seventeen beam bending experiments, both notched and unnotched, were conducted using blocks of cohesive dry snow extracted from an alpine snowpack. Material properties and fracture parameters were calculated from the experimental data using beam theory and quasi-brittle fracture mechanics. Using these parameters, a nonlocal isotropic damage model was applied to two-dimensional finite element meshes of the same scale as the experiments. The model was capable of simulating the propagation
A first order system model of fracture healing
Institute of Scientific and Technical Information of China (English)
WANG Xiao-ping; ZHANG Xian-long; LI Zhu-guo; YU Xin-gang
2005-01-01
A first order system model is proposed for simulating the influence of stress stimulation on fracture strength during fracture healing. To validate the model, the diaphyses of bilateral tibiae in 70 New Zealand rabbits were osteotomized and fixed with rigid plates and stress-relaxation plates, respectively. Stress shielding rate and ultimate bending strength of the healing bone were measured at 2 to 48 weeks postoperatively. Ratios of stress stimulation and fracture strength of the healing bone to those of intact bone were taken as the system input and output. The assumed first order system model can approximate the experimental data on fracture strength from the input of stress stimulation over time, both for the rigid plate group and the stress-relaxation plate group, with different system parameters of time constant and gain. The fitting curve indicates that the effect of mechanical stimulus occurs mainly in late stages of healing. First order system can model the stress adaptation process of fracture healing. This approach presents a simple bio-mathematical model of the relationship between stress stimulation and fracture strength, and has the potential to optimize planning of functional exercises and conduct parametric studies.
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
Institute of Scientific and Technical Information of China (English)
CHEN Jun; PAN Tongyan; HUANG Xiaoming
2011-01-01
We established a user-defined micromechanical model using discrete element method (DEM) to investigate the cracking behavior of asphalt concrete (AC).Using the “Fish” language provided in the particle flow code in 3-Demensions (PFC3D),the air voids and mastics in asphalt concrete were realistically built as two distinct phases.With the irregular shape of individual aggregate particles modeled using a clump of spheres of different sizes,the three-dimensional (3D) discrete element model was able to account for aggregate gradation and fraction.Laboratory uniaxial complex modulus test and indirect tensile strength test were performed to obtain input material parameters for the numerical simulation.A set of the indirect tensile test were simulated to study the cracking behavior of AC at two levels of temperature,i e,-10 ℃ and 15 ℃.The predicted results of the numerical simulation were compared with laboratory experimental measurements.Results show that the 3D DEM model is able to predict accurately the fracture pattern of different asphalt mixtures.Based on the DEM model,the effects of air void content and aggregate volumetric fraction on the cracking behavior of asphalt concrete were evaluated.
A discrete epidemic model for bovine Babesiosis disease and tick populations
Directory of Open Access Journals (Sweden)
Aranda Diego F.
2017-06-01
Full Text Available In this paper, we provide and study a discrete model for the transmission of Babesiosis disease in bovine and tick populations. This model supposes a discretization of the continuous-time model developed by us previously. The results, here obtained by discrete methods as opposed to continuous ones, show that similar conclusions can be obtained for the discrete model subject to the assumption of some parametric constraints which were not necessary in the continuous case. We prove that these parametric constraints are not artificial and, in fact, they can be deduced from the biological significance of the model. Finally, some numerical simulations are given to validate the model and verify our theoretical study.
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.
Generalized computer-aided discrete time domain modeling and analysis of dc-dc converters
Lee, F. C.; Iwens, R. P.; Yu, Y.; Triner, J. E.
1977-01-01
A generalized discrete time domain modeling and analysis technique is presented for all types of switching regulators using any type of duty-cycle controller, and operating in both continuous and discontinuous inductor current. State space techniques are employed to derive an equivalent nonlinear discrete time model that describes the converter exactly. The system is linearized about its equilibrium state to obtain a linear discrete time model for small signal performance evaluations, such as stability, audiosusceptibility and transient response. The analysis makes extensive use of the digital computer as an analytical tool. It is universal, exact and easy to use.
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. PMID:19949529
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.
Generation of Random Particle Packings for Discrete Element Models
Abe, S.; Weatherley, D.; Ayton, T.
2012-04-01
An important step in the setup process of Discrete Element Model (DEM) simulations is the generation of a suitable particle packing. There are quite a number of properties such a granular material specimen should ideally have, such as high coordination number, isotropy, the ability to fill arbitrary bounding volumes and the absence of locked-in stresses. An algorithm which is able to produce specimens fulfilling these requirements is the insertion based sphere packing algorithm originally proposed by Place and Mora, 2001 [2] and extended in this work. The algorithm works in two stages. First a number of "seed" spheres are inserted into the bounding volume. In the second stage the gaps between the "seed" spheres are filled by inserting new spheres in a way so they have D+1 (i.e. 3 in 2D, 4 in 3D) touching contacts with either other spheres or the boundaries of the enclosing volume. Here we present an implementation of the algorithm and a systematic statistical analysis of the generated sphere packings. The analysis of the particle radius distribution shows that they follow a power-law with an exponent ≈ D (i.e. ≈3 for a 3D packing and ≈2 for 2D). Although the algorithm intrinsically guarantees coordination numbers of at least 4 in 3D and 3 in 2D, the coordination numbers realized in the generated packings can be significantly higher, reaching beyond 50 if the range of particle radii is sufficiently large. Even for relatively small ranges of particle sizes (e.g. Rmin = 0.5Rmax) the maximum coordination number may exceed 10. The degree of isotropy of the generated sphere packing is also analysed in both 2D and 3D, by measuring the distribution of orientations of vectors joining the centres of adjacent particles. If the range of particle sizes is small, the packing algorithm yields moderate anisotropy approaching that expected for a face-centred cubic packing of equal-sized particles. However, once Rmin 2D and 3D. The analysis demonstrates that this space
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.
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
2006-12-01
NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA MBA PROFESSIONAL REPORT Discrete-Event Simulation Modeling of the Repairable...TYPE AND DATES COVERED MBA Professional Report 4. TITLE AND SUBTITLE: Discrete-Event Simulation Modeling of the Repairable Inventory Process to...Advanced Concept Technology Demonstration; Agile Rapid Global Combat Support; Discrete- Event Simulation Modeling of the Repairable Inventory Process to
ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra
Hinkelmann, Franziska; Guang, Bonny; McNeill, Rustin; Blekherman, Grigoriy; Veliz-Cuba, Alan; Laubenbacher, Reinhard
2010-01-01
Motivation: Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, bounded Petri nets, and agent-based models. Simulation is a common practice for analyzing discrete models, but many systems are far too large to capture all the relevant dynamical features through simulation alone. Results: We convert discrete models into algebraic models and apply tools from computational algebra to analyze their dynamics. The key feature of biological systems that is exploited by our algorithms is their sparsity: while the number of nodes in a biological network may be quite large, each node is affected only by a small number of other nodes. In our experience with models arising in systems biology and random models, this structure leads to fast computations when using algebraic models, and thus efficient analysis. Availability: All algorithms and methods are available in our package Analysis of Dynamic Algebraic Models (ADAM), a user friendly web-interf...
Johnson, C. D.; Kastrinos, J. R.; Haeni, F. P.
2005-12-01
A multi-disciplined and team-based approach was used to integrate geophysical, hydrologic, and chemical data to characterize lithology, fractures, and hydraulic properties of fractured crystalline bedrock and to determine the nature and extent of ground-water contamination from a landfill and former chemical-waste disposal pits at the University of Connecticut. Detection of volatile organic compounds (VOCs) in domestic bedrock wells in the mid-1980s led to this investigation, in which a team comprised of hydrologists, engineers, geophysicists, geologists, chemists, toxicologists, and community-involvement personnel collected, analyzed, and evaluated data; developed and refined a conceptual model of the ground-water flow and contaminant distribution at the site; and evaluated alternatives and implemented a final remediation plan. The characterization phase began in 1999 and the remediation phase is currently ongoing. An integrated and iterative approach of using multiple methods in phases was important for corroborating the interpretation of individual methods and essential for guiding the design and implementation of additional testing at the site. The use of geophysical data early in the investigation allowed the study team to obtain detailed subsurface information using a minimum of boreholes. Surface geophysical methods were used to target potential discharge of contaminants from the landfill for further investigation. Borehole geophysical methods were used to investigate the anomalies identified by surface geophysical methods, the location and orientation of fractures that intersect and surround each well, the direction and magnitude of ambient flow in the wells, and the transmissive fractures that could provide pathways for contaminant migration. Borehole geophysical and hydraulic data were used to design discrete-zone monitoring systems for the collection of hydraulic head and chemical data and to prevent cross contamination through the boreholes. The results
Pressure transient modeling of a fractured geothermal reservior
Energy Technology Data Exchange (ETDEWEB)
Robinson, B.A.
1990-01-01
A fracture network model has been developed to simulate transient fluid flow behavior in a fractured rock mass. Included is a pressure-dependent aperture submodel to simulate behavior often seen in fractured systems. The model is used to simulate data from the Fenton Hill Hot Dry Rock (HDR) geothermal reservoir. Both low-pressure/low-flow-rate and high-pressure/high-flow-rate transient data are adequately simulated. The model parameters obtained suggest ways in which the model can be refined to achieve even more realistic fits to the data. The model is then used to demonstrate more efficient operating modes than the two-well circulating mode usually proposed for HDR reservoirs. 11 refs., 9 figs., 1 tab.
DEM Modelling of Granule Rearrangement and Fracture Behaviours During a Closed-Die Compaction.
Furukawa, Ryoichi; Kadota, Kazunori; Noguchi, Tetsuro; Shimosaka, Atsuko; Shirakawa, Yoshiyuki
2017-01-26
The closed-die compaction behaviour of D-mannitol granules has been simulated by the discrete element method (DEM) to investigate the granule rearrangement and fracture behaviour during compaction which affects the compactibility of the tablet. The D-mannitol granules produced in a fluidized bed were modelled as agglomerates of primary particles connected by linear spring bonds. The validity of the model granule used in the DEM simulation was demonstrated by comparing to the experimental results of a uniaxial compression test. During uniaxial compression, the numerical results of the force-displacement curve corresponded reasonably well to the experimental data. The closed-die compaction of the modelled granules was carried out to investigate the rearrangement and fracture behaviours of the granule at different upper platen velocities. The forces during closed-die compaction calculated by DEM fluctuated in the low-pressure region due to the rearrangement of granules. A Heckel analysis showed that the force fluctuation occurred at the initial bending region of the Heckel plot, which represents the granule rearrangement and fracture. Furthermore, the upper platen velocity affected the trend of compaction forces, which can lead to compaction failure due to capping. These results could contribute to designing the appropriate granules during closed-die compaction.
Numerical modelling of sandstone uniaxial compression test using a mix-mode cohesive fracture model
Gui, Yilin; Kodikara, Jayantha
2015-01-01
A mix-mode cohesive fracture model considering tension, compression and shear material behaviour is presented, which has wide applications to geotechnical problems. The model considers both elastic and inelastic displacements. Inelastic displacement comprises fracture and plastic displacements. The norm of inelastic displacement is used to control the fracture behaviour. Meantime, a failure function describing the fracture strength is proposed. Using the internal programming FISH, the cohesive fracture model is programmed into a hybrid distinct element algorithm as encoded in Universal Distinct Element Code (UDEC). The model is verified through uniaxial tension and direct shear tests. The developed model is then applied to model the behaviour of a uniaxial compression test on Gosford sandstone. The modelling results indicate that the proposed cohesive fracture model is capable of simulating combined failure behaviour applicable to rock.
Zhang, Yufeng; Zhang, Xiangzhi; Wang, Yan; Liu, Jiangen
2017-01-01
With the help of R-matrix approach, we present the Toda lattice systems that have extensive applications in statistical physics and quantum physics. By constructing a new discrete integrable formula by R-matrix, the discrete expanding integrable models of the Toda lattice systems and their Lax pairs are generated, respectively. By following the constructing formula again, we obtain the corresponding (2+1)-dimensional Toda lattice systems and their Lax pairs, as well as their (2+1)-dimensional discrete expanding integrable models. Finally, some conservation laws of a (1+1)-dimensional generalised Toda lattice system and a new (2+1)-dimensional lattice system are generated, respectively.
A discrete force allocation algorithm for modelling wind turbines in computational fluid dynamics
DEFF Research Database (Denmark)
Réthoré, Pierre-Elouan; Sørensen, Niels N.
2012-01-01
This paper describes an algorithm for allocating discrete forces in computational fluid dynamics (CFD). Discrete forces are useful in wind energy CFD. They are used as an approximation of the wind turbine blades’ action on the wind (actuator disc/line), to model forests and to model turbulent......, this algorithm does not address the specific cases where discrete forces are present. The velocities and pressure exhibit some significant numerical fluctuations at the position where the body forces are applied. While this issue is limited in space, it is usually critical to accurately estimate the velocity...
Parameter estimation for the subcritical Heston model based on discrete time observations
2014-01-01
We study asymptotic properties of some (essentially conditional least squares) parameter estimators for the subcritical Heston model based on discrete time observations derived from conditional least squares estimators of some modified parameters.
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.
Fracture propagation in Indiana Limestone interpreted via linear softening cohesive fracture model
Rinehart, Alex J.; Bishop, Joseph E.; Dewers, Thomas
2015-04-01
We examine the use of a linear softening cohesive fracture model (LCFM) to predict single-trace fracture growth in short-rod (SR) and notched 3-point-bend (N3PB) test configurations in Indiana Limestone. The broad goal of this work is to (a) understand the underlying assumptions of LCFM and (b) use experimental similarities and deviations from the LCFM to understand the role of loading paths of tensile fracture propagation. Cohesive fracture models are being applied in prediction of structural and subsurface fracture propagation in geomaterials. They lump the inelastic processes occurring during fracture propagation into a thin zone between elastic subdomains. LCFM assumes that the cohesive zone initially deforms elastically to a maximum tensile stress (σmax) and then softens linearly from the crack opening width at σmax to zero stress at a critical crack opening width w1. Using commercial finite element software, we developed LCFMs for the SR and N3PB configurations. After fixing σmax with results from cylinder splitting tests and finding an initial Young's modulus (E) with unconfined compressive strength tests, we manually calibrate E and w1 in the SR model against an envelope of experimental data. We apply the calibrated LCFM parameters in the N3PB geometry and compare the model against an envelope of N3PB experiments. For accurate simulation of fracture propagation, simulated off-crack stresses are high enough to require inclusion of damage. Different elastic moduli are needed in tension and compression. We hypothesize that the timing and location of shear versus extensional micromechanical failures control the qualitative macroscopic force-versus-displacement response in different tests. For accurate prediction, the LCFM requires a constant style of failure, which the SR configuration maintains until very late in deformation. The N3PB configuration does not maintain this constancy. To be broadly applicable between geometries and failure styles, the LCFM
Jensen, K. A.; Ripoll, J.-F.; Wray, A. A.; Joseph, D.; ElHafi, M.
2004-01-01
Five computational methods for solution of the radiative transfer equation in an absorbing-emitting and non-scattering gray medium were compared on a 2 m JP-8 pool fire. The temperature and absorption coefficient fields were taken from a synthetic fire due to the lack of a complete set of experimental data for fires of this size. These quantities were generated by a code that has been shown to agree well with the limited quantity of relevant data in the literature. Reference solutions to the governing equation were determined using the Monte Carlo method and a ray tracing scheme with high angular resolution. Solutions using the discrete transfer method, the discrete ordinate method (DOM) with both S(sub 4) and LC(sub 11) quadratures, and moment model using the M(sub 1) closure were compared to the reference solutions in both isotropic and anisotropic regions of the computational domain. DOM LC(sub 11) is shown to be the more accurate than the commonly used S(sub 4) quadrature technique, especially in anisotropic regions of the fire domain. This represents the first study where the M(sub 1) method was applied to a combustion problem occurring in a complex three-dimensional geometry. The M(sub 1) results agree well with other solution techniques, which is encouraging for future applications to similar problems since it is computationally the least expensive solution technique. Moreover, M(sub 1) results are comparable to DOM S(sub 4).
Three dimensional modeling of fractures in rock: From data to a regionalized parent-daughter model
Energy Technology Data Exchange (ETDEWEB)
Hestir, K.; Chiles, J.P.; Long, J.; Billaux, D.
1987-04-01
We introduce a stochastic model for fracture systems called the parent-daughter model. The model uses circular discs to represent fractures. The discs are placed in three-dimensional space according to a random process called the parent-daughter point process. This process will give a clustering of fractures that cannot be produced with the usual Poisson process. We then outline a procedure for fitting the model to a particular data set.
Design and modeling of small scale multiple fracturing experiments
Energy Technology Data Exchange (ETDEWEB)
Cuderman, J F
1981-12-01
Recent experiments at the Nevada Test Site (NTS) have demonstrated the existence of three distinct fracture regimes. Depending on the pressure rise time in a borehole, one can obtain hydraulic, multiple, or explosive fracturing behavior. The use of propellants rather than explosives in tamped boreholes permits tailoring of the pressure risetime over a wide range since propellants having a wide range of burn rates are available. This technique of using the combustion gases from a full bore propellant charge to produce controlled borehole pressurization is termed High Energy Gas Fracturing (HEGF). Several series of HEGF, in 0.15 m and 0.2 m diameter boreholes at 12 m depths, have been completed in a tunnel complex at NTS where mineback permitted direct observation of fracturing obtained. Because such large experiments are costly and time consuming, smaller scale experiments are desirable, provided results from small experiments can be used to predict fracture behavior in larger boreholes. In order to design small scale gas fracture experiments, the available data from previous HEGF experiments were carefully reviewed, analytical elastic wave modeling was initiated, and semi-empirical modeling was conducted which combined predictions for statically pressurized boreholes with experimental data. The results of these efforts include (1) the definition of what constitutes small scale experiments for emplacement in a tunnel complex at the Nevada Test Site, (2) prediction of average crack radius, in ash fall tuff, as a function of borehole size and energy input per unit length, (3) definition of multiple-hydraulic and multiple-explosive fracture boundaries as a function of boreholes size and surface wave velocity, (4) semi-empirical criteria for estimating stress and acceleration, and (5) a proposal that multiple fracture orientations may be governed by in situ stresses.
A General Discrete Time Model of Population Dynamics in the Presence of an Infection
Directory of Open Access Journals (Sweden)
Giuseppe Izzo
2009-01-01
Full Text Available We present a set of difference equations which generalizes that proposed in the work of G. Izzo and A. Vecchio (2007 and represents the discrete counterpart of a larger class of continuous model concerning the dynamics of an infection in an organism or in a host population. The limiting behavior of this new discrete model is studied and a threshold parameter playing the role of the basic reproduction number is derived.
Modeling the Fracture of Ice Sheets on Parallel Computers
Energy Technology Data Exchange (ETDEWEB)
Waisman, Haim [Columbia University; Tuminaro, Ray [Sandia National Labs
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
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.
Wegner estimate for discrete alloy-type models
Veselić, Ivan
2010-01-01
We study discrete alloy-type random Schr\\"odinger operators on $\\ell^2(\\mathbb{Z}^d)$. Wegner estimates are bounds on the average number of eigenvalues in an energy interval of finite box restrictions of these types of operators. If the single site potential is compactly supported and the distribution of the coupling constant is of bounded variation a Wegner estimate holds. The bound is polynomial in the volume of the box and thus applicable as an ingredient for a localisation proof via multiscale analysis.
Directory of Open Access Journals (Sweden)
Urai J.L.
2010-06-01
Full Text Available We compare analogue and numerical models of dilatational fractures at low confining stress. These structures form an effective conduit for fluid flow in the field, but are difficult to model since they form in cohesive materials at low stresses. We use a truly cohesive powder for the analogue models and a Discrete Element Model (DEM with brittle-elastic bonds for the numerical modelling. We show that despite variations in the model type, small differences in the location of initial fractures and the way these structures link-up to control the evolution of the model, the observed structures are robust. Three structural zones develop where different fault types dominate. In 3D numerical models we show an increase of the porosity on the fault zone with increasing deformation. The progradation direction is shown to be controlled by the position of the fracture. The combination of analogue models with cohesive powder and DEMs with internal cohesion is an excellent tool to study the evolution of open fractures.
A unified framework for modeling landscape evolution by discrete flows
Shelef, Eitan; Hilley, George E.
2016-05-01
Topographic features such as branched valley networks and undissected convex-up hillslopes are observed in disparate physical environments. In some cases, these features are formed by sediment transport processes that occur discretely in space and time, while in others, by transport processes that are uniformly distributed across the landscape. This paper presents an analytical framework that reconciles the basic attributes of such sediment transport processes with the topographic features that they form and casts those in terms that are likely common to different physical environments. In this framework, temporal changes in surface elevation reflect the frequency with which the landscape is traversed by geophysical flows generated discretely in time and space. This frequency depends on the distance to which flows travel downslope, which depends on the dynamics of individual flows, the lithologic and topographic properties of the underlying substrate, and the coevolution of topography, erosion, and the routing of flows over the topographic surface. To explore this framework, we postulate simple formulations for sediment transport and flow runout distance and demonstrate that the conditions for hillslope and channel network formation can be cast in terms of fundamental parameters such as distance from drainage divide and a friction-like coefficient that describes a flow's resistance to motion. The framework we propose is intentionally general, but the postulated formulas can be substituted with those that aim to describe a specific process and to capture variations in the size distribution of such flow events.
Fractal modeling of natural fracture networks. Final report, June 1994--June 1995
Energy Technology Data Exchange (ETDEWEB)
Ferer, M.V.; Dean, B.H.; Mick, C.
1996-04-01
Recovery from naturally fractured, tight-gas reservoirs is controlled by the fracture network. Reliable characterization of the actual fracture network in the reservoir is severely limited. The location and orientation of fractures intersecting the borehole can be determined, but the length of these fractures cannot be unambiguously determined. Fracture networks can be determined for outcrops, but there is little reason to believe that the network in the reservoir should be identical because of the differences in stresses and history. Because of the lack of detailed information about the actual fracture network, modeling methods must represent the porosity and permeability associated with the fracture network, as accurately as possible with very little apriori information. Three rather different types of approaches have been used: (1) dual porosity simulations; (2) `stochastic` modeling of fracture networks, and (3) fractal modeling of fracture networks. Stochastic models which assume a variety of probability distributions of fracture characteristics have been used with some success in modeling fracture networks. The advantage of these stochastic models over the dual porosity simulations is that real fracture heterogeneities are included in the modeling process. In the sections provided in this paper the authors will present fractal analysis of the MWX site, using the box-counting procedure; (2) review evidence testing the fractal nature of fracture distributions and discuss the advantages of using their fractal analysis over a stochastic analysis; (3) present an efficient algorithm for producing a self-similar fracture networks which mimic the real MWX outcrop fracture network.
Modelling karst aquifer evolution in fractured, porous rocks
Kaufmann, Georg
2016-12-01
The removal of material in soluble rocks by physical and chemical dissolution is an important process enhancing the secondary porosity of soluble rocks. Depending on the history of the soluble rock, dissolution can occur either along fractures and bedding partings of the rock in the case of a telogenetic origin, or within the interconnected pore space in the case of eogenetic origin. In soluble rocks characterised by both fractures and pore space, dissolution in both flow compartments is possible. We investigate the dissolution of calcite both along fractures and within the pore space of a limestone rock by numerical modelling. The limestone rock is treated as fractured, porous aquifer, in which the hydraulic conductivity increases with time both for the fractures and the pore spaces. We show that enlargement of pore space by dissolution will accelerate the development of a classical fracture-dominated telogenetic karst aquifer, breakthrough occurs faster. In the case of a pore-controlled aquifer as in eogenetic rocks, enlargement of pores results in a front of enlarged pore spaces migrating into the karst aquifer, with more homogeneous enlargement around this dissolution front, and later breakthrough.
Optimal fixation of oblique scaphoid fractures: a cadaver model.
Luria, Shai; Lenart, Lado; Lenart, Borut; Peleg, Eran; Kastelec, Matej
2012-07-01
Acute scaphoid fractures are commonly fixed with headless cannulated screws positioned in the center of the proximal fragment. Central placement of the screw may be difficult and may violate the scaphotrapezial joint. We hypothesize that placement of the screw through the scaphoid tuberosity will achieve perpendicular fixation of an oblique waist fracture and result in more stable fixation than a screw in the center of the proximal fragment. We designed oblique osteotomies for 8 matched pairs of cadaver scaphoids and fixed each specimen with a headless cannulated screw. In 1 specimen, we positioned the screw at the center of the proximal fragment; we placed its matched pair perpendicular to the fracture. The perpendicular screw was directed through the scaphoid tuberosity. We placed the specimen under the increasing load of a pneumatically driven plunger. We compared stiffness, load, distance at failure, and mechanism of failure between the central and perpendicular screw groups. We found no difference between groups. Stiffness was identical in both groups (131 N/mm) and load to failure was similar (central screw, 137 N vs perpendicular screw, 148 N). In this biomechanical model of an unstable scaphoid fracture, we found that similar stability of fixation had been achieved with a screw perpendicular to the fracture plane with entry through the tuberosity, compared with a screw in a central position in the proximal fragment. This study suggests that placing the screw through the tuberosity, perpendicular to a short oblique fracture, will not impair fixation stability. Percutaneous fixation of scaphoid fractures has become popular although it is technically challenging. An easier distal approach through the tuberosity, without violating the scaphotrapezial joint, may not impair the fixation stability of an oblique fracture. Copyright © 2012 American Society for Surgery of the Hand. Published by Elsevier Inc. All rights reserved.
Multi-scale peridynamic modeling of dynamic fracture in concrete
Lammi, Christopher J.; Zhou, Min
2017-01-01
Peridynamics simulations of the dynamic deformation and failure of high-performance concrete are performed at the meso-scale. A pressure-dependent, peridynamic plasticity model and failure criteria are used to capture pressure-sensitive granular flow and fracture. The meso-scale framework explicitly resolves reinforcing phases, pores, and intrinsic flaws. A novel scaling approach is formulated to inform the engineering-scale plasticity model parameters with meso-scale simulation results. The effects of composition, porosity, and fracture energy at the meso-scale on the engineering-scale impact resistance are assessed. The fracture process zone at the meso-scale is found to propagate along adjacent pores and reinforcing phases under tensile and shear loading conditions. The simulations show that tensile strength decreases and dissipation increases as the porosity in the concrete increases. The framework and modeling approach allow the delineation of trends that can be used to design more impact-resistant materials.
Institute of Scientific and Technical Information of China (English)
Zhao Zhi-Jin; Zheng Shi-Lian; Xu Chun-Yun; Kong Xian-Zheng
2007-01-01
Hidden Markov models (HMMs) have been used to model burst error sources of wireless channels. This paper proposes a hybrid method of using genetic algorithm (GA) and simulated annealing (SA) to train HMM for discrete channel modelling. The proposed method is compared with pure GA, and experimental results show that the HMMs trained by the hybrid method can better describe the error sequences due to SA's ability of facilitating hill-climbing at the later stage of the search. The burst error statistics of the HMMs trained by the proposed method and the corresponding error sequences are also presented to validate the proposed method.
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
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.
Figueiredo, Bruno; Tsang, Chin-Fu; Niemi, Auli; Lindgren, Georg
2016-05-01
Laboratory and field experiments done on fractured rock show that flow and solute transport often occur along flow channels. `Sparse channels' refers to the case where these channels are characterised by flow in long flow paths separated from each other by large spacings relative to the size of flow domain. A literature study is presented that brings together information useful to assess whether a sparse-channel network concept is an appropriate representation of the flow system in tight fractured rock of low transmissivity, such as that around a nuclear waste repository in deep crystalline rocks. A number of observations are made in this review. First, conventional fracture network models may lead to inaccurate results for flow and solute transport in tight fractured rocks. Secondly, a flow dimension of 1, as determined by the analysis of pressure data in well testing, may be indicative of channelised flow, but such interpretation is not unique or definitive. Thirdly, in sparse channels, the percolation may be more influenced by the fracture shape than the fracture size and orientation but further studies are needed. Fourthly, the migration of radionuclides from a waste canister in a repository to the biosphere may be strongly influenced by the type of model used (e.g. discrete fracture network, channel model). Fifthly, the determination of appropriateness of representing an in situ flow system by a sparse-channel network model needs parameters usually neglected in site characterisation, such as the density of channels or fracture intersections.
Figueiredo, Bruno; Tsang, Chin-Fu; Niemi, Auli; Lindgren, Georg
2016-11-01
Laboratory and field experiments done on fractured rock show that flow and solute transport often occur along flow channels. `Sparse channels' refers to the case where these channels are characterised by flow in long flow paths separated from each other by large spacings relative to the size of flow domain. A literature study is presented that brings together information useful to assess whether a sparse-channel network concept is an appropriate representation of the flow system in tight fractured rock of low transmissivity, such as that around a nuclear waste repository in deep crystalline rocks. A number of observations are made in this review. First, conventional fracture network models may lead to inaccurate results for flow and solute transport in tight fractured rocks. Secondly, a flow dimension of 1, as determined by the analysis of pressure data in well testing, may be indicative of channelised flow, but such interpretation is not unique or definitive. Thirdly, in sparse channels, the percolation may be more influenced by the fracture shape than the fracture size and orientation but further studies are needed. Fourthly, the migration of radionuclides from a waste canister in a repository to the biosphere may be strongly influenced by the type of model used (e.g. discrete fracture network, channel model). Fifthly, the determination of appropriateness of representing an in situ flow system by a sparse-channel network model needs parameters usually neglected in site characterisation, such as the density of channels or fracture intersections.
Risk Assessment in Fractured Clayey Tills - Which Modeling Tools?
DEFF Research Database (Denmark)
Chambon, Julie Claire Claudia; Bjerg, Poul Løgstrup; Binning, Philip John
2012-01-01
assessment is challenging and the inclusion of the relevant processes is difficult. Furthermore the lack of long-term monitoring data prevents from verifying the accuracy of the different conceptual models. Further investigations based on long-term data and numerical modeling are needed to accurately......The article presents different tools available for risk assessment in fractured clayey tills and their advantages and limitations are discussed. Because of the complex processes occurring during contaminant transport through fractured media, the development of simple practical tools for risk...
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.
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.
Coupled discrete element modeling of fluid injection into dense granular media
Zhang, Fengshou; Damjanac, Branko; Huang, Haiying
2013-06-01
The coupled displacement process of fluid injection into a dense granular medium is investigated numerically using a discrete element method (DEM) code PFC2D® coupled with a pore network fluid flow scheme. How a dense granular medium behaves in response to fluid injection is a subject of fundamental and applied research interests to better understand subsurface processes such as fluid or gas migration and formation of intrusive features as well as engineering applications such as hydraulic fracturing and geological storage in unconsolidated formations. The numerical analysis is performed with DEM executing the mechanical calculation and the network model solving the Hagen-Poiseuille equation between the pore spaces enclosed by chains of particles and contacts. Hydromechanical coupling is realized by data exchanging at predetermined time steps. The numerical results show that increase in the injection rate and the invading fluid viscosity and decrease in the modulus and permeability of the medium result in fluid flow behaviors displaying a transition from infiltration-governed to infiltration-limited and the granular medium responses evolving from that of a rigid porous medium to localized failure leading to the development of preferential paths. The transition in the fluid flow and granular medium behaviors is governed by the ratio between the characteristic times associated with fluid injection and hydromechanical coupling. The peak pressures at large injection rates when fluid leakoff is limited compare well with those from the injection experiments in triaxial cells in the literature. The numerical analysis also reveals intriguing tip kinematics field for the growth of a fluid channel, which may shed light on the occurrence of the apical inverted-conical features in sandstone and magma intrusion in unconsolidated formations.
Exact solution of a delay difference equation modeling traffic flow and their ultra-discrete limit
Matsuya, Keisuke; Kanai, Masahiro
2015-01-01
We consider a car-following model described by a delay difference equation and give its exact solutions that present propagation of a traffic jam. This model is a discrete-time version of the delayed optimal-velocity model; in the continuum limit, we recover the delay differential equation for this model and the exact solutions as well. We then work in the ultra-discrete limit, obtaining a delay cellular-automaton model, which successfully inherits the solutions. Also the dispersion relation ...
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.
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.
Impedance Matching for Discrete, Periodic Media and Application to Two-Scale Wave Propagation Models
Thirunavukkarasu, Senganal
This dissertation introduces the idea of an equivalent continuous medium (ECM) that has the same impedance as that of an unbounded discrete periodic medium. Contrary to existing knowledge, we constructively show that it is indeed possible to achieve perfect matching for periodic and discrete media. We present analytical results relating the propagation characteristics of periodic media and the corresponding ECM, leading to the development of numerical methods for wave propagation in these media. In this dissertation, we present the main idea of ECM and apply it, with mixed results, to seemingly different problems requiring effective numerical methods for modeling wave propagation in unbounded media. An immediate application of ECM is in developing absorbing boundary conditions (ABCs) for wave propagation in unbounded discrete media. Using the idea of ECM, and building on class of continuous ABCs called perfectly matched discrete layers (PMDL), we propose a new class of discrete ABCs called discrete PMDL and develop frequency domain formulations that are shown to be superior to continuous ABCs. Another application that is explored in this dissertation is the design of interface conditions for concurrent coupling of two-scale wave propagation models, e.g. Atomistic-to-Continuum (AtC) coupling. We propose a domain-decomposition (DD) approach and develop accurate interface conditions that are critical for the concurrent coupling of the two-scale models. It turns out that time-domain discrete ABCs are key to the the accuracy of these interface conditions. Since discrete PMDL is well-posed and accurate for the model problem, we build on it to propose an efficient and accurate interface condition for two-scale wave propagation models. Although many open problems remain with respect to implementation, we believe that the proposed DD based approach is a good first step towards achieving efficient coupling of two-scale wave propagation models. Time-domain discrete PMDL can
Convergence of discrete duality finite volume schemes for the cardiac bidomain model
Andreianov, Boris; Karlsen, Kenneth H; Pierre, Charles
2010-01-01
We prove convergence of discrete duality finite volume (DDFV) schemes on distorted meshes for a class of simplified macroscopic bidomain models of the electrical activity in the heart. Both time-implicit and linearised time-implicit schemes are treated. A short description is given of the 3D DDFV meshes and of some of the associated discrete calculus tools. Several numerical tests are presented.
Majid, Mazlina Abdul; Siebers, Peer-Olaf
2010-01-01
In this paper, we investigate output accuracy for a Discrete Event Simulation (DES) model and Agent Based Simulation (ABS) model. The purpose of this investigation is to find out which of these simulation techniques is the best one for modelling human reactive behaviour in the retail sector. In order to study the output accuracy in both models, we have carried out a validation experiment in which we compared the results from our simulation models to the performance of a real system. Our experiment was carried out using a large UK department store as a case study. We had to determine an efficient implementation of management policy in the store's fitting room using DES and ABS. Overall, we have found that both simulation models were a good representation of the real system when modelling human reactive behaviour.
ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra
Directory of Open Access Journals (Sweden)
Blekherman Grigoriy
2011-07-01
Full Text Available Abstract Background 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. Results 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. Conclusions 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
DEFF Research Database (Denmark)
Batley, Richard; Ibáñez Rivas, Juan Nicolás
2013-01-01
The apparatus of the Random Utility Model (RUM) first emerged in the early 1960s, with Marschak (1960) and Block and Marschak (1960) translating models originally developed for discriminant analysis in psychophysics (Thurstone, 1927) to the alternative domain of discrete choice analysis in econom......The apparatus of the Random Utility Model (RUM) first emerged in the early 1960s, with Marschak (1960) and Block and Marschak (1960) translating models originally developed for discriminant analysis in psychophysics (Thurstone, 1927) to the alternative domain of discrete choice analysis...
Two-dimensional discrete mathematical model of tumor-induced angiogenesis
Institute of Scientific and Technical Information of China (English)
Gai-ping ZHAO; Er-yun CHEN; Jie WU; Shi-xiong XU; M.W. Collins; Quan LONG
2009-01-01
A 2D discrete mathematical model of a nine-point finite difference scheme is built to simulate tumor-induced angiogenesis. Nine motion directions of an individual endothelial cell and two parent vessels are extended in the present model. The process of tumor-induced angiogenesis is performed by coupling random motility, chemotaxis, and haptotaxis of endothelial cell in different mechanical environments inside and outside the tumor. The results show that nearly realistic tumor microvascular networks with neoplastic pathophysiological characteristics can be generated from the present model. Moreover, the theoretical capillary networks generated in numerical simulations of the discrete model may provide useful information for further clinical research.
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.
Macroscopic model and truncation error of discrete Boltzmann method
Hwang, Yao-Hsin
2016-10-01
A derivation procedure to secure the macroscopically equivalent equation and its truncation error for discrete Boltzmann method is proffered in this paper. Essential presumptions of two time scales and a small parameter in the Chapman-Enskog expansion are disposed of in the present formulation. Equilibrium particle distribution function instead of its original non-equilibrium form is chosen as key variable in the derivation route. Taylor series expansion encompassing fundamental algebraic manipulations is adequate to realize the macroscopically differential counterpart. A self-contained and comprehensive practice for the linear one-dimensional convection-diffusion equation is illustrated in details. Numerical validations on the incurred truncation error in one- and two-dimensional cases with various distribution functions are conducted to verify present formulation. As shown in the computational results, excellent agreement between numerical result and theoretical prediction are found in the test problems. Straightforward extensions to more complicated systems including convection-diffusion-reaction, multi-relaxation times in collision operator as well as multi-dimensional Navier-Stokes equations are also exposed in the Appendix to point out its expediency in solving complicated flow problems.
Gauthier, B.D.M.; Bisdom, K.; Bertotti, G.
2012-01-01
The full 3D characterization of fracture networks is a key issue in naturally fractured reservoir modeling. Fracture geometry (e.g., orientation, size, spacing), fracture scale (e.g., bed-confined fractures, fracture corridors), lateral and vertical variations, need to be defined from limited, gener
Model of Fracture, Friction, and Wear Phenomena of Porous Iron
Directory of Open Access Journals (Sweden)
A. A. Shatsov
2011-01-01
Full Text Available Mechanical and tribotechnical features of powdered materials are strongly influenced by pore volume, fracture character, impurities, alloying, concentration inhomogeneity, friction conditions, and other factors. Pores also have influence on acceleration of diffusion processes and reduce undercooled austenite resistance. Annealed in hydrogen, ultra pure iron powder was used to study porous iron features. Toughness fracture and tribotechnical features had nonmonotonic dependence from porosity different from all known dependences got from technical iron powders. Researches brought out the fact that in process of porosity reduction by pressing and annealing cycles, the average dimension of porous is changed. According to the analysis of porous structure were created models of friction, wear, and fracture of pure porous iron.
Discrete kink dynamics in hydrogen-bonded chains: The two-component model
DEFF Research Database (Denmark)
Karpan, V.M.; Zolotaryuk, Yaroslav; Christiansen, Peter Leth
2004-01-01
We study discrete topological solitary waves (kinks and antikinks) in two nonlinear diatomic chain models that describe the collective dynamics of proton transfers in one-dimensional hydrogen-bonded networks. The essential ingredients of the models are (i) a realistic (anharmonic) ion-proton inte......We study discrete topological solitary waves (kinks and antikinks) in two nonlinear diatomic chain models that describe the collective dynamics of proton transfers in one-dimensional hydrogen-bonded networks. The essential ingredients of the models are (i) a realistic (anharmonic) ion...... principal differences, like a significant difference in the stability switchings behavior for the kinks and the antikinks. Water-filled carbon nanotubes are briefly discussed as possible realistic systems, where topological discrete (anti)kink states might exist....