A discrete-element model for viscoelastic deformation and fracture of glacial ice

Science.gov (United States)

Riikilä, T. I.; Tallinen, T.; Åström, J.; Timonen, J.

2015-10-01

A discrete-element model was developed to study the behavior of viscoelastic materials that are allowed to fracture. Applicable to many materials, the main objective of this analysis was to develop a model specifically for ice dynamics. A realistic model of glacial ice must include elasticity, brittle fracture and slow viscous deformations. Here the model is described in detail and tested with several benchmark simulations. The model was used to simulate various ice-specific applications with resulting flow rates that were compatible with Glen's law, and produced under fragmentation fragment-size distributions that agreed with the known analytical and experimental results.

A Discrete Fracture Network Model with Stress-Driven Nucleation and Growth

Science.gov (United States)

Lavoine, E.; Darcel, C.; Munier, R.; Davy, P.

2017-12-01

The realism of Discrete Fracture Network (DFN) models, beyond the bulk statistical properties, relies on the spatial organization of fractures, which is not issued by purely stochastic DFN models. The realism can be improved by injecting prior information in DFN from a better knowledge of the geological fracturing processes. We first develop a model using simple kinematic rules for mimicking the growth of fractures from nucleation to arrest, in order to evaluate the consequences of the DFN structure on the network connectivity and flow properties. The model generates fracture networks with power-law scaling distributions and a percentage of T-intersections that are consistent with field observations. Nevertheless, a larger complexity relying on the spatial variability of natural fractures positions cannot be explained by the random nucleation process. We propose to introduce a stress-driven nucleation in the timewise process of this kinematic model to study the correlations between nucleation, growth and existing fracture patterns. The method uses the stress field generated by existing fractures and remote stress as an input for a Monte-Carlo sampling of nuclei centers at each time step. Networks so generated are found to have correlations over a large range of scales, with a correlation dimension that varies with time and with the function that relates the nucleation probability to stress. A sensibility analysis of input parameters has been performed in 3D to quantify the influence of fractures and remote stress field orientations.

An Efficient Upscaling Procedure Based on Stokes-Brinkman Model and Discrete Fracture Network Method for Naturally Fractured Carbonate Karst Reservoirs

KAUST Repository

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.

Simulated evolution of fractures and fracture networks subject to thermal cooling: A coupled discrete element and heat conduction model

Energy Technology Data Exchange (ETDEWEB)

Huang, Hai; Plummer, Mitchell; Podgorney, Robert

2013-02-01

Advancement of EGS requires improved prediction of fracture development and growth during reservoir stimulation and long-term operation. This, in turn, requires better understanding of the dynamics of the strongly coupled thermo-hydro-mechanical (THM) processes within fractured rocks. We have developed a physically based rock deformation and fracture propagation simulator by using a quasi-static discrete element model (DEM) to model mechanical rock deformation and fracture propagation induced by thermal stress and fluid pressure changes. We also developed a network model to simulate fluid flow and heat transport in both fractures and porous rock. In this paper, we describe results of simulations in which the DEM model and network flow & heat transport model are coupled together to provide realistic simulation of the changes of apertures and permeability of fractures and fracture networks induced by thermal cooling and fluid pressure changes within fractures. Various processes, such as Stokes flow in low velocity pores, convection-dominated heat transport in fractures, heat exchange between fluid-filled fractures and solid rock, heat conduction through low-permeability matrices and associated mechanical deformations are all incorporated into the coupled model. The effects of confining stresses, developing thermal stress and injection pressure on the permeability evolution of fracture and fracture networks are systematically investigated. Results are summarized in terms of implications for the development and evolution of fracture distribution during hydrofracturing and thermal stimulation for EGS.

Study on the methodology for hydrogeological site descriptive modelling by discrete fracture networks

International Nuclear Information System (INIS)

Tanaka, Tatsuya; Ando, Kenichi; Hashimoto, Shuuji; Saegusa, Hiromitsu; Takeuchi, Shinji; Amano, Kenji

2007-01-01

This study aims to establish comprehensive techniques for site descriptive modelling considering the hydraulic heterogeneity due to the Water Conducting Features in fractured rocks. The WCFs was defined by the interpretation and integration of geological and hydrogeological data obtained from the deep borehole investigation campaign in the Mizunami URL project and Regional Hydrogeological Study. As a result of surface based investigation phase, the block-scale hydrogeological descriptive model was generated using hydraulic discrete fracture networks. Uncertainties and remaining issues associated with the assumption in interpreting the data and its modelling were addressed in a systematic way. (author)

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

Discrete Feature Model (DFM) User Documentation

International Nuclear Information System (INIS)

Geier, Joel

2008-06-01

This manual describes the Discrete-Feature Model (DFM) software package for modelling groundwater flow and solute transport in networks of discrete features. A discrete-feature conceptual model represents fractures and other water-conducting features around a repository as discrete conductors surrounded by a rock matrix which is usually treated as impermeable. This approximation may be valid for crystalline rocks such as granite or basalt, which have very low permeability if macroscopic fractures are excluded. A discrete feature is any entity that can conduct water and permit solute transport through bedrock, and can be reasonably represented as a piecewise-planar conductor. Examples of such entities may include individual natural fractures (joints or faults), fracture zones, and disturbed-zone features around tunnels (e.g. blasting-induced fractures or stress-concentration induced 'onion skin' fractures around underground openings). In a more abstract sense, the effectively discontinuous nature of pathways through fractured crystalline bedrock may be idealized as discrete, equivalent transmissive features that reproduce large-scale observations, even if the details of connective paths (and unconnected domains) are not precisely known. A discrete-feature model explicitly represents the fundamentally discontinuous and irregularly connected nature of systems of such systems, by constraining flow and transport to occur only within such features and their intersections. Pathways for flow and solute transport in this conceptualization are a consequence not just of the boundary conditions and hydrologic properties (as with continuum models), but also the irregularity of connections between conductive/transmissive features. The DFM software package described here is an extensible code for investigating problems of flow and transport in geological (natural or human-altered) systems that can be characterized effectively in terms of discrete features. With this software, the

Optimization of flow modeling in fractured media with discrete fracture network via percolation theory

Science.gov (United States)

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

Geological discrete-fracture network model (version 1) for the Olkiluoto site, Finland

International Nuclear Information System (INIS)

Fox, A.; Buoro, A.; Dahlbo, K.; Wiren, L.

2009-10-01

This report describes the methods, analyses, and conclusions of the modelling team in the production of a discrete-fracture network (DFN) model for the Olkiluoto Site in Finland. The geological DFN is a statistical model for stochastically simulating rock fractures and minor faults at a scale ranging from approximately 0.05 m to approximately 500 m; an upper scale limit is not expressly defined, but the DFN model explicitly excludes structures at deformation-zone scales (∼ 500 m) and larger. The DFN model is presented as a series of tables summarizing probability distributions for several parameters necessary for fracture modelling: fracture orientation, fracture size, fracture intensity, and associated spatial constraints. The geological DFN is built from data collected during site characterization (SC) activities at Olkiluoto, which is currently planned to function as a final deep geological repository for spent fuel and nuclear waste from the Finnish nuclear power program. Data used in the DFN analyses include fracture maps from surface outcrops and trenches (as of July 2007), geological and structural data from cored boreholes (as of July 2007), and fracture information collected during the construction of the main tunnels and shafts at the ONKALO laboratory (January 2008). The modelling results suggest that the rock volume at Olkiluoto surrounding the ONKALO tunnel can be separated into three distinct volumes (fracture domains): an upper block, an intermediate block, and a lower block. The three fracture domains are bounded horizontally and vertically by large deformation zones. Fracture properties, such as fracture orientation and relative orientation set intensity, vary between fracture domains. The rock volume at Olkiluoto is dominated by three distinct fracture sets: subhorizontally-dipping fractures striking north-northeast and dipping to the east, a subvertically-dipping fracture set striking roughly north-south, and a subverticallydipping fracture set

Geological discrete fracture network model for the Laxemar site. Site Descriptive Modelling. SDM-Site Laxemar

Energy Technology Data Exchange (ETDEWEB)

La Pointe, Paul; Fox, Aaron (Golder Associates Inc (United States)); Hermanson, Jan; Oehman, Johan (Golder Associates AB, Stockholm (Sweden))

2008-12-15

The Swedish Nuclear Fuel and Waste Management Company (SKB) is performing site characterization at two different locations, Forsmark and Laxemar, in order to locate a site for a final geologic repository for spent nuclear fuel. The program is built upon the development of Site Descriptive Models (SDMs) at specific timed data freezes. Each SDM is formed from discipline-specific reports from across the scientific spectrum. This report describes the methods, analyses, and conclusions of the modelling team in the production of the SDM-Site Laxemar geological discrete-fracture network (DFN) model. The DFN builds upon the work of other geological models, including the deformation zone and rock domain models. The geological DFN is a statistical model for stochastically simulating rock fractures and minor deformation zones at a scale of less than 1,000 m (the lower cut-off of the DZ models). The geological DFN is valid within six distinct fracture domains inside the Laxemar local model subarea: FSM{sub C}, FSM{sub E}W007, FSM{sub N}, FSM{sub N}E005, FSM{sub S}, and FSM{sub W}. The models are built using data from detailed surface outcrop maps, geophysical lineament maps, and the cored borehole record at Laxemar. The conceptual model for the SDM-Site Laxemar geological DFN model revolves around the identification of fracture domains based on relative fracture set intensities, orientation clustering, and the regional tectonic framework (including deformation zones). A single coupled fracture size/fracture intensity concept (the Base Model) based on a Pareto (power-law) distribution for fracture sizes was chosen as the recommended parameterisation. A slew of alternative size-intensity models were also carried through the fracture analyses and into the uncertainty and model verification analyses. Uncertainty is modelled by analysing the effects on fracture intensity (P32) that alternative model cases can have. Uncertainty is parameterised as a ratio between the P32 of the

Geological discrete fracture network model for the Laxemar site. Site Descriptive Modelling. SDM-Site Laxemar

International Nuclear Information System (INIS)

La Pointe, Paul; Fox, Aaron; Hermanson, Jan; Oehman, Johan

2008-10-01

The Swedish Nuclear Fuel and Waste Management Company (SKB) is performing site characterization at two different locations, Forsmark and Laxemar, in order to locate a site for a final geologic repository for spent nuclear fuel. The program is built upon the development of Site Descriptive Models (SDMs) at specific timed data freezes. Each SDM is formed from discipline-specific reports from across the scientific spectrum. This report describes the methods, analyses, and conclusions of the modelling team in the production of the SDM-Site Laxemar geological discrete-fracture network (DFN) model. The DFN builds upon the work of other geological models, including the deformation zone and rock domain models. The geological DFN is a statistical model for stochastically simulating rock fractures and minor deformation zones at a scale of less than 1,000 m (the lower cut-off of the DZ models). The geological DFN is valid within six distinct fracture domains inside the Laxemar local model subarea: FSM C , FSM E W007, FSM N , FSM N E005, FSM S , and FSM W . The models are built using data from detailed surface outcrop maps, geophysical lineament maps, and the cored borehole record at Laxemar. The conceptual model for the SDM-Site Laxemar geological DFN model revolves around the identification of fracture domains based on relative fracture set intensities, orientation clustering, and the regional tectonic framework (including deformation zones). A single coupled fracture size/fracture intensity concept (the Base Model) based on a Pareto (power-law) distribution for fracture sizes was chosen as the recommended parameterisation. A slew of alternative size-intensity models were also carried through the fracture analyses and into the uncertainty and model verification analyses. Uncertainty is modelled by analysing the effects on fracture intensity (P32) that alternative model cases can have. Uncertainty is parameterised as a ratio between the P32 of the alternative model and the P

Fractured reservoir discrete feature network technologies. Final report, March 7, 1996 to September 30, 1998

Energy Technology Data Exchange (ETDEWEB)

Dershowitz, William S.; Einstein, Herbert H.; LaPoint, Paul R.; Eiben, Thorsten; Wadleigh, Eugene; Ivanova, Violeta

1998-12-01

This report summarizes research conducted for the Fractured Reservoir Discrete Feature Network Technologies Project. The five areas studied are development of hierarchical fracture models; fractured reservoir compartmentalization, block size, and tributary volume analysis; development and demonstration of fractured reservoir discrete feature data analysis tools; development of tools for data integration and reservoir simulation through application of discrete feature network technologies for tertiary oil production; quantitative evaluation of the economic value of this analysis approach.

Visualization and Hierarchical Analysis of Flow in Discrete Fracture Network Models

Science.gov (United States)

Aldrich, G. A.; Gable, C. W.; Painter, S. L.; Makedonska, N.; Hamann, B.; Woodring, J.

2013-12-01

Flow and transport in low permeability fractured rock is primary in interconnected fracture networks. Prediction and characterization of flow and transport in fractured rock has important implications in underground repositories for hazardous materials (eg. nuclear and chemical waste), contaminant migration and remediation, groundwater resource management, and hydrocarbon extraction. We have developed methods to explicitly model flow in discrete fracture networks and track flow paths using passive particle tracking algorithms. Visualization and analysis of particle trajectory through the fracture network is important to understanding fracture connectivity, flow patterns, potential contaminant pathways and fast paths through the network. However, occlusion due to the large number of highly tessellated and intersecting fracture polygons preclude the effective use of traditional visualization methods. We would also like quantitative analysis methods to characterize the trajectory of a large number of particle paths. We have solved these problems by defining a hierarchal flow network representing the topology of particle flow through the fracture network. This approach allows us to analyses the flow and the dynamics of the system as a whole. We are able to easily query the flow network, and use paint-and-link style framework to filter the fracture geometry and particle traces based on the flow analytics. This allows us to greatly reduce occlusion while emphasizing salient features such as the principal transport pathways. Examples are shown that demonstrate the methodology and highlight how use of this new method allows quantitative analysis and characterization of flow and transport in a number of representative fracture networks.

Discrete-fracture-model of multi–scale time-splitting two–phase flow including nanoparticles transport in fractured porous media

KAUST Repository

El-Amin, Mohamed

2017-11-23

In this article, we consider a two-phase immiscible incompressible flow including nanoparticles transport in fractured heterogeneous porous media. The system of the governing equations consists of water saturation, Darcy’s law, nanoparticles concentration in water, deposited nanoparticles concentration on the pore-wall, and entrapped nanoparticles concentration in the pore-throat, as well as, porosity and permeability variation due to the nanoparticles deposition/entrapment on/in the pores. The discrete-fracture model (DFM) is used to describe the flow and transport in fractured porous media. Moreover, multiscale time-splitting strategy has been employed to manage different time-step sizes for different physics, such as saturation, concentration, etc. Numerical examples are provided to demonstrate the efficiency of the proposed multi-scale time splitting approach.

Discrete-fracture-model of multi–scale time-splitting two–phase flow including nanoparticles transport in fractured porous media

KAUST Repository

El-Amin, Mohamed; Kou, Jisheng; Sun, Shuyu

2017-01-01

In this article, we consider a two-phase immiscible incompressible flow including nanoparticles transport in fractured heterogeneous porous media. The system of the governing equations consists of water saturation, Darcy’s law, nanoparticles concentration in water, deposited nanoparticles concentration on the pore-wall, and entrapped nanoparticles concentration in the pore-throat, as well as, porosity and permeability variation due to the nanoparticles deposition/entrapment on/in the pores. The discrete-fracture model (DFM) is used to describe the flow and transport in fractured porous media. Moreover, multiscale time-splitting strategy has been employed to manage different time-step sizes for different physics, such as saturation, concentration, etc. Numerical examples are provided to demonstrate the efficiency of the proposed multi-scale time splitting approach.

Adaptive Finite Element-Discrete Element Analysis for Microseismic Modelling of Hydraulic Fracture Propagation of Perforation in Horizontal Well considering Pre-Existing Fractures

Directory of Open Access Journals (Sweden)

Yongliang Wang

2018-01-01

Full Text Available Hydrofracturing technology of perforated horizontal well has been widely used to stimulate the tight hydrocarbon reservoirs for gas production. To predict the hydraulic fracture propagation, the microseismicity can be used to infer hydraulic fractures state; by the effective numerical methods, microseismic events can be addressed from changes of the computed stresses. In numerical models, due to the challenges in accurately representing the complex structure of naturally fractured reservoir, the interaction between hydraulic and pre-existing fractures has not yet been considered and handled satisfactorily. To overcome these challenges, the adaptive finite element-discrete element method is used to refine mesh, effectively identify the fractures propagation, and investigate microseismic modelling. Numerical models are composed of hydraulic fractures, pre-existing fractures, and microscale pores, and the seepage analysis based on the Darcy’s law is used to determine fluid flow; then moment tensors in microseismicity are computed based on the computed stresses. Unfractured and naturally fractured models are compared to assess the influences of pre-existing fractures on hydrofracturing. The damaged and contact slip events were detected by the magnitudes, B-values, Hudson source type plots, and focal spheres.

Hydraulic Fracture Growth in a Layered Formation based on Fracturing Experiments and Discrete Element Modeling

Science.gov (United States)

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.

Sensitivity analysis of a coupled hydro-mechanical paleo-climate model of density-dependent groundwater flow in discretely fractured crystalline rock

International Nuclear Information System (INIS)

Normani, S.D.; Sykes, J.F.

2011-01-01

A high resolution three-dimensional sub-regional scale (104 km 2 ) density-dependent, discretely fractured groundwater flow model with hydro-mechanical coupling and pseudo-permafrost was developed from a larger 5734 km 2 regional-scale groundwater flow model of a Canadian Shield setting. The objective of the work is to determine the sensitivity of modelled groundwater system evolution to the hydro-mechanical parameters. The discrete fracture dual continuum numerical model FRAC3DVS-OPG was used for all simulations. A discrete fracture network model delineated from surface features was superimposed onto an approximate 790 000 element domain mesh with approximately 850 000 nodes. Orthogonal fracture faces (between adjacent finite element grid blocks) were used to best represent the irregular discrete fracture zone network. Interconnectivity of the permeable fracture zones is an important pathway for the possible migration and subsequent reduction in groundwater and contaminant residence times. The crystalline rock matrix between these structural discontinuities was assigned mechanical and flow properties characteristic of those reported for the Canadian Shield. The variation of total dissolved solids with depth was assigned using literature data for the Canadian Shield. Performance measures for the sensitivity analysis include equivalent freshwater heads, environmental heads, linear velocities, and depth of penetration by conservative non-decaying tracers released at the surface. A 121 000 year North American continental scale paleo-climate simulation was applied to the domain with ice-sheet histories estimated by the University of Toronto Glacial Systems Model (UofT GSM). Hydro-mechanical coupling between the rock matrix and the pore fluid, due to the ice sheet normal stress, was included in the simulations. The flow model included the influence of vertical strain and assumed that areal loads were homogeneous. Permafrost depth was applied as a permeability reduction

Numerical simulation of the heat extraction in EGS with thermal-hydraulic-mechanical coupling method based on discrete fractures model

International Nuclear Information System (INIS)

Sun, Zhi-xue; Zhang, Xu; Xu, Yi; Yao, Jun; Wang, Hao-xuan; Lv, Shuhuan; Sun, Zhi-lei; Huang, Yong; Cai, Ming-yu; Huang, Xiaoxue

2017-01-01

The Enhanced Geothermal System (EGS) creates an artificial geothermal reservoir by hydraulic fracturing which allows heat transmission through the fractures by the circulating fluids as they extract heat from Hot Dry Rock (HDR). The technique involves complex thermal–hydraulic–mechanical (THM) coupling process. A numerical approach is presented in this paper to simulate and analyze the heat extraction process in EGS. The reservoir is regarded as fractured porous media consisting of rock matrix blocks and discrete fracture networks. Based on thermal non-equilibrium theory, the mathematical model of THM coupling process in fractured rock mass is used. The proposed model is validated by comparing it with several analytical solutions. An EGS case from Cooper Basin, Australia is simulated with 2D stochastically generated fracture model to study the characteristics of fluid flow, heat transfer and mechanical response in geothermal reservoir. The main parameters controlling the outlet temperature of EGS are also studied by sensitivity analysis. The results shows the significance of taking into account the THM coupling effects when investigating the efficiency and performance of EGS. - Highlights: • EGS reservoir comprising discrete fracture networks and matrix rock is modeled. • A THM coupling model is proposed for simulating the heat extraction in EGS. • The numerical model is validated by comparing with several analytical solutions. • A case study is presented for understanding the main characteristics of EGS. • The THM coupling effects are shown to be significant factors to EGS's running performance.

Numerical simulation on ferrofluid flow in fractured porous media based on discrete-fracture model

Science.gov (United States)

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

Numerical Experiments on Advective Transport in Large Three-Dimensional Discrete Fracture Networks

Science.gov (United States)

Makedonska, N.; Painter, S. L.; Karra, S.; Gable, C. W.

2013-12-01

Modeling of flow and solute transport in discrete fracture networks is an important approach for understanding the migration of contaminants in impermeable hard rocks such as granite, where fractures provide dominant flow and transport pathways. The discrete fracture network (DFN) model attempts to mimic discrete pathways for fluid flow through a fractured low-permeable rock mass, and may be combined with particle tracking simulations to address solute transport. However, experience has shown that it is challenging to obtain accurate transport results in three-dimensional DFNs because of the high computational burden and difficulty in constructing a high-quality unstructured computational mesh on simulated fractures. An integrated DFN meshing [1], flow, and particle tracking [2] simulation capability that enables accurate flow and particle tracking simulation on large DFNs has recently been developed. The new capability has been used in numerical experiments on advective transport in large DFNs with tens of thousands of fractures and millions of computational cells. The modeling procedure starts from the fracture network generation using a stochastic model derived from site data. A high-quality computational mesh is then generated [1]. Flow is then solved using the highly parallel PFLOTRAN [3] code. PFLOTRAN uses the finite volume approach, which is locally mass conserving and thus eliminates mass balance problems during particle tracking. The flow solver provides the scalar fluxes on each control volume face. From the obtained fluxes the Darcy velocity is reconstructed for each node in the network [4]. Velocities can then be continuously interpolated to any point in the domain of interest, thus enabling random walk particle tracking. In order to describe the flow field on fractures intersections, the control volume cells on intersections are split into four planar polygons, where each polygon corresponds to a piece of a fracture near the intersection line. Thus

Geological discrete fracture network model for the Olkiluoto site, Eurajoki, Finland. Version 2.0

International Nuclear Information System (INIS)

Fox, A.; Forchhammer, K.; Pettersson, A.; La Pointe, P.; Lim, D-H.

2012-06-01

This report describes the methods, analyses, and conclusions of the modeling team in the production of the 2010 revision to the geological discrete fracture network (DFN) model for the Olkiluoto Site in Finland. The geological DFN is a statistical model for stochastically simulating rock fractures and minor faults at a scale ranging from approximately 0.05 m to approximately 565m; deformation zones are expressly excluded from the DFN model. The DFN model is presented as a series of tables summarizing probability distributions for several parameters necessary for fracture modeling: fracture orientation, fracture size, fracture intensity, and associated spatial constraints. The geological DFN is built from data collected during site characterization (SC) activities at Olkiluoto, which is selected to function as a final deep geological repository for spent fuel and nuclear waste from the Finnish nuclear power program. Data used in the DFN analyses include fracture maps from surface outcrops and trenches, geological and structural data from cored drillholes, and fracture information collected during the construction of the main tunnels and shafts at the ONKALO laboratory. Unlike the initial geological DFN, which was focused on the vicinity of the ONKALO tunnel, the 2010 revisions present a model parameterization for the entire island. Fracture domains are based on the tectonic subdivisions at the site (northern, central, and southern tectonic units) presented in the Geological Site Model (GSM), and are further subdivided along the intersection of major brittle-ductile zones. The rock volume at Olkiluoto is dominated by three distinct fracture sets: subhorizontally-dipping fractures striking north-northeast and dipping to the east that is subparallel to the mean bedrock foliation direction, a subvertically-dipping fracture set striking roughly north-south, and a subvertically-dipping fracture set striking approximately east-west. The subhorizontally-dipping fractures

Geological discrete fracture network model for the Olkiluoto site, Eurajoki, Finland. Version 2.0

Energy Technology Data Exchange (ETDEWEB)

Fox, A.; Forchhammer, K.; Pettersson, A. [Golder Associates AB, Stockholm (Sweden); La Pointe, P.; Lim, D-H. [Golder Associates Inc. (Finland)

2012-06-15

This report describes the methods, analyses, and conclusions of the modeling team in the production of the 2010 revision to the geological discrete fracture network (DFN) model for the Olkiluoto Site in Finland. The geological DFN is a statistical model for stochastically simulating rock fractures and minor faults at a scale ranging from approximately 0.05 m to approximately 565m; deformation zones are expressly excluded from the DFN model. The DFN model is presented as a series of tables summarizing probability distributions for several parameters necessary for fracture modeling: fracture orientation, fracture size, fracture intensity, and associated spatial constraints. The geological DFN is built from data collected during site characterization (SC) activities at Olkiluoto, which is selected to function as a final deep geological repository for spent fuel and nuclear waste from the Finnish nuclear power program. Data used in the DFN analyses include fracture maps from surface outcrops and trenches, geological and structural data from cored drillholes, and fracture information collected during the construction of the main tunnels and shafts at the ONKALO laboratory. Unlike the initial geological DFN, which was focused on the vicinity of the ONKALO tunnel, the 2010 revisions present a model parameterization for the entire island. Fracture domains are based on the tectonic subdivisions at the site (northern, central, and southern tectonic units) presented in the Geological Site Model (GSM), and are further subdivided along the intersection of major brittle-ductile zones. The rock volume at Olkiluoto is dominated by three distinct fracture sets: subhorizontally-dipping fractures striking north-northeast and dipping to the east that is subparallel to the mean bedrock foliation direction, a subvertically-dipping fracture set striking roughly north-south, and a subvertically-dipping fracture set striking approximately east-west. The subhorizontally-dipping fractures

An Embedded 3D Fracture Modeling Approach for Simulating Fracture-Dominated Fluid Flow and Heat Transfer in Geothermal Reservoirs

Energy Technology Data Exchange (ETDEWEB)

Johnston, Henry [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Wang, Cong [Colorado School of Mines; Winterfeld, Philip [Colorado School of Mines; Wu, Yu-Shu [Colorado School of Mines

2018-02-14

An efficient modeling approach is described for incorporating arbitrary 3D, discrete fractures, such as hydraulic fractures or faults, into modeling fracture-dominated fluid flow and heat transfer in fractured geothermal reservoirs. This technique allows 3D discrete fractures to be discretized independently from surrounding rock volume and inserted explicitly into a primary fracture/matrix grid, generated without including 3D discrete fractures in prior. An effective computational algorithm is developed to discretize these 3D discrete fractures and construct local connections between 3D fractures and fracture/matrix grid blocks of representing the surrounding rock volume. The constructed gridding information on 3D fractures is then added to the primary grid. This embedded fracture modeling approach can be directly implemented into a developed geothermal reservoir simulator via the integral finite difference (IFD) method or with TOUGH2 technology This embedded fracture modeling approach is very promising and computationally efficient to handle realistic 3D discrete fractures with complicated geometries, connections, and spatial distributions. Compared with other fracture modeling approaches, it avoids cumbersome 3D unstructured, local refining procedures, and increases computational efficiency by simplifying Jacobian matrix size and sparsity, while keeps sufficient accuracy. Several numeral simulations are present to demonstrate the utility and robustness of the proposed technique. Our numerical experiments show that this approach captures all the key patterns about fluid flow and heat transfer dominated by fractures in these cases. Thus, this approach is readily available to simulation of fractured geothermal reservoirs with both artificial and natural fractures.

Discrete Fracture Network Models for Risk Assessment of Carbon Sequestration in Coal

Energy Technology Data Exchange (ETDEWEB)

Jack Pashin; Guohai Jin; Chunmiao Zheng; Song Chen; Marcella McIntyre

2008-07-01

A software package called DFNModeler has been developed to assess the potential risks associated with carbon sequestration in coal. Natural fractures provide the principal conduits for fluid flow in coal-bearing strata, and these fractures present the most tangible risks for the leakage of injected carbon dioxide. The objectives of this study were to develop discrete fracture network (DFN) modeling tools for risk assessment and to use these tools to assess risks in the Black Warrior Basin of Alabama, where coal-bearing strata have high potential for carbon sequestration and enhanced coalbed methane recovery. DFNModeler provides a user-friendly interface for the construction, visualization, and analysis of DFN models. DFNModeler employs an OpenGL graphics engine that enables real-time manipulation of DFN models. Analytical capabilities in DFNModeler include display of structural and hydrologic parameters, compartmentalization analysis, and fluid pathways analysis. DFN models can be exported to third-party software packages for flow modeling. DFN models were constructed to simulate fracturing in coal-bearing strata of the upper Pottsville Formation in the Black Warrior Basin. Outcrops and wireline cores were used to characterize fracture systems, which include joint systems, cleat systems, and fault-related shear fractures. DFN models were constructed to simulate jointing, cleating, faulting, and hydraulic fracturing. Analysis of DFN models indicates that strata-bound jointing compartmentalizes the Pottsville hydrologic system and helps protect shallow aquifers from injection operations at reservoir depth. Analysis of fault zones, however, suggests that faulting can facilitate cross-formational flow. For this reason, faults should be avoided when siting injection wells. DFN-based flow models constructed in TOUGH2 indicate that fracture aperture and connectivity are critical variables affecting the leakage of injected CO{sub 2} from coal. Highly transmissive joints

Fracture Failure of Reinforced Concrete Slabs Subjected to Blast Loading Using the Combined Finite-Discrete Element Method

Directory of Open Access Journals (Sweden)

Z. M. Jaini

Full Text Available Abstract Numerical modeling of fracture failure is challenging due to various issues in the constitutive law and the transition of continuum to discrete bodies. Therefore, this study presents the application of the combined finite-discrete element method to investigate the fracture failure of reinforced concrete slabs subjected to blast loading. In numerical modeling, the interaction of non-uniform blast loading on the concrete slab was modeled using the incorporation of the finite element method with a crack rotating approach and the discrete element method to model crack, fracture onset and its post-failures. A time varying pressure-time history based on the mapping method was adopted to define blast loading. The Mohr-Coulomb with Rankine cut-off and von-Mises criteria were applied for concrete and steel reinforcement respectively. The results of scabbing, spalling and fracture show a reliable prediction of damage and fracture.

Discrete fracture network modelling of a KBS-3H repository at Olkiluoto

Energy Technology Data Exchange (ETDEWEB)

Lanyon, G.W. (Fracture Systems Ltd, St Ives (United Kingdom)); Marschall, P. (Nagra, Wettingen (Switzerland))

2008-06-15

This report presents Discrete Fracture Network (DFN) models of groundwater flow around a KBS-3H repository situated at Olkiluoto. The study was performed in support of the Safety Case for the KBS-3H Concept, being jointly studied by SKB and Posiva. As part of the preliminary assessment of long term safety of a KBS-3H repository, a Process Report and an Evolution Report (evolution of the disposal system from the emplacement of the first canister to the long term) are being produced. In the course of the task definition the project team identified the need for complementary modelling studies aimed at increasing insight into the hydrodynamic evolution of the disposal system after waste emplacement. In particular, the following issues were identified as requiring input from hydrodynamic models: Probability of high inflow points which may cause buffer erosion. Time transients of inflows after construction of deposition drifts. Interference between deposition drifts and transport tunnels. The DFN models represent the fault and fracture system in the planned repository volume at Olkiluoto. In particular, they represent the hydro geologically significant features. The types of hydrogeological features included in the models are: Major Fracture Zones (MFZs). Local Fracture Zones (LFZs) and associated water conducting features (LFZ-WCFs). Water Conducting Features in the background rock (BR-WCFs). These feature types are derived from the current geological and hydrogeological interpretations developed by Posiva. Several model variants were developed during the study and these variants were used for geometric simulations of the WCF network around the deposition drifts. A simple layout adaptation scheme has been applied to the network models to derive statistics for performance measures relating to the deposition drifts, compartments, plugs and super-containers. A single fracture transient flow model was developed to provide insight to transient flow behaviour around

Discrete fracture network modelling of a KBS-3H repository at Olkiluoto

International Nuclear Information System (INIS)

Lanyon, G.W.; Marschall, P.

2008-06-01

This report presents Discrete Fracture Network (DFN) models of groundwater flow around a KBS-3H repository situated at Olkiluoto. The study was performed in support of the Safety Case for the KBS-3H Concept, being jointly studied by SKB and Posiva. As part of the preliminary assessment of long term safety of a KBS-3H repository, a Process Report and an Evolution Report (evolution of the disposal system from the emplacement of the first canister to the long term) are being produced. In the course of the task definition the project team identified the need for complementary modelling studies aimed at increasing insight into the hydrodynamic evolution of the disposal system after waste emplacement. In particular, the following issues were identified as requiring input from hydrodynamic models: Probability of high inflow points which may cause buffer erosion. Time transients of inflows after construction of deposition drifts. Interference between deposition drifts and transport tunnels. The DFN models represent the fault and fracture system in the planned repository volume at Olkiluoto. In particular, they represent the hydro geologically significant features. The types of hydrogeological features included in the models are: Major Fracture Zones (MFZs). Local Fracture Zones (LFZs) and associated water conducting features (LFZ-WCFs). Water Conducting Features in the background rock (BR-WCFs). These feature types are derived from the current geological and hydrogeological interpretations developed by Posiva. Several model variants were developed during the study and these variants were used for geometric simulations of the WCF network around the deposition drifts. A simple layout adaptation scheme has been applied to the network models to derive statistics for performance measures relating to the deposition drifts, compartments, plugs and super-containers. A single fracture transient flow model was developed to provide insight to transient flow behaviour around

Internal fracture heterogeneity in discrete fracture network modelling: Effect of correlation length and textures with connected and disconnected permeability field

Science.gov (United States)

Frampton, A.; Hyman, J.; Zou, L.

2017-12-01

Analysing flow and transport in sparsely fractured media is important for understanding how crystalline bedrock environments function as barriers to transport of contaminants, with important applications towards subsurface repositories for storage of spent nuclear fuel. Crystalline bedrocks are particularly favourable due to their geological stability, low advective flow and strong hydrogeochemical retention properties, which can delay transport of radionuclides, allowing decay to limit release to the biosphere. There are however many challenges involved in quantifying and modelling subsurface flow and transport in fractured media, largely due to geological complexity and heterogeneity, where the interplay between advective and dispersive flow strongly impacts both inert and reactive transport. A key to modelling transport in a Lagrangian framework involves quantifying pathway travel times and the hydrodynamic control of retention, and both these quantities strongly depend on heterogeneity of the fracture network at different scales. In this contribution, we present recent analysis of flow and transport considering fracture networks with single-fracture heterogeneity described by different multivariate normal distributions. A coherent triad of fields with identical correlation length and variance are created but which greatly differ in structure, corresponding to textures with well-connected low, medium and high permeability structures. Through numerical modelling of multiple scales in a stochastic setting we quantify the relative impact of texture type and correlation length against network topological measures, and identify key thresholds for cases where flow dispersion is controlled by single-fracture heterogeneity versus network-scale heterogeneity. This is achieved by using a recently developed novel numerical discrete fracture network model. Furthermore, we highlight enhanced flow channelling for cases where correlation structure continues across

Hydraulic Parameter Generation Technique Using a Discrete Fracture Network with Bedrock Heterogeneity in Korea

Directory of Open Access Journals (Sweden)

Jae-Yeol Cheong

2017-12-01

Full Text Available In instances of damage to engineered barriers containing nuclear waste material, surrounding bedrock is a natural barrier that retards radionuclide movement by way of adsorption and delay due to groundwater flow through highly tortuous fractured rock pathways. At the Gyeongju nuclear waste disposal site, groundwater mainly flows through granitic and sedimentary rock fractures. Therefore, to understand the nuclide migration path, it is necessary to understand discrete fracture networks based on heterogeneous fracture orientations, densities, and size characteristics. In this study, detailed heterogeneous fracture distribution, including the density and orientation of the fractures, was considered for a region that has undergone long periods of change from various geological activities at and around the Gyeongju site. A site-scale discrete fracture network (DFN model was constructed taking into account: (i regional fracture heterogeneity constrained by a multiple linear regression analysis of fracture intensity on faults and electrical resistivity; and (ii the connectivity of conductive fractures having fracture hydraulic parameters, using transient flow simulation. Geometric and hydraulic heterogeneity of the DFN was upscaled into equivalent porous media for flow and transport simulation for a large-scale model.

Statistical methodology for discrete fracture model - including fracture size, orientation uncertainty together with intensity uncertainty and variability

Energy Technology Data Exchange (ETDEWEB)

Darcel, C. (Itasca Consultants SAS (France)); Davy, P.; Le Goc, R.; Dreuzy, J.R. de; Bour, O. (Geosciences Rennes, UMR 6118 CNRS, Univ. def Rennes, Rennes (France))

2009-11-15

the lineament scale (k{sub t} = 2) on the other, addresses the issue of the nature of the transition. We develop a new 'mechanistic' model that could help in modeling why and where this transition can occur. The transition between both regimes would occur for a fracture length of 1-10 m and even at a smaller scale for the few outcrops that follow the self-similar density model. A consequence for the disposal issue is that the model that is likely to apply in the 'blind' scale window between 10-100 m is the self-similar model as it is defined for large-scale lineaments. The self-similar model, as it is measured for some outcrops and most lineament maps, is definitely worth being investigated as a reference for scales above 1-10 m. In the rest of the report, we develop a methodology for incorporating uncertainty and variability into the DFN modeling. Fracturing properties arise from complex processes which produce an intrinsic variability; characterizing this variability as an admissible variation of model parameter or as the division of the site into subdomains with distinct DFN models is a critical point of the modeling effort. Moreover, the DFN model encompasses a part of uncertainty, due to data inherent uncertainties and sampling limits. Both effects must be quantified and incorporated into the DFN site model definition process. In that context, all available borehole data including recording of fracture intercept positions, pole orientation and relative uncertainties are used as the basis for the methodological development and further site model assessment. An elementary dataset contains a set of discrete fracture intercepts from which a parent orientation/density distribution can be computed. The elementary bricks of the site, from which these initial parent density distributions are computed, rely on the former Single Hole Interpretation division of the boreholes into sections whose local boundaries are expected to reflect - locally - geology

Discrete fracture 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...

Statistical methodology for discrete fracture model - including fracture size, orientation uncertainty together with intensity uncertainty and variability

International Nuclear Information System (INIS)

Darcel, C.; Davy, P.; Le Goc, R.; Dreuzy, J.R. de; Bour, O.

2009-11-01

the other, addresses the issue of the nature of the transition. We develop a new 'mechanistic' model that could help in modeling why and where this transition can occur. The transition between both regimes would occur for a fracture length of 1-10 m and even at a smaller scale for the few outcrops that follow the self-similar density model. A consequence for the disposal issue is that the model that is likely to apply in the 'blind' scale window between 10-100 m is the self-similar model as it is defined for large-scale lineaments. The self-similar model, as it is measured for some outcrops and most lineament maps, is definitely worth being investigated as a reference for scales above 1-10 m. In the rest of the report, we develop a methodology for incorporating uncertainty and variability into the DFN modeling. Fracturing properties arise from complex processes which produce an intrinsic variability; characterizing this variability as an admissible variation of model parameter or as the division of the site into subdomains with distinct DFN models is a critical point of the modeling effort. Moreover, the DFN model encompasses a part of uncertainty, due to data inherent uncertainties and sampling limits. Both effects must be quantified and incorporated into the DFN site model definition process. In that context, all available borehole data including recording of fracture intercept positions, pole orientation and relative uncertainties are used as the basis for the methodological development and further site model assessment. An elementary dataset contains a set of discrete fracture intercepts from which a parent orientation/density distribution can be computed. The elementary bricks of the site, from which these initial parent density distributions are computed, rely on the former Single Hole Interpretation division of the boreholes into sections whose local boundaries are expected to reflect - locally - geology and fracturing properties main characteristics. From that

Statistical geological discrete fracture network model. Forsmark modelling stage 2.2

Energy Technology Data Exchange (ETDEWEB)

Fox, Aaron; La Pointe, Paul [Golder Associates Inc (United States); Simeonov, Assen [Swedish Nuclear Fuel and Waste Management Co., Stockholm (Sweden); Hermanson, Jan; Oehman, Johan [Golder Associates AB, Stockholm (Sweden)

2007-11-15

The Swedish Nuclear Fuel and Waste Management Company (SKB) is performing site characterization at two different locations, Forsmark and Laxemar, in order to locate a site for a final geologic repository for spent nuclear fuel. The program is built upon the development of Site Descriptive Models (SDMs) at specific timed data freezes. Each SDM is formed from discipline-specific reports from across the scientific spectrum. This report describes the methods, analyses, and conclusions of the geological modeling team with respect to a geological and statistical model of fractures and minor deformation zones (henceforth referred to as the geological DFN), version 2.2, at the Forsmark site. The geological DFN builds upon the work of other geological modelers, including the deformation zone (DZ), rock domain (RD), and fracture domain (FD) models. The geological DFN is a statistical model for stochastically simulating rock fractures and minor deformation zones as a scale of less than 1,000 m (the lower cut-off of the DZ models). The geological DFN is valid within four specific fracture domains inside the local model region, and encompassing the candidate volume at Forsmark: FFM01, FFM02, FFM03, and FFM06. The models are build using data from detailed surface outcrop maps and the cored borehole record at Forsmark. The conceptual model for the Forsmark 2.2 geological revolves around the concept of orientation sets; for each fracture domain, other model parameters such as size and intensity are tied to the orientation sets. Two classes of orientation sets were described; Global sets, which are encountered everywhere in the model region, and Local sets, which represent highly localized stress environments. Orientation sets were described in terms of their general cardinal direction (NE, NW, etc). Two alternatives are presented for fracture size modeling: - the tectonic continuum approach (TCM, TCMF) described by coupled size-intensity scaling following power law distributions

Statistical geological discrete fracture network model. Forsmark modelling stage 2.2

International Nuclear Information System (INIS)

Fox, Aaron; La Pointe, Paul; Simeonov, Assen; Hermanson, Jan; Oehman, Johan

2007-11-01

The Swedish Nuclear Fuel and Waste Management Company (SKB) is performing site characterization at two different locations, Forsmark and Laxemar, in order to locate a site for a final geologic repository for spent nuclear fuel. The program is built upon the development of Site Descriptive Models (SDMs) at specific timed data freezes. Each SDM is formed from discipline-specific reports from across the scientific spectrum. This report describes the methods, analyses, and conclusions of the geological modeling team with respect to a geological and statistical model of fractures and minor deformation zones (henceforth referred to as the geological DFN), version 2.2, at the Forsmark site. The geological DFN builds upon the work of other geological modelers, including the deformation zone (DZ), rock domain (RD), and fracture domain (FD) models. The geological DFN is a statistical model for stochastically simulating rock fractures and minor deformation zones as a scale of less than 1,000 m (the lower cut-off of the DZ models). The geological DFN is valid within four specific fracture domains inside the local model region, and encompassing the candidate volume at Forsmark: FFM01, FFM02, FFM03, and FFM06. The models are build using data from detailed surface outcrop maps and the cored borehole record at Forsmark. The conceptual model for the Forsmark 2.2 geological revolves around the concept of orientation sets; for each fracture domain, other model parameters such as size and intensity are tied to the orientation sets. Two classes of orientation sets were described; Global sets, which are encountered everywhere in the model region, and Local sets, which represent highly localized stress environments. Orientation sets were described in terms of their general cardinal direction (NE, NW, etc). Two alternatives are presented for fracture size modeling: - the tectonic continuum approach (TCM, TCMF) described by coupled size-intensity scaling following power law distributions

Analysis for preliminary evaluation of discrete fracture flow and large-scale permeability in sedimentary rocks

International Nuclear Information System (INIS)

Kanehiro, B.Y.; Lai, C.H.; Stow, S.H.

1987-05-01

Conceptual models for sedimentary rock settings that could be used in future evaluation and suitability studies are being examined through the DOE Repository Technology Program. One area of concern for the hydrologic aspects of these models is discrete fracture flow analysis as related to the estimation of the size of the representative elementary volume, evaluation of the appropriateness of continuum assumptions and estimation of the large-scale permeabilities of sedimentary rocks. A basis for preliminary analysis of flow in fracture systems of the types that might be expected to occur in low permeability sedimentary rocks is presented. The approach used involves numerical modeling of discrete fracture flow for the configuration of a large-scale hydrologic field test directed at estimation of the size of the representative elementary volume and large-scale permeability. Analysis of fracture data on the basis of this configuration is expected to provide a preliminary indication of the scale at which continuum assumptions can be made

Coupled hydromechanical paleoclimate analyses of density-dependant groundwater flow in discretely fractured crystalline rock settings

Science.gov (United States)

Normani, S. D.; Sykes, J. F.; Jensen, M. R.

2009-04-01

A high resolution sub-regional scale (84 km2) density-dependent, fracture zone network groundwater flow model with hydromechanical coupling and pseudo-permafrost, was developed from a larger 5734 km2 regional scale groundwater flow model of a Canadian Shield setting in fractured crystalline rock. The objective of the work is to illustrate aspects of regional and sub-regional groundwater flow that are relevant to the long-term performance of a hypothetical nuclear fuel repository. The discrete fracture dual continuum numerical model FRAC3DVS-OPG was used for all simulations. A discrete fracture zone network model delineated from surface features was superimposed onto an 789887 element flow domain mesh. Orthogonal fracture faces (between adjacent finite element grid blocks) were used to best represent the irregular discrete fracture zone network. The crystalline rock between these structural discontinuities was assigned properties characteristic of those reported for the Canadian Shield at the Underground Research Laboratory at Pinawa, Manitoba. Interconnectivity of permeable fracture features is an important pathway for the possibly relatively rapid migration of average water particles and subsequent reduction in residence times. The multiple 121000 year North American continental scale paleoclimate simulations are provided by W.R. Peltier using the University of Toronto Glacial Systems Model (UofT GSM). Values of ice sheet normal stress, and proglacial lake depth from the UofT GSM are applied to the sub-regional model as surface boundary conditions, using a freshwater head equivalent to the normal stress imposed by the ice sheet at its base. Permafrost depth is applied as a permeability reduction to both three-dimensional grid blocks and fractures that lie within the time varying permafrost zone. Two different paleoclimate simulations are applied to the sub-regional model to investigate the effect on the depth of glacial meltwater migration into the subsurface. In

A new computer code for discrete fracture network modelling

Science.gov (United States)

Xu, Chaoshui; Dowd, Peter

2010-03-01

The authors describe a comprehensive software package for two- and three-dimensional stochastic rock fracture simulation using marked point processes. Fracture locations can be modelled by a Poisson, a non-homogeneous, a cluster or a Cox point process; fracture geometries and properties are modelled by their respective probability distributions. Virtual sampling tools such as plane, window and scanline sampling are included in the software together with a comprehensive set of statistical tools including histogram analysis, probability plots, rose diagrams and hemispherical projections. The paper describes in detail the theoretical basis of the implementation and provides a case study in rock fracture modelling to demonstrate the application of the software.

Electrical Conductivity Distributions in Discrete Fluid-Filled Fractures

Science.gov (United States)

James, S. C.; Ahmmed, B.; Knox, H. A.; Johnson, T.; Dunbar, J. A.

2017-12-01

It is commonly asserted that hydraulic fracturing enhances permeability by generating new fractures in the reservoir. Furthermore, it is assumed that in the fractured system predominant flow occurs in these newly formed and pre-existing fractures. Among the phenomenology that remains enigmatic are fluid distributions inside fractures. Therefore, determining fluid distribution and their associated temporal and spatial evolution in fractures is critical for safe and efficient hydraulic fracturing. Previous studies have used both forward modeling and inversion of electrical data to show that a geologic system consisting of fluid filled fractures has a conductivity distribution, where fractures act as electrically conductive bodies when the fluids are more conductive than the host material. We will use electrical inversion for estimating electrical conductivity distribution within multiple fractures from synthetic and measured data. Specifically, we will use data and well geometries from an experiment performed at Blue Canyon Dome in Socorro, NM, which was used as a study site for subsurface technology, engineering, and research (SubTER) funded by DOE. This project used a central borehole for energetically stimulating the system and four monitoring boreholes, emplaced in the cardinal directions. The electrical data taken during this project used 16 temporary electrodes deployed in the stimulation borehole and 64 permanent electrodes in the monitoring wells (16 each). We present results derived using E4D from scenarios with two discrete fractures, thereby discovering the electric potential response of both spatially and temporarily variant fluid distribution and the resolution of fluid and fracture boundaries. These two fractures have dimensions of 3m × 0.01m × 7m and are separated by 1m. These results can be used to develop stimulation and flow tests at the meso-scale that will be important for model validation. Sandia National Laboratories is a multi

Quantifying Discrete Fracture Network Connectivity in Hydraulic Fracturing Stimulation

Science.gov (United States)

Urbancic, T.; Ardakani, E. P.; Baig, A.

2017-12-01

Hydraulic fracture stimulations generally result in microseismicity that is associated with the activation or extension of pre-existing microfractures and discontinuities. Microseismic events acquired under 3D downhole sensor coverage provide accurate event locations outlining hydraulic fracture growth. Combined with source characteristics, these events provide a high quality input for seismic moment tensor inversion and eventually constructing the representative discrete fracture network (DFN). In this study, we investigate the strain and stress state, identified fracture orientation, and DFN connectivity and performance for example stages in a multistage perf and plug completion in a North American shale play. We use topology, the familiar concept in many areas of structural geology, to further describe the relationships between the activated fractures and their effectiveness in enhancing permeability. We explore how local perturbations of stress state lead to the activation of different fractures sets and how that effects the DFN interaction and complexity. In particular, we observe that a more heterogeneous stress state shows a higher percentage of sub-horizontal fractures or bedding plane slips. Based on topology, the fractures are evenly distributed from the injection point, with decreasing numbers of connections by distance. The dimensionless measure of connection per branch and connection per line are used for quantifying the DFN connectivity. In order to connect the concept of connectivity back to productive volume and stimulation efficiency, the connectivity is compared with the character of deformation in the reservoir as deduced from the collective behavior of microseismicity using robustly determined source parameters.

Experimental Investigation and Discrete Element Modelling of Composite Hollow Spheres Subjected to Dynamic Fracture

Directory of Open Access Journals (Sweden)

Arthur Coré

2017-01-01

Full Text Available This paper deals with the characterization and the numerical modelling of the collapse of composite hollow spherical structures developed to absorb energy during high velocity impacts. The structure is composed of hollow spheres (ϕ=2–30 mm made of epoxy resin and mineral powder. First of all, quasi-static and dynamic (v=5 mm·min−1 to v=2 m·s−1 compression tests are conducted at room temperature on a single sphere to study energy dissipation mechanisms. Fracture of the material appears to be predominant. A numerical model based on the discrete element method is investigated to simulate the single sphere crushing. The stress-strain-time relationship of the material based on the Ree-Eyring law is numerically implemented. The DEM modelling takes naturally into account the dynamic fracture and the crack path computed is close to the one observed experimentally in uniaxial compression. Eventually, high velocity impacts (v>100 m·s−1 of a hollow sphere on a rigid surface are conducted with an air cannon. The numerical results are in good agreement with the experimental data and demonstrate the ability of the present model to correctly describe the mechanical behavior of brittle materials at high strain rate.

DEM Particle Fracture Model

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.

Simulation of a field scale tritium tracer experiment in a fractured, weathered shale using discrete-fracture/matrix-diffusion and equivalent porous medium models

Energy Technology Data Exchange (ETDEWEB)

Stafford, Paige L. [Univ. of Tennessee, Knoxville, TN (United States). Dept. of Geological Sciences

1996-05-01

Simulations of a tritium tracer experiment in fractured shale saprolite, conducted at the Oak Ridge National Laboratory, were performed using 1D and 2D equivalent porous medium (EPM) and discrete-fracture/matrix-diffusion (DFMD) models. The models successfully reproduced the general shape of the breakthrough curves in down-gradient monitoring wells which are characterized by rapid first arrival, a slow-moving center of mass, and a persistent ``tail`` of low concentration. In plan view, the plume shows a large degree of transverse spreading with the width almost as great as the length. EPM models were sensitive to dispersivity coefficient values which had to be large (relative to the 3.7m distance between the injection and monitoring wells) to fit the tail and transverse spreading. For example, to fit the tail a longitudinal dispersivity coefficient, α_L, of 0.8 meters for the 2D simulations was used. To fit the transverse spreading, a transverse dispersivity coefficient, α_T, of 0.8 to 0.08 meters was used indicating an α_L/α_T ratio between 10 and 1. Transverse spreading trends were also simulated using a 2D DFMD model using a few larger aperture fractures superimposed onto an EPM. Of the fracture networks studied, only those with truncated fractures caused transverse spreading. Simulated tritium levels in all of the cases were larger than observed values by a factor of approximately 100. Although this is partly due to input of too much tritium mass by the models it appears that dilution in the wells, which were not purged prior to sampling, is also a significant factor. The 1D and 2D EPM models were fitted to monitoring data from the first five years of the experiment and then used to predict future tritium concentrations.

Simulation of a field scale tritium tracer experiment in a fractured, weathered shale using discrete-fracture/matrix-diffusion and equivalent porous medium models

International Nuclear Information System (INIS)

Stafford, P.L.

1996-05-01

Simulations of a tritium tracer experiment in fractured shale saprolite, conducted at the Oak Ridge National Laboratory, were performed using 1D and 2D equivalent porous medium (EPM) and discrete-fracture/matrix-diffusion (DFMD) models. The models successfully reproduced the general shape of the breakthrough curves in down-gradient monitoring wells which are characterized by rapid first arrival, a slow-moving center of mass, and a persistent ''tail'' of low concentration. In plan view, the plume shows a large degree of transverse spreading with the width almost as great as the length. EPM models were sensitive to dispersivity coefficient values which had to be large (relative to the 3.7m distance between the injection and monitoring wells) to fit the tail and transverse spreading. For example, to fit the tail a longitudinal dispersivity coefficient, α L , of 0.8 meters for the 2D simulations was used. To fit the transverse spreading, a transverse dispersivity coefficient, α T , of 0.8 to 0.08 meters was used indicating an α L /α T ratio between 10 and 1. Transverse spreading trends were also simulated using a 2D DFMD model using a few larger aperture fractures superimposed onto an EPM. Of the fracture networks studied, only those with truncated fractures caused transverse spreading. Simulated tritium levels in all of the cases were larger than observed values by a factor of approximately 100. Although this is partly due to input of too much tritium mass by the models it appears that dilution in the wells, which were not purged prior to sampling, is also a significant factor. The 1D and 2D EPM models were fitted to monitoring data from the first five years of the experiment and then used to predict future tritium concentrations

Shale Fracture Analysis using the Combined Finite-Discrete Element Method

Science.gov (United States)

Carey, J. W.; Lei, Z.; Rougier, E.; Knight, E. E.; Viswanathan, H.

2014-12-01

Hydraulic fracturing (hydrofrac) is a successful method used to extract oil and gas from highly carbonate rocks like shale. However, challenges exist for industry experts estimate that for a single $10 million dollar lateral wellbore fracking operation, only 10% of the hydrocarbons contained in the rock are extracted. To better understand how to improve hydrofrac recovery efficiencies and to lower its costs, LANL recently funded the Laboratory Directed Research and Development (LDRD) project: "Discovery Science of Hydraulic Fracturing: Innovative Working Fluids and Their Interactions with Rocks, Fractures, and Hydrocarbons". Under the support of this project, the LDRD modeling team is working with the experimental team to understand fracture initiation and propagation in shale rocks. LANL's hybrid hydro-mechanical (HM) tool, the Hybrid Optimization Software Suite (HOSS), is being used to simulate the complex fracture and fragment processes under a variety of different boundary conditions. HOSS is based on the combined finite-discrete element method (FDEM) and has been proven to be a superior computational tool for multi-fracturing problems. In this work, the comparison of HOSS simulation results to triaxial core flooding experiments will be presented.

Hydraulic Fracturing and Production Optimization in Eagle Ford Shale Using Coupled Geomechanics and Fluid Flow Model

Science.gov (United States)

Suppachoknirun, Theerapat; Tutuncu, Azra N.

2017-12-01

With increasing production from shale gas and tight oil reservoirs, horizontal drilling and multistage hydraulic fracturing processes have become a routine procedure in unconventional field development efforts. Natural fractures play a critical role in hydraulic fracture growth, subsequently affecting stimulated reservoir volume and the production efficiency. Moreover, the existing fractures can also contribute to the pressure-dependent fluid leak-off during the operations. Hence, a reliable identification of the discrete fracture network covering the zone of interest prior to the hydraulic fracturing design needs to be incorporated into the hydraulic fracturing and reservoir simulations for realistic representation of the in situ reservoir conditions. In this research study, an integrated 3-D fracture and fluid flow model have been developed using a new approach to simulate the fluid flow and deliver reliable production forecasting in naturally fractured and hydraulically stimulated tight reservoirs. The model was created with three key modules. A complex 3-D discrete fracture network model introduces realistic natural fracture geometry with the associated fractured reservoir characteristics. A hydraulic fracturing model is created utilizing the discrete fracture network for simulation of the hydraulic fracture and flow in the complex discrete fracture network. Finally, a reservoir model with the production grid system is used allowing the user to efficiently perform the fluid flow simulation in tight formations with complex fracture networks. The complex discrete natural fracture model, the integrated discrete fracture model for the hydraulic fracturing, the fluid flow model, and the input dataset have been validated against microseismic fracture mapping and commingled production data obtained from a well pad with three horizontal production wells located in the Eagle Ford oil window in south Texas. Two other fracturing geometries were also evaluated to optimize

Modeling of Hydraulic Fracture Propagation at the kISMET Site Using a Fully Coupled 3D Network-Flow and Quasi- Static Discrete Element Model

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.

Ongoing Model Development Analyzing Glass Fracture

DEFF Research Database (Denmark)

Molnar, G.; Bojtar, I.; Nielsen, Jens Henrik

2013-01-01

Present subject deals with an ongoing experimental and numerical analysis of inplane loaded glass plates. The main goal of the investigation is to develop a hybrid – discrete and finite element – model which could follow the fracture process in annealed and in tempered glass. Measurements of the ...... an overview of the structure of the research and a summary of current status archived so far.......Present subject deals with an ongoing experimental and numerical analysis of inplane loaded glass plates. The main goal of the investigation is to develop a hybrid – discrete and finite element – model which could follow the fracture process in annealed and in tempered glass. Measurements...... of the residual stress state before failure and high-speed camera recordings of the failure are being performed in order to verify the numerical model. The primary goal of this research is to follow the overall fracture of a structural element – e.g. beam – loaded inplane. Present paper would like to give...

A discrete element model for damage and fracture of geomaterials under fatigue loading

Science.gov (United States)

Gao, Xiaofeng; Koval, Georg; Chazallon, Cyrille

2017-06-01

Failure processes in geomaterials (concrete, asphalt concrete, masonry, etc.) under fatigue loading (repeated moving loads, cycles of temperature, etc.) are responsible for most of the dysfunctions in pavements, brick structures, etc. In the beginning of the lifetime of a structure, the material presents only inner defects (micro cracks, voids, etc.). Due to the effect of the cyclic loading, these small defects tend to grow in size and quantity which damage the material, reducing its stiffness. With a relatively high number of cycles, these growing micro cracks become large cracks, which characterizes the fracture behavior. From a theoretical point of view, both mechanisms are treated differently. Fracture is usually described locally, with the propagation of cracks defined by the energy release rate at the crack tip; damage is usually associated to non-local approaches. In the present work, damage and fracture mechanics are combined in a local discrete element approach.

Evaluation of scale effects on hydraulic characteristics of fractured rock using fracture network model

International Nuclear Information System (INIS)

Ijiri, Yuji; Sawada, Atsushi; Uchida, Masahiro; Ishiguro, Katsuhiko; Umeki, Hiroyuki; Sakamoto, Kazuhiko; Ohnishi, Yuzo

2001-01-01

It is important to take into account scale effects on fracture geometry if the modeling scale is much larger than the in-situ observation scale. The scale effect on fracture trace length, which is the most scale dependent parameter, is investigated using fracture maps obtained at various scales in tunnel and dam sites. We found that the distribution of fracture trace length follows negative power law distribution in regardless of locations and rock types. The hydraulic characteristics of fractured rock is also investigated by numerical analysis of discrete fracture network (DFN) model where power law distribution of fracture radius is adopted. We found that as the exponent of power law distribution become larger, the hydraulic conductivity of DFN model increases and the travel time in DFN model decreases. (author)

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.

Fractured reservoir discrete feature network technologies. Annual report, March 7, 1996--February 28, 1997

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.

Modeling of brittle-viscous flow using discrete particles

Science.gov (United States)

Thordén Haug, Øystein; Barabasch, Jessica; Virgo, Simon; Souche, Alban; Galland, Olivier; Mair, Karen; Abe, Steffen; Urai, Janos L.

2017-04-01

Many geological processes involve both viscous flow and brittle fractures, e.g. boudinage, folding and magmatic intrusions. Numerical modeling of such viscous-brittle materials poses challenges: one has to account for the discrete fracturing, the continuous viscous flow, the coupling between them, and potential pressure dependence of the flow. The Discrete Element Method (DEM) is a numerical technique, widely used for studying fracture of geomaterials. However, the implementation of viscous fluid flow in discrete element models is not trivial. In this study, we model quasi-viscous fluid flow behavior using Esys-Particle software (Abe et al., 2004). We build on the methodology of Abe and Urai (2012) where a combination of elastic repulsion and dashpot interactions between the discrete particles is implemented. Several benchmarks are presented to illustrate the material properties. Here, we present extensive, systematic material tests to characterize the rheology of quasi-viscous DEM particle packing. We present two tests: a simple shear test and a channel flow test, both in 2D and 3D. In the simple shear tests, simulations were performed in a box, where the upper wall is moved with a constant velocity in the x-direction, causing shear deformation of the particle assemblage. Here, the boundary conditions are periodic on the sides, with constant forces on the upper and lower walls. In the channel flow tests, a piston pushes a sample through a channel by Poisseuille flow. For both setups, we present the resulting stress-strain relationships over a range of material parameters, confining stress and strain rate. Results show power-law dependence between stress and strain rate, with a non-linear dependence on confining force. The material is strain softening under some conditions (which). Additionally, volumetric strain can be dilatant or compactant, depending on porosity, confining pressure and strain rate. Constitutive relations are implemented in a way that limits the

Fracture size and transmissivity correlations: Implications for transport simulations in sparse three-dimensional discrete fracture networks following a truncated power law distribution of fracture size

Science.gov (United States)

Hyman, J.; Aldrich, G. A.; Viswanathan, H. S.; Makedonska, N.; Karra, S.

2016-12-01

We characterize how different fracture size-transmissivity relationships influence flow and transport simulations through sparse three-dimensional discrete fracture networks. Although it is generally accepted that there is a positive correlation between a fracture's size and its transmissivity/aperture, the functional form of that relationship remains a matter of debate. Relationships that assume perfect correlation, semi-correlation, and non-correlation between the two have been proposed. To study the impact that adopting one of these relationships has on transport properties, we generate multiple sparse fracture networks composed of circular fractures whose radii follow a truncated power law distribution. The distribution of transmissivities are selected so that the mean transmissivity of the fracture networks are the same and the distributions of aperture and transmissivity in models that include a stochastic term are also the same.We observe that adopting a correlation between a fracture size and its transmissivity leads to earlier breakthrough times and higher effective permeability when compared to networks where no correlation is used. While fracture network geometry plays the principal role in determining where transport occurs within the network, the relationship between size and transmissivity controls the flow speed. These observations indicate DFN modelers should be aware that breakthrough times and effective permeabilities can be strongly influenced by such a relationship in addition to fracture and network statistics.

The brush model - a new approach to numerical modeling of matrix diffusion in fractured clay stone

International Nuclear Information System (INIS)

Lege, T.; Shao, H.

1998-01-01

A special approach for numerical modeling of contaminant transport in fractured clay stone is presented. The rock matrix and the fractures are simulated with individual formulations for FE grids and transport, coupled into a single model. The capacity of the rock matrix to take up contaminants is taken into consideration with a discrete simulation of matrix diffusion. Thus, the natural process of retardation due to matrix diffusion can be better simulated than by a standard introduction of an empirical parameter into the transport equation. Transport in groundwater in fractured clay stone can be simulated using a model called a 'brush model'. The 'brush handle' is discretized by 2-D finite elements. Advective-dispersive transport in groundwater in the fractures is assumed. The contaminant diffuses into 1D finite elements perpendicular to the fractures, i.e., the 'bristles of the brush'. The conclusion is drawn that matrix diffusion is an important property of fractured clay stone for contaminant retardation. (author)

Discrete Fracture Network Modeling and Simulation of Subsurface Transport for the Topopah Springs and Lava Flow Aquifers at Pahute Mesa, FY 15 Progress Report

Energy Technology Data Exchange (ETDEWEB)

Makedonska, Nataliia [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Kwicklis, Edward Michael [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Birdsell, Kay Hanson [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Harrod, Jeremy Ashcraft [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Karra, Satish [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2016-10-18

This progress report for fiscal year 2015 (FY15) describes the development of discrete fracture network (DFN) models for Pahute Mesa. DFN models will be used to upscale parameters for simulations of subsurface flow and transport in fractured media in Pahute Mesa. The research focuses on modeling of groundwater flow and contaminant transport using DFNs generated according to fracture characteristics observed in the Topopah Spring Aquifer (TSA) and the Lava Flow Aquifer (LFA). This work will improve the representation of radionuclide transport processes in large-scale, regulatory-focused models with a view to reduce pessimistic bounding approximations and provide more realistic contaminant boundary calculations that can be used to describe the future extent of contaminated groundwater. Our goal is to refine a modeling approach that can translate parameters to larger-scale models that account for local-scale flow and transport processes, which tend to attenuate migration.

A numerical study of the effects of a discrete fracture and an excavation damage zone on 129I transport through the geosphere

International Nuclear Information System (INIS)

Chan, T.; Scheier, N.W.; O'Connor, P.A.

1997-10-01

A numerical study has been conducted to investigate the effects of a discrete fracture and an excavation damage zone (EDZ) on groundwater mediated transport of I2 9 from a hypothetical nuclear fuel waste disposal vault through saturated, sparsely fractured plutonic rock to the biosphere. The reference disposal system simulated in the present work is based on the median value case of the postclosure assessment case study presented by AECL to support the Environmental Impact Statement (EIS) submitted to the Canadian Environmental Assessment Agency (CEAA). In particular, the reference geosphere is based mainly on hydrogeological characteristics at the site of AECL's Underground Research Laboratory in the Whiteshell Research Area, southeastern Manitoba. Several features not explicitly simulated in the EIS postclosure assessment case study are investigated in this study. These include the hypothetical possibility of a discrete fracture or a narrow fracture zone existing in the rock in the immediate vicinity of the disposal vault. This hypothetical fracture is modeled as a discrete fracture that connects or almost connects the vault to nearby fracture zone LD1. Simulations are performed using a combination of three-dimensional flow model and corresponding two-dimensional transport models, and the MOTIF finite-element code. It should be emphasized that the primary purpose of the present study it to investigate the relative importance of the various possible features in the rock in the immediate vicinity of the vault. Detailed numerical modelling of the effectiveness of various engineered barriers that could be used to mitigate any negative effects of such features is beyond the scope of this study

A Two-Scale Reduced Model for Darcy Flow in Fractured Porous Media

KAUST Repository

Chen, Huangxin; Sun, Shuyu

2016-01-01

scale, and the effect of fractures on each coarse scale grid cell intersecting with fractures is represented by the discrete fracture model (DFM) on the fine scale. In the DFM used on the fine scale, the matrix-fracture system are resolved

Discrete modeling of multiple discontinuities in rock mass using XFEM

OpenAIRE

Das, Kamal C.; Ausas, Roberto Federico; Carol, Ignacio; Rodrigues, Eduardo; Sandeep, Sandra; Vargas, P. E.; Gonzalez, Nubia Aurora; Segura, Josep María; Lakshmikantha, Ramasesha Mookanahallipatna; Mello,, U.

2017-01-01

Modeling of discontinuities (fractures and fault surfaces) is of major importance to assess the geomechanical behavior of oil and gas reservoirs, especially for tight and unconventional reservoirs. Numerical analysis of discrete discontinuities traditionally has been studied using interface element concepts, however more recently there are attempts to use extended finite element method (XFEM). The development of an XFEM tool for geo-mechanical fractures/faults modeling has significant industr...

Parallel numerical modeling of hybrid-dimensional compositional non-isothermal Darcy flows in fractured porous media

Science.gov (United States)

Xing, F.; Masson, R.; Lopez, S.

2017-09-01

This paper introduces a new discrete fracture model accounting for non-isothermal compositional multiphase Darcy flows and complex networks of fractures with intersecting, immersed and non-immersed fractures. The so called hybrid-dimensional model using a 2D model in the fractures coupled with a 3D model in the matrix is first derived rigorously starting from the equi-dimensional matrix fracture model. Then, it is discretized using a fully implicit time integration combined with the Vertex Approximate Gradient (VAG) finite volume scheme which is adapted to polyhedral meshes and anisotropic heterogeneous media. The fully coupled systems are assembled and solved in parallel using the Single Program Multiple Data (SPMD) paradigm with one layer of ghost cells. This strategy allows for a local assembly of the discrete systems. An efficient preconditioner is implemented to solve the linear systems at each time step and each Newton type iteration of the simulation. The numerical efficiency of our approach is assessed on different meshes, fracture networks, and physical settings in terms of parallel scalability, nonlinear convergence and linear convergence.

Modeling contaminant plumes in fractured limestone aquifers

DEFF Research Database (Denmark)

Mosthaf, Klaus; Brauns, Bentje; Fjordbøge, Annika Sidelmann

Determining the fate and transport of contaminant plumes from contaminated sites in limestone aquifers is important because they are a major drinking water resource. This is challenging because they are often heavily fractured and contain chert layers and nodules, resulting in a complex transport...... model. The paper concludes with recommendations on how to identify and employ suitable models to advance the conceptual understanding and as decision support tools for risk assessment and the planning of remedial actions....... behavior. Improved conceptual models are needed for this type of site. Here conceptual models are developed by combining numerical models with field data. Several types of fracture flow and transport models are available for the modeling of contaminant transport in fractured media. These include...... the established approaches of the equivalent porous medium, discrete fracture and dual continuum models. However, these modeling concepts are not well tested for contaminant plume migration in limestone geologies. Our goal was to develop and evaluate approaches for modeling the transport of dissolved contaminant...

Application of Tempered-Stable Time Fractional-Derivative Model to Upscale Subdiffusion for Pollutant Transport in Field-Scale Discrete Fracture Networks

Directory of Open Access Journals (Sweden)

Bingqing Lu

2018-01-01

Full Text Available Fractional calculus provides efficient physical models to quantify non-Fickian dynamics broadly observed within the Earth system. The potential advantages of using fractional partial differential equations (fPDEs for real-world problems are often limited by the current lack of understanding of how earth system properties influence observed non-Fickian dynamics. This study explores non-Fickian dynamics for pollutant transport in field-scale discrete fracture networks (DFNs, by investigating how fracture and rock matrix properties influence the leading and tailing edges of pollutant breakthrough curves (BTCs. Fractured reservoirs exhibit erratic internal structures and multi-scale heterogeneity, resulting in complex non-Fickian dynamics. A Monte Carlo approach is used to simulate pollutant transport through DFNs with a systematic variation of system properties, and the resultant non-Fickian transport is upscaled using a tempered-stable fractional in time advection–dispersion equation. Numerical results serve as a basis for determining both qualitative and quantitative relationships between BTC characteristics and model parameters, in addition to the impacts of fracture density, orientation, and rock matrix permeability on non-Fickian dynamics. The observed impacts of medium heterogeneity on tracer transport at late times tend to enhance the applicability of fPDEs that may be parameterized using measurable fracture–matrix characteristics.

Fracture network modeling and GoldSim simulation support

International Nuclear Information System (INIS)

Sugita, Kenichirou; Dershowitz, W.

2005-01-01

During Heisei-16, Golder Associates provided support for JNC Tokai through discrete fracture network data analysis and simulation of the Mizunami Underground Research Laboratory (MIU), participation in Task 6 of the AEspoe Task Force on Modeling of Groundwater Flow and Transport, and development of methodologies for analysis of repository site characterization strategies and safety assessment. MIU support during H-16 involved updating the H-15 FracMan discrete fracture network (DFN) models for the MIU shaft region, and developing improved simulation procedures. Updates to the conceptual model included incorporation of 'Step2' (2004) versions of the deterministic structures, and revision of background fractures to be consistent with conductive structure data from the DH-2 borehole. Golder developed improved simulation procedures for these models through the use of hybrid discrete fracture network (DFN), equivalent porous medium (EPM), and nested DFN/EPM approaches. For each of these models, procedures were documented for the entire modeling process including model implementation, MMP simulation, and shaft grouting simulation. Golder supported JNC participation in Task 6AB, 6D and 6E of the AEspoe Task Force on Modeling of Groundwater Flow and Transport during H-16. For Task 6AB, Golder developed a new technique to evaluate the role of grout in performance assessment time-scale transport. For Task 6D, Golder submitted a report of H-15 simulations to SKB. For Task 6E, Golder carried out safety assessment time-scale simulations at the block scale, using the Laplace Transform Galerkin method. During H-16, Golder supported JNC's Total System Performance Assessment (TSPA) strategy by developing technologies for the analysis of the use site characterization data in safety assessment. This approach will aid in the understanding of the use of site characterization to progressively reduce site characterization uncertainty. (author)

A new Eulerian-Lagrangian finite element simulator for solute transport in discrete fracture-matrix systems

Energy Technology Data Exchange (ETDEWEB)

Birkholzer, J.; Karasaki, K. [Lawrence Berkeley National Lab., CA (United States). Earth Sciences Div.

1996-07-01

Fracture network simulators have extensively been used in the past for obtaining a better understanding of flow and transport processes in fractured rock. However, most of these models do not account for fluid or solute exchange between the fractures and the porous matrix, although diffusion into the matrix pores can have a major impact on the spreading of contaminants. In the present paper a new finite element code TRIPOLY is introduced which combines a powerful fracture network simulator with an efficient method to account for the diffusive interaction between the fractures and the adjacent matrix blocks. The fracture network simulator used in TRIPOLY features a mixed Lagrangian-Eulerian solution scheme for the transport in fractures, combined with an adaptive gridding technique to account for sharp concentration fronts. The fracture-matrix interaction is calculated with an efficient method which has been successfully used in the past for dual-porosity models. Discrete fractures and matrix blocks are treated as two different systems, and the interaction is modeled by introducing sink/source terms in both systems. It is assumed that diffusive transport in the matrix can be approximated as a one-dimensional process, perpendicular to the adjacent fracture surfaces. A direct solution scheme is employed to solve the coupled fracture and matrix equations. The newly developed combination of the fracture network simulator and the fracture-matrix interaction module allows for detailed studies of spreading processes in fractured porous rock. The authors present a sample application which demonstrate the codes ability of handling large-scale fracture-matrix systems comprising individual fractures and matrix blocks of arbitrary size and shape.

Preferences of older patient regarding hip fracture rehabilitation service configuration: A feasibility discrete choice experiment.

Science.gov (United States)

Charles, Joanna M; Roberts, Jessica L; Din, Nafees Ud; Williams, Nefyn H; Yeo, Seow Tien; Edwards, Rhiannon T

2018-05-14

As part of a wider feasibility study, the feasibility of gaining older patients' views for hip fracture rehabilitation services was tested using a discrete choice experiment in a UK context. Discrete choice experiment is a method used for eliciting individuals' preferences about goods and services. The discrete choice experiment was administered to 41 participants who had experienced hip fracture (mean age 79.3 years; standard deviation (SD) 7.5 years), recruited from a larger feasibility study exploring a new multidisciplinary rehabilitation for hip fracture. Attributes and levels for this discrete choice experiment were identified from a systematic review and focus groups. The questionnaire was administered at the 3-month follow-up. Participants indicated a significant preference for a fully-qualified physiotherapist or occupational therapist to deliver the rehabilitation sessions (β = 0·605, 95% confidence interval (95% CI) 0.462-0.879), and for their rehabilitation session to last less than 90 min (β = -0.192, 95% CI -0.381 to -0.051). The design of the discrete choice experiment using attributes associated with service configuration could have the potential to inform service implementation, and assist rehabilitation service design that incorporates the preferences of patients.

CVD-MPFA full pressure support, coupled unstructured discrete fracture-matrix Darcy-flux approximations

Science.gov (United States)

Ahmed, Raheel; Edwards, Michael G.; Lamine, Sadok; Huisman, Bastiaan A. H.; Pal, Mayur

2017-11-01

Two novel control-volume methods are presented for flow in fractured media, and involve coupling the control-volume distributed multi-point flux approximation (CVD-MPFA) constructed with full pressure support (FPS), to two types of discrete fracture-matrix approximation for simulation on unstructured grids; (i) involving hybrid grids and (ii) a lower dimensional fracture model. Flow is governed by Darcy's law together with mass conservation both in the matrix and the fractures, where large discontinuities in permeability tensors can occur. Finite-volume FPS schemes are more robust than the earlier CVD-MPFA triangular pressure support (TPS) schemes for problems involving highly anisotropic homogeneous and heterogeneous full-tensor permeability fields. We use a cell-centred hybrid-grid method, where fractures are modelled by lower-dimensional interfaces between matrix cells in the physical mesh but expanded to equi-dimensional cells in the computational domain. We present a simple procedure to form a consistent hybrid-grid locally for a dual-cell. We also propose a novel hybrid-grid for intersecting fractures, for the FPS method, which reduces the condition number of the global linear system and leads to larger time steps for tracer transport. The transport equation for tracer flow is coupled with the pressure equation and provides flow parameter assessment of the fracture models. Transport results obtained via TPS and FPS hybrid-grid formulations are compared with the corresponding results of fine-scale explicit equi-dimensional formulations. The results show that the hybrid-grid FPS method applies to general full-tensor fields and provides improved robust approximations compared to the hybrid-grid TPS method for fractured domains, for both weakly anisotropic permeability fields and very strong anisotropic full-tensor permeability fields where the TPS scheme exhibits spurious oscillations. The hybrid-grid FPS formulation is extended to compressible flow and the

Fracture network modeling and GoldSim simulation support

International Nuclear Information System (INIS)

Sugita, Kenichiro; Dershowitz, William

2004-01-01

During Heisei-15, Golder Associates provided support for JNC Tokai through discrete fracture network data analysis and simulation of the MIU Underground Rock Laboratory, participation in Task 6 of the Aespoe Task Force on Modelling of Groundwater Flow and Transport, and development of methodologies for analysis of repository site characterization strategies and safety assessment. MIU Underground Rock Laboratory support during H-15 involved development of new discrete fracture network (DFN) models for the MIU Shoba-sama Site, in the region of shaft development. Golder developed three DFN models for the site using discrete fracture network, equivalent porous medium (EPM), and nested DFN/EPM approaches. Each of these models were compared based upon criteria established for the multiple modeling project (MMP). Golder supported JNC participation in Task 6AB, 6D and 6E of the Aespoe Task Force on Modelling of Groundwater Flow and Transport during H-15. For Task 6AB, Golder implemented an updated microstructural model in GoldSim, and used this updated model to simulate the propagation of uncertainty from experimental to safety assessment time scales, for 5 m scale transport path lengths. Task 6D and 6E compared safety assessment (PA) and experimental time scale simulations in a 200 m scale discrete fracture network. For Task 6D, Golder implemented a DFN model using FracMan/PA Works, and determined the sensitivity of solute transport to a range of material property and geometric assumptions. For Task 6E, Golder carried out demonstration FracMan/PA Works transport calculations at a 1 million year time scale, to ensure that task specifications are realistic. The majority of work for Task 6E will be carried out during H-16. During H-15, Golder supported JNC's Total System Performance Assessment (TSPO) strategy by developing technologies for the analysis of precipitant concentration. These approaches were based on the GoldSim precipitant data management features, and were

Hydraulic fracture propagation modeling and data-based fracture identification

Science.gov (United States)

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

Comparing flows to a tunnel for single porosity, double porosity and discrete fracture representations of the EDZ

International Nuclear Information System (INIS)

Hawkins, I.; Swift, B.; Hoch, A.; Wendling, J.

2010-01-01

Document available in extended abstract form only. Andra is studying the Callovo-Oxfordian mud-stones, located at a depth of approximately 500 m beneath the borders of the Meuse and the Haute-Marne Departements, in order to assess the feasibility of constructing a repository for radioactive waste in this low-permeability geological formation. The construction of a repository will lead to the formation of a zone adjacent to the repository (the Excavation Damaged Zone, or EDZ) in which the rock suffers mechanical damage. In the EDZ, fractures and cracks will develop, and therefore the hydraulic properties (including the permeability) will be different from those of the undamaged rock. There are some experimental data which, despite significant uncertainties, allow a conceptual model of the fractures to be defined. The objectives of this study were: - To develop a Discrete Fracture Network (DFN) model of the EDZ; - To derive effective properties for both single continuum and Multiple Interacting Continua (MINC) models from the DFN model; and - To use the various models to simulate desaturation of the rock during the operational phase of the repository, and subsequent re-saturation of a tunnel post-closure (a period of thousands of years). The approaches to modelling flow and transport in fractured systems fall into two rough classes: DFN models; and continuum models. DFN models account explicitly for the effects of individual fractures on fluid flow and solute transport, and usually do not consider the interaction between the fractures and the rock matrix. Continuum models may be single continuum, double continuum or MINC. Single continuum models are applicable when the interaction between the fractures and the rock matrix is sufficient to establish a local equilibrium. Double continuum models account for the two interacting systems (i.e. fractures and rock matrix) by conceptualising each as a continuum occupying the entire domain. An exchange function describes mass

Streaming potential modeling in fractured rock: Insights into the identification of hydraulically active fractures

Science.gov (United States)

Roubinet, D.; Linde, N.; Jougnot, D.; Irving, J.

2016-05-01

Numerous field experiments suggest that the self-potential (SP) geophysical method may allow for the detection of hydraulically active fractures and provide information about fracture properties. However, a lack of suitable numerical tools for modeling streaming potentials in fractured media prevents quantitative interpretation and limits our understanding of how the SP method can be used in this regard. To address this issue, we present a highly efficient two-dimensional discrete-dual-porosity approach for solving the fluid flow and associated self-potential problems in fractured rock. Our approach is specifically designed for complex fracture networks that cannot be investigated using standard numerical methods. We then simulate SP signals associated with pumping conditions for a number of examples to show that (i) accounting for matrix fluid flow is essential for accurate SP modeling and (ii) the sensitivity of SP to hydraulically active fractures is intimately linked with fracture-matrix fluid interactions. This implies that fractures associated with strong SP amplitudes are likely to be hydraulically conductive, attracting fluid flow from the surrounding matrix.

Coupled models in porous media: reactive transport and fractures

International Nuclear Information System (INIS)

Amir, L.

2008-12-01

This thesis deals with numerical simulation of coupled models for flow and transport in porous media. We present a new method for coupling chemical reactions and transport by using a Newton-Krylov method, and we also present a model of flow in fractured media, based on a domain decomposition method that takes into account the case of intersecting fractures. This study is composed of three parts: the first part contains an analysis, and implementation, of various numerical methods for discretizing advection-diffusion problems, in particular by using operator splitting methods. The second part is concerned with a fully coupled method for modeling transport and chemistry problems. The coupled transport-chemistry model is described, after discretization in time, by a system of nonlinear equations. The size of the system, namely the number of grid points times the number a chemical species, precludes a direct solution of the linear system. To alleviate this difficulty, we solve the system by a Newton-Krylov method, so as to avoid forming and factoring the Jacobian matrix. In the last part, we present a model of flow in 3D for intersecting fractures, by using a domain decomposition method. The fractures are treated as interfaces between sub-domains. We show existence and uniqueness of the solution, and we validate the model by numerical tests. (author)

Effect of Discrete Fracture Network Characteristics on the Sustainability of Heat Production in Enhanced Geothermal Reservoirs

Science.gov (United States)

Riahi, A.; Damjanac, B.

2013-12-01

Viability of an enhanced or engineered geothermal reservoir is determined by the rate of produced fluid at production wells and the rate of temperature drawdown in the reservoir as well as that of the produced fluid. Meeting required targets demands sufficient permeability and flow circulation in a relatively large volume of rock mass. In-situ conditions such overall permeability of the bedrock formation, magnitude and orientation of stresses, and the characteristics of the existing Discrete Fracture Network (DFN) greatly affect sustainable heat production. Because much of the EGS resources are in formations with low permeability, different stimulation techniques are required prior to the production phase to enhance fluid circulation. Shear stimulation or hydro-shearing is the method of injecting a fluid into the reservoir with the aim of increasing the fluid pressure in the naturally fractured rock and inducing shear failure or slip events. This mechanism can enhance the system's permeability through permanent dilatational opening of the sheared fractures. Using a computational modeling approach, the correlation between heat production and DFN statistical characteristics, namely the fracture length distribution, fracture orientation, and also fracture density is studied in this paper. Numerical analyses were completed using two-dimensional distinct element code UDEC (Itasca, 2011), which represents rock masses as an assembly of interacting blocks separated by fractures. UDEC allows for simulation of fracture propagation along the predefined planes only (i.e., the trajectory of the hydraulic fracture is not part of the solution of the problem). Thus, the hydraulic fracture is assumed to be planar, aligned with the direction of the major principal stress. The pre-existing fractures were represented explicitly. They are discontinuities which deform elastically, but also can open and slip (Coulomb slip law) as a function of pressure and total stress changes. The fluid

Discrete fracture network for the Forsmark site

International Nuclear Information System (INIS)

Darcel, C.; Davy, P.; Bour, O.; Dreuzy, J.R. de

2006-08-01

In this report, we aim at defining a self-consistent method for analyzing the fracture patterns from boreholes, outcrops and lineaments. The objective was both to point out some variations in the fracture network parameters, and to define the global scaling fracture models that can encompass all the constraints brought by the different datasets. Although a full description of the DFN model variability is obviously fundamental for the future, we have put emphasis on the determination of mean parameters. The main parameters of the disc-shaped DFN model are the fracture size, orientations and spatial density distribution. The scaling model is defined as an extrapolation of existing i) observations at specific scales and ii) local fitting models to the whole range of scales. The range of possible models is restricted to the power-law scaling models. During the project we have put emphasize on the definition of the theory and methodology necessary to assess a sound comparison between data taken at different scales, with different techniques. Both 'local' and 'global' models have been investigated. Local models are linked exactly to the dataset they represent. Then, the global DFN models arise from the association of local models, different scales and different sample support shapes. Discrepancies between local and global model illustrate the variability associated to the DFN models. We define two possible Global Scaling Models (GSM). The first one is consistent with the scaling measured in the outcrops (Model A). Its scaling exponent is a 3d =3.5 (eq. to k r =2.5); it overestimates the fracture densities observed in the lineament maps. The second one assumes that both lineaments and outcrops belong to the same distribution model (Model B), which entails a scaling exponent a 3d =3.9 (eq. to k r =2.9). Both models have been tested by looking for the best consistency in the fracture density-dip relationships, between boreholes data at depth (based on boreholes KFM02A, KFM

Numerical research of two-phase flow in fractured-porous media based on discrete fracture fetwork model

Science.gov (United States)

Pyatkov, A. A.; Kosyakov, V. P.; Rodionov, S. P.; Botalov, A. Y.

2018-03-01

In this work was the study of the processes of isothermal and non-isothermal flow of high viscosity oil in a fractured-porous reservoir. The numerical experiment was done using our own reservoir simulator with the possibility of modeling of fluid motion in conditions of non-isothermal processes and long fractures in the formation.

Implications of the "observer effect" on modelling a long-term pumping test with hydraulically conductive boreholes in a discrete fracture network system.

Science.gov (United States)

Holton, D.; Frampton, A.; Cvetkovic, V.

2006-12-01

The Onkalo underground research facility for rock characterisation for nuclear waste disposal is located at Olkiluoto island, just off the Finnish coast in the Baltic Sea. Prior to the start of the excavation of the Onkalo facility, an extensive amount of hydraulic data has been collected during various pumping experiments from a large number of boreholes placed throughout an area of approximately 10 km2, reaching depths of 1000 meters below sea level. In particular, the hydraulic borehole data includes classical measurements of pressure, but also new measurements of flow rate and flow direction in boreholes (so called flow-logging). These measurements indicate large variations in heterogeneity and are a clear reflection of the discrete nature of the system. Here we present results from an ongoing project which aims to explore and asses the implications of these new flow-logging measurements to site descriptive modelling and modelling at performance assessment scales. The main challange of the first phase of this project is to obtain a greater understanding of a strongly heterogenious and anisotropic groundwater system in which open boreholes are located; that is, a system in which the observation boreholes themselves create new hydraulic conductive features of the groundwater system. The results presented are from recent hydraulic flow modelling simulations with a combined continuous porous media and discrete fracture network approach using a commercial finite-element software. An advantage of this approach is we may adapt a continuum mesh on the regional scale, were only a few conductive features are known, together with a local scale discrete fracture network approach, where detailed site-investigation has revealed a large amount of conductive features. Current findings indicate the system is sensitive to certain combinations of hydraulic features, and we quantify the significance of including these variations in terms of their implications for reduction of

Reduced Fracture Finite Element Model Analysis of an Efficient Two-Scale Hybrid Embedded Fracture Model

KAUST Repository

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.

Reduced Fracture Finite Element Model Analysis of an Efficient Two-Scale Hybrid Embedded Fracture Model

KAUST Repository

Amir, Sahar Z.; Chen, Huangxin; Sun, Shuyu

2017-01-01

A Hybrid Embedded Fracture (HEF) model was developed to reduce various computational costs while maintaining physical accuracy (Amir and Sun, 2016). HEF splits the computations into fine scale and coarse scale. Fine scale solves analytically for the matrix-fracture flux exchange parameter. Coarse scale solves for the properties of the entire system. In literature, fractures were assumed to be either vertical or horizontal for simplification (Warren and Root, 1963). Matrix-fracture flux exchange parameter was given few equations built on that assumption (Kazemi, 1968; Lemonnier and Bourbiaux, 2010). However, such simplified cases do not apply directly for actual random fracture shapes, directions, orientations …etc. This paper shows that the HEF fine scale analytic solution (Amir and Sun, 2016) generates the flux exchange parameter found in literature for vertical and horizontal fracture cases. For other fracture cases, the flux exchange parameter changes according to the angle, slop, direction, … etc. This conclusion rises from the analysis of both: the Discrete Fracture Network (DFN) and the HEF schemes. The behavior of both schemes is analyzed with exactly similar fracture conditions and the results are shown and discussed. Then, a generalization is illustrated for any slightly compressible single-phase fluid within fractured porous media and its results are discussed.

IDENTIFYING FRACTURE ORIGIN IN CERAMICS BY COMBINATION OF NONDESTRUCTIVE TESTING AND DISCRETE ELEMENT ANALYSIS

International Nuclear Information System (INIS)

Senapati, Rajeev; Zhang Jianmei

2010-01-01

Advanced ceramic materials have been extensively applied in aerospace, automobile and other industries. However, the reliability of the advanced ceramics is a major concern because of the brittle nature of the materials. In this paper, combination of nondestructive testing and numerical modeling Discrete Element Method is proposed to identify the fracture origin in ceramics. The nondestructive testing--laser scattering technology is first performed on the ceramic components to reveal the machining-induced damage such as cracks and the material-inherent flaws such as voids, then followed by the four point bending test. Discrete Element software package PFC 2D is used to simulate the four point bending test and try to identify where the fractures start. The numerical representation of the ceramic materials is done by generating a densely packed particle system using the specimen genesis procedure and then applying the suitable microparameters to the particle system. Simulation of four point bending test is performed on materials having no defects, materials having manufacturing-induced defects like cracks, and materials having material-inherent flaws like voids. The initiation and propagation of defects is modeled and the mean contact force on the loading ball is also plotted. The simulation prediction results are well in accordance with the nondestructive testing results.

Modeling of strongly heat-driven flow in partially saturated fractured porous media

International Nuclear Information System (INIS)

Pruess, K.; Tsang, Y.W.; Wang, J.S.Y.

1985-01-01

The authors have performed modeling studies on the simultaneous transport of heat, liquid water, vapor, and air in partially saturated fractured porous media, with particular emphasis on strongly heat-driven flow. The presence of fractures makes the transport problem very complex, both in terms of flow geometry and physics. The numerical simulator used for their flow calculations takes into account most of the physical effects which are important in multi-phase fluid and heat flow. It has provisions to handle the extreme non-linearities which arise in phase transitions, component disappearances, and capillary discontinuities at fracture faces. They model a region around an infinite linear string of nuclear waste canisters, taking into account both the discrete fractures and the porous matrix. From an analysis of the results obtained with explicit fractures, they develop equivalent continuum models which can reproduce the temperature, saturation, and pressure variation, and gas and liquid flow rates of the discrete fracture-porous matrix calculations. The equivalent continuum approach makes use of a generalized relative permeability concept to take into account the fracture effects. This results in a substantial simplification of the flow problem which makes larger scale modeling of complicated unsaturated fractured porous systems feasible. Potential applications for regional scale simulations and limitations of the continuum approach are discussed. 27 references, 13 figures, 2 tables

Modeling of strongly heat-driven flow in partially saturated fractured porous media

International Nuclear Information System (INIS)

Pruess, K.; Tsang, Y.W.; Wang, J.S.Y.

1984-10-01

We have performed modeling studies on the simultaneous transport of heat, liquid water, vapor, and air in partially saturated fractured porous media, with particular emphasis on strongly heat-driven flow. The presence of fractures makes the transport problem very complex, both in terms of flow geometry and physics. The numerical simulator used for our flow calculations takes into account most of the physical effects which are important in multi-phase fluid and heat flow. It has provisions to handle the extreme non-linearities which arise in phase transitions, component disappearances, and capillary discontinuities at fracture faces. We model a region around an infinite linear string of nuclear waste canisters, taking into account both the discrete fractures and the porous matrix. From an analysis of the results obtained with explicit fractures, we develop equivalent continuum models which can reproduce the temperature, saturation, and pressure variation, and gas and liquid flow rates of the discrete fracture-porous matrix calculations. The equivalent continuum approach makes use of a generalized relative permeability concept to take into account for fracture effects. This results in a substantial simplification of the flow problem which makes larger scale modeling of complicated unsaturated fractured porous systems feasible. Potential applications for regional scale simulations and limitations of the continuum approach are discussed. 27 references, 13 figures, 2 tables

Recent developments in the use of discrete fractures models for investigating the siting of an underground repository of radioactive waste

International Nuclear Information System (INIS)

Billaux, D.; Guerin, F.; Riss, J.; Dewiere, L.; Fillion, E.

2000-01-01

The sitting of a nuclear waste repository in a geological medium involves, among other aspects, predicting water inflows in the shafts and drifts, and evaluating possible geometries for the waste handling and storage galleries. In sedimentary host rocks, porous medium hydrogeology can be used easily to provide water inflow estimates, while geology will describe the geometry of the various layers, as well as the limited number of faults that may cut them. However, crystalline rocks such as the Vienne site, may be cut by numerous faults and fractures. To deal with such host rocks, we need new concepts - which have been under development during the last 15 years - in order to describe properly the spatial arrangement of discontinuities, its consequences in terms of the site hydrogeology, and in terms of the geometry of volumes available between faults for designing the underground storage cavities. A starting point is building a model of the fractures, using the statistical description of the investigated fracture field, including dips, dip directions, sizes, and intensities noted in boreholes or on outcrops. Such a model can then be used to compute flows. It is based on idealizing fractures as planar objects, often disks, with statistical geometrical properties inferred from available data. The model realism can be improved by conditioning the geometry on data, either directly observed - by fixing in space observed fractures - or indirectly inferred - by integrating the results of hydraulic, or even tracer tests. Discrete fracture models can then be used for many treatments, well beyond simple flow and transport computations. We illustrate this through two studies applied to the crystalline Vienne massif. First, image analysis techniques that were first developed for two dimensions, and have been recently extended to three dimensions, help with describing the space available between discontinuities, in order to define the sound rock blocks available for the waste

Discrete-Feature Model Implementation of SDM-Site Forsmark

Energy Technology Data Exchange (ETDEWEB)

Geier, Joel (Clearwater Hardrock Consulting, Corvallis, OR (United States))

2010-03-15

A discrete-feature model (DFM) was implemented for the Forsmark repository site based on the final site descriptive model from surface based investigations. The discrete-feature conceptual model represents deformation zones, individual fractures, and other water-conducting features around a repository as discrete conductors surrounded by a rock matrix which, in the present study, is treated as impermeable. This approximation is reasonable for sites in crystalline rock which has very low permeability, apart from that which results from macroscopic fracturing. Models are constructed based on the geological and hydrogeological description of the sites and engineering designs. Hydraulic heads and flows through the network of water-conducting features are calculated by the finite-element method, and are used in turn to simulate migration of non-reacting solute by a particle-tracking method, in order to estimate the properties of pathways by which radionuclides could be released to the biosphere. Stochastic simulation is used to evaluate portions of the model that can only be characterized in statistical terms, since many water-conducting features within the model volume cannot be characterized deterministically. Chapter 2 describes the methodology by which discrete features are derived to represent water-conducting features around the hypothetical repository at Forsmark (including both natural features and features that result from the disturbance of excavation), and then assembled to produce a discrete-feature network model for numerical simulation of flow and transport. Chapter 3 describes how site-specific data and repository design are adapted to produce the discrete-feature model. Chapter 4 presents results of the calculations. These include utilization factors for deposition tunnels based on the emplacement criteria that have been set forth by the implementers, flow distributions to the deposition holes, and calculated properties of discharge paths as well as

Discrete-Feature Model Implementation of SDM-Site Forsmark

International Nuclear Information System (INIS)

Geier, Joel

2010-03-01

A discrete-feature model (DFM) was implemented for the Forsmark repository site based on the final site descriptive model from surface based investigations. The discrete-feature conceptual model represents deformation zones, individual fractures, and other water-conducting features around a repository as discrete conductors surrounded by a rock matrix which, in the present study, is treated as impermeable. This approximation is reasonable for sites in crystalline rock which has very low permeability, apart from that which results from macroscopic fracturing. Models are constructed based on the geological and hydrogeological description of the sites and engineering designs. Hydraulic heads and flows through the network of water-conducting features are calculated by the finite-element method, and are used in turn to simulate migration of non-reacting solute by a particle-tracking method, in order to estimate the properties of pathways by which radionuclides could be released to the biosphere. Stochastic simulation is used to evaluate portions of the model that can only be characterized in statistical terms, since many water-conducting features within the model volume cannot be characterized deterministically. Chapter 2 describes the methodology by which discrete features are derived to represent water-conducting features around the hypothetical repository at Forsmark (including both natural features and features that result from the disturbance of excavation), and then assembled to produce a discrete-feature network model for numerical simulation of flow and transport. Chapter 3 describes how site-specific data and repository design are adapted to produce the discrete-feature model. Chapter 4 presents results of the calculations. These include utilization factors for deposition tunnels based on the emplacement criteria that have been set forth by the implementers, flow distributions to the deposition holes, and calculated properties of discharge paths as well as

Discrete fracture network for the Forsmark site

Energy Technology Data Exchange (ETDEWEB)

Darcel, C. [Itasca Consultants, Ecully (France); Davy, P.; Bour, O.; Dreuzy, J.R. de [Geosciences, Rennes (France)

2006-08-15

In this report, we aim at defining a self-consistent method for analyzing the fracture patterns from boreholes, outcrops and lineaments. The objective was both to point out some variations in the fracture network parameters, and to define the global scaling fracture models that can encompass all the constraints brought by the different datasets. Although a full description of the DFN model variability is obviously fundamental for the future, we have put emphasis on the determination of mean parameters. The main parameters of the disc-shaped DFN model are the fracture size, orientations and spatial density distribution. The scaling model is defined as an extrapolation of existing i) observations at specific scales and ii) local fitting models to the whole range of scales. The range of possible models is restricted to the power-law scaling models. During the project we have put emphasize on the definition of the theory and methodology necessary to assess a sound comparison between data taken at different scales, with different techniques. Both 'local' and 'global' models have been investigated. Local models are linked exactly to the dataset they represent. Then, the global DFN models arise from the association of local models, different scales and different sample support shapes. Discrepancies between local and global model illustrate the variability associated to the DFN models. We define two possible Global Scaling Models (GSM). The first one is consistent with the scaling measured in the outcrops (Model A). Its scaling exponent is a{sub 3d}=3.5 (eq. to k{sub r}=2.5); it overestimates the fracture densities observed in the lineament maps. The second one assumes that both lineaments and outcrops belong to the same distribution model (Model B), which entails a scaling exponent a{sub 3d}=3.9 (eq. to k{sub r}=2.9). Both models have been tested by looking for the best consistency in the fracture density-dip relationships, between boreholes data at

Mathematical algorithm development and parametric studies with the GEOFRAC three-dimensional stochastic model of natural rock fracture systems

Science.gov (United States)

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.

New approach for simulating groundwater flow in discrete fracture network

Science.gov (United States)

Fang, H.; Zhu, J.

2017-12-01

In this study, we develop a new approach to calculate groundwater flowrate and hydraulic head distribution in two-dimensional discrete fracture network (DFN) where both laminar and turbulent flows co-exist in individual fractures. The cubic law is used to calculate hydraulic head distribution and flow behaviors in fractures where flow is laminar, while the Forchheimer's law is used to quantify turbulent flow behaviors. Reynolds number is used to distinguish flow characteristics in individual fractures. The combination of linear and non-linear equations is solved iteratively to determine flowrates in all fractures and hydraulic heads at all intersections. We examine potential errors in both flowrate and hydraulic head from the approach of uniform flow assumption. Applying the cubic law in all fractures regardless of actual flow conditions overestimates the flowrate when turbulent flow may exist while applying the Forchheimer's law indiscriminately underestimate the flowrate when laminar flows exist in the network. The contrast of apertures of large and small fractures in the DFN has significant impact on the potential errors of using only the cubic law or the Forchheimer's law. Both the cubic law and Forchheimer's law simulate similar hydraulic head distributions as the main difference between these two approaches lies in predicting different flowrates. Fracture irregularity does not significantly affect the potential errors from using only the cubic law or the Forchheimer's law if network configuration remains similar. Relative density of fractures does not significantly affect the relative performance of the cubic law and Forchheimer's law.

Modeling CO2 Storage in Fractured Reservoirs: Fracture-Matrix Interactions of Free-Phase and Dissolved CO2

Science.gov (United States)

Oldenburg, C. M.; Zhou, Q.; Birkholzer, J. T.

2017-12-01

The injection of supercritical CO2 (scCO2) in fractured reservoirs has been conducted at several storage sites. However, no site-specific dual-continuum modeling for fractured reservoirs has been reported and modeling studies have generally underestimated the fracture-matrix interactions. We developed a conceptual model for enhanced CO2 storage to take into account global scCO2 migration in the fracture continuum, local storage of scCO2 and dissolved CO2 (dsCO2) in the matrix continuum, and driving forces for scCO2 invasion and dsCO2 diffusion from fractures. High-resolution discrete fracture-matrix models were developed for a column of idealized matrix blocks bounded by vertical and horizontal fractures and for a km-scale fractured reservoir. The column-scale simulation results show that equilibrium storage efficiency strongly depends on matrix entry capillary pressure and matrix-matrix connectivity while the time scale to reach equilibrium is sensitive to fracture spacing and matrix flow properties. The reservoir-scale modeling results shows that the preferential migration of scCO2 through fractures is coupled with bulk storage in the rock matrix that in turn retards the fracture scCO2 plume. We also developed unified-form diffusive flux equations to account for dsCO2 storage in brine-filled matrix blocks and found solubility trapping is significant in fractured reservoirs with low-permeability matrix.

An efficient fully-implicit multislope MUSCL method for multiphase flow with gravity in discrete fractured media

Science.gov (United States)

Jiang, Jiamin; Younis, Rami M.

2017-06-01

The first-order methods commonly employed in reservoir simulation for computing the convective fluxes introduce excessive numerical diffusion leading to severe smoothing of displacement fronts. We present a fully-implicit cell-centered finite-volume (CCFV) framework that can achieve second-order spatial accuracy on smooth solutions, while at the same time maintain robustness and nonlinear convergence performance. A novel multislope MUSCL method is proposed to construct the required values at edge centroids in a straightforward and effective way by taking advantage of the triangular mesh geometry. In contrast to the monoslope methods in which a unique limited gradient is used, the multislope concept constructs specific scalar slopes for the interpolations on each edge of a given element. Through the edge centroids, the numerical diffusion caused by mesh skewness is reduced, and optimal second order accuracy can be achieved. Moreover, an improved smooth flux-limiter is introduced to ensure monotonicity on non-uniform meshes. The flux-limiter provides high accuracy without degrading nonlinear convergence performance. The CCFV framework is adapted to accommodate a lower-dimensional discrete fracture-matrix (DFM) model. Several numerical tests with discrete fractured system are carried out to demonstrate the efficiency and robustness of the numerical model.

Modelisation of transport in fractured media with a smeared fractures modeling approach: special focus on matrix diffusion process.

Science.gov (United States)

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

Simulation of water flow in fractured porous medium by using discretized virtual internal bond

Science.gov (United States)

Peng, Shujun; Zhang, Zhennan; Li, Chunfang; He, Guofu; Miao, Guoqing

2017-12-01

The discretized virtual internal bond (DVIB) is adopted to simulate the water flow in fractured porous medium. The intact porous medium is permeable because it contains numerous micro cracks and pores. These micro discontinuities construct a fluid channel network. The representative volume of this fluid channel network is modeled as a lattice bond cell with finite number of bonds in statistical sense. Each bond serves as a fluid channel. In fractured porous medium, many bond cells are cut by macro fractures. The conductivity of the fracture facet in a bond cell is taken over by the bonds parallel to the flow direction. The equivalent permeability and volumetric storage coefficient of a micro bond are calibrated based on the ideal bond cell conception, which makes it unnecessary to consider the detailed geometry of a specific element. Such parameter calibration method is flexible and applicable to any type of element. The accuracy check results suggest this method has a satisfying accuracy in both the steady and transient flow simulation. To simulate the massive fractures in rockmass, the bond cells intersected by fracture are assigned aperture values, which are assumed random numbers following a certain distribution law. By this method, any number of fractures can be implicitly incorporated into the background mesh, avoiding the setup of fracture element and mesh modification. The fracture aperture heterogeneity is well represented by this means. The simulation examples suggest that the present method is a feasible, simple and efficient approach to the numerical simulation of water flow in fractured porous medium.

Hydromechanical modeling of clay rock including fracture damage

Science.gov (United States)

Asahina, D.; Houseworth, J. E.; Birkholzer, J. T.

2012-12-01

Argillaceous rock typically acts as a flow barrier, but under certain conditions significant and potentially conductive fractures may be present. Fracture formation is well-known to occur in the vicinity of underground excavations in a region known as the excavation disturbed zone. Such problems are of particular importance for low-permeability, mechanically weak rock such as clays and shales because fractures can be relatively transient as a result of fracture self-sealing processes. Perhaps not as well appreciated is the fact that natural fractures can form in argillaceous rock as a result of hydraulic overpressure caused by phenomena such as disequlibrium compaction, changes in tectonic stress, and mineral dehydration. Overpressure conditions can cause hydraulic fracturing if the fluid pressure leads to tensile effective stresses that exceed the tensile strength of the material. Quantitative modeling of this type of process requires coupling between hydrogeologic processes and geomechanical processes including fracture initiation and propagation. Here we present a computational method for three-dimensional, hydromechanical coupled processes including fracture damage. Fractures are represented as discrete features in a fracture network that interact with a porous rock matrix. Fracture configurations are mapped onto an unstructured, three-dimensonal, Voronoi grid, which is based on a random set of spatial points. Discrete fracture networks (DFN) are represented by the connections of the edges of a Voronoi cells. This methodology has the advantage that fractures can be more easily introduced in response to coupled hydro-mechanical processes and generally eliminates several potential issues associated with the geometry of DFN and numerical gridding. A geomechanical and fracture-damage model is developed here using the Rigid-Body-Spring-Network (RBSN) numerical method. The hydrogelogic and geomechanical models share the same geometrical information from a 3D Voronoi

The Effect of Loading Rate on Hydraulic Fracturing in Synthetic Granite - a Discrete Element Study

Science.gov (United States)

Tomac, I.; Gutierrez, M.

2015-12-01

Hydraulic fracture initiation and propagation from a borehole in hard synthetic rock is modeled using the two dimensional Discrete Element Method (DEM). DEM uses previously established procedure for modeling the strength and deformation parameters of quasi-brittle rocks with the Bonded Particle Model (Itasca, 2004). A series of simulations of laboratory tests on granite in DEM serve as a reference for synthetic rock behavior. Fracturing is enabled by breaking parallel bonds between DEM particles as a result of the local stress state. Subsequent bond breakage induces fracture propagation during a time-stepping procedure. Hydraulic fracturing occurs when pressurized fluid induces hoop stresses around the wellbore which cause rock fracturing and serves for geo-reservoir permeability enhancement in oil, gas and geothermal industries. In DEM, a network of fluid pipes and reservoirs is used for mathematical calculation of fluid flow through narrow channels between DEM particles, where the hydro-mechanical coupling is fully enabled. The fluid flow calculation is superimposed with DEM stress-strain calculation at each time step. As a result, the fluid pressures during borehole pressurization in hydraulic fracturing, as well as, during the fracture propagation from the borehole, can be simulated. The objective of this study is to investigate numerically a hypothesis that fluid pressurization rate, or the fluid flow rate, influences upon character, shape and velocity of fracture propagation in rock. The second objective is to better understand and define constraints which are important for successful fracture propagation in quasi-brittle rock from the perspective of flow rate, fluid density, viscosity and compressibility relative to the rock physical properties. Results from this study indicate that not only too high fluid flow rates cause fracture arrest and multiple fracture branching from the borehole, but also that the relative compressibility of fracturing fluid and

Sensitivity analysis of a discrete fracture network model for performance assessment of Aberg

International Nuclear Information System (INIS)

Outters, N.; Shuttle, D.

2000-12-01

This report presents a sensitivity analysis of pathway simulations in a DFN model. The DFN model consists of two sets of stochastic fractures at different scales and the canister locations of a hypothetical repository layout. The hydrogeological base case model is defined by constant head boundary conditions on the edges of a 2000 x 2000 x 1000 m 3 block. The pathway analysis carried out by the program PAWorks provides pathway parameters (pathway length, pathway width, transport aperture, reactive surface area, pathway transmissivity), canister statistics (average number of pathways per canister, percentage of canister locations with pathways) and visualisation of pathways. The project provided the following results from the alternative cases: Case 1: Model with a 100 m thick fracture network at the repository scale instead of 50 m in the base case. The model is little sensitive to the increase of the thickness of the local fracture network. Case 2: Model including fracture networks where the mean size and size standard deviation is twice the ones used in the base case. The travel times to the biosphere is slightly shortened by increasing the fracture diameter. Case 3: Two models with alternative hydraulic boundary conditions: two different flux boundary conditions are tested instead of head boundary conditions in the base case. The advective travel time is shortened by changing the boundary conditions in both alternative cases; in some cases it is reduced to less than a year. Case 4: Study of alternative pathway search algorithms: the pathway search is here based on minimum travel time. The pathway search algorithm of PAWorks based on minimum travel time gives much more optimistic results than the base case where the maximum flow rate was used. The mean travel time is about 5000 years. Due to editorial reasons only a subset of all this information is treated in this report

A Two-Scale Reduced Model for Darcy Flow in Fractured Porous Media

KAUST Repository

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.

Introduction to numerical modeling of thermohydrologic flow in fractured rock masses

International Nuclear Information System (INIS)

Wang, J.S.Y.

1980-01-01

More attention is being given to the possibility of nuclear waste isolation in hard rock formations. The waste will generate heat which raises the temperature of the surrounding fractured rock masses and induces buoyancy flow and pressure change in the fluid. These effects introduce the potential hazard of radionuclides being carried to the biosphere, and affect the structure of a repository by stress changes in the rock formation. The thermohydrological and thermomechanical responses are determined by the fractures as well as the intact rock blocks. The capability of modeling fractured rock masses is essential to site characterization and repository evaluation. The fractures can be modeled either as a discrete system, taking into account the detailed fracture distributions, or as a continuum representing the spatial average of the fractures. A numerical model is characterized by the governing equations, the numerical methods, the computer codes, the validations, and the applications. These elements of the thermohydrological models are discussed. Along with the general review, some of the considerations in modeling fractures are also discussed. Some remarks on the research needs in modeling fractured rock mass conclude the paper

Modelling for the Stripa site characterization and validation drift inflow: prediction of flow through fractured rock

International Nuclear Information System (INIS)

Herbert, A.; Gale, J.; MacLeod, R.; Lanyon, G.

1991-12-01

We present our approach to predicting flow through a fractured rock site; the site characterization and validation region in the Stripa mine. Our approach is based on discrete fracture network modelling using the NAPSAC computer code. We describe the conceptual models and assumptions that we have used to interpret the geometry and flow properties of the fracture networks, from measurements at the site. These are used to investigate large scale properties of the network and we show that for flows on scales larger than about 10 m, porous medium approximation should be used. The porous medium groundwater flow code CFEST is used to predict the large scale flows through the mine and the SCV region. This, in turn, is used to provide boundary conditions for more detailed models, which predict the details of flow, using a discrete fracture network model, on scales of less than 10 m. We conclude that a fracture network approach is feasible and that it provides a better understanding of details of flow than conventional porous medium approaches and a quantification of the uncertainty associated with predictive flow modelling characterised from field measurement in fractured rock. (au)

The Predictive Capability of Conditioned Simulation of Discrete Fracture Networks using Structural and Hydraulic Data from the ONKALO Underground Research Facility, Finland

Science.gov (United States)

Williams, T. R. N.; Baxter, S.; Hartley, L.; Appleyard, P.; Koskinen, L.; Vanhanarkaus, O.; Selroos, J. O.; Munier, R.

2017-12-01

Discrete fracture network (DFN) models provide a natural analysis framework for rock conditions where flow is predominately through a series of connected discrete features. Mechanistic models to predict the structural patterns of networks are generally intractable due to inherent uncertainties (e.g. deformation history) and as such fracture characterisation typically involves empirical descriptions of fracture statistics for location, intensity, orientation, size, aperture etc. from analyses of field data. These DFN models are used to make probabilistic predictions of likely flow or solute transport conditions for a range of applications in underground resource and construction projects. However, there are many instances when the volumes in which predictions are most valuable are close to data sources. For example, in the disposal of hazardous materials such as radioactive waste, accurate predictions of flow-rates and network connectivity around disposal areas are required for long-term safety evaluation. The problem at hand is thus: how can probabilistic predictions be conditioned on local-scale measurements? This presentation demonstrates conditioning of a DFN model based on the current structural and hydraulic characterisation of the Demonstration Area at the ONKALO underground research facility. The conditioned realisations honour (to a required level of similarity) the locations, orientations and trace lengths of fractures mapped on the surfaces of the nearby ONKALO tunnels and pilot drillholes. Other data used as constraints include measurements from hydraulic injection tests performed in pilot drillholes and inflows to the subsequently reamed experimental deposition holes. Numerical simulations using this suite of conditioned DFN models provides a series of prediction-outcome exercises detailing the reliability of the DFN model to make local-scale predictions of measured geometric and hydraulic properties of the fracture system; and provides an understanding

Tuning Fractures With Dynamic Data

Science.gov (United States)

Yao, Mengbi; Chang, Haibin; Li, Xiang; Zhang, Dongxiao

2018-02-01

Flow in fractured porous media is crucial for production of oil/gas reservoirs and exploitation of geothermal energy. Flow behaviors in such media are mainly dictated by the distribution of fractures. Measuring and inferring the distribution of fractures is subject to large uncertainty, which, in turn, leads to great uncertainty in the prediction of flow behaviors. Inverse modeling with dynamic data may assist to constrain fracture distributions, thus reducing the uncertainty of flow prediction. However, inverse modeling for flow in fractured reservoirs is challenging, owing to the discrete and non-Gaussian distribution of fractures, as well as strong nonlinearity in the relationship between flow responses and model parameters. In this work, building upon a series of recent advances, an inverse modeling approach is proposed to efficiently update the flow model to match the dynamic data while retaining geological realism in the distribution of fractures. In the approach, the Hough-transform method is employed to parameterize non-Gaussian fracture fields with continuous parameter fields, thus rendering desirable properties required by many inverse modeling methods. In addition, a recently developed forward simulation method, the embedded discrete fracture method (EDFM), is utilized to model the fractures. The EDFM maintains computational efficiency while preserving the ability to capture the geometrical details of fractures because the matrix is discretized as structured grid, while the fractures being handled as planes are inserted into the matrix grids. The combination of Hough representation of fractures with the EDFM makes it possible to tune the fractures (through updating their existence, location, orientation, length, and other properties) without requiring either unstructured grids or regridding during updating. Such a treatment is amenable to numerous inverse modeling approaches, such as the iterative inverse modeling method employed in this study, which is

SITE-94. Discrete-feature modelling of the Aespoe site: 2. Development of the integrated site-scale model

International Nuclear Information System (INIS)

Geier, J.E.

1996-12-01

A 3-dimensional, discrete-feature hydrological model is developed. The model integrates structural and hydrologic data for the Aespoe site, on scales ranging from semi regional fracture zones to individual fractures in the vicinity of the nuclear waste canisters. Hydrologic properties of the large-scale structures are initially estimated from cross-hole hydrologic test data, and automatically calibrated by numerical simulation of network flow, and comparison with undisturbed heads and observed drawdown in selected cross-hole tests. The calibrated model is combined with a separately derived fracture network model, to yield the integrated model. This model is partly validated by simulation of transient responses to a long-term pumping test and a convergent tracer test, based on the LPT2 experiment at Aespoe. The integrated model predicts that discharge from the SITE-94 repository is predominantly via fracture zones along the eastern shore of Aespoe. Similar discharge loci are produced by numerous model variants that explore uncertainty with regard to effective semi regional boundary conditions, hydrologic properties of the site-scale structures, and alternative structural/hydrological interpretations. 32 refs

SITE-94. Discrete-feature modelling of the Aespoe site: 2. Development of the integrated site-scale model

Energy Technology Data Exchange (ETDEWEB)

Geier, J.E. [Golder Associates AB, Uppsala (Sweden)

1996-12-01

A 3-dimensional, discrete-feature hydrological model is developed. The model integrates structural and hydrologic data for the Aespoe site, on scales ranging from semi regional fracture zones to individual fractures in the vicinity of the nuclear waste canisters. Hydrologic properties of the large-scale structures are initially estimated from cross-hole hydrologic test data, and automatically calibrated by numerical simulation of network flow, and comparison with undisturbed heads and observed drawdown in selected cross-hole tests. The calibrated model is combined with a separately derived fracture network model, to yield the integrated model. This model is partly validated by simulation of transient responses to a long-term pumping test and a convergent tracer test, based on the LPT2 experiment at Aespoe. The integrated model predicts that discharge from the SITE-94 repository is predominantly via fracture zones along the eastern shore of Aespoe. Similar discharge loci are produced by numerous model variants that explore uncertainty with regard to effective semi regional boundary conditions, hydrologic properties of the site-scale structures, and alternative structural/hydrological interpretations. 32 refs.

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.

An element-based finite-volume method approach for naturally fractured compositional reservoir simulation

Energy Technology Data Exchange (ETDEWEB)

Marcondes, Francisco [Federal University of Ceara, Fortaleza (Brazil). Dept. of Metallurgical Engineering and Material Science], e-mail: marcondes@ufc.br; Varavei, Abdoljalil; Sepehrnoori, Kamy [The University of Texas at Austin (United States). Petroleum and Geosystems Engineering Dept.], e-mails: varavei@mail.utexas.edu, kamys@mail.utexas.edu

2010-07-01

An element-based finite-volume approach in conjunction with unstructured grids for naturally fractured compositional reservoir simulation is presented. In this approach, both the discrete fracture and the matrix mass balances are taken into account without any additional models to couple the matrix and discrete fractures. The mesh, for two dimensional domains, can be built of triangles, quadrilaterals, or a mix of these elements. However, due to the available mesh generator to handle both matrix and discrete fractures, only results using triangular elements will be presented. The discrete fractures are located along the edges of each element. To obtain the approximated matrix equation, each element is divided into three sub-elements and then the mass balance equations for each component are integrated along each interface of the sub-elements. The finite-volume conservation equations are assembled from the contribution of all the elements that share a vertex, creating a cell vertex approach. The discrete fracture equations are discretized only along the edges of each element and then summed up with the matrix equations in order to obtain a conservative equation for both matrix and discrete fractures. In order to mimic real field simulations, the capillary pressure is included in both matrix and discrete fracture media. In the implemented model, the saturation field in the matrix and discrete fractures can be different, but the potential of each phase in the matrix and discrete fracture interface needs to be the same. The results for several naturally fractured reservoirs are presented to demonstrate the applicability of the method. (author)

An evaluation of the active fracture concept with modeling unsaturated flow and transport in a fractured meter-sized block of rock

International Nuclear Information System (INIS)

Seol, Yongkoo; Kneafsey, Timothy J.; Ito, Kazumasa

2003-01-01

Numerical simulation is an effective and economical tool for optimally designing laboratory experiments and deriving practical experimental conditions. We executed a detailed numerical simulation study to examine the active fracture concept (AFC, Liu et al., 1998) using a cubic meter-sized block model. The numerical simulations for this study were performed by applying various experimental conditions, including different bottom flow boundaries, varying injection rates, and different fracture-matrix interaction (by increasing absolute matrix permeability at the fracture matrix boundary) for a larger fracture interaction under transient or balanced-state flow regimes. Two conceptual block models were developed based on different numerical approaches: a two-dimensional discrete-fracture-network model (DFNM) and a one-dimensional dual continuum model (DCM). The DFNM was used as a surrogate for a natural block to produce synthetic breakthrough curves of water and tracer concentration under transient or balanced-state conditions. The DCM is the approach typically used for the Yucca Mountain Project because of its computational efficiency. The AFC was incorporated into the DCM to capture heterogeneous flow patterns that occur in unsaturated fractured rocks. The simulation results from the DCM were compared with the results from the DFNM to determine whether the DCM could predict the water flow and tracer transport observed in the DFNM at the scale of the experiment. It was found that implementing the AFC in the DCM improved the prediction of unsaturated flow and that the flow and transport experiments with low injection rates in the DFNM were compared better with the AFC implemented DCM at the meter scale. However, the estimated AFC parameter varied from 0.38 to 1.0 with different flow conditions, suggesting that the AFC parameter was not a sufficient to fully capture the complexity of the flow processes in a one meter sized discrete fracture network

Numerical modelling of flow and transport in rough fractures

Directory of Open Access Journals (Sweden)

Scott Briggs

2014-12-01

Full Text Available Simulation of flow and transport through rough walled rock fractures is investigated using the lattice Boltzmann method (LBM and random walk (RW, respectively. The numerical implementation is developed and validated on general purpose graphic processing units (GPGPUs. Both the LBM and RW method are well suited to parallel implementation on GPGPUs because they require only next-neighbour communication and thus can reduce expenses. The LBM model is an order of magnitude faster on GPGPUs than published results for LBM simulations run on modern CPUs. The fluid model is verified for parallel plate flow, backward facing step and single fracture flow; and the RW model is verified for point-source diffusion, Taylor-Aris dispersion and breakthrough behaviour in a single fracture. Both algorithms place limitations on the discrete displacement of fluid or particle transport per time step to minimise the numerical error that must be considered during implementation.

Investigation of gas-oil gravity drainage in naturally fractured reservoirs using discrete fracture and matrix numerical model

International Nuclear Information System (INIS)

Bazr-Afkan, S.

2012-01-01

To simulate fluid flow in Naturally Fractured Reservoirs (NFRs), a new Descrete Fracture and Matrix (DFM) simulation technique is developed as a physically more realistic alternative to the dual continuum approach. This Finite-Element Centered Finite-Volume method (FECFVM) has the advantage over earlier FECFVM approaches that it honors saturation dicontinuities that can arise at material interfaces from the interplay of viscous, capillary and gravitational forces. By contrast with an earlier embedded-discontinuity DFEFVM method, the FECFVM achieves this without introducing additional degrees of freedom. It also allows to simulate capillary- and other fracture-matrix exchange processes using a lower dimensional representation of fractures, simplifying model construction and unstructured meshing as well as speeding up computations. A further step-up is obtained by solving the two-phase fluid-flow and saturation transport equations only on 'active elements'. This also diminishes round-off and truncation errors, reducing numerical diffusion during the solution of the transport equation. The FECFVM is verified by comparing IMPES operator-splitting sequential solutions with analytical ones, as well as benchmarking it against commercial reservoir simulators on simple geometries that these can represent. This testing confirms that my 2D FECFVM implementation simulates gravitational segregation, capillary redistribution, capillary barriers, and combinations thereof physically realistically, achieving (at least) first-order solution accuracy. Following this verification, the FECFVM is applied to study Gas-Oil Gravity Drainage (GOGD) process in cross-sectional models of layered NFRs. Here comparisons with dual continua simulations show that these do not capture a range of block-to-block effects, yielding over-optimistic drainage rates. Observations made on individual matrix blocks in the DFM simulations further reveal that their saturation evolution is at odds with the

Characterizing the influence of stress-induced microcracks on the laboratory strength and fracture development in brittle rocks using a finite-discrete element method-micro discrete fracture network FDEM-μDFN approach

Directory of Open Access Journals (Sweden)

Pooya Hamdi

2015-12-01

Full Text Available Heterogeneity is an inherent component of rock and may be present in different forms including mineral heterogeneity, geometrical heterogeneity, weak grain boundaries and micro-defects. Microcracks are usually observed in crystalline rocks in two forms: natural and stress-induced; the amount of stress-induced microcracking increases with depth and in-situ stress. Laboratory results indicate that the physical properties of rocks such as strength, deformability, P-wave velocity and permeability are influenced by increase in microcrack intensity. In this study, the finite-discrete element method (FDEM is used to model microcrack heterogeneity by introducing into a model sample sets of microcracks using the proposed micro discrete fracture network (μDFN approach. The characteristics of the microcracks required to create μDFN models are obtained through image analyses of thin sections of Lac du Bonnet granite adopted from published literature. A suite of two-dimensional laboratory tests including uniaxial, triaxial compression and Brazilian tests is simulated and the results are compared with laboratory data. The FDEM-μDFN models indicate that micro-heterogeneity has a profound influence on both the mechanical behavior and resultant fracture pattern. An increase in the microcrack intensity leads to a reduction in the strength of the sample and changes the character of the rock strength envelope. Spalling and axial splitting dominate the failure mode at low confinement while shear failure is the dominant failure mode at high confinement. Numerical results from simulated compression tests show that microcracking reduces the cohesive component of strength alone, and the frictional strength component remains unaffected. Results from simulated Brazilian tests show that the tensile strength is influenced by the presence of microcracks, with a reduction in tensile strength as microcrack intensity increases. The importance of microcrack heterogeneity in

Hierarchical multiscale modeling for flows in fractured media using generalized multiscale finite element method

KAUST Repository

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.

Expected lifetime numbers, risks, and burden of osteoporotic fractures for 50-year old Chinese women: a discrete event simulation incorporating FRAX.

Science.gov (United States)

Jiang, Yawen; Ni, Weiyi

2016-11-01

This work was undertaken to provide an estimation of expected lifetime numbers, risks, and burden of fractures for 50-year-old Chinese women. A discrete event simulation model was developed to simulate the lifetime fractures of 50-year-old Chinese women at average risk of osteoporotic fracture. Main events in the model included hip fracture, clinical vertebral fracture, wrist fracture, humerus fracture, and other fracture. Fracture risks were calculated using the FRAX ® tool. Simulations of 50-year-old Chinese women without fracture risks were also carried out as a comparison to determine the burden of fractures. A 50-year-old Chinese woman at average risk of fracture is expected to experience 0.135 (95 % CI: 0.134-0.137) hip fractures, 0.120 (95 % CI: 0.119-0.122) clinical vertebral fractures, 0.095 (95 % CI: 0.094-0.096) wrist fractures, 0.079 (95 % CI: 0.078-0.080) humerus fractures, and 0.407 (95 % CI: 0.404-0.410) other fractures over the remainder of her life. The residual lifetime risk of any fracture, hip fracture, clinical vertebral fracture, wrist fracture, humerus fracture, and other fracture for a 50-year-old Chinese woman is 37.36, 11.77, 10.47, 8.61, 7.30, and 27.80 %, respectively. The fracture-attributable excess quality-adjusted life year (QALY) loss and lifetime costs are estimated at 0.11 QALYs (95 % CI: 0.00-0.22 QALYs) and US $714.61 (95 % CI: US $709.20-720.02), totaling a net monetary benefit loss of US $1,104.43 (95 % CI: US $904.09-1,304.78). Chinese women 50 years of age are at high risk of osteoporotic fracture, and the expected economic and quality-of-life burden attributable to osteoporotic fractures among Chinese women is substantial.

Structural and geochemical techniques for the hydrogeological characterisation and stochastic modelling of fractured media

International Nuclear Information System (INIS)

Vela, A.; Elorza, F.J.; Florez, F.; Paredes, C.; Mazadiego, L.; Llamas, J.F.; Perez, E.; Vives, L.; Carrera, J.; Munoz, A.; De Vicente, G.; Casquet, C.

1999-01-01

Safety analysis of radioactive waste storage systems require fractured rock studies. The performance assessment studies of this type of problems include the development of radionuclide flow and transport models to predict the evolution of possible contaminants released from the repository to the biosphere. The methodology developed in the HIDROBAP project and some results obtained with its application in El Berrocal granite batholith are presented. It integrates modern tools belonging to different disciplines. A Discrete Fracture Network model (DFT) was selected to simulate the fractured medium and a 3D finite element flow and transport model that includes the inverse problem techniques has been coupled to the DFT model to simulate the water movement trough the fracture network system. Preliminary results show that this integrated methodology can be very useful for the hydrogeological characterisation of rock fractured media. (author)

Development of a formalism of movable cellular automaton method for numerical modeling of fracture of heterogeneous elastic-plastic materials

Directory of Open Access Journals (Sweden)

S. Psakhie

2013-04-01

Full Text Available A general approach to realization of models of elasticity, plasticity and fracture of heterogeneous materials within the framework of particle-based numerical methods is proposed in the paper. It is based on building many-body forces of particle interaction, which provide response of particle ensemble correctly conforming to the response (including elastic-plastic behavior and fracture of simulated solids. Implementation of proposed approach within particle-based methods is demonstrated by the example of the movable cellular automaton (MCA method, which integrates the possibilities of particle-based discrete element method (DEM and cellular automaton methods. Emergent advantages of the developed approach to formulation of many-body interaction are discussed. Main of them are its applicability to various realizations of the concept of discrete elements and a possibility to realize various rheological models (including elastic-plastic or visco-elastic-plastic and models of fracture to study deformation and fracture of solid-phase materials and media. Capabilities of particle-based modeling of heterogeneous solids are demonstrated by the problem of simulation of deformation and fracture of particle-reinforced metal-ceramic composites.

Computational models of the hydrodynamics of fractured-porous media

International Nuclear Information System (INIS)

Grandi, G.M.

1989-01-01

The prediction of the flow pattern in fractured-porous media has great importance in the assessment of the local thermohydrological effects of the siting of a nuclear waste repository, among many other technological applications. Computational models must be used due to the complexity of the different phenomena involved which restricts the use of analytical techniques. A new numerical method, based on the boundary-fitted finite-difference technique, is presented in this thesis. The boundaries are external (the boundary of the physical domain), and internal (which correspond to the fracture network). The inclusion of the discrete fracture representation in the volume that represents the porous medium is the difference between the usual approach and the present one. The numerical model has been used in the prediction of the flow pattern in several internationally recognized verification cases and to hypothetical problems of our interest. The results obtained proved that the numerical approach considered gives accurate and reliable predictions of the hydrodynamics of fractured-porous media, allowing its use for the above mentioned studies. (Author) [es

Hydraulic tomography of discrete networks of conduits and fractures in a karstic aquifer by using a deterministic inversion algorithm

Science.gov (United States)

Fischer, P.; Jardani, A.; Lecoq, N.

2018-02-01

In this paper, we present a novel inverse modeling method called Discrete Network Deterministic Inversion (DNDI) for mapping the geometry and property of the discrete network of conduits and fractures in the karstified aquifers. The DNDI algorithm is based on a coupled discrete-continuum concept to simulate numerically water flows in a model and a deterministic optimization algorithm to invert a set of observed piezometric data recorded during multiple pumping tests. In this method, the model is partioned in subspaces piloted by a set of parameters (matrix transmissivity, and geometry and equivalent transmissivity of the conduits) that are considered as unknown. In this way, the deterministic optimization process can iteratively correct the geometry of the network and the values of the properties, until it converges to a global network geometry in a solution model able to reproduce the set of data. An uncertainty analysis of this result can be performed from the maps of posterior uncertainties on the network geometry or on the property values. This method has been successfully tested for three different theoretical and simplified study cases with hydraulic responses data generated from hypothetical karstic models with an increasing complexity of the network geometry, and of the matrix heterogeneity.

Modeling of flow in faulted and fractured media

Energy Technology Data Exchange (ETDEWEB)

Oeian, Erlend

2004-03-01

The work on this thesis has been done as part of a collaborative and inter disciplinary effort to improve the understanding of oil recovery mechanisms in fractured reservoirs. This project has been organized as a Strategic University Program (SUP) at the University of Bergen, Norway. The complex geometries of fractured reservoirs combined with flow of several fluid phases lead to difficult mathematical and numerical problems. In an effort to try to decrease the gap between the geological description and numerical modeling capabilities, new techniques are required. Thus, the main objective has been to improve the ATHENA flow simulator and utilize it within a fault modeling context. Specifically, an implicit treatment of the advection dominated mass transport equations within a domain decomposition based local grid refinement framework has been implemented. Since large computational tasks may arise, the implicit formulation has also been included in a parallel version of the code. Within the current limits of the simulator, appropriate up scaling techniques has also been considered. Part I of this thesis includes background material covering the basic geology of fractured porous media, the mathematical model behind the in-house flow simulator ATHENA and the additions implemented to approach simulation of flow through fractured and faulted porous media. In Part II, a set of research papers stemming from Part I is presented. A brief outline of the thesis follows below. In Chapt. 1 important aspects of the geological description and physical parameters of fractured and faulted porous media is presented. Based on this the scope of this thesis is specified having numerical issues and consequences in mind. Then, in Chapt. 2, the mathematical model and discretizations in the flow simulator is given followed by the derivation of the implicit mass transport formulation. In order to be fairly self-contained, most of the papers in Part II also includes the mathematical model

Modeling of flow in faulted and fractured media

Energy Technology Data Exchange (ETDEWEB)

Oeian, Erlend

2004-03-01

The work on this thesis has been done as part of a collaborative and inter disciplinary effort to improve the understanding of oil recovery mechanisms in fractured reservoirs. This project has been organized as a Strategic University Program (SUP) at the University of Bergen, Norway. The complex geometries of fractured reservoirs combined with flow of several fluid phases lead to difficult mathematical and numerical problems. In an effort to try to decrease the gap between the geological description and numerical modeling capabilities, new techniques are required. Thus, the main objective has been to improve the ATHENA flow simulator and utilize it within a fault modeling context. Specifically, an implicit treatment of the advection dominated mass transport equations within a domain decomposition based local grid refinement framework has been implemented. Since large computational tasks may arise, the implicit formulation has also been included in a parallel version of the code. Within the current limits of the simulator, appropriate up scaling techniques has also been considered. Part I of this thesis includes background material covering the basic geology of fractured porous media, the mathematical model behind the in-house flow simulator ATHENA and the additions implemented to approach simulation of flow through fractured and faulted porous media. In Part II, a set of research papers stemming from Part I is presented. A brief outline of the thesis follows below. In Chapt. 1 important aspects of the geological description and physical parameters of fractured and faulted porous media is presented. Based on this the scope of this thesis is specified having numerical issues and consequences in mind. Then, in Chapt. 2, the mathematical model and discretizations in the flow simulator is given followed by the derivation of the implicit mass transport formulation. In order to be fairly self-contained, most of the papers in Part II also includes the mathematical model

Anomalous transport in disordered fracture networks: Spatial Markov model for dispersion with variable injection modes

Science.gov (United States)

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.

The Stochastic-Deterministic Transition in Discrete Fracture Network Models and its Implementation in a Safety Assessment Application by Means of Conditional Simulation

Science.gov (United States)

Selroos, J. O.; Appleyard, P.; Bym, T.; Follin, S.; Hartley, L.; Joyce, S.; Munier, R.

2015-12-01

In 2011 the Swedish Nuclear Fuel and Waste Management Company (SKB) applied for a license to start construction of a final repository for spent nuclear fuel at Forsmark in Northern Uppland, Sweden. The repository is to be built at approximately 500 m depth in crystalline rock. A stochastic, discrete fracture network (DFN) concept was chosen for interpreting the surface-based (incl. boreholes) data, and for assessing the safety of the repository in terms of groundwater flow and flow pathways to and from the repository. Once repository construction starts, also underground data such as tunnel pilot borehole and tunnel trace data will become available. It is deemed crucial that DFN models developed at this stage honors the mapped structures both in terms of location and geometry, and in terms of flow characteristics. The originally fully stochastic models will thus increase determinism towards the repository. Applying the adopted probabilistic framework, predictive modeling to support acceptance criteria for layout and disposal can be performed with the goal of minimizing risks associated with the repository. This presentation describes and illustrates various methodologies that have been developed to condition stochastic realizations of fracture networks around underground openings using borehole and tunnel trace data, as well as using hydraulic measurements of inflows or hydraulic interference tests. The methodologies, implemented in the numerical simulators ConnectFlow and FracMan/MAFIC, are described in some detail, and verification tests and realistic example cases are shown. Specifically, geometric and hydraulic data are obtained from numerical synthetic realities approximating Forsmark conditions, and are used to test the constraining power of the developed methodologies by conditioning unconditional DFN simulations following the same underlying fracture network statistics. Various metrics are developed to assess how well the conditional simulations compare to

Using the discrete element method to simulate brittle fracture in the indentation of a silica glass with a blunt indenter

International Nuclear Information System (INIS)

Andre, Damien; Iordanoff, Ivan; Charles, Jean-luc; Jebahi, Mohamed; Neauport, Jerome

2013-01-01

The mechanical behavior of materials is usually simulated by a continuous mechanics approach. However, non-continuous phenomena such as multi-fracturing cannot be accurately simulated using a continuous description. The discrete element method (DEM) naturally accounts for discontinuities and is therefore a good alternative to the continuum approach. This work uses a discrete element model based on interaction given by 3D beam model. This model has proved to correctly simulate the elastic properties at the macroscopic scale. The simulation of brittle cracks is now tackled. This goal is attained by computing a failure criterion based on an equivalent hydrostatic stress. This microscopic criterion is then calibrated to fit experimental values of the macroscopic failure stress. Then, the simulation results are compared to experimental results of indentation tests in which a spherical indenter is used to load a silica glass, which is considered to be a perfectly brittle elastic material. (authors)

Numerical modeling of the dynamic behavior of structures under impact with a discrete elements / finite elements coupling

International Nuclear Information System (INIS)

Rousseau, J.

2009-07-01

That study focuses on concrete structures submitted to impact loading and is aimed at predicting local damage in the vicinity of an impact zone as well as the global response of the structure. The Discrete Element Method (DEM) seems particularly well suited in this context for modeling fractures. An identification process of DEM material parameters from macroscopic data (Young's modulus, compressive and tensile strength, fracture energy, etc.) will first be presented for the purpose of enhancing reproducibility and reliability of the simulation results with DE samples of various sizes. Then, a particular interaction, between concrete and steel elements, was developed for the simulation of reinforced concrete. The discrete elements method was validated on quasi-static and dynamic tests carried out on small samples of concrete and reinforced concrete. Finally, discrete elements were used to simulate impacts on reinforced concrete slabs in order to confront the results with experimental tests. The modeling of a large structure by means of DEM may lead to prohibitive computation times. A refined discretization becomes required in the vicinity of the impact, while the structure may be modeled using a coarse FE mesh further from the impact area, where the material behaves elastically. A coupled discrete-finite element approach is thus proposed: the impact zone is modeled by means of DE and elastic FE are used on the rest of the structure. An existing method for 3D finite elements was extended to shells. This new method was then validated on many quasi-static and dynamic tests. The proposed approach is then applied to an impact on a concrete structure in order to validate the coupled method and compare computation times. (author)

Investigation on the Productivity Behaviour in Deformable Heterogeneous Fractured Reservoirs

DEFF Research Database (Denmark)

Kadeethum, Teeratorn; Salimzadeh, Saeed; Nick, Hamid

reasons for this reduction. Discrete fracture and matrix (DFM) modelling is selected in this investigation because of its ability to represent fracture behaviours more realistically. Moreover, it has become a preferential method for modelling flow in fractured formations for the past decade (Bisdom et al...

SITE-94. Discrete-feature modelling of the Aespoe Site: 3. Predictions of hydrogeological parameters for performance assessment

International Nuclear Information System (INIS)

Geier, J.E.

1996-12-01

A 3-dimensional, discrete-feature hydrological model is developed. The model integrates structural and hydrologic data for the Aespoe site, on scales ranging from semi regional fracture zones to individual fractures in the vicinity of the nuclear waste canisters. Predicted parameters for the near field include fracture spacing, fracture aperture, and Darcy velocity at each of forty canister deposition holes. Parameters for the far field include discharge location, Darcy velocity, effective longitudinal dispersion coefficient and head gradient, flow porosity, and flow wetted surface, for each canister source that discharges to the biosphere. Results are presented in the form of statistical summaries for a total of 42 calculation cases, which treat a set of 25 model variants in various combinations. The variants for the SITE-94 Reference Case model address conceptual and parametric uncertainty related to the site-scale hydrogeologic model and its properties, the fracture network within the repository, effective semi regional boundary conditions for the model, and the disturbed-rock zone around the repository tunnels and shafts. Two calculation cases simulate hydrologic conditions that are predicted to occur during future glacial episodes. 30 refs

Modelling of Radionuclide Transport by Groundwater Motion in Fractured Bedrock for Performance Assessment Purposes

International Nuclear Information System (INIS)

Woerman, Anders; Shulan Xu

2003-10-01

Field data of physical properties in heterogeneous crystalline bedrock, like fracture zones, fracture connectivity, matrix porosity and fracture aperture, is associated with uncertainty that can have a significant impact on the analysis of solute transport in fractured rock. The purpose of this study is to develop a performance assessment (PA) model for analyses of radionuclide transport in the geosphere, in which the model takes into account both the effect of heterogeneities of hydrological and geochemical rock properties. By using a travel time description of radionuclide transport in rock fractures, we decompose the transport problem into a one-dimensional mass transfer problem along a distribution of transport pathways and a multi-dimensional flow problem in the fractured bedrock. The hydraulic/flow problem is solved based on a statistical discrete-fracture model (DFM) that represents the network of fractures around the repository and in the surrounding geosphere. A Monte Carlo technique reflects the fact that the representation of the fracture network is uncertain. If the flow residence time PDF exhibits multiple peaks or in another way shows a more erratic hydraulic response on the network scale, the three-dimensional travel time approach is superior to a one-dimensional transport modeling. Examples taken from SITE 94, a study performed by the Swedish Nuclear Power Inspectorate, showed that such cases can be found in safety assessments based on site data. The solute transport is formulated based on partial, differential equations and perturbations (random spatial variability in bedrock properties) are introduced in the coefficients to reflect an uncertainty of the exact appearance of the bedrock associated with the discrete data collection. The combined approach for water flow and solute transport, thereby, recognises an uncertainty in our knowledge in both 1) bedrock properties along individual pathways and 2) the distribution of pathways. Solutions to the

Insights to Engineered Geothermal System Performance Using Gringarten-Witherspoon-Ohnishi Analytical Solutions and Fracture Network Models

Science.gov (United States)

Doe, T.; McLaren, R.; Finilla, A.

2017-12-01

An enduring legacy of Paul Witherspoon and his students and colleagues has been both the development of geothermal energy and the bases of modern fractured-rock hydrogeology. One of the seminal contributions to the geothermal field was Gringarten, Witherspoon, and Ohnishi's analytical models for enhanced geothermal systems. Although discrete fracture network (DFN) modeling developed somewhat independently in the late 1970s, Paul Witherspoon's foresight in promoting underground in situ testing at the Stripa Mine in Sweden was a major driver in Lawrence Berkeley Laboratory's contributions to its development.This presentation looks extensions of Gringarten's analytical model into discrete fracture network modeling as a basis for providing further insights into the challenges and opportunities of engineered geothermal systems. The analytical solution itself has many insightful applications beyond those presented in the original paper. The definition of dimensionless time by itself shows that thermal breakthrough has a second power dependence on surface area and on flow rate. The fracture intensity also plays a strong role, as it both increases the surface area and decrease his flow rate per fracture. The improvement of EGS performance with fracture intensity reaches a limit where thermal depletion of the rock lags only slightly behind the thermal breakthrough of cold water in the fracture network.Simple network models, which couple a DFN generator (FracMan) with a hydrothermally coupled flow solver (HydroGeoSphere) expand on Gringarten's concepts to show that realistic heterogeneity of spacing and transmissivity significantly degrades EGS performance. EGS production in networks of stimulated fractures initially follows Gringarten's type curves, with a later deviation is the smaller rock blocks thermally deplete and the entire stimulated volume acts as a single sink. Three-dimensional models of EGS performance show the critical importance of the relative magnitudes of

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

Efficient and robust compositional two-phase reservoir simulation in fractured media

Science.gov (United States)

Zidane, A.; Firoozabadi, A.

2015-12-01

Compositional and compressible two-phase flow in fractured media has wide applications including CO2 injection. Accurate simulations are currently based on the discrete fracture approach using the cross-flow equilibrium model. In this approach the fractures and a small part of the matrix blocks are combined to form a grid cell. The major drawback is low computational efficiency. In this work we use the discrete-fracture approach to model the fractures where the fracture entities are described explicitly in the computational domain. We use the concept of cross-flow equilibrium in the fractures (FCFE). This allows using large matrix elements in the neighborhood of the fractures. We solve the fracture transport equations implicitly to overcome the Courant-Freidricks-Levy (CFL) condition in the small fracture elements. Our implicit approach is based on calculation of the derivative of the molar concentration of component i in phase (cαi ) with respect to the total molar concentration (ci ) at constant volume V and temperature T. This contributes to significant speed up of the code. The hybrid mixed finite element method (MFE) is used to solve for the velocity in both the matrix and the fractures coupled with the discontinuous Galerkin (DG) method to solve the species transport equations in the matrix, and a finite volume (FV) discretization in the fractures. In large scale problems the proposed approach is orders of magnitude faster than the existing models.

Water Inrush Analysis of the Longmen Mountain Tunnel Based on a 3D Simulation of the Discrete Fracture Network

Science.gov (United States)

Xiong, Ziming; Wang, Mingyang; Shi, ShaoShuai; Xia, YuanPu; Lu, Hao; Bu, Lin

2017-12-01

The construction of tunnels and underground engineering in China has developed rapidly in recent years in both the number and the length of tunnels. However, with the development of tunnel construction technology, risk assessment of the tunnels has become increasingly important. Water inrush is one of the most important causes of engineering accidents worldwide, resulting in considerable economic and environmental losses. Accordingly, water inrush prediction is important for ensuring the safety of tunnel construction. Therefore, in this study, we constructed a three-dimensional discrete network fracture model using the Monte Carlo method first with the basic data from the engineering geological map of the Longmen Mountain area, the location of the Longmen Mountain tunnel. Subsequently, we transformed the discrete fracture networks into a pipe network model. Next, the DEM of the study area was analysed and a submerged analysis was conducted to determine the water storage area. Finally, we attempted to predict the water inrush along the Longmen Mountain tunnel based on the Darcy flow equation. Based on the contrast of water inrush between the proposed approach, groundwater dynamics and precipitation infiltration method, we conclude the following: the water inflow determined using the groundwater dynamics simulation results are basically consistent with those in the D2K91+020 to D2K110+150 mileage. Specifically, in the D2K91+020 to D2K94+060, D2K96+440 to D2K98+100 and other sections of the tunnel, the simulated and measured results are in close agreement and show that this method is effective. In general, we can predict the water inflow in the area of the Longmen Mountain tunnel based on the existing fracture joint parameters and the hydrogeological data of the Longmen Mountain area, providing a water inrush simulation and guiding the tunnel excavation and construction stages.

Study of Anti-Sliding Stability of a Dam Foundation Based on the Fracture Flow Method with 3D Discrete Element Code

Directory of Open Access Journals (Sweden)

Chong Shi

2017-10-01

Full Text Available Fractured seepage is an important factor affecting the interface stability of rock mass. It is closely related to fracture properties and hydraulic conditions. In this study, the law of seepage in a single fracture surface based on modified cubic law is described, and the three-dimensional discrete element method is used to simulate the dam foundation structure of the Capulin San Pablo (Costa Rica hydropower station. The effect of construction joints and developed structure on dam stability is studied, and its permeability law and sliding stability are also evaluated. It is found that the hydraulic-mechanical coupling with strength reduction method in DEM is more appropriate to use to study the seepage-related problems of fractured rock mass, which considers practical conditions, such as the roughness of and the width of fracture. The strength reduction method provides a more accurate safety factor of dam when considering the deformation coordination with bedrocks. It is an important method with which to study the stability of seepage conditions in complex structures. The discrete method also provided an effective and reasonable way of determining seepage control measures.

Discrete/Finite Element Modelling of Rock Cutting with a TBM Disc Cutter

Science.gov (United States)

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.

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

Simulation of a multistage fractured horizontal well in a water-bearing tight fractured gas reservoir under non-Darcy flow

Science.gov (United States)

Zhang, Rui-Han; Zhang, Lie-Hui; Wang, Rui-He; Zhao, Yu-Long; Huang, Rui

2018-06-01

Reservoir development for unconventional resources such as tight gas reservoirs is in increasing demand due to the rapid decline of production in conventional reserves. Compared with conventional reservoirs, fluid flow in water-bearing tight gas reservoirs is subject to more nonlinear multiphase flow and gas slippage in nano/micro matrix pores because of the strong collisions between rock and gas molecules. Economic gas production from tight gas reservoirs depends on extensive application of water-based hydraulic fracturing of horizontal wells, associated with non-Darcy flow at a high flow rate, geomechanical stress sensitivity of un-propped natural fractures, complex flow geometry and multiscale heterogeneity. How to efficiently and accurately predict the production performance of a multistage fractured horizontal well (MFHW) is challenging. In this paper, a novel multicontinuum, multimechanism, two-phase simulator is established based on unstructured meshes and the control volume finite element method to analyze the production performance of MFHWs. The multiple interacting continua model and discrete fracture model are coupled to integrate the unstimulated fractured reservoir, induced fracture networks (stimulated reservoir volumes, SRVs) and irregular discrete hydraulic fractures. Several simulations and sensitivity analyses are performed with the developed simulator for determining the key factors affecting the production performance of MFHWs. Two widely applied fracturing models, classic hydraulic fracturing which generates long double-wing fractures and the volumetric fracturing aimed at creating large SRVs, are compared to identify which of them can make better use of tight gas reserves.

SITE-94. Discrete-feature modelling of the Aespoe site: 4. Source data and detailed analysis procedures

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.

SITE-94. Discrete-feature modelling of the Aespoe site: 4. Source data and detailed analysis procedures

International Nuclear Information System (INIS)

Geier, J.E.

1996-12-01

Specific procedures and source data are described for the construction and application of discrete-feature hydrological models for the vicinity of Aespoe. Documentation is given for all major phases of the work, including: Statistical analyses to develop and validate discrete-fracture network models, Preliminary evaluation, construction, and calibration of the site-scale model based on the SITE-94 structural model of Aespoe, Simulation of multiple realizations of the integrated model, and variations, to predict groundwater flow, and Evaluation of near-field and far-field parameters for performance assessment calculations. Procedures are documented in terms of the computer batch files and executable scripts that were used to perform the main steps in these analyses, to provide for traceability of results that are used in the SITE-94 performance assessment calculations. 43 refs

Well test analysis in fractured media

Energy Technology Data Exchange (ETDEWEB)

Karasaki, K.

1986-04-01

In this study the behavior of fracture systems under well test conditions and methods for analyzing well test data from fractured media are investigated. Several analytical models are developed to be used for analyzing well test data from fractured media. Numerical tools that may be used to simulate fluid flow in fractured media are also presented. Three types of composite models for constant flux tests are investigated. Several slug test models with different geometric conditions that may be present in fractured media are also investigated. A finite element model that can simulate transient fluid flow in fracture networks is used to study the behavior of various two-dimensional fracture systems under well test conditions. A mesh generator that can be used to model mass and heat flow in a fractured-porous media is presented. This model develops an explicit solution in the porous matrix as well as in the discrete fractures. Because the model does not require the assumptions of the conventional double porosity approach, it may be used to simulate cases where double porosity models fail.

The Fracture Mechanical Markov Chain Fatigue Model Compared with Empirical Data

DEFF Research Database (Denmark)

Gansted, L.; Brincker, Rune; Hansen, Lars Pilegaard

The applicability of the FMF-model (Fracture Mechanical Markov Chain Fatigue Model) introduced in Gansted, L., R. Brincker and L. Pilegaard Hansen (1991) is tested by simulations and compared with empirical data. Two sets of data have been used, the Virkler data (aluminium alloy) and data...... established at the Laboratory of Structural Engineering at Aalborg University, the AUC-data, (mild steel). The model, which is based on the assumption, that the crack propagation process can be described by a discrete Space Markov theory, is applicable to constant as well as random loading. It is shown...

Integrated workflow for characterizing and modeling fracture network in unconventional reservoirs using microseismic data

Science.gov (United States)

Ayatollahy Tafti, Tayeb

We develop a new method for integrating information and data from different sources. We also construct a comprehensive workflow for characterizing and modeling a fracture network in unconventional reservoirs, using microseismic data. The methodology is based on combination of several mathematical and artificial intelligent techniques, including geostatistics, fractal analysis, fuzzy logic, and neural networks. The study contributes to scholarly knowledge base on the characterization and modeling fractured reservoirs in several ways; including a versatile workflow with a novel objective functions. Some the characteristics of the methods are listed below: 1. The new method is an effective fracture characterization procedure estimates different fracture properties. Unlike the existing methods, the new approach is not dependent on the location of events. It is able to integrate all multi-scaled and diverse fracture information from different methodologies. 2. It offers an improved procedure to create compressional and shear velocity models as a preamble for delineating anomalies and map structures of interest and to correlate velocity anomalies with fracture swarms and other reservoir properties of interest. 3. It offers an effective way to obtain the fractal dimension of microseismic events and identify the pattern complexity, connectivity, and mechanism of the created fracture network. 4. It offers an innovative method for monitoring the fracture movement in different stages of stimulation that can be used to optimize the process. 5. Our newly developed MDFN approach allows to create a discrete fracture network model using only microseismic data with potential cost reduction. It also imposes fractal dimension as a constraint on other fracture modeling approaches, which increases the visual similarity between the modeled networks and the real network over the simulated volume.

Discrete Feature Approach for Heterogeneous Reservoir Production Enhancement

Energy Technology Data Exchange (ETDEWEB)

Dershowitz, William S.; Cladouhos, Trenton

2001-09-06

This progress report describes activities during the period January 1, 1999 to June 30, 1999. Work was carried out on 21 tasks. The major activity during the reporting period was the development and preliminary application of discrete fracture network (DFN) models for Stoney Point, South Oregon Basin, and North Oregon Basins project study sites. In addition, research was carried out on analysis algorithms for discrete future orientation.

Modeling flow and transport in fracture networks using graphs

Science.gov (United States)

Karra, S.; O'Malley, D.; Hyman, J. D.; Viswanathan, H. S.; Srinivasan, G.

2018-03-01

Fractures form the main pathways for flow in the subsurface within low-permeability rock. For this reason, accurately predicting flow and transport in fractured systems is vital for improving the performance of subsurface applications. Fracture sizes in these systems can range from millimeters to kilometers. Although modeling flow and transport using the discrete fracture network (DFN) approach is known to be more accurate due to incorporation of the detailed fracture network structure over continuum-based methods, capturing the flow and transport in such a wide range of scales is still computationally intractable. Furthermore, if one has to quantify uncertainty, hundreds of realizations of these DFN models have to be run. To reduce the computational burden, we solve flow and transport on a graph representation of a DFN. We study the accuracy of the graph approach by comparing breakthrough times and tracer particle statistical data between the graph-based and the high-fidelity DFN approaches, for fracture networks with varying number of fractures and degree of heterogeneity. Due to our recent developments in capabilities to perform DFN high-fidelity simulations on fracture networks with large number of fractures, we are in a unique position to perform such a comparison. We show that the graph approach shows a consistent bias with up to an order of magnitude slower breakthrough when compared to the DFN approach. We show that this is due to graph algorithm's underprediction of the pressure gradients across intersections on a given fracture, leading to slower tracer particle speeds between intersections and longer travel times. We present a bias correction methodology to the graph algorithm that reduces the discrepancy between the DFN and graph predictions. We show that with this bias correction, the graph algorithm predictions significantly improve and the results are very accurate. The good accuracy and the low computational cost, with O (104) times lower times than

Fracture in quasi-brittle materials: experimental and numerical approach for the determination of an incremental model with generalized variables

International Nuclear Information System (INIS)

Morice, Erwan

2014-01-01

Fracture in quasi-brittle materials, such as ceramics or concrete, can be represented schematically by series of events of nucleation and coalescence of micro-cracks. Modeling this process is an important challenge for the reliability and life prediction of concrete structures, in particular the prediction of the permeability of damaged structures. A multi-scale approach is proposed. The global behavior is modeled within the fracture mechanics framework and the local behavior is modeled by the discrete element method. An approach was developed to condense the non linear behavior of the mortar. A model reduction technic is used to extract the relevant information from the discrete elements method. To do so, the velocity field is partitioned into mode I, II, linear and non-linear components, each component being characterized by an intensity factor and a fixed spatial distribution. The response of the material is hence condensed in the evolution of the intensity factors, used as non-local variables. A model was also proposed to predict the behavior of the crack for proportional and non-proportional mixed mode I+II loadings. An experimental campaign was finally conducted to characterize the fatigue and fracture behavior of mortar. The results show that fatigue crack growth can be of significant importance. The experimental velocity field determined, in the crack tip region, by DIC, were analyzed using the same technic as that used for analyzing the fields obtained by the discrete element method showing consistent results. (author)

Evaluation of Different Modeling Approaches to Simulate Contaminant Transport in a Fractured Limestone Aquifer

Science.gov (United States)

Mosthaf, K.; Rosenberg, L.; Balbarini, N.; Broholm, M. M.; Bjerg, P. L.; Binning, P. J.

2014-12-01

It is important to understand the fate and transport of contaminants in limestone aquifers because they are a major drinking water resource. This is challenging because they are highly heterogeneous; with micro-porous grains, flint inclusions, and being heavily fractured. Several modeling approaches have been developed to describe contaminant transport in fractured media, such as the discrete fracture (with various fracture geometries), equivalent porous media (with and without anisotropy), and dual porosity models. However, these modeling concepts are not well tested for limestone geologies. Given available field data and model purpose, this paper therefore aims to develop, examine and compare modeling approaches for transport of contaminants in fractured limestone aquifers. The model comparison was conducted for a contaminated site in Denmark, where a plume of a dissolved contaminant (PCE) has migrated through a fractured limestone aquifer. Multilevel monitoring wells have been installed at the site and available data includes information on spill history, extent of contamination, geology and hydrogeology. To describe the geology and fracture network, data from borehole logs was combined with an analysis of heterogeneities and fractures from a nearby excavation (analog site). Methods for translating the geological information and fracture mapping into each of the model concepts were examined. Each model was compared with available field data, considering both model fit and measures of model suitability. An analysis of model parameter identifiability and sensitivity is presented. Results show that there is considerable difference between modeling approaches, and that it is important to identify the right one for the actual scale and model purpose. A challenge in the use of field data is the determination of relevant hydraulic properties and interpretation of aqueous and solid phase contaminant concentration sampling data. Traditional water sampling has a bias

Fracture network modeling and GoldSim simulation support

International Nuclear Information System (INIS)

Sugita, Kenichiro; Dershowitz, William

2003-01-01

During Heisei-14, Golder Associates provided support for JNC Tokai through data analysis and simulation of the MIU Underground Rock Laboratory, participation in Task 6 of the Aespoe Task Force on Modelling of Groundwater Flow and Transport, and analysis of repository safety assessment technologies including cell networks for evaluation of the disturbed rock zone (DRZ) and total systems performance assessment (TSPA). MIU Underground Rock Laboratory support during H-14 involved discrete fracture network (DFN) modelling in support of the Multiple Modelling Project (MMP) and the Long Term Pumping Test (LPT). Golder developed updated DFN models for the MIU site, reflecting updated analyses of fracture data. Golder also developed scripts to support JNC simulations of flow and transport pathways within the MMP. Golder supported JNC participation in Task 6 of the Aespoe Task Force on Modelling of Groundwater Flow and Transport during H-14. Task 6A and 6B compared safety assessment (PA) and experimental time scale simulations along a pipe transport pathway. Task 6B2 extended Task 6B simulations from 1-D to 2-D. For Task 6B2, Golder carried out single fracture transport simulations on a wide variety of generic heterogeneous 2D fractures using both experimental and safety assessment boundary conditions. The heterogeneous 2D fractures were implemented according to a variety of in plane heterogeneity patterns. Multiple immobile zones were considered including stagnant zones, infillings, altered wall rock, and intact rock. During H-14, JNC carried out extensive studies of the distributed rock zone (DRZ) surrounding repository tunnels and drifts. Golder supported this activity be evaluating the calculation time necessary for simulating a reference heterogeneous DRZ cell network for a range of computational strategies. To support the development of JNC's total system performance assessment (TSPA) strategy, Golder carried out a review of the US DOE Yucca Mountain Project TSPA. This

Sensitivity of using blunt and sharp crack models in elastic-plastic fracture mechanics

International Nuclear Information System (INIS)

Pan, Y.C.; Kennedy, J.M.; Marchertas, A.H.

1985-01-01

J-integral values are calculated for both the blunt (smeared) crack and the sharp (discrete) crack models in elastic-plastic fracture mechanics problems involving metallic materials. A sensitivity study is performed to show the relative strengths and weaknesses of the two cracking models. It is concluded that the blunt crack model is less dependent on the orientation of the mesh. For the mesh which is in line with the crack direction, however, the sharp crack model is less sensitive to the mesh size. Both models yield reasonable results for a properly discretized finite-element mesh. A subcycling technique is used in this study in the explicit integration scheme so that large time steps can be used for the coarse elements away from the crack tip. The savings of computation time by this technique are reported. 6 refs., 9 figs

Statistics of modelled conductive fractures based on Laxemar and Forsmark. Site descriptive model data

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

Statistics of modelled conductive fractures based on Laxemar and Forsmark. Site descriptive model data

International Nuclear Information System (INIS)

Stigsson, Martin

2009-12-01

The objectives of this report is to investigate the frequency of fractures assumed to be water conductive, i.e. open or partly open and directly or indirectly connected to a source. Also the distribution of total transmissivity in 100 m and 20 m horizontal sections and 8 m vertical sections is calculated. The report is only intended to serve as input to the SER, Site Engineering Report, at Laxemar and Forsmark. The input data for the analyses is taken, as is, from the Discrete Fracture Network sections in published reports. No evaluation that the model parameters are appropriate for the task or sensitivity analysis is performed. The tunnels and deposition holes are modelled as scanlines which is a very coarse approximation, but it may give some rough estimation of the frequency of the water bearing features, especially for the larger ones, and the total transmissivity in a section

Ductile fracture theories for pressurised pipes and containers

Science.gov (United States)

Erdogan, F.

1976-01-01

Two mechanisms of fracture are distinguished. Plane strain fractures occur in materials which do not undergo large-scale plastic deformations prior to and during a possible fracture deformation. Plane stress or high energy fractures are generally accompanied by large inelastic deformations. Theories for analyzing plane stress are based on the concepts of critical crack opening stretch, K(R) characterization, J-integral, and plastic instability. This last is considered in some detail. The ductile fracture process involves fracture initiation followed by a stable crack growth and the onset of unstable fracture propagation. The ductile fracture propagation process may be characterized by either a multiparameter (discrete) model, or some type of a resistance curve which may be considered as a continuous model expressed graphically. These models are studied and an alternative model is also proposed for ductile fractures which cannot be modeled as progressive crack growth phenomena.

Understanding hydraulic fracturing: a multi-scale problem

Science.gov (United States)

Hyman, J. D.; Jiménez-Martínez, J.; Viswanathan, H. S.; Carey, J. W.; Porter, M. L.; Rougier, E.; Karra, S.; Kang, Q.; Frash, L.; Chen, L.; Lei, Z.; O’Malley, D.; Makedonska, N.

2016-01-01

Despite the impact that hydraulic fracturing has had on the energy sector, the physical mechanisms that control its efficiency and environmental impacts remain poorly understood in part because the length scales involved range from nanometres to kilometres. We characterize flow and transport in shale formations across and between these scales using integrated computational, theoretical and experimental efforts/methods. At the field scale, we use discrete fracture network modelling to simulate production of a hydraulically fractured well from a fracture network that is based on the site characterization of a shale gas reservoir. At the core scale, we use triaxial fracture experiments and a finite-discrete element model to study dynamic fracture/crack propagation in low permeability shale. We use lattice Boltzmann pore-scale simulations and microfluidic experiments in both synthetic and shale rock micromodels to study pore-scale flow and transport phenomena, including multi-phase flow and fluids mixing. A mechanistic description and integration of these multiple scales is required for accurate predictions of production and the eventual optimization of hydrocarbon extraction from unconventional reservoirs. Finally, we discuss the potential of CO2 as an alternative working fluid, both in fracturing and re-stimulating activities, beyond its environmental advantages. This article is part of the themed issue ‘Energy and the subsurface’. PMID:27597789

Handbook on modelling for discrete optimization

CERN Document Server

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...

Numerical simulation of hydraulic fracturing and associated microseismicity using finite-discrete element method

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.

Fully Coupled Geomechanics and Discrete Flow Network Modeling of Hydraulic Fracturing for Geothermal Applications

Energy Technology Data Exchange (ETDEWEB)

Fu, P; Johnson, S M; Hao, Y; Carrigan, C R

2011-01-18

The primary objective of our current research is to develop a computational test bed for evaluating borehole techniques to enhance fluid flow and heat transfer in enhanced geothermal systems (EGS). Simulating processes resulting in hydraulic fracturing and/or the remobilization of existing fractures, especially the interaction between propagating fractures and existing fractures, represents a critical goal of our project. To this end, we are continuing to develop a hydraulic fracturing simulation capability within the Livermore Distinct Element Code (LDEC), a combined FEM/DEM analysis code with explicit solid-fluid mechanics coupling. LDEC simulations start from an initial fracture distribution which can be stochastically generated or upscaled from the statistics of an actual fracture distribution. During the hydraulic stimulation process, LDEC tracks the propagation of fractures and other modifications to the fracture system. The output is transferred to the Non-isothermal Unsaturated Flow and Transport (NUFT) code to capture heat transfer and flow at the reservoir scale. This approach is intended to offer flexibility in the types of analyses we can perform, including evaluating the effects of different system heterogeneities on the heat extraction rate as well as seismicity associated with geothermal operations. This paper details the basic methodology of our approach. Two numerical examples showing the capability and effectiveness of our simulator are also presented.

Role of geomechanically grown fractures on dispersive transport in heterogeneous geological formations

NARCIS (Netherlands)

Nick, H.M.; Paluszny, A.; Blunt, M.J.; Matthai, S.K.

2011-01-01

A second order in space accurate implicit scheme for time-dependent advection-dispersion equations and a discrete fracture propagation model are employed to model solute transport in porous media.We study the impact of the fractures on mass transport and dispersion. To model flowand transport,

Discrete ellipsoidal statistical BGK model and Burnett equations

Science.gov (United States)

Zhang, Yu-Dong; Xu, Ai-Guo; Zhang, Guang-Cai; Chen, Zhi-Hua; Wang, Pei

2018-06-01

A new discrete Boltzmann model, the discrete ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) model, is proposed to simulate nonequilibrium compressible flows. Compared with the original discrete BGK model, the discrete ES-BGK has a flexible Prandtl number. For the discrete ES-BGK model in the Burnett level, two kinds of discrete velocity model are introduced and the relations between nonequilibrium quantities and the viscous stress and heat flux in the Burnett level are established. The model is verified via four benchmark tests. In addition, a new idea is introduced to recover the actual distribution function through the macroscopic quantities and their space derivatives. The recovery scheme works not only for discrete Boltzmann simulation but also for hydrodynamic ones, for example, those based on the Navier-Stokes or the Burnett equations.

Discrete fracture network code development

Energy Technology Data Exchange (ETDEWEB)

Dershowitz, W.; Doe, T.; Shuttle, D.; Eiben, T.; Fox, A.; Emsley, S.; Ahlstrom, E. [Golder Associates Inc., Redmond, Washington (United States)

1999-02-01

This report presents the results of fracture flow model development and application performed by Golder Associates Inc. during the fiscal year 1998. The primary objective of the Golder Associates work scope was to provide theoretical and modelling support to the JNC performance assessment effort in fiscal year 2000. In addition, Golder Associates provided technical support to JNC for the Aespoe project. Major efforts for performance assessment support included extensive flow and transport simulations, analysis of pathway simplification, research on excavation damage zone effects, software verification and cross-verification, and analysis of confidence bounds on Monte Carlo simulations. In addition, a Fickian diffusion algorithm was implemented for Laplace Transform Galerkin solute transport. Support for the Aespoe project included predictive modelling of sorbing tracer transport in the TRUE-1 rock block, analysis of 1 km geochemical transport pathways for Task 5', and data analysis and experimental design for the TRUE Block Scale experiment. Technical information about Golder Associates support to JNC is provided in the appendices to this report. (author)

Predictions of first passage times in sparse discrete fracture networks using graph-based reductions

Science.gov (United States)

Hyman, J.; Hagberg, A.; Srinivasan, G.; Mohd-Yusof, J.; Viswanathan, H. S.

2017-12-01

We present a graph-based methodology to reduce the computational cost of obtaining first passage times through sparse fracture networks. We derive graph representations of generic three-dimensional discrete fracture networks (DFNs) using the DFN topology and flow boundary conditions. Subgraphs corresponding to the union of the k shortest paths between the inflow and outflow boundaries are identified and transport on their equivalent subnetworks is compared to transport through the full network. The number of paths included in the subgraphs is based on the scaling behavior of the number of edges in the graph with the number of shortest paths. First passage times through the subnetworks are in good agreement with those obtained in the full network, both for individual realizations and in distribution. Accurate estimates of first passage times are obtained with an order of magnitude reduction of CPU time and mesh size using the proposed method.

Streaming Potential Modeling to Understand the Identification of Hydraulically Active Fractures and Fracture-Matrix Fluid Interactions Using the Self-Potential Method

Science.gov (United States)

Jougnot, D.; Roubinet, D.; Linde, N.; Irving, J.

2016-12-01

Quantifying fluid flow in fractured media is a critical challenge in a wide variety of research fields and applications. To this end, geophysics offers a variety of tools that can provide important information on subsurface physical properties in a noninvasive manner. Most geophysical techniques infer fluid flow by data or model differencing in time or space (i.e., they are not directly sensitive to flow occurring at the time of the measurements). An exception is the self-potential (SP) method. When water flows in the subsurface, an excess of charge in the pore water that counterbalances electric charges at the mineral-pore water interface gives rise to a streaming current and an associated streaming potential. The latter can be measured with the SP technique, meaning that the method is directly sensitive to fluid flow. Whereas numerous field experiments suggest that the SP method may allow for the detection of hydraulically active fractures, suitable tools for numerically modeling streaming potentials in fractured media do not exist. Here, we present a highly efficient two-dimensional discrete-dual-porosity approach for solving the fluid-flow and associated self-potential problems in fractured domains. Our approach is specifically designed for complex fracture networks that cannot be investigated using standard numerical methods due to computational limitations. We then simulate SP signals associated with pumping conditions for a number of examples to show that (i) accounting for matrix fluid flow is essential for accurate SP modeling and (ii) the sensitivity of SP to hydraulically active fractures is intimately linked with fracture-matrix fluid interactions. This implies that fractures associated with strong SP amplitudes are likely to be hydraulically conductive, attracting fluid flow from the surrounding matrix.

A discrete control model of PLANT

Science.gov (United States)

Mitchell, C. M.

1985-01-01

A model of the PLANT system using the discrete control modeling techniques developed by Miller is described. Discrete control models attempt to represent in a mathematical form how a human operator might decompose a complex system into simpler parts and how the control actions and system configuration are coordinated so that acceptable overall system performance is achieved. Basic questions include knowledge representation, information flow, and decision making in complex systems. The structure of the model is a general hierarchical/heterarchical scheme which structurally accounts for coordination and dynamic focus of attention. Mathematically, the discrete control model is defined in terms of a network of finite state systems. Specifically, the discrete control model accounts for how specific control actions are selected from information about the controlled system, the environment, and the context of the situation. The objective is to provide a plausible and empirically testable accounting and, if possible, explanation of control behavior.

Computer model for ductile fracture

International Nuclear Information System (INIS)

Moran, B.; Reaugh, J. E.

1979-01-01

A computer model is described for predicting ductile fracture initiation and propagation. The computer fracture model is calibrated by simple and notched round-bar tension tests and a precracked compact tension test. The model is used to predict fracture initiation and propagation in a Charpy specimen and compare the results with experiments. The calibrated model provides a correlation between Charpy V-notch (CVN) fracture energy and any measure of fracture toughness, such as J/sub Ic/. A second simpler empirical correlation was obtained using the energy to initiate fracture in the Charpy specimen rather than total energy CVN, and compared the results with the empirical correlation of Rolfe and Novak

Discrete modeling considerations in multiphase fluid dynamics

International Nuclear Information System (INIS)

Ransom, V.H.; Ramshaw, J.D.

1988-01-01

The modeling of multiphase flows play a fundamental role in light water reactor safety. The main ingredients in our discrete modeling Weltanschauung are the following considerations: (1) Any physical model must be cast into discrete form for a digital computer. (2) The usual approach of formulating models in differential form and then discretizing them is potentially hazardous. It may be preferable to formulate the model in discrete terms from the outset. (3) Computer time and storage constraints limit the resolution that can be employed in practical calculations. These limits effectively define the physical phenomena, length scales, and time scales which cannot be directly represented in the calculation and therefore must be modeled. This information should be injected into the model formulation process at an early stage. (4) Practical resolution limits are generally so coarse that traditional convergence and truncation-error analyses become irrelevant. (5) A discrete model constitutes a reduced description of a physical system, from which fine-scale details are eliminated. This elimination creates a statistical closure problem. Methods from statistical physics may therefore be useful in the formulation of discrete models. In the present paper we elaborate on these themes and illustrate them with simple examples. 48 refs

Simulation of two-phase flow in horizontal fracture networks with numerical manifold method

Science.gov (United States)

Ma, G. W.; Wang, H. D.; Fan, L. F.; Wang, B.

2017-10-01

The paper presents simulation of two-phase flow in discrete fracture networks with numerical manifold method (NMM). Each phase of fluids is considered to be confined within the assumed discrete interfaces in the present method. The homogeneous model is modified to approach the mixed fluids. A new mathematical cover formation for fracture intersection is proposed to satisfy the mass conservation. NMM simulations of two-phase flow in a single fracture, intersection, and fracture network are illustrated graphically and validated by the analytical method or the finite element method. Results show that the motion status of discrete interface significantly depends on the ratio of mobility of two fluids rather than the value of the mobility. The variation of fluid velocity in each fracture segment and the driven fluid content are also influenced by the ratio of mobility. The advantages of NMM in the simulation of two-phase flow in a fracture network are demonstrated in the present study, which can be further developed for practical engineering applications.

Model of T-Type Fracture in Coal Fracturing and Analysis of Influence Factors of Fracture Morphology

Directory of Open Access Journals (Sweden)

Yuwei Li

2018-05-01

Full Text Available Special T-type fractures can be formed when coal is hydraulically fractured and there is currently no relevant theoretical model to calculate and describe them. This paper first establishes the height calculation model of vertical fractures in multi-layered formations and deduces the stress intensity factor (SIF at the upper and lower sides of the fracture in the process of vertical fracture extension. Combined with the fracture tip stress analysis method of fracture mechanics theory, the horizontal bedding is taken into account for tensile and shear failure, and the critical mechanical conditions for the formation of horizontal fracture in coal are obtained. Finally, the model of T-type fracture in coal fracturing is established, and it is verified by fracturing simulation experiments. The model calculation result shows that the increase of vertical fracture height facilitates the increase of horizontal fracture length. The fracture toughness of coal has a significant influence on the length of horizontal fracture and there is a threshold. When the fracture toughness is less than the threshold, the length of horizontal fracture remains unchanged, otherwise, the length of horizontal fracture increases rapidly with the increase of fracture toughness. When the shear strength of the interface between the coalbed and the interlayer increases, the length of the horizontal fracture of the T-type fracture rapidly decreases.

An Efficient Mesh Generation Method for Fractured Network System Based on Dynamic Grid Deformation

Directory of Open Access Journals (Sweden)

Shuli Sun

2013-01-01

Full Text Available Meshing quality of the discrete model influences the accuracy, convergence, and efficiency of the solution for fractured network system in geological problem. However, modeling and meshing of such a fractured network system are usually tedious and difficult due to geometric complexity of the computational domain induced by existence and extension of fractures. The traditional meshing method to deal with fractures usually involves boundary recovery operation based on topological transformation, which relies on many complicated techniques and skills. This paper presents an alternative and efficient approach for meshing fractured network system. The method firstly presets points on fractures and then performs Delaunay triangulation to obtain preliminary mesh by point-by-point centroid insertion algorithm. Then the fractures are exactly recovered by local correction with revised dynamic grid deformation approach. Smoothing algorithm is finally applied to improve the quality of mesh. The proposed approach is efficient, easy to implement, and applicable to the cases of initial existing fractures and extension of fractures. The method is successfully applied to modeling of two- and three-dimensional discrete fractured network (DFN system in geological problems to demonstrate its effectiveness and high efficiency.

3-D Reservoir and Stochastic Fracture Network Modeling for Enhanced Oil Recovery, Circle Ridge Phosphoria/Tensleep Reservoir, and River Reservation, Arapaho and Shoshone Tribes, Wyoming

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.

Identification of parameters of discrete-continuous models

International Nuclear Information System (INIS)

Cekus, Dawid; Warys, Pawel

2015-01-01

In the paper, the parameters of a discrete-continuous model have been identified on the basis of experimental investigations and formulation of optimization problem. The discrete-continuous model represents a cantilever stepped Timoshenko beam. The mathematical model has been formulated and solved according to the Lagrange multiplier formalism. Optimization has been based on the genetic algorithm. The presented proceeding’s stages make the identification of any parameters of discrete-continuous systems possible

Identification of parameters of discrete-continuous models

Energy Technology Data Exchange (ETDEWEB)

Cekus, Dawid, E-mail: cekus@imipkm.pcz.pl; Warys, Pawel, E-mail: warys@imipkm.pcz.pl [Institute of Mechanics and Machine Design Foundations, Czestochowa University of Technology, Dabrowskiego 73, 42-201 Czestochowa (Poland)

2015-03-10

In the paper, the parameters of a discrete-continuous model have been identified on the basis of experimental investigations and formulation of optimization problem. The discrete-continuous model represents a cantilever stepped Timoshenko beam. The mathematical model has been formulated and solved according to the Lagrange multiplier formalism. Optimization has been based on the genetic algorithm. The presented proceeding’s stages make the identification of any parameters of discrete-continuous systems possible.

Thermo-hydro-mechanical modelling of fractured rock masses application to radioactive wastes storage

International Nuclear Information System (INIS)

Vuillod, E.

1995-01-01

This work belongs to the Decovalex project (international cooperative project for the development of coupled models and their validation against experiments in nuclear waste isolation) of thermo-hydro-mechanical (THM) modeling of fractured rock massifs inside which high level radioactive waste disposal sites are simulated. The mathematical laws controlling the behaviour of the environment are resolved analytically in the case of a continuous environment (definition of an equivalent environment) and numerically if the environment is discontinuous (modeling of joints behaviour). The coupled THM models strongly influence the behaviour of a model. Modeling performed with the UDEC code shows the importance of HM couplings depending on whether the calculations are made in permanent or transient regime, and the influence of the loading path in the case of TM modeling. The geometry of fractures also influences the behaviour of the model. Studying the connexity of a fractures network allows to determine its degree of homogeneity. The comparison between two methods, continuous environment and discontinuous environment, has been carried out by determining the permeability tensor and the stress-deformation relations on fractured test-samples. It shows the differences in behaviour between an homogenized environment and a discrete environment. Finally two exercises of THM modeling of radioactive waste disposal sites illustrate the researches carried out. A far field model has permitted to compare the results obtained with calculation codes using different logics. The second model, a near field one, focusses more on the importance played by fracturing on the behaviour of the massif. The high density of the reference network has required some mathematical developments, in order to determine the representative equivalent volume (continuous approaches), and some mathematical analyses, to correctly simplify the environment (discontinuous approaches). These methods and analyses are

CHARACTERIZATION OF IN-SITU STRESS AND PERMEABILITY IN FRACTURED RESERVOIRS

Energy Technology Data Exchange (ETDEWEB)

Daniel R. Burns; M. Nafi Toksoz

2004-07-19

Expanded details and additional results are presented on two methods for estimating fracture orientation and density in subsurface reservoirs from scattered seismic wavefield signals. In the first, fracture density is estimated from the wavenumber spectra of the integrated amplitudes of the scattered waves as a function of offset in pre-stack data. Spectral peaks correctly identified the 50m, 35m, and 25m fracture spacings from numerical model data using a 40Hz source wavelet. The second method, referred to as the Transfer Function-Scattering Index Method, is based upon observations from 3D finite difference modeling that regularly spaced, discrete vertical fractures impart a ringing coda-type signature to any seismic energy that is transmitted through or reflected off of them. This coda energy is greatest when the acquisition direction is parallel to the fractures, the seismic wavelengths are tuned to the fracture spacing, and when the fractures have low stiffness. The method uses surface seismic reflection traces to derive a transfer function, which quantifies the change in an apparent source wavelet propagating through a fractured interval. The transfer function for an interval with low scattering will be more spike-like and temporally compact. The transfer function for an interval with high scattering will ring and be less temporally compact. A Scattering Index is developed based on a time lag weighting of the transfer function. When a 3D survey is acquired with a full range of azimuths, the Scattering Index allows the identification of subsurface areas with high fracturing and the orientation (or strike) of those fractures. The method was calibrated with model data and then applied to field data from a fractured reservoir giving results that agree with known field measurements. As an aid to understanding the scattered wavefield seen in finite difference models, a series of simple point scatterers was used to create synthetic seismic shot records collected over

Discrete dispersion models and their Tweedie asymptotics

DEFF Research Database (Denmark)

Jørgensen, Bent; Kokonendji, Célestin C.

2016-01-01

The paper introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The equidispersed Poisson model has a special place in this ap......The paper introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The equidispersed Poisson model has a special place...... in this approach, whereas several overdispersed discrete distributions, such as the Neyman Type A, Pólya-Aeppli, negative binomial and Poisson-inverse Gaussian, turn out to be Poisson-Tweedie factorial dispersion models with power dispersion functions, analogous to ordinary Tweedie exponential dispersion models...... with power variance functions. Using the factorial cumulant generating function as tool, we introduce a dilation operation as a discrete analogue of scaling, generalizing binomial thinning. The Poisson-Tweedie factorial dispersion models are closed under dilation, which in turn leads to a Poisson...

Modelling of 3D fractured geological systems - technique and application

Science.gov (United States)

Cacace, M.; Scheck-Wenderoth, M.; Cherubini, Y.; Kaiser, B. O.; Bloecher, G.

2011-12-01

All rocks in the earth's crust are fractured to some extent. Faults and fractures are important in different scientific and industry fields comprising engineering, geotechnical and hydrogeological applications. Many petroleum, gas and geothermal and water supply reservoirs form in faulted and fractured geological systems. Additionally, faults and fractures may control the transport of chemical contaminants into and through the subsurface. Depending on their origin and orientation with respect to the recent and palaeo stress field as well as on the overall kinematics of chemical processes occurring within them, faults and fractures can act either as hydraulic conductors providing preferential pathways for fluid to flow or as barriers preventing flow across them. The main challenge in modelling processes occurring in fractured rocks is related to the way of describing the heterogeneities of such geological systems. Flow paths are controlled by the geometry of faults and their open void space. To correctly simulate these processes an adequate 3D mesh is a basic requirement. Unfortunately, the representation of realistic 3D geological environments is limited by the complexity of embedded fracture networks often resulting in oversimplified models of the natural system. A technical description of an improved method to integrate generic dipping structures (representing faults and fractures) into a 3D porous medium is out forward. The automated mesh generation algorithm is composed of various existing routines from computational geometry (e.g. 2D-3D projection, interpolation, intersection, convex hull calculation) and meshing (e.g. triangulation in 2D and tetrahedralization in 3D). All routines have been combined in an automated software framework and the robustness of the approach has been tested and verified. These techniques and methods can be applied for fractured porous media including fault systems and therefore found wide applications in different geo-energy related

Fluid transfers in fractured media: scale effects

International Nuclear Information System (INIS)

Bour, Olivier

1996-01-01

As there has been a growing interest in the study of fluid circulations in fractured media for the last fifteen years, for example for projects of underground storage of different waste types, or to improve water resources, or for exploitation of underground oil products or geothermal resources, this research thesis first gives a large overview of the modelling and transport properties of fractured media. He presents the main notions related to fluid transfers in fractured media (structures of fracture networks, hydraulic properties of fractured media), and the various adopted approaches (the effective medium theory, the percolation theory, double porosity models, deterministic discrete fracture models, equivalent discontinuous model, fractal models), and outlines the originality of the approach developed in this research: scale change, conceptual hypotheses, methodology, tools). The second part addresses scale rules in fracture networks: presentation of fracture networks (mechanical aspects, statistical analysis), distribution of fracture lengths and of fracture networks, length-position relationship, modelling attempt, lessons learned and consequences in terms of hydraulic and mechanical properties, and of relationship between length distribution and fractal dimension. The third part proposes two articles published by the author and addressing the connectivity properties of fracture networks. The fifth chapter reports the application to natural media. It contains an article on the application of percolation theory to 2D natural fracture networks, and reports information collected on a site [fr

On discrete models of space-time

International Nuclear Information System (INIS)

Horzela, A.; Kempczynski, J.; Kapuscik, E.; Georgia Univ., Athens, GA; Uzes, Ch.

1992-02-01

Analyzing the Einstein radiolocation method we come to the conclusion that results of any measurement of space-time coordinates should be expressed in terms of rational numbers. We show that this property is Lorentz invariant and may be used in the construction of discrete models of space-time different from the models of the lattice type constructed in the process of discretization of continuous models. (author)

Coupled hydro-thermo-mechanical modeling of hydraulic fracturing in quasi-brittle rocks using BPM-DEM

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.

Bioremediation in fractured rock: 1. Modeling to inform design, monitoring, and expectations

Science.gov (United States)

Tiedeman, Claire; Shapiro, Allen M.; Hsieh, Paul A.; Imbrigiotta, Thomas; Goode, Daniel J.; Lacombe, Pierre; DeFlaun, Mary F.; Drew, Scott R.; Johnson, Carole D.; Williams, John H.; Curtis, Gary P.

2018-01-01

Field characterization of a trichloroethene (TCE) source area in fractured mudstones produced a detailed understanding of the geology, contaminant distribution in fractures and the rock matrix, and hydraulic and transport properties. Groundwater flow and chemical transport modeling that synthesized the field characterization information proved critical for designing bioremediation of the source area. The planned bioremediation involved injecting emulsified vegetable oil and bacteria to enhance the naturally occurring biodegradation of TCE. The flow and transport modeling showed that injection will spread amendments widely over a zone of lower‐permeability fractures, with long residence times expected because of small velocities after injection and sorption of emulsified vegetable oil onto solids. Amendments transported out of this zone will be diluted by groundwater flux from other areas, limiting bioremediation effectiveness downgradient. At nearby pumping wells, further dilution is expected to make bioremediation effects undetectable in the pumped water. The results emphasize that in fracture‐dominated flow regimes, the extent of injected amendments cannot be conceptualized using simple homogeneous models of groundwater flow commonly adopted to design injections in unconsolidated porous media (e.g., radial diverging or dipole flow regimes). Instead, it is important to synthesize site characterization information using a groundwater flow model that includes discrete features representing high‐ and low‐permeability fractures. This type of model accounts for the highly heterogeneous hydraulic conductivity and groundwater fluxes in fractured‐rock aquifers, and facilitates designing injection strategies that target specific volumes of the aquifer and maximize the distribution of amendments over these volumes.

Current density and continuity in discretized models

International Nuclear Information System (INIS)

Boykin, Timothy B; Luisier, Mathieu; Klimeck, Gerhard

2010-01-01

Discrete approaches have long been used in numerical modelling of physical systems in both research and teaching. Discrete versions of the Schroedinger equation employing either one or several basis functions per mesh point are often used by senior undergraduates and beginning graduate students in computational physics projects. In studying discrete models, students can encounter conceptual difficulties with the representation of the current and its divergence because different finite-difference expressions, all of which reduce to the current density in the continuous limit, measure different physical quantities. Understanding these different discrete currents is essential and requires a careful analysis of the current operator, the divergence of the current and the continuity equation. Here we develop point forms of the current and its divergence valid for an arbitrary mesh and basis. We show that in discrete models currents exist only along lines joining atomic sites (or mesh points). Using these results, we derive a discrete analogue of the divergence theorem and demonstrate probability conservation in a purely localized-basis approach.

Local discrete symmetries from superstring derived models

International Nuclear Information System (INIS)

Faraggi, A.E.

1996-10-01

Discrete and global symmetries play an essential role in many extensions of the Standard Model, for example, to preserve the proton lifetime, to prevent flavor changing neutral currents, etc. An important question is how can such symmetries survive in a theory of quantum gravity, like superstring theory. In a specific string model the author illustrates how local discrete symmetries may arise in string models and play an important role in preventing fast proton decay and flavor changing neutral currents. The local discrete symmetry arises due to the breaking of the non-Abelian gauge symmetries by Wilson lines in the superstring models and forbids, for example dimension five operators which mediate rapid proton decay, to all orders of nonrenormalizable terms. In the context of models of unification of the gauge and gravitational interactions, it is precisely this type of local discrete symmetries that must be found in order to insure that a given model is not in conflict with experimental observations

Chaotic properties between the nonintegrable discrete nonlinear Schroedinger equation and a nonintegrable discrete Heisenberg model

International Nuclear Information System (INIS)

Ding Qing

2007-01-01

We prove that the integrable-nonintegrable discrete nonlinear Schroedinger equation (AL-DNLS) introduced by Cai, Bishop and Gronbech-Jensen (Phys. Rev. Lett. 72 591(1994)) is the discrete gauge equivalent to an integrable-nonintegrable discrete Heisenberg model from the geometric point of view. Then we study whether the transmission and bifurcation properties of the AL-DNLS equation are preserved under the action of discrete gauge transformations. Our results reveal that the transmission property of the AL-DNLS equation is completely preserved and the bifurcation property is conditionally preserved to those of the integrable-nonintegrable discrete Heisenberg model

An Improved Computing Method for 3D Mechanical Connectivity Rates Based on a Polyhedral Simulation Model of Discrete Fracture Network in Rock Masses

Science.gov (United States)

Li, Mingchao; Han, Shuai; Zhou, Sibao; Zhang, Ye

2018-06-01

Based on a 3D model of a discrete fracture network (DFN) in a rock mass, an improved projective method for computing the 3D mechanical connectivity rate was proposed. The Monte Carlo simulation method, 2D Poisson process and 3D geological modeling technique were integrated into a polyhedral DFN modeling approach, and the simulation results were verified by numerical tests and graphical inspection. Next, the traditional projective approach for calculating the rock mass connectivity rate was improved using the 3D DFN models by (1) using the polyhedral model to replace the Baecher disk model; (2) taking the real cross section of the rock mass, rather than a part of the cross section, as the test plane; and (3) dynamically searching the joint connectivity rates using different dip directions and dip angles at different elevations to calculate the maximum, minimum and average values of the joint connectivity at each elevation. In a case study, the improved method and traditional method were used to compute the mechanical connectivity rate of the slope of a dam abutment. The results of the two methods were further used to compute the cohesive force of the rock masses. Finally, a comparison showed that the cohesive force derived from the traditional method had a higher error, whereas the cohesive force derived from the improved method was consistent with the suggested values. According to the comparison, the effectivity and validity of the improved method were verified indirectly.

Assessing geotechnical centrifuge modelling in addressing variably saturated flow in soil and fractured rock.

Science.gov (United States)

Jones, Brendon R; Brouwers, Luke B; Van Tonder, Warren D; Dippenaar, Matthys A

2017-05-01

The vadose zone typically comprises soil underlain by fractured rock. Often, surface water and groundwater parameters are readily available, but variably saturated flow through soil and rock are oversimplified or estimated as input for hydrological models. In this paper, a series of geotechnical centrifuge experiments are conducted to contribute to the knowledge gaps in: (i) variably saturated flow and dispersion in soil and (ii) variably saturated flow in discrete vertical and horizontal fractures. Findings from the research show that the hydraulic gradient, and not the hydraulic conductivity, is scaled for seepage flow in the geotechnical centrifuge. Furthermore, geotechnical centrifuge modelling has been proven as a viable experimental tool for the modelling of hydrodynamic dispersion as well as the replication of similar flow mechanisms for unsaturated fracture flow, as previously observed in literature. Despite the imminent challenges of modelling variable saturation in the vadose zone, the geotechnical centrifuge offers a powerful experimental tool to physically model and observe variably saturated flow. This can be used to give valuable insight into mechanisms associated with solid-fluid interaction problems under these conditions. Findings from future research can be used to validate current numerical modelling techniques and address the subsequent influence on aquifer recharge and vulnerability, contaminant transport, waste disposal, dam construction, slope stability and seepage into subsurface excavations.

Transport of a Two-Member Decay Chain of Radionuclides Through a Discrete Fracture in a Porous Rock Matrix in the Presence of Colloids

International Nuclear Information System (INIS)

Tien, N.-C.; Li Shihhai

2002-01-01

Many physical and chemical processes dominate the transport of radionuclides in groundwater. Among these processes, the decay chain process of radionuclides was frequently disregarded in previous research. However, the daughter products may travel much farther than their parents along the fracture. Therefore, some models neglecting the effect of the decay chain may underestimate the transport radionuclide concentration in geological media. The transport of radionuclides in groundwater is also controlled by colloidal particles. The radionuclides may be enhanced or retarded by the colloids, according to the mobility of these colloidal particles. This work describes a novel model of the transport of a two-member decay chain of radionuclides through a discrete fracture in a porous rock matrix in the presence of colloids. The model addresses the following processes: (a) advective transport in the fracture, (b) mechanical dispersion and molecular diffusion along the fracture, (c) molecular diffusion from the fracture to the rock matrix, (d) adsorption onto the fracture wall, (e) adsorption in the rock matrix, and (f) radioactive decay. Furthermore, colloids are assumed to be excluded from the matrix pores because of their size. A fully developed concentration profile system with nonreactive colloids is used to understand the effect of colloidal sizes by using hydrodynamic chromatography. The external forces acting on the colloid surface, such as the inertial, the van der Waals attractive force, the double layer force, and the gravitational force are accounted for. The parameters, the average velocity of the colloid, the dispersion coefficient of the colloid, and the distribution coefficient of radionuclides with colloids are modified according to the colloidal size. The transport equations for the parent radionuclides are solved analytically using the Laplace transformation and inversion method. However, for the transformed solution of the daughter products along the

Discrete stochastic analogs of Erlang epidemic models.

Science.gov (United States)

Getz, Wayne M; Dougherty, Eric R

2018-12-01

Erlang differential equation models of epidemic processes provide more realistic disease-class transition dynamics from susceptible (S) to exposed (E) to infectious (I) and removed (R) categories than the ubiquitous SEIR model. The latter is itself is at one end of the spectrum of Erlang SE[Formula: see text]I[Formula: see text]R models with [Formula: see text] concatenated E compartments and [Formula: see text] concatenated I compartments. Discrete-time models, however, are computationally much simpler to simulate and fit to epidemic outbreak data than continuous-time differential equations, and are also much more readily extended to include demographic and other types of stochasticity. Here we formulate discrete-time deterministic analogs of the Erlang models, and their stochastic extension, based on a time-to-go distributional principle. Depending on which distributions are used (e.g. discretized Erlang, Gamma, Beta, or Uniform distributions), we demonstrate that our formulation represents both a discretization of Erlang epidemic models and generalizations thereof. We consider the challenges of fitting SE[Formula: see text]I[Formula: see text]R models and our discrete-time analog to data (the recent outbreak of Ebola in Liberia). We demonstrate that the latter performs much better than the former; although confining fits to strict SEIR formulations reduces the numerical challenges, but sacrifices best-fit likelihood scores by at least 7%.

Cost comparison of orthopaedic fracture pathways using discrete event simulation in a Glasgow hospital

Science.gov (United States)

Jenkins, Paul J; McDonald, David A; Van Der Meer, Robert; Morton, Alec; Nugent, Margaret; Rymaszewski, Lech A

2017-01-01

Objective Healthcare faces the continual challenge of improving outcome while aiming to reduce cost. The aim of this study was to determine the micro cost differences of the Glasgow non-operative trauma virtual pathway in comparison to a traditional pathway. Design Discrete event simulation was used to model and analyse cost and resource utilisation with an activity-based costing approach. Data for a full comparison before the process change was unavailable so we used a modelling approach, comparing a virtual fracture clinic (VFC) with a simulated traditional fracture clinic (TFC). Setting The orthopaedic unit VFC pathway pioneered at Glasgow Royal Infirmary has attracted significant attention and interest and is the focus of this cost study. Outcome measures Our study focused exclusively on patients with non-operative trauma attending emergency department or the minor injuries unit and the subsequent step in the patient pathway. Retrospective studies of patient outcomes as a result of the protocol introductions for specific injuries are presented in association with activity costs from the models. Results Patients are satisfied with the new pathway, the information provided and the outcome of their injuries (Evidence Level IV). There was a 65% reduction in the number of first outpatient face-to-face (f2f) attendances in orthopaedics. In the VFC pathway, the resources required per day were significantly lower for all staff groups (p≤0.001). The overall cost per patient of the VFC pathway was £22.84 (95% CI 21.74 to 23.92) per patient compared with £36.81 (95% CI 35.65 to 37.97) for the TFC pathway. Conclusions Our results give a clearer picture of the cost comparison of the virtual pathway over a wholly traditional f2f clinic system. The use of simulation-based stochastic costings in healthcare economic analysis has been limited to date, but this study provides evidence for adoption of this method as a basis for its application in other healthcare settings

Discretization-dependent model for weakly connected excitable media

Science.gov (United States)

Arroyo, Pedro André; Alonso, Sergio; Weber dos Santos, Rodrigo

2018-03-01

Pattern formation has been widely observed in extended chemical and biological processes. Although the biochemical systems are highly heterogeneous, homogenized continuum approaches formed by partial differential equations have been employed frequently. Such approaches are usually justified by the difference of scales between the heterogeneities and the characteristic spatial size of the patterns. Under different conditions, for example, under weak coupling, discrete models are more adequate. However, discrete models may be less manageable, for instance, in terms of numerical implementation and mesh generation, than the associated continuum models. Here we study a model to approach discreteness which permits the computer implementation on general unstructured meshes. The model is cast as a partial differential equation but with a parameter that depends not only on heterogeneities sizes, as in the case of quasicontinuum models, but also on the discretization mesh. Therefore, we refer to it as a discretization-dependent model. We validate the approach in a generic excitable media that simulates three different phenomena: the propagation of action membrane potential in cardiac tissue, in myelinated axons of neurons, and concentration waves in chemical microemulsions.

An integrated workflow for stress and flow modelling using outcrop-derived discrete fracture networks

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...

Numerical Modeling and Investigation of Fluid-Driven Fracture Propagation in Reservoirs Based on a Modified Fluid-Mechanically Coupled Model in Two-Dimensional Particle Flow Code

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.

XFEM modeling of hydraulic fracture in porous rocks with natural fractures

Science.gov (United States)

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.

Continuous time random walk analysis of solute transport in fractured porous media

Energy Technology Data Exchange (ETDEWEB)

Cortis, Andrea; Cortis, Andrea; Birkholzer, Jens

2008-06-01

The objective of this work is to discuss solute transport phenomena in fractured porous media, where the macroscopic transport of contaminants in the highly permeable interconnected fractures can be strongly affected by solute exchange with the porous rock matrix. We are interested in a wide range of rock types, with matrix hydraulic conductivities varying from almost impermeable (e.g., granites) to somewhat permeable (e.g., porous sandstones). In the first case, molecular diffusion is the only transport process causing the transfer of contaminants between the fractures and the matrix blocks. In the second case, additional solute transfer occurs as a result of a combination of advective and dispersive transport mechanisms, with considerable impact on the macroscopic transport behavior. We start our study by conducting numerical tracer experiments employing a discrete (microscopic) representation of fractures and matrix. Using the discrete simulations as a surrogate for the 'correct' transport behavior, we then evaluate the accuracy of macroscopic (continuum) approaches in comparison with the discrete results. However, instead of using dual-continuum models, which are quite often used to account for this type of heterogeneity, we develop a macroscopic model based on the Continuous Time Random Walk (CTRW) framework, which characterizes the interaction between the fractured and porous rock domains by using a probability distribution function of residence times. A parametric study of how CTRW parameters evolve is presented, describing transport as a function of the hydraulic conductivity ratio between fractured and porous domains.

Simulating Dynamic Fracture in Oxide Fuel Pellets Using Cohesive Zone Models

Energy Technology Data Exchange (ETDEWEB)

R. L. Williamson

2009-08-01

It is well known that oxide fuels crack during the first rise to power, with continued fracture occurring during steady operation and especially during power ramps or accidental transients. Fractures have a very strong influence on the stress state in the fuel which, in turn, drives critical phenomena such as fission gas release, fuel creep, and eventual fuel/clad mechanical interaction. Recently, interest has been expressed in discrete fracture methods, such as the cohesive zone approach. Such models are attractive from a mechanistic and physical standpoint, since they reflect the localized nature of cracking. The precise locations where fractures initiate, as well as the crack evolution characteristics, are determined as part of the solution. This paper explores the use of finite element cohesive zone concepts to predict dynamic crack behavior in oxide fuel pellets during power-up, steady operation, and power ramping. The aim of this work is first to provide an assessment of cohesive zone models for application to fuel cracking and explore important numerical issues associated with this fracture approach. A further objective is to provide basic insight into where and when cracks form, how they interact, and how cracking effects the stress field in a fuel pellet. The ABAQUS commercial finite element code, which includes powerful cohesive zone capabilities, was used for this study. Fully-coupled thermo-mechanical behavior is employed, including the effects of thermal expansion, swelling due to solid and gaseous fission products, and thermal creep. Crack initiation is determined by a temperature-dependent maximum stress criterion, based on measured fracture strengths for UO2. Damage evolution is governed by a traction-separation relation, calibrated to data from temperature and burn-up dependent fracture toughness measurements. Numerical models are first developed in 2D based on both axisymmetric (to explore axial cracking) and plane strain (to explore radial

Preliminary - discrete fracture network modelling of tracer migration experiments at the SCV site

International Nuclear Information System (INIS)

Dershowitz, W.S.; Wallmann, P.; Geier, J.E.; Lee, G.

1991-09-01

This report describes a numerical modelling study of solute transport within the Site Characterization and Validation (SCV) block at the Stripa site. The study was carried out with the FracMan/MAFIC package, utilizing statistics from stages 3 and 4 of the Stripa phase 3 Site Characterization and Validation project. Simulations were carried out to calibrate fracture solute transport properties against observations in the first stage of saline injection radar experiments. These results were then used to predict the performance of planned tracer experiments, using both particle tracking network solute transport, and pathways analysis approaches. Simulations were also carried out to predict results of the second stage of saline injection radar experiments. (au) (34 refs.)

Anisotropy of strength and deformability of fractured rocks

Directory of Open Access Journals (Sweden)

Majid Noorian Bidgoli

2014-04-01

Full Text Available Anisotropy of the strength and deformation behaviors of fractured rock masses is a crucial issue for design and stability assessments of rock engineering structures, due mainly to the non-uniform and non-regular geometries of the fracture systems. However, no adequate efforts have been made to study this issue due to the current practical impossibility of laboratory tests with samples of large volumes containing many fractures, and the difficulty for controlling reliable initial and boundary conditions for large-scale in situ tests. Therefore, a reliable numerical predicting approach for evaluating anisotropy of fractured rock masses is needed. The objective of this study is to systematically investigate anisotropy of strength and deformability of fractured rocks, which has not been conducted in the past, using a numerical modeling method. A series of realistic two-dimensional (2D discrete fracture network (DFN models were established based on site investigation data, which were then loaded in different directions, using the code UDEC of discrete element method (DEM, with changing confining pressures. Numerical results show that strength envelopes and elastic deformability parameters of tested numerical models are significantly anisotropic, and vary with changing axial loading and confining pressures. The results indicate that for design and safety assessments of rock engineering projects, the directional variations of strength and deformability of the fractured rock mass concerned must be treated properly with respect to the directions of in situ stresses. Traditional practice for simply positioning axial orientation of tunnels in association with principal stress directions only may not be adequate for safety requirements. Outstanding issues of the present study and suggestions for future study are also presented.

Fractured rock modeling in the National Waste Terminal Storage Program: a review of requirements and status

International Nuclear Information System (INIS)

St John, C.; Krug, A.; Key, S.; Monsees, J.

1983-05-01

Generalized computer codes capable of forming the basis for numerical models of fractured rock masses are being used within the NWTS program. Little additional development of these codes is considered justifiable, except in the area of representation of discrete fractures. On the other hand, model preparation requires definition of medium-specific constitutive descriptions and site characteristics and is therefore legitimately conducted by each of the media-oriented projects within the National Waste Terminal Storage program. However, it is essential that a uniform approach to the role of numerical modeling be adopted, including agreement upon the contribution of modeling to the design and licensing process and the need for, and means of, model qualification for particular purposes. This report discusses the role of numerical modeling, reviews the capabilities of several computer codes that are being used to support design or performance assessment, and proposes a framework for future numerical modeling activities within the NWTS program

Discrete approximations to vector spin models

Energy Technology Data Exchange (ETDEWEB)

Van Enter, Aernout C D [University of Groningen, Johann Bernoulli Institute of Mathematics and Computing Science, Postbus 407, 9700 AK Groningen (Netherlands); Kuelske, Christof [Ruhr-Universitaet Bochum, Fakultaet fuer Mathematik, D44801 Bochum (Germany); Opoku, Alex A, E-mail: A.C.D.v.Enter@math.rug.nl, E-mail: Christof.Kuelske@ruhr-uni-bochum.de, E-mail: opoku@math.leidenuniv.nl [Mathematisch Instituut, Universiteit Leiden, Postbus 9512, 2300 RA, Leiden (Netherlands)

2011-11-25

We strengthen a result from Kuelske and Opoku (2008 Electron. J. Probab. 13 1307-44) on the existence of effective interactions for discretized continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of discretizing continuous-spin models, and show that except for very low temperatures, they behave similarly in two dimensions. We also discuss some possibilities in higher dimensions. (paper)

Discrete approximations to vector spin models

International Nuclear Information System (INIS)

Van Enter, Aernout C D; Külske, Christof; Opoku, Alex A

2011-01-01

We strengthen a result from Külske and Opoku (2008 Electron. J. Probab. 13 1307–44) on the existence of effective interactions for discretized continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of discretizing continuous-spin models, and show that except for very low temperatures, they behave similarly in two dimensions. We also discuss some possibilities in higher dimensions. (paper)

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

Mathematical modelling of fracture hydrology

International Nuclear Information System (INIS)

Herbert, A.W.; Hodgkinson, D.P.; Lever, D.A.; Robinson, P.C.; Rae, J.

1985-06-01

This report summarises the work performed between January 1983 and December 1984 for the CEC/DOE contract 'Mathematical Modelling of Fracture Hydrology', under the following headings: 1) Statistical fracture network modelling, 2) Continuum models of flow and transport, 3) Simplified models, 4) Analysis of laboratory experiments and 5) Analysis of field experiments. (author)

Characterization of Fractures in the Chicxulub Peak Ring: Preliminary Results from IODP/ICDP Expedition 364

Science.gov (United States)

McCall, N.; Gulick, S. P. S.; Morgan, J. V.; Hall, B. J.; Jones, L.; Expedition 364 Science Party, I. I.

2017-12-01

During Expedition 364, IODP/ICDP drilled the peak ring of the Chicxulub impact crater at Site M0077, recovering core from 505.7 to 1334.7 mbsf. The core has been imaged via X-ray Computer Tomography (CT) as a noninvasive method to create a 3-dimensional model of the core, providing information on the density and internal structure at a 0.3 mm resolution. Results from the expedition show that from 748 mbsf and deeper the peak ring is largely composed of uplifted and fractured granitic basement rocks originally sourced from approximately 8-10 km depth. Impact crater modeling suggests the peak ring was formed through dynamic collapse of a rebounding central peak within 10 minutes of impact, requiring the target rocks to temporarily behave as a viscous fluid. The newly recovered core provides a rare opportunity to investigate the cratering process, specifically how the granite was weakened, as well as the extent of the hydrothermal system created after the impact. Based on the CT data, we identify four classes of fractures based on their CT facies deforming the granitoids: pervasive fine fractures, discrete fine fractures, discrete filled fractures, and discrete open fractures. Pervasive fine fractures were most commonly found proximal to dikes and impact melt rock. Discrete filled fractures often displayed a cataclastic texture. We present density trends for the different facies and compare these to petrophysical properties (density, NGR, P-wave seismic velocity). Fractured areas have a lower density than the surrounding granite, as do most filled fractures. This reduction suggests that fluid migrating through the peak ring in the wake of the impact either deposited lower density minerals within the fractures and/or altered the original fracture fill. The extent and duration of fluid flow recorded in these fractures will assist in the characterization of the post-impact hydrothermal system. Future work includes combining information from CT images with thin sections

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.

Assessing alternative conceptual models of fracture flow

International Nuclear Information System (INIS)

Ho, C.K.

1995-01-01

The numerical code TOUGH2 was used to assess alternative conceptual models of fracture flow. The models that were considered included the equivalent continuum model (ECM) and the dual permeability (DK) model. A one-dimensional, layered, unsaturated domain was studied with a saturated bottom boundary and a constant infiltration at the top boundary. Two different infiltration rates were used in the studies. In addition, the connection areas between the fracture and matrix elements in the dual permeability model were varied. Results showed that the two conceptual models of fracture flow produced different saturation and velocity profiles-even under steady-state conditions. The magnitudes of the discrepancies were sensitive to two parameters that affected the flux between the fractures and matrix in the dual permeability model: (1) the fracture-matrix connection areas and (2) the capillary pressure gradients between the fracture and matrix elements

Characterizing hydraulic fractures in shale gas reservoirs using transient pressure tests

Directory of Open Access Journals (Sweden)

Cong Wang

2015-06-01

This work presents an unconventional gas reservoir simulator and its application to quantify hydraulic fractures in shale gas reservoirs using transient pressure data. The numerical model incorporates most known physical processes for gas production from unconventional reservoirs, including two-phase flow of liquid and gas, Klinkenberg effect, non-Darcy flow, and nonlinear adsorption. In addition, the model is able to handle various types and scales of fractures or heterogeneity using continuum, discrete or hybrid modeling approaches under different well production conditions of varying rate or pressure. Our modeling studies indicate that the most sensitive parameter of hydraulic fractures to early transient gas flow through extremely low permeability rock is actually the fracture-matrix contacting area, generated by fracturing stimulation. Based on this observation, it is possible to use transient pressure testing data to estimate the area of fractures generated from fracturing operations. We will conduct a series of modeling studies and present a methodology using typical transient pressure responses, simulated by the numerical model, to estimate fracture areas created or to quantity hydraulic fractures with traditional well testing technology. The type curves of pressure transients from this study can be used to quantify hydraulic fractures in field application.

Adaptive mixed finite element methods for Darcy flow in fractured porous media

KAUST Repository

Chen, Huangxin; Salama, Amgad; Sun, Shuyu

2016-01-01

In this paper, we propose adaptive mixed finite element methods for simulating the single-phase Darcy flow in two-dimensional fractured porous media. The reduced model that we use for the simulation is a discrete fracture model coupling Darcy flows in the matrix and the fractures, and the fractures are modeled by one-dimensional entities. The Raviart-Thomas mixed finite element methods are utilized for the solution of the coupled Darcy flows in the matrix and the fractures. In order to improve the efficiency of the simulation, we use adaptive mixed finite element methods based on novel residual-based a posteriori error estimators. In addition, we develop an efficient upscaling algorithm to compute the effective permeability of the fractured porous media. Several interesting examples of Darcy flow in the fractured porous media are presented to demonstrate the robustness of the algorithm.

Adaptive mixed finite element methods for Darcy flow in fractured porous media

KAUST Repository

Chen, Huangxin

2016-09-21

In this paper, we propose adaptive mixed finite element methods for simulating the single-phase Darcy flow in two-dimensional fractured porous media. The reduced model that we use for the simulation is a discrete fracture model coupling Darcy flows in the matrix and the fractures, and the fractures are modeled by one-dimensional entities. The Raviart-Thomas mixed finite element methods are utilized for the solution of the coupled Darcy flows in the matrix and the fractures. In order to improve the efficiency of the simulation, we use adaptive mixed finite element methods based on novel residual-based a posteriori error estimators. In addition, we develop an efficient upscaling algorithm to compute the effective permeability of the fractured porous media. Several interesting examples of Darcy flow in the fractured porous media are presented to demonstrate the robustness of the algorithm.

Challenging and improving conceptual models for isothermal flow in unsaturated, fractured rock through exploration of small-scale processes

International Nuclear Information System (INIS)

Glass, R.J.; Nicholl, M.J.; Tidwell, V.C.

1996-01-01

Over the past several years, the authors have performed experimental studies focused on understanding small-scale flow processes within discrete fractures and individual matrix blocks; much of the understanding gained in that time differs from that underlying the basic assumptions used in effective media representations. Here they synthesize the process level understanding gained from their laboratory studies to explore how such small-scale processes may influence the behavior of fluid flow in fracture networks and ensembles of matrix blocks at levels sufficient to impact the formulation of intermediate-scale effective media properties. They also explore, by means of a thought experiment, how these same small-scale processes could couple to produce a large-scale system response inconsistent with current conceptual models based on continuum representations of flow through unsaturated, fractured rock. Based on their findings, a number of modifications to existing dual permeability models are suggested that should allow them improved applicability; however, even with these modifications, it is likely that continuum representations of flow through unsaturated fractured rock will have limited validity and must therefore be applied with caution

FTRANS, Radionuclide Flow in Groundwater and Fractured Rock

International Nuclear Information System (INIS)

Huyakorn, P.; Golis, M.J.

1987-01-01

1 - Description of program or function: FTRANS (Fractured flow and Transport of Radionuclides) is a two-dimensional finite-element code designed to simulate ground-water flow and transport of radioactive nuclides in a fractured porous return medium. FTRANS takes into account fluid interactions between the fractures and porous matrix blocks, advective-dispersive transport in the fractures and diffusion in the porous matrix blocks, and chain reactions of radionuclide components. It has the capability to model the fractured system using either the dual-porosity or the discrete- fracture modeling approach or a combination of both. FTRANS can be used to perform two-dimensional near-field or far-field predictive analyses of ground-water flow and to perform risk assessments of radionuclide transport from nuclear waste repository subsystems to the biosphere. 2 - Restrictions on the complexity of the problem: Although FTRANS does cannot account for deformation processes which can affect the flow capacity and velocity field

The discretized Schroedinger equation and simple models for semiconductor quantum wells

International Nuclear Information System (INIS)

Boykin, Timothy B; Klimeck, Gerhard

2004-01-01

The discretized Schroedinger equation is one of the most commonly employed methods for solving one-dimensional quantum mechanics problems on the computer, yet many of its characteristics remain poorly understood. The differences with the continuous Schroedinger equation are generally viewed as shortcomings of the discrete model and are typically described in purely mathematical terms. This is unfortunate since the discretized equation is more productively viewed from the perspective of solid-state physics, which naturally links the discrete model to realistic semiconductor quantum wells and nanoelectronic devices. While the relationship between the discrete model and a one-dimensional tight-binding model has been known for some time, the fact that the discrete Schroedinger equation admits analytic solutions for quantum wells has gone unnoted. Here we present a solution to this new analytically solvable problem. We show that the differences between the discrete and continuous models are due to their fundamentally different bandstructures, and present evidence for our belief that the discrete model is the more physically reasonable one

Channel flow and trichloroethylene treatment in a partly iron-filled fracture: Experimental and model results

Science.gov (United States)

Cai, Zuansi; Merly, Corrine; Thomson, Neil R.; Wilson, Ryan D.; Lerner, David N.

2007-08-01

Technical developments have now made it possible to emplace granular zero-valent iron (Fe 0) in fractured media to create a Fe 0 fracture reactive barrier (Fe 0 FRB) for the treatment of contaminated groundwater. To evaluate this concept, we conducted a laboratory experiment in which trichloroethylene (TCE) contaminated water was flushed through a single uniform fracture created between two sandstone blocks. This fracture was partly filled with what was intended to be a uniform thickness of iron. Partial treatment of TCE by iron demonstrated that the concept of a Fe 0 FRB is practical, but was less than anticipated for an iron layer of uniform thickness. When the experiment was disassembled, evidence of discrete channelised flow was noted and attributed to imperfect placement of the iron. To evaluate the effect of the channel flow, an explicit Channel Model was developed that simplifies this complex flow regime into a conceptualised set of uniform and parallel channels. The mathematical representation of this conceptualisation directly accounts for (i) flow channels and immobile fluid arising from the non-uniform iron placement, (ii) mass transfer from the open fracture to iron and immobile fluid regions, and (iii) degradation in the iron regions. A favourable comparison between laboratory data and the results from the developed mathematical model suggests that the model is capable of representing TCE degradation in fractures with non-uniform iron placement. In order to apply this Channel Model concept to a Fe 0 FRB system, a simplified, or implicit, Lumped Channel Model was developed where the physical and chemical processes in the iron layer and immobile fluid regions are captured by a first-order lumped rate parameter. The performance of this Lumped Channel Model was compared to laboratory data, and benchmarked against the Channel Model. The advantages of the Lumped Channel Model are that the degradation of TCE in the system is represented by a first

Quadratic Term Structure Models in Discrete Time

OpenAIRE

Marco Realdon

2006-01-01

This paper extends the results on quadratic term structure models in continuos time to the discrete time setting. The continuos time setting can be seen as a special case of the discrete time one. Recursive closed form solutions for zero coupon bonds are provided even in the presence of multiple correlated underlying factors. Pricing bond options requires simple integration. Model parameters may well be time dependent without scuppering such tractability. Model estimation does not require a r...

Parallel, Multigrid Finite Element Simulator for Fractured/Faulted and Other Complex Reservoirs based on Common Component Architecture (CCA)

Energy Technology Data Exchange (ETDEWEB)

Milind Deo; Chung-Kan Huang; Huabing Wang

2008-08-31

Black-oil, compositional and thermal simulators have been developed to address different physical processes in reservoir simulation. A number of different types of discretization methods have also been proposed to address issues related to representing the complex reservoir geometry. These methods are more significant for fractured reservoirs where the geometry can be particularly challenging. In this project, a general modular framework for reservoir simulation was developed, wherein the physical models were efficiently decoupled from the discretization methods. This made it possible to couple any discretization method with different physical models. Oil characterization methods are becoming increasingly sophisticated, and it is possible to construct geologically constrained models of faulted/fractured reservoirs. Discrete Fracture Network (DFN) simulation provides the option of performing multiphase calculations on spatially explicit, geologically feasible fracture sets. Multiphase DFN simulations of and sensitivity studies on a wide variety of fracture networks created using fracture creation/simulation programs was undertaken in the first part of this project. This involved creating interfaces to seamlessly convert the fracture characterization information into simulator input, grid the complex geometry, perform the simulations, and analyze and visualize results. Benchmarking and comparison with conventional simulators was also a component of this work. After demonstration of the fact that multiphase simulations can be carried out on complex fracture networks, quantitative effects of the heterogeneity of fracture properties were evaluated. Reservoirs are populated with fractures of several different scales and properties. A multiscale fracture modeling study was undertaken and the effects of heterogeneity and storage on water displacement dynamics in fractured basements were investigated. In gravity-dominated systems, more oil could be recovered at a given pore

Cost comparison of orthopaedic fracture pathways using discrete event simulation in a Glasgow hospital.

Science.gov (United States)

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

A study on the stochastic model for nuclide transport in the fractured porous rock using continuous time Markov process

International Nuclear Information System (INIS)

Lee, Youn Myoung

1995-02-01

As a newly approaching model, a stochastic model using continuous time Markov process for nuclide decay chain transport of arbitrary length in the fractured porous rock medium has been proposed, by which the need for solving a set of partial differential equations corresponding to various sets of side conditions can be avoided. Once the single planar fracture in the rock matrix is represented by a series of finite number of compartments having region wise constant parameter values in them, the medium is continuous in view of various processes associated with nuclide transport but discrete in medium space and such geologic system is assumed to have Markov property, since the Markov process requires that only the present value of the time dependent random variable be known to determine the future value of random variable, nuclide transport in the medium can then be modeled as a continuous time Markov process. Processes that are involved in nuclide transport are advective transport due to groundwater flow, diffusion into the rock matrix, adsorption onto the wall of the fracture and within the pores in the rock matrix, and radioactive decay chain. The transition probabilities for nuclide from the transition intensities between and out of the compartments are represented utilizing Chapman-Kolmogorov equation, through which the expectation and the variance of nuclide distribution for each compartment or the fractured rock medium can be obtained. Some comparisons between Markov process model developed in this work and available analytical solutions for one-dimensional layered porous medium, fractured medium with rock matrix diffusion, and porous medium considering three member nuclide decay chain without rock matrix diffusion have been made showing comparatively good agreement for all cases. To verify the model developed in this work another comparative study was also made by fitting the experimental data obtained with NaLS and uranine running in the artificial fractured

Multiphase flow models for hydraulic fracturing technology

Science.gov (United States)

Osiptsov, Andrei A.

2017-10-01

The technology of hydraulic fracturing of a hydrocarbon-bearing formation is based on pumping a fluid with particles into a well to create fractures in porous medium. After the end of pumping, the fractures filled with closely packed proppant particles create highly conductive channels for hydrocarbon flow from far-field reservoir to the well to surface. The design of the hydraulic fracturing treatment is carried out with a simulator. Those simulators are based on mathematical models, which need to be accurate and close to physical reality. The entire process of fracture placement and flowback/cleanup can be conventionally split into the following four stages: (i) quasi-steady state effectively single-phase suspension flow down the wellbore, (ii) particle transport in an open vertical fracture, (iii) displacement of fracturing fluid by hydrocarbons from the closed fracture filled with a random close pack of proppant particles, and, finally, (iv) highly transient gas-liquid flow in a well during cleanup. The stage (i) is relatively well described by the existing hydralics models, while the models for the other three stages of the process need revisiting and considerable improvement, which was the focus of the author’s research presented in this review paper. For stage (ii), we consider the derivation of a multi-fluid model for suspension flow in a narrow vertical hydraulic fracture at moderate Re on the scale of fracture height and length and also the migration of particles across the flow on the scale of fracture width. At the stage of fracture cleanaup (iii), a novel multi-continua model for suspension filtration is developed. To provide closure relationships for permeability of proppant packings to be used in this model, a 3D direct numerical simulation of single phase flow is carried out using the lattice-Boltzmann method. For wellbore cleanup (iv), we present a combined 1D model for highly-transient gas-liquid flow based on the combination of multi-fluid and

Water flow and solute transport through fractured rock

International Nuclear Information System (INIS)

Bourke, P.J.; Kingdon, R.D.; Bolt, J.E.; Pascoe, D.M.; Watkins, V.M.B.

1991-01-01

In densely fractured slate at the Nirex research site in Cornwall, the positions, orientations and hydraulic conductivities of the 380 fractures intersecting a drill hole between 9 and 50 m depths have been individually measured. These data have been used: - to determine the dimensions of statistically representative volumes of the sheetwork of fractures; - to predict; using discrete flowpath modelling and the NAPSAC code; the total flows into the fractures when large numbers are simultaneously pressurised along various lengths of the hole; Corresponding measurements, which proved the modelling and validated the code to factor of two accuracy, are reported. Possibilities accounting for this factor are noted for experimental investigation, and continuing, more extensive inter-hole flow and transport measurements are outlined. The application of this experimental and theoretical approach for calculating radionuclide transport in less densely fractured rock suitable for waste disposal is discussed. 7 figs., 9 refs

Radionuclide Transport in Fractured Rock: Numerical Assessment for High Level Waste Repository

Directory of Open Access Journals (Sweden)

Claudia Siqueira da Silveira

2013-01-01

Full Text Available Deep and stable geological formations with low permeability have been considered for high level waste definitive repository. A common problem is the modeling of radionuclide migration in a fractured medium. Initially, we considered a system consisting of a rock matrix with a single planar fracture in water saturated porous rock. Transport in the fracture is assumed to obey an advection-diffusion equation, while molecular diffusion is considered the dominant mechanism of transport in porous matrix. The partial differential equations describing the movement of radionuclides were discretized by finite difference methods, namely, fully explicit, fully implicit, and Crank-Nicolson schemes. The convective term was discretized by the following numerical schemes: backward differences, centered differences, and forward differences. The model was validated using an analytical solution found in the literature. Finally, we carried out a simulation with relevant spent fuel nuclide data with a system consisting of a horizontal fracture and a vertical fracture for assessing the performance of a hypothetical repository inserted into the host rock. We have analysed the bentonite expanded performance at the beginning of fracture, the quantified radionuclide released from a borehole, and an estimated effective dose to an adult, obtained from ingestion of well water during one year.

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.

A multi-scale experimental and simulation approach for fractured subsurface systems

Science.gov (United States)

Viswanathan, H. S.; Carey, J. W.; Frash, L.; Karra, S.; Hyman, J.; Kang, Q.; Rougier, E.; Srinivasan, G.

2017-12-01

Fractured systems play an important role in numerous subsurface applications including hydraulic fracturing, carbon sequestration, geothermal energy and underground nuclear test detection. Fractures that range in scale from microns to meters and their structure control the behavior of these systems which provide over 85% of our energy and 50% of US drinking water. Determining the key mechanisms in subsurface fractured systems has been impeded due to the lack of sophisticated experimental methods to measure fracture aperture and connectivity, multiphase permeability, and chemical exchange capacities at the high temperature, pressure, and stresses present in the subsurface. In this study, we developed and use microfluidic and triaxial core flood experiments required to reveal the fundamental dynamics of fracture-fluid interactions. In addition we have developed high fidelity fracture propagation and discrete fracture network flow models to simulate these fractured systems. We also have developed reduced order models of these fracture simulators in order to conduct uncertainty quantification for these systems. We demonstrate an integrated experimental/modeling approach that allows for a comprehensive characterization of fractured systems and develop models that can be used to optimize the reservoir operating conditions over a range of subsurface conditions.

Discrete dynamic modeling of cellular signaling networks.

Science.gov (United States)

Albert, Réka; Wang, Rui-Sheng

2009-01-01

Understanding signal transduction in cellular systems is a central issue in systems biology. Numerous experiments from different laboratories generate an abundance of individual components and causal interactions mediating environmental and developmental signals. However, for many signal transduction systems there is insufficient information on the overall structure and the molecular mechanisms involved in the signaling network. Moreover, lack of kinetic and temporal information makes it difficult to construct quantitative models of signal transduction pathways. Discrete dynamic modeling, combined with network analysis, provides an effective way to integrate fragmentary knowledge of regulatory interactions into a predictive mathematical model which is able to describe the time evolution of the system without the requirement for kinetic parameters. This chapter introduces the fundamental concepts of discrete dynamic modeling, particularly focusing on Boolean dynamic models. We describe this method step-by-step in the context of cellular signaling networks. Several variants of Boolean dynamic models including threshold Boolean networks and piecewise linear systems are also covered, followed by two examples of successful application of discrete dynamic modeling in cell biology.

Fundamental aspects of brittle damage processes -- discrete systems

International Nuclear Information System (INIS)

Krajcinovic, D.; Lubarda, V.

1993-01-01

The analysis of cooperative brittle processes are performed on simple discrete models admitting closed form solutions. A connection between the damage and fracture mechanics is derived and utilized to illustrate the relation between two theories. The performed analyses suggest that the stress concentrations (direct interaction between defects) represent a second order effect during the hardening part of the response in the case of disordered solids

An Efficient Upscaling Process Based on a Unified Fine-scale Multi-Physics Model for Flow Simulation in Naturally Fracture Carbonate Karst Reservoirs

KAUST Repository

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.

Simulation of quasistatic deformations using discrete rod models

OpenAIRE

Linn, J.; Stephan, T.

2008-01-01

Recently we developed a discrete model of elastic rods with symmetric cross section suitable for a fast simulation of quasistatic deformations [33]. The model is based on Kirchhoff’s geometrically exact theory of rods. Unlike simple models of “mass & spring” type typically used in VR applications, our model provides a proper coupling of bending and torsion. The computational approach comprises a variational formulation combined with a finite difference discretization of the continuum model. A...

Discrete-time rewards model-checked

NARCIS (Netherlands)

Larsen, K.G.; Andova, S.; Niebert, Peter; Hermanns, H.; Katoen, Joost P.

2003-01-01

This paper presents a model-checking approach for analyzing discrete-time Markov reward models. For this purpose, the temporal logic probabilistic CTL is extended with reward constraints. This allows to formulate complex measures – involving expected as well as accumulated rewards – in a precise and

Analysis hierarchical model for discrete event systems

Science.gov (United States)

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.

Hydrogeological characterisation and modelling of deformation zones and fracture domains, Forsmark modelling stage 2.2

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 discrete time-to-event data

CERN Document Server

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...

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

A discrete-space urban model with environmental amenities

Science.gov (United States)

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...

Discrete Element Modeling

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.

Towards an integrated numerical simulator for crack-seal vein microstructure: Coupling phase-field with the Discrete Element Method

Science.gov (United States)

Virgo, Simon; Ankit, Kumar; Nestler, Britta; Urai, Janos L.

2016-04-01

Crack-seal veins form in a complex interplay of coupled thermal, hydraulic, mechanical and chemical processes. Their formation and cyclic growth involves brittle fracturing and dilatancy, phases of increased fluid flow and the growth of crystals that fill the voids and reestablish the mechanical strength. Existing numerical models of vein formation focus on selected aspects of the coupled process. Until today, no model exists that is able to use a realistic representation of the fracturing AND sealing processes, simultaneously. To address this challenge, we propose the bidirectional coupling of two numerical methods that have proven themselves as very powerful to model the fundamental processes acting in crack-seal systems: Phase-field and the Discrete Element Method (DEM). The phase-field Method was recently successfully extended to model the precipitation of quartz crystals from an aqueous solution and applied to model the sealing of a vein over multiple opening events (Ankit et al., 2013; Ankit et al., 2015a; Ankit et al., 2015b). The advantage over former, purely kinematic approaches is that in phase-field, the crystal growth is modeled based on thermodynamic and kinetic principles. Different driving forces for microstructure evolution, such as chemical bulk free energy, interfacial energy, elastic strain energy and different transport processes, such as mass diffusion and advection, can be coupled and the effect on the evolution process can be studied in 3D. The Discrete Element Method was already used in several studies to model the fracturing of rocks and the incremental growth of veins by repeated fracturing (Virgo et al., 2013; Virgo et al., 2014). Materials in DEM are represented by volumes of packed spherical particles and the response to the material to stress is modeled by interaction of the particles with their nearest neighbours. For rocks, in 3D, the method provides a realistic brittle failure behaviour. Exchange Routines are being developed that

Continuum equivalent model for the fractured EDZ around underground galleries in clay-stone

International Nuclear Information System (INIS)

Pouya, A.; Bourgeois, E.; Larbi, B.; Poutrel, A.

2010-01-01

, parallel and equidistant fractures perpendicular to n, the vector normal to the local fractures surface. This behaviour has thus the axial symmetry around the axis n. We have studied this problem first for a linear elastic behaviour of the intact rock and of fractures and then extended it to more complex behaviours. In this case, the local elastic behaviour of the CEM is defined by a tensor which has the transversal isotropy around n. Because of the finite size of the studied domain, the assumption of uniform stress or uniform strain at the boundary leads to different CEM models called 1 and 2 in the following. To validate the 'homogenization' procedure, we compare the displacement and stress fields calculated around the galleries with two approaches: the first one uses a discrete model (with individual representation of the fractures) and the other one relies on the CEM model of the EDZ. Both models assume the same geometry with axial symmetry. In the first case, fractures are represented numerically by the Goodman (1966) 'joint elements' implemented in the finite element code CESAR, and in the second case, the special anisotropic and position depending elastic model (1) implemented in CESAR is used. The total displacement at the wall obtained by the first method and the two CEM models given by the procedure described above is shown. Except for the beginning of the gallery where boundary effects are dominant, CEM models give nearly the same displacements that the discontinuous model. The comparison between the stresses leads also to a good agreement between the results. This approach was extended to the elastoplastic behaviour of the rock and of the fractures with also taking into account the curvature of the fractures. A good agreement between the discontinuous and CEM models could be obtained for these cases also. This shows the possibility of replacing effectively in the numerical models the fractured EDZ by a CEM determined by homogenization

Origin of Permeability and Structure of Flows in Fractured Media

Science.gov (United States)

De Dreuzy, J.; Darcel, C.; Davy, P.; Erhel, J.; Le Goc, R.; Maillot, J.; Meheust, Y.; Pichot, G.; Poirriez, B.

2013-12-01

its consequence for crustal hydromechanics, Journal of Geophysical Research-Solid Earth, 115, 13. de Dreuzy, J.-R., et al. (2012a), Influence of fracture scale heterogeneity on the flow properties of three-dimensional Discrete Fracture Networks (DFN), J. Geophys. Res.-Earth Surf., 117(B11207), 21 PP. de Dreuzy, J.-R., et al. (2012b), Synthetic benchmark for modeling flow in 3D fractured media, Computers and Geosciences(0). Pichot, G., et al. (2010), A Mixed Hybrid Mortar Method for solving flow in Discrete Fracture Networks, Applicable Analysis, 89(10), 1729-1643. Pichot, G., et al. (2012), Flow simulation in 3D multi-scale fractured networks using non-matching meshes, SIAM Journal on Scientific Computing (SISC), 34(1). Figure: (a) Fracture network with a broad-range of fracture lengths. (b) Flows (log-scale) with homogeneous fractures. (c) Flows (log-scale) with heterogeneous fractures [de Dreuzy et al., 2012a]. The impact of the fracture apertures (c) is illustrated on the organization of flows.

Current Density and Continuity in Discretized Models

Science.gov (United States)

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…

Model-Checking Discrete Duration Calculus

DEFF Research Database (Denmark)

Hansen, Michael Reichhardt

1994-01-01

can do model-checking. The subset we consider is expressive enough to formalize the requirements to the gas burner system given by A.P. Ravn (1993); but only for a discrete time domain. Model-checking is done by reducing the correctness problem ℳ|=𝒟 to the inclusion problem of regular...

First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media

Science.gov (United States)

Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.

2018-01-01

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell’s equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell–Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell–Lorentz equations, we trace the development

First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media

International Nuclear Information System (INIS)

Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.

2016-01-01

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell’s equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell–Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell–Lorentz equations, we trace the development

First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media

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

First-Principles Modeling Of Electromagnetic Scattering By Discrete and Discretely Heterogeneous Random Media

Science.gov (United States)

Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.

2016-01-01

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell's equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell- Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of

a Fractal Network Model for Fractured Porous Media

Science.gov (United States)

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.

A discrete dislocation–transformation model for austenitic single crystals

International Nuclear Information System (INIS)

Shi, J; Turteltaub, S; Remmers, J J C; Van der Giessen, E

2008-01-01

A discrete model for analyzing the interaction between plastic flow and martensitic phase transformations is developed. The model is intended for simulating the microstructure evolution in a single crystal of austenite that transforms non-homogeneously into martensite. The plastic flow in the untransformed austenite is simulated using a plane-strain discrete dislocation model. The phase transformation is modeled via the nucleation and growth of discrete martensitic regions embedded in the austenitic single crystal. At each instant during loading, the coupled elasto-plasto-transformation problem is solved using the superposition of analytical solutions for the discrete dislocations and discrete transformation regions embedded in an infinite homogeneous medium and the numerical solution of a complementary problem used to enforce the actual boundary conditions and the heterogeneities in the medium. In order to describe the nucleation and growth of martensitic regions, a nucleation criterion and a kinetic law suitable for discrete regions are specified. The constitutive rules used in discrete dislocation simulations are supplemented with additional evolution rules to account for the phase transformation. To illustrate the basic features of the model, simulations of specimens under plane-strain uniaxial extension and contraction are analyzed. The simulations indicate that plastic flow reduces the average stress at which transformation begins, but it also reduces the transformation rate when compared with benchmark simulations without plasticity. Furthermore, due to local stress fluctuations caused by dislocations, martensitic systems can be activated even though transformation would not appear to be favorable based on the average stress. Conversely, the simulations indicate that the plastic hardening behavior is influenced by the reduction in the effective austenitic grain size due to the evolution of transformation. During cyclic simulations, the coupled plasticity

Compensatory neurofuzzy model for discrete data classification in biomedical

Science.gov (United States)

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.

Role of geomechanically grown fractures on dispersive transport in heterogeneous geological formations

KAUST Repository

Nick, H. M.

2011-11-04

A second order in space accurate implicit scheme for time-dependent advection-dispersion equations and a discrete fracture propagation model are employed to model solute transport in porous media. We study the impact of the fractures on mass transport and dispersion. To model flow and transport, pressure and transport equations are integrated using a finite-element, node-centered finite-volume approach. Fracture geometries are incrementally developed from a random distributions of material flaws using an adoptive geomechanical finite-element model that also produces fracture aperture distributions. This quasistatic propagation assumes a linear elastic rock matrix, and crack propagation is governed by a subcritical crack growth failure criterion. Fracture propagation, intersection, and closure are handled geometrically. The flow and transport simulations are separately conducted for a range of fracture densities that are generated by the geomechanical finite-element model. These computations show that the most influential parameters for solute transport in fractured porous media are as follows: fracture density and fracture-matrix flux ratio that is influenced by matrix permeability. Using an equivalent fracture aperture size, computed on the basis of equivalent permeability of the system, we also obtain an acceptable prediction of the macrodispersion of poorly interconnected fracture networks. The results hold for fractures at relatively low density. © 2011 American Physical Society.

Role of geomechanically grown fractures on dispersive transport in heterogeneous geological formations

KAUST Repository

Nick, H. M.; Paluszny, A.; Blunt, M. J.; Matthai, S. K.

2011-01-01

A second order in space accurate implicit scheme for time-dependent advection-dispersion equations and a discrete fracture propagation model are employed to model solute transport in porous media. We study the impact of the fractures on mass transport and dispersion. To model flow and transport, pressure and transport equations are integrated using a finite-element, node-centered finite-volume approach. Fracture geometries are incrementally developed from a random distributions of material flaws using an adoptive geomechanical finite-element model that also produces fracture aperture distributions. This quasistatic propagation assumes a linear elastic rock matrix, and crack propagation is governed by a subcritical crack growth failure criterion. Fracture propagation, intersection, and closure are handled geometrically. The flow and transport simulations are separately conducted for a range of fracture densities that are generated by the geomechanical finite-element model. These computations show that the most influential parameters for solute transport in fractured porous media are as follows: fracture density and fracture-matrix flux ratio that is influenced by matrix permeability. Using an equivalent fracture aperture size, computed on the basis of equivalent permeability of the system, we also obtain an acceptable prediction of the macrodispersion of poorly interconnected fracture networks. The results hold for fractures at relatively low density. © 2011 American Physical Society.

Effects of simplifying fracture network representation on inert chemical migration in fracture-controlled aquifers

Science.gov (United States)

Wellman, Tristan; Shapiro, Allen M.; Hill, Mary C.

2009-01-01

While it is widely recognized that highly permeable 'large-scale' fractures dominate chemical migration in many fractured aquifers, recent studies suggest that the pervasive 'small-scale' fracturing once considered of less significance can be equally important for characterizing the spatial extent and residence time associated with transport processes. A detailed examination of chemical migration through fracture-controlled aquifers is used to advance this conceptual understanding. The influence of fracture structure is evaluated by quantifying the effects to transport caused by a systematic removal of fractures from three-dimensional discrete fracture models whose attributes are derived from geologic and hydrologic conditions at multiple field sites. Results indicate that the effects to transport caused by network simplification are sensitive to the fracture network characteristics, degree of network simplification, and plume travel distance, but primarily in an indirect sense since correlation to individual attributes is limited. Transport processes can be 'enhanced' or 'restricted' from network simplification meaning that the elimination of fractures may increase or decrease mass migration, mean travel time, dispersion, and tailing of the concentration plume. The results demonstrate why, for instance, chemical migration may not follow the classic advection-dispersion equation where dispersion approximates the effect of the ignored geologic structure as a strictly additive process to the mean flow. The analyses further reveal that the prediction error caused by fracture network simplification is reduced by at least 50% using the median estimate from an ensemble of simplified fracture network models, and that the error from network simplification is at least 70% less than the stochastic variability from multiple realizations. Copyright 2009 by the American Geophysical Union.

On-line Optimization-Based Simulators for Fractured and Non-fractured Reservoirs

Energy Technology Data Exchange (ETDEWEB)

Milind D. Deo

2005-08-31

Oil field development is a multi-million dollar business. Reservoir simulation is often used to guide the field management and development process. Reservoir characterization and geologic modeling tools have become increasingly sophisticated. As a result the geologic models produced are complex. Most reservoirs are fractured to a certain extent. The new geologic characterization methods are making it possible to map features such as faults and fractures, field-wide. Significant progress has been made in being able to predict properties of the faults and of the fractured zones. Traditionally, finite difference methods have been employed in discretizing the domains created by geologic means. For complex geometries, finite-element methods of discretization may be more suitable. Since reservoir simulation is a mature science, some of the advances in numerical methods (linear, nonlinear solvers and parallel computing) have not been fully realized in the implementation of most of the simulators. The purpose of this project was to address some of these issues. {sm_bullet} One of the goals of this project was to develop a series of finite-element simulators to handle problems of complex geometry, including systems containing faults and fractures. {sm_bullet} The idea was to incorporate the most modern computing tools; use of modular object-oriented computer languages, the most sophisticated linear and nonlinear solvers, parallel computing methods and good visualization tools. {sm_bullet} One of the tasks of the project was also to demonstrate the construction of fractures and faults in a reservoir using the available data and to assign properties to these features. {sm_bullet} Once the reservoir model is in place, it is desirable to find the operating conditions, which would provide the best reservoir performance. This can be accomplished by utilization optimization tools and coupling them with reservoir simulation. Optimization-based reservoir simulation was one of the

Development and experimental evaluation of models for low capillary number two-phase flows in rough walled fractures relevant to natural gradient conditions

International Nuclear Information System (INIS)

Glass, R.J.; Yarrington, L.; Nicholl, M.J.

1997-09-01

The major results from SNL's Conceptual Model Development and Validation Task (WBS 1.2.5.4.6) as developed through exploration of small scale processes were synthesized in Glass et al. to give guidance to Performance Assessment on improving conceptual models for isothermal flow in unsaturated, fractured rock. There, pressure saturation and relative permeability curves for single fractures were proposed to be a function of both fracture orientation within the gravity field and initial conditions. We refer the reader to Glass et al. for a discussion of the implications of this behavior for Performance Assessment. The scientific research we report here substantiates this proposed behavior. We address the modeling of phase structure within fractures under natural gradient conditions relevant to unsaturated flow through fractures. This phase structure underlies the calculation of effective properties for individual fractures and hence fracture networks as required for Performance Assessment. Standard Percolation (SP) and Invasion Percolation (IP) approaches have been recently proposed to model the underlying phase saturation structures within the individual fractures during conditions of two-phase flow. Subsequent analysis of these structures yields effective two-phase pressure-saturation and relative permeability relations for the fracture. However, both of these approaches yield structures that are at odds with physical reality as we see in experiments and thus effective properties calculated from these structures are in error. Here we develop and evaluate a Modified Invasion Percolation (MIP) approach to better model quasi-static immiscible displacement in fractures. The effects of gravity, contact angle, local aperature field geometry, and local in-plane interfacial curvature between phases are included in the calculation of invasion pressure for individual sites in a discretized aperture field

Radionuclide transport in fractured rock: quantifying releases from final disposal of high level waste

International Nuclear Information System (INIS)

Silveira, Claudia S. da; Alvim, Antonio C.M.

2013-01-01

Crystalline rock has been considered as a potentially suitable matrix for high-level radioactive waste (HLW) repository because it is found in very stable geological formations and may have very low permeability. In this study the adopted physical system consists of the rock matrix containing a discrete horizontal fracture in a water saturated porous rock and a system of vertical fractures as a lineament. The transport in the fractures - horizontal and vertical, is assumed to obey a relation convection-diffusion, while the molecular diffusion is considered dominant mechanism of transport in porous rock. In this model the decay chain is considered. We use a code in Fortran 90, where the partial differential equations that describe the movement of radionuclides were discretized by finite differences methods. We use the fully implicit method for temporal discretization schemes. The simulation was performed with relevant data of nuclides in spent fuel for performance assessment in a hypothetical repository, thus quantifying the radionuclides released into the host rock. (author)

CHARACTERIZATION OF IN-SITU STRESS AND PERMEABILITY IN FRACTURED RESERVOIRS

Energy Technology Data Exchange (ETDEWEB)

Daniel R. Burns; M. Nafi Toksoz

2002-12-31

We have extended a three-dimensional finite difference elastic wave propagation model previously developed at the Massachusetts Institute of Technology (MIT) Earth Resources Laboratory (ERL) for modeling and analyzing the effect of fractures on seismic waves. The code has been translated into C language and parallelized [using message passing interface (MPI)] to allow for larger models to be run on Linux PC computer clusters. We have also obtained another 3-D code from Lawrence Berkeley Laboratory, which we will use for verification of our ERL code results and also to run discrete fracture models. Testing of both codes is underway. We are working on a new finite difference model of borehole wave propagation for stressed formations. This code includes coordinate stretching to provide stable, variable grid sizes that will allow us to model the thin fluid annulus layers in borehole problems, especially for acoustic logging while drilling (LWD) applications. We are also extending our analysis routines for the inversion of flexural wave dispersion measurements for in situ stress estimates. Initial results on synthetic and limited field data are promising for a method to invert cross dipole data for the rotation angle and stress state simultaneously. A meeting is being scheduled between MIT and Shell Oil Company scientists to look at data from a fractured carbonate reservoir that may be made available to the project. The Focus/Disco seismic processing system from Paradigm Geophysical has been installed at ERL for field data analysis and as a platform for new analysis modules. We have begun to evaluate the flow properties of discrete fracture distributions through a simple 2D numerical model. Initial results illustrate how fluid flow pathways are very sensitive to variations in the geometry and apertures of fracture network.

Fracture modelling of a high performance armour steel

Science.gov (United States)

Skoglund, P.; Nilsson, M.; Tjernberg, A.

2006-08-01

The fracture characteristics of the high performance armour steel Armox 500T is investigated. Tensile mechanical experiments using samples with different notch geometries are used to investigate the effect of multi-axial stress states on the strain to fracture. The experiments are numerically simulated and from the simulation the stress at the point of fracture initiation is determined as a function of strain and these data are then used to extract parameters for fracture models. A fracture model based on quasi-static experiments is suggested and the model is tested against independent experiments done at both static and dynamic loading. The result show that the fracture model give reasonable good agreement between simulations and experiments at both static and dynamic loading condition. This indicates that multi-axial loading is more important to the strain to fracture than the deformation rate in the investigated loading range. However on-going work will further characterise the fracture behaviour of Armox 500T.

Modeling ground water flow and radioactive transport in a fractured aquifer

International Nuclear Information System (INIS)

Pohll, G.; Hassan, A.E.; Chapman, J.B.; Papelis, C.; Andricevic, R.

1999-01-01

Three-dimensional numerical modeling is used to characterize ground water flow and contaminant transport at the Shoal nuclear test site in north-central Nevada. The fractured rock aquifer at the site is modeled using an equivalent porous medium approach. Field data are used to characterize the fracture system into classes: large, medium, and no/small fracture zones. Hydraulic conductivities are assigned based on discrete interval measurements. Contaminants from the Shoal test are assumed to all be located within the cavity. Several challenging issues are addressed in this study. Radionuclides are apportioned between surface deposits and volume deposits in nuclear melt glass, based on their volatility and previous observations. Surface-deposited radionuclides are released hydraulically after equilibration of the cavity with the surrounding ground water system, and as a function of ground water flow through the higher-porosity cavity into the low-porosity surrounding aquifer. Processes that are modeled include the release functions, retardation, radioactive decay, prompt injection, and in growth of daughter products. Prompt injection of radionuclides away from the cavity is found to increase the arrival of mass at the control plane but is not found to significantly impact calculated concentrations due to increased spreading. Behavior of the other radionuclides is affected by the slow chemical release and retardation behavior. The transport calculations are sensitive to many flow and transport parameters. Most important are the heterogeneity of the flow field and effective porosity. The effect of porosity in radioactive decay is crucial and has not been adequately addressed in the literature. For reactive solutes, retardation and the glass dissolution rate are also critical

Representative elements: A step to large-scale fracture system simulation

International Nuclear Information System (INIS)

Clemo, T.M.

1987-01-01

Large-scale simulation of flow and transport in fractured media requires the development of a technique to represent the effect of a large number of fractures. Representative elements are used as a tool to model a subset of a fracture system as a single distributed entity. Representative elements are part of a modeling concept called dual permeability. Dual permeability modeling combines discrete fracture simulation of the most important fractures with the distributed modeling of the less important fracture of a fracture system. This study investigates the use of stochastic analysis to determine properties of representative elements. Given an assumption of fully developed laminar flow, the net fracture conductivities and hence flow velocities can be determined from descriptive statistics of fracture spacing, orientation, aperture, and extent. The distribution of physical characteristics about their mean leads to a distribution of the associated conductivities. The variance of hydraulic conductivity induces dispersion into the transport process. Simple fracture systems are treated to demonstrate the usefulness of stochastic analysis. Explicit equations for conductivity of an element are developed and the dispersion characteristics are shown. Explicit formulation of the hydraulic conductivity and transport dispersion reveals the dependence of these important characteristics on the parameters used to describe the fracture system. Understanding these dependencies will help to focus efforts to identify the characteristics of fracture systems. Simulations of stochastically generated fracture sets do not provide this explicit functional dependence on the fracture system parameters. 12 refs., 6 figs

Contaminant transport in fractured porous media: analytical solution for a two-member decay chain in a single fracture

International Nuclear Information System (INIS)

Sudicky, E.A.; Frind, E.O.

1984-01-01

An analytical solution is presented for the problem of radionuclide chain decay during transport through a discrete fracture situated in a porous rock matrix. The solution takes into account advection along the fracture, molecular diffusion from the fracture to the porous matrix, adsorption on the fracture face, adsorption in the rock matrix, and radioactive decay. The solution for the daughter product is in the form of a double integral which is evaluated by Gauss-Legendre quadrature. Results show that the daughter product tends to advance ahead of the parent nuclide even when the half-life of the parent is larger. This is attributed to the effect of chain decay in the matrix, which tends to reduce the diffusive loss of the daughter along the fracture. The examples also demonstrate that neglecting the parent nuclide and modeling its daughter as a single species can result in significant overestimation of arrival times at some point along the fracture. Although the analytical solution is restricted to a two-member chain for practical reasons, it represents a more realistic description of nuclide transport along a fracture than available single-species models. The solution may be of use for application to other contaminants undergoing different types of first-order transformation reactions

The hydro-mechanical modeling of the fractured media; Modelisation hydromecanique des milieux fractures

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

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.

Integrated Experimental and Computational Study of Hydraulic Fracturing and the Use of Alternative Fracking Fluids

Science.gov (United States)

Viswanathan, H.; Carey, J. W.; Karra, S.; Porter, M. L.; Rougier, E.; Zhang, D.; Makedonska, N.; Middleton, R. S.; Currier, R.; Gupta, R.; Lei, Z.; Kang, Q.; O'Malley, D.; Hyman, J.

2014-12-01

Shale gas is an unconventional fossil energy resource that is already having a profound impact on US energy independence and is projected to last for at least 100 years. Production of methane and other hydrocarbons from low permeability shale involves hydrofracturing of rock, establishing fracture connectivity, and multiphase fluid-flow and reaction processes all of which are poorly understood. The result is inefficient extraction with many environmental concerns. A science-based capability is required to quantify the governing mesoscale fluid-solid interactions, including microstructural control of fracture patterns and the interaction of engineered fluids with hydrocarbon flow. These interactions depend on coupled thermo-hydro-mechanical-chemical (THMC) processes over scales from microns to tens of meters. Determining the key mechanisms in subsurface THMC systems has been impeded due to the lack of sophisticated experimental methods to measure fracture aperture and connectivity, multiphase permeability, and chemical exchange capacities at the high temperature, pressure, and stresses present in the subsurface. This project uses innovative high-pressure microfluidic and triaxial core flood experiments on shale to explore fracture-permeability relations and the extraction of hydrocarbon. These data are integrated with simulations including lattice Boltzmann modeling of pore-scale processes, finite-element/discrete element models of fracture development in the near-well environment, discrete-fracture modeling of the reservoir, and system-scale models to assess the economics of alternative fracturing fluids. The ultimate goal is to make the necessary measurements to develop models that can be used to determine the reservoir operating conditions necessary to gain a degree of control over fracture generation, fluid flow, and interfacial processes over a range of subsurface conditions.

PHASE CHAOS IN THE DISCRETE KURAMOTO MODEL

DEFF Research Database (Denmark)

Maistrenko, V.; Vasylenko, A.; Maistrenko, Y.

2010-01-01

The paper describes the appearance of a novel, high-dimensional chaotic regime, called phase chaos, in a time-discrete Kuramoto model of globally coupled phase oscillators. This type of chaos is observed at small and intermediate values of the coupling strength. It arises from the nonlinear...... interaction among the oscillators, while the individual oscillators behave periodically when left uncoupled. For the four-dimensional time-discrete Kuramoto model, we outline the region of phase chaos in the parameter plane and determine the regions where phase chaos coexists with different periodic...

Modeling and simulation of discrete event systems

CERN Document Server

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

ADAM: analysis of discrete models of biological systems using computer algebra.

Science.gov (United States)

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

Discrete competing risk model with application to modeling bus-motor failure data

International Nuclear Information System (INIS)

Jiang, R.

2010-01-01

Failure data are often modeled using continuous distributions. However, a discrete distribution can be appropriate for modeling interval or grouped data. When failure data come from a complex system, a simple discrete model can be inappropriate for modeling such data. This paper presents two types of discrete distributions. One is formed by exponentiating an underlying distribution, and the other is a two-fold competing risk model. The paper focuses on two special distributions: (a) exponentiated Poisson distribution and (b) competing risk model involving a geometric distribution and an exponentiated Poisson distribution. The competing risk model has a decreasing-followed-by-unimodal mass function and a bathtub-shaped failure rate. Five classical data sets on bus-motor failures can be simultaneously and appropriately fitted by a general 5-parameter competing risk model with the parameters being functions of the number of successive failures. The lifetime and aging characteristics of the fitted distribution are analyzed.

Discrete gradients in discrete classical mechanics

International Nuclear Information System (INIS)

Renna, L.

1987-01-01

A simple model of discrete classical mechanics is given where, starting from the continuous Hamilton equations, discrete equations of motion are established together with a proper discrete gradient definition. The conservation laws of the total discrete momentum, angular momentum, and energy are demonstrated

A constrained Delaunay discretization method for adaptively meshing highly discontinuous geological media

Science.gov (United States)

Wang, Yang; Ma, Guowei; Ren, Feng; Li, Tuo

2017-12-01

A constrained Delaunay discretization method is developed to generate high-quality doubly adaptive meshes of highly discontinuous geological media. Complex features such as three-dimensional discrete fracture networks (DFNs), tunnels, shafts, slopes, boreholes, water curtains, and drainage systems are taken into account in the mesh generation. The constrained Delaunay triangulation method is used to create adaptive triangular elements on planar fractures. Persson's algorithm (Persson, 2005), based on an analogy between triangular elements and spring networks, is enriched to automatically discretize a planar fracture into mesh points with varying density and smooth-quality gradient. The triangulated planar fractures are treated as planar straight-line graphs (PSLGs) to construct piecewise-linear complex (PLC) for constrained Delaunay tetrahedralization. This guarantees the doubly adaptive characteristic of the resulted mesh: the mesh is adaptive not only along fractures but also in space. The quality of elements is compared with the results from an existing method. It is verified that the present method can generate smoother elements and a better distribution of element aspect ratios. Two numerical simulations are implemented to demonstrate that the present method can be applied to various simulations of complex geological media that contain a large number of discontinuities.

An Efficient XFEM Approximation of Darcy Flows in Arbitrarily Fractured Porous Media

Directory of Open Access Journals (Sweden)

Fumagalli Alessio

2014-07-01

Full Text Available Subsurface flows are influenced by the presence of faults and large fractures which act as preferential paths or barriers for the flow. In literature models were proposed to handle fractures in a porous medium as objects of codimension 1. In this work we consider the case of a network of intersecting fractures, with the aim of deriving physically consistent and effective interface conditions to impose at the intersection between fractures. This new model accounts for the angle between fractures at the intersections and allows for jumps of pressure across the intersection. This latter property permits to describe more accurately the flow when fractures are characterised by different properties, than other models that impose pressure continuity. The main mathematical properties of the model, derived in the two-dimensional setting, are analysed. As concerns the numerical discretization we allow the grids of the fractures to be independent, thus in general non-matching at the intersection, by means of the Extended Finite Element Method (XFEM, to increase the flexibility of the method in the case of complex geometries characterized by a high number of fractures.

A discrete stress-strength interference model based on universal generating function

International Nuclear Information System (INIS)

An Zongwen; Huang Hongzhong; Liu Yu

2008-01-01

Continuous stress-strength interference (SSI) model regards stress and strength as continuous random variables with known probability density function. This, to some extent, results in a limitation of its application. In this paper, stress and strength are treated as discrete random variables, and a discrete SSI model is presented by using the universal generating function (UGF) method. Finally, case studies demonstrate the validity of the discrete model in a variety of circumstances, in which stress and strength can be represented by continuous random variables, discrete random variables, or two groups of experimental data

Statistical model of fractures and deformation zones. Preliminary site description, Laxemar subarea, version 1.2

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.

Physical models on discrete space and time

International Nuclear Information System (INIS)

Lorente, M.

1986-01-01

The idea of space and time quantum operators with a discrete spectrum has been proposed frequently since the discovery that some physical quantities exhibit measured values that are multiples of fundamental units. This paper first reviews a number of these physical models. They are: the method of finite elements proposed by Bender et al; the quantum field theory model on discrete space-time proposed by Yamamoto; the finite dimensional quantum mechanics approach proposed by Santhanam et al; the idea of space-time as lattices of n-simplices proposed by Kaplunovsky et al; and the theory of elementary processes proposed by Weizsaecker and his colleagues. The paper then presents a model proposed by the authors and based on the (n+1)-dimensional space-time lattice where fundamental entities interact among themselves 1 to 2n in order to build up a n-dimensional cubic lattice as a ground field where the physical interactions take place. The space-time coordinates are nothing more than the labelling of the ground field and take only discrete values. 11 references

Discrete-Slots Models of Visual Working-Memory Response Times

Science.gov (United States)

Donkin, Christopher; Nosofsky, Robert M.; Gold, Jason M.; Shiffrin, Richard M.

2014-01-01

Much recent research has aimed to establish whether visual working memory (WM) is better characterized by a limited number of discrete all-or-none slots or by a continuous sharing of memory resources. To date, however, researchers have not considered the response-time (RT) predictions of discrete-slots versus shared-resources models. To complement the past research in this field, we formalize a family of mixed-state, discrete-slots models for explaining choice and RTs in tasks of visual WM change detection. In the tasks under investigation, a small set of visual items is presented, followed by a test item in 1 of the studied positions for which a change judgment must be made. According to the models, if the studied item in that position is retained in 1 of the discrete slots, then a memory-based evidence-accumulation process determines the choice and the RT; if the studied item in that position is missing, then a guessing-based accumulation process operates. Observed RT distributions are therefore theorized to arise as probabilistic mixtures of the memory-based and guessing distributions. We formalize an analogous set of continuous shared-resources models. The model classes are tested on individual subjects with both qualitative contrasts and quantitative fits to RT-distribution data. The discrete-slots models provide much better qualitative and quantitative accounts of the RT and choice data than do the shared-resources models, although there is some evidence for “slots plus resources” when memory set size is very small. PMID:24015956

Experimental Characterization and Modeling of the Fracturing Behavior of Marcellus Shale

Science.gov (United States)

Jin, C.; Li, W.; Sageman, B. B.; Cusatis, G.

2014-12-01

Adequate knowledge and prediction of mechanical properties of shale are pivotal to the design of hydraulic fractures. The urgent technical challenge of such an endeavor is how to translate the highly heterogeneous nature of shale into a predictive model of the mechanical properties. Our group addressed this challenge by adopting a combined experimental and numerical approach to investigate fracture processes and failure mechanisms of shale.Lattice Discrete Particle Model (LDPM), having shown superior capabilities in predicting qualitative and quantitative behavior of concrete and concrete-like materials, as shown in Fig. 1, has been adopted to simulate mesoscale behavior of shale. The polyhedral cell system defining the geometric attributes of the rock microstructure is built via a 3D tessellation procedure based on X-ray microtomography results of microstructure and grain size distribution of shale specimens. The adopted tessellation procedure makes use of well-established packing algorithms for no-contact spherical particle placement and non-overlapping volume tessellation. The polyhedral particles interact through triangular facets where appropriate measure of stresses and strains are defined. Especially, LDPM is extended to simulate transversely isotropic materials by using orientation-dependent and strain-dependent strength limits coupled with orientation-dependent normal and shear stiffnesses on each facet. Appropriate interface constitutive equations are formulated to simulate all phenomena occurring at a scale that is smaller than the resolution of LDPM system, including microscopic fracture, frictional contact, particle breakage, pore collapse, and distributed damage. Bedding planes and natural joints are characterized by greatly decreased strength limits for facets within that region. To calibrate/validate the LDPM model, microscopic and mesoscopic experiments, including Brazilian tests, uniaxial compression tests, and three point-bending tests, are

Upscaling permeability for three-dimensional fractured porous rocks with the multiple boundary method

Science.gov (United States)

Chen, Tao; Clauser, Christoph; Marquart, Gabriele; Willbrand, Karen; Hiller, Thomas

2018-02-01

Upscaling permeability of grid blocks is crucial for groundwater models. A novel upscaling method for three-dimensional fractured porous rocks is presented. The objective of the study was to compare this method with the commonly used Oda upscaling method and the volume averaging method. First, the multiple boundary method and its computational framework were defined for three-dimensional stochastic fracture networks. Then, the different upscaling methods were compared for a set of rotated fractures, for tortuous fractures, and for two discrete fracture networks. The results computed by the multiple boundary method are comparable with those of the other two methods and fit best the analytical solution for a set of rotated fractures. The errors in flow rate of the equivalent fracture model decrease when using the multiple boundary method. Furthermore, the errors of the equivalent fracture models increase from well-connected fracture networks to poorly connected ones. Finally, the diagonal components of the equivalent permeability tensors tend to follow a normal or log-normal distribution for the well-connected fracture network model with infinite fracture size. By contrast, they exhibit a power-law distribution for the poorly connected fracture network with multiple scale fractures. The study demonstrates the accuracy and the flexibility of the multiple boundary upscaling concept. This makes it attractive for being incorporated into any existing flow-based upscaling procedures, which helps in reducing the uncertainty of groundwater models.

Ecological monitoring in a discrete-time prey-predator model.

Science.gov (United States)

Gámez, M; López, I; Rodríguez, C; Varga, Z; Garay, J

2017-09-21

The paper is aimed at the methodological development of ecological monitoring in discrete-time dynamic models. In earlier papers, in the framework of continuous-time models, we have shown how a systems-theoretical methodology can be applied to the monitoring of the state process of a system of interacting populations, also estimating certain abiotic environmental changes such as pollution, climatic or seasonal changes. In practice, however, there may be good reasons to use discrete-time models. (For instance, there may be discrete cycles in the development of the populations, or observations can be made only at discrete time steps.) Therefore the present paper is devoted to the development of the monitoring methodology in the framework of discrete-time models of population ecology. By monitoring we mean that, observing only certain component(s) of the system, we reconstruct the whole state process. This may be necessary, e.g., when in a complex ecosystem the observation of the densities of certain species is impossible, or too expensive. For the first presentation of the offered methodology, we have chosen a discrete-time version of the classical Lotka-Volterra prey-predator model. This is a minimal but not trivial system where the methodology can still be presented. We also show how this methodology can be applied to estimate the effect of an abiotic environmental change, using a component of the population system as an environmental indicator. Although this approach is illustrated in a simplest possible case, it can be easily extended to larger ecosystems with several interacting populations and different types of abiotic environmental effects. Copyright © 2017 Elsevier Ltd. All rights reserved.

Cohesive fracture model for functionally graded fiber reinforced concrete

International Nuclear Information System (INIS)

Park, Kyoungsoo; Paulino, Glaucio H.; Roesler, Jeffery

2010-01-01

A simple, effective, and practical constitutive model for cohesive fracture of fiber reinforced concrete is proposed by differentiating the aggregate bridging zone and the fiber bridging zone. The aggregate bridging zone is related to the total fracture energy of plain concrete, while the fiber bridging zone is associated with the difference between the total fracture energy of fiber reinforced concrete and the total fracture energy of plain concrete. The cohesive fracture model is defined by experimental fracture parameters, which are obtained through three-point bending and split tensile tests. As expected, the model describes fracture behavior of plain concrete beams. In addition, it predicts the fracture behavior of either fiber reinforced concrete beams or a combination of plain and fiber reinforced concrete functionally layered in a single beam specimen. The validated model is also applied to investigate continuously, functionally graded fiber reinforced concrete composites.

Specimen-specific modeling of hip fracture pattern and repair.

Science.gov (United States)

Ali, Azhar A; Cristofolini, Luca; Schileo, Enrico; Hu, Haixiang; Taddei, Fulvia; Kim, Raymond H; Rullkoetter, Paul J; Laz, Peter J

2014-01-22

Hip fracture remains a major health problem for the elderly. Clinical studies have assessed fracture risk based on bone quality in the aging population and cadaveric testing has quantified bone strength and fracture loads. Prior modeling has primarily focused on quantifying the strain distribution in bone as an indicator of fracture risk. Recent advances in the extended finite element method (XFEM) enable prediction of the initiation and propagation of cracks without requiring a priori knowledge of the crack path. Accordingly, the objectives of this study were to predict femoral fracture in specimen-specific models using the XFEM approach, to perform one-to-one comparisons of predicted and in vitro fracture patterns, and to develop a framework to assess the mechanics and load transfer in the fractured femur when it is repaired with an osteosynthesis implant. Five specimen-specific femur models were developed from in vitro experiments under a simulated stance loading condition. Predicted fracture patterns closely matched the in vitro patterns; however, predictions of fracture load differed by approximately 50% due to sensitivity to local material properties. Specimen-specific intertrochanteric fractures were induced by subjecting the femur models to a sideways fall and repaired with a contemporary implant. Under a post-surgical stance loading, model-predicted load sharing between the implant and bone across the fracture surface varied from 59%:41% to 89%:11%, underscoring the importance of considering anatomic and fracture variability in the evaluation of implants. XFEM modeling shows potential as a macro-level analysis enabling fracture investigations of clinical cohorts, including at-risk groups, and the design of robust implants. © 2013 Published by Elsevier Ltd.

Water flow and solute transport through fractured rock

International Nuclear Information System (INIS)

Bolt, J.E.; Bourke, P.J.; Pascoe, D.M.; Watkins, V.M.B.; Kingdon, R.D.

1990-09-01

In densely fractured slate at the Nirex research site in Cornwall, the positions, orientations and hydraulic conductivities of the 380 fractures intersecting a drill hole between 9 and 50 m depth have been individually measured. These data have been used: to determine the dimensions of statistically representative volumes of the network of fractures and to predict, using discrete flow path modelling and the NAPSAC code, the total flows into the fractures when large numbers are simultaneously pressurised along various lengths of the hole. Corresponding measurements, which validated the NAPSAC code to factor of two accuracy for the Cornish site, are reported. Possibilities accounting for this factor are noted for experimental investigation, and continuing, more extensive, inter hole flow and transport measurements are outlined. The application of this experimental and theoretical approach for calculating radionuclide transport in less densely fractured rock suitable for waste disposal is discussed. (Author)

Numerical studies of fluid and heat flow near high-level nuclear waste packages emplaced in partially saturated fractured tuff

International Nuclear Information System (INIS)

Pruess, K.; Tsang, Y.W.; Wang, J.S.Y.

1984-11-01

We have performed modeling studies on the simultaneous transport of heat, liquid water, vapor, and air in partially saturated fractured porous rock. Formation parameters were chosen as representative of the potential repository horizon in the Topopah Spring Unit of the Yucca Mountain tuffs. The presence of fractures makes the transport problem very complex, both in terms of flow geometry and physics. The numerical simulator ''TOUGH'' used for our flow calculations takes into account most of the physical effects which are important in multi-phase fluid and heat flow. It has provisions for handling the extreme non-linearities which arise in phase transitions, component disappearances, and capillary discontinuities at fracture faces. We model a region around an infinite linear string of nuclear waste canisters, taking into account both the discrete fractures and the porous matrix. From an analysis of the results obtained with explicit fractures, we develop equivalent continuum models which can reproduce the temperature, saturation, and pressure variation, and gas and liquid flow rates of the discrete fracture-porous matrix calculations. The equivalent continuum approach makes use of a generalized relative permeability concept to take into account the fracture effects. This results in a substantial simplification of the flow problem which makes larger scale modeling of complicated unsaturated fractured porous systems feasible. Potential applications for regional scale simulations and limitations of the continuum approach are discussed. 35 refs., 14 figs., 4 tabs

Modelling tracer transport in fractured rock at Stripa

International Nuclear Information System (INIS)

Herbert, A.

1992-01-01

We present the results of a modelling study, making predictions for tracer transport experiments carried out within the H-zone feature in the Stripa mine. We use a direct fracture network approach to represent the system of interconnected flow-conducting fractures comprising this zone. It is a highly fractured granite, and our fracture-network models include up to 60000 fractures. We have had to develop efficient algorithms to calculate the flow and transport through these networks; these techniques are described and justified. The first stage of modelling addressed two saline injection experiments. The results of these were known to us and so in addition to 'predicting' the results of these experiments, we used them to calibrate a flow model of the experimental site. This model was then used to make true 'blind' predictions for a set of tracer experiments carried out in the natural head-field, caused by an open drift. Where our flow model was good, our predictions were found to be very accurate, explaining the dispersion in the tracer breakthrough in terms of the fracture network geometry. Discrepancies for experiments in less well characterised regions of the H-zone are presented, and we suggest that the errors in these predictions are a consequence of the inaccuracies of the flow-field. We have demonstrated the use of large-scale fracture network modelling. It has proved very successful, and made very accurate predictions of field experiments carried out at the Stripa mine. The measured dispersion of tracers can be accounted for by the geometry of the fracture network flow system. (14 refs.) (au)

Measuring and Modeling Flow in Welded Fractured Tuffs

International Nuclear Information System (INIS)

R. Salve; C. Doughty; J.S. Wang

2001-01-01

We have carried out a series of in situ liquid-release experiments in conjunction with a numerical modeling study to examine the effect of the rock matrix on liquid flow and transport occurring primarily through the fracture network. Field experiments were conducted in the highly fractured Topopah Spring welded tuff at a site accessed from the Exploratory Studies Facility (ESFS), an underground laboratory in the unsaturated zone at Yucca Mountain, Nevada. During the experiment, wetting-front movement, flow-field evolution, and drainage of fracture flow paths were evaluated. Modeling was used to aid in experimental design, predict experimental results, and study the physical processes accompanying liquid flow through unsaturated fractured welded tuff. Field experiments and modeling suggest that it may not be sufficient to conceptualize the fractured tuff as consisting of a single network of high-permeability fractures embedded in a low-permeability matrix. The need to include a secondary fracture network is demonstrated by comparison to the liquid flow observed in the field

Sensitivity Analysis of the Bone Fracture Risk Model

Science.gov (United States)

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

Modelling road accident blackspots data with the discrete generalized Pareto distribution.

Science.gov (United States)

Prieto, Faustino; Gómez-Déniz, Emilio; Sarabia, José María

2014-10-01

This study shows how road traffic networks events, in particular road accidents on blackspots, can be modelled with simple probabilistic distributions. We considered the number of crashes and the number of fatalities on Spanish blackspots in the period 2003-2007, from Spanish General Directorate of Traffic (DGT). We modelled those datasets, respectively, with the discrete generalized Pareto distribution (a discrete parametric model with three parameters) and with the discrete Lomax distribution (a discrete parametric model with two parameters, and particular case of the previous model). For that, we analyzed the basic properties of both parametric models: cumulative distribution, survival, probability mass, quantile and hazard functions, genesis and rth-order moments; applied two estimation methods of their parameters: the μ and (μ+1) frequency method and the maximum likelihood method; used two goodness-of-fit tests: Chi-square test and discrete Kolmogorov-Smirnov test based on bootstrap resampling; and compared them with the classical negative binomial distribution in terms of absolute probabilities and in models including covariates. We found that those probabilistic models can be useful to describe the road accident blackspots datasets analyzed. Copyright © 2014 Elsevier Ltd. All rights reserved.

Mathematical modelling of fracture hydrology

International Nuclear Information System (INIS)

Herbert, A.W.; Hodgkindon, D.P.; Lever, D.A.; Robinson, P.C.; Rae, J.

1985-01-01

This report reviews work carried out between January 1983 and December 1984 for the CEC/DOE contract 'Mathematical Modelling of Fracture Hydrology' which forms part of the CEC Mirage project (CEC 1984. Come 1985. Bourke et. al. 1983). It describes the development and use of a variety of mathematical models for the flow of water and transport of radionuclides in flowing groundwater. These models have an important role to play in assessing the long-term safety of radioactive waste burial, and in the planning and interpretation of associated experiments. The work is reported under five headings, namely 1) Statistical fracture network modelling, 2) Continuum models of flow and transport, 3) Simplified models, 4) Analysis of laboratory experiments, 5) Analysis of field experiments

Thermal modelling using discrete vasculature for thermal therapy: a review

Science.gov (United States)

Kok, H.P.; Gellermann, J.; van den Berg, C.A.T.; Stauffer, P.R.; Hand, J.W.; Crezee, J.

2013-01-01

Reliable temperature information during clinical hyperthermia and thermal ablation is essential for adequate treatment control, but conventional temperature measurements do not provide 3D temperature information. Treatment planning is a very useful tool to improve treatment quality and substantial progress has been made over the last decade. Thermal modelling is a very important and challenging aspect of hyperthermia treatment planning. Various thermal models have been developed for this purpose, with varying complexity. Since blood perfusion is such an important factor in thermal redistribution of energy in in vivo tissue, thermal simulations are most accurately performed by modelling discrete vasculature. This review describes the progress in thermal modelling with discrete vasculature for the purpose of hyperthermia treatment planning and thermal ablation. There has been significant progress in thermal modelling with discrete vasculature. Recent developments have made real-time simulations possible, which can provide feedback during treatment for improved therapy. Future clinical application of thermal modelling with discrete vasculature in hyperthermia treatment planning is expected to further improve treatment quality. PMID:23738700

Evaluation on the cost-effective threshold of osteoporosis treatment on elderly women in China using discrete event simulation model.

Science.gov (United States)

Ni, W; Jiang, Y

2017-02-01

This study used a simulation model to determine the cost-effective threshold of fracture risk to treat osteoporosis among elderly Chinese women. Osteoporosis treatment is cost-effective among average-risk women who are at least 75 years old and above-average-risk women who are younger than 75 years old. Aging of the Chinese population is imposing increasing economic burden of osteoporosis. This study evaluated the cost-effectiveness of osteoporosis treatment among the senior Chinese women population. A discrete event simulation model using age-specific probabilities of hip fracture, clinical vertebral fracture, wrist fracture, humerus fracture, and other fracture; costs (2015 US dollars); and quality-adjusted life years (QALYs) was used to assess the cost-effectiveness of osteoporosis treatment. Incremental cost-effectiveness ratio (ICER) was calculated. The willingness to pay (WTP) for a QALY in China was compared with the calculated ICER to decide the cost-effectiveness. To determine the absolute 10-year hip fracture probability at which the osteoporosis treatment became cost-effective, average age-specific probabilities for all fractures were multiplied by a relative risk (RR) that was systematically varied from 0 to 10 until the WTP threshold was observed for treatment relative to no intervention. Sensitivity analyses were also performed to evaluate the impacts from WTP and annual treatment costs. In baseline analysis, simulated ICERs were higher than the WTP threshold among Chinese women younger than 75, but much lower than the WTP among the older population. Sensitivity analyses indicated that cost-effectiveness could vary due to a higher WTP threshold or a lower annual treatment cost. A 30 % increase in WTP or a 30 % reduction in annual treatment costs will make osteoporosis treatment cost-effective for Chinese women population from 55 to 85. The current study provides evidence that osteoporosis treatment is cost-effective among a subpopulation of

Modelling of Local Necking and Fracture in Aluminium Alloys

International Nuclear Information System (INIS)

Achani, D.; Eriksson, M.; Hopperstad, O. S.; Lademo, O.-G.

2007-01-01

Non-linear Finite Element simulations are extensively used in forming and crashworthiness studies of automotive components and structures in which fracture need to be controlled. For thin-walled ductile materials, the fracture-related phenomena that must be properly represented are thinning instability, ductile fracture and through-thickness shear instability. Proper representation of the fracture process relies on the accuracy of constitutive and fracture models and their parameters that need to be calibrated through well defined experiments. The present study focuses on local necking and fracture which is of high industrial importance, and uses a phenomenological criterion for modelling fracture in aluminium alloys. As an accurate description of plastic anisotropy is important, advanced phenomenological constitutive equations based on the yield criterion YLD2000/YLD2003 are used. Uniaxial tensile tests and disc compression tests are performed for identification of the constitutive model parameters. Ductile fracture is described by the Cockcroft-Latham fracture criterion and an in-plane shear tests is performed to identify the fracture parameter. The reason is that in a well designed in-plane shear test no thinning instability should occur and it thus gives more direct information about the phenomenon of ductile fracture. Numerical simulations have been performed using a user-defined material model implemented in the general-purpose non-linear FE code LS-DYNA. The applicability of the model is demonstrated by correlating the predicted and experimental response in the in-plane shear tests and additional plane strain tension tests

Analysis of compressive fracture in rock using statistical techniques

Energy Technology Data Exchange (ETDEWEB)

Blair, S.C.

1994-12-01

Fracture of rock in compression is analyzed using a field-theory model, and the processes of crack coalescence and fracture formation and the effect of grain-scale heterogeneities on macroscopic behavior of rock are studied. The model is based on observations of fracture in laboratory compression tests, and incorporates assumptions developed using fracture mechanics analysis of rock fracture. The model represents grains as discrete sites, and uses superposition of continuum and crack-interaction stresses to create cracks at these sites. The sites are also used to introduce local heterogeneity. Clusters of cracked sites can be analyzed using percolation theory. Stress-strain curves for simulated uniaxial tests were analyzed by studying the location of cracked sites, and partitioning of strain energy for selected intervals. Results show that the model implicitly predicts both development of shear-type fracture surfaces and a strength-vs-size relation that are similar to those observed for real rocks. Results of a parameter-sensitivity analysis indicate that heterogeneity in the local stresses, attributed to the shape and loading of individual grains, has a first-order effect on strength, and that increasing local stress heterogeneity lowers compressive strength following an inverse power law. Peak strength decreased with increasing lattice size and decreasing mean site strength, and was independent of site-strength distribution. A model for rock fracture based on a nearest-neighbor algorithm for stress redistribution is also presented and used to simulate laboratory compression tests, with promising results.

Adaptive Multiscale Modeling of Geochemical Impacts on Fracture Evolution

Science.gov (United States)

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

Numerical Study of Critical Role of Rock Heterogeneity in Hydraulic Fracture Propagation

Energy Technology Data Exchange (ETDEWEB)

J. Zhou; H. Huang; M. Deo

2016-03-01

Log and seismic data indicate that most shale formations have strong heterogeneity. Conventional analytical and semi-analytical fracture models are not enough to simulate the complex fracture propagation in these highly heterogeneous formation. Without considering the intrinsic heterogeneity, predicted morphology of hydraulic fracture may be biased and misleading in optimizing the completion strategy. In this paper, a fully coupling fluid flow and geomechanics hydraulic fracture simulator based on dual-lattice Discrete Element Method (DEM) is used to predict the hydraulic fracture propagation in heterogeneous reservoir. The heterogeneity of rock is simulated by assigning different material force constant and critical strain to different particles and is adjusted by conditioning to the measured data and observed geological features. Based on proposed model, the effects of heterogeneity at different scale on micromechanical behavior and induced macroscopic fractures are examined. From the numerical results, the microcrack will be more inclined to form at the grain weaker interface. The conventional simulator with homogeneous assumption is not applicable for highly heterogeneous shale formation.

Natural fracturing of rocks: application to the Ahnet basin (Algeria); Fracturation naturelle des roches: application au bassin de l`Ahnet (Algerie)

Energy Technology Data Exchange (ETDEWEB)

Badsi, M

1998-07-06

In the Ahnet basin, the production seems to be unrelated to lithological variations in the reservoirs. In these large anticline structures, located in the central Ahnet basin, the presence of gas has been proven, but only a few production wells have been moderately successful. This inconsistency is probably related to the spatial distribution of fracturing throughout the reservoir. In order to investigate several hypothesis, we used several approach to solve problems posed by the interpreter: namely understanding the deformation process, predicting the fractured zones and building the discrete model of fracture network. This approach combines several methods, including sand box modelling, numerical modelling and Statistics rules, often related with fractal behaviour of faults families, have been used for extrapolating observations from seismic or from wells. The numerical tools and sand box analysis have allowed us to answer to the questions related to the formation of this large anticlines in the Ahnet basin and suggest a probable origin of the variation in the spatial distribution of natural fractures. The deterministic predictions of small-scale faults use probabilistic approaches for spatial interpolation assuming implicitly relationship between detected large faults and unresolved small faults. The statistical modelling is used to carry out analysis of the spatial variation of mean fracture attributes at the global scale (a few kilometers) and a 3D stochastic modelling of the fracture system at the local scale (a few ten of meters). (author) 139 refs.

Discrete modelling of drapery systems

Science.gov (United States)

Thoeni, Klaus; Giacomini, Anna

2016-04-01

Drapery systems are an efficient and cost-effective measure in preventing and controlling rockfall hazards on rock slopes. The simplest form consists of a row of ground anchors along the top of the slope connected to a horizontal support cable from which a wire mesh is suspended down the face of the slope. Such systems are generally referred to as simple or unsecured draperies (Badger and Duffy 2012). Variations such as secured draperies, where a pattern of ground anchors is incorporated within the field of the mesh, and hybrid systems, where the upper part of an unsecured drapery is elevated to intercept rockfalls originating upslope of the installation, are becoming more and more popular. This work presents a discrete element framework for simulation of unsecured drapery systems and its variations. The numerical model is based on the classical discrete element method (DEM) and implemented into the open-source framework YADE (Šmilauer et al., 2010). The model takes all relevant interactions between block, drapery and slope into account (Thoeni et al., 2014) and was calibrated and validated based on full-scale experiments (Giacomini et al., 2012).The block is modelled as a rigid clump made of spherical particles which allows any shape to be approximated. The drapery is represented by a set of spherical particle with remote interactions. The behaviour of the remote interactions is governed by the constitutive behaviour of the wire and generally corresponds to a piecewise linear stress-strain relation (Thoeni et al., 2013). The same concept is used to model wire ropes. The rock slope is represented by rigid triangular elements where material properties (e.g., normal coefficient of restitution, friction angle) are assigned to each triangle. The capabilities of the developed model to simulate drapery systems and estimate the residual hazard involved with such systems is shown. References Badger, T.C., Duffy, J.D. (2012) Drapery systems. In: Turner, A.K., Schuster R

Experimental Fracture Model versus Osteotomy Model in Metacarpal Bone Plate Fixation

Directory of Open Access Journals (Sweden)

S. Ochman

2011-01-01

Full Text Available Introduction. Osteotomy or fracture models can be used to evaluate mechanical properties of fixation techniques of the hand skeleton in vitro. Although many studies make use of osteotomy models, fracture models simulate the clinical situation more realistically. This study investigates monocortical and bicortical plate fixation on metacarpal bones considering both aforementioned models to decide which method is best suited to test fixation techniques. Methods. Porcine metacarpal bones (=40 were randomized into 4 groups. In groups I and II bones were fractured with a modified 3-point bending test. The intact bones represented a further control group to which the other groups after fixation were compared. In groups III and IV a standard osteotomy was carried out. Bones were fixated with plates monocortically (group I, III and bicortically (group II, IV and tested for failure. Results. Bones fractured at a mean maximum load of 482.8 N ± 104.8 N with a relative standard deviation (RSD of 21.7%, mean stiffness was 122.3 ± 35 N/mm. In the fracture model, there was a significant difference (=0.01 for maximum load of monocortically and bicortically fixed bones in contrast to the osteotomy model (=0.9. Discussion. In the fracture model, because one can use the same bone for both measurements in the intact state and the bone-plate construct states, the impact of inter-individual differences is reduced. In contrast to the osteotomy model there are differences between monocortical and bicortical fixations in the fracture model. Thus simulation of the in vivo situation is better and seems to be suitable for the evaluation of mechanical properties of fixation techniques on metacarpals.

Anisotropic composite human skull model and skull fracture validation against temporo-parietal skull fracture.

Science.gov (United States)

Sahoo, Debasis; Deck, Caroline; Yoganandan, Narayan; Willinger, Rémy

2013-12-01

A composite material model for skull, taking into account damage is implemented in the Strasbourg University finite element head model (SUFEHM) in order to enhance the existing skull mechanical constitutive law. The skull behavior is validated in terms of fracture patterns and contact forces by reconstructing 15 experimental cases. The new SUFEHM skull model is capable of reproducing skull fracture precisely. The composite skull model is validated not only for maximum forces, but also for lateral impact against actual force time curves from PMHS for the first time. Skull strain energy is found to be a pertinent parameter to predict the skull fracture and based on statistical (binary logistical regression) analysis it is observed that 50% risk of skull fracture occurred at skull strain energy of 544.0mJ. © 2013 Elsevier Ltd. All rights reserved.

Modeling of flow through fractured tuff at Fran Ridge

International Nuclear Information System (INIS)

Eaton, R.R.; Ho, C.K.; Glass, R.J.; Nicholl, M.J.; Arnold, B.W.

1996-01-01

Numerical studies have modeled an infiltration experiment at Fran Ridge, using the TOUGH2 code, to aid in the selection of computational models for waste repository performance assessment. This study investigates the capabilities of TOUGH2 to simulate transient flows through highly fractured tuff, and provides a possible means of calibrating hydrologic parameters such as effective fracture aperture and fracture-matrix connectivity. Two distinctly different conceptual models were used in the TOUGH2 code, the dual permeability model and the equivalent continuum model. The field experiments involved the infiltration of dyed ponded water in highly fractured tuff. The infiltration observed in the experiment was subsequently modeled using Fran Ridge fracture frequencies, obtained during post-experiment site excavation. Comparison of the TOUGH2 results obtained using the two conceptual models gives insight into their relative strengths and weaknesses

Modeling discrete and rhythmic movements through motor primitives: a review.

Science.gov (United States)

Degallier, Sarah; Ijspeert, Auke

2010-10-01

Rhythmic and discrete movements are frequently considered separately in motor control, probably because different techniques are commonly used to study and model them. Yet the increasing interest in finding a comprehensive model for movement generation requires bridging the different perspectives arising from the study of those two types of movements. In this article, we consider discrete and rhythmic movements within the framework of motor primitives, i.e., of modular generation of movements. In this way we hope to gain an insight into the functional relationships between discrete and rhythmic movements and thus into a suitable representation for both of them. Within this framework we can define four possible categories of modeling for discrete and rhythmic movements depending on the required command signals and on the spinal processes involved in the generation of the movements. These categories are first discussed in terms of biological concepts such as force fields and central pattern generators and then illustrated by several mathematical models based on dynamical system theory. A discussion on the plausibility of theses models concludes the work.

An application of a discrete fixed point theorem to the Cournot model

OpenAIRE

Sato, Junichi

2008-01-01

In this paper, we apply a discrete fixed point theorem of [7] to the Cournot model [1]. Then we can deal with the Cournot model where the production of the enterprises is discrete. To handle it, we define a discrete Cournot-Nash equilibrium, and prove its existence.

Comparing the Discrete and Continuous Logistic Models

Science.gov (United States)

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.)

Partially to fully saturated flow through smooth, clean, open fractures: qualitative experimental studies

Science.gov (United States)

Jones, Brendon R.; Brouwers, Luke B.; Dippenaar, Matthys A.

2018-05-01

Fractures are both rough and irregular but can be expressed by a simple model concept of two smooth parallel plates and the associated cubic law governing discharge through saturated fractures. However, in natural conditions and in the intermediate vadose zone, these assumptions are likely violated. This paper presents a qualitative experimental study investigating the cubic law under variable saturation in initially dry free-draining discrete fractures. The study comprised flow visualisation experiments conducted on transparent replicas of smooth parallel plates with inlet conditions of constant pressure and differing flow rates over both vertical and horizontal inclination. Flow conditions were altered to investigate the influence of intermittent and continuous influx scenarios. Findings from this research proved, for instance, that saturated laminar flow is not likely achieved, especially in nonhorizontal fractures. In vertical fractures, preferential flow occupies the minority of cross-sectional area despite the water supply. Movement of water through the fractured vadose zone therefore becomes a matter of the continuity principle, whereby water should theoretically be transported downward at significantly higher flow rates given the very low degree of water saturation. Current techniques that aim to quantify discrete fracture flow, notably at partial saturation, are questionable. Inspired by the results of this study, it is therefore hypothetically improbable to achieve saturation in vertical fractures under free-draining wetting conditions. It does become possible under extremely excessive water inflows or when not free-draining; however, the converse is not true, as a wet vertical fracture can be drained.

Partially to fully saturated flow through smooth, clean, open fractures: qualitative experimental studies

Science.gov (United States)

Jones, Brendon R.; Brouwers, Luke B.; Dippenaar, Matthys A.

2017-11-01

Fractures are both rough and irregular but can be expressed by a simple model concept of two smooth parallel plates and the associated cubic law governing discharge through saturated fractures. However, in natural conditions and in the intermediate vadose zone, these assumptions are likely violated. This paper presents a qualitative experimental study investigating the cubic law under variable saturation in initially dry free-draining discrete fractures. The study comprised flow visualisation experiments conducted on transparent replicas of smooth parallel plates with inlet conditions of constant pressure and differing flow rates over both vertical and horizontal inclination. Flow conditions were altered to investigate the influence of intermittent and continuous influx scenarios. Findings from this research proved, for instance, that saturated laminar flow is not likely achieved, especially in nonhorizontal fractures. In vertical fractures, preferential flow occupies the minority of cross-sectional area despite the water supply. Movement of water through the fractured vadose zone therefore becomes a matter of the continuity principle, whereby water should theoretically be transported downward at significantly higher flow rates given the very low degree of water saturation. Current techniques that aim to quantify discrete fracture flow, notably at partial saturation, are questionable. Inspired by the results of this study, it is therefore hypothetically improbable to achieve saturation in vertical fractures under free-draining wetting conditions. It does become possible under extremely excessive water inflows or when not free-draining; however, the converse is not true, as a wet vertical fracture can be drained.

Galerkin v. discrete-optimal projection in nonlinear model reduction

Energy Technology Data Exchange (ETDEWEB)

Carlberg, Kevin Thomas [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Barone, Matthew Franklin [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Antil, Harbir [George Mason Univ., Fairfax, VA (United States)

2015-04-01

Discrete-optimal model-reduction techniques such as the Gauss{Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible ow problems where standard Galerkin techniques have failed. However, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform projection at the time-continuous level, while discrete-optimal techniques do so at the time-discrete level. This work provides a detailed theoretical and experimental comparison of the two techniques for two common classes of time integrators: linear multistep schemes and Runge{Kutta schemes. We present a number of new ndings, including conditions under which the discrete-optimal ROM has a time-continuous representation, conditions under which the two techniques are equivalent, and time-discrete error bounds for the two approaches. Perhaps most surprisingly, we demonstrate both theoretically and experimentally that decreasing the time step does not necessarily decrease the error for the discrete-optimal ROM; instead, the time step should be `matched' to the spectral content of the reduced basis. In numerical experiments carried out on a turbulent compressible- ow problem with over one million unknowns, we show that increasing the time step to an intermediate value decreases both the error and the simulation time of the discrete-optimal reduced-order model by an order of magnitude.

A generalized multiscale finite element method for elastic wave propagation in fractured media

KAUST Repository

Chung, Eric T.

2016-02-26

In this paper, we consider elastic wave propagation in fractured media applying a linear-slip model to represent the effects of fractures on the wavefield. Fractured media, typically, are highly heterogeneous due to multiple length scales. Direct numerical simulations for wave propagation in highly heterogeneous fractured media can be computationally expensive and require some type of model reduction. We develop a multiscale model reduction technique that captures the complex nature of the media (heterogeneities and fractures) in the coarse scale system. The proposed method is based on the generalized multiscale finite element method, where the multiscale basis functions are constructed to capture the fine-scale information of the heterogeneous, fractured media and effectively reduce the degrees of freedom. These multiscale basis functions are coupled via the interior penalty discontinuous Galerkin method, which provides a block-diagonal mass matrix. The latter is needed for fast computation in an explicit time discretization, which is used in our simulations. Numerical results are presented to show the performance of the presented multiscale method for fractured media. We consider several cases where fractured media contain fractures of multiple lengths. Our numerical results show that the proposed reduced-order models can provide accurate approximations for the fine-scale solution.

A generalized multiscale finite element method for elastic wave propagation in fractured media

KAUST Repository

Chung, Eric T.; Efendiev, Yalchin R.; Gibson, Richard L.; Vasilyeva, Maria

2016-01-01

In this paper, we consider elastic wave propagation in fractured media applying a linear-slip model to represent the effects of fractures on the wavefield. Fractured media, typically, are highly heterogeneous due to multiple length scales. Direct numerical simulations for wave propagation in highly heterogeneous fractured media can be computationally expensive and require some type of model reduction. We develop a multiscale model reduction technique that captures the complex nature of the media (heterogeneities and fractures) in the coarse scale system. The proposed method is based on the generalized multiscale finite element method, where the multiscale basis functions are constructed to capture the fine-scale information of the heterogeneous, fractured media and effectively reduce the degrees of freedom. These multiscale basis functions are coupled via the interior penalty discontinuous Galerkin method, which provides a block-diagonal mass matrix. The latter is needed for fast computation in an explicit time discretization, which is used in our simulations. Numerical results are presented to show the performance of the presented multiscale method for fractured media. We consider several cases where fractured media contain fractures of multiple lengths. Our numerical results show that the proposed reduced-order models can provide accurate approximations for the fine-scale solution.

Video modeling to train staff to implement discrete-trial instruction.

Science.gov (United States)

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.

Fracture flow code

International Nuclear Information System (INIS)

Dershowitz, W; Herbert, A.; Long, J.

1989-03-01

The hydrology of the SCV site will be modelled utilizing discrete fracture flow models. These models are complex, and can not be fully cerified by comparison to analytical solutions. The best approach for verification of these codes is therefore cross-verification between different codes. This is complicated by the variation in assumptions and solution techniques utilized in different codes. Cross-verification procedures are defined which allow comparison of the codes developed by Harwell Laboratory, Lawrence Berkeley Laboratory, and Golder Associates Inc. Six cross-verification datasets are defined for deterministic and stochastic verification of geometric and flow features of the codes. Additional datasets for verification of transport features will be documented in a future report. (13 figs., 7 tabs., 10 refs.) (authors)

Modelling Laccoliths: Fluid-Driven Fracturing in the Lab

Science.gov (United States)

Ball, T. V.; Neufeld, J. A.

2017-12-01

Current modelling of the formation of laccoliths neglects the necessity to fracture rock layers for propagation to occur [1]. In magmatic intrusions at depth the idea of fracture toughness is used to characterise fracturing, however an analogue for near surface intrusions has yet to be explored [2]. We propose an analytical model for laccolith emplacement that accounts for the energy required to fracture at the tip of an intrusion. For realistic physical parameters we find that a lag region exists between the fluid magma front and the crack tip where large negative pressures in the tip cause volatiles to exsolve from the magma. Crucially, the dynamics of this tip region controls the spreading due to the competition between viscous forces and fracture energy. We conduct a series of complementary experiments to investigate fluid-driven fracturing of adhered layers and confirm the existence of two regimes: viscosity dominant spreading, controlled by the pressure in the lag region, and fracture energy dominant spreading, controlled by the energy required to fracture layers. Our experiments provide the first observations, and evolution, of a vapour tip. These experiments and our simplified model provide insight into the key physical processes in near surface magmatic intrusions with applications to fluid-driven fracturing more generally. Michaut J. Geophys. Res. 116(B5), B05205. Bunger & Cruden J. Geophys. Res. 116(B2), B02203.

Performance analysis of chi models using discrete-time probabilistic reward graphs

NARCIS (Netherlands)

Trcka, N.; Georgievska, S.; Markovski, J.; Andova, S.; Vink, de E.P.

2008-01-01

We propose the model of discrete-time probabilistic reward graphs (DTPRGs) for performance analysis of systems exhibiting discrete deterministic time delays and probabilistic behavior, via their interpretation as discrete-time Markov reward chains, full-fledged platform for qualitative and

The hydro-mechanical modeling of the fractured media

International Nuclear Information System (INIS)

Kadiri, I.

2002-10-01

The hydro-mechanical modeling of the fractured media is quite complex. Simplifications are necessary for the modeling of such media, but, not always justified, Only permeable fractures are often considered. The rest of the network is approximated by an equivalent continuous medium. Even if we suppose that this approach is validated, the hydraulic and mechanical properties of the fractures and of the continuous medium are seldom known. Calibrations are necessary for the determination of these properties. Until now, one does not know very well the nature of measurements which must be carried out in order to carry on a modeling in discontinuous medium, nor elements of enough robust validation for this kind of modeling. For a better understanding of the hydro-mechanical phenomena in fractured media, two different sites have been selected for the work. The first is the site of Grimsel in Switzerland in which an underground laboratory is located at approximately 400 m of depth. The FEBEX experiment aims at the in-situ study of the consecutive phenomena due to the installation of a heat source representative of radioactive waste in the last 17 meters of the FEBEX tunnel in the laboratory of Grimsel. Only, the modeling of the hydro-mechanical of the excavation was model. The modeling of the Febex enabled us to establish a methodology of calibration of the hydraulic properties in the discontinuous media. However, this kind of study on such complex sites does not make possible to answer all the questions which arise on the hydro-mechanical behavior of the fractured media. We thus carried out modeling on an other site, smaller than the fist one and more accessible. The experimental site of Coaraze, in the Maritime Alps, is mainly constituted of limestone and fractures. Then the variation of water pressure along fractures is governed by the opening/closure sequence of a water gate. Normal displacement as well as the pore pressure along these fractures are recorded, and then

A residual-based a posteriori error estimator for single-phase Darcy flow in fractured porous media

KAUST Repository

Chen, Huangxin

2016-12-09

In this paper we develop an a posteriori error estimator for a mixed finite element method for single-phase Darcy flow in a two-dimensional fractured porous media. The discrete fracture model is applied to model the fractures by one-dimensional fractures in a two-dimensional domain. We consider Raviart–Thomas mixed finite element method for the approximation of the coupled Darcy flows in the fractures and the surrounding porous media. We derive a robust residual-based a posteriori error estimator for the problem with non-intersecting fractures. The reliability and efficiency of the a posteriori error estimator are established for the error measured in an energy norm. Numerical results verifying the robustness of the proposed a posteriori error estimator are given. Moreover, our numerical results indicate that the a posteriori error estimator also works well for the problem with intersecting fractures.

Discrete-Feature Modelling of Groundwater Flow and Solute Transport for SR-Can Review. External review contribution in support of SKI's and SSI's review of SR-Can

Energy Technology Data Exchange (ETDEWEB)

Geier, Joel (Clearwater Hardrock Consulting, Corvallis, OR (US))

2008-03-15

Discrete-feature models were developed to represent the main classes of water-conducting features at the Laxemar and Forsmark candidate sites for a high-level radioactive waste repository. The models encompass features on scales ranging from individual fractures 2 m or larger in radius around deposition holes, or spalled zones around deposition holes and tunnels, to deformation zones on the scale of kilometres. Equivalent discontinuum features are used to represent the aggregate properties of fractures outside of the vicinity of deposition holes where an explicit representation is used. Deposition hole locations within the repository layout are conditioned to each stochastic realization of the discrete-fracture population, using a full-perimeter-intersection criterion to identify discriminating fractures that pose a seismic risk, and a simulated pilot-hole criterion to exclude deposition-hole locations with excessive flows. The utilization factors of 0.70 obtained here for the full repository at Forsmark and = 0.53 for the full repository at Laxemar are significantly lower than the corresponding values = 0.93 and 0.88 for the most nearly comparable case presented in the SR-Can Main Report. Further investigation is needed to discern whether this discrepancy is primarily due to possible nonconservative assumptions in SKB's analytical modelling approach, or due to artefacts of the simulation approach using finite domains, which could lead to overly conservative values in the present study. Flows through the discrete-feature model variants are calculated by finite-element simulation. Distributions of flows to deposition holes are presented for the Laxemar base case and for an initial suite of variants for Forsmark. Results for Forsmark indicate that the distribution of flow to deposition holes is robust with respect to the set of variants considered, and that a given single realization of the discrete-fracture network (DFN) submodel produces representative results

A quasi steady state method for solving transient Darcy flow in complex 3D fractured networks accounting for matrix to fracture flow

Science.gov (United States)

Nœtinger, B.

2015-02-01

Modeling natural Discrete Fracture Networks (DFN) receives more and more attention in applied geosciences, from oil and gas industry, to geothermal recovery and aquifer management. The fractures may be either natural, or artificial in case of well stimulation. Accounting for the flow inside the fracture network, and accounting for the transfers between the matrix and the fractures, with the same level of accuracy is an important issue for calibrating the well architecture and for setting up optimal resources recovery strategies. Recently, we proposed an original method allowing to model transient pressure diffusion in the fracture network only [1]. The matrix was assumed to be impervious. A systematic approximation scheme was built, allowing to model the initial DFN by a set of N unknowns located at each identified intersection between fractures. The higher N, the higher the accuracy of the model. The main assumption was using a quasi steady state hypothesis, that states that the characteristic diffusion time over one single fracture is negligible compared with the characteristic time of the macroscopic problem, e.g. change of boundary conditions. In that context, the lowest order approximation N = 1 has the form of solving a transient problem in a resistor/capacitor network, a so-called pipe network. Its topology is the same as the network of geometrical intersections between fractures. In this paper, we generalize this approach in order to account for fluxes from matrix to fractures. The quasi steady state hypothesis at the fracture level is still kept. Then, we show that in the case of well separated time scales between matrix and fractures, the preceding model needs only to be slightly modified in order to incorporate these fluxes. The additional knowledge of the so-called matrix to fracture transfer function allows to modify the mass matrix that becomes a time convolution operator. This is reminiscent of existing space averaged transient dual porosity models.

Nonparametric Identification and Estimation of Finite Mixture Models of Dynamic Discrete Choices

OpenAIRE

Hiroyuki Kasahara; Katsumi Shimotsu

2006-01-01

In dynamic discrete choice analysis, controlling for unobserved heterogeneity is an important issue, and finite mixture models provide flexible ways to account for unobserved heterogeneity. This paper studies nonparametric identifiability of type probabilities and type-specific component distributions in finite mixture models of dynamic discrete choices. We derive sufficient conditions for nonparametric identification for various finite mixture models of dynamic discrete choices used in appli...