Fractal modeling of natural fracture networks
Energy Technology Data Exchange (ETDEWEB)
Ferer, M.; Dean, B.; Mick, C.
1995-06-01
West Virginia University will implement procedures for a fractal analysis of fractures in reservoirs. This procedure will be applied to fracture networks in outcrops and to fractures intersecting horizontal boreholes. The parameters resulting from this analysis will be used to generate synthetic fracture networks with the same fractal characteristics as the real networks. Recovery from naturally fractured, tight-gas reservoirs is controlled by the fracture network. Reliable characterization of the actual fracture network in the reservoir is severely limited. The location and orientation of fractures intersecting the borehole can be determined, but the length of these fractures cannot be unambiguously determined. Because of the lack of detailed information about the actual fracture network, modeling methods must represent the porosity and permeability associated with the fracture network, as accurately as possible with very little a priori information. In the sections following, the authors will (1) present fractal analysis of the MWX site, using the box-counting procedure; (2) review evidence testing the fractal nature of fracture distributions and discuss the advantages of using the fractal analysis over a stochastic analysis; and (3) present an efficient algorithm for producing a self-similar fracture networks which mimic the real MWX outcrop fracture network.
Compartmentalization analysis using discrete fracture network models
Energy Technology Data Exchange (ETDEWEB)
La Pointe, P.R.; Eiben, T.; Dershowitz, W. [Golder Associates, Redmond, VA (United States); Wadleigh, E. [Marathon Oil Co., Midland, TX (United States)
1997-08-01
This paper illustrates how Discrete Fracture Network (DFN) technology can serve as a basis for the calculation of reservoir engineering parameters for the development of fractured reservoirs. It describes the development of quantitative techniques for defining the geometry and volume of structurally controlled compartments. These techniques are based on a combination of stochastic geometry, computational geometry, and graph the theory. The parameters addressed are compartment size, matrix block size and tributary drainage volume. The concept of DFN models is explained and methodologies to compute these parameters are demonstrated.
A Spatial Clustering Approach for Stochastic Fracture Network Modelling
Seifollahi, S.; Dowd, P. A.; Xu, C.; Fadakar, A. Y.
2014-07-01
Fracture network modelling plays an important role in many application areas in which the behaviour of a rock mass is of interest. These areas include mining, civil, petroleum, water and environmental engineering and geothermal systems modelling. The aim is to model the fractured rock to assess fluid flow or the stability of rock blocks. One important step in fracture network modelling is to estimate the number of fractures and the properties of individual fractures such as their size and orientation. Due to the lack of data and the complexity of the problem, there are significant uncertainties associated with fracture network modelling in practice. Our primary interest is the modelling of fracture networks in geothermal systems and, in this paper, we propose a general stochastic approach to fracture network modelling for this application. We focus on using the seismic point cloud detected during the fracture stimulation of a hot dry rock reservoir to create an enhanced geothermal system; these seismic points are the conditioning data in the modelling process. The seismic points can be used to estimate the geographical extent of the reservoir, the amount of fracturing and the detailed geometries of fractures within the reservoir. The objective is to determine a fracture model from the conditioning data by minimizing the sum of the distances of the points from the fitted fracture model. Fractures are represented as line segments connecting two points in two-dimensional applications or as ellipses in three-dimensional (3D) cases. The novelty of our model is twofold: (1) it comprises a comprehensive fracture modification scheme based on simulated annealing and (2) it introduces new spatial approaches, a goodness-of-fit measure for the fitted fracture model, a measure for fracture similarity and a clustering technique for proposing a locally optimal solution for fracture parameters. We use a simulated dataset to demonstrate the application of the proposed approach
Discrete modeling of hydraulic fracturing processes in a complex pre-existing fracture network
Kim, K.; Rutqvist, J.; Nakagawa, S.; Houseworth, J. E.; Birkholzer, J. T.
2015-12-01
Hydraulic fracturing and stimulation of fracture networks are widely used by the energy industry (e.g., shale gas extraction, enhanced geothermal systems) to increase permeability of geological formations. Numerous analytical and numerical models have been developed to help understand and predict the behavior of hydraulically induced fractures. However, many existing models assume simple fracturing scenarios with highly idealized fracture geometries (e.g., propagation of a single fracture with assumed shapes in a homogeneous medium). Modeling hydraulic fracture propagation in the presence of natural fractures and homogeneities can be very challenging because of the complex interactions between fluid, rock matrix, and rock interfaces, as well as the interactions between propagating fractures and pre-existing natural fractures. In this study, the TOUGH-RBSN code for coupled hydro-mechanical modeling is utilized to simulate hydraulic fracture propagation and its interaction with pre-existing fracture networks. The simulation tool combines TOUGH2, a simulator of subsurface multiphase flow and mass transport based on the finite volume approach, with the implementation of a lattice modeling approach for geomechanical and fracture-damage behavior, named Rigid-Body-Spring Network (RBSN). The discrete fracture network (DFN) approach is facilitated in the Voronoi discretization via a fully automated modeling procedure. The numerical program is verified through a simple simulation for single fracture propagation, in which the resulting fracture geometry is compared to an analytical solution for given fracture length and aperture. Subsequently, predictive simulations are conducted for planned laboratory experiments using rock-analogue (soda-lime glass) samples containing a designed, pre-existing fracture network. The results of a preliminary simulation demonstrate selective fracturing and fluid infiltration along the pre-existing fractures, with additional fracturing in part
Hydrofracture Modeling Using Discrete Fracture Network in Barnett Shale
Yaghoubi, A.; Zoback, M. D.
2012-12-01
Shale gas has become an important source of unconventional reservoir in the united state over the past decade. Since the shale gas formations are impermeable, hydraulic fracturing from vertical and horizontal well are commonly approach to extract natural gas deposit from these unconventional sources. Hydraulic fracturing has been a successful and relatively inexpensive stimulation method for stimulation and enhances hydrocarbon recovery. Multistage hydro fracturing treatments in horizontal well creates a large stimulated reservoir volume. However, modeling hydraulic fracturing requires to prior knowledge of natural fracture network. This problem can be deal with Discrete Fracture network modeling. The objective of this study is first to model discrete fracture network and then simulate hydro-fracturing in five horizontal well of a case study in Barnett shale gas reservoir. In the case study, five horizontal wells have been drilled in Barnett shale gas reservoir in which each of them has 10 stages of hydro-fracturing stimulation. Of all five wells, just well C has a full comprehensive logging data. Fracture date detected using FMI image log of well C for building DFN model are associated with different sources of uncertainty; orientation, density and length. After building reservoir geomechanics model and detecting natural fracture form image log from well C, DFN model has built based on fracture parameters, orientation, intensity, shape size and permeability detected from image log and core data. Modeling hydrofractuing in five wells are consistent with critically stressed-fracture and micro-seismic events.
Directory of Open Access Journals (Sweden)
Junling Fang
2017-02-01
Full Text Available This paper presents an integrated approach of discrete fracture network modelling for a naturally fractured buried-hill carbonate reservoir in the Jingbei Oilfield by using a 3D seismic survey, conventional well logs, and core data. The ant tracking attribute, extracted from 3D seismic data, is used to detect the faults and large-scale fractures. Fracture density and dip angle are evaluated by observing drilling cores of seven wells. The fracture density distribution in spatiality was predicted in four steps; firstly, the ant tracking attribute was extracted as a geophysical log; then an artificial neural network model was built by relating the fracture density with logs, e.g., acoustic, gamma ray, compensated neutron, density, and ant tracking; then 3D distribution models of acoustic, gamma ray, compensated neutron and density were generated by using a Gaussian random function simulation; and, finally, the fracture density distribution in 3D was predicted by using the generated artificial neural network model. Then, different methods were used to build the discrete fracture network model for different types of fractures of which large-scale fractures were modelled deterministically and small-scale fractures were modelled stochastically. The results show that the workflow presented in this study is effective for building discrete fracture network models for naturally fractured reservoirs.
a Fractal Network Model for Fractured Porous Media
Xu, Peng; Li, Cuihong; Qiu, Shuxia; Sasmito, Agus Pulung
2016-04-01
The transport properties and mechanisms of fractured porous media are very important for oil and gas reservoir engineering, hydraulics, environmental science, chemical engineering, etc. In this paper, a fractal dual-porosity model is developed to estimate the equivalent hydraulic properties of fractured porous media, where a fractal tree-like network model is used to characterize the fracture system according to its fractal scaling laws and topological structures. The analytical expressions for the effective permeability of fracture system and fractured porous media, tortuosity, fracture density and fraction are derived. The proposed fractal model has been validated by comparisons with available experimental data and numerical simulation. It has been shown that fractal dimensions for fracture length and aperture have significant effect on the equivalent hydraulic properties of fractured porous media. The effective permeability of fracture system can be increased with the increase of fractal dimensions for fracture length and aperture, while it can be remarkably lowered by introducing tortuosity at large branching angle. Also, a scaling law between the fracture density and fractal dimension for fracture length has been found, where the scaling exponent depends on the fracture number. The present fractal dual-porosity model may shed light on the transport physics of fractured porous media and provide theoretical basis for oil and gas exploitation, underground water, nuclear waste disposal and geothermal energy extraction as well as chemical engineering, etc.
Fractal modeling of natural fracture networks. Final report, June 1994--June 1995
Energy Technology Data Exchange (ETDEWEB)
Ferer, M.V.; Dean, B.H.; Mick, C.
1996-04-01
Recovery from naturally fractured, tight-gas reservoirs is controlled by the fracture network. Reliable characterization of the actual fracture network in the reservoir is severely limited. The location and orientation of fractures intersecting the borehole can be determined, but the length of these fractures cannot be unambiguously determined. Fracture networks can be determined for outcrops, but there is little reason to believe that the network in the reservoir should be identical because of the differences in stresses and history. Because of the lack of detailed information about the actual fracture network, modeling methods must represent the porosity and permeability associated with the fracture network, as accurately as possible with very little apriori information. Three rather different types of approaches have been used: (1) dual porosity simulations; (2) `stochastic` modeling of fracture networks, and (3) fractal modeling of fracture networks. Stochastic models which assume a variety of probability distributions of fracture characteristics have been used with some success in modeling fracture networks. The advantage of these stochastic models over the dual porosity simulations is that real fracture heterogeneities are included in the modeling process. In the sections provided in this paper the authors will present fractal analysis of the MWX site, using the box-counting procedure; (2) review evidence testing the fractal nature of fracture distributions and discuss the advantages of using their fractal analysis over a stochastic analysis; (3) present an efficient algorithm for producing a self-similar fracture networks which mimic the real MWX outcrop fracture network.
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
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The continuum approach in fluid flow modeling is generally applied to porous geological media,but has limitel applicability to fractured rocks. With the presence of a discrete fracture network relatively sparsely distributed in the matrix, it may be difficult or erroneous to use a porous medium fluid flow model with continuum assumptions to describe the fluid flow in fractured rocks at small or even large field scales. A discrete fracture fluid flow approach incorporating a stochastic fracture network with numerical fluid flow simulations could have the capability of capturing fluid flow behaviors such as inhomogeneity and anisotropy while reflecting the changes of hydraulic features at different scales.Moreover, this approach can be implemented to estimate the size of the representative elementary volume (REV) in order to find out the scales at which a porous medium flow model could be applied, and then to determine the hydraulic conductivity tensor for fractured rocks. The following topics are focused on in this study: (a) conceptual discrete fracture fluid flow modeling incorporating a stochastic fracture network with numerical flow simulations; (b) estimation of REVand hydraulic conductivity tensor for fractured rocks utilizing a stochastic fracture network with numerical fluid flow simulations; (c) investigation of the effect of fracture orientation and density on the hydraulic conductivity and REV by implementing a stochastic fracture network with numerical fluid flow simulations, and (d) fluid flow conceptual models accounting for major and minor fractures in the 2-D or 3-D flow fields incorporating a stochastic fracture network with numerical fluid flow simulations.``
Discrete Fracture Networks Groundwater Modelling at Bedding Control Fractured Sedimentary Rock mass
Pin, Yeh; Yuan-Chieh, Wu
2017-04-01
Groundwater flow modelling in fractured rock mass is an important challenging work in predicting the transport of contamination. So far as we know about the numerical analysis method was consider for crystalline rock, which means discontinuous are treated as stochastic distribution in homogeneous rock mass. Based on the understanding of geology in Taiwan in past few decades, we know that the hydraulic conductivities of Quaternary and Tertiary system rock mass are strongly controlled by development of sedimentary structures (bedding plane). The main purpose of this study is to understand how Discrete Fracture Networks (DFN) affects numerical results in terms of hydraulic behavior using different DFN generation methods. Base on surface geology investigation and core drilling work (3 boreholes with a total length of 120m), small scale fracture properties with in Cho-lan formation (muddy sandstone) are defined, including gently dip of bedding and 2 sub-vertical joint sets. Two FracMan/MAFIC numerical modellings are conducted, using ECPM approach (Equivalent Continuum Porous Media); case A considered all fracture were Power law distribution with Poisson fracture center; case B considered all bedding plans penetrate into modelling region, and remove the bedding count to recalculate joint fracture parameters. Modelling results show that Case B gives stronger groundwater pathways than Case A and have impact on flow field. This preliminary modelling result implicates the groundwater flow modelling work in some fractured sedimentary rock mass, might be considerate to rock sedimentary structure development itself, discontinuous maybe not follow the same stochastic DFN parameter.
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.
Jia, Pin; Cheng, Linsong; Huang, Shijun; Wu, Yonghui
2016-06-01
This paper presents a semi-analytical model for the flow behavior of naturally fractured formations with multi-scale fracture networks. The model dynamically couples an analytical dual-porosity model with a numerical discrete fracture model. The small-scale fractures with the matrix are idealized as a dual-porosity continuum and an analytical flow solution is derived based on source functions in Laplace domain. The large-scale fractures are represented explicitly as the major fluid conduits and the flow is numerically modeled, also in Laplace domain. This approach allows us to include finer details of the fracture network characteristics while keeping the computational work manageable. For example, the large-scale fracture network may have complex geometry and varying conductivity, and the computations can be done at predetermined, discrete times, without any grids in the dual-porosity continuum. The validation of the semi-analytical model is demonstrated in comparison to the solution of ECLIPSE reservoir simulator. The simulation is fast, gridless and enables rapid model setup. On the basis of the model, we provide detailed analysis of the flow behavior of a horizontal production well in fractured reservoir with multi-scale fracture networks. The study has shown that the system may exhibit six flow regimes: large-scale fracture network linear flow, bilinear flow, small-scale fracture network linear flow, pseudosteady-state flow, interporosity flow and pseudoradial flow. During the first four flow periods, the large-scale fracture network behaves as if it only drains in the small-scale fracture network; that is, the effect of the matrix is negligibly small. The characteristics of the bilinear flow and the small-scale fracture network linear flow are predominantly determined by the dimensionless large-scale fracture conductivity. And low dimensionless fracture conductivity will generate large pressure drops in the large-scale fractures surrounding the wellbore. With
Gauthier, B.D.M.; Bisdom, K.; Bertotti, G.
2012-01-01
The full 3D characterization of fracture networks is a key issue in naturally fractured reservoir modeling. Fracture geometry (e.g., orientation, size, spacing), fracture scale (e.g., bed-confined fractures, fracture corridors), lateral and vertical variations, need to be defined from limited, gener
Directory of Open Access Journals (Sweden)
Jonas Nesland Vevatne
2014-04-01
Full Text Available Fracturing and refreezing of sea ice in the Kara sea are investigated using complex networkanalysis. By going to the dual network, where the fractures are nodes and their intersectionslinks, we gain access to topological features which are easy to measure and hence comparewith modeled networks. Resulting network reveal statistical properties of the fracturing process.The dual networks have a broad degree distribution, with a scale-free tail, high clusteringand efficiency. The degree-degree correlation profile shows disassortative behavior, indicatingpreferential growth. This implies that long, dominating fractures appear earlier than shorterfractures, and that the short fractures which are created later tend to connect to the longfractures.The knowledge of the fracturing process is used to construct growing fracture network (GFNmodel which provides insight into the generation of fracture networks. The GFN model isprimarily based on the observation that fractures in sea ice are likely to end when hitting existingfractures. Based on an investigation of which fractures survive over time, a simple model forrefreezing is also added to the GFN model, and the model is analyzed and compared to the realnetworks.
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
Directory of Open Access Journals (Sweden)
Yu Wang
2016-05-01
Full Text Available In this study, variable injection-rate technology was numerically investigated in a pre-existing discrete fracture network (DFN formation, the Tarim Basin in China. A flow-stress-damage (FSD coupling model has been used in an initial attempt towards how reservoir response to variable injection-rates at different hydraulic fracturing stages. The established numerical model simultaneously considered the macroscopic and microscopic heterogeneity characteristics. Eight numerical cases were studied. Four cases were used to study the variable injection-rate technology, and the other four cases were applied for a constant injection-rate in order to compare with the variable injection-rate technology. The simulation results show that the variable injection-rate technology is a potentially good method to a form complex fracturing networks. The hydraulic fracturing effectiveness when increasing the injection-rate at each stage is the best, also, the total injected fluid is at a minimum. At the initial stage, many under-fracturing points appear around the wellbore with a relatively low injection-rate; the sudden increase of injection rate drives the dynamic propagation of hydraulic fractures along many branching fracturing points. However, the case with decreasing injection rate is the worst. By comparing with constant injection-rate cases, the hydraulic fracturing effectiveness with variable flow rate technology is generally better than those with constant injection-rate technology. This work strongly links the production technology and hydraulic fracturing effectiveness evaluation and aids in the understanding and optimization of hydraulic fracturing simulations in naturally fractured reservoirs.
Discrete fracture network modeling of hydraulic stimulation coupling flow and geomechanics
McClure, Mark
2013-01-01
Discrete Fracture Network Modeling of Hydraulic Stimulation describes the development and testing of a model that couples fluid-flow, deformation, friction weakening, and permeability evolution in large, complex two-dimensional discrete fracture networks. The model can be used to explore the behavior of hydraulic stimulation in settings where matrix permeability is low and preexisting fractures play an important role, such as Enhanced Geothermal Systems and gas shale. Used also to describe pure shear stimulation, mixed-mechanism stimulation, or pure opening-mode stimulation. A variety of nov
Upscaling Fracture Network Models to Continua: An Example Using Weathered Granitic Rock
Clark, A.; Doe, T.; Jones, J. W.
2006-12-01
In the early 1990's, a proposed landfill site on the Campo Indian Reservation in San Diego County, California, was the object of a characterization program involving over ninety exploration and monitoring wells, geophysical investigations, flow meter logging, tracer testing, and fracture characterization. This intensively studied site rests on deeply weathered tonalite. The weathered zone extends several tens to about 100 feet below the surface; however, the deeply weathered material follows hydraulically active fractures to even greater depths. The flow meter logging was especially valuable both for locating conductive fractures but also, in un- pumped mode, for defining regions of upward and downward vertical flow. The deep weathering on the conductive fractures gives each pathway a large effective porosity that translates to lower flow velocities compared with unweathered fractures with similar transmissivities. The simulation of the groundwater flow at this site used a local-scale fracture network model which was upscaled to a continuum code at regional scales. At the largest scale we generated a small number of major fractures to match the topographic lineaments. At an intermediate scale we had geophysical lineaments that were deterministic under the site footprint, and stochastic elsewhere using generation parameters based on the lengths, orientations and intensities of the deterministic features. The fractures of the most detailed scale were background fractures that were stochastically generated from borehole data. The site-scale fracture network model was incorporated into a regional-scale MODFLOW model, by overlaying the MODFLOW grid on the fracture network model and calculating equivalent porous medium properties for each MODFLOW grid cell using the Oda tensor method. This fast algorithm calculates a permeability tensor for each MODFLOW grid cell by summing the oriented area-weighted permeabilities of each fracture. The resulting MODFLOW model was then
Energy Technology Data Exchange (ETDEWEB)
Hartley, Lee; Roberts, David
2013-04-15
The Swedish Nuclear Fuel and Waste Management Company (SKB) is responsible for the development of a deep geological repository for spent nuclear fuel. The permitting of such a repository is informed by assessment studies to estimate the risks of the disposal method. One of the potential risks involves the transport of radionuclides in groundwater from defective canisters in the repository to the accessible environment. The Swedish programme for geological disposal of spent nuclear fuel has involved undertaking detailed surface-based site characterisation studies at two different sites, Forsmark and Laxemar-Simpevarp. A key component of the hydrogeological modelling of these two sites has been the development of Discrete Fracture Network (DFN) concepts of groundwater flow through the fractures in the crystalline rocks present. A discrete fracture network model represents some of the characteristics of fractures explicitly, such as their, orientation, intensity, size, spatial distribution, shape and transmissivity. This report summarises how the discrete fracture network methodology has been applied to model groundwater flow and transport at Forsmark and Laxemar. The account has involved summarising reports previously published by SKB between 2001 and 2011. The report describes the conceptual framework and assumptions used in interpreting site data, and in particular how data has been used to calibrate the various parameters that define the discrete fracture network representation of bedrock hydrogeology against borehole geologic and hydraulic data. Steps taken to confirm whether the developed discrete fracture network models provide a description of regional-scale groundwater flow and solute transport consistent with wider hydraulic tests hydrochemical data from Forsmark and Laxemar are discussed. It illustrates the use of derived hydrogeological DFN models in the simulations of the temperate period hydrogeology that provided input to radionuclide transport
Mendoza-Torres, F.; Diaz-Viera, M. A.
2015-12-01
In many natural fractured porous media, such as aquifers, soils, oil and geothermal reservoirs, fractures play a crucial role in their flow and transport properties. An approach that has recently gained popularity for modeling fracture systems is the Discrete Fracture Network (DFN) model. This approach consists in applying a stochastic boolean simulation method, also known as object simulation method, where fractures are represented as simplified geometric objects (line segments in 2D and polygons in 3D). One of the shortcomings of this approach is that it usually does not consider the dependency relationships that may exist between the geometric properties of fractures (direction, length, aperture, etc), that is, each property is simulated independently. In this work a method for modeling such dependencies by copula theory is introduced. In particular, a nonparametric model using Bernstein copulas for direction-length fracture dependency in 2D is presented. The application of this method is illustrated in a case study for a fractured rock sample from a carbonate reservoir outcrop.
Energy Technology Data Exchange (ETDEWEB)
Dreuzy, J.R. de
1999-12-15
Fractured medium are studied in the general framework of oil and water supply and more recently for the underground storage of high level nuclear wastes. As fractures are generally far more permeable than the embedding medium, flow is highly channeled in a complex network of fractures. The complexity of the network comes from the broad distributions of fracture length and permeability at the fracture scale and appears through the increase of the equivalent permeability at the network scale. The goal of this thesis is to develop models of fracture networks consistent with both local-scale and global-scale observations. Bidimensional models of fracture networks display a wide variety of flow structures ranging from the sole permeable fracture to the equivalent homogeneous medium. The type of the relevant structure depends not only on the density and the length and aperture distributions but also on the observation scale. In several models, a crossover scale separates complex structures highly channeled from more distributed and homogeneous-like flow patterns at larger scales. These models, built on local characteristics and validated by global properties, have been settled in steady state. They have also been compared to natural well test data obtained in Ploemeur (Morbihan) in transient state. The good agreement between models and data reinforces the relevance of the models. Once validated and calibrated, the models are used to estimate the global tendencies of the main flow properties and the risk associated with the relative lack of data on natural fractures media. (author)
Geological discrete fracture network model for the Olkiluoto site, Eurajoki, Finland. Version 2.0
Energy Technology Data Exchange (ETDEWEB)
Fox, A.; Forchhammer, K.; Pettersson, A. [Golder Associates AB, Stockholm (Sweden); La Pointe, P.; Lim, D-H. [Golder Associates Inc. (Finland)
2012-06-15
This report describes the methods, analyses, and conclusions of the modeling team in the production of the 2010 revision to the geological discrete fracture network (DFN) model for the Olkiluoto Site in Finland. The geological DFN is a statistical model for stochastically simulating rock fractures and minor faults at a scale ranging from approximately 0.05 m to approximately 565m; deformation zones are expressly excluded from the DFN model. The DFN model is presented as a series of tables summarizing probability distributions for several parameters necessary for fracture modeling: fracture orientation, fracture size, fracture intensity, and associated spatial constraints. The geological DFN is built from data collected during site characterization (SC) activities at Olkiluoto, which is selected to function as a final deep geological repository for spent fuel and nuclear waste from the Finnish nuclear power program. Data used in the DFN analyses include fracture maps from surface outcrops and trenches, geological and structural data from cored drillholes, and fracture information collected during the construction of the main tunnels and shafts at the ONKALO laboratory. Unlike the initial geological DFN, which was focused on the vicinity of the ONKALO tunnel, the 2010 revisions present a model parameterization for the entire island. Fracture domains are based on the tectonic subdivisions at the site (northern, central, and southern tectonic units) presented in the Geological Site Model (GSM), and are further subdivided along the intersection of major brittle-ductile zones. The rock volume at Olkiluoto is dominated by three distinct fracture sets: subhorizontally-dipping fractures striking north-northeast and dipping to the east that is subparallel to the mean bedrock foliation direction, a subvertically-dipping fracture set striking roughly north-south, and a subvertically-dipping fracture set striking approximately east-west. The subhorizontally-dipping fractures
Discrete Fracture Network Models for Risk Assessment of Carbon Sequestration in Coal
Energy Technology Data Exchange (ETDEWEB)
Jack Pashin; Guohai Jin; Chunmiao Zheng; Song Chen; Marcella McIntyre
2008-07-01
A software package called DFNModeler has been developed to assess the potential risks associated with carbon sequestration in coal. Natural fractures provide the principal conduits for fluid flow in coal-bearing strata, and these fractures present the most tangible risks for the leakage of injected carbon dioxide. The objectives of this study were to develop discrete fracture network (DFN) modeling tools for risk assessment and to use these tools to assess risks in the Black Warrior Basin of Alabama, where coal-bearing strata have high potential for carbon sequestration and enhanced coalbed methane recovery. DFNModeler provides a user-friendly interface for the construction, visualization, and analysis of DFN models. DFNModeler employs an OpenGL graphics engine that enables real-time manipulation of DFN models. Analytical capabilities in DFNModeler include display of structural and hydrologic parameters, compartmentalization analysis, and fluid pathways analysis. DFN models can be exported to third-party software packages for flow modeling. DFN models were constructed to simulate fracturing in coal-bearing strata of the upper Pottsville Formation in the Black Warrior Basin. Outcrops and wireline cores were used to characterize fracture systems, which include joint systems, cleat systems, and fault-related shear fractures. DFN models were constructed to simulate jointing, cleating, faulting, and hydraulic fracturing. Analysis of DFN models indicates that strata-bound jointing compartmentalizes the Pottsville hydrologic system and helps protect shallow aquifers from injection operations at reservoir depth. Analysis of fault zones, however, suggests that faulting can facilitate cross-formational flow. For this reason, faults should be avoided when siting injection wells. DFN-based flow models constructed in TOUGH2 indicate that fracture aperture and connectivity are critical variables affecting the leakage of injected CO{sub 2} from coal. Highly transmissive joints
Energy Technology Data Exchange (ETDEWEB)
Dershowitz, B.; Eiben, T. [Golder Associates Inc., Seattle (United States); Follin, S.; Andersson, Johan [Golder Grundteknik KB, Stockholm (Sweden)
1999-08-01
As part of studies into the siting of a deep repository for nuclear waste, Swedish Nuclear Fuel and Waste Management Company (SKB) has commissioned the Alternative Models Project (AMP). The AMP is a comparison of three alternative modeling approaches for geosphere performance assessment for a single hypothetical site. The hypothetical site, arbitrarily named Aberg is based on parameters from the Aespoe Hard Rock Laboratory in southern Sweden. The Aberg model domain, boundary conditions and canister locations are defined as a common reference case to facilitate comparisons between approaches. This report presents the results of a discrete fracture pathways analysis of the Aberg site, within the context of the SR 97 performance assessment exercise. The Aberg discrete fracture network (DFN) site model is based on consensus Aberg parameters related to the Aespoe HRL site. Discrete fracture pathways are identified from canister locations in a prototype repository design to the surface of the island or to the sea bottom. The discrete fracture pathways analysis presented in this report is used to provide the following parameters for SKB's performance assessment transport codes FARF31 and COMP23: * F-factor: Flow wetted surface normalized with regards to flow rate (yields an appreciation of the contact area available for diffusion and sorption processes) [TL{sup -1}]. * Travel Time: Advective transport time from a canister location to the environmental discharge [T]. * Canister Flux: Darcy flux (flow rate per unit area) past a representative canister location [LT{sup -1}]. In addition to the above, the discrete fracture pathways analysis in this report also provides information about: additional pathway parameters such as pathway length, pathway width, transport aperture, reactive surface area and transmissivity, percentage of canister locations with pathways to the surface discharge, spatial pattern of pathways and pathway discharges, visualization of pathways, and
Kang, Peter K.; Dentz, Marco; Le Borgne, Tanguy; Lee, Seunghak; Juanes, Ruben
2017-08-01
We investigate tracer transport on random discrete fracture networks that are characterized by the statistics of the fracture geometry and hydraulic conductivity. While it is well known that tracer transport through fractured media can be anomalous and particle injection modes can have major impact on dispersion, the incorporation of injection modes into effective transport modeling has remained an open issue. The fundamental reason behind this challenge is that-even if the Eulerian fluid velocity is steady-the Lagrangian velocity distribution experienced by tracer particles evolves with time from its initial distribution, which is dictated by the injection mode, to a stationary velocity distribution. We quantify this evolution by a Markov model for particle velocities that are equidistantly sampled along trajectories. This stochastic approach allows for the systematic incorporation of the initial velocity distribution and quantifies the interplay between velocity distribution and spatial and temporal correlation. The proposed spatial Markov model is characterized by the initial velocity distribution, which is determined by the particle injection mode, the stationary Lagrangian velocity distribution, which is derived from the Eulerian velocity distribution, and the spatial velocity correlation length, which is related to the characteristic fracture length. This effective model leads to a time-domain random walk for the evolution of particle positions and velocities, whose joint distribution follows a Boltzmann equation. Finally, we demonstrate that the proposed model can successfully predict anomalous transport through discrete fracture networks with different levels of heterogeneity and arbitrary tracer injection modes.
Discrete 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
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.
Directory of Open Access Journals (Sweden)
Ja’fari A.
2014-01-01
Full Text Available Image logs provide useful information for fracture study in naturally fractured reservoir. Fracture dip, azimuth, aperture and fracture density can be obtained from image logs and have great importance in naturally fractured reservoir characterization. Imaging all fractured parts of hydrocarbon reservoirs and interpreting the results is expensive and time consuming. In this study, an improved method to make a quantitative correlation between fracture densities obtained from image logs and conventional well log data by integration of different artificial intelligence systems was proposed. The proposed method combines the results of Adaptive Neuro-Fuzzy Inference System (ANFIS and Neural Networks (NN algorithms for overall estimation of fracture density from conventional well log data. A simple averaging method was used to obtain a better result by combining results of ANFIS and NN. The algorithm applied on other wells of the field to obtain fracture density. In order to model the fracture density in the reservoir, we used variography and sequential simulation algorithms like Sequential Indicator Simulation (SIS and Truncated Gaussian Simulation (TGS. The overall algorithm applied to Asmari reservoir one of the SW Iranian oil fields. Histogram analysis applied to control the quality of the obtained models. Results of this study show that for higher number of fracture facies the TGS algorithm works better than SIS but in small number of fracture facies both algorithms provide approximately same results.
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
MacFarlane, Jake; Thiel, Stephan; Pek, Josef; Peacock, Jared; Heinson, Graham
2014-11-01
As opinions regarding the future of energy production shift towards renewable sources, enhanced geothermal systems (EGS) are becoming an attractive prospect. The characterisation of fracture permeability at depth is central to the success of EGS. Recent magnetotelluric (MT) studies of the Paralana geothermal system (PGS), an EGS in South Australia, have measured changes in MT responses which were attributed to fracture networks generated during fluid injection experiments. However, extracting permeabilities from these measurements remains problematic as conventional isotropic MT modelling is unable to accommodate for the complexities present within an EGS. To circumvent this problem, we introduce an electrical anisotropy representation to allow better characterisation of volumes at depth. Forward modelling shows that MT measurements are sensitive to subtle variations in anisotropy. Subsequent two-dimensional anisotropic forward modelling shows that electrical anisotropy is able to reproduce the directional response associated with fractures generated by fluid injection experiments at the PGS. As such, we conclude that MT monitoring combined with anisotropic modelling is a promising alternative to the micro-seismic method when characterising fluid reservoirs within geothermal and coal seam gas reservoirs.
The fracture network model of Shen 229 block buried hill:A case study from Liaohe Basin, China
Institute of Scientific and Technical Information of China (English)
XING Yu-zhong; FAN Tai-liang; ZHENG Li-hui
2006-01-01
High oil production from the Proterozoic formation of Shen 229 block in Damingtun Depression, Liaohe Basin, China,indicates the presence of natural fractured reservoir whose production potential is dominated by the structural fracture. A consistent structural model and good knowledge of the fracture systems are therefore of key importance in reducing risk in the development strategies. So data from cores and image logs have been collected to account for the basic characteristics of fracture, and then the analyzed results were integrated with the structural model in order to restrict the fracture network development during the structural evolvement. The structural evolution of the Proterozoic reservoir with time forms the basis for understanding the development of the 3D fracture system. Seismic interpretation and formation correlation were used to build a 3D geological model.The fault blocks that compose the Proterozoic formation reservoir were subsequently restored to their pre-deformation. From here,the structures were kinematically modeled to simulate the structural evolution of the reservoirs. At each time step, the dilatational and cumulative strain was calculated throughout the modelling history. The total strain which records the total spatial variation in the reservoir due to its structural history, together with core data, well data and the lithology distribution, was used to simulate geologically realistic discrete fracture networks. The benefit of this technique over traditional curvature analysis is that the structural evolution is taken into account, a factor that mostly dominates fracture formation.
Statistical analysis of fracture data, adapted for modelling Discrete Fracture Networks-Version 2
Energy Technology Data Exchange (ETDEWEB)
Munier, Raymond
2004-04-01
The report describes the parameters which are necessary for DFN modelling, the way in which they can be extracted from the data base acquired during site investigations, and their assignment to geometrical objects in the geological model. The purpose here is to present a methodology for use in SKB modelling projects. Though the methodology is deliberately tuned to facilitate subsequent DFN modelling with other tools, some of the recommendations presented here are applicable to other aspects of geo-modelling as well. For instance, we here recommend a nomenclature to be used within SKB modelling projects, which are truly multidisciplinary, to ease communications between scientific disciplines and avoid misunderstanding of common concepts. This report originally occurred as an appendix to a strategy report for geological modelling (SKB-R--03-07). Strategy reports were intended to be successively updated to include experience gained during site investigations and site modelling. Rather than updating the entire strategy report, we choose to present the update of the appendix as a stand-alone document. This document thus replaces Appendix A2 in SKB-R--03-07. In short, the update consists of the following: The target audience has been broadened and as a consequence thereof, the purpose of the document. Correction of errors found in various formulae. All expressions have been rewritten. Inclusion of more worked examples in each section. A new section describing area normalisation. A new section on spatial correlation. A new section describing anisotropy. A new chapter describing the expected output from DFN modelling, within SKB projects.
de La Bernardie, Jérôme; de Dreuzy, Jean-Raynald; Bour, Olivier; Thierion, Charlotte; Ausseur, Jean-Yves; Lesuer, Hervé; Le Borgne, Tanguy
2016-04-01
Geothermal energy is a renewable energy source particularly attractive due to associated low greenhouse gas emission rates. Crystalline rocks are in general considered of poor interest for geothermal applications at shallow depths (energy storage at these shallow depths is still remaining very challenging because of the complexity of fractured media. The purpose of this study is to test the possibility of efficient thermal energy storage in shallow fractured rocks with a single well semi open loop heat exchanger (standing column well). For doing so, a simplified numerical model of fractured media is considered with few fractures. Here we present the different steps for building the model and for achieving the sensitivity analysis. First, an analytical and dimensional study on the equations has been achieved to highlight the main parameters that control the optimization of the system. In a second step, multiphysics software COMSOL was used to achieve numerical simulations in a very simplified model of fractured media. The objective was to test the efficiency of such a system to store and recover thermal energy depending on i) the few parameters controlling fracture network geometry (size and number of fractures) and ii) the frequency of cycles used to store and recover thermal energy. The results have then been compared to reference shallow geothermal systems already set up for porous media. Through this study, relationships between structure, heat exchanges and storage may be highlighted.
Energy Technology Data Exchange (ETDEWEB)
Ito, Kazumasa; Yongkoo, Seol
2003-04-09
Water fluxes in unsaturated, fractured rock involve the physical processes occurring at fracture-matrix interfaces within fracture networks. Modeling these water fluxes using a discrete fracture network model is a complicated effort. Existing preprocessors for TOUGH2 are not suitable to generate grids for fracture networks with various orientations and inclinations. There are several 3-D discrete-fracture-network simulators for flow and transport, but most of them do not capture fracture-matrix interaction. We have developed a new 3-D discrete-fracture-network mesh generator, FRACMESH, to provide TOUGH2 with information about the fracture network configuration and fracture-matrix interactions. FRACMESH transforms a discrete fracture network into a 3 dimensional uniform mesh, in which fractures are considered as elements with unique rock material properties and connected to surrounding matrix elements. Using FRACMESH, individual fractures may have uniform or random aperture distributions to consider heterogeneity. Fracture element volumes and interfacial areas are calculated from fracture geometry within individual elements. By using FRACMESH and TOUGH2, fractures with various inclinations and orientations, and fracture-matrix interaction, can be incorporated. In this paper, results of flow and transport simulations in a fractured rock block utilizing FRACMESH are presented.
Estrada, Ernesto
2016-01-01
We propose a new model to account for the main structural characteristics of rock fracture networks (RFNs). The model is based on a generalization of the random neighborhood graphs to consider fractures embedded into rectangular spaces. We study a series of 29 real-world RFNs and find the best fit with the random rectangular neighborhood graphs (RRNGs) proposed here. We show that this model captures most of the structural characteristics of the RFNs and allows a distinction between small and more spherical rocks and large and more elongated ones. We use a diffusion equation on the graphs in order to model diffusive processes taking place through the channels of the RFNs. We find a small set of structural parameters that highly correlates with the average diffusion time in the RFNs. In particular, the second smallest eigenvalue of the Laplacian matrix is a good predictor of the average diffusion time on RFNs, showing a Pearson correlation coefficient larger than $0.99$ with the average diffusion time on RFNs. ...
Characterisation of fracture network and groundwater preferential ...
African Journals Online (AJOL)
2014-03-18
Mar 18, 2014 ... generally showed that there are 3 to 5 sets of fractures, includ- ing bedding ... the field measurements, the bedding planes trend to the south- west, from ... In order to avoid the boundary effect, central coordinates (x, y) should be ..... components using a three-dimensional fracture network model in volcanic ...
Formation of parallel joint sets and shear band/fracture networks in physical models
Jorand, C.; Chemenda, A. I.; Petit, J.-P.
2012-12-01
Both oedometric and plane-strain tests were performed with parallelepipedic samples made of synthetic granular, cohesive, frictional and dilatant rock analogue material GRAM2. For the first time parallel sets of fractures that have all the characteristics of natural joints were reproduced in the laboratory. The fractures are regularly spaced, normal to σ3, and have plumose morphology very similar to that of natural joints. These fractures can form at tensile stress σ3 much smaller in magnitude than the tensile strength of material and even at slightly compressive σ3. When mean stress σ exceeds a certain value, the fractures become oblique to σ1 (the obliquity increases with σ), forming networks of conjugate shear bands/fractures. These results of plane-strain experiments are in good agreement with those of better controlled conventional axisymmetric tests on a similar material in Chemenda et al. (2011b) and are closer to real geological situations. Both types of experiments are complementary. Their results lead to the conclusion that at least certain categories of natural fractures (including joints, and conjugate shear fractures/bands) were initiated as deformation localization bands. The band orientation is defined by the constitutive properties/parameters (notably the dilatancy factor) that are sensitive to σ.
Vilhelm, Jan; Jirků, Jaroslav; Janeček, Josef; Slavík, Lubomír; Bárta, Jaroslav
2017-04-01
Recently we have developed and tested system for long-term monitoring of underground excavation stability in granitic rocks. It is based on repeated ultrasonic time-of-flight measurement and electrical resistivity tomography (ERT) measurement. The ERT measurement is performed directly on the rock wall using 48 electrodes. The spacing between electrodes was selected 20 centimeters. Based on sensitivity function it can be expected that maximum penetration depth of ERT is about 1.5 m. The observed time changes in apparent resistivity are expected to be mainly result of changes in fracture water saturation. To get some basic knowledge about relation between electrical resistivity in the rock fracture zone and its saturation a series of laboratory tests with rock samples with different porosity and different saturation was performed. The model of crystalline rock with sparse net of fractures is highly inhomogeneous medium and can be hardly considered as 2D layered model, which is usually used in ERT inversion. Therefore, we prepared resistor-network model for the qualitative/quantitative interpretation of observed apparent resistivity changes. Some preliminary results of our experience with this new type of resistivity model are presented. The results can be used for underground storage monitoring projects. Acknowledgments: This work was partially supported by the Technology Agency of the Czech Republic, project No. TA 0302408
Energy Technology Data Exchange (ETDEWEB)
McKoy, M.L., Sams, W.N.
1997-10-01
The US Department of Energy, Federal Energy Technology Center, has sponsored a project to simulate the behavior of tight, fractured, strata-bound gas reservoirs that arise from irregular discontinuous, or clustered networks of fractures. New FORTRAN codes have been developed to generate fracture networks, or simulate reservoir drainage/recharge, and to plot the fracture networks and reservoirs pressures. Ancillary codes assist with raw data analysis.
Indian Academy of Sciences (India)
R Vidya Sagar; B K Raghu Prasad
2009-12-01
In this paper, numerical modelling of fracture in concrete using two-dimensional lattice model is presented and also a few issues related to lattice modelling technique applicable to concrete fracture are reviewed. A comparison is made with acoustic emission (AE) events with the number of fractured elements. To implement the heterogeneity of the plain concrete, two methods namely, by generating grain structure of the concrete using Fuller’s distribution and the concrete material properties are randomly distributed following Gaussian distribution are used. In the ﬁrst method, the modelling of the concrete at meso level is carried out following the existing methods available in literature. The shape of the aggregates present in the concrete are assumed as perfect spheres and shape of the same in two-dimensional lattice network is circular. A three-point bend (TPB) specimen is tested in the experiment under crack mouth opening displacement (CMOD) control at a rate of 0·0004 mm/sec and the fracture process in the same TPB specimen is modelled using regular triangular 2D lattice network. Load versus crack mouth opening displacement (CMOD) plots thus obtained by using both the methods are compared with experimental results. It was observed that the number of fractured elements increases near the peak load and beyond the peak load. That is once the crack starts to propagate. AE hits also increase rapidly beyond the peak load. It is compulsory here to mention that although the lattice modelling of concrete fracture used in this present study is very similar to those already available in literature, the present work brings out certain ﬁner details which are not available explicitly in the earlier works.
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.
Deformation and fracture of echinoderm collagen networks
Ovaska, Markus; Miksic, Amandine; Sugni, Michela; Di Benedetto, Cristiano; Ferrario, Cinzia; Leggio, Livio; Guidetti, Luca; Alava, Mikko J; La Porta, Caterina A M; Zapperi, Stefano
2016-01-01
Collagen networks provide the main structural component of most tissues and represent an important ingredient for bio-mimetic materials for bio-medical applications. Here we study the mechanical properties of stiff collagen networks derived from three different echinoderms and show that they exhibit non-linear stiffening followed by brittle fracture. The disordered nature of the network leads to strong sample-to-sample fluctuations in elasticity and fracture strength. We perform numerical simulations of a three dimensional model for the deformation of a cross-linked elastic fibril network which is able to reproduce the macroscopic features of the experimental results and provide insights into the internal mechanics of stiff collagen networks. Our numerical model provides an avenue for the design of collagen membranes with tunable mechanical properties.
Percolation of fracture networks and stereology
Thovert, Jean-Francois; Mourzenko, Valeri; Adler, Pierre
2017-04-01
The overall properties of fractured porous media depend on the percolative character of the fracture network in a crucial way. The most important examples are permeability and transport. In a recent systematic study, a very wide range of regular, irregular and random fracture shapes is considered, in monodisperse or polydisperse networks containing fractures with different shapes and/or sizes. A simple and new model involving a dimensionless density and a new shape factor is proposed for the percolation threshold, which accounts very efficiently for the influence of the fracture shape. It applies with very good accuracy to monodisperse or moderately polydisperse networks, and provides a good first estimation in other situations. A polydispersity index is shown to control the need for a correction, and the corrective term is modelled for the investigated size distributions. Moreover, and this is crucial for practical applications, the relevant quantities which are present in the expression of the percolation threshold can all be determined from trace maps. An exact and complete set of relations can be derived when the fractures are assumed to be Identical, Isotropically Oriented and Uniformly Distributed (I2OUD). Therefore, the dimensionless density of such networks can be derived directly from the trace maps and its percolating character can be a priori predicted. These relations involve the first five moments of the trace lengths. It is clear that the higher order moments are sensitive to truncation due to the boundaries of the sampling domain. However, it can be shown that the truncation effect can be fully taken into account and corrected, for any fracture shape, size and orientation distributions, if the fractures are spatially uniformly distributed. Systematic applications of these results are made to real fracture networks that we previously analyzed by other means and to numerically simulated networks. It is important to know if the stereological results and
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.
Directory of Open Access Journals (Sweden)
Jianming He
2017-05-01
Full Text Available In this paper, configurations of pre-existing fractures in cubic rock blocks were investigated and reconstructed for the modeling of experimental hydraulic fracturing. The fluid-rock coupling process of hydraulic fracturing was simulated based on the displacement discontinuities method. The numerical model was validated against the related laboratory experiments. The stimulated fracture configurations under different conditions can be clearly shown using the validated numerical model. First, a dominated fracture along the maximum principle stress direction is always formed when the stress difference is large enough. Second, there are less reopened pre-existing fractures, more newly formed fractures and less shear fractures with the increase of the cohesion value of pre-existing fractures. Third, the length of the stimulated shear fracture decreases rapidly with the increase of the friction coefficient, while the length of the tensile fracture has no correlation to the fiction coefficient. Finally, the increase of the fluid injection rate is favorable to the formation of a fracture network. The unfavorable effects of the large stress difference and the large cohesion of pre-existing fractures can be partly suppressed by an increase of the injection rate in the hydraulic fracturing treatment. The results of this paper are useful for understanding fracture propagation behaviors during the hydraulic fracturing of shale reservoirs with pre-existing fractures.
Simulation of complex fracture networks influenced by natural fractures in shale gas reservoir
Directory of Open Access Journals (Sweden)
Zhao Jinzhou
2014-10-01
Full Text Available When hydraulic fractures intersect with natural fractures, the geometry and complexity of a fracture network are determined by the initiation and propagation pattern which is affected by a number of factors. Based on the fracture mechanics, the criterion for initiation and propagation of a fracture was introduced to analyze the tendency of a propagating angle and factors affecting propagating pressure. On this basis, a mathematic model with a complex fracture network was established to investigate how the fracture network form changes with different parameters, including rock mechanics, in-situ stress distribution, fracture properties, and frac treatment parameters. The solving process of this model was accelerated by classifying the calculation nodes on the extending direction of the fracture by equal pressure gradients, and solving the geometrical parameters prior to the iteration fitting flow distribution. With the initiation and propagation criterion as the bases for the propagation of branch fractures, this method decreased the iteration times through eliminating the fitting of the fracture length in conventional 3D fracture simulation. The simulation results indicated that the formation with abundant natural fractures and smaller in-situ stress difference is sufficient conditions for fracture network development. If the pressure in the hydraulic fractures can be kept at a high level by temporary sealing or diversion, the branch fractures will propagate further with minor curvature radius, thus enlarging the reservoir stimulation area. The simulated shape of fracture network can be well matched with the field microseismic mapping in data point range and distribution density, validating the accuracy of this model.
Lambert, Cédric; Thoeni, Klaus; Giacomini, Anna; Casagrande, Davide; Sloan, Scott
2012-09-01
Developing an accurate representation of the rock mass fabric is a key element in rock fall hazard analysis. The orientation, persistence and density of fractures control the volume and shape of unstable blocks or compartments. In this study, the discrete fracture modelling technique and digital photogrammetry were used to accurately depict the fabric. A volume distribution of unstable blocks was derived combining polyhedral modelling and kinematic analyses. For each block size, probabilities of failure and probabilities of propagation were calculated. A complete energy distribution was obtained by considering, for each block size, its occurrence in the rock mass, its probability of falling, its probability to reach a given location, and the resulting distribution of energies at each location. This distribution was then used with an energy-frequency diagram to assess the hazard.
Follin, Sven; Hartley, Lee; Rhén, Ingvar; Jackson, Peter; Joyce, Steven; Roberts, David; Swift, Ben
2014-03-01
The large-scale geological structure of the crystalline rock at the proposed high-level nuclear waste repository site at Forsmark, Sweden, has been classified in terms of deformation zones of elevated fracture frequency. The rock between deformation zones was divided into fracture domains according to fracture frequency. A methodology to constrain the geometric and hydraulic parameters that define a discrete fracture network (DFN) model for each fracture domain is presented. The methodology is based on flow logging and down-hole imaging in cored boreholes in combination with DFN realizations, fracture connectivity analysis and pumping test simulations. The simulations suggest that a good match could be obtained for a power law size distribution where the value of the location parameter equals the borehole radius but with different values for the shape parameter, depending on fracture domain and fracture set. Fractures around 10-100 m in size are the ones that typically form the connected network, giving inflows in the simulations. The report also addresses the issue of up-scaling of DFN properties to equivalent continuous porous medium (ECPM) bulk flow properties. Comparisons with double-packer injection tests provide confidence that the derived DFN formulation of detailed flows within individual fractures is also suited to simulating mean bulk flow properties and their spatial variability.
Discrete fracture network for the Forsmark site
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
Hydraulic fracture propagation modeling and data-based fracture identification
Zhou, Jing
Successful shale gas and tight oil production is enabled by the engineering innovation of horizontal drilling and hydraulic fracturing. Hydraulically induced fractures will most likely deviate from the bi-wing planar pattern and generate complex fracture networks due to mechanical interactions and reservoir heterogeneity, both of which render the conventional fracture simulators insufficient to characterize the fractured reservoir. Moreover, in reservoirs with ultra-low permeability, the natural fractures are widely distributed, which will result in hydraulic fractures branching and merging at the interface and consequently lead to the creation of more complex fracture networks. Thus, developing a reliable hydraulic fracturing simulator, including both mechanical interaction and fluid flow, is critical in maximizing hydrocarbon recovery and optimizing fracture/well design and completion strategy in multistage horizontal wells. A novel fully coupled reservoir flow and geomechanics model based on the dual-lattice system is developed to simulate multiple nonplanar fractures' propagation in both homogeneous and heterogeneous reservoirs with or without pre-existing natural fractures. Initiation, growth, and coalescence of the microcracks will lead to the generation of macroscopic fractures, which is explicitly mimicked by failure and removal of bonds between particles from the discrete element network. This physics-based modeling approach leads to realistic fracture patterns without using the empirical rock failure and fracture propagation criteria required in conventional continuum methods. Based on this model, a sensitivity study is performed to investigate the effects of perforation spacing, in-situ stress anisotropy, rock properties (Young's modulus, Poisson's ratio, and compressive strength), fluid properties, and natural fracture properties on hydraulic fracture propagation. In addition, since reservoirs are buried thousands of feet below the surface, the
Gable, C. W.; Hyman, J.; Karra, S.; Makedonska, N.; Painter, S. L.; Viswanathan, H. S.
2015-12-01
dfnWorks generates discrete fracture networks (DFN) of planar polygons, creates a high quality conforming Delaunay triangulation of the intersecting DFN polygons, assigns properties (aperture, permeability) using geostatistics, sets boundary and initial conditions, solves pressure/flow in single or multi-phase fluids (water, air, CO2) using the parallel PFLOTRAN or serial FEHM, and solves for transport using Lagrangian particle tracking. We outline the dfnWorks workflow and present applications from a range of fractured rock systems. dfnWorks (http://www.lanl.gov/expertise/teams/view/dfnworks) is composed of three main components, all of which are freely available. dfnGen generates a distribution of fracture polygons from site characterization data (statistics or deterministic fractures) and utilizes the FRAM (Feature Rejection Algorithm for Meshing) to guarantee the mesh generation package LaGriT (lagrit.lanl.gov) will generate a high quality conforming Delaunay triangular mesh. dfnWorks links the mesh to either PFLOTRAN (pflotran.org) or FEHM (fehm.lanl.gov) for solving flow and transport. The various physics options available in FEHM and PFLOTRAN such as single and multi-phase flow and reactive transport are all available with appropriate initial and boundary conditions and material property models. dfnTrans utilizes explicit Lagrangian particle tracking on the DFN using a velocity field reconstructed from the steady state pressure/flow field solution obtained in PFLOTRAN or FEHM. Applications are demonstrated for nuclear waste repository in fractured granite, CO2 sequestration and extraction of unconventional hydrocarbon resources.
Estimating the hydraulic conductivity of two-dimensional fracture networks
Leung, C. T.; Zimmerman, R. W.
2010-12-01
Most oil and gas reservoirs, as well as most potential sites for nuclear waste disposal, are naturally fractured. In these sites, the network of fractures will provide the main path for fluid to flow through the rock mass. In many cases, the fracture density is so high as to make it impractical to model it with a discrete fracture network (DFN) approach. For such rock masses, it would be useful to have recourse to analytical, or semi-analytical, methods to estimate the macroscopic hydraulic conductivity of the fracture network. We have investigated single-phase fluid flow through stochastically generated two-dimensional fracture networks. The centres and orientations of the fractures are uniformly distributed, whereas their lengths follow either a lognormal distribution or a power law distribution. We have considered the case where the fractures in the network each have the same aperture, as well as the case where the aperture of each fracture is directly proportional to the fracture length. The discrete fracture network flow and transport simulator NAPSAC, developed by Serco (Didcot, UK), is used to establish the “true” macroscopic hydraulic conductivity of the network. We then attempt to match this conductivity using a simple estimation method that does not require extensive computation. For our calculations, fracture networks are represented as networks composed of conducting segments (bonds) between nodes. Each bond represents the region of a single fracture between two adjacent intersections with other fractures. We assume that the bonds are arranged on a kagome lattice, with some fraction of the bonds randomly missing. The conductance of each bond is then replaced with some effective conductance, Ceff, which we take to be the arithmetic mean of the individual conductances, averaged over each bond, rather than over each fracture. This is in contrast to the usual approximation used in effective medium theories, wherein the geometric mean is used. Our
Directory of Open Access Journals (Sweden)
Kh. Qarqori
2012-01-01
Full Text Available Direct current Resistivity (DCR method was carried out to characterize the hydrogeological connection between the Tabular Middle Atlas (TMA and the Saïs Basin. The TMA is one of the most important aquifers in northern Morocco that supplies the deep aquifer of the Saïs Basin. Electrical resistivity tomography (ERT survey was focused on the Bittit area that is one of the most important outlet discharges, and it is representative of the relations between the TMA and the Saïs Basin. The high resolution capabilities of the electrical tomography were used to define the geological draining features in the framework of water paths from the TMA to the karstic springs. The synthetic data were calculated for the similar model expected in field data inversion and inversion result of these synthetic data used as a guide for the interpretation of the inverse data resistivity sections. Joint interpretation of geophysical, geological, structural, and synthetic simulation data allowed identifying a conductive horizontal shallow layer overlying two subvertical families of fractures of NE-SW and NW-SE directions. This result leads to propose hydrological behaviour of water from the Tabular Middle Atlas and the Saïs Basin at the Bittit Spring, which takes into account for both horizontal flows through stratification joints or karst and through subvertical fractures.
Two-Dimensional Heat Transfer in a Heterogeneous Fracture Network
Gisladottir, V. R.; Roubinet, D.; Tartakovsky, D. M.
2015-12-01
Geothermal energy harvesting requires extraction and injection of geothermal fluid. Doing so in an optimal way requires a quantitative understanding of site-specific heat transfer between geothermal fluid and the ambient rock. We develop a heat transfer particle-tracking approach to model that interaction. Fracture-network models of heat transfer in fractured rock explicitly account for the presence of individual fractures, ambient rock matrix, and fracture-matrix interfaces. Computational domains of such models span the meter scale, whereas fracture apertures are on the millimeter scale. The computations needed to model these multi-scale phenomenon can be prohibitively expensive, even for methods using nonuniform meshes. Our approach appreciably decreases the computational costs. Current particle-tracking methods usually assume both infinite matrix and one-dimensional (1D) heat transfer in the matrix blocks. They rely on 1D analytical solutions for heat transfer in a single fracture, which can lead to large predictive errors. Our two-dimensional (2D) heat transfer simulation algorithm is mesh-free and takes into account both longitudinal and transversal heat conduction in the matrix. It uses a probabilistic model to transfer particle to the appropriate neighboring fracture unless it returns to the fracture of origin or remains in the matrix. We use this approach to look at the impact of a fracture-network topology (e.g. the importance of smaller scale fractures), as well as the matrix block distribution on the heat transport in heterogeneous fractured rocks.
Transport efficiency and dynamics of hydraulic fracture networks
Sachau, Till; Bons, Paul; Gomez-Rivas, Enrique
2015-08-01
Intermittent fluid pulses in the Earth's crust can explain a variety of geological phenomena, for instance the occurrence of hydraulic breccia. Fluid transport in the crust is usually modeled as continuous darcian flow, ignoring that sufficient fluid overpressure can cause hydraulic fractures as fluid pathways with very dynamic behavior. Resulting hydraulic fracture networks are largely self-organized: opening and healing of hydraulic fractures depends on local fluid pressure, which is, in turn, largely controlled by the fracture network. We develop a crustal-scale 2D computer model designed to simulate this process. To focus on the dynamics of the process we chose a setup as simple as possible. Control factors are constant overpressure at a basal fluid source and a constant 'viscous' parameter controlling fracture-healing. Our results indicate that at large healing rates hydraulic fractures are mobile, transporting fluid in intermittent pulses to the surface and displaying a 1/fα behavior. Low healing rates result in stable networks and constant flow. The efficiency of the fluid transport is independent from the closure dynamics of veins or fractures. More important than preexisting fracture networks is the distribution of fluid pressure. A key requirement for dynamic fracture networks is the presence of a fluid pressure gradient.
Transport efficiency and dynamics of hydraulic fracture networks
Directory of Open Access Journals (Sweden)
Till eSachau
2015-08-01
Full Text Available Intermittent fluid pulses in the Earth's crust can explain a variety of geological phenomena, for instance the occurrence of hydraulic breccia. Fluid transport in the crust is usually modeled as continuous darcian flow, ignoring that sufficient fluid overpressure can cause hydraulic fractures as fluid pathways with very dynamic behavior. Resulting hydraulic fracture networks are largely self-organized: opening and healing of hydraulic fractures depends on local fluid pressure, which is, in turn, largely controlled by the fracture network. We develop a crustal-scale 2D computer model designed to simulate this process. To focus on the dynamics of the process we chose a setup as simple as possible. Control factors are constant overpressure at a basal fluid source and a constant 'viscous' parameter controlling fracture-healing. Our results indicate that at large healing rates hydraulic fractures are mobile, transporting fluid in intermittent pulses to the surface and displaying a 1/fα behavior. Low healing rates result in stable networks and constant flow. The efficiency of the fluid transport is independent from the closure dynamics of veins or fractures. More important than preexisting fracture networks is the distribution of fluid pressure. A key requirement for dynamic fracture networks is the presence of a fluid pressure gradient.
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...
Wellman, T.P.; Shapiro, A.M.; Hill, M.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.
Shahkarami, Pirouz; Liu, Longcheng; Moreno, Luis; Neretnieks, Ivars
2016-09-01
An essential task of performance assessment of radioactive waste repositories is to predict radionuclide release into the environment. For such a quantitative assessment, the Channel Network Model and the corresponding computer program, CHAN3D, have been used to simulate radionuclide transport in crystalline bedrocks. Recent studies suggest, however, that the model may tend to underestimate the rock retarding capability, because it ignores the presence of stagnant water zones, STWZs, situated in the fracture plane. Once considered, the STWZ can provide additional surface area over which radionuclides diffuse into the rock matrix and thereby contribute to their retardation. The main objective of this paper is to extend the Channel Network Model and its computer implementation to account for diffusion into STWZs and their adjacent rock matrices. In the first part of the paper, the overall impact of STWZs in retarding radionuclide transport is investigated through a deterministic calculation of far-field releases at Forsmark, Sweden. Over the time-scale of the repository safety assessments, radionuclide breakthrough curves are calculated for increasing STWZ width. It is shown that the presence of STWZs enhances the retardation of most long-lived radionuclides except for 36Cl and 129I. The rest of the paper is devoted to the probabilistic calculation of radionuclide transport in fractured rocks. The model that is developed for transport through a single channel is embedded into the Channel Network Model and new computer codes are provided for the CHAN3D. The program is used to (I) simulate the tracer test experiment performed at Äspö HRL, STT-1 and (II) investigate the short- and long-term effect of diffusion into STWZs. The required data for the model are obtained from detailed hydraulic tests in boreholes intersecting the rock mass where the tracer tests were made. The simulation results fairly well predict the release of the sorbing tracer 137Cs. It is found that
Energy Technology Data Exchange (ETDEWEB)
Zhang, Boning [Univ. of Colorado, Boulder, CO (United States); Herbold, Eric B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Homel, Michael A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Regueiro, Richard A. [Univ. of Colorado, Boulder, CO (United States)
2015-12-01
An adaptive particle fracture model in poly-ellipsoidal Discrete Element Method is developed. The poly-ellipsoidal particle will break into several sub-poly-ellipsoids by Hoek-Brown fracture criterion based on continuum stress and the maximum tensile stress in contacts. Also Weibull theory is introduced to consider the statistics and size effects on particle strength. Finally, high strain-rate split Hopkinson pressure bar experiment of silica sand is simulated using this newly developed model. Comparisons with experiments show that our particle fracture model can capture the mechanical behavior of this experiment very well, both in stress-strain response and particle size redistribution. The effects of density and packings o the samples are also studied in numerical examples.
Energy Technology Data Exchange (ETDEWEB)
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.
Hodgetts, David; Seers, Thomas
2015-04-01
-deterministic, outcrop constrained discrete fracture network modeling code to derive volumetric fault intensity measures (fault area per unit volume / fault volume per unit volume). Producing per-vertex measures of volumetric intensity; our method captures the spatial variability in 3D fault density across a surveyed outcrop, enabling first order controls to be probed. We demonstrate our approach on pervasively faulted exposures of a Permian aged reservoir analogue from the Vale of Eden Basin, UK.
Fracture energy of polymer gels with controlled network structures
Akagi, Yuki; Sakurai, Hayato; Gong, Jian Ping; Chung, Ung-il; Sakai, Takamasa
2013-10-01
We have investigated the fracture behaviors of tetra-arm polyethylene glycol (Tetra-PEG) gels with controlled network structures. Tetra-PEG gels were prepared by AB-type crosslink-coupling of mutually reactive tetra-arm prepolymers with different concentrations and molecular weights. This series of controlled network structures, for the first time, enabled us to quantitatively examine the Lake-Thomas model, which is the most popular model predicting fracture energies of elastomers. The experimental data showed good agreement with the Lake-Thomas model, and indicated a new molecular interpretation for the displacement length (L), the area around a crack tip within which the network strands are fully stretched. L corresponded to the three times of end-to-end distance of network strands, regardless of all parameters examined. We conclude that the Lake-Thomas model can quantitatively predict the fracture energy of polymer network without trapped entanglements, with the enhancement factor being near 3.
Directory of Open Access Journals (Sweden)
Zhaobin Zhang
2016-09-01
Full Text Available As hydraulic fracturing is a fluid-rock coupling process, the permeability of the hydraulic-stimulated fracture network in the initial stage has great effects on the propagation of the hydraulic fracture network in the following stages. In this work, the permeability of the hydraulic-stimulated fracture network in shale gas reservoirs is investigated by a newly-proposed model based on the displacement discontinuity method. The permeability of the fracture network relies heavily on fracture apertures, which can be calculated with high precision by the displacement discontinuity method. The hydraulic fracturing processes are simulated based on the natural fracture networks reconstructed from the shale samples in the Longmaxi formation of China. The flow fields are simulated and the permeability is calculated based on the fracture configurations and fracture apertures after hydraulic fracturing treatment. It is found that the anisotropy of the permeability is very strong, and the permeability curves have similar shapes. Therefore, a fitting equation of the permeability curve is given for convenient use in the future. The permeability curves under different fluid pressures and crustal stress directions are obtained. The results show that the permeability anisotropy is stronger when the fluid pressure is higher. Moreover, the permeability anisotropy reaches the minimum value when the maximum principle stress direction is perpendicular to the main natural fracture direction. The investigation on the permeability is useful for answering how the reservoirs are hydraulically stimulated and is useful for predicting the propagation behaviors of the hydraulic fracture network in shale gas reservoirs.
Directory of Open Access Journals (Sweden)
Yuliang Su
Full Text Available Stimulated reservoir volume (SRV fracturing in tight oil reservoirs often induces complex fracture-network growth, which has a fundamentally different formation mechanism from traditional planar bi-winged fracturing. To reveal the mechanism of fracture network propagation, this paper employs a modified displacement discontinuity method (DDM, mechanical mechanism analysis and initiation and propagation criteria for the theoretical model of fracture network propagation and its derivation. A reasonable solution of the theoretical model for a tight oil reservoir is obtained and verified by a numerical discrete method. Through theoretical calculation and computer programming, the variation rules of formation stress fields, hydraulic fracture propagation patterns (FPP and branch fracture propagation angles and pressures are analyzed. The results show that during the process of fracture propagation, the initial orientation of the principal stress deflects, and the stress fields at the fracture tips change dramatically in the region surrounding the fracture. Whether the ideal fracture network can be produced depends on the geological conditions and on the engineering treatments. This study has both theoretical significance and practical application value by contributing to a better understanding of fracture network propagation mechanisms in unconventional oil/gas reservoirs and to the improvement of the science and design efficiency of reservoir fracturing.
Su, Yuliang; Ren, Long; Meng, Fankun; Xu, Chen; Wang, Wendong
2015-01-01
Stimulated reservoir volume (SRV) fracturing in tight oil reservoirs often induces complex fracture-network growth, which has a fundamentally different formation mechanism from traditional planar bi-winged fracturing. To reveal the mechanism of fracture network propagation, this paper employs a modified displacement discontinuity method (DDM), mechanical mechanism analysis and initiation and propagation criteria for the theoretical model of fracture network propagation and its derivation. A reasonable solution of the theoretical model for a tight oil reservoir is obtained and verified by a numerical discrete method. Through theoretical calculation and computer programming, the variation rules of formation stress fields, hydraulic fracture propagation patterns (FPP) and branch fracture propagation angles and pressures are analyzed. The results show that during the process of fracture propagation, the initial orientation of the principal stress deflects, and the stress fields at the fracture tips change dramatically in the region surrounding the fracture. Whether the ideal fracture network can be produced depends on the geological conditions and on the engineering treatments. This study has both theoretical significance and practical application value by contributing to a better understanding of fracture network propagation mechanisms in unconventional oil/gas reservoirs and to the improvement of the science and design efficiency of reservoir fracturing.
Energy Technology Data Exchange (ETDEWEB)
Crichlow, H.B.; Crichlow, H.B. (ed.)
1980-02-07
A design tool is discussed whereby the various components that enter the design process of a hydraulic fracturing job are combined to provide a realistic appraisal of a stimulation job in the field. An interactive computer model is used to solve the problem numerically to obtain the effects of various parameters on the overall behavior of the system.
Wang, Peitao; Cai, Meifeng; Ren, Fenhua; Li, Changhong; Yang, Tianhong
2017-07-01
This paper develops a numerical approach to determine the mechanical behavior of discrete fractures network (DFN) models based on digital image processing technique and particle flow code (PFC2D). A series of direct shear tests of jointed rocks were numerically performed to study the effect of normal stress, friction coefficient and joint bond strength on the mechanical behavior of joint rock and evaluate the influence of micro-parameters on the shear properties of jointed rocks using the proposed approach. The complete shear stress-displacement curve of the DFN model under direct shear tests was presented to evaluate the failure processes of jointed rock. The results show that the peak and residual strength are sensitive to normal stress. A higher normal stress has a greater effect on the initiation and propagation of cracks. Additionally, an increase in the bond strength ratio results in an increase in the number of both shear and normal cracks. The friction coefficient was also found to have a significant influence on the shear strength and shear cracks. Increasing in the friction coefficient resulted in the decreasing in the initiation of normal cracks. The unique contribution of this paper is the proposed modeling technique to simulate the mechanical behavior of jointed rock mass based on particle mechanics approaches.
Particle Swarm Transport in Fracture Networks
Pyrak-Nolte, L. J.; Mackin, T.; Boomsma, E.
2012-12-01
Colloidal particles of many types occur in fractures in the subsurface as a result of both natural and industrial processes (e.g., environmental influences, synthetic nano- & micro-particles from consumer products, chemical and mechanical erosion of geologic material, proppants used in gas and oil extraction, etc.). The degree of localization and speed of transport of such particles depends on the transport mechanisms, the chemical and physical properties of the particles and the surrounding rock, and the flow path geometry through the fracture. In this study, we investigated the transport of particle swarms through artificial fracture networks. A synthetic fracture network was created using an Objet Eden 350V 3D printer to build a network of fractures. Each fracture in the network had a rectangular cross-sectional area with a constant depth of 7 mm but with widths that ranged from 2 mm to 11 mm. The overall dimensions of the network were 132 mm by 166 mm. The fracture network had 7 ports that were used either as the inlet or outlet for fluid flow through the sample or for introducing a particle swarm. Water flow rates through the fracture were controlled with a syringe pump, and ranged from zero flow to 6 ml/min. Swarms were composed of a dilute suspension (2% by mass) of 3 μm fluorescent polystyrene beads in water. Swarms with volumes of 5, 10, 20, 30 and 60 μl were used and delivered into the network using a second syringe pump. The swarm behavior was imaged using an optical fluorescent imaging system illuminated by green (525 nm) LED arrays and captured by a CCD camera. For fracture networks with quiescent fluids, particle swarms fell under gravity and remained localized within the network. Large swarms (30-60 μl) were observed to bifurcate at shallower depths resulting in a broader dispersal of the particles than for smaller swarm volumes. For all swarm volumes studied, particle swarms tended to bifurcate at the intersection between fractures. These
Experimental Study of Heat Transport in Fractured Network
Pastore, Nicola; Cherubini, Claudia; Giasi, Concetta I.; Allegretti, Nicoletta M.; Redondo, Jose M.; Tarquis, Ana Maria
2015-04-01
Fractured rocks play an important role in transport of natural resources or contaminants transport through subsurface systems. In recent years, interest has grown in investigating heat transport by means of tracer tests, driven by the important current development of geothermal applications. In literature different methods are available for predicting thermal breakthrough in fractured reservoirs based on the information coming from tracer tests. Geothermal energy is one of the largest sources of renewable energies that are extracted from the earth. The growing interest in this new energy source has stimulated attempts to develop methods and technologies for extracting energy also from ground resource at low temperature. An example is the exploitation of low enthalpy geothermal energy that can be obtained at any place with the aid of ground-source heat pump system from the soil, rock and groundwater. In such geothermal systems the fluid movement and thermal behavior in the fractured porous media is very important and critical. Existing theory of fluid flow and heat transport through porous media is of limited usefulness when applied to fractured rocks. Many field and laboratory tracer tests in fractured media show that fracture -matrix exchange is more significant for heat than mass tracers, thus thermal breakthrough curves (BTCs) are strongly controlled by matrix thermal diffusivity. In this study the behaviour of heat transport in a fractured network at bench scale has been investigated. Heat tracer tests on an artificially created fractured rock sample have been carried out. The observed thermal BTCs obtained with six thermocouple probes located at different locations in the fractured medium have been modeled with the Explicit Network Model (ENM) based an adaptation of Tang's solution for solute transport in a semi-infinite single fracture embedded in a porous matrix. The ENM model is able to represent the behavior of observed heat transport except where the
Barnhoorn, A.; Cox, S.F.
2012-01-01
Fracturing experiments on very low-porosity dolomite rocks shows a difference in growth of fracture networks by stress-driven fracturing and fluid-driven fracturing. Stress-driven fracture growth, in the absence of fluid pressure, initially forms fractures randomly throughout the rocks followed by g
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)
Influence of fracture networks on radionuclide transport from solidified waste forms
Energy Technology Data Exchange (ETDEWEB)
Seetharam, S.C., E-mail: suresh.seetharam@sckcen.be [Performance Assessments Unit, Institute for Environment, Health and Safety, Belgian Nuclear Research Centre (SCK CEN), Boeretang 200, B-2400 Mol (Belgium); Perko, J.; Jacques, D. [Performance Assessments Unit, Institute for Environment, Health and Safety, Belgian Nuclear Research Centre (SCK CEN), Boeretang 200, B-2400 Mol (Belgium); Mallants, D. [CSIRO Land and Water, Waite Road – Gate 4, Glen Osmond, SA 5064 (Australia)
2014-04-01
Highlights: • Magnitude of peak radionuclide fluxes is less sensitive to the fracture network geometry. • Time of peak radionuclide fluxes is sensitive to the fracture networks. • Uniform flow model mimics a limiting case of a porous medium with large number of fine fractures. • Effect of fracture width on radionuclide flux depends on the ratio of fracture to matrix conductivity. • Effect of increased dispersivity in fractured media does not always result in a lower peak flux for specific fracture networks due to higher concentrations adjacent to the fracture plane. - Abstract: Analysis of the effect of fractures in porous media on fluid flow and mass transport is of great interest in many fields including geotechnical, petroleum, hydrogeology and waste management. This paper presents sensitivity analyses examining the effect of various hypothetical fracture networks on the performance of a planned near surface disposal facility in terms of radionuclide transport behaviour. As it is impossible to predict the initiation and evolution of fracture networks and their characteristics in concrete structures over time scales of interest, several fracture networks have been postulated to test the sensitivity of radionuclide release from a disposal facility. Fluid flow through concrete matrix and fracture networks are modelled via Darcy's law. A single species radionuclide transport equation is employed for both matrix and fracture networks, which include the processes advection, diffusion, dispersion, sorption/desorption and radioactive decay. The sensitivity study evaluates variations in fracture network configuration and fracture width together with different sorption/desorption characteristics of radionuclides in a cement matrix, radioactive decay constants and matrix dispersivity. The effect of the fractures is illustrated via radionuclide breakthrough curves, magnitude and time of peak mass flux, cumulative mass flux and concentration profiles. For the
Periodic Hydraulic Testing for Discerning Fracture Network Connections
Becker, M.; Le Borgne, T.; Bour, O.; Guihéneuf, N.; Cole, M.
2015-12-01
Discrete fracture network (DFN) models often predict highly variable hydraulic connections between injection and pumping wells used for enhanced oil recovery, geothermal energy extraction, and groundwater remediation. Such connections can be difficult to verify in fractured rock systems because standard pumping or pulse interference tests interrogate too large a volume to pinpoint specific connections. Three field examples are presented in which periodic hydraulic tests were used to obtain information about hydraulic connectivity in fractured bedrock. The first site, a sandstone in New York State, involves only a single fracture at a scale of about 10 m. The second site, a granite in Brittany, France, involves a fracture network at about the same scale. The third site, a granite/schist in the U.S. State of New Hampshire, involves a complex network at scale of 30-60 m. In each case periodic testing provided an enhanced view of hydraulic connectivity over previous constant rate tests. Periodic testing is particularly adept at measuring hydraulic diffusivity, which is a more effective parameter than permeability for identify the complexity of flow pathways between measurement locations. Periodic tests were also conducted at multiple frequencies which provides a range in the radius of hydraulic penetration away from the oscillating well. By varying the radius of penetration, we attempt to interrogate the structure of the fracture network. Periodic tests, therefore, may be uniquely suited for verifying and/or calibrating DFN models.
FROMS3D: New Software for 3-D Visualization of Fracture Network System in Fractured Rock Masses
Noh, Y. H.; Um, J. G.; Choi, Y.
2014-12-01
A new software (FROMS3D) is presented to visualize fracture network system in 3-D. The software consists of several modules that play roles in management of borehole and field fracture data, fracture network modelling, visualization of fracture geometry in 3-D and calculation and visualization of intersections and equivalent pipes between fractures. Intel Parallel Studio XE 2013, Visual Studio.NET 2010 and the open source VTK library were utilized as development tools to efficiently implement the modules and the graphical user interface of the software. The results have suggested that the developed software is effective in visualizing 3-D fracture network system, and can provide useful information to tackle the engineering geological problems related to strength, deformability and hydraulic behaviors of the fractured rock masses.
Shahkarami, P. Mr; Neretnieks, I. E.
2016-12-01
An essential task of performance assessment of radioactive waste repositories is to predict radionuclide release into the environment. For such a quantitative assessment, the Channel Network Model and the corresponding computer program, CHAN3D, have been used to simulate radionuclide transport in crystalline bedrocks. Recent studies suggest, however, that the model may tend to underestimate the rock retarding capability, because it ignores the presence of stagnant water zones, STWZs, situated in the fracture plane. Once considered, the STWZ can provide additional surface area over which radionuclides diffuse into the rock matrix and thereby contribute to their retardation. The main objective of this contribution is to extend the Channel Network Model and its computer implementation to account for diffusion into STWZs and their adjacent rock matrices. A series of deterministic and probabilistic calculations are performed in this study. The deterministic calculations aimed to investigate the overall impact of STWZs in retarding radionuclide transport and their far-field releases at Forsmark, Sweden. While, the probabilistic calculations aimed to (I) simulate the tracer test experiment performed at Äspö HRL, STT-1 and (II) investigate the short- and long-term effect of diffusion into STWZs. The deterministic calculation results suggest that over the time-scale of the repository safety assessments, the presence of STWZs enhances the retardation of most long-lived radionuclides except for 36Cl and 129I. The probabilistic calculation results suggest that over the short time-scale of the tracer experiment, the effect of diffusion into STWZs is not as pronounced as that of matrix diffusion directly from the flow channel, and the latter remains the main retarding mechanism. Predictions for longer time-scale, tens of years and more, show that the effect of STWZs becomes strong and tends to increase with transport time. It is shown that over the long times of interest for
Energy Technology Data Exchange (ETDEWEB)
Paul La Pointe; Jan Hermanson; Robert Parney; Thorsten Eiben; Mike Dunleavy; Ken Steele; John Whitney; Darrell Eubanks; Roger Straub
2002-11-18
This report describes the results made in fulfillment of contract DE-FG26-00BC15190, ''3-D Reservoir and Stochastic Fracture Network Modeling for Enhanced Oil Recovery, Circle Ridge Phosphoria/Tensleep Reservoir, Wind River Reservation, Arapaho and Shoshone Tribes, Wyoming''. The goal of this project is to improve the recovery of oil from the Tensleep and Phosphoria Formations in 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. Fields in which natural fractures dominate reservoir permeability, such as the Circle Ridge Field, often experience sub-optimal recovery when recovery processes are designed and implemented that do not take advantage of the fracture systems. For example, a conventional waterflood in a main structural block of the Field was implemented and later suspended due to unattractive results. It is estimated that somewhere less than 20% of the OOIP in the Circle Ridge Field have been recovered after more than 50 years' production. Marathon Oil Company identified the Circle Ridge Field as an attractive candidate for several advanced IOR processes that explicitly take advantage of the natural fracture system. These processes require knowledge of the distribution of matrix porosity, permeability and oil saturations; and understanding of where fracturing is likely to be well-developed or poorly developed; how the fracturing may compartmentalize the reservoir; and how smaller, relatively untested subthrust fault blocks may be connected to the main overthrust block. For this reason, the project focused on improving knowledge of the matrix properties, the fault block architecture and to develop a model that could be used to predict fracture intensity, orientation and fluid flow/connectivity properties. Knowledge
Modelling of Specimen Fracture
2013-09-23
the plate center. An end load of 1.0 MPa was applied. 1 2 3 Modelling of Specimen Fracture – Final Report 11 TR-13-47 Figure 2.5: Crack Geometry Figure...Christopher Bayley DRDC Atlantic Dockyard Laboratory Pacific CFB Esquimalt, Building 199 PO Box 17000, Station Forces Victoria, British Columbia Canada...q The weighting function, q , can be any arbitrary function within the J-integral domain, and must be zero on the domain boundary . An easy function
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.
Three-phase flow simulations in discrete fracture networks
Geiger, S.; Niessner, J.; Matthai, S. K.; Helmig, R.
2006-12-01
Fractures are often the key conduits for fluid flow in otherwise low permeability rocks. Their presence in hydrocarbon reservoirs leads to complex production histories, unpredictable coupling of wells, rapidly changing flow rates, possibly early water breakthrough, and low final recovery. Recently, it has been demonstrated that a combination of finite volume and finite element discretization is well suited to model incompressible, immiscible two-phase flow in 3D discrete fracture networks (DFN) representing complexly fractured rocks. Such an approach has been commercialized in Golder Associates' FracMan Reservoir Edition software. For realistic reservoir simulations, however, it would be desirable if a third compressible gas phase can be included which is often present at reservoir conditions. Here we present the extension of an existing node-centred finite volume - finite element (FEFV) discretization for the efficient and accurate simulations of three-component - three-phase flow in geologically realistic representations of fractured porous media. Two possible types of fracture networks can be used: In 2D, they are detailed geometrical representations of fractured rock masses mapped in field studies. In 3D, they are geologically constrained, stochastically generated discrete fracture networks. Flow and transport can be simulated for fractures only or for fractures and matrix combined. The governing equations are solved decoupled using an implicit-pressure, explicit-saturation (IMPES) approach. Flux and concentration terms can be treated with higher-order accuracy in the finite volume scheme to preserve shock fronts. The method is locally mass conservative and works on unstructured, spatially refined grids. Flash calculations are carried out by a new description of the Black-Oil model. Capillary and gravity effects are included in this formulation. The robustness and accuracy of this formulation is shown in several applications. First, grid convergence is
Hao, Y.; Settgast, R. R.; Fu, P.; Tompson, A. F. B.; Morris, J.; Ryerson, F. J.
2016-12-01
It has long been recognized that multiphase flow and transport in fractured porous media is very important for various subsurface applications. Hydrocarbon fluid flow and production from hydraulically fractured shale reservoirs is an important and complicated example of multiphase flow in fractured formations. The combination of horizontal drilling and hydraulic fracturing is able to create extensive fracture networks in low permeability shale rocks, leading to increased formation permeability and enhanced hydrocarbon production. However, unconventional wells experience a much faster production decline than conventional hydrocarbon recovery. Maintaining sustainable and economically viable shale gas/oil production requires additional wells and re-fracturing. Excessive fracturing fluid loss during hydraulic fracturing operations may also drive up operation costs and raise potential environmental concerns. Understanding and modeling processes that contribute to decreasing productivity and fracturing fluid loss represent a critical component for unconventional hydrocarbon recovery analysis. Towards this effort we develop a discrete fracture model (DFM) in GEOS (LLNL multi-physics computational code) to simulate multiphase flow and transfer in hydraulically fractured reservoirs. The DFM model is able to explicitly account for both individual fractures and their surrounding rocks, therefore allowing for an accurate prediction of impacts of fracture-matrix interactions on hydrocarbon production. We apply the DFM model to simulate three-phase (water, oil, and gas) flow behaviors in fractured shale rocks as a result of different hydraulic stimulation scenarios. Numerical results show that multiphase flow behaviors at the fracture-matrix interface play a major role in controlling both hydrocarbon production and fracturing fluid recovery rates. The DFM model developed in this study will be coupled with the existing hydro-fracture model to provide a fully integrated
An analytical thermohydraulic model for discretely fractured geothermal reservoirs
Fox, Don B.; Koch, Donald L.; Tester, Jefferson W.
2016-09-01
In discretely fractured reservoirs such as those found in Enhanced/Engineered Geothermal Systems (EGS), knowledge of the fracture network is important in understanding the thermal hydraulics, i.e., how the fluid flows and the resulting temporal evolution of the subsurface temperature. The purpose of this study was to develop an analytical model of the fluid flow and heat transport in a discretely fractured network that can be used for a wide range of modeling applications and serve as an alternative analysis tool to more computationally intensive numerical codes. Given the connectivity and structure of a fracture network, the flow in the system was solved using a linear system of algebraic equations for the pressure at the nodes of the network. With the flow determined, the temperature in the fracture was solved by coupling convective heat transport in the fracture with one-dimensional heat conduction perpendicular to the fracture, employing the Green's function derived solution for a single discrete fracture. The predicted temperatures along the fracture surfaces from the analytical solution were compared to numerical simulations using the TOUGH2 reservoir code. Through two case studies, we showed the capabilities of the analytical model and explored the effect of uncertainty in the fracture apertures and network structure on thermal performance. While both sources of uncertainty independently produce large variations in production temperature, uncertainty in the network structure, whenever present, had a predominant influence on thermal performance.
Towards effective flow simulations in realistic discrete fracture networks
Berrone, Stefano; Pieraccini, Sandra; Scialò, Stefano
2016-04-01
We focus on the simulation of underground flow in fractured media, modeled by means of Discrete Fracture Networks. Focusing on a new recent numerical approach proposed by the authors for tackling the problem avoiding mesh generation problems, we further improve the new family of methods making a step further towards effective simulations of large, multi-scale, heterogeneous networks. Namely, we tackle the imposition of Dirichlet boundary conditions in weak form, in such a way that geometrical complexity of the DFN is not an issue; we effectively solve DFN problems with fracture transmissivities spanning many orders of magnitude and approaching zero; furthermore, we address several numerical issues for improving the numerical solution also in quite challenging networks.
XFEM modeling of hydraulic fracture in porous rocks with natural fractures
Wang, Tao; Liu, ZhanLi; Zeng, QingLei; Gao, Yue; Zhuang, Zhuo
2017-08-01
Hydraulic fracture (HF) in porous rocks is a complex multi-physics coupling process which involves fluid flow, diffusion and solid deformation. In this paper, the extended finite element method (XFEM) coupling with Biot theory is developed to study the HF in permeable rocks with natural fractures (NFs). In the recent XFEM based computational HF models, the fluid flow in fractures and interstitials of the porous media are mostly solved separately, which brings difficulties in dealing with complex fracture morphology. In our new model the fluid flow is solved in a unified framework by considering the fractures as a kind of special porous media and introducing Poiseuille-type flow inside them instead of Darcy-type flow. The most advantage is that it is very convenient to deal with fluid flow inside the complex fracture network, which is important in shale gas extraction. The weak formulation for the new coupled model is derived based on virtual work principle, which includes the XFEM formulation for multiple fractures and fractures intersection in porous media and finite element formulation for the unified fluid flow. Then the plane strain Kristianovic-Geertsma-de Klerk (KGD) model and the fluid flow inside the fracture network are simulated to validate the accuracy and applicability of this method. The numerical results show that large injection rate, low rock permeability and isotropic in-situ stresses tend to lead to a more uniform and productive fracture network.
Fractured-basement reservoir modeling using continuous fracture modeling (CFM) method
Isniarny, Nadya; Haris, Abdul; Nurdin, Safrizal
2016-02-01
The challenge in oil and gas exploration has now shifted due to increasingly difficult to get back up economic value in a conventional reservoir. Explorationist are developing various drilling technology, optimizing conventional reserves and unconventional reserve in reservoirs. One of the unconventional reservoir that has been developed is the basement reservoir. This rock type has no primary porosity and the permeability of the rocks of this type are generally influenced by the naturally fracture networks. The purpose of this study is to map the fracture intensity distribution in the basement reservoir using Continuous Fracture Modeling (CFM) method. CFM method applies the basic concepts of neural network in finding a relationship between well data with seismic data in order to build a model of fracture intensity. The Formation Micro Imager (FMI) interpretation data is used to identify the presence of fracture along the well as dip angle and dip azimuth. This indicator will be laterally populated in 3D grid model. Several seismic attribute which are generated from seismic data is used as a guidance to populate fracture intensity in the model. The results from the model were validated with Drill Stem Test (DST) data. Zones of high fracture intensity on the model correlates positively with the presence of fluid in accordance with DST data.
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.
Makedonska, Nataliia; Hyman, Jeffrey D.; Karra, Satish; Painter, Scott L.; Gable, Carl W.; Viswanathan, Hari S.
2016-08-01
The apertures of natural fractures in fractured rock are highly heterogeneous. However, in-fracture aperture variability is often neglected in flow and transport modeling and individual fractures are assumed to have uniform aperture distribution. The relative importance of in-fracture variability in flow and transport modeling within kilometer-scale field-scale fracture networks has been under a matter of debate for a long time because the flow in each single fracture is controlled not only by in-fracture variability but also by boundary conditions. Computational limitations have previously prohibited researchers from investigating the relative importance of in-fracture variability in flow and transport modeling within large-scale fracture networks. We address this question by incorporating internal heterogeneity of individual fractures into flow simulations within kilometer scale three-dimensional fracture networks, where fracture intensity, P32 (ratio between total fracture area and domain volume) is between 0.027 and 0.031 [1/m]. A recently developed discrete fracture network (DFN) simulation capability, dfnWorks, is used to generate DFNs that include in-fracture aperture variability represented by a stationary log-normal stochastic field with various correlation lengths and variances. The Lagrangian transport parameters, non-reacting travel time and cumulative retention, are calculated along particles streamlines. It is observed that due to local flow channeling early particle travel times are more sensitive to in-fracture variability than the tails of travel time distributions, where no significant effect of the in-fracture transmissivity variations and spatial correlation length is observed.
Simulation of Hydraulic and Natural Fracture Interaction Using a Coupled DFN-DEM Model
Energy Technology Data Exchange (ETDEWEB)
J. Zhou; H. Huang; M. Deo
2016-03-01
The presence of natural fractures will usually result in a complex fracture network due to the interactions between hydraulic and natural fracture. The reactivation of natural fractures can generally provide additional flow paths from formation to wellbore which play a crucial role in improving the hydrocarbon recovery in these ultra-low permeability reservoir. Thus, accurate description of the geometry of discrete fractures and bedding is highly desired for accurate flow and production predictions. Compared to conventional continuum models that implicitly represent the discrete feature, Discrete Fracture Network (DFN) models could realistically model the connectivity of discontinuities at both reservoir scale and well scale. In this work, a new hybrid numerical model that couples Discrete Fracture Network (DFN) and Dual-Lattice Discrete Element Method (DL-DEM) is proposed to investigate the interaction between hydraulic fracture and natural fractures. Based on the proposed model, the effects of natural fracture orientation, density and injection properties on hydraulic-natural fractures interaction are investigated.
Characterization of EGS Fracture Network Lifecycles
Energy Technology Data Exchange (ETDEWEB)
Gillian R. Foulger
2008-03-31
Geothermal energy is relatively clean, and is an important non-hydrocarbon source of energy. It can potentially reduce our dependence on fossil fuels and contribute to reduction in carbon emissions. High-temperature geothermal areas can be used for electricity generation if they contain permeable reservoirs of hot water or steam that can be extracted. The biggest challenge to achieving the full potential of the nation’s resources of this kind is maintaining and creating the fracture networks required for the circulation, heating, and extraction of hot fluids. The fundamental objective of the present research was to understand how fracture networks are created in hydraulic borehole injection experiments, and how they subsequently evolve. When high-pressure fluids are injected into boreholes in geothermal areas, they flow into hot rock at depth inducing thermal cracking and activating critically stressed pre-existing faults. This causes earthquake activity which, if monitored, can provide information on the locations of the cracks formed, their time-development and the type of cracking underway, e.g., whether shear movement on faults occurred or whether cracks opened up. Ultimately it may be possible to monitor the critical earthquake parameters in near-real-time so the information can be used to guide the hydraulic injection while it is in progress, e.g., how to adjust factors such as injectate pressure, volume and temperature. In order to achieve this, it is necessary to mature analysis techniques and software that were, at the start of this project, in an embryonic developmental state. Task 1 of the present project was to develop state-of-the-art techniques and software for calculating highly accurate earthquake locations, earthquake source mechanisms (moment tensors) and temporal changes in reservoir structure. Task 2 was to apply the new techniques to hydrofracturing (Enhanced Geothermal Systems, or “EGS”) experiments performed at the Coso geothermal field
Roubinet, D; Jougnot, D; Irving, J
2016-01-01
Numerous field experiments suggest that the self-potential (SP) geophysical method may allow for the detection of hydraulically active fractures and provide information about fracture properties. However, a lack of suitable numerical tools for modeling streaming potentials in fractured media prevents quantitative interpretation and limits our understanding of how the SP method can be used in this regard. To address this issue, we present a highly efficient two-dimensional discrete-dual-porosity approach for solving the fluid flow and associated self-potential problems in fractured rock. Our approach is specifically designed for complex fracture networks that cannot be investigated using standard numerical methods. We then simulate SP signals associated with pumping conditions for a number of examples to show that (i) accounting for matrix fluid flow is essential for accurate SP modeling and (ii) the sensitivity of SP to hydraulically active fractures is intimately linked with fracture-matrix fluid interaction...
Hadgu, Teklu; Karra, Satish; Kalinina, Elena; Makedonska, Nataliia; Hyman, Jeffrey D.; Klise, Katherine; Viswanathan, Hari S.; Wang, Yifeng
2017-10-01
One of the major challenges of simulating flow and transport in the far field of a geologic repository in crystalline host rock is related to reproducing the properties of the fracture network over the large volume of rock with sparse fracture characterization data. Various approaches have been developed to simulate flow and transport through the fractured rock. The approaches can be broadly divided into Discrete Fracture Network (DFN) and Equivalent Continuum Model (ECM). The DFN explicitly represents individual fractures, while the ECM uses fracture properties to determine equivalent continuum parameters. We compare DFN and ECM in terms of upscaled observed transport properties through generic fracture networks. The major effort was directed on making the DFN and ECM approaches similar in their conceptual representations. This allows for separating differences related to the interpretation of the test conditions and parameters from the differences between the DFN and ECM approaches. The two models are compared using a benchmark test problem that is constructed to represent the far field (1 × 1 × 1 km3) of a hypothetical repository in fractured crystalline rock. The test problem setting uses generic fracture properties that can be expected in crystalline rocks. The models are compared in terms of the: 1) effective permeability of the domain, and 2) nonreactive solute breakthrough curves through the domain. The principal differences between the models are mesh size, network connectivity, matrix diffusion and anisotropy. We demonstrate how these differences affect the flow and transport. We identify the factors that should be taken in consideration when selecting an approach most suitable for the site-specific conditions.
Analysis of Fracturing Network Evolution Behaviors in Random Naturally Fractured Rock Blocks
Wang, Y.; Li, X.; Zhang, B.
2016-11-01
Shale gas has been discovered in the Upper Triassic Yanchang Formation, Ordos Basin, China. Due to the weak tectonic activities in the shale plays, core observations indicate abundant random non-tectonic micro-fractures in the producing shales. The role of micro-fractures in hydraulic fracturing for shale gas development is currently poorly understood yet potentially critical. In a series of scaled true triaxial laboratory experiments, we investigate the interaction of propagating fracturing network with natural fractures. The influence of dominating factors was studied and analyzed, with an emphasis on non-tectonic fracture density, injection rate, and stress ratio. A new index of P-SRV is proposed to evaluate the fracturing effectiveness. From the test results, three types of fracturing network geometry of radial random net-fractures, partly vertical fracture with random branches, and vertical main fracture with multiple branches were observed. It is suggested from qualitative and quantitative analysis that great micro-fracture density and injection rate tend to maximum the fracturing network; however, it tends to decrease the fracturing network with the increase in horizontal stress ratio. The function fitting results further proved that the injection rate has the most obvious influence on fracturing effectiveness.
Automatic fracture density update using smart well data and artificial neural networks
Al-Anazi, A.; Babadagli, T.
2010-03-01
This paper presents a new methodology to continuously update and improve fracture network models. We begin with a hypothetical model whose fracture network parameters and geological information are known. After generating the "exact" fracture network with known characteristics, the data were exported to a reservoir simulator and simulations were run over a period of time. Intelligent wells equipped with downhole multiple pressure and flow sensors were placed throughout the reservoir and put into production. These producers were completed in different fracture zones to create a representative pressure and production response. We then considered a number of wells of which static (cores and well logs) and dynamic (production) data were used to model well fracture density. As new wells were opened, historical static and dynamic data from previous wells and static data from the new wells were used to update the fracture density using Artificial Neural Networks (ANN). The accuracy of the prediction model depends significantly on the representation of the available data of the existing fracture network. The importance of conventional data (surface production data) and smart well data prediction capability was also investigated. Highly sensitive input data were selected through a forward selection scheme to train the ANN. Well geometric locations were included as a new link in the ANN regression process. Once the relationship between fracture network parameters and well performance data was established, the ANN model was used to predict fracture density at newly drilled locations. Finally, an error analysis through a correlation coefficient and percentage absolute relative error performance was performed to examine the accuracy of the proposed inverse modeling methodology. It was shown that fracture dominated production performance data collected from both conventional and smart wells allow for automatically updating the fracture network model. The proposed technique helps
Characterization of EGS Fracture Network Lifecycles
Energy Technology Data Exchange (ETDEWEB)
Gillian R. Foulger
2008-03-31
Geothermal energy is relatively clean, and is an important non-hydrocarbon source of energy. It can potentially reduce our dependence on fossil fuels and contribute to reduction in carbon emissions. High-temperature geothermal areas can be used for electricity generation if they contain permeable reservoirs of hot water or steam that can be extracted. The biggest challenge to achieving the full potential of the nation’s resources of this kind is maintaining and creating the fracture networks required for the circulation, heating, and extraction of hot fluids. The fundamental objective of the present research was to understand how fracture networks are created in hydraulic borehole injection experiments, and how they subsequently evolve. When high-pressure fluids are injected into boreholes in geothermal areas, they flow into hot rock at depth inducing thermal cracking and activating critically stressed pre-existing faults. This causes earthquake activity which, if monitored, can provide information on the locations of the cracks formed, their time-development and the type of cracking underway, e.g., whether shear movement on faults occurred or whether cracks opened up. Ultimately it may be possible to monitor the critical earthquake parameters in near-real-time so the information can be used to guide the hydraulic injection while it is in progress, e.g., how to adjust factors such as injectate pressure, volume and temperature. In order to achieve this, it is necessary to mature analysis techniques and software that were, at the start of this project, in an embryonic developmental state. Task 1 of the present project was to develop state-of-the-art techniques and software for calculating highly accurate earthquake locations, earthquake source mechanisms (moment tensors) and temporal changes in reservoir structure. Task 2 was to apply the new techniques to hydrofracturing (Enhanced Geothermal Systems, or “EGS”) experiments performed at the Coso geothermal field
Jia, Pin; Cheng, Linsong; Huang, Shijun; Xu, Zhongyi; Xue, Yongchao; Cao, Renyi; Ding, Guanyang
2017-08-01
This paper provides a comprehensive model for the flow behavior of a two-zone system with discrete fracture network. The discrete fracture network within the inner zone is represented explicitly by fracture segments. The Laplace-transform finite-difference method is used to numerically model discrete fracture network flow, with sufficient flexibility to consider arbitrary fracture geometries and conductivity distributions. Boundary-element method and line-source functions in the Laplace domain are employed to derive a semi-analytical flow solution for the two-zone system. By imposing the continuity of flux and pressure on discrete fracture surfaces, the semi-analytical two-zone system flow model and the numerical fracture flow model are coupled dynamically. The main advantage of the approach occurring in the Laplace domain is that simulation can be done with nodes only for discrete fractures and elements for boundaries and at predetermined, discrete times. Thus, stability and convergence problems caused by time discretization are avoided and the burden of gridding and computation is decreased without loss of important fracture characteristics. The model is validated by comparison with the results from an analytical solution and a fully numerical solution. Flow regime analysis shows that a two-zone system with discrete fracture network may develop six flow regimes: fracture linear flow, bilinear flow, inner zone linear flow, inner zone pseudosteady-state flow, outer zone pseudoradial flow and outer zone boundary-dominated flow. Especially, local solutions for the inner-zone linear flow have the same form with that of a finite conductivity planar fracture and can be correlated with the total length of discrete fractures and an intercept term. In the inner zone pseudosteady-state flow period, the discrete fractures, along with the boundary of the inner zone, will act as virtual closed boundaries, due to the pressure interference caused by fracture network and the
Multiple-point statistical prediction on fracture networks at Yucca Mountain
Energy Technology Data Exchange (ETDEWEB)
Liu, X.Y; Zhang, C.Y.; Liu, Q.S.; Birkholzer, J.T.
2009-05-01
In many underground nuclear waste repository systems, such as at Yucca Mountain, water flow rate and amount of water seepage into the waste emplacement drifts are mainly determined by hydrological properties of fracture network in the surrounding rock mass. Natural fracture network system is not easy to describe, especially with respect to its connectivity which is critically important for simulating the water flow field. In this paper, we introduced a new method for fracture network description and prediction, termed multi-point-statistics (MPS). The process of the MPS method is to record multiple-point statistics concerning the connectivity patterns of a fracture network from a known fracture map, and to reproduce multiple-scale training fracture patterns in a stochastic manner, implicitly and directly. It is applied to fracture data to study flow field behavior at the Yucca Mountain waste repository system. First, the MPS method is used to create a fracture network with an original fracture training image from Yucca Mountain dataset. After we adopt a harmonic and arithmetic average method to upscale the permeability to a coarse grid, THM simulation is carried out to study near-field water flow in the surrounding waste emplacement drifts. Our study shows that connectivity or patterns of fracture networks can be grasped and reconstructed by MPS methods. In theory, it will lead to better prediction of fracture system characteristics and flow behavior. Meanwhile, we can obtain variance from flow field, which gives us a way to quantify model uncertainty even in complicated coupled THM simulations. It indicates that MPS can potentially characterize and reconstruct natural fracture networks in a fractured rock mass with advantages of quantifying connectivity of fracture system and its simulation uncertainty simultaneously.
Multiple-point statistical prediction on fracture networks at Yucca Mountain
Liu, Xiaoyan; Zhang, Chengyuan; Liu, Quansheng; Birkholzer, Jens
2009-05-01
In many underground nuclear waste repository systems, such as Yucca Mountain project, water flow rate and amount of water seepage into the waste emplacement drifts are mainly determined by hydrological properties of fracture network in the surrounding rock mass. Natural fracture network system is not easy to describe, especially with respect to its connectivity which is critically important for simulating the water flow field. In this paper, we introduced a new method for fracture network description and prediction, termed multi-point-statistics (MPS). The process of Multi-point Statistical method is to record multiple-point statistics concerning the connectivity patterns of fracture network from a known fracture map, and to reproduce multiple-scale training fracture patterns in a stochastic manner, implicitly and directly. It is applied to fracture data to study flow field behavior at Yucca Mountain waste repository system. First, MPS method is used to create fracture network with original fracture training image from Yucca Mountain dataset. After we adopt a harmonic and arithmetic average method to upscale the permeability to a coarse grid, THM simulation is carried out to study near-field water flow in surrounding rock of waste emplacement drifts. Our study shows that connectivity or pattern of fracture network can be grasped and reconstructed by Multi-Point-Statistical method. In theory, it will lead to better prediction of fracture system characteristics and flow behavior. Meanwhile, we can obtain variance from flow field, which gives us a way to quantify uncertainty of models even in complicated coupled THM simulation. It indicates that Multi-Point Statistics is a potential method to characterize and reconstruct natural fracture network in a fractured rock mass with advantages of quantifying connectivity of fracture system and its simulation uncertainty simultaneously.
Directory of Open Access Journals (Sweden)
Zhaohui Chong
2017-07-01
Full Text Available Hydraulic fracturing is an important method to enhance permeability in oil and gas exploitation projects and weaken hard roofs of coal seams to reduce dynamic disasters, for example, rock burst. It is necessary to fully understand the mechanism of the initiation, propagation, and coalescence of hydraulic fracture network (HFN caused by fluid flow in rock formations. In this study, a coupled hydro-mechanical model was built based on synthetic rock mass (SRM method to investigate the effects of natural fracture (NF density on HFN propagation. Firstly, the geometrical structures of NF obtained from borehole images at the field scale were applied to the model. Secondly, the micro-parameters of the proposed model were validated against the interaction between NF and hydraulic fracture (HF in physical experiments. Finally, a series of numerical simulations were performed to study the mechanism of HFN propagation. In addition, confining pressure ratio (CPR and injection rate were also taken into consideration. The results suggested that the increase of NF density drives the growth of stimulated reservoir volume (SRV, concentration area of injection pressure (CAIP, and the number of cracks caused by NF. The number of tensile cracks caused by rock matrix decrease gradually with the increase of NF density, and the number of shear cracks caused by rock matrix are almost immune to the change of NF density. The propagation orientation of HFN and the breakdown pressure in rock formations are mainly controlled by CPR. Different injection rates would result in a relatively big difference in the gradient of injection pressure, but this difference would be gradually narrowed with the increase of NF density. Natural fracture density is the key factor that influences the percentages of different crack types in HFN, regardless of the value of CPR and injection rate. The proposed model may help predict HFN propagation and optimize fracturing treatment designs in
Emanuele Rizzo, Roberto; Healy, David; De Siena, Luca
2016-04-01
The success of any predictive model is largely dependent on the accuracy with which its parameters are known. When characterising fracture networks in fractured rock, one of the main issues is accurately scaling the parameters governing the distribution of fracture attributes. Optimal characterisation and analysis of fracture attributes (lengths, apertures, orientations and densities) is fundamental to the estimation of permeability and fluid flow, which are of primary importance in a number of contexts including: hydrocarbon production from fractured reservoirs; geothermal energy extraction; and deeper Earth systems, such as earthquakes and ocean floor hydrothermal venting. Our work links outcrop fracture data to modelled fracture networks in order to numerically predict bulk permeability. We collected outcrop data from a highly fractured upper Miocene biosiliceous mudstone formation, cropping out along the coastline north of Santa Cruz (California, USA). Using outcrop fracture networks as analogues for subsurface fracture systems has several advantages, because key fracture attributes such as spatial arrangements and lengths can be effectively measured only on outcrops [1]. However, a limitation when dealing with outcrop data is the relative sparseness of natural data due to the intrinsic finite size of the outcrops. We make use of a statistical approach for the overall workflow, starting from data collection with the Circular Windows Method [2]. Then we analyse the data statistically using Maximum Likelihood Estimators, which provide greater accuracy compared to the more commonly used Least Squares linear regression when investigating distribution of fracture attributes. Finally, we estimate the bulk permeability of the fractured rock mass using Oda's tensorial approach [3]. The higher quality of this statistical analysis is fundamental: better statistics of the fracture attributes means more accurate permeability estimation, since the fracture attributes feed
Factors Controlling DNAPL Migration in a Fracture Network: Experiments and Simulations
Ji, S.; Yeo, I.; Lee, K.
2002-12-01
Groundwater contamination by dense nonaqueous phase liquids (DNAPLs) has received considerable attention in recent years, and the attention on characterizing and quantifying the migration of DNAPL in geological formations has been given to the migration of DNAPL in porous media, not much in fractured rock. The spilled DNAPL that is heavier than water migrates downward to fractured bedrocks under the influence of gravity and is a long-term contaminant source. Although the progress has been accomplished on the development of algorithms for the numerical solution of the macroscopic models of contaminant transport in rock fractures, a lack of fundamental understanding exists concerning the interactive effects of the structural characteristics of fractures and fluid rheology on the patterns of DNAPL migration in a fracture network. In particular, little experimental work has been done on DNAPL migration in a fracture network. The two-dimensional fracture network was built up. Water was applied to both sides of a fracture network to have intended hydraulic head, and TCE was injected into one of vertical fractures. TCE migration process was recorded with digital camcorder. The dynamic macro-modified invasion percolation (DMMIP) model is suggested by integrating groundwater flow factor with MMIP that reflects the capillary effect, gravity-destabilization condition and viscous force of DNAPL. The information gained from experiments was analyzed and used for testing the DMMIP model to characterize the DNAPL migration pathway in a fracture network. DMMIP simulations and laboratory experiments show a good agreement. The results of DMMIP simulations and laboratory experiments show that in addition to gravity force, water viscous force considerably affects migration of DNAPL in rock fractures. This study will provide a step-stone for further developing reliable numerical simulators of the DNAPL migration in a fracture network that are required for the implementation of rational
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.
Bisdom, K.; Bertotti, G.; Gauthier, B.D.M.; Hardebol, N.J.
2013-01-01
Fluid flow in carbonate reservoirs is largely controlled by multiscale fracture networks. Significant variations of fracture network porosity and permeability are caused by the 3D heterogeneity of the fracture network characteristics, such as intensity, orientation and size. Characterizing fracture
Energy Technology Data Exchange (ETDEWEB)
Hoch, A
1998-05-01
Groundwater flow in many low permeability rocks is believed to occur within discrete fractures. Radionuclides in solution can diffuse away from the fractures into immobile water in the rock matrix. This process (rock-matrix diffusion) is important in determining the performance of a repository situated in fractured rock because it retards the transport of radionuclides that might otherwise return more rapidly towards the biosphere. NAPSAC is a computer program used to model groundwater flow and radionuclide transport in fractured rock. This report describes the implementation of a rock-matrix diffusion model in NAPSAC. (author)
Hooker, J. N.; Eichhubl, P.; Xu, G.; Ahn, H.; Fall, A.; Hargrove, P.; Laubach, S.; Ukar, E.
2011-12-01
The Cambrian Eriboll Formation quartzarenites contain abundant fractures with varying degrees of quartz cement infill. Fractures exist that are entirely sealed; are locally sealed by bridging cements but preserve pore space among bridges; are mostly open but lined with veneers of cement; or are devoid of cement. Fracture propagation in the Eriboll Formation is highly sensitive to the presence of pre-existing fractures. Fracture reactivation occurs in opening mode as individual fractures repeatedly open and are filled or bridged by syn-kinematic cements. As well, reactivation occurs in shear as opening of one fracture orientation coincides with shear displacement along pre-existing fractures of different orientations. The tendency for pre-existing fractures to slip varies in part by the extent of cement infill, yet we observe shear and opening-mode reactivation even among sealed fractures. Paleotemperature analysis of fluid inclusions within fracture cements suggests some fractures now in outcrop formed deep in the subsurface. Fractures within the Eriboll Formation may therefore affect later fracture propagation throughout geologic time. With progressive strain, fault zones develop within fracture networks by a sequence of opening-mode fracture formation, fracture reactivation and linkage, fragmentation, cataclasis, and the formation of slip surfaces. Cataclasite within fault zones is commonly more thoroughly cemented than fractures in the damage zone or outside the fault zone. This variance of cement abundance is likely the result of (1) continued exposure of freshly broken quartz surfaces within cataclasite, promoting quartz precipitation, and (2) possibly more interconnected pathways for mass transfer within the fault zone. Enhanced cementation of cataclasite results in strengthening or diagenetic strain hardening of the evolving fault zone. Further slip is accommodated by shear localization along discrete slip surfaces. With further linkage of fault segments
Review: Mathematical expressions for estimating equivalent permeability of rock fracture networks
Liu, Richeng; Li, Bo; Jiang, Yujing; Huang, Na
2016-06-01
Fracture networks play a more significant role in conducting fluid flow and solute transport in fractured rock masses, comparing with that of the rock matrix. Accurate estimation of the permeability of fracture networks would help researchers and engineers better assess the performance of projects associated with fluid flow in fractured rock masses. This study provides a review of previous works that have focused on the estimation of equivalent permeability of two-dimensional (2-D) discrete fracture networks (DFNs) considering the influences of geometric properties of fractured rock masses. Mathematical expressions for the effects of nine important parameters that significantly impact on the equivalent permeability of DFNs are summarized, including (1) fracture-length distribution, (2) aperture distribution, (3) fracture surface roughness, (4) fracture dead-end, (5) number of intersections, (6) hydraulic gradient, (7) boundary stress, (8) anisotropy, and (9) scale. Recent developments of 3-D fracture networks are briefly reviewed to underline the importance of utilizing 3-D models in future research.
Review: Mathematical expressions for estimating equivalent permeability of rock fracture networks
Liu, Richeng; Li, Bo; Jiang, Yujing; Huang, Na
2016-11-01
Fracture networks play a more significant role in conducting fluid flow and solute transport in fractured rock masses, comparing with that of the rock matrix. Accurate estimation of the permeability of fracture networks would help researchers and engineers better assess the performance of projects associated with fluid flow in fractured rock masses. This study provides a review of previous works that have focused on the estimation of equivalent permeability of two-dimensional (2-D) discrete fracture networks (DFNs) considering the influences of geometric properties of fractured rock masses. Mathematical expressions for the effects of nine important parameters that significantly impact on the equivalent permeability of DFNs are summarized, including (1) fracture-length distribution, (2) aperture distribution, (3) fracture surface roughness, (4) fracture dead-end, (5) number of intersections, (6) hydraulic gradient, (7) boundary stress, (8) anisotropy, and (9) scale. Recent developments of 3-D fracture networks are briefly reviewed to underline the importance of utilizing 3-D models in future research.
Institute of Scientific and Technical Information of China (English)
LIU Hua-mei; WANG Ming-yu; SONG Xian-feng
2011-01-01
Determinations of fracture network connections would help the investigators remove those “meaningless” no-flow-passing fractures,providing an updated and more effective fracture network that could considerably improve the computation efficiency in the pertinent numerical simulations of fluid flow and solute transport.The effective algorithms with higher computational efficiency are needed to accomplish this task in large-scale fractured rock masses.A new approach using R tree indexing was proposed for determining fracture connection in 3D stochastically distributed fracture network.By comparing with the traditional exhaustion algorithm,it was observed that from the simulation results,this approach was much more effective; and the more the fractures were investigated,the more obvious the advantages of the approach were.Furthermore,it was indicated that the runtime used for creating the R tree indexing has a major part in the total of the runtime used for calculating Minimum Bounding Rectangles(MBRs),creating the R tree indexing,precisely finding out fracture intersections,and identifying flow paths,which are four important steps to determine fracture connections.This proposed approach for the determination of fracture connections in three-dimensional fractured rocks are expected to provide efficient preprocessing and critical database for practically accomplishing numerical computation of fluid flow and solute transport in large-scale fractured rock masses.
Unified pipe network method for simulation of water flow in fractured porous rock
Ren, Feng; Ma, Guowei; Wang, Yang; Li, Tuo; Zhu, Hehua
2017-04-01
Rock masses are often conceptualized as dual-permeability media containing fractures or fracture networks with high permeability and porous matrix that is less permeable. In order to overcome the difficulties in simulating fluid flow in a highly discontinuous dual-permeability medium, an effective unified pipe network method is developed, which discretizes the dual-permeability rock mass into a virtual pipe network system. It includes fracture pipe networks and matrix pipe networks. They are constructed separately based on equivalent flow models in a representative area or volume by taking the advantage of the orthogonality of the mesh partition. Numerical examples of fluid flow in 2-D and 3-D domain including porous media and fractured porous media are presented to demonstrate the accuracy, robustness, and effectiveness of the proposed unified pipe network method. Results show that the developed method has good performance even with highly distorted mesh. Water recharge into the fractured rock mass with complex fracture network is studied. It has been found in this case that the effect of aperture change on the water recharge rate is more significant in the early stage compared to the fracture density change.
Institute of Scientific and Technical Information of China (English)
刘雄; 田昌炳; 万英杰; 王方; 徐秋枫
2015-01-01
针对裂缝性致密油藏，基于拉普拉斯变换及Stehfest数值反演，建立了一种可用于直井体积改造产能评价的半解析两区复合模型，模型内区包含有限条无限导流水力裂缝，外区是经典的Warren-Root双重介质系统。并分析了导压系数比α、裂缝传导率比β、储容比ω、窜流系数λ以及改造半径reD等参数敏感性，绘制了产量递减图版。结果表明：从产量递减曲线，可以看出体积改造直井产能遵循“L”形递减规律；导压系数比越大，初期产量越高；裂缝传导率比对整个生产周期的产能都有影响，裂缝传导率比越大，单井产量越高，同时还会伴有明显的复合边界流特征；储容比和窜流系数分别影响双重介质基质－裂缝系统窜流发生的程度和时间；内区人工主裂缝条数越多或改造渗透率越大，复合边界流越明显，产能也越高，这说明改造程度与改造体积对产能的增加都很重要，应注意两者的合理优化。矿场实例验证了该模型在裂缝性封闭边界油藏直井多次压裂改造以及裂缝性致密油藏直井体积改造方面的适用性和实用性。%In this study,based on Laplace transformation and Stehfest numerical algorithm,a vertical well frac-ture network reconstruction semi-analytical deliverability evaluation model which can be used for fractured tight oil reservoirs was established.The proposed model is a composite system with two concentric regions.The inner region contains finite number of hydraulic fractures and the flow in each fracture is assumed linear.The outer region is modeled with the classical Warren-Root model and radial flow takes place in this region.The influ-ences of related parameters,such as diffusivity coefficient ratio,fracture conductivity ratio,storativity ratio, cross-flow factor and so forth,on the seepage flow were analyzed by using the established model.The results show that the
Follin, S.; Stigsson, M.; Levén, J.
2006-12-01
Difference flow logging is a relatively new hydraulic test method. It offers a superior geometrical resolution compared to the classic double-packer injection test method. Other significant features of the difference flow logging method are the long duration of the test period and the line source flow regime. These three features are vital for the characterization and the modeling of the conductive fracture frequency in crystalline rocks. Further, combining difference flow logging with core mapping and in situ borehole wall image logging (BIPS) allows for an enhanced geological cross correlation and structural interpretation. The data and analyses presented here come from the ongoing site investigations for a high-level nuclear waste repository in Forsmark managed by the Swedish Nuclear Fuel and Waste Management Co. First, we demonstrate the statistical properties of the fracture transmissivities acquired by difference flow logging for a number of one-kilometer-long cored boreholes. Secondly, we make a hydraulic comparison between these data and the transmissivities acquired by double-packer injection tests. Thirdly, we present a method for investigating the geometrical connectivity of open fractures in fracture network simulations and how this connectivity can be cross correlated to the fracture transmissivity distribution acquired by difference flow logging. Finally, we discuss the geometrical properties of flowing fractures as acquired by BIPS data and the correlation to the current stress situation in Forsmark. The geometrical anisotropy observed in the transmissivity data suggests that the current stress situation is very important for the flow field in Forsmark. This puts constraints on the collection and use of geological/structural data for hydrogeological discrete fracture network modeling.
Partially decoupled modeling of hydraulic fracturing processes
Energy Technology Data Exchange (ETDEWEB)
Settari, A.; Puchyr, P.J.; Bachman, R.C. (Simtech Consulting Services, Calgary (CA))
1990-02-01
A new method of partial decoupling of the problem of modeling a hydraulic fracture in a reservoir is described. According to the authors this approach has significant advantages over previous methods with fully coupled or completely uncoupled models. Better accuracy can be achieved in modeling the fracture propagation, and the new system is very efficient and versatile. Virtually any reservoir model can be used for predicting postfracture productivity. Examples of single- and multiphase applications for modeling fractured wells are discussed.
Bistacchi, A.; Mittempergher, S.; Di Toro, G.; Smith, S. A. F.; Garofalo, P. S.
2016-12-01
The Gole Larghe Fault Zone (GLFZ) was exhumed from 8 km depth, where it was characterized by seismic activity (pseudotachylytes) and hydrous fluid flow (alteration halos and precipitation of hydrothermal minerals in veins and cataclasites). Thanks to glacier-polished outcrops exposing the 400 m-thick fault zone over a continuous area > 1.5 km2, the fault zone architecture has been quantitatively described with an unprecedented detail, providing a rich dataset to generate 3D Discrete Fracture Network (DFN) models and simulate the fault zone hydraulic properties. The fault and fracture network has been characterized combining > 2 km of scanlines and semi-automatic mapping of faults and fractures on several photogrammetric 3D Digital Outcrop Models (3D DOMs). This allowed obtaining robust probability density functions for parameters of fault and fracture sets: orientation, fracture intensity and density, spacing, persistency, length, thickness/aperture, termination. The spatial distribution of fractures (random, clustered, anticlustered…) has been characterized with geostatistics. Evidences of fluid/rock interaction (alteration halos, hydrothermal veins, etc.) have been mapped on the same outcrops, revealing sectors of the fault zone strongly impacted, vs. completely unaffected, by fluid/rock interaction, separated by convolute infiltration fronts. Field and microstructural evidence revealed that higher permeability was obtained in the syn- to early post-seismic period, when fractures were (re)opened by off-fault deformation. We have developed a parametric hydraulic model of the GLFZ and calibrated it, varying the fraction of faults/fractures that were open in the post-seismic, with the goal of obtaining realistic fluid flow and permeability values, and a flow pattern consistent with the observed alteration/mineralization pattern. The fraction of open fractures is very close to the percolation threshold of the DFN, and the permeability tensor is strongly anisotropic
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.
Yushi, Zou; Xinfang, Ma; Shicheng, Zhang; Tong, Zhou; Han, Li
2016-09-01
Shale formations are often characterized by low matrix permeability and contain numerous bedding planes (BPs) and natural fractures (NFs). Massive hydraulic fracturing is an important technology for the economic development of shale formations in which a large-scale hydraulic fracture network (HFN) is generated for hydrocarbon flow. In this study, HFN propagation is numerically investigated in a horizontally layered and naturally fractured shale formation by using a newly developed complex fracturing model based on the 3D discrete element method. In this model, a succession of continuous horizontal BP interfaces and vertical NFs is explicitly represented and a shale matrix block is considered impermeable, transversely isotropic, and linearly elastic. A series of simulations is performed to illustrate the influence of anisotropy, associated with the presence of BPs, on the HFN propagation geometry in shale formations. Modeling results reveal that the presence of BP interfaces increases the injection pressure during fracturing. HF deflection into a BP interface tends to occur under high strength and elastic anisotropy as well as in low vertical stress anisotropy conditions, which generate a T-shaped or horizontal fracture. Opened BP interfaces may limit the growth of the fracture upward and downward, resulting in a very low stimulated thickness. However, the opened BP interfaces favor fracture complexity because of the improved connection between HFs and NFs horizontally under moderate vertical stress anisotropy. This study may help predict the HF growth geometry and optimize the fracturing treatment designs in shale formations with complex depositional heterogeneity.
Modeling Electric Current Flow in 3D Fractured Media
Demirel, S.; Roubinet, D.; Irving, J.
2014-12-01
The study of fractured rocks is extremely important in a variety of research fields and applications such as hydrogeology, hydrocarbon extraction and long-term storage of toxic waste. As fractures are highly conductive structures in comparison to the surrounding rock, their presence can be either an advantage or a drawback. For hydrocarbon extraction, fractures allow for quick and easy access to the resource whereas for toxic waste storage their presence increases the risk of leakage and migration of pollutants. In both cases, the identification of fracture network characteristics is an essential step. Recently, we have developed an approach for modeling electric current flow in 2D fractured media. This approach is based on a discrete-dual-porosity model where fractures are represented explicitly, the matrix is coarsely discretized into blocks, and current flow exchange between the fractures and matrix is analytically evaluated at the fracture-scale and integrated at the block-scale [1]. Although this approach has shown much promise and has proven its efficiency for 2D simulations, its extension to 3D remains to be addressed. To this end, we assume that fractures can be represented as two-dimensional finite planes embedded in the surrounding matrix, and we express analytically the distribution of electric potential at the fracture scale. This fracture-scale expression takes into account the electric-current-flow exchange with the surrounding matrix and flow conservation is enforced at the fracture intersections. The fracture-matrix exchange is then integrated at the matrix-block scale where the electric current flow conservation at the block boundaries is formulated with a modified finite volume method. With the objective of providing a low-computational-cost modeling approach adapted to 3D simulations in fractured media, our model is (i) validated and compared to existing modeling approaches and, (ii) used to evaluate the impact of the presence of fractures on
Carbonate fracture stratigraphy: An integrated outcrop and 2D discrete element modelling study
Spence, Guy; Finch, Emma
2013-04-01
Constraining fracture stratigraphy is important as natural fractures control primary fluid flow in low matrix permeability naturally fractured carbonate hydrocarbon reservoirs. Away from the influence of folds and faults, stratigraphic controls are known to be the major control on fracture networks. The fracture stratigraphy of carbonate nodular-chert rhythmite successions are investigated using a Discrete Element Modelling (DEM) technique and validated against observations from outcrops. Comparisons are made to the naturally fractured carbonates of the Eocene Thebes Formation exposed in the west central Sinai of Egypt, which form reservoir rocks in the nearby East Ras Budran Field. DEM allows mechanical stratigraphy to be defined as the starting conditions from which forward numerical modelling can generate fracture stratigraphy. DEM can incorporate both stratigraphic and lateral heterogeneity, and enable mechanical and fracture stratigraphy to be characterised separately. Stratally bound stratified chert nodules below bedding surfaces generate closely spaced lateral heterogeneity in physical properties at stratigraphic mechanical interfaces. This generates extra complexity in natural fracture networks in addition to that caused by bed thickness and lithological physical properties. A series of representative geologically appropriate synthetic mechanical stratigraphic models were tested. Fracture networks generated in 15 DEM experiments designed to isolate and constrain the effects of nodular chert rhythmites on carbonate fracture stratigraphy are presented. The discrete element media used to model the elastic strengths of rocks contain 72,866 individual elements. Mechanical stratigraphies and the fracture networks generated are placed in a sequence stratigraphic framework. Nodular chert rhythmite successions are shown to be a distinct type of naturally fractured carbonate reservoir. Qualitative stratigraphic rules for predicting the distribution, lengths, spacing
Hydraulic fracturing model based on the discrete fracture model and the generalized J integral
Liu, Z. Q.; Liu, Z. F.; Wang, X. H.; Zeng, B.
2016-08-01
The hydraulic fracturing technique is an effective stimulation for low permeability reservoirs. In fracturing models, one key point is to accurately calculate the flux across the fracture surface and the stress intensity factor. To achieve high precision, the discrete fracture model is recommended to calculate the flux. Using the generalized J integral, the present work obtains an accurate simulation of the stress intensity factor. Based on the above factors, an alternative hydraulic fracturing model is presented. Examples are included to demonstrate the reliability of the proposed model and its ability to model the fracture propagation. Subsequently, the model is used to describe the relationship between the geometry of the fracture and the fracturing equipment parameters. The numerical results indicate that the working pressure and the pump power will significantly influence the fracturing process.
Physical model studies of dispersion in fracture systems
Energy Technology Data Exchange (ETDEWEB)
Hull, L.C.
1985-04-01
The purposes of the laboratory-scale fracture network experiments are to study mechanisms controlling solute transport under conditions of known fracture parameters, to evaluate injection-backflow test procedures under conditions of known reservoir parameters, and to acquire data for validation of numerical models. Validation of computer codes against laboratory data collected under controlled conditions provides reassurance that the codes deal with important processes in a realistic manner. Preliminary simulations of the dual-permeability physical model have been made using the FRACSL reservoir code. These simulations permit locating electrodes and piezometers in the most advantageous positions to record tracer migration and pressure response. Much of the physical modeling effort this year was oriented towards validating the particle tracking algorithm used in FRACSL, and developing a better theoretical understanding of transport processes in fractures. Experiments were conducted in single fractures and single fracture junctions, and data on tracer migration collected. The Prickett, Naymik, and Lonnquist Random Walk aquifer simulation program has been modfied to simulate flow in single fractures. The particle tracking algorithm was also used to simulate infinite parallel plates under conditions where analytical solutions to the transport equation could be derived. The first case is for zero diffusion in the fracture, and transport based on a parabolic velocity profile. The second case is for diffusion homogenizing the tracer solution across the fracture. The particle tracking algorithm matched both analytical solutions quite well, with the same grid for both simulations. 48 refs., 41 figs., 2 tabs.
Modeling fracture porosity evolution in dolostone
Gale, Julia F. W.; Lander, Robert H.; Reed, Robert M.; Laubach, Stephen E.
2010-09-01
Opening-mode fractures in dolostones buried to depths of ˜1-5 km contain synkinematic dolomite cement, the amount and internal structure of which has a systematic relationship to fracture size. Narrow fractures (cement or cement with a crack-seal texture that indicates multiple incremental openings. Wider fractures can preserve considerable effective porosity, but anomalously thick dolomite cement bridges are commonly present in fractures that are otherwise lined with a thin veneer of cement. Dolomite bridges resemble quartz bridges that are common in fractured sandstones. We developed a geometric crystal growth model for synkinematic dolomite fracture fill in fractured dolostones, where periodic incremental fracture-opening events are introduced with concurrent cement growth. We assumed constant temperature and supersaturation with respect to dolomite. A key assumption in the model is that rapid dolomite accumulation within bridges is governed by high cement-growth rates on repeatedly broken grain surfaces during the process of crack seal. Slower cement-growth rates occur on euhedral crystals. This assumption is made on the basis of a comparison with quartz cement growth in fractured sandstones. Simulations with different fracture-opening rates mimic bridge and lining cement morphologies, including characteristic rhombic shapes of dolomite bridges.
Directory of Open Access Journals (Sweden)
Xiaobing Chen
2014-01-01
Full Text Available In this study, physical experiments and numerical simulations are combined to provide a detailed understanding of flow dynamics in fracture network. Hydraulic parameters such as pressure head, velocity field, Reynolds number on certain monitoring cross points, and total flux rate are examined under various clogging conditions. Applying the COMSOL Multiphysics code to solve the Navier-Stokes equation instead of Reynolds equation and using the measured data to validate the model, the fluid flow in the horizontal 2D cross-sections of the fracture network was simulated. Results show that local clogging leads to a significant reshaping of the flow velocity field and a reduction of the transport capacity of the entire system. The flow rate distribution is highly influenced by the fractures connected to the dominant flow channels, although local disturbances in velocity field are unlikely to spread over the whole network. Also, modeling results indicate that water flow in a fracture network, compared with that in a single fracture, is likely to transit into turbulence earlier under the same hydraulic gradient due to the influence of fracture intersections.
Development of a new software for analyzing 3-D fracture network
Um, Jeong-Gi; Noh, Young-Hwan; Choi, Yosoon
2014-05-01
A new software is presented to analyze fracture network in 3-D. Recently, we completed the software package based on information given in EGU2013. The software consists of several modules that play roles in management of borehole data, stochastic modelling of fracture network, construction of analysis domain, visualization of fracture geometry in 3-D, calculation of equivalent pipes and production of cross-section diagrams. Intel Parallel Studio XE 2013, Visual Studio.NET 2010 and the open source VTK library were utilized as development tools to efficiently implement the modules and the graphical user interface of the software. A case study was performed to analyze 3-D fracture network system at the Upper Devonian Grosmont Formation in Alberta, Canada. The results have suggested that the developed software is effective in modelling and visualizing 3-D fracture network system, and can provide useful information to tackle the geomechanical problems related to strength, deformability and hydraulic behaviours of the fractured rock masses. This presentation describes the concept and details of the development and implementation of the software.
Directory of Open Access Journals (Sweden)
Shanyong Liu
2016-05-01
Full Text Available Volume fracturing in shale gas forms complex fracture networks and increases stimulated reservoir volume through large-scale fracturing operation with plug-perforation technology. However, some perforation clusters are stimulated unevenly after fracturing. This study aims to solve this problem by analyzing the shortcomings of the conventional fracturing model and developing a coupled model based on the 2D fracture motion equation, energy conservation law, linear elastic mechanics, and stress superposition principle. First, a multi-fracture in-situ stress model was built by studying the induced stress produced by the fracture initiation to deduce the multi-fracture induced stress impact factor on the basis of the stress superposition principle. Then, the classical Perkins–Kern–Nordgren model was utilized with the crustal stress model. Finally, a precise fracturing design method was used to optimize perforation and fracturing parameters under the new model. Results demonstrate that the interference effect among fractures is the major factor causing the non-uniform propagation of each fracture. Compression on the main horizontal stress increases the net pressure. Therefore, both the degree of operation difficulty and the complexity of fracture geometry are improved. After applying the optimal design, the production is increased by 20%, and the cost is reduced by 15%.
Application of Discrete Fracture Modeling and Upscaling Techniques to Complex Fractured Reservoirs
Karimi-Fard, M.; Lapene, A.; Pauget, L.
2012-12-01
During the last decade, an important effort has been made to improve data acquisition (seismic and borehole imaging) and workflow for reservoir characterization which has greatly benefited the description of fractured reservoirs. However, the geological models resulting from the interpretations need to be validated or calibrated against dynamic data. Flow modeling in fractured reservoirs remains a challenge due to the difficulty of representing mass transfers at different heterogeneity scales. The majority of the existing approaches are based on dual continuum representation where the fracture network and the matrix are represented separately and their interactions are modeled using transfer functions. These models are usually based on idealized representation of the fracture distribution which makes the integration of real data difficult. In recent years, due to increases in computer power, discrete fracture modeling techniques (DFM) are becoming popular. In these techniques the fractures are represented explicitly allowing the direct use of data. In this work we consider the DFM technique developed by Karimi-Fard et al. [1] which is based on an unstructured finite-volume discretization. The mass flux between two adjacent control-volumes is evaluated using an optimized two-point flux approximation. The result of the discretization is a list of control-volumes with the associated pore-volumes and positions, and a list of connections with the associated transmissibilities. Fracture intersections are simplified using a connectivity transformation which contributes considerably to the efficiency of the methodology. In addition, the method is designed for general purpose simulators and any connectivity based simulator can be used for flow simulations. The DFM technique is either used standalone or as part of an upscaling technique. The upscaling techniques are required for large reservoirs where the explicit representation of all fractures and faults is not possible
A new equi-dimensional fracture model using polyhedral cells for microseismic data sets
Al-Hinai, Omar
2017-04-09
We present a method for modeling flow in porous media in the presence of complex fracture networks. The approach utilizes the Mimetic Finite Difference (MFD) method. We employ a novel equi-dimensional approach for meshing fractures. By using polyhedral cells we avoid the common challenge in equi-dimensional fracture modeling of creating small cells at the intersection point. We also demonstrate how polyhedra can mesh complex fractures without introducing a large number of cells. We use polyhedra and the MFD method a second time for embedding fracture boundaries in the matrix domain using a “cut-cell” paradigm. The embedding approach has the advantage of being simple and localizes irregular cells to the area around the fractures. It also circumvents the need for conventional mesh generation, which can be challenging when applied to complex fracture geometries. We present numerical results confirming the validity of our approach for complex fracture networks and for different flow models. In our first example, we compare our method to the popular dual-porosity technique. Our second example compares our method with directly meshed fractures (single-porosity) for two-phase flow. The third example demonstrates two-phase flow for the case of intersecting ellipsoid fractures in three-dimensions, which are typical in microseismic analysis of fractures. Finally, we demonstrate our method on a two-dimensional fracture network produced from microseismic field data.
Pressure transient modeling of a fractured geothermal reservior
Energy Technology Data Exchange (ETDEWEB)
Robinson, B.A.
1990-01-01
A fracture network model has been developed to simulate transient fluid flow behavior in a fractured rock mass. Included is a pressure-dependent aperture submodel to simulate behavior often seen in fractured systems. The model is used to simulate data from the Fenton Hill Hot Dry Rock (HDR) geothermal reservoir. Both low-pressure/low-flow-rate and high-pressure/high-flow-rate transient data are adequately simulated. The model parameters obtained suggest ways in which the model can be refined to achieve even more realistic fits to the data. The model is then used to demonstrate more efficient operating modes than the two-well circulating mode usually proposed for HDR reservoirs. 11 refs., 9 figs., 1 tab.
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.
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
Performance of an artificial neural network for vertical root fracture detection: an ex vivo study.
Kositbowornchai, Suwadee; Plermkamon, Supattra; Tangkosol, Tawan
2013-04-01
To develop an artificial neural network for vertical root fracture detection. A probabilistic neural network design was used to clarify whether a tooth root was sound or had a vertical root fracture. Two hundred images (50 sound and 150 vertical root fractures) derived from digital radiography--used to train and test the artificial neural network--were divided into three groups according to the number of training and test data sets: 80/120,105/95 and 130/70, respectively. Either training or tested data were evaluated using grey-scale data per line passing through the root. These data were normalized to reduce the grey-scale variance and fed as input data of the neural network. The variance of function in recognition data was calculated between 0 and 1 to select the best performance of neural network. The performance of the neural network was evaluated using a diagnostic test. After testing data under several variances of function, we found the highest sensitivity (98%), specificity (90.5%) and accuracy (95.7%) occurred in Group three, for which the variance of function in recognition data was between 0.025 and 0.005. The neural network designed in this study has sufficient sensitivity, specificity and accuracy to be a model for vertical root fracture detection. © 2012 John Wiley & Sons A/S.
Hydraulic fracture model comparison study: Complete results
Energy Technology Data Exchange (ETDEWEB)
Warpinski, N.R. [Sandia National Labs., Albuquerque, NM (United States); Abou-Sayed, I.S. [Mobil Exploration and Production Services (United States); Moschovidis, Z. [Amoco Production Co. (US); Parker, C. [CONOCO (US)
1993-02-01
Large quantities of natural gas exist in low permeability reservoirs throughout the US. Characteristics of these reservoirs, however, make production difficult and often economic and stimulation is required. Because of the diversity of application, hydraulic fracture design models must be able to account for widely varying rock properties, reservoir properties, in situ stresses, fracturing fluids, and proppant loads. As a result, fracture simulation has emerged as a highly complex endeavor that must be able to describe many different physical processes. The objective of this study was to develop a comparative study of hydraulic-fracture simulators in order to provide stimulation engineers with the necessary information to make rational decisions on the type of models most suited for their needs. This report compares the fracture modeling results of twelve different simulators, some of them run in different modes for eight separate design cases. Comparisons of length, width, height, net pressure, maximum width at the wellbore, average width at the wellbore, and average width in the fracture have been made, both for the final geometry and as a function of time. For the models in this study, differences in fracture length, height and width are often greater than a factor of two. In addition, several comparisons of the same model with different options show a large variability in model output depending upon the options chosen. Two comparisons were made of the same model run by different companies; in both cases the agreement was good. 41 refs., 54 figs., 83 tabs.
Fracture model of radiation blistering
Energy Technology Data Exchange (ETDEWEB)
Kamada, K.; Higashida, Y.
1979-06-01
The formation process of blisters is interpreted by a fracture model on the basis of the stress fields around a lenticular bubble calculated in a previous paper. This model implicitly presumes a microcrack nucleated at a depth near the projected range of the ions. Two factors are separated theoretically to explain the blister formation: One is a geometrical factor which depends only on the ratio of size to depth, from a free surface, and the other factor is proportional to the square of the ratio between the internal gas pressure of the bubble to plastic yield stress of the target materials, depending entirely on the physical and chemical properties of the materials and gas atoms. The relation between the blister diameter and the cover thickness must be basically linear as expected from the first factor, but is modulated by the second factor, giving a slight departure from linearity as observed by experiment. The ratio of the gas pressure to the yield stress must be 0.02--0.2 in magnitude and depends on the ion energy and the target materials. This value leads to an estimation that the amount of gas atoms contained in the blister is about 10% of the injected ions. Griffith's criterion for the crack propagation in the subsurface layer with taking into account of ductility of the materials near the crack tip was derived, and showed that the estimated internal pressure of the blister is far smaller than the necessary pressure to satisfy the criterion. The objections against the gas-pressure model were criticized on the basis of the present model.
A descriptive study of fracture networks in rocks using complex network metrics
Santiago, Elizabeth; Velasco-Hernández, Jorge X.; Romero-Salcedo, Manuel
2016-03-01
In this paper we describe the static topological fracture structure of five rock samples from three regions in Eastern Mexico by the application of centrality and communicability measures used in the area of complex networks. The information obtained from fracture images is used to characterize the fracture networks. The analysis is divided into two groups of characteristics. The first provides a general summary of the fracture network through the description of the number of nodes, edges, diameter, radius, lengths and clustering coefficients. A second group of features centers on the description of communicability in the network by means of three indexes recently proposed. In addition, we apply centrality measures (betweenness, closeness, eigenvector and eccentricity) for quantifying the importance of nodes in the entire network. Finally, we identify a topology for fracture networks using a classification based on the degree of communicability. The most important results obtained in this work are focused in the topological characteristic patterns found in fracture networks applying the approach of complex networks that in general provide local and global parameters of connectivity and communicability.
Multi-scale approach to invasion percolation of rock fracture networks
Ebrahimi, Ali N; Araújo, Nuno A M; Herrmann, Hans J
2014-01-01
A multi-scale scheme for the invasion percolation of rock fracture networks with heterogeneous fracture aperture fields is proposed. Inside fractures, fluid transport is calculated on the finest scale and found to be localized in channels as a consequence of the aperture field. The channel network is characterized and reduced to a vectorized artificial channel network (ACN). Different realizations of ACNs are used to systematically calculate efficient apertures for fluid transport inside differently sized fractures as well as fracture intersection and entry properties. Typical situations in fracture networks are parameterized by fracture inclination, flow path length along the fracture and intersection lengths in the entrance and outlet zones of fractures. Using these scaling relations obtained from the finer scales, we simulate the invasion process of immiscible fluids into saturated discrete fracture networks, which were studied in previous works.
Ezzedine, S. M.
2009-12-01
Fractures and fracture networks are the principal pathways for transport of water and contaminants in groundwater systems, enhanced geothermal system fluids, migration of oil and gas, carbon dioxide leakage from carbon sequestration sites, and of radioactive and toxic industrial wastes from underground storage repositories. A major issue to overcome when characterizing a fractured reservoir is that of data limitation due to accessibility and affordability. Moreover, the ability to map discontinuities in the rock with available geological and geophysical tools tends to decrease particularly as the scale of the discontinuity goes down. Geological characterization data include measurements of fracture density, orientation, extent, and aperture, and are based on analysis of outcrops, borehole optical and acoustic televiewer logs, aerial photographs, and core samples, among other techniques. All of these measurements are taken at the field scale through a very sparse limited number of deep boreholes. These types of data are often reduced to probability distribution functions for predictive modeling and simulation in a stochastic framework such as a stochastic discrete fracture network. Stochastic discrete fracture network models enable, through Monte Carlo realizations and simulations, probabilistic assessment of flow and transport phenomena that are not adequately captured using continuum models. Despite the fundamental uncertainties inherited within the probabilistic reduction of the sparse data collected, very little work has been conducted on quantifying uncertainty on the reduced probabilistic distribution functions. In the current study, using nested Monte Carlo simulations, we present the impact of parameter uncertainties of the distribution functions of fracture density, orientation, aperture and size on the flow and transport using topological measures such as fracture connectivity, physical characteristics such as effective hydraulic conductivity tensors, and
New software for 3D fracture network analysis and visualization
Song, J.; Noh, Y.; Choi, Y.; Um, J.; Hwang, S.
2013-12-01
This study presents new software to perform analysis and visualization of the fracture network system in 3D. The developed software modules for the analysis and visualization, such as BOUNDARY, DISK3D, FNTWK3D, CSECT and BDM, have been developed using Microsoft Visual Basic.NET and Visualization TookKit (VTK) open-source library. Two case studies revealed that each module plays a role in construction of analysis domain, visualization of fracture geometry in 3D, calculation of equivalent pipes, production of cross-section map and management of borehole data, respectively. The developed software for analysis and visualization of the 3D fractured rock mass can be used to tackle the geomechanical problems related to strength, deformability and hydraulic behaviors of the fractured rock masses.
Ezzedine, S. M.
2010-12-01
Fractures and fracture networks are the principle pathways for migration of water, heat and mass in enhanced geothermal systems, oil and gas reservoirs, CO2 leakage from saline aquifers, and radioactive and toxic industrial wastes from underground storage repositories. A major issue to overcome when characterizing a fractured reservoir is that of data limitation due to accessibility and affordability. Moreover, the ability to map discontinuities in the rock with available geological and geophysical tools tends to decrease particularly as the scale of the discontinuity goes down. Geological characterization data include measurements of fracture density, orientation, extent, and aperture, and are based on analysis of outcrops, borehole optical and acoustic televiewer logs, aerial photographs, and core samples among others. All of these measurements are taken at the field scale through a very sparse limited number of deep boreholes. These types of data are often reduced to probability distributions function for predictive modeling and simulation in a stochastic framework such as stochastic discrete fracture network. Stochastic discrete fracture network models enable, through Monte Carlo realizations and simulations, for probabilistic assessment of flow and transport phenomena that are not adequately captured using continuum models. Despite the fundamental uncertainties inherited within the probabilistic reduction of the sparse data collected, very little work has been conducted on quantifying uncertainty on the reduced probabilistic distribution functions. In the current study, using nested Monte Carlo simulations, we present the impact of parameter uncertainties of the distribution functions that characterize discrete fracture networks on the flow, heat and mass transport. Numerical results of first, second and third moments, normalized to a base case scenario, are presented and compared to theoretical results extended from percolation theory.
Energy Technology Data Exchange (ETDEWEB)
Bossart, P. [Geotechnical Inst. Ltd., Bern (Switzerland); Hermanson, Jan [Golder Associates, Stockholm (Sweden); Mazurek, M. [Univ. of Bern (Switzerland)
2001-05-01
Fracture networks at Aespoe have been studied for several rock types exhibiting different degrees of ductile and brittle deformation, as well as on different scales. Mesoscopic fault systems have been characterised and classified in an earlier report, this report focuses mainly on fracture networks derived on smaller scales, but also includes mesoscopic and larger scales. The TRUE-1 block has been selected for detailed structural analysis on a small scale due to the high density of relevant information. In addition to the data obtained from core materials, structural maps, BIP data and the results of hydro tests were synthesised to derive a conceptual structural model. The approach used to derive this conceptual model is based on the integration of deterministic structural evidence, probabilistic information and both upscaling and downscaling of observations and concepts derived on different scales. Twelve fracture networks mapped at different sites and scales and exhibiting various styles of tectonic deformation were analysed for fractal properties and structural and hydraulic interconnectedness. It was shown that these analysed fracture networks are not self-similar. An important result is the structural and hydraulic interconnectedness of fracture networks on all scales in the Aespoe rocks, which is further corroborated by geochemical evidence. Due to the structural and hydraulic interconnectedness of fracture systems on all scales at Aespoe, contaminants from waste canisters placed in tectonically low deformation environments would be transported - after having passed through the engineered barriers -from low-permeability fractures towards higher permeability fractures and may thus eventually reach high-permeability features.
Micromechanics Modeling of Fracture in Nanocrystalline Metals
Glaessgen, E. H.; Piascik, R. S.; Raju, I. S.; Harris, C. E.
2002-01-01
Nanocrystalline metals have very high theoretical strength, but suffer from a lack of ductility and toughness. Therefore, it is critical to understand the mechanisms of deformation and fracture of these materials before their full potential can be achieved. Because classical fracture mechanics is based on the comparison of computed fracture parameters, such as stress intlmsity factors, to their empirically determined critical values, it does not adequately describe the fundamental physics of fracture required to predict the behavior of nanocrystalline metals. Thus, micromechanics-based techniques must be considered to quanti@ the physical processes of deformation and fracture within nanocrystalline metals. This paper discusses hndamental physicsbased modeling strategies that may be useful for the prediction Iof deformation, crack formation and crack growth within nanocrystalline metals.
Hip fracture in the elderly: a re-analysis of the EPIDOS study with causal Bayesian networks.
Directory of Open Access Journals (Sweden)
Pascal Caillet
Full Text Available Hip fractures commonly result in permanent disability, institutionalization or death in elderly. Existing hip-fracture predicting tools are underused in clinical practice, partly due to their lack of intuitive interpretation. By use of a graphical layer, Bayesian network models could increase the attractiveness of fracture prediction tools. Our aim was to study the potential contribution of a causal Bayesian network in this clinical setting. A logistic regression was performed as a standard control approach to check the robustness of the causal Bayesian network approach.EPIDOS is a multicenter study, conducted in an ambulatory care setting in five French cities between 1992 and 1996 and updated in 2010. The study included 7598 women aged 75 years or older, in which fractures were assessed quarterly during 4 years. A causal Bayesian network and a logistic regression were performed on EPIDOS data to describe major variables involved in hip fractures occurrences.Both models had similar association estimations and predictive performances. They detected gait speed and mineral bone density as variables the most involved in the fracture process. The causal Bayesian network showed that gait speed and bone mineral density were directly connected to fracture and seem to mediate the influence of all the other variables included in our model. The logistic regression approach detected multiple interactions involving psychotropic drug use, age and bone mineral density.Both approaches retrieved similar variables as predictors of hip fractures. However, Bayesian network highlighted the whole web of relation between the variables involved in the analysis, suggesting a possible mechanism leading to hip fracture. According to the latter results, intervention focusing concomitantly on gait speed and bone mineral density may be necessary for an optimal prevention of hip fracture occurrence in elderly people.
Tatomir, Alexandru Bogdan A. C.; Flemisch, Bernd; Class, Holger; Helmig, Rainer; Sauter, Martin
2017-04-01
Geological storage of CO2 represents one viable solution to reduce greenhouse gas emission in the atmosphere. Potential leakage of CO2 storage can occur through networks of interconnected fractures. The geometrical complexity of these networks is often very high involving fractures occurring at various scales and having hierarchical structures. Such multiphase flow systems are usually hard to solve with a discrete fracture modelling (DFM) approach. Therefore, continuum fracture models assuming average properties are usually preferred. The multiple interacting continua (MINC) model is an extension of the classic double porosity model (Warren and Root, 1963) which accounts for the non-linear behaviour of the matrix-fracture interactions. For CO2 storage applications the transient representation of the inter-porosity two phase flow plays an important role. This study tests the accuracy and computational efficiency of the MINC method complemented with the multiple sub-region (MSR) upscaling procedure versus the DFM. The two phase flow MINC simulator is implemented in the free-open source numerical toolbox DuMux (www.dumux.org). The MSR (Gong et al., 2009) determines the inter-porosity terms by solving simplified local single-phase flow problems. The DFM is considered as the reference solution. The numerical examples consider a quasi-1D reservoir with a quadratic fracture system , a five-spot radial symmetric reservoir, and a completely random generated fracture system. Keywords: MINC, upscaling, two-phase flow, fractured porous media, discrete fracture model, continuum fracture model
Evolution of a mining induced fracture network in the overburden strata of an inclined coal seam
Institute of Scientific and Technical Information of China (English)
Wei; Xiujun; Gao; Mingzhong; Lv; Youchang; Shi; Xiangchao; Gao; Hailian; Zhou; Hongwei
2012-01-01
The geological conditions of the Pingdingshan coal mining group were used to construct a physical model used to study the distribution and evolution of mining induced cracks in the overburden strata.Digital graphics technology and fractal theory are introduced to characterize the distribution and growth of the mining induced fractures in the overburden strata of an inclined coal seam.A relationship between fractal dimension of the fracture network and the pressure in the overburden strata is suggested.Mining induced fractures spread dynamically to the mining face and up into the roof as the length of advance increases.Moreover,the fractal dimension of the fracture network increases with increased mining length,in general,but decreases during a period from overburden strata separation until the main roof collapses.It is a1so shown that overburden strata pressure plays an important role in the evolution of mining induced fractures and that the fractal dimension of the fractures increases with the pressure of the overburden.
Merrien-Soukatchoff, V.; Korini, T.; Thoraval, A.
2012-03-01
The paper presents the Discrete Fracture Network code RESOBLOK, which couples geometrical block system construction and a quick iterative stability analysis in the same package. The deterministic or stochastic geometry of a fractured rock mass can be represented and interactively displayed in 3D using two different fracture generators: one mainly used for hydraulic purposes and another designed to allow block stability evaluation. RESOBLOK has downstream modules that can quickly compute stability (based on limit equilibrium or energy-based analysis), display geometric information and create links to other discrete software. The advantage of the code is that it couples stochastic geometrical representation and a quick iterative stability analysis to allow risk-analysis with or without reinforcement and, for the worst cases, more accurate analysis using stress-strain analysis computer codes. These different aspects are detailed for embankment and underground works.
Bonded-cell model for particle fracture
Nguyen, Duc-Hanh; Azéma, Émilien; Sornay, Philippe; Radjaï, Farhang
2015-01-01
International audience; Particle degradation and fracture play an important role in natural granular flows and in many applications of granular materials. We analyze the fracture properties of two-dimensional disklike particles modeled as aggregates of rigid cells bonded along their sides by a cohesive Mohr-Coulomb law and simulated by the contact dynamics method. We show that the compressive strength scales with tensile strength between cells but depends also on the friction coefficient and ...
Cohesive mixed mode fracture modelling and experiments
DEFF Research Database (Denmark)
Walter, Rasmus; Olesen, John Forbes
2008-01-01
A nonlinear mixed mode model originally developed by Wernersson [Wernersson H. Fracture characterization of wood adhesive joints. Report TVSM-1006, Lund University, Division of Structural Mechanics; 1994], based on nonlinear fracture mechanics, is discussed and applied to model interfacial cracking...... in a steel–concrete interface. The model is based on the principles of Hillerborgs fictitious crack model, however, the Mode I softening description is modified taking into account the influence of shear. The model couples normal and shear stresses for a given combination of Mode I and II fracture...... curves, which may be interpreted using the nonlinear mixed mode model. The interpretation of test results is carried out in a two step inverse analysis applying numerical optimization tools. It is demonstrated how to perform the inverse analysis, which couples the assumed individual experimental load...
Challenges in Continuum Modelling of Intergranular Fracture
DEFF Research Database (Denmark)
Coffman, Valerie; Sethna, James P.; Ingraffea, A. R.;
2011-01-01
Intergranular fracture in polycrystals is often simulated by finite elements coupled to a cohesive zone model for the interfaces, requiring cohesive laws for grain boundaries as a function of their geometry. We discuss three challenges in understanding intergranular fracture in polycrystals. First......, 3D grain boundary geometries comprise a five-dimensional space. Second, the energy and peak stress of grain boundaries have singularities for all commensurate grain boundaries, especially those with short repeat distances. Thirdly, fracture nucleation and growth depend not only upon the properties...... properties. To address the last challenge, we demonstrate a method for atomistically extracting the fracture properties of geometrically complex local regions on the fly from within a finite element simulation....
Universal asymptotic umbrella for hydraulic fracture modeling
Linkov, Aleksandr M
2014-01-01
The paper presents universal asymptotic solution needed for efficient modeling of hydraulic fractures. We show that when neglecting the lag, there is universal asymptotic equation for the near-front opening. It appears that apart from the mechanical properties of fluid and rock, the asymptotic opening depends merely on the local speed of fracture propagation. This implies that, on one hand, the global problem is ill-posed, when trying to solve it as a boundary value problem under a fixed position of the front. On the other hand, when properly used, the universal asymptotics drastically facilitates solving hydraulic fracture problems (both analytically and numerically). We derive simple universal asymptotics and comment on their employment for efficient numerical simulation of hydraulic fractures, in particular, by well-established Level Set and Fast Marching Methods.
Lattice modeling of fracture processes in numerical concrete with irregular shape aggregates
Qian, Z.; Schlangen, H.E.J.G.
2013-01-01
The fracture processes in concrete can be simulated by lattice fracture model [1]. A lattice network is usually constructed on top of the material structure of concrete, and then the mechanical properties of lattice elements are assigned, corresponding with the phases they represent. The material st
Latham, J.P.; Xiang, J.; Belayneh, M.; Nick, H.M.; Tsang, C.F.; Blunt, M.J.
2013-01-01
The influence of in-situ stresses on flow processes in fractured rock is investigated using a novel modelling approach. The combined finite-discrete element method (FEMDEM) is used to model the deformation of a fractured rock mass. The fracture wall displacements and aperture changes are modelled in
Model on surface borehole squeezing deformation fracture*
Institute of Scientific and Technical Information of China (English)
SUN Hai-tao; HU Qian-ting; HUANG Sheng-shu
2009-01-01
As a good method to solve the problem of high methane on the workface and in the goaf, drawing coal strata methane through a surface borehole is used. However, the excavation affected the overlying rock strata greatly. When the excavation face passed through the surface borehole position, the surface borehole fractures fast. This problem was seriously related to the unformed squeeze effect. Therefore, a squeezing deformation fracture model based on the rock strata squeezing effect was set up. At the same time, a 3DEC simulation model is presented to confirm the theory. The result shows that the mod-el is reliable and has a good engineering application value.
Institute of Scientific and Technical Information of China (English)
朱磊; 陈玖泓; 刘德东
2016-01-01
Preferential flow refers to such a flow transport pattern that water and solute flow round soil matrix, which accelerates soil water movement. Soil cracks are a part of reasons that lead to preferential flow. This study aimed to analyze soil preferential flow pattern in order to establish a model of preferential model based on soil fracture network. A field color tracer experiment was carried out in Ningxia University from July to September in 2015 under precipitation intensity of 20 and 50 mm/h, and rainfall duration of 20-60 min. The results showed that when the rainfall intensity was 20 mm/h, the water infiltration depth increased with the increase of rainfall duration and the preferential flow began to develop, but it was still overall-matrix flow and the preferential flow was only locally developed. When precipitation intensity was 50mm/h and the duration of rainfall was 20min, water flows bypassed the soil matrix and preferential flow phenomena was observed obviously. The infiltration depth exceeded the fracture depth after duration of rainfall increased to 50min, soil fracture had not play a major role in the soil water movement, and the flow patterns were overall-matrix flow. The results showed that the flow patterns were mainly matrix flow under lower rainfall or irrigation intensity, and preferential flow under higher rainfall or irrigation intensity. A coupling model of soil matrix and fracture network for simulating preferential flow was established (CP model). In this model, the soil medium was divided into matrix and fracture networks formed by flow channels, each having its own saturated hydraulic conductivity and water movement equation. These equations were solved by using the control volume finite element method, and the nonlinear equations were linearized by Newton-Raphson methods to improve the convergence, and shorten the operation time. Equation of water movement in matrix and fracture network flow equation were coupled using global approach
Zimmerman, R. W.; Leung, C. T.
2009-12-01
Most oil and gas reservoirs, as well as most potential sites for nuclear waste disposal, are naturally fractured. In these sites, the network of fractures will provide the main path for fluid to flow through the rock mass. In many cases, the fracture density is so high as to make it impractical to model it with a discrete fracture network (DFN) approach. For such rock masses, it would be useful to have recourse to analytical, or semi-analytical, methods to estimate the macroscopic hydraulic conductivity of the fracture network. We have investigated single-phase fluid flow through generated stochastically two-dimensional fracture networks. The centers and orientations of the fractures are uniformly distributed, whereas their lengths follow a lognormal distribution. The aperture of each fracture is correlated with its length, either through direct proportionality, or through a nonlinear relationship. The discrete fracture network flow and transport simulator NAPSAC, developed by Serco (Didcot, UK), is used to establish the “true” macroscopic hydraulic conductivity of the network. We then attempt to match this value by starting with the individual fracture conductances, and using various upscaling methods. Kirkpatrick’s effective medium approximation, which works well for pore networks on a core scale, generally underestimates the conductivity of the fracture networks. We attribute this to the fact that the conductances of individual fracture segments (between adjacent intersections with other fractures) are correlated with each other, whereas Kirkpatrick’s approximation assumes no correlation. The power-law averaging approach proposed by Desbarats for porous media is able to match the numerical value, using power-law exponents that generally lie between 0 (geometric mean) and 1 (harmonic mean). The appropriate exponent can be correlated with statistical parameters that characterize the fracture density.
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.
Bisdom, Kevin; Bertotti, Giovanni; Nick, Hamidreza M.
2016-05-01
Predicting equivalent permeability in fractured reservoirs requires an understanding of the fracture network geometry and apertures. There are different methods for defining aperture, based on outcrop observations (power law scaling), fundamental mechanics (sublinear length-aperture scaling), and experiments (Barton-Bandis conductive shearing). Each method predicts heterogeneous apertures, even along single fractures (i.e., intrafracture variations), but most fractured reservoir models imply constant apertures for single fractures. We compare the relative differences in aperture and permeability predicted by three aperture methods, where permeability is modeled in explicit fracture networks with coupled fracture-matrix flow. Aperture varies along single fractures, and geomechanical relations are used to identify which fractures are critically stressed. The aperture models are applied to real-world large-scale fracture networks. (Sub)linear length scaling predicts the largest average aperture and equivalent permeability. Barton-Bandis aperture is smaller, predicting on average a sixfold increase compared to matrix permeability. Application of critical stress criteria results in a decrease in the fraction of open fractures. For the applied stress conditions, Coulomb predicts that 50% of the network is critically stressed, compared to 80% for Barton-Bandis peak shear. The impact of the fracture network on equivalent permeability depends on the matrix hydraulic properties, as in a low-permeable matrix, intrafracture connectivity, i.e., the opening along a single fracture, controls equivalent permeability, whereas for a more permeable matrix, absolute apertures have a larger impact. Quantification of fracture flow regimes using only the ratio of fracture versus matrix permeability is insufficient, as these regimes also depend on aperture variations within fractures.
Modelling localised fracture of reinforced concrete structures
Liao, F; Huang, Z.
2015-01-01
This paper presents a robust finite element procedure for simulating the localised fracture of reinforced concrete members. In this new model the concrete member is modelled as an assembly of plain concrete, reinforcing steel bar and bond-link elements. The 4-node quadrilateral elements are used for 2D modelling of plain concrete elements, in which the extended finite element method is adopted to simulate the formation and growth of individual cracks. The reinforcing steel bars are modelled b...
Porosity, permeability and 3D fracture network characterisation of dolomite reservoir rock samples.
Voorn, Maarten; Exner, Ulrike; Barnhoorn, Auke; Baud, Patrick; Reuschlé, Thierry
2015-03-01
With fractured rocks making up an important part of hydrocarbon reservoirs worldwide, detailed analysis of fractures and fracture networks is essential. However, common analyses on drill core and plug samples taken from such reservoirs (including hand specimen analysis, thin section analysis and laboratory porosity and permeability determination) however suffer from various problems, such as having a limited resolution, providing only 2D and no internal structure information, being destructive on the samples and/or not being representative for full fracture networks. In this paper, we therefore explore the use of an additional method - non-destructive 3D X-ray micro-Computed Tomography (μCT) - to obtain more information on such fractured samples. Seven plug-sized samples were selected from narrowly fractured rocks of the Hauptdolomit formation, taken from wellbores in the Vienna basin, Austria. These samples span a range of different fault rocks in a fault zone interpretation, from damage zone to fault core. We process the 3D μCT data in this study by a Hessian-based fracture filtering routine and can successfully extract porosity, fracture aperture, fracture density and fracture orientations - in bulk as well as locally. Additionally, thin sections made from selected plug samples provide 2D information with a much higher detail than the μCT data. Finally, gas- and water permeability measurements under confining pressure provide an important link (at least in order of magnitude) towards more realistic reservoir conditions. This study shows that 3D μCT can be applied efficiently on plug-sized samples of naturally fractured rocks, and that although there are limitations, several important parameters can be extracted. μCT can therefore be a useful addition to studies on such reservoir rocks, and provide valuable input for modelling and simulations. Also permeability experiments under confining pressure provide important additional insights. Combining these and
Modeling contaminant plumes in fractured limestone aquifers
DEFF Research Database (Denmark)
Mosthaf, Klaus; Brauns, Bentje; Fjordbøge, Annika Sidelmann
the established approaches of the equivalent porous medium, discrete fracture and dual continuum models. However, these modeling concepts are not well tested for contaminant plume migration in limestone geologies. Our goal was to develop and evaluate approaches for modeling the transport of dissolved contaminant...... in the planning of field tests and to update the conceptual model in an iterative process. Field data includes information on spill history, distribution of the contaminant (multilevel sampling), geology and hydrogeology. To describe the geology and fracture system, data from borehole logs, packer tests, optical...... distribution in the aquifer. Different models were used for the planning and interpretation of the pump and tracer test. The models were evaluated by examining their ability to describe collected field data. The comparison with data showed that the models have substantially different representations...
Creating permeable fracture networks for EGS: Engineered systems versus nature
Energy Technology Data Exchange (ETDEWEB)
Stephen L Karner
2005-10-01
The United States Department of Energy has set long-term national goals for the development of geothermal energy that are significantly accelerated compared to historical development of the resource. To achieve these goals, it is crucial to evaluate the performance of previous and existing efforts to create enhanced geothermal systems (EGS). Two recently developed EGS sites are evaluated from the standpoint of geomechanics. These sites have been established in significantly different tectonic regimes: 1. compressional Cooper Basin (Australia), and 2. extensional Soultz-sous-Fôrets (France). Mohr-Coulomb analyses of the stimulation procedures employed at these sites, coupled with borehole observations, indicate that pre-existing fractures play a significant role in the generation of permeability networks. While pre-existing fabric can be exploited to produce successful results for geothermal energy development, such fracture networks may not be omnipresent. For mostly undeformed reservoirs, it may be necessary to create new fractures using processes that merge existing technologies or use concepts borrowed from natural hydrofracture examples (e.g. dyke swarms).
Ongoing Model Development Analyzing Glass Fracture
DEFF Research Database (Denmark)
Molnar, G.; Bojtar, I.; Nielsen, Jens Henrik
2013-01-01
Present subject deals with an ongoing experimental and numerical analysis of inplane loaded glass plates. The main goal of the investigation is to develop a hybrid – discrete and finite element – model which could follow the fracture process in annealed and in tempered glass. Measurements...
Ongoing Model Development Analyzing Glass Fracture
DEFF Research Database (Denmark)
Molnar, G.; Bojtar, I.; Nielsen, Jens Henrik
2013-01-01
Present subject deals with an ongoing experimental and numerical analysis of inplane loaded glass plates. The main goal of the investigation is to develop a hybrid – discrete and finite element – model which could follow the fracture process in annealed and in tempered glass. Measurements...... an overview of the structure of the research and a summary of current status archived so far....
Kavousi Ghahfarokhi, Payam
The Tensleep oil reservoir at Teapot Dome, Wyoming, USA, is a naturally fractured tight sandstone reservoir that has been considered for carbon-dioxide enhanced oil recovery (CO2-EOR) and sequestration. CO2-EOR analysis requires a thorough understanding of the Tensleep fracture network. Wireline image logs from the field suggest that the reservoir fracture network is dominated by early formed structural hinge oblique fractures with interconnectivity enhanced by hinge parallel and hinge perpendicular fracture sets. Available post stack 3D seismic data are used to generate a seismic fracture intensity attribute for the reservoir fracture network. The resulting seismic fracture intensity is qualitatively correlated to the field production history. Wells located on hinge-oblique discontinuities are more productive than other wells in the field. We use Oda's method to upscale the fracture permeabilities in the discrete fracture network for use in a dual porosity fluid flow simulator. We analytically show that Oda's method is sensitive to the grid orientation relative to fracture set strike. Results show that the calculated permeability tensors have maximum geometric mean for the non-zero permeability components (kxx,kyy,kzz,kxy) when the dominant fracture set cuts diagonally through the grid cell at 45° relative to the grid cell principal directions (i,j). The geometric mean of the permeability tensor components falls to a minimum when the dominant fracture set is parallel to either grid wall (i or j principal directions). The latter case has off-diagonal permeability terms close to zero. We oriented the Tensleep reservoir grid to N72°W to minimize the off-diagonal permeability terms. The seismic fracture intensity attribute is then used to generate a realization of the reservoir fracture network. Subsequently, fracture properties are upscaled to the reservoir grid scale for a fully compositional flow simulation. We implemented a PVT analysis using CO2 swelling test
Analysis of microseismicity using fuzzy logic and fractals for fracture network characterization
Aminzadeh, F.; Ayatollahy Tafti, T.; Maity, D.; Boyle, K.; Sahimi, M.; Sammis, C. G.
2010-12-01
The area where microseismic events occur may be correlated with the fracture network at a geothermal field. For an Enhanced Geothermal System (EGS) reservoir, an extensive fracture network with a large aerial distribution is required. Pore-pressure increase, temperature changes, volume change due to fluid withdrawal/injection and chemical alteration of fracture surfaces are all mechanisms that may explain microseismic events at a geothermal field. If these mechanisms are operative, any fuzzy cluster of the microseismic events should represent a connected fracture network. Drilling new EGS wells (both injection and production wells) in these locations may facilitate the creation of an EGS reservoir. In this article we use the fuzzy clustering technique to find the location and characteristics of fracture networks in the Geysers geothermal field. We also show that the centers of these fuzzy clusters move in time, which may represent fracture propagation or fluid movement within the fracture network. Furthermore, analyzing the distribution of fuzzy hypocenters and quantifying their fractal structure helps us to develop an accurate fracture map for the reservoir. Combining the fuzzy clustering results with the fractal analysis allows us to better understand the mechanisms for fracture stimulation and better characterize the evolution of the fracture network. We also show how micro-earthquake date collected in different time periods can be correlated with drastic changes in the distribution of active fractures resulting from injection, production or other transient events.
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
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.
Fracture network evaluation program (FraNEP): A software for analyzing 2D fracture trace-line maps
Zeeb, Conny; Gomez-Rivas, Enrique; Bons, Paul D.; Virgo, Simon; Blum, Philipp
2013-10-01
Fractures, such as joints, faults and veins, strongly influence the transport of fluids through rocks by either enhancing or inhibiting flow. Techniques used for the automatic detection of lineaments from satellite images and aerial photographs, LIDAR technologies and borehole televiewers significantly enhanced data acquisition. The analysis of such data is often performed manually or with different analysis software. Here we present a novel program for the analysis of 2D fracture networks called FraNEP (Fracture Network Evaluation Program). The program was developed using Visual Basic for Applications in Microsoft Excel™ and combines features from different existing software and characterization techniques. The main novelty of FraNEP is the possibility to analyse trace-line maps of fracture networks applying the (1) scanline sampling, (2) window sampling or (3) circular scanline and window method, without the need of switching programs. Additionally, binning problems are avoided by using cumulative distributions, rather than probability density functions. FraNEP is a time-efficient tool for the characterisation of fracture network parameters, such as density, intensity and mean length. Furthermore, fracture strikes can be visualized using rose diagrams and a fitting routine evaluates the distribution of fracture lengths. As an example of its application, we use FraNEP to analyse a case study of lineament data from a satellite image of the Oman Mountains.
A Network Approach to Fracture: The Effect of Heterogeneity and Loading Conditions
Reuschlé, T.
Fracture in a heterogeneous solid is simulated on a triangular network of bonds which figure the potential cracks of the medium. Heterogeneity is introduced by assuming a statistical strength distribution for the bonds. External stresses are applied to the network and the evolution of the bond population is analyzed when the stresses are increased. Bond-breaking is controlled by the crack-exten sion force which takes into account crack interactions by using an iterative procedure. Crack propaga tion leads to the coalescence of broken bonds crack clusters are formed. By using this kind of approach which combines fracture mechanics and network modelling, we are able to simulate the rupture of a rock specimen under various loading conditions without heavy computation. We discuss physical properties of the rupture process by examining the rupture stress and the geometric properties of the macroscopic fracture and their dependence on loading conditions and heterogeneity. Analysis of the geometric characteristics shows that the number of broken bonds can be fitted by a power law of the lattice size, the exponent depending on the loading conditions. Furthermore, an approximate computation of the mechanical response of the network demonstrates that the threshold secant modulus may be a more legitimate choice for a damage parameter in terms of system size independence.
Armbruster, Benjamin
2011-01-01
We analyze random networks that change over time. First we analyze a dynamic Erdos-Renyi model, whose edges change over time. We describe its stationary distribution, its convergence thereto, and the SI contact process on the network, which has relevance for connectivity and the spread of infections. Second, we analyze the effect of node turnover, when nodes enter and leave the network, which has relevance for network models incorporating births, deaths, aging, and other demographic factors.
Hu, Mengsu; Rutqvist, Jonny; Wang, Yuan
2016-11-01
In this study, a numerical manifold method (NMM) model is developed to analyze flow in porous media with discrete fractures in a non-conforming mesh. This new model is based on a two-cover-mesh system with a uniform triangular mathematical mesh and boundary/fracture-divided physical covers, where local independent cover functions are defined. The overlapping parts of the physical covers are elements where the global approximation is defined by the weighted average of the physical cover functions. The mesh is generated by a tree-cutting algorithm. A new model that does not introduce additional degrees of freedom (DOF) for fractures was developed for fluid flow in fractures. The fracture surfaces that belong to different physical covers are used to represent fracture flow in the direction of the fractures. In the direction normal to the fractures, the fracture surfaces are regarded as Dirichlet boundaries to exchange fluxes with the rock matrix. Furthermore, fractures that intersect with Dirichlet or Neumann boundaries are considered. Simulation examples are designed to verify the efficiency of the tree-cutting algorithm, the calculation's independency from the mesh orientation, and accuracy when modeling porous media that contain fractures with multiple intersections and different orientations. The simulation results show good agreement with available analytical solutions. Finally, the model is applied to cases that involve nine intersecting fractures and a complex network of 100 fractures, both of which achieve reasonable results. The new model is very practical for modeling flow in fractured porous media, even for a geometrically complex fracture network with large hydraulic conductivity contrasts between fractures and the matrix.
Simulation of Fracture Nucleation in Cross-Linked Polymer Networks
Moller, J. C.; Barr, S. A.; Schultz, E. J.; Breitzman, T. D.; Berry, R. J.
2013-02-01
A novel atomistic simulation method is developed whereby polymer systems can undergo strain-rate-controlled deformation while bond scission is enabled. The aim is to provide insight into the nanoscale origins of fracture. Various highly cross-linked epoxy systems including various resin chain lengths and levels of nonreactive dilution were examined. Consistent with the results of physical experiments, cured resin strength increased and ductility decreased with increasing cross-link density. An analysis of dihedral angle activity shows the locations in the molecular network that are most absorptive of mechanical energy. Bond scission occurred principally at cross-link sites as well as between phenyl rings in the bisphenol moiety. Scissions typically occurred well after yield and were accompanied by steady increases in void size and dihedral angle motion between bisphenol moieties and at cross-link sites. The methods developed here could be more broadly applied to explore and compare the atomistic nature of deformation for various polymers such that mechanical and fracture properties could be tuned in a rational way. This method and its results could become part of a solution system that spans multiple length and time scales and that could more completely represent such mechanical events as fracture.
An Efficient Two-Scale Hybrid Embedded Fracture Model for Shale Gas Simulation
Amir, Sahar
2016-12-27
Natural and hydraulic fractures existence and state differs on a reservoir-by-reservoir or even on a well-by-well basis leading to the necessity of exploring the flow regimes variations with respect to the diverse fracture-network shapes forged. Conventional Dual-Porosity Dual-Permeability (DPDP) schemes are not adequate to model such complex fracture-network systems. To overcome this difficulty, in this paper, an iterative Hybrid Embedded multiscale (two-scale) Fracture model (HEF) is applied on a derived fit-for-purpose shale gas model. The HEF model involves splitting the fracture computations into two scales: 1) fine-scale solves for the flux exchange parameter within each grid cell; 2) coarse-scale solves for the pressure applied to the domain grid cells using the flux exchange parameter computed at each grid cell from the fine-scale. After that, the D dimensions matrix pressure and the (D-1) lower dimensional fracture pressure are solved as a system to apply the matrix-fracture coupling. HEF model combines the DPDP overlapping continua concept, the DFN lower dimensional fractures concept, the HFN hierarchical fracture concept, and the CCFD model simplicity. As for the fit-for-purpose shale gas model, various fit-for-purpose shale gas models can be derived using any set of selected properties plugged in one of the most popularly used proposed literature models as shown in the appendix. Also, this paper shows that shale extreme low permeability cause flow behavior to be dominated by the structure and magnitude of high permeability fractures.
Xiang, G.L.; Vire, A.; Pavlidis, D.; Pain, C.
2015-01-01
A three-dimensional fracture model developed in the context of the combined finite-discrete element method is incorporated into a two-way fluid-solid coupling model. The fracture model is capable of simulating the whole fracturing process. It includes pre-peak hardening deformation, post-peak strain
COHESIVE ZONE FINITE ELEMENT-BASED MODELING OF HYDRAULIC FRACTURES
Institute of Scientific and Technical Information of China (English)
Zuorong Chen; A.P. Bunger; Xi Zhang; Robert G. Jeffrey
2009-01-01
Hydraulic fracturing is a powerful technology used to stimulate fluid production from reservoirs. The fully 3-D numerical simulation of the hydraulic fracturing process is of great importance to the efficient application of this technology, but is also a great challenge because of the strong nonlinear coupling between the viscous flow of fluid and fracture propagation. By taking advantage of a cohesive zone method to simulate the fracture process, a finite element model based on the existing pore pressure cohesive finite elements has been established to investigate the propagation of a penny-shaped hydraulic fracture in an infinite elastic medium. The effect of cohesive material parameters and fluid viscosity on the hydraulic fracture behaviour has been investigated. Excellent agreement between the finite element results and analytical solutions for the limiting case where the fracture process is dominated by rock fracture toughness demonstrates the ability of the cohesive zone finite element model in simulating the hydraulic fracture growth for this case.
Dynamic model of normal behavior of rock fractures
Institute of Scientific and Technical Information of China (English)
YANG Wen-yi; KONG Guang-ya; CAI Jun-gang
2005-01-01
Based on laboratory tests of artificial fractures in mortar material, established the dynamic constitutive model of normal behaviour of rock fracture,. The tests were systematically conducted under quasi-static and dynamic monotonic loading conditions. The fractures were of different numbers of asperities in contact and were subsequently of different initial contact areas, which imitated the natural rock fractures. The rate of compressive load applied normal to the fractures covers a wide range from 10-1 MPa/s (quasi-static) up to 103 MPa/s (highly dynamic). The normal stress-closure responses of fractures were measured for different loading rates. Based on the stress-closure relation curves measured, a nonlinear (hyperbolic) dynamic model of fracture, normal behaviour, termed as dynamic BB model, was proposed, which was modified from the existing BB model of static normal behaviour of fractures by taking into account the effect of loading rate.
Bonded-cell model for particle fracture.
Nguyen, Duc-Hanh; Azéma, Emilien; Sornay, Philippe; Radjai, Farhang
2015-02-01
Particle degradation and fracture play an important role in natural granular flows and in many applications of granular materials. We analyze the fracture properties of two-dimensional disklike particles modeled as aggregates of rigid cells bonded along their sides by a cohesive Mohr-Coulomb law and simulated by the contact dynamics method. We show that the compressive strength scales with tensile strength between cells but depends also on the friction coefficient and a parameter describing cell shape distribution. The statistical scatter of compressive strength is well described by the Weibull distribution function with a shape parameter varying from 6 to 10 depending on cell shape distribution. We show that this distribution may be understood in terms of percolating critical intercellular contacts. We propose a random-walk model of critical contacts that leads to particle size dependence of the compressive strength in good agreement with our simulation data.
Energy Technology Data Exchange (ETDEWEB)
Auzias, V.
1995-10-27
In order to understand joint network organisation in oil reservoirs, as a first step we have adapted to technique (the photo-elasticimetry) to study stress fields in 2D. This method allows to determine the principal stress trajectories near faults, as well as the associated joint network organisation. Natural joint networks perturbed near faults are modeled and the parameters that control stress perturbation are proposed. With the aim of extrapolating joint data from a well to the entire reservoir our modelling is based on both 3 D seismic data and local joint data. The second part of our research was dedicated to studying joint propagation mechanisms in a natural reservoir analogue (flat-lying Devonian Old Red Sandstones of Caitness in North Scotland). Several exposure observation at different scales and in 3D (horizontal and cliff sections) allow to reconstitute the fracturing geometry from centimeter to kilometer scale and to link these to the regional tectonic history. This study shows that it is possible to differentiate three types of joints major joints, `classic` joints and micro-joints, each with different vertical persistence. New concepts on the 3D joint organisation have been deduced from field quantitative data, which can be applied to reservoir fracture modeling. In particular the non-coexistence phenomenon in a single bed of two regional joint sets with close strikes. Some joint development mechanisms are discussed: interaction between joints and sedimentary interfaces, joint distribution near faults, origin of en echelon arrays associated with joints. (author) 142 refs.
Productivity Analysis of Volume Fractured Vertical Well Model in Tight Oil Reservoirs
Directory of Open Access Journals (Sweden)
Jiahang Wang
2017-01-01
Full Text Available This paper presents a semianalytical model to simulate the productivity of a volume fractured vertical well in tight oil reservoirs. In the proposed model, the reservoir is a composite system which contains two regions. The inner region is described as formation with finite conductivity hydraulic fracture network and the flow in fracture is assumed to be linear, while the outer region is simulated by the classical Warren-Root model where radial flow is applied. The transient rate is calculated, and flow patterns and characteristic flowing periods caused by volume fractured vertical well are analyzed. Combining the calculated results with actual production data at the decline stage shows a good fitting performance. Finally, the effects of some sensitive parameters on the type curves are also analyzed extensively. The results demonstrate that the effect of fracture length is more obvious than that of fracture conductivity on improving production in tight oil reservoirs. When the length and conductivity of main fracture are constant, the contribution of stimulated reservoir volume (SRV to the cumulative oil production is not obvious. When the SRV is constant, the length of fracture should also be increased so as to improve the fracture penetration and well production.
A Fracture Mechanical Model and a Cohesive Zone Model of Interface Fracture
DEFF Research Database (Denmark)
Jensen, Henrik Myhre
2006-01-01
A comparison between the prediction of crack propagation through an adhesive interface based on a fracture mechanics approach and a cohesive zone approach is presented. Attention is focussed on predicting the shape of the crack front and the critical stress required to propagate the crack under...... quasi-static conditions. The cohesive zone model has several advantages over the fracture mechanics based model. It is easier to generalise the cohesive zone model to take into account effects such as plastic deformation in the adherends, and to take into account effects of large local curvatures...... of the interface crack front. The comparison shows a convergence of the results based on the cohesive zone model towards the results based on a fracture mechanics approach in the limit where the size of the cohesive zone becomes smaller than other relevant geometrical lengths for the problem....
Klammler, Harald; Hatfield, Kirk; Newman, Mark A.; Cho, Jaehyun; Annable, Michael D.; Parker, Beth L.; Cherry, John A.; Perminova, Irina
2016-07-01
This paper presents the fundamental theory and laboratory test results on a new device that is deployed in boreholes in fractured rock aquifers to characterize vertical distributions of water and contaminant fluxes, aquifer hydraulic properties, and fracture network properties (e.g., active fracture density and orientation). The device, a fractured rock passive flux meter (FRPFM), consists of an inflatable core assembled with upper and lower packers that isolate the zone of interest from vertical gradients within the borehole. The outer layer of the core consists of an elastic fabric mesh equilibrated with a visible dye which is used to provide visual indications of active fractures and measures of fracture location, orientation, groundwater flux, and the direction of that flux. Beneath the outer layer is a permeable sorbent that is preloaded with known amounts of water soluble tracers which are eluted at rates proportional to groundwater flow. This sorbent also captures target contaminants present in intercepted groundwater. The mass of contaminant sorbed is used to quantify cumulative contaminant flux; whereas, the mass fractions of resident tracers lost are used to provide measures of water flux. In this paper, the FRPFM is bench tested over a range of fracture velocities (2-20 m/day) using a single fracture flow apparatus (fracture aperture = 0.5 mm). Test results show a discoloration in visible dye corresponding to the location of the active fracture. The geometry of the discoloration can be used to discern fracture orientation as well as direction and magnitude of flow in the fracture. Average contaminant fluxes were measured within 16% and water fluxes within 25% of known imposed fluxes.
Modeling worldwide highway networks
Villas Boas, Paulino R.; Rodrigues, Francisco A.; da F. Costa, Luciano
2009-12-01
This Letter addresses the problem of modeling the highway systems of different countries by using complex networks formalism. More specifically, we compare two traditional geographical models with a modified geometrical network model where paths, rather than edges, are incorporated at each step between the origin and the destination vertices. Optimal configurations of parameters are obtained for each model and used for the comparison. The highway networks of Australia, Brazil, India, and Romania are considered and shown to be properly modeled by the modified geographical model.
Fracture and Medium Modeling, by Analizing Hidraulic Fracturing Induced Microseismicity
Gomez Alba, S.; Vargas Jiménez, C. A.
2014-12-01
Hydraulic fracturing is an essential technology for most unconventional hydrocarbon resources and many conventional ones as well. The primary limitation on the improvement and optimization of the fracturing process is the minimal access to observe the behavior of the fracture in the subsurface. Without direct observational evidence, hypothetical mechanisms must be assumed and then tested for their validity with indirect information such as wellbore measurements, indirect production and pressure behavior. One of the most important sources of information today is the relation made between micro seismic source mechanisms and fracture behavior. Hydraulic fractures induce some level of micro seismicity when the stress conditions in the Earth are altered by changes in stress during the operations. The result is the sudden movement between rock elements and the radiation of both compressional and shear energy in a seismic range that can be detected and recorded with sensitive receivers. The objective of this work is to provide reasonable information when applying inversion methods in order to estimate the vertical and horizontal spatial heterogeneities in medium and energy radiation distribution of microseisms while fracking operations. The method consist in record microseisms at a previous lineal array of stations (triaxial accelerometers) which are located close to the source coordinates and cover the area of study. The analysis clarify some ideas about what information can be gained from the micro seismic source data and according to the obtained results, what kind of comparisons and associations might be done to evaluate the fracking performance operation. Non uniformities in medium such as faults would be revealed by interpreted scattering coefficients. Fracture properties like distance, velocity and orientation would be also determined by analyzing energy radiation.
Identifying Training Images from Fracture Outcrops for MPS-based Modeling
Roy, A.; Mukerji, T.; Caers, J.
2014-12-01
Various MPS (multi-point geostatistics) based techniques have been successfully employed for modeling heterogeneous geologic features such as channel bodies. However, few studies exist on modeling fracture networks implementing MPS. Selecting a TI (training image) that is representative of the target subsurface fracture pattern is key to an effective implementation of any MPS algorithm. While recent research has employed equivalent continuum models created from Discrete Fracture Networks (DFN) to serve as TIs, the present research explores the direct usage of outcrop analogues of fracture networks for this purpose. A set of nested-fracture maps from the Devonian Sandstone of Hornelen basin created at multiple scales and resolutions is considered. These maps have been previously classified as belonging to a single fractal system characterized by a fractal dimension but having slightly different spatial organization at each scale. Our research implements unconditional image quilting in generating multiple realizations of fracture networks from these maps. This pattern-based algorithm requires a template-size to be chosen which is representative of the heterogeneity of the pattern of interest. Lacunarity is a technique that essentially quantifies the distribution of spaces or gaps in a pattern and can thus delineate scale-dependent heterogeneity. It is therefore investigated if this technique, in conjunction with Entropy (a measure for randomness), can be applied for choosing the template-size required for reproducing a desired pattern from a given TI. Finally, it will be tested if fracture networks generated from two or more TIs at different scales but belonging to the same fractal-fracture system, can capture similar ranges of uncertainty.
A New Physics-Based Modeling of Multiple Non-Planar Hydraulic Fractures Propagation
Energy Technology Data Exchange (ETDEWEB)
Zhou, Jing [University of Utah; Huang, Hai [Idaho National Lab. (INL), Idaho Falls, ID (United States); Deo, Milind [University of Utah; Jiang, Shu [Energy & Geoscience Institute
2015-10-01
Because of the low permeability in shale plays, closely spaced hydraulic fractures and multilateral horizontal wells are generally required to improve production. Therefore, understanding the potential fracture interaction and stress evolution is critical in optimizing fracture/well design and completion strategy in multi-stage horizontal wells. In this paper, a novel fully coupled reservoir flow and geomechanics model based on the dual-lattice system is developed to simulate multiple non-planar fractures propagation. The numerical model from Discrete Element Method (DEM) is used to simulate the mechanics of fracture propagations and interactions, while a conjugate irregular lattice network is generated to represent fluid flow in both fractures and formation. The fluid flow in the formation is controlled by Darcy’s law, but within fractures it is simulated by using cubic law for laminar flow through parallel plates. Initiation, growth and coalescence of the microcracks will lead to the generation of macroscopic fractures, which is explicitly mimicked by failure and removal of bonds between particles from the discrete element network. We investigate the fracture propagation path in both homogeneous and heterogeneous reservoirs using the simulator developed. Stress shadow caused by the transverse fracture will change the orientation of principal stress in the fracture neighborhood, which may inhibit or alter the growth direction of nearby fracture clusters. However, the initial in-situ stress anisotropy often helps overcome this phenomenon. Under large in-situ stress anisotropy, the hydraulic fractures are more likely to propagate in a direction that is perpendicular to the minimum horizontal stress. Under small in-situ stress anisotropy, there is a greater chance for fractures from nearby clusters to merge with each other. Then, we examine the differences in fracture geometry caused by fracturing in cemented or uncemented wellbore. Moreover, the impact of
Le Borgne, T.; Bochet, O.; Klepikova, M.; Kang, P. K.; Shakas, A.; Aquilina, L.; Dufresne, A.; Linde, N.; Dentz, M.; Bour, O.
2016-12-01
Transport processes in fractured media and associated reactions are governed by multiscale heterogeneity ranging from fracture wall roughness at small scale to broadly distributed fracture lengths at network scale. This strong disorder induces a variety of emerging phenomena, including flow channeling, anomalous transport and heat transfer, enhanced mixing and reactive hotspot development. These processes are generally difficult to isolate and monitor in the field because of the high degree of complexity and coupling between them. We report in situ experimental observations from the Ploemeur fractured rock observatory (http://hplus.ore.fr/en/ploemeur) that provide new insights on the dynamics of transport and reaction processes in fractured media. These include dipole and push pull tracer tests that allow understanding and modelling anomalous transport processes characterized by heavy-tailed residence time distributions (Kang et al. 2015), thermal push pull tests that show the existence of highly channeled flow with a strong control on fracture matrix exchanges (Klepikova et al. 2016) and time lapse hydrogeophysical monitoring of saline tracer tests that allow quantifying the distribution of transport length scales governing dispersion processes (Shakas et al. 2016). These transport processes are then shown to induce rapid oxygen delivery and mixing at depth leading to massive biofilm development (Bochet et al., in prep.). Hence, this presentation will attempt to link these observations made at different scales to quantify and model the coupling between flow channeling, non-Fickian transport, mixing and chemical reactions in fractured media. References: Bochet et al. Biofilm blooms driven by enhanced mixing in fractured rock, in prep. Klepikova et al. 2016, Heat as a tracer for understanding transport processes in fractured media: theory and field assessment from multi-scale thermal push-pull tracer tests, Water Resour. Res. 52Shakas et al. 2016, Hydrogeophysical
DEFF Research Database (Denmark)
Andersen, Kasper Winther
Three main topics are presented in this thesis. The first and largest topic concerns network modelling of functional Magnetic Resonance Imaging (fMRI) and Diffusion Weighted Imaging (DWI). In particular nonparametric Bayesian methods are used to model brain networks derived from resting state f...... for their ability to reproduce node clustering and predict unseen data. Comparing the models on whole brain networks, BCD and IRM showed better reproducibility and predictability than IDM, suggesting that resting state networks exhibit community structure. This also points to the importance of using models, which...... allow for complex interactions between all pairs of clusters. In addition, it is demonstrated how the IRM can be used for segmenting brain structures into functionally coherent clusters. A new nonparametric Bayesian network model is presented. The model builds upon the IRM and can be used to infer...
Particle Decision Making Processes in Fractured Media: The Battle Between Models
Sund, N. L.; Parashar, R.; Pham, H. V.
2016-12-01
During a random walk through a discrete fracture network, a particle moves at a constant velocity through a fracture segment and when it arrives at a fracture intersection it chooses a path, changes velocity, and repeats the process. The set of possible velocities the particle may choose depends on which intersection it is at, inducing a correlation between its current and next velocity. This process of traveling at a constant velocity then choosing a new velocity is also a good approximation to transport in (non-fractured) porous media.For times greater than the Taylor time scale (L^2/D, where L is the length scale over which a particle must travel to sample the full range of velocities in the system and D is the diffusion coefficient), the particle's decision making process can be neglected. In fractured and highly heterogeneous porous media, however, this length scale (and time scale consequently) can be prohibitively long. Even for field scale applications, it's possible that this decision making process may not be neglected. Several upscaled models have been developed that either explicitly or implicitly model this decision making process, including continuous time random walk with a coupled space and time step distribution, multi-rate mass transfer models, the spatial Markov model, and a hybrid approach based on the Boltzmann transport equation. We ask: how do these models perform in predicting transport at scales of interest? To answer this question, we upscale transport using a variety of models in simple 2D discrete fracture networks, where transport through each fracture is purely advective (no longitudinal diffusion), yet fully mixed (infinite transverse diffusion) and there is no mass exchange between the fracture network and the rock matrix it is embedded in. This simplified testing ground reveals whether the question of "how" to model the decision process is as important as "whether" to model it.
Modeling Epidemic Network Failures
DEFF Research Database (Denmark)
Ruepp, Sarah Renée; Fagertun, Anna Manolova
2013-01-01
This paper presents the implementation of a failure propagation model for transport networks when multiple failures occur resulting in an epidemic. We model the Susceptible Infected Disabled (SID) epidemic model and validate it by comparing it to analytical solutions. Furthermore, we evaluate...... the SID model’s behavior and impact on the network performance, as well as the severity of the infection spreading. The simulations are carried out in OPNET Modeler. The model provides an important input to epidemic connection recovery mechanisms, and can due to its flexibility and versatility be used...... to evaluate multiple epidemic scenarios in various network types....
Fadakar Alghalandis, Younes
2017-05-01
Rapidly growing topic, the discrete fracture network engineering (DFNE), has already attracted many talents from diverse disciplines in academia and industry around the world to challenge difficult problems related to mining, geothermal, civil, oil and gas, water and many other projects. Although, there are few commercial software capable of providing some useful functionalities fundamental for DFNE, their costs, closed code (black box) distributions and hence limited programmability and tractability encouraged us to respond to this rising demand with a new solution. This paper introduces an open source comprehensive software package for stochastic modeling of fracture networks in two- and three-dimension in discrete formulation. Functionalities included are geometric modeling (e.g., complex polygonal fracture faces, and utilizing directional statistics), simulations, characterizations (e.g., intersection, clustering and connectivity analyses) and applications (e.g., fluid flow). The package is completely written in Matlab scripting language. Significant efforts have been made to bring maximum flexibility to the functions in order to solve problems in both two- and three-dimensions in an easy and united way that is suitable for beginners, advanced and experienced users.
Artificial neural network modelling
Samarasinghe, Sandhya
2016-01-01
This book covers theoretical aspects as well as recent innovative applications of Artificial Neural networks (ANNs) in natural, environmental, biological, social, industrial and automated systems. It presents recent results of ANNs in modelling small, large and complex systems under three categories, namely, 1) Networks, Structure Optimisation, Robustness and Stochasticity 2) Advances in Modelling Biological and Environmental Systems and 3) Advances in Modelling Social and Economic Systems. The book aims at serving undergraduates, postgraduates and researchers in ANN computational modelling. .
A reservoir simulation approach for modeling of naturally fractured reservoirs
Directory of Open Access Journals (Sweden)
H. Mohammadi
2012-12-01
Full Text Available In this investigation, the Warren and Root model proposed for the simulation of naturally fractured reservoir was improved. A reservoir simulation approach was used to develop a 2D model of a synthetic oil reservoir. Main rock properties of each gridblock were defined for two different types of gridblocks called matrix and fracture gridblocks. These two gridblocks were different in porosity and permeability values which were higher for fracture gridblocks compared to the matrix gridblocks. This model was solved using the implicit finite difference method. Results showed an improvement in the Warren and Root model especially in region 2 of the semilog plot of pressure drop versus time, which indicated a linear transition zone with no inflection point as predicted by other investigators. Effects of fracture spacing, fracture permeability, fracture porosity, matrix permeability and matrix porosity on the behavior of a typical naturally fractured reservoir were also presented.
Hsu, Shih-Meng; Ke, Chien-Chung; Lo, Hung-Chieh; Lin, Yen-Tsu; Huang, Chi-Chao
2016-04-01
On the basis of a relatively sparse data set, fractured aquifers are difficult to be characterized and modelled. The three-dimensional configuration of transmissive fractures and fracture zones is needed to be understood flow heterogeneity in the aquifer. Innovative technologies for the improved interpretation are necessary to facilitate the development of accurate predictive models of ground-water flow and solute transport or to precisely estimate groundwater potential. To this end, this paper presents a procedure for characterizing and modelling preferential flow path in the fractured rock aquifer carried out at Fractured Rock Hydrogeology Research Site in Shuangliou Forest Recreation Area, Pingtung County, Southern Taiwan. The Shuangliou well field is a 40 by 30-meter area consisting of 6 wells (one geological well, one pumping well and four hydrogeological testing wells). The bedrock at the site is mainly composed of slate and intercalated by meta-sandstone. The overburden consists of about 5.6 m of gravel deposits. Based on results of 100 m geological borehole with borehole televiewer logging, vertical flow logging and full-wave sonic logging, high transmissivity zones in the bedrock underlying the well field were identified. One of transmissivity zone (at the depths of 30~32 m) and its fracture orientation(N56/54) selected for devising a multiple well system with 4 boreholes (borehole depths :45m, 35m, 35m and 25m, respectively), which were utilized to perform cross-borehole flow velocity data under the ambient flow and pumped flow conditions to identify preferential flow paths. Results from the cross-borehole test show the preferential flow pathways are corresponding to the predicted ones. Subsequently, a 3-D discrete fracture network model based on outcrop data was generated by the FracMan code. A validation between observed and simulated data has proved that the present model can accurately predict the hydrogeological properties (e.g., number of fractures
Directory of Open Access Journals (Sweden)
Yu-Tzu Chang
2012-01-01
Full Text Available This paper aims to find the optimal set of initial weights to enhance the accuracy of artificial neural networks (ANNs by using genetic algorithms (GA. The sample in this study included 228 patients with first low-trauma hip fracture and 215 patients without hip fracture, both of them were interviewed with 78 questions. We used logistic regression to select 5 important factors (i.e., bone mineral density, experience of fracture, average hand grip strength, intake of coffee, and peak expiratory flow rate for building artificial neural networks to predict the probabilities of hip fractures. Three-layer (one hidden layer ANNs models with back-propagation training algorithms were adopted. The purpose in this paper is to find the optimal initial weights of neural networks via genetic algorithm to improve the predictability. Area under the ROC curve (AUC was used to assess the performance of neural networks. The study results showed the genetic algorithm obtained an AUC of 0.858±0.00493 on modeling data and 0.802 ± 0.03318 on testing data. They were slightly better than the results of our previous study (0.868±0.00387 and 0.796±0.02559, resp.. Thus, the preliminary study for only using simple GA has been proved to be effective for improving the accuracy of artificial neural networks.
Topological impact of constrained fracture growth
Directory of Open Access Journals (Sweden)
Sigmund Mongstad Hope
2015-09-01
Full Text Available The topology of two discrete fracture network models is compared to investigate the impact of constrained fracture growth. In the Poissonian discrete fracture network model the fractures are assigned length, position and orientation independent of all other fractures, while in the mechanical discrete fracture network model the fractures grow and the growth can be limited by the presence of other fractures. The topology is found to be impacted by both the choice of model, as well as the choice of rules for the mechanical model. A significant difference is the degree mixing. In two dimensions the Poissonian model results in assortative networks, while the mechanical model results in disassortative networks. In three dimensions both models produce disassortative networks, but the disassortative mixing is strongest for the mechanical model.
Institute of Scientific and Technical Information of China (English)
王培涛; 杨天鸿; 于庆磊; 刘洪磊; 夏冬; 张鹏海
2013-01-01
节理岩体几何结构非常复杂，研究其渗流特性对于指导含水岩层稳定性分析具有重要价值。应用离散裂隙网络模型DFN方法，基于VC++6.0软件平台，建立了平面渗流分析方法，分析了节理岩体不同几何分布情况下的渗透率张量特征，通过定义渗流定向性系数对岩体渗流的定向性特征进行了定量分析。结果表明：单组节理岩体渗流具有明显的各向异性特征，渗流定向性随着节理角度变化显著；节理随着节理贯通性增加，节理渗透率呈现对数增加趋势；两组节理情况下，各向异性特征随着节理组间夹角变化；两组节理岩体渗流特征研究中，正交分布下，岩体仍存在各向异性，但渗流定向性系数较低；当节理倾角服从正态分布时，随着节理倾角标准差增大，渗透率增加；两组节理夹角不同时，节理渗透主方向倾角随着夹角增大而相应增大，基本沿两组节理夹角方向的角平分线方向。%Joint systems in rock masses are geometrically complex; and investigation of the hydraulic properties is important for understanding the hydraulic behavior of jointed rock masses and stability analysis of rock engineering. A discrete fracture network (DFN) model was designed using C++language based on VC++6.0 platform to realize a fracture network for seepage analysis. The permeability coefficients, possibility of equivalent permeability tensors of the jointed rock masses were examined by simulating flow through DFN models of varying joint properties. A directionality coefficient was defined to quantitatively assess the principal flow direction in jointed rock masses. The results show that the permeability coefficients are anisotropic according to permeability tensor analysis for rock masses with only one set of joints. The degree of obliquities of joint plane affects obviously the principal direction of permeability. The permeability coefficients
Hu, Mengsu; Rutqvist, Jonny; Wang, Yuan
2017-04-01
In this study, a numerical manifold method (NMM) model was developed for fully coupled analysis of hydro-mechanical (HM) processes in porous rock masses with discrete fractures. Using an NMM two-cover-mesh system of mathematical and physical covers, fractures are conveniently discretized by dividing the mathematical cover along fracture traces to physical cover, resulting in a discontinuous model on a non-conforming mesh. In this model, discrete fracture deformation (e.g. open and slip) and fracture fluid flow within a permeable and deformable porous rock matrix are rigorously considered. For porous rock, direct pore-volume coupling was modeled based on an energy-work scheme. For mechanical analysis of fractures, a fracture constitutive model for mechanically open states was introduced. For fluid flow in fractures, both along-fracture and normal-to-fracture fluid flow are modeled without introducing additional degrees of freedom. When the mechanical aperture of a fracture is changing, its hydraulic aperture and hydraulic conductivity is updated. At the same time, under the effect of coupled deformation and fluid flow, the contact state may dynamically change, and the corresponding contact constraint is updated each time step. Therefore, indirect coupling is realized under stringent considerations of coupled HM effects and fracture constitutive behavior transfer dynamically. To verify the new model, examples involving deformable porous media containing a single and two sets of fractures were designed, showing good accuracy. Last, the model was applied to analyze coupled HM behavior of fractured porous rock domains with complex fracture networks under effects of loading and injection.
Modeling Network Interdiction Tasks
2015-09-17
minimize the operating costs for manufacturing 50 the item. This simple example illustrates the hierarchical structure that can be modeled using...fixed. The resulting model is linearized and the product of the dual variable and the (1−γij) term replaced with βij. This allows certain...the standard network interdiction model based on its tight linear programming relaxation. 2.3.3 Network Disruption. In practice, whenever an object is
Analysis and Visualization of Discrete Fracture Networks Using a Flow Topology Graph.
Aldrich, Garrett; Hyman, Jeffrey; Karra, Satish; Gable, Carl; Makedonska, Nataliia; Viswanathan, Hari; Woodring, Jonathan; Hamann, Bernd
2016-06-20
We present an analysis and visualization prototype using the concept of a flow topology graph (FTG) for characterization of flow in constrained networks, with a focus on discrete fracture networks (DFN), developed collaboratively by geoscientists and visualization scientists. Our method allows users to understand and evaluate flow and transport in DFN simulations by computing statistical distributions, segment paths of interest, and cluster particles based on their paths. The new approach enables domain scientists to evaluate the accuracy of the simulations, visualize features of interest, and compare multiple realizations over a specific domain of interest. Geoscientists can simulate complex transport phenomena modeling large sites for networks consisting of several thousand fractures without compromising the geometry of the network. However, few tools exist for performing higher-level analysis and visualization of simulated DFN data. The prototype system we present addresses this need. We demonstrate its effectiveness for increasingly complex examples of DFNs, covering two distinct use cases - hydrocarbon extraction from unconventional resources and transport of dissolved contaminant from a spent nuclear fuel repository.
Thrombin related peptide TP508 promoted fracture repair in a mouse high energy fracture model
Directory of Open Access Journals (Sweden)
Pan Xiao-Hua
2009-01-01
Full Text Available Abstract Background Thrombin related peptide (TP508 is a 23 amino-acid synthetic peptide that represents a portion of the receptor-binding domain of thrombin molecule. Previous studies have shown that TP508 can accelerate musculoskeletal tissue repair including fracture healing. Objectives The aim of this study was to investigate the effect of TP508 on fracture healing in a murine fracture model representing high energy fracture situation. Methods Eighty CD 1 mice underwent controlled quadriceps muscle crush and open transverse mid diaphyseal femoral fracture that was then fixed with an external fixator. Animals were randomised into four groups to receive an intra-operative dose of either 100 μg TP508 into the fracture gap; 100 μg TP508 into the surrounding damaged muscle tissues; 10 μg TP508 into the fracture gap, or control equal amount of saline into the fracture gap. Radiographic assessment was performed weekly for 5 weeks; histological analysis was at 3 and 5 weeks post fracture and biomechanical testing of the fractured bone was performed at 5 weeks post fracture. Results Mechanical testing data showed that the fracture stiffness was significantly higher in the group receiving 100 μg TP508 into the fracture gap than other groups. Histological and radiographic analysis revealed a trend of increase in bone formation in the 100 μg TP508 injected into the fracture gap group compared to the saline control group. It was noted that the scar tissues was significantly less in Group II comparing with the saline control group and there was increased blood vessel formation in the crushed muscles and fracture gap areas in the groups receiving TP508 comparing to the saline control group. Conclusion The results from this study demonstrated the use of thrombin related peptide TP508 in the situation of a high energy fracture can promote fracture healing and reduce the potential complications such as muscle fibrosis and fracture delayed or non-union.
Numerical modelling in non linear fracture mechanics
Directory of Open Access Journals (Sweden)
Viggo Tvergaard
2007-07-01
Full Text Available Some numerical studies of crack propagation are based on using constitutive models that accountfor damage evolution in the material. When a critical damage value has been reached in a materialpoint, it is natural to assume that this point has no more carrying capacity, as is done numerically in the elementvanish technique. In the present review this procedure is illustrated for micromechanically based materialmodels, such as a ductile failure model that accounts for the nucleation and growth of voids to coalescence, and a model for intergranular creep failure with diffusive growth of grain boundary cavities leading to micro-crack formation. The procedure is also illustrated for low cycle fatigue, based on continuum damage mechanics. In addition, the possibility of crack growth predictions for elastic-plastic solids using cohesive zone models to represent the fracture process is discussed.
Phase-field modeling of hydraulic fracture
Wilson, Zachary A.; Landis, Chad M.
2016-11-01
In this work a theoretical framework implementing the phase-field approach to fracture is used to couple the physics of flow through porous media and cracks with the mechanics of fracture. The main modeling challenge addressed in this work, which is a challenge for all diffuse crack representations, is on how to allow for the flow of fluid and the action of fluid pressure on the aggregate within the diffuse damage zone of the cracks. The theory is constructed by presenting the general physical balance laws and conducting a consistent thermodynamic analysis to constrain the constitutive relationships. Constitutive equations that reproduce the desired responses at the various limits of the phase-field parameter are proposed in order to capture Darcy-type flow in the intact porous medium and Stokes-type flow within open cracks. A finite element formulation for the solution of the governing model equations is presented and discussed. Finally, the theoretical and numerical model is shown to compare favorably to several important analytical solutions. More complex and interesting calculations are also presented to illustrate some of the advantageous features of the approach.
Lacunarity analysis of fracture networks: Evidence for scale-dependent clustering
Roy, Ankur; Perfect, Edmund; Dunne, William M.; Odling, Noelle; Kim, Jung-Woo
2010-10-01
Previous studies on fracture networks have shown that fractures contained within distinct mechanical units ("stratabound") are regularly spaced while those that terminate within the rock mass are clustered ("non-stratabound"). Lacunarity is a parameter which can quantify the distribution of spaces between rock fractures. When normalized to account for differences in fracture abundance, lacunarity characterizes the distribution of spaces as the degree of clustering in the fracture network. Normalized lacunarity curves, L∗( r), computed using the gliding-box algorithm and plotted as a function of box-size, r, were constructed for natural fracture patterns from Telpyn Point, Wales and the Hornelen basin, Norway. The results from analysis of the Telpyn Point fractures indicate that such curves are sensitive to differences in the clustering of different fracture sets at the same scale. For fracture networks mapped at different scales from the Hornelen basin, our analysis shows that clustering increases with decreasing spatial scale. This trend is attributed to the transition from a "stratabound" system at the scale of sedimentary cycles (100-200 m) that act as distinct mechanical units to a "non-stratabound" fracture system geometry at the finer 10's of meters thick bedding scale.
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
Modeling of Fracture Toughness of Electroless Nickel (EN) Coatings
Institute of Scientific and Technical Information of China (English)
K. Zangeneh; S.M. Monir-vaghefi; F. Ashrafizadeh
2004-01-01
In the present reserch, a model has been proposed for estimate fracture toughness of Nickel-phosphorus (EN)layers. For this purpose, high phosphorus (9%) EN coatings with thicknesses of 6, 12, 24, 36 and 48 μm were applied on steel substrates and then treated as conventional process. Fracture toughness of coatings was obtained using Vickers indentation method. It is found that fracture toughness increses as coating thickness reduces. Effect of coating thickness on fracture toughness was exhibited by various models. Evaluation of models revealed good agreement between of proposed model (Kc=f(t,t2)) and experimental data.
Modelling deformation and fracture in confectionery wafers
Energy Technology Data Exchange (ETDEWEB)
Mohammed, Idris K.; Charalambides, Maria N.; Williams, J. Gordon; Rasburn, John [Mechanical Engineering Department, Imperial College London, South Kensington, London, SW7 2AZ, United Kingdom and Nestec York Ltd., Nestlé Product Technology Centre, Haxby Road, PO Box 204, York YO91 1XY (United Kingdom)
2015-01-22
The aim of this research is to model the deformation and fracture behaviour of brittle wafers often used in chocolate confectionary products. Three point bending and compression experiments were performed on beam and circular disc samples respectively to determine the 'apparent' stress-strain curves in bending and compression. The deformation of the wafer for both these testing types was observed in-situ within an SEM. The wafer is modeled analytically and numerically as a composite material with a core which is more porous than the skins. X-ray tomography was used to generate a three dimensional volume of the wafer microstructure which was then meshed and used for quantitative analysis. A linear elastic material model, with a damage function and element deletion, was used and the XMT generated architecture was loaded in compression. The output from the FE simulations correlates closely to the load-deflection deformation observed experimentally.
Modelling deformation and fracture in confectionery wafers
Mohammed, Idris K.; Charalambides, Maria N.; Williams, J. Gordon; Rasburn, John
2015-01-01
The aim of this research is to model the deformation and fracture behaviour of brittle wafers often used in chocolate confectionary products. Three point bending and compression experiments were performed on beam and circular disc samples respectively to determine the 'apparent' stress-strain curves in bending and compression. The deformation of the wafer for both these testing types was observed in-situ within an SEM. The wafer is modeled analytically and numerically as a composite material with a core which is more porous than the skins. X-ray tomography was used to generate a three dimensional volume of the wafer microstructure which was then meshed and used for quantitative analysis. A linear elastic material model, with a damage function and element deletion, was used and the XMT generated architecture was loaded in compression. The output from the FE simulations correlates closely to the load-deflection deformation observed experimentally.
New model for well test analysis in a purely fractured medium
Energy Technology Data Exchange (ETDEWEB)
Karasaki, K.; Long, J.C.S.; Witherspoon, P.A.
1985-01-01
In a porous medium the flow conduits are small and a large number of conduits are connected to the well. For this reason the medium appears to behave like a continuum on the scale of the well test, and volumetric averaging and continuum approximations are justified. On the contrary, in a fractured medium, only a small number of fractures may intersect the pumping well. These particular fractures will be stressed by a large gradient under well test conditions. Consequently, the early time behavior will be dominated by these fractures. The volumetrically averaged permeability does not control flow in the vicinity of an active well. The individual fractures close to the well must be characterized in order to understand the well test behavior especially if the hydraulic parameters of these fractures are significantly different from the average values for the entire system. In the present study, a new analytical model is proposed for well test problems in fracture networks where the matrix is impermeable. The model accounts for the difference in the flow regime around the active well from that of the system as a whole. The analytical solutions are presented in a series of type curves for ranges of dimensionless parameters. The flow properties of the fracture system can be determined by curve matching.
Modeling Epidemic Network Failures
DEFF Research Database (Denmark)
Ruepp, Sarah Renée; Fagertun, Anna Manolova
2013-01-01
the SID model’s behavior and impact on the network performance, as well as the severity of the infection spreading. The simulations are carried out in OPNET Modeler. The model provides an important input to epidemic connection recovery mechanisms, and can due to its flexibility and versatility be used......This paper presents the implementation of a failure propagation model for transport networks when multiple failures occur resulting in an epidemic. We model the Susceptible Infected Disabled (SID) epidemic model and validate it by comparing it to analytical solutions. Furthermore, we evaluate...
Modeling Evolving Innovation Networks
Koenig, Michael D.; Battiston, Stefano; Schweitzer, Frank
2007-01-01
We develop a new framework for modeling innovation networks which evolve over time. The nodes in the network represent firms, whereas the directed links represent unilateral interactions between the firms. Both nodes and links evolve according to their own dynamics and on different time scales. The model assumes that firms produce knowledge based on the knowledge exchange with other firms, which involves both costs and benefits for the participating firms. In order to increase their knowledge...
Energy Technology Data Exchange (ETDEWEB)
Zhou, Jing [Universiyt of Utah; Huang, Hai [Idaho National Lab. (INL), Idaho Falls, ID (United States); Deo, Milind
2015-10-01
The interaction between hydraulic fractures (HF) and natural fractures (NF) will lead to complex fracture networks due to the branching and merging of natural and hydraulic fractures in unconventional reservoirs. In this paper, a newly developed hydraulic fracturing simulator based on discrete element method is used to predict the generation of complex fracture network in the presence of pre-existing natural fractures. By coupling geomechanics and reservoir flow within a dual lattice system, this simulator can effectively capture the poro-elastic effects and fluid leakoff into the formation. When HFs are intercepting single or multiple NFs, complex mechanisms such as direct crossing, arresting, dilating and branching can be simulated. Based on the model, the effects of injected fluid rate and viscosity, the orientation and permeability of NFs and stress anisotropy on the HF-NF interaction process are investigated. Combined impacts from multiple parameters are also examined in the paper. The numerical results show that large values of stress anisotropy, intercepting angle, injection rate and viscosity will impede the opening of NFs.
Upscaling of the specific surface area for reactive transport modelling in fractured rock
Cvetkovic, Vladimir
2014-05-01
The impact of flow heterogeneity on chemical transport from single to multiple fractures, is investigated. The emphasis is on the dynamic nature of the specific surface area (SSA) due to heterogeneity of the flow, relative to a purely geometrical definition. It is shown how to account for SSA as a random variable in modelling multi-component reactions. The flow-dependent SSA is interpreted probabilistically, following inert tracer particles along individual fractures. Upscaling to a fracture network is proposed as a time-domain random walk based on the statistics of SSA for single fractures. Statistics of SSA are investigated for three correlation structures of transmissivity, one classical multi-gaussian, and two non-Gaussian. The coefficient of variation of single fracture SSA decreases monotonously with the distance over the fracture length; the CV of the upscaled SSA reduces further such that after ca 20 fractures it is under 0.1 for a disconnected field, and around 0.2 for connected and multi-gaussian fields. This implies that after 10-20 fractures, uncertainty in SSA is significantly reduced, justifying the use of an effective value. A conservative, lower bound for the dimensionless upscaled effective SSA was found to be 1, suitable for all heterogeneity structures, assuming the cubic hydraulic law applicable.
Multiscale model reduction for shale gas transport in fractured media
Akkutlu, I Y; Vasilyeva, Maria
2015-01-01
In this paper, we develop a multiscale model reduction technique that describes shale gas transport in fractured media. Due to the pore-scale heterogeneities and processes, we use upscaled models to describe the matrix. We follow our previous work \\cite{aes14}, where we derived an upscaled model in the form of generalized nonlinear diffusion model to describe the effects of kerogen. To model the interaction between the matrix and the fractures, we use Generalized Multiscale Finite Element Method. In this approach, the matrix and the fracture interaction is modeled via local multiscale basis functions. We developed the GMsFEM and applied for linear flows with horizontal or vertical fracture orientations on a Cartesian fine grid. In this paper, we consider arbitrary fracture orientations and use triangular fine grid and developed GMsFEM for nonlinear flows. Moreover, we develop online basis function strategies to adaptively improve the convergence. The number of multiscale basis functions in each coarse region ...
A multiscale model of distributed fracture and permeability in solids in all-round compression
De Bellis, Maria Laura; Ortiz, Michael; Pandolfi, Anna
2016-01-01
We present a microstructural model of permeability in fractured solids, where the fractures are described in terms of recursive families of parallel, equidistant cohesive faults. Faults originate upon the attainment of a tensile or shear resistance in the undamaged material. Secondary faults may form in a hierarchical orga- nization, creating a complex network of connected fractures that modify the permeability of the solid. The undamaged solid may possess initial porosity and permeability. The particular geometry of the superposed micro-faults lends itself to an explicit analytical quantification of the porosity and permeability of the dam- aged material. The approach is particularly appealing as a means of modeling low permeability oil and gas reservoirs stimulated by hydraulic fracturing.
A microfluidic investigation of gas exsolution in glass and shale fracture networks
Porter, M. L.; Jimenez-Martinez, J.; Harrison, A.; Currier, R.; Viswanathan, H. S.
2016-12-01
Microfluidic investigations of pore-scale fluid flow and transport phenomena has steadily increased in recent years. In these investigations fluid flow is restricted to two-dimensions allowing for real-time visualization and quantification of complex flow and reactive transport behavior, which is difficult to obtain in other experimental systems. In this work, we describe a unique high pressure (up to 10.3 MPa) and temperature (up to 80 °C) microfluidics experimental system that allows us to investigate fluid flow and transport in geo-material (e.g., shale, Portland cement, etc.) micromodels. The use of geo-material micromodels allows us to better represent fluid-rock interactions including wettability, chemical reactivity, and nano-scale porosity at conditions representative of natural subsurface environments. Here, we present experimental results in fracture systems with applications to hydrocarbon mobility in fractured rocks. Complex fracture network patterns are derived from 3D x-ray tomography images of actual fractures created in shale rock cores. We use both shale and glass micromodels, allowing for a detailed comparison between flow phenomena in the different materials. We discuss results from two-phase gas (CO2 and N2) injection experiments designed to enhance oil recovery. In these experiments gas was injected into micromodels saturated with oil and allowed to soak for approximately 12 hours at elevated pressures. The pressure in the system was then decreased to atmospheric, causing the gas to expand and/or dissolve out of solution, subsequently mobilizing the oil. In addition to the experimental results, we present a relatively simple model designed to quantify the amount of oil mobilized as a function of decreasing system pressure. We will show comparisons between the experiments and model, and discuss the potential use of the model in field-scale reservoir simulations.
Modeling Dynamic Fracture of Cryogenic Pellets
Energy Technology Data Exchange (ETDEWEB)
Parks, Paul [General Atomics, San Diego, CA (United States)
2016-06-30
This work is part of an investigation with the long-range objective of predicting the size distribution function and velocity dispersion of shattered pellet fragments after a large cryogenic pellet impacts a solid surface at high velocity. The study is vitally important for the shattered pellet injection (SPI) technique, one of the leading technologies being implemented at ORNL for the mitigation of disruption damage on current tokamaks and ITER. The report contains three parts that are somewhat interwoven. In Part I we formulated a self-similar model for the expansion dynamics and velocity dispersion of the debris cloud following pellet impact against a thick (rigid) target plate. Also presented in Part I is an analytical fracture model that predicts the nominal or mean size of the fragments in the debris cloud and agrees well with known SPI data. The aim of Part II is to gain an understanding of the pellet fracturing process when a pellet is shattered inside a miter tube with a sharp bend. Because miter tubes have a thin stainless steel (SS) wall a permanent deformation (dishing) of the wall is produced at the site of the impact. A review of the literature indicates that most projectile impact on thin plates are those for which the target is deformed and the projectile is perfectly rigid. Such impacts result in “projectile embedding” where the projectile speed is reduced to zero during the interaction so that all the kinetic energy (KE) of the projectile goes into the energy stored in plastic deformation. Much of the literature deals with perforation of the target. The problem here is quite different; the softer pellet easily undergoes complete material failure causing only a small transfer of KE to stored energy of wall deformation. For the real miter tube, we derived a strain energy function for the wall deflection using a non-linear (plastic) stress-strain relation for 304 SS. Using a dishing profile identical to the linear Kirchkoff-Love profile (for lack
A cubic matrix-fracture geometry model for radial tracer flow in naturally fractured reservoirs
Energy Technology Data Exchange (ETDEWEB)
Jetzabeth Ramirez-Sabag; Fernando Samaniego V.
1992-01-01
This study presents a general solution for the radial flow of tracers in naturally fractured reservoirs, with cubic blocks matrix-fracture geometry. Continuous and finite step injection of chemical and radioactive tracers are considered. The reservoir is treated as being composed of two regions: a mobile where dispersion and convection take place and a stagnant where only diffusion and adsorption are allowed. Radioactive decay is considered in both regions. The model of this study is thoroughly compared under proper simplified conditions to those previously presented in the literature. The coupled matrix to fracture solution in the Laplace space is numerically inverted by means of the Crump algorithm. A detailed validation of the model with respect to solutions previously presented and/or simplified physical conditions solutions (i.e., homogeneous case) or limit solutions (i.e., naturally fractured nearly homogeneous) was carried out. The influence of the three of the main dimensionless parameters that enter into the solution was carefully investigated. A comparison of results for three different naturally fractured systems, vertical fractures (linear flow), horizontal fractures (radial flow) and the cubic geometry model of this study, is presented.
Directory of Open Access Journals (Sweden)
Enan Chi
2015-06-01
Full Text Available The fracture and fragmentation of rock materials are basic and important problem in geomechanics and blasting engineering. An approach, which can simulate the process of fracture and fragmentation of rock materials, is introduced in this work. A beam–particle model is first introduced in the frame of the discrete element method. In the beam–particle model, the neighboring elements are connected by beams. Consequently, a beam network is formed in the particle system. The strength characteristics of rock materials are reflected by the beam network. The strength criterion was then built to verify whether a beam exists or not. The process of rock fracture and fragmentation is described by the gradual disappearance of beams. Finally, two cases were presented to indicate the validity of the method proposed in this work.
Lean business model and implementation of a geriatric fracture center.
Kates, Stephen L
2014-05-01
Geriatric hip fracture is a common event associated with high costs of care and often with suboptimal outcomes for the patients. Ideally, a new care model to manage geriatric hip fractures would address both quality and safety of patient care as well as the need for reduced costs of care. The geriatric fracture center model of care is one such model reported to improve both outcomes and quality of care. It is a lean business model applied to medicine. This article describes basic lean business concepts applied to geriatric fracture care and information needed to successfully implement a geriatric fracture center. It is written to assist physicians and surgeons in their efforts to implement an improved care model for their patients. Copyright © 2014 Elsevier Inc. All rights reserved.
Discrete fracture modeling of hydro-mechanical damage processes in geological systems
Kim, K.; Rutqvist, J.; Houseworth, J. E.; Birkholzer, J. T.
2014-12-01
This study presents a modeling approach for investigating coupled thermal-hydrological-mechanical (THM) behavior, including fracture development, within geomaterials and structures. In the model, the coupling procedure consists of an effective linkage between two codes: TOUGH2, a simulator of subsurface multiphase flow and mass transport based on the finite volume approach; and an implementation of the rigid-body-spring network (RBSN) method, a discrete (lattice) modeling approach to represent geomechanical behavior. One main advantage of linking these two codes is that they share the same geometrical mesh structure based on the Voronoi discretization, so that a straightforward representation of discrete fracture networks (DFN) is available for fluid flow processes. The capabilities of the TOUGH-RBSN model are demonstrated through simulations of hydraulic fracturing, where fluid pressure-induced fracturing and damage-assisted flow are well represented. The TOUGH-RBSN modeling methodology has been extended to enable treatment of geomaterials exhibiting anisotropic characteristics. In the RBSN approach, elastic spring coefficients and strength parameters are systematically formulated based on the principal bedding direction, which facilitate a straightforward representation of anisotropy. Uniaxial compression tests are simulated for a transversely isotropic material to validate the new modeling scheme. The model is also used to simulate excavation fracture damage for the HG-A microtunnel in the Opalinus Clay rock, located at the Mont Terri underground research laboratory (URL) near Saint-Ursanne, Switzerland. The Opalinus Clay has transversely isotropic material properties caused by natural features such as bedding, foliation, and flow structures. Preferential fracturing and tunnel breakouts were observed following excavation, which are believed to be strongly influenced by the mechanical anisotropy of the rock material. The simulation results are qualitatively
Poroelastic modeling of seismic boundary conditions across a fracture.
Nakagawa, Seiji; Schoenberg, Michael A
2007-08-01
Permeability of a fracture can affect how the fracture interacts with seismic waves. To examine this effect, a simple mathematical model that describes the poroelastic nature of wave-fracture interaction is useful. In this paper, a set of boundary conditions is presented which relate wave-induced particle velocity (or displacement) and stress including fluid pressure across a compliant, fluid-bearing fracture. These conditions are derived by modeling a fracture as a thin porous layer with increased compliance and finite permeability. Assuming a small layer thickness, the boundary conditions can be derived by integrating the governing equations of poroelastic wave propagation. A finite jump in the stress and velocity across a fracture is expressed as a function of the stress and velocity at the boundaries. Further simplification for a thin fracture yields a set of characteristic parameters that control the seismic response of single fractures with a wide range of mechanical and hydraulic properties. These boundary conditions have potential applications in simplifying numerical models such as finite-difference and finite-element methods to compute seismic wave scattering off nonplanar (e.g., curved and intersecting) fractures.
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.
Energy Technology Data Exchange (ETDEWEB)
Wiggins, Michael L.; Brown, Raymon L.; Civan, Frauk; Hughes, Richard G.
2001-08-15
Research continues on characterizing and modeling the behavior of naturally fractured reservoir systems. Work has progressed on developing techniques for estimating fracture properties from seismic and well log data, developing naturally fractured wellbore models, and developing a model to characterize the transfer of fluid from the matrix to the fracture system for use in the naturally fractured reservoir simulator.
Creep and fracture of a model yoghurt
Manneville, Sebastien; Leocmach, Mathieu; Perge, Christophe; Divoux, Thibaut
2014-11-01
Biomaterials such as protein or polysaccharide gels are known to behave qualitatively as soft solids and to rupture under an external load. Combining optical and ultrasonic imaging to shear rheology we show that the failure scenario of a model yoghurt, namely a casein gel, is reminiscent of brittle solids: after a primary creep regime characterized by a macroscopically homogeneous deformation and a power-law behavior which exponent is fully accounted for by linear viscoelasticity, fractures nucleate and grow logarithmically perpendicularly to shear, up to the sudden rupture of the gel. A single equation accounting for those two successive processes nicely captures the full rheological response. The failure time follows a decreasing power-law with the applied shear stress, similar to the Basquin law of fatigue for solids. These results are in excellent agreement with recent fiber-bundle models that include damage accumulation on elastic fibers and exemplify protein gels as model, brittle-like soft solids. Work funded by the European Research Council under Grant Agreement No. 258803.
Models of educational institutions' networking
Shilova Olga Nikolaevna
2015-01-01
The importance of educational institutions' networking in modern sociocultural conditions and a definition of networking in education are presented in the article. The results of research levels, methods and models of educational institutions' networking are presented and substantially disclosed.
Models of educational institutions' networking
Shilova Olga Nikolaevna
2015-01-01
The importance of educational institutions' networking in modern sociocultural conditions and a definition of networking in education are presented in the article. The results of research levels, methods and models of educational institutions' networking are presented and substantially disclosed.
Three-Dimensional Modeling of Fracture Clusters in Geothermal Reservoirs
Energy Technology Data Exchange (ETDEWEB)
Ghassemi, Ahmad [Univ. of Oklahoma, Norman, OK (United States)
2017-08-11
The objective of this is to develop a 3-D numerical model for simulating mode I, II, and III (tensile, shear, and out-of-plane) propagation of multiple fractures and fracture clusters to accurately predict geothermal reservoir stimulation using the virtual multi-dimensional internal bond (VMIB). Effective development of enhanced geothermal systems can significantly benefit from improved modeling of hydraulic fracturing. In geothermal reservoirs, where the temperature can reach or exceed 350oC, thermal and poro-mechanical processes play an important role in fracture initiation and propagation. In this project hydraulic fracturing of hot subsurface rock mass will be numerically modeled by extending the virtual multiple internal bond theory and implementing it in a finite element code, WARP3D, a three-dimensional finite element code for solid mechanics. The new constitutive model along with the poro-thermoelastic computational algorithms will allow modeling the initiation and propagation of clusters of fractures, and extension of pre-existing fractures. The work will enable the industry to realistically model stimulation of geothermal reservoirs. The project addresses the Geothermal Technologies Office objective of accurately predicting geothermal reservoir stimulation (GTO technology priority item). The project goal will be attained by: (i) development of the VMIB method for application to 3D analysis of fracture clusters; (ii) development of poro- and thermoelastic material sub-routines for use in 3D finite element code WARP3D; (iii) implementation of VMIB and the new material routines in WARP3D to enable simulation of clusters of fractures while accounting for the effects of the pore pressure, thermal stress and inelastic deformation; (iv) simulation of 3D fracture propagation and coalescence and formation of clusters, and comparison with laboratory compression tests; and (v) application of the model to interpretation of injection experiments (planned by our
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
A Graph Theoretic Approach for Hydraulic Fracturing and Wellbore Leakage Risk Modeling
Glosser, D.; Rose, K.; Bauer, J. R.; Warner, T.
2016-12-01
Recent large scale development of unconventional formations for fossil energy has raised concerns over the potential for fluid leakage between subsurface systems and wellbores. This is particularly true in regions with extensive drilling history, where spatial densities of wellbores are higher, and where significant uncertainties in the location and mechanical integrity of such wellbores exist. The generation of induced fracture networks during hydraulic fracturing may increase subsurface connectivity, and create the potential for unwanted fluid migration between operational and legacy wellbores and subsurface fracture networks. We present a graph theoretic approach for identifying geospatial regions and wellbores at increased risk for subsurface connectivity based on wellbore proximity and local geologic characteristics. The algorithm transforms user inputted geospatial data (geologic and wellbore x,y,z) to graph structure, where wellbores are represented as nodes, and where potential overlapping fracture network zones are represented as edges. The algorithm can be used to complement existing fracture models to better account for the reach of induced fractures, and to identify spatial extents at increased risk for unwanted subsurface connectivity. Additionally, the model can be used to identify regions in need of geophysical detection methods for locating undocumented wells. As a result, the method can be part of a cumulative strategy to reduce uncertainty inherent to combined geologic and engineered systems. The algorithm has been successfully tested against a known leakage scenario in Pennsylvania. In addition to identifying wells associated with the leakage event, the algorithm identified two other higher risk networks in the region. The algorithm output provides valuable information for industry to develop environmentally safe drilling and injection plans; and for regulators to identify specific wellbores at greater risk for leakage, and to develop targeted
Fracture and ductile vs. brittle behavior -- Theory, modeling and experiment
Energy Technology Data Exchange (ETDEWEB)
Beltz, G.E. [ed.] [Univ. of California, Santa Barbara, CA (United States); Selinger, R.L.B. [ed.] [Catholic Univ., Washington, DC (United States); Kim, K.S. [ed.] [Brown Univ., Providence, RI (United States); Marder, M.P. [ed.] [Univ. of Texas, Austin, TX (United States)
1999-08-01
The symposium brought together the many communities that investigate the fundamentals of fracture, with special emphasis on the ductile/brittle transition across a broad spectrum of material classes, fracture at interfaces, and modelling fracture over various length scales. Theoretical techniques discussed ranged from first-principles electronic structure theory to atomistic simulation to mesoscale and continuum theories, along with studies of fractals and scaling in fracture. Experimental and theoretical talks were interspersed throughout all sessions, rather than being segregated. The contributions to this volume generally follow the topical outline upon which the symposium was organized. The first part, dealing with ductile vs. brittle behavior in metals, concerns itself with investigations of high-strength steel, magnesium alloys, ordered intermetallics, and Fe-Cr-Al alloys. The development of analytical methods based on micromechanical models, such as dislocation mechanics and cohesive/contact zone models, are covered in a follow-up section. Nonmetals, including silicon, are considered in Parts 3 and 4. Fractals, chaos, and scaling theories are taken up in Part 5, with a special emphasis on fracture in heterogeneous solids. Modelling based on large populations of dislocations has substantially progressed during the past three years; hence, a section devoted to crystal plasticity and mesoscale dislocation modelling appears next. Finally, the technologically significant area of interfacial fracture, with applications to composites and intergranular fracture, is taken up in Part 7. Separate abstracts were prepared for most of the papers in this book.
Developing fracture density models using terrestrial laser scan data
Pollyea, R.; Fairley, J. P.; Podgorney, R. K.; McLing, T. L.
2010-12-01
Characterizing fracture heterogeneity for subsurface flow and transport modeling has been of interest to the hydrogeologic community for many years. Currently, stochastic continuum and discrete fracture representations have come to be accepted as two of the most commonly used tools for incorporating fracture heterogeneity into subsurface flow and transport models. In this research, ground-based lidar data are used to model the surface roughness of vertical basalt exposures in the East Snake River Plain, Idaho (ESRP) as a surrogate for fracture density. The surface roughness is modeled by discretizing the dataset over a regular grid and fitting a regression plane to each gridblock. The standard deviation of distance from the block data to the regression plane is then assumed to represent a measure of roughness for each gridblock. Two-dimensional plots of surface roughness from ESRP exposures indicate discrete fractures can be quantitatively differentiated from unfractured rock at 0.25- meter resolution. This methodology may have broad applications for characterizing fracture heterogeneity. One application, demonstrated here, is to capture high resolution (low noise) covariance statistics for building stochastic property sets to be used in large scale flow simulations. Additional applications may include using surface roughness datasets as training images for multiple-point geostatistics analysis and for constraining discrete fracture models.
Numerical modeling of multiphase flow in rough and propped fractures
Dabrowski, Marcin; Dzikowski, Michał; Jasinski, Lukasz; Olkiewicz, Piotr
2017-04-01
crystalline rocks. The detailed pattern of flow paths and effective fracture conductivity are largely dependent on the level of confining stresses and fracture wall roughness, which both determine the shape and distribution of fracture apertures and contact areas. The distribution of proppant grains, which are used to maintain apertures of hydraulic fractures, is a key factor governing fracture flow in industrial applications. The flow of multiphase fluids in narrow apertures of rock fractures may substantially differ from the flow of a single-phase fluid. For example, multiphase flow effects play an important role during all stages of unconventional reservoir life cycle. Multiphase flow conditions are also expected to prevail in high temperature geothermal fields and during the transport of non aqueous phase liquid contaminants in groundwaters. We use direct numerical simulations to study single- and multiphase flow in rough and propped fractures. We compute the fluid flow using either the finite element or the lattice Boltzmann method. Body-fitting, unstructured computational meshes are used to improve the numerical accuracy. The fluid-fluid and fluid-solid interfaces are directly resolved and an implicit approach to surface tension is used to alleviate restrictions due to capillary CFL condition. In FEM simulations, the Beltrami-Laplace operator is integrated by parts to avoid interface curvature computation during evaluation of the surface tension term. We derive and validate an upscaled approach to Stokes flow in propped and rough fractures. Our upscaled 2.5D fracture flow model features a Brinkman term and is capable of treating no-slip boundary conditions on the rims of proppant grains and fracture wall contact areas. The Stokes-Brinkman fracture flow model provides an improvement over the Reynolds model, both in terms of the effective fracture permeability and the local flow pattern. We present numerical and analytical models for the propped fracture
Mechanical transport in two-dimensional networks of fractures
Energy Technology Data Exchange (ETDEWEB)
Endo, H.K.
1984-04-01
The objectives of this research are to evaluate directional mechanical transport parameters for anisotropic fracture systems, and to determine if fracture systems behave like equivalent porous media. The tracer experiments used to measure directional tortuosity, longitudinal geometric dispersivity, and hydraulic effective porosity are conducted with a uniform flow field and measurements are made from the fluid flowing within a test section where linear length of travel is constant. Since fluid flow and mechanical transport are coupled processes, the directional variations of specific discharge and hydraulic effective porosity are measured in regions with constant hydraulic gradients to evaluate porous medium equivalence for the two processes, respectively. If the fracture region behaves like an equivalent porous medium, the system has the following stable properties: (1) specific discharge is uniform in any direction and can be predicted from a permeability tensor; and (2) hydraulic effective porosity is directionally stable. Fracture systems with two parallel sets of continuous fractures satisfy criterion 1. However, in these systems hydraulic effective porosity is directionally dependent, and thus, criterion 2 is violated. Thus, for some fracture systems, fluid flow can be predicted using porous media assumptions, but it may not be possible to predict transport using porous media assumptions. Two discontinuous fracture systems were studied which satisfied both criteria. Hydraulic effective porosity for both systems has a value between rock effective porosity and total porosity. A length-density analysis (LDS) of Canadian fracture data shows that porous media equivalence for fluid flow and transport is likely when systems have narrow aperture distributions. 54 references, 90 figures, 7 tables.
A hybrid mortar virtual element method for discrete fracture network simulations
Benedetto, Matías Fernando; Berrone, Stefano; Borio, Andrea; Pieraccini, Sandra; Scialò, Stefano
2016-02-01
The most challenging issue in performing underground flow simulations in Discrete Fracture Networks (DFN) is to effectively tackle the geometrical difficulties of the problem. In this work we put forward a new application of the Virtual Element Method combined with the Mortar method for domain decomposition: we exploit the flexibility of the VEM in handling polygonal meshes in order to easily construct meshes conforming to the traces on each fracture, and we resort to the mortar approach in order to "weakly" impose continuity of the solution on intersecting fractures. The resulting method replaces the need for matching grids between fractures, so that the meshing process can be performed independently for each fracture. Numerical results show optimal convergence and robustness in handling very complex geometries.
Directed network discovery with dynamic network modelling.
Anzellotti, Stefano; Kliemann, Dorit; Jacoby, Nir; Saxe, Rebecca
2017-05-01
Cognitive tasks recruit multiple brain regions. Understanding how these regions influence each other (the network structure) is an important step to characterize the neural basis of cognitive processes. Often, limited evidence is available to restrict the range of hypotheses a priori, and techniques that sift efficiently through a large number of possible network structures are needed (network discovery). This article introduces a novel modelling technique for network discovery (Dynamic Network Modelling or DNM) that builds on ideas from Granger Causality and Dynamic Causal Modelling introducing three key changes: (1) efficient network discovery is implemented with statistical tests on the consistency of model parameters across participants, (2) the tests take into account the magnitude and sign of each influence, and (3) variance explained in independent data is used as an absolute (rather than relative) measure of the quality of the network model. In this article, we outline the functioning of DNM, we validate DNM in simulated data for which the ground truth is known, and we report an example of its application to the investigation of influences between regions during emotion recognition, revealing top-down influences from brain regions encoding abstract representations of emotions (medial prefrontal cortex and superior temporal sulcus) onto regions engaged in the perceptual analysis of facial expressions (occipital face area and fusiform face area) when participants are asked to switch between reporting the emotional valence and the age of a face. Copyright © 2017 Elsevier Ltd. All rights reserved.
Fractal characterization of fracture networks: An improved box-counting technique
Roy, Ankur; Perfect, Edmund; Dunne, William M.; McKay, Larry D.
2007-12-01
Box counting is widely used for characterizing fracture networks as fractals and estimating their fractal dimensions (D). If this analysis yields a power law distribution given by N ∝ r-D, where N is the number of boxes containing one or more fractures and r is the box size, then the network is considered to be fractal. However, researchers are divided in their opinion about which is the best box-counting algorithm to use, or whether fracture networks are indeed fractals. A synthetic fractal fracture network with a known D value was used to develop a new algorithm for the box-counting method that returns improved estimates of D. The method is based on identifying the lower limit of fractal behavior (rcutoff) using the condition ds/dr → 0, where s is the standard deviation from a linear regression equation fitted to log(N) versus log(r) with data for r sequentially excluded. A set of 7 nested fracture maps from the Hornelen Basin, Norway was used to test the improved method and demonstrate its accuracy for natural patterns. We also reanalyzed a suite of 17 fracture trace maps that had previously been evaluated for their fractal nature. The improved estimates of D for these maps ranged from 1.56 ± 0.02 to 1.79 ± 0.02, and were much greater than the original estimates. These higher D values imply a greater degree of fracture connectivity and thus increased propensity for fracture flow and the transport of miscible or immiscible chemicals.
Adaptive Multiscale Modeling of Geochemical Impacts on Fracture Evolution
Molins, S.; Trebotich, D.; Steefel, C. I.; Deng, H.
2016-12-01
Understanding fracture evolution is essential for many subsurface energy applications, including subsurface storage, shale gas production, fracking, CO2 sequestration, and geothermal energy extraction. Geochemical processes in particular play a significant role in the evolution of fractures through dissolution-driven widening, fines migration, and/or fracture sealing due to precipitation. One obstacle to understanding and exploiting geochemical fracture evolution is that it is a multiscale process. However, current geochemical modeling of fractures cannot capture this multi-scale nature of geochemical and mechanical impacts on fracture evolution, and is limited to either a continuum or pore-scale representation. Conventional continuum-scale models treat fractures as preferential flow paths, with their permeability evolving as a function (often, a cubic law) of the fracture aperture. This approach has the limitation that it oversimplifies flow within the fracture in its omission of pore scale effects while also assuming well-mixed conditions. More recently, pore-scale models along with advanced characterization techniques have allowed for accurate simulations of flow and reactive transport within the pore space (Molins et al., 2014, 2015). However, these models, even with high performance computing, are currently limited in their ability to treat tractable domain sizes (Steefel et al., 2013). Thus, there is a critical need to develop an adaptive modeling capability that can account for separate properties and processes, emergent and otherwise, in the fracture and the rock matrix at different spatial scales. Here we present an adaptive modeling capability that treats geochemical impacts on fracture evolution within a single multiscale framework. Model development makes use of the high performance simulation capability, Chombo-Crunch, leveraged by high resolution characterization and experiments. The modeling framework is based on the adaptive capability in Chombo
Radon transport in fractured soil. Laboratory experiments and modelling
Energy Technology Data Exchange (ETDEWEB)
Hoff, A.
1997-10-01
Radon (Rn-222) transport in fractured soil has been investigated by laboratory experiments and by modelling. Radon transport experiments have been performed with two sand columns (homogeneous and inhomogeneous) and one undisturbed clayey till column containing a net of preferential flow paths (root holes). A numerical model (the finite-element model FRACTRAN) and an analytic model (a pinhole model) have been applied in simulations if soil gas and radon transport in fractured soil. Experiments and model calculations are included in a discussion of radon entry rates into houses placed on fractured soil. The main conclusion is, that fractures does not in general alter transport of internally generated radon out of soil, when the pressure and flow conditions in the soil is comparable to the conditions prevailing under a house. This indicates the important result, that fractures in soil have no impact on radon entry into a house beyond that of an increased gas permeability, but a more thorough investigation of this subject is needed. Only in the case where the soil is exposed to large pressure gradients, relative to gradients induced by a house, may it be possible to observe effects of radon exchange between fractures and matrix. (au) 52 tabs., 60 ill., 5 refs.
A Modeling Approach to Fiber Fracture in Melt Impregnation
Ren, Feng; Zhang, Cong; Yu, Yang; Xin, Chunling; Tang, Ke; He, Yadong
2017-02-01
The effect of process variables such as roving pulling speed, melt temperature and number of pins on the fiber fracture during the processing of thermoplastic based composites was investigated in this study. The melt impregnation was used in this process of continuous glass fiber reinforced thermoplastic composites. Previous investigators have suggested a variety of models for melt impregnation, while comparatively little effort has been spent on modeling the fiber fracture caused by the viscous resin. Herein, a mathematical model was developed for impregnation process to predict the fiber fracture rate and describe the experimental results with the Weibull intensity distribution function. The optimal parameters of this process were obtained by orthogonal experiment. The results suggest that the fiber fracture is caused by viscous shear stress on fiber bundle in melt impregnation mold when pulling the fiber bundle.
Cheng, Xiang; Zhang, Qiquan; Yu, Xiangjiang; Du, Wei; Liu, Runchao; Bian, Qing; Wang, Zhendong; Zhang, Tuo; Guo, Zhaojie
2017-01-01
The Huangshi structure, as one of the NWW-trending S-shaped structures in the southwestern Qaidam Basin, holds important implications for unraveling the regional structural pattern. There are four dominant sets of surface strike-slip fractures at the core of the Huangshi structure. The fractures with orientations of N28°E, N47°E and N65°E correlate well with conjugate Riedel shears (R‧), tension fractures (T) and Riedel shears (R) in the Riedel shear model, respectively. Two conjugate strike-slip fracture sets occur at the surface of the Hongpan structure (secondary to the Huangshi structure) and the southwestern part of the Huangshi structure. In seismic sections, the Huangshi structure is present as a positive flower or Y-shaped structure governed by steeply dipping faults, whereas Hongpan and Xiaoshaping structures, located symmetrically to the Huangshi structure, are thrust-controlled anticlines. The Riedel shear pattern of surface strike-slip fractures, the positive flower or Y-shaped structure in seismic sections and the NW-trending secondary compressional anticlines consistently demonstrate that the Huangshi structure is dominated by left-lateral strike-slip faults which comprise a strike-slip fault network. Considering the similar S-shaped configuration and NWW trend of structures across the southwestern Qaidam Basin, it can be further speculated that these structures are also predominantly of left-lateral strike-slip types.
Fictitious Crack Model of Concrete Fracture
DEFF Research Database (Denmark)
Brincker, Rune; Dahl, H.
1989-01-01
The substructure method introduced by Petersson is reformulated for the three-point bending specimen in order to obtain complete load-displacement relations without significant truncation. The problem of instability caused by the linearization of the softening in the fracture zone is discussed......, and an alternative energy formulation is given so that it is possible to distinguish between stable and unstable situations. The reformulated substructure method is implemented on computer to give a multilinear stress crack opening displacement relation for the material in the fracture zone, and some qualitative...
Network Meta-Analysis of Pharmacological Agents for Osteoporosis Treatment and Fracture Prevention
Directory of Open Access Journals (Sweden)
Xu-cheng Yang
2016-12-01
Full Text Available Background and Objective: Osteoporosis afflicts a large number of populations in the world and is featured by systemic impairment of bone mass and strength which may further trigger an increase in the risk of fragile fractures. This network meta-analysis (NMA is designed to distinguish therapies more preferable than others with respect to efficacy and safety. Methods: We searched the medical literature for relevant studies systematically. Both direct and indirect evidence were synthesized to compare the efficacy, described by odds ratios (OR and 95% credible intervals (CrI. Moreover, the surface under cumulative ranking curve was calculated to rank probabilities with respect to clinical outcomes. The new non-vertebral fractures, hip and wrist fractures, and adverse events were evaluated in this NMA. Results: Patients treated by alendronate, denosumab, teriparatide were associated with a reduced risk of new non-vertebral fractures compared to those treated by placebo. Alendronate, denosumab and zoledronic acid had better efficacy in preventing hip fractures. With respect to wrist fractures prevention, no significant difference was observed. Zoledronic acid exhibited significantly increased risk of adverse events than placebo, alendronate, denosumab, and raloxifene. According to SUCRA, teriparatide ranked highest in new non-vertebral fractures prevention, etidronate and denosumab balanced safety and efficacy well. Conclusion: In summary, teriparatide appeared to be the most efficacious drug for preventing new non-vertebral fractures, while etidronate and denosumab were preferable for balancing safety and efficacy well.
Tyukhova, A.; Castineira, D.; Juanes, R.
2016-12-01
Triggered and induced seismicity is at the cornerstone of discussions surrounding a wide range of subsurface technologies, e.g. unconventional hydrocarbon recovery, geologic carbon sequestration, underground gas storage, and geothermal energy extraction. We revisit the geothermal experiment in Basel, Switzerland, in which over 11 thousand cubic meters of water were injected into deep fractured crystalline rock. The injection took place in December 2006 and was performed at a single injection well, in three stages with increasing injection rate. Seismicity in the region increased during the experiment—with most of the seismic events occurring in the month following injection—and declined slowly after, but with seismic events still being recorded years after injection. The increase in seismicity is caused by reactivation of the pre-existing fractures: an increase in pore pressure decreases the normal effective stress across the fracture, which according to the Mohr-Coulomb failure criterion are therefore more prone to slip. The underlying processes, however, may be more complex. It is unclear the role that enhanced hydraulic connectivity in the fracture network plays on triggered seismicity, and on the emergence of seismicity clusters in space. It is also unclear what determines the delay between injection and recorded seismicity, and whether it can be explained by means of pressure propagation and/or dynamic weakening of fractures due to a drop in the friction coefficient as a result of decreased roughness from fracture slip. Here, we employ a computational model of coupled flow and geomechanics to quantitatively assess the impact of fluid injection on the recorded seismicity. We develop a simulation model that incorporates more than ten fractures, whose location, rake and dip are consistent with clusters of seismicity from a relocation of hypocenters and focal mechanisms. We adopt a multiscale description of flow (representing these fractures planes explicitly
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 elastic tensile fractures in snow using nonlocal damage mechanics
Borstad, C. P.; McClung, D. M.
2011-12-01
The initiation and propagation of tensile fractures in snow and ice are fundamental to numerous important physical processes in the cryosphere, from iceberg calving to ice shelf rift propagation to slab avalanche release. The heterogeneous nature of snow and ice, their proximity to the melting temperature, and the varied governing timescales typically lead to nonlinear fracture behavior which does not follow the predictions of Linear Elastic Fracture Mechanics (LEFM). Furthermore, traditional fracture mechanics is formally inapplicable for predicting crack initiation in the absence of a pre-existing flaw or stress concentration. An alternative to fracture mechanics is continuum damage mechanics, which accounts for the material degradation associated with cracking in a numerically efficient framework. However, damage models which are formulated locally (e.g. stress and strain are defined as point properties) suffer from mesh-sensitive crack trajectories, spurious localization of damage and improper fracture energy dissipation with mesh refinement. Nonlocal formulations of damage, which smear the effects of the material heterogeneity over an intrinsic length scale related to the material microstructure, overcome these difficulties and lead to numerically efficient and mesh-objective simulations of the tensile failure of heterogeneous materials. We present the results of numerical simulations of tensile fracture initiation and propagation in cohesive snow using a nonlocal damage model. Seventeen beam bending experiments, both notched and unnotched, were conducted using blocks of cohesive dry snow extracted from an alpine snowpack. Material properties and fracture parameters were calculated from the experimental data using beam theory and quasi-brittle fracture mechanics. Using these parameters, a nonlocal isotropic damage model was applied to two-dimensional finite element meshes of the same scale as the experiments. The model was capable of simulating the propagation
Coevolutionary modeling in network formation
Al-Shyoukh, Ibrahim
2014-12-03
Network coevolution, the process of network topology evolution in feedback with dynamical processes over the network nodes, is a common feature of many engineered and natural networks. In such settings, the change in network topology occurs at a comparable time scale to nodal dynamics. Coevolutionary modeling offers the possibility to better understand how and why network structures emerge. For example, social networks can exhibit a variety of structures, ranging from almost uniform to scale-free degree distributions. While current models of network formation can reproduce these structures, coevolutionary modeling can offer a better understanding of the underlying dynamics. This paper presents an overview of recent work on coevolutionary models of network formation, with an emphasis on the following three settings: (i) dynamic flow of benefits and costs, (ii) transient link establishment costs, and (iii) latent preferential attachment.
A first order system model of fracture healing
Institute of Scientific and Technical Information of China (English)
WANG Xiao-ping; ZHANG Xian-long; LI Zhu-guo; YU Xin-gang
2005-01-01
A first order system model is proposed for simulating the influence of stress stimulation on fracture strength during fracture healing. To validate the model, the diaphyses of bilateral tibiae in 70 New Zealand rabbits were osteotomized and fixed with rigid plates and stress-relaxation plates, respectively. Stress shielding rate and ultimate bending strength of the healing bone were measured at 2 to 48 weeks postoperatively. Ratios of stress stimulation and fracture strength of the healing bone to those of intact bone were taken as the system input and output. The assumed first order system model can approximate the experimental data on fracture strength from the input of stress stimulation over time, both for the rigid plate group and the stress-relaxation plate group, with different system parameters of time constant and gain. The fitting curve indicates that the effect of mechanical stimulus occurs mainly in late stages of healing. First order system can model the stress adaptation process of fracture healing. This approach presents a simple bio-mathematical model of the relationship between stress stimulation and fracture strength, and has the potential to optimize planning of functional exercises and conduct parametric studies.
Groundwater degassing in fractured rock: Modelling and data comparison
Energy Technology Data Exchange (ETDEWEB)
Jarsjoe, J.; Destouni, G. [Royal Inst. of Tech., Stockholm (Sweden). Water Resources Engineering
1998-11-01
Dissolved gas may be released from deep groundwater in the vicinity of open boreholes and drifts, where the water pressures are relatively low. Degassing of groundwater may influence observations of hydraulic conditions made in drifts, interpretation of experiments performed close to drifts, and buffer mass and backfill performance, particularly during emplacement and repository closure. Under certain conditions, considerable fracture inflow and transmissivity reductions have been observed during degassing experiments in the field and in the laboratory; such reductions affect the outcome and interpretation of both hydraulic and tracer tests. We develop models for the estimation of the resulting degree of fracture gas saturation and the associated transmissivity reduction due to groundwater degassing in fractured rock. Derived expressions for bubble trapping probability show that fracture aperture variability and correlation length influence the conditions for capillary bubble trapping and gas accumulation. The laboratory observations of bubble trapping in an Aespoe fracture replica are consistent with the prediction of a relatively high probability of bubble trapping in this fracture. The prediction was based on the measured aperture distribution of the Aespoe fracture and the applied hydraulic gradient. Results also show that the conceptualisation of gas and water occupancy in a fracture greatly influences model predictions of gas saturation and relative transmissivity. Images from laboratory degassing experiments indicate that tight apertures are completely filled with water, whereas both gas and water exist in wider apertures under degassing conditions; implementation of this relation in our model resulted in the best agreement between predictions and laboratory observations. Model predictions for conditions similar to those prevailing in field for single fractures at great depths indicate that degassing effects in boreholes should generally be small, unless the
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.
Relating Cohesive Zone Model to Linear Elastic Fracture Mechanics
Wang, John T.
2010-01-01
The conditions required for a cohesive zone model (CZM) to predict a failure load of a cracked structure similar to that obtained by a linear elastic fracture mechanics (LEFM) analysis are investigated in this paper. This study clarifies why many different phenomenological cohesive laws can produce similar fracture predictions. Analytical results for five cohesive zone models are obtained, using five different cohesive laws that have the same cohesive work rate (CWR-area under the traction-separation curve) but different maximum tractions. The effect of the maximum traction on the predicted cohesive zone length and the remote applied load at fracture is presented. Similar to the small scale yielding condition for an LEFM analysis to be valid. the cohesive zone length also needs to be much smaller than the crack length. This is a necessary condition for a CZM to obtain a fracture prediction equivalent to an LEFM result.
Energy Technology Data Exchange (ETDEWEB)
Cotte, F.P.; Doughty, C.; Birkholzer, J.
2010-11-01
The ability to reliably predict flow and transport in fractured porous rock is an essential condition for performance evaluation of geologic (underground) nuclear waste repositories. In this report, a suite of programs (TRIPOLY code) for calculating and analyzing flow and transport in two-dimensional fracture-matrix systems is used to model single-well injection-withdrawal (SWIW) tracer tests. The SWIW test, a tracer test using one well, is proposed as a useful means of collecting data for site characterization, as well as estimating parameters relevant to tracer diffusion and sorption. After some specific code adaptations, we numerically generated a complex fracture-matrix system for computation of steady-state flow and tracer advection and dispersion in the fracture network, along with solute exchange processes between the fractures and the porous matrix. We then conducted simulations for a hypothetical but workable SWIW test design and completed parameter sensitivity studies on three physical parameters of the rock matrix - namely porosity, diffusion coefficient, and retardation coefficient - in order to investigate their impact on the fracture-matrix solute exchange process. Hydraulic fracturing, or hydrofracking, is also modeled in this study, in two different ways: (1) by increasing the hydraulic aperture for flow in existing fractures and (2) by adding a new set of fractures to the field. The results of all these different tests are analyzed by studying the population of matrix blocks, the tracer spatial distribution, and the breakthrough curves (BTCs) obtained, while performing mass-balance checks and being careful to avoid some numerical mistakes that could occur. This study clearly demonstrates the importance of matrix effects in the solute transport process, with the sensitivity studies illustrating the increased importance of the matrix in providing a retardation mechanism for radionuclides as matrix porosity, diffusion coefficient, or retardation
Model Diagnostics for Bayesian Networks
Sinharay, Sandip
2006-01-01
Bayesian networks are frequently used in educational assessments primarily for learning about students' knowledge and skills. There is a lack of works on assessing fit of Bayesian networks. This article employs the posterior predictive model checking method, a popular Bayesian model checking tool, to assess fit of simple Bayesian networks. A…
Sensitivity Analysis of the Bone Fracture Risk Model
Lewandowski, Beth; Myers, Jerry; Sibonga, Jean Diane
2017-01-01
Introduction: The probability of bone fracture during and after spaceflight is quantified to aid in mission planning, to determine required astronaut fitness standards and training requirements and to inform countermeasure research and design. Probability is quantified with a probabilistic modeling approach where distributions of model parameter values, instead of single deterministic values, capture the parameter variability within the astronaut population and fracture predictions are probability distributions with a mean value and an associated uncertainty. Because of this uncertainty, the model in its current state cannot discern an effect of countermeasures on fracture probability, for example between use and non-use of bisphosphonates or between spaceflight exercise performed with the Advanced Resistive Exercise Device (ARED) or on devices prior to installation of ARED on the International Space Station. This is thought to be due to the inability to measure key contributors to bone strength, for example, geometry and volumetric distributions of bone mass, with areal bone mineral density (BMD) measurement techniques. To further the applicability of model, we performed a parameter sensitivity study aimed at identifying those parameter uncertainties that most effect the model forecasts in order to determine what areas of the model needed enhancements for reducing uncertainty. Methods: The bone fracture risk model (BFxRM), originally published in (Nelson et al) is a probabilistic model that can assess the risk of astronaut bone fracture. This is accomplished by utilizing biomechanical models to assess the applied loads; utilizing models of spaceflight BMD loss in at-risk skeletal locations; quantifying bone strength through a relationship between areal BMD and bone failure load; and relating fracture risk index (FRI), the ratio of applied load to bone strength, to fracture probability. There are many factors associated with these calculations including
El-Amin, Mohamed F.
2017-06-06
Recently, applications of nanoparticles have been considered in many branches of petroleum engineering, especially, enhanced oil recovery. The current paper is devoted to investigate the problem of nanoparticles transport in fractured porous media, numerically. We employed the discrete-fracture model (DFM) to represent the flow and transport in the fractured formations. The system of the governing equations consists of the mass conservation law, Darcy\\'s law, nanoparticles concentration in water, deposited nanoparticles concentration on the pore-wall, and entrapped nanoparticles concentration in the pore-throat. The variation of porosity and permeability due to the nanoparticles deposition/entrapment on/in the pores is also considered. We employ the multiscale time-splitting strategy to control different time-step sizes for different physics, such as pressure and concentration. The cell-centered finite difference (CCFD) method is used for the spatial discretization. Numerical examples are provided to demonstrate the efficiency of the proposed multiscale time splitting approach.
Numerical simulation on ferrofluid flow in fractured porous media based on discrete-fracture model
Huang, Tao; Yao, Jun; Huang, Zhaoqin; Yin, Xiaolong; Xie, Haojun; Zhang, Jianguang
2017-06-01
Water flooding is an efficient approach to maintain reservoir pressure and has been widely used to enhance oil recovery. However, preferential water pathways such as fractures can significantly decrease the sweep efficiency. Therefore, the utilization ratio of injected water is seriously affected. How to develop new flooding technology to further improve the oil recovery in this situation is a pressing problem. For the past few years, controllable ferrofluid has caused the extensive concern in oil industry as a new functional material. In the presence of a gradient in the magnetic field strength, a magnetic body force is produced on the ferrofluid so that the attractive magnetic forces allow the ferrofluid to be manipulated to flow in any desired direction through the control of the external magnetic field. In view of these properties, the potential application of using the ferrofluid as a new kind of displacing fluid for flooding in fractured porous media is been studied in this paper for the first time. Considering the physical process of the mobilization of ferrofluid through porous media by arrangement of strong external magnetic fields, the magnetic body force was introduced into the Darcy equation and deals with fractures based on the discrete-fracture model. The fully implicit finite volume method is used to solve mathematical model and the validity and accuracy of numerical simulation, which is demonstrated through an experiment with ferrofluid flowing in a single fractured oil-saturated sand in a 2-D horizontal cell. At last, the water flooding and ferrofluid flooding in a complex fractured porous media have been studied. The results showed that the ferrofluid can be manipulated to flow in desired direction through control of the external magnetic field, so that using ferrofluid for flooding can raise the scope of the whole displacement. As a consequence, the oil recovery has been greatly improved in comparison to water flooding. Thus, the ferrofluid
de La Bernardie, Jérôme; Bour, Olivier; de Dreuzy, Jean-Raynald; Guihéneuf, Nicolas; Chatton, Eliot; Labasque, Thierry; Le Borgne, Tanguy
2017-04-01
Geothermal energy is a renewable energy source particularly attractive due to associated low greenhouse gas emission rates. Crystalline rocks are in general considered of poor interest for geothermal applications at shallow depths (energy storage at these shallow depths is still remaining very challenging because of the low storativity of the medium. Within this framework, the purpose of this study is to test the possibility of efficient thermal energy storage in shallow fractured rocks. For doing so, several heat tracer tests have been carried on in a single well between two connected fractures. We completed this experimental work with numerical modeling of thermal transport in fractures embedded in an impermeable conductive matrix. The thermal tracer tests were achieved in a crystalline rock aquifer at the experimental site of Ploemeur (H+ observatory network). The experimental setup consists in injecting hot water in a fracture isolated by a double straddle packer in the borehole while pumping and monitoring the temperature in a fracture crossing the same borehole at greater elevation. Several tracer tests were achieved at different pumping and injection rates. This experimental set up allowed to estimate temperature breakthrough for different tracer test durations and hydraulic configurations from fully convergent to perfect dipole tracer tests. Thanks to those tests and numerical modeling of heat transport in fractures, we demonstrate that temperature recovery is highly dependent on flow rate and streamlines shape. Thus, thermal storage rate is inversely proportional to flow and is maximized in perfect dipole configuration. These thermal tracer tests and numerical modeling allow to define the most efficient configuration for optimizing shallow geothermal storage in fractured rock.
Energy Technology Data Exchange (ETDEWEB)
Niemi, A. [Royal Institute of Technology, Stockholm (Sweden); Kontio, K.; Kuusela-Lahtinen, A.; Vaittinen, T. [VTT Communities and Infrastructure, Espoo (Finland)
1999-03-01
This study looks at heterogeneity in hydraulic conductivity at Romuvaara site. It concentrates on the average rock outside the deterministic fracture zones, especially in the deeper parts of the bedrock. A large number of stochastic fracture networks is generated based on geometrical data on fracture geometry from the site. The hydraulic properties of the fractures are determined by calibrating the networks against well test data. The calibration is done by starting from an initial estimate for fracture transmissivity distribution based on 2 m interval flow meter data, simulating the 10 m constant head injection test behaviour in a number of fracture network realisations and comparing the simulated well tests statistics to the measured ones. A large number of possible combinations of mean and standard deviation of fracture transmissivities are tested and the goodness-of-fit between the measured and simulated results determined by means of the bootstrapping method. As the result, a range of acceptable fracture transmissivity distribution parameters is obtained. In the accepted range, the mean of log transmissivity varies between -13.9 and -15.3 and standard deviation between 4.0 and 3.2, with increase in standard deviation compensating for decrease in mean. The effect of spatial autocorrelation was not simulated. The variogram analysis did, however, give indications that an autocorrelation range of the order of 10 m might be realistic for the present data. Based on the calibrated fracture networks, equivalent continuum conductivities of the calibrated 30 m x 30 m x 30 m conductivity blocks were determined. For each realisation, three sets of simulations was carried out with the main gradient in x, y and z directions, respectively. Based on these results the components of conductivity tensor were determined. Such data can be used e.g. for stochastic continuum type Monte Carlo simulations with larger scale models. The hydraulic conductivities in the direction of the
Numerical modelling of sandstone uniaxial compression test using a mix-mode cohesive fracture model
Gui, Yilin; Kodikara, Jayantha
2015-01-01
A mix-mode cohesive fracture model considering tension, compression and shear material behaviour is presented, which has wide applications to geotechnical problems. The model considers both elastic and inelastic displacements. Inelastic displacement comprises fracture and plastic displacements. The norm of inelastic displacement is used to control the fracture behaviour. Meantime, a failure function describing the fracture strength is proposed. Using the internal programming FISH, the cohesive fracture model is programmed into a hybrid distinct element algorithm as encoded in Universal Distinct Element Code (UDEC). The model is verified through uniaxial tension and direct shear tests. The developed model is then applied to model the behaviour of a uniaxial compression test on Gosford sandstone. The modelling results indicate that the proposed cohesive fracture model is capable of simulating combined failure behaviour applicable to rock.
Mining and modeling character networks
Bonato, Anthony; Elenberg, Ethan R; Gleich, David F; Hou, Yangyang
2016-01-01
We investigate social networks of characters found in cultural works such as novels and films. These character networks exhibit many of the properties of complex networks such as skewed degree distribution and community structure, but may be of relatively small order with a high multiplicity of edges. Building on recent work of beveridge, we consider graph extraction, visualization, and network statistics for three novels: Twilight by Stephanie Meyer, Steven King's The Stand, and J.K. Rowling's Harry Potter and the Goblet of Fire. Coupling with 800 character networks from films found in the http://moviegalaxies.com/ database, we compare the data sets to simulations from various stochastic complex networks models including random graphs with given expected degrees (also known as the Chung-Lu model), the configuration model, and the preferential attachment model. Using machine learning techniques based on motif (or small subgraph) counts, we determine that the Chung-Lu model best fits character networks and we ...
Figueiredo, Bruno; Tsang, Chin-Fu; Niemi, Auli; Lindgren, Georg
2016-05-01
Laboratory and field experiments done on fractured rock show that flow and solute transport often occur along flow channels. `Sparse channels' refers to the case where these channels are characterised by flow in long flow paths separated from each other by large spacings relative to the size of flow domain. A literature study is presented that brings together information useful to assess whether a sparse-channel network concept is an appropriate representation of the flow system in tight fractured rock of low transmissivity, such as that around a nuclear waste repository in deep crystalline rocks. A number of observations are made in this review. First, conventional fracture network models may lead to inaccurate results for flow and solute transport in tight fractured rocks. Secondly, a flow dimension of 1, as determined by the analysis of pressure data in well testing, may be indicative of channelised flow, but such interpretation is not unique or definitive. Thirdly, in sparse channels, the percolation may be more influenced by the fracture shape than the fracture size and orientation but further studies are needed. Fourthly, the migration of radionuclides from a waste canister in a repository to the biosphere may be strongly influenced by the type of model used (e.g. discrete fracture network, channel model). Fifthly, the determination of appropriateness of representing an in situ flow system by a sparse-channel network model needs parameters usually neglected in site characterisation, such as the density of channels or fracture intersections.
Figueiredo, Bruno; Tsang, Chin-Fu; Niemi, Auli; Lindgren, Georg
2016-11-01
Laboratory and field experiments done on fractured rock show that flow and solute transport often occur along flow channels. `Sparse channels' refers to the case where these channels are characterised by flow in long flow paths separated from each other by large spacings relative to the size of flow domain. A literature study is presented that brings together information useful to assess whether a sparse-channel network concept is an appropriate representation of the flow system in tight fractured rock of low transmissivity, such as that around a nuclear waste repository in deep crystalline rocks. A number of observations are made in this review. First, conventional fracture network models may lead to inaccurate results for flow and solute transport in tight fractured rocks. Secondly, a flow dimension of 1, as determined by the analysis of pressure data in well testing, may be indicative of channelised flow, but such interpretation is not unique or definitive. Thirdly, in sparse channels, the percolation may be more influenced by the fracture shape than the fracture size and orientation but further studies are needed. Fourthly, the migration of radionuclides from a waste canister in a repository to the biosphere may be strongly influenced by the type of model used (e.g. discrete fracture network, channel model). Fifthly, the determination of appropriateness of representing an in situ flow system by a sparse-channel network model needs parameters usually neglected in site characterisation, such as the density of channels or fracture intersections.
Fracture propagation in Indiana Limestone interpreted via linear softening cohesive fracture model
Rinehart, Alex J.; Bishop, Joseph E.; Dewers, Thomas
2015-04-01
We examine the use of a linear softening cohesive fracture model (LCFM) to predict single-trace fracture growth in short-rod (SR) and notched 3-point-bend (N3PB) test configurations in Indiana Limestone. The broad goal of this work is to (a) understand the underlying assumptions of LCFM and (b) use experimental similarities and deviations from the LCFM to understand the role of loading paths of tensile fracture propagation. Cohesive fracture models are being applied in prediction of structural and subsurface fracture propagation in geomaterials. They lump the inelastic processes occurring during fracture propagation into a thin zone between elastic subdomains. LCFM assumes that the cohesive zone initially deforms elastically to a maximum tensile stress (σmax) and then softens linearly from the crack opening width at σmax to zero stress at a critical crack opening width w1. Using commercial finite element software, we developed LCFMs for the SR and N3PB configurations. After fixing σmax with results from cylinder splitting tests and finding an initial Young's modulus (E) with unconfined compressive strength tests, we manually calibrate E and w1 in the SR model against an envelope of experimental data. We apply the calibrated LCFM parameters in the N3PB geometry and compare the model against an envelope of N3PB experiments. For accurate simulation of fracture propagation, simulated off-crack stresses are high enough to require inclusion of damage. Different elastic moduli are needed in tension and compression. We hypothesize that the timing and location of shear versus extensional micromechanical failures control the qualitative macroscopic force-versus-displacement response in different tests. For accurate prediction, the LCFM requires a constant style of failure, which the SR configuration maintains until very late in deformation. The N3PB configuration does not maintain this constancy. To be broadly applicable between geometries and failure styles, the LCFM
Discrete Modeling of Early-Life Thermal Fracture in Ceramic Nuclear Fuel
Energy Technology Data Exchange (ETDEWEB)
Spencer, Benjamin W. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Huang, Hai [Idaho National Lab. (INL), Idaho Falls, ID (United States); Dolbow, John E. [Duke Univ., Durham, NC (United States); Hales, Jason D. [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2015-03-01
Fracturing of ceramic fuel pellets heavily influences performance of light water reactor (LWR) fuel. Early in the life of fuel, starting with the initial power ramp, large thermal gradients cause high tensile hoop and axial stresses in the outer region of the fuel pellets, resulting in the formation of radial and axial cracks. Circumferential cracks form due to thermal gradients that occur when the power is ramped down. These thermal cracks cause the fuel to expand radially, closing the pellet/cladding gap and enhancing the thermal conductance across that gap, while decreasing the effective conductivity of the fuel in directions normal to the cracking. At lower length scales, formation of microcracks is an important contributor to the decrease in bulk thermal conductivity that occurs over the life of the fuel as the burnup increases. Because of the important effects that fracture has on fuel performance, a realistic, physically based fracture modeling capability is essential to predict fuel behavior in a wide variety of normal and abnormal conditions. Modeling fracture within the context of the finite element method, which is based on continuous interpolations of solution variables, has always been challenging because fracture is an inherently discontinuous phenomenon. Work is underway at Idaho National Laboratory to apply two modeling techniques model fracture as a discrete displacement discontinuity to nuclear fuel: The extended finite element method (XFEM), and discrete element method (DEM). XFEM is based on the standard finite element method, but with enhancements to represent discontinuous behavior. DEM represents a solid as a network of particles connected by bonds, which can arbitrarily fail if a fracture criterion is reached. This paper presents initial results applying the aforementioned techniques to model fuel fracturing. This work has initially focused on early life behavior of ceramic LWR fuel. A coupled thermal-mechanical XFEM method that includes
Three dimensional modeling of fractures in rock: From data to a regionalized parent-daughter model
Energy Technology Data Exchange (ETDEWEB)
Hestir, K.; Chiles, J.P.; Long, J.; Billaux, D.
1987-04-01
We introduce a stochastic model for fracture systems called the parent-daughter model. The model uses circular discs to represent fractures. The discs are placed in three-dimensional space according to a random process called the parent-daughter point process. This process will give a clustering of fractures that cannot be produced with the usual Poisson process. We then outline a procedure for fitting the model to a particular data set.
Design and modeling of small scale multiple fracturing experiments
Energy Technology Data Exchange (ETDEWEB)
Cuderman, J F
1981-12-01
Recent experiments at the Nevada Test Site (NTS) have demonstrated the existence of three distinct fracture regimes. Depending on the pressure rise time in a borehole, one can obtain hydraulic, multiple, or explosive fracturing behavior. The use of propellants rather than explosives in tamped boreholes permits tailoring of the pressure risetime over a wide range since propellants having a wide range of burn rates are available. This technique of using the combustion gases from a full bore propellant charge to produce controlled borehole pressurization is termed High Energy Gas Fracturing (HEGF). Several series of HEGF, in 0.15 m and 0.2 m diameter boreholes at 12 m depths, have been completed in a tunnel complex at NTS where mineback permitted direct observation of fracturing obtained. Because such large experiments are costly and time consuming, smaller scale experiments are desirable, provided results from small experiments can be used to predict fracture behavior in larger boreholes. In order to design small scale gas fracture experiments, the available data from previous HEGF experiments were carefully reviewed, analytical elastic wave modeling was initiated, and semi-empirical modeling was conducted which combined predictions for statically pressurized boreholes with experimental data. The results of these efforts include (1) the definition of what constitutes small scale experiments for emplacement in a tunnel complex at the Nevada Test Site, (2) prediction of average crack radius, in ash fall tuff, as a function of borehole size and energy input per unit length, (3) definition of multiple-hydraulic and multiple-explosive fracture boundaries as a function of boreholes size and surface wave velocity, (4) semi-empirical criteria for estimating stress and acceleration, and (5) a proposal that multiple fracture orientations may be governed by in situ stresses.
Modeling the Fracture of Ice Sheets on Parallel Computers
Energy Technology Data Exchange (ETDEWEB)
Waisman, Haim [Columbia University; Tuminaro, Ray [Sandia National Labs
2013-10-10
The objective of this project was to investigate the complex fracture of ice and understand its role within larger ice sheet simulations and global climate change. This objective was achieved by developing novel physics based models for ice, novel numerical tools to enable the modeling of the physics and by collaboration with the ice community experts. At the present time, ice fracture is not explicitly considered within ice sheet models due in part to large computational costs associated with the accurate modeling of this complex phenomena. However, fracture not only plays an extremely important role in regional behavior but also influences ice dynamics over much larger zones in ways that are currently not well understood. To this end, our research findings through this project offers significant advancement to the field and closes a large gap of knowledge in understanding and modeling the fracture of ice sheets in the polar regions. Thus, we believe that our objective has been achieved and our research accomplishments are significant. This is corroborated through a set of published papers, posters and presentations at technical conferences in the field. In particular significant progress has been made in the mechanics of ice, fracture of ice sheets and ice shelves in polar regions and sophisticated numerical methods that enable the solution of the physics in an efficient way.
Transport modeling of sorbing tracers in artificial fractures
Energy Technology Data Exchange (ETDEWEB)
Keum, Dong Kwon; Baik, Min Hoon; Park, Chung Kyun; Cho, Young Hwan; Hahn, Phil Soo
1998-02-01
This study was performed as part of a fifty-man year attachment program between AECL (Atomic Energy Canada Limited) and KAERI. Three kinds of computer code, HDD, POMKAP and VAMKAP, were developed to predict transport of contaminants in fractured rock. MDDM was to calculate the mass transport of contaminants in a single fracture using a simple hydrodynamic dispersion diffusion model. POMKAP was to predict the mass transport of contaminants by a two-dimensional variable aperture model. In parallel with modeling, the validation of models was also performed through the analysis of the migration experimental data obtained in acrylic plastic and granite artificial fracture system at the Whiteshell laboratories, AECL, Canada. (author). 34 refs., 11 tabs., 76 figs.
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.
A multiscale model of distributed fracture and permeability in solids in all-round compression
De Bellis, Maria Laura; Della Vecchia, Gabriele; Ortiz, Michael; Pandolfi, Anna
2017-07-01
We present a microstructural model of permeability in fractured solids, where the fractures are described in terms of recursive families of parallel, equidistant cohesive faults. Faults originate upon the attainment of tensile or shear strength in the undamaged material. Secondary faults may form in a hierarchical organization, creating a complex network of connected fractures that modify the permeability of the solid. The undamaged solid may possess initial porosity and permeability. The particular geometry of the superposed micro-faults lends itself to an explicit analytical quantification of the porosity and permeability of the damaged material. The model is the finite kinematics version of a recently proposed porous material model, applied with success to the simulation of laboratory tests and excavation problems [De Bellis, M. L., Della Vecchia, G., Ortiz, M., Pandolfi, A., 2016. A linearized porous brittle damage material model with distributed frictional-cohesive faults. Engineering Geology 215, 10-24. Cited By 0. 10.1016/j.enggeo.2016.10.010]. The extension adds over and above the linearized kinematics version for problems characterized by large deformations localized in narrow zones, while the remainder of the solid undergoes small deformations, as typically observed in soil and rock mechanics problems. The approach is particularly appealing as a means of modeling a wide scope of engineering problems, ranging from the prevention of water or gas outburst into underground mines, to the prediction of the integrity of reservoirs for CO2 sequestration or hazardous waste storage, to hydraulic fracturing processes.
Modelling karst aquifer evolution in fractured, porous rocks
Kaufmann, Georg
2016-12-01
The removal of material in soluble rocks by physical and chemical dissolution is an important process enhancing the secondary porosity of soluble rocks. Depending on the history of the soluble rock, dissolution can occur either along fractures and bedding partings of the rock in the case of a telogenetic origin, or within the interconnected pore space in the case of eogenetic origin. In soluble rocks characterised by both fractures and pore space, dissolution in both flow compartments is possible. We investigate the dissolution of calcite both along fractures and within the pore space of a limestone rock by numerical modelling. The limestone rock is treated as fractured, porous aquifer, in which the hydraulic conductivity increases with time both for the fractures and the pore spaces. We show that enlargement of pore space by dissolution will accelerate the development of a classical fracture-dominated telogenetic karst aquifer, breakthrough occurs faster. In the case of a pore-controlled aquifer as in eogenetic rocks, enlargement of pores results in a front of enlarged pore spaces migrating into the karst aquifer, with more homogeneous enlargement around this dissolution front, and later breakthrough.
Optimal fixation of oblique scaphoid fractures: a cadaver model.
Luria, Shai; Lenart, Lado; Lenart, Borut; Peleg, Eran; Kastelec, Matej
2012-07-01
Acute scaphoid fractures are commonly fixed with headless cannulated screws positioned in the center of the proximal fragment. Central placement of the screw may be difficult and may violate the scaphotrapezial joint. We hypothesize that placement of the screw through the scaphoid tuberosity will achieve perpendicular fixation of an oblique waist fracture and result in more stable fixation than a screw in the center of the proximal fragment. We designed oblique osteotomies for 8 matched pairs of cadaver scaphoids and fixed each specimen with a headless cannulated screw. In 1 specimen, we positioned the screw at the center of the proximal fragment; we placed its matched pair perpendicular to the fracture. The perpendicular screw was directed through the scaphoid tuberosity. We placed the specimen under the increasing load of a pneumatically driven plunger. We compared stiffness, load, distance at failure, and mechanism of failure between the central and perpendicular screw groups. We found no difference between groups. Stiffness was identical in both groups (131 N/mm) and load to failure was similar (central screw, 137 N vs perpendicular screw, 148 N). In this biomechanical model of an unstable scaphoid fracture, we found that similar stability of fixation had been achieved with a screw perpendicular to the fracture plane with entry through the tuberosity, compared with a screw in a central position in the proximal fragment. This study suggests that placing the screw through the tuberosity, perpendicular to a short oblique fracture, will not impair fixation stability. Percutaneous fixation of scaphoid fractures has become popular although it is technically challenging. An easier distal approach through the tuberosity, without violating the scaphotrapezial joint, may not impair the fixation stability of an oblique fracture. Copyright © 2012 American Society for Surgery of the Hand. Published by Elsevier Inc. All rights reserved.
Numerical modelling of flow and transport in rough fractures
Institute of Scientific and Technical Information of China (English)
Scott Briggs; Bryan W. Karney; Brent E. Sleep
2014-01-01
Simulation of flow and transport through rough walled rock fractures is investigated using the lattice Boltzmann method (LBM) and random walk (RW), respectively. The numerical implementation is developed and validated on general purpose graphic processing units (GPGPUs). Both the LBM and RW method are well suited to parallel implementation on GPGPUs because they require only next-neighbour communication and thus can reduce expenses. The LBM model is an order of magnitude faster on GPGPUs than published results for LBM simulations run on modern CPUs. The fluid model is verified for parallel plate flow, backward facing step and single fracture flow;and the RW model is verified for point-source diffusion, Taylor-Aris dispersion and breakthrough behaviour in a single fracture. Both algorithms place limitations on the discrete displacement of fluid or particle transport per time step to minimise the numerical error that must be considered during implementation.
Multi-scale peridynamic modeling of dynamic fracture in concrete
Lammi, Christopher J.; Zhou, Min
2017-01-01
Peridynamics simulations of the dynamic deformation and failure of high-performance concrete are performed at the meso-scale. A pressure-dependent, peridynamic plasticity model and failure criteria are used to capture pressure-sensitive granular flow and fracture. The meso-scale framework explicitly resolves reinforcing phases, pores, and intrinsic flaws. A novel scaling approach is formulated to inform the engineering-scale plasticity model parameters with meso-scale simulation results. The effects of composition, porosity, and fracture energy at the meso-scale on the engineering-scale impact resistance are assessed. The fracture process zone at the meso-scale is found to propagate along adjacent pores and reinforcing phases under tensile and shear loading conditions. The simulations show that tensile strength decreases and dissipation increases as the porosity in the concrete increases. The framework and modeling approach allow the delineation of trends that can be used to design more impact-resistant materials.
Effect of Natural Fractures on Hydraulic Fracturing
Ben, Y.; Wang, Y.; Shi, G.
2012-12-01
Hydraulic Fracturing has been used successfully in the oil and gas industry to enhance oil and gas production in the past few decades. Recent years have seen the great development of tight gas, coal bed methane and shale gas. Natural fractures are believed to play an important role in the hydraulic fracturing of such formations. Whether natural fractures can benefit the fracture propagation and enhance final production needs to be studied. Various methods have been used to study the effect of natural fractures on hydraulic fracturing. Discontinuous Deformation Analysis (DDA) is a numerical method which belongs to the family of discrete element methods. In this paper, DDA is coupled with a fluid pipe network model to simulate the pressure response in the formation during hydraulic fracturing. The focus is to study the effect of natural fractures on hydraulic fracturing. In particular, the effect of rock joint properties, joint orientations and rock properties on fracture initiation and propagation will be analyzed. The result shows that DDA is a promising tool to study such complex behavior of rocks. Finally, the advantages of disadvantages of our current model and future research directions will be discussed.
Multiscale model reduction for shale gas transport in fractured media
Akkutlu, I. Y.
2016-05-18
In this paper, we develop a multiscale model reduction technique that describes shale gas transport in fractured media. Due to the pore-scale heterogeneities and processes, we use upscaled models to describe the matrix. We follow our previous work (Akkutlu et al. Transp. Porous Media 107(1), 235–260, 2015), where we derived an upscaled model in the form of generalized nonlinear diffusion model to describe the effects of kerogen. To model the interaction between the matrix and the fractures, we use Generalized Multiscale Finite Element Method (Efendiev et al. J. Comput. Phys. 251, 116–135, 2013, 2015). In this approach, the matrix and the fracture interaction is modeled via local multiscale basis functions. In Efendiev et al. (2015), we developed the GMsFEM and applied for linear flows with horizontal or vertical fracture orientations aligned with a Cartesian fine grid. The approach in Efendiev et al. (2015) does not allow handling arbitrary fracture distributions. In this paper, we (1) consider arbitrary fracture distributions on an unstructured grid; (2) develop GMsFEM for nonlinear flows; and (3) develop online basis function strategies to adaptively improve the convergence. The number of multiscale basis functions in each coarse region represents the degrees of freedom needed to achieve a certain error threshold. Our approach is adaptive in a sense that the multiscale basis functions can be added in the regions of interest. Numerical results for two-dimensional problem are presented to demonstrate the efficiency of proposed approach. © 2016 Springer International Publishing Switzerland
Method for efficient simulation of radionuclide transport in discrete fracture networks
Painter, S. L.; Cvetkovic, V.; Mancillas, J. W.; Selroos, J.
2006-12-01
Limitations of the advection-dispersion equation for predicting transport in sparsely or moderately fractured rock are well known and have prompted many to consider discrete fracture network (DFN) simulation combined with particle tracking as an alternative. Although it is relatively straightforward to track particles moving only by advection through DFN-derived flow fields, more complex processes such as matrix diffusion, longitudinal dispersion, and decay/in-growth of radionuclides are more difficult and more computationally demanding. Moreover, the DFN simulations themselves are computationally intensive and are usually limited to relatively small volumes. A new time-domain particle method has been developed to efficiently simulate radionuclide transport in pathways derived from DFN simulations. The algorithm moves particles from node to node on a segmented pathway. The time to complete each segment is sampled from residence time distributions that include the effects of advection, longitudinal dispersion, and a variety of matrix retention processes. The method has been extended to include transport of decay chains and transient flow fields. The result of the simulation is a set of arrival times that can be post-processed with a log-normal kernel method to construct mass discharge (breakthrough) versus time. The approach can be used directly on pathways extracted from DFN models, or it may be combined with pathway simulation algorithms (Painter and Cvetkovic, Water Resources Research 41, 2005) that use information extracted from DFNs to construct realistic artificial pathways. The latter variant helps recover the effects of sub-grid velocity variability in flow fields constructed from continuum flow models. Thus, when combined with flow models based on upscaled permeability tensors, the result is a type of multiscale simulation that is applicable at large scales without making continuum-type assumptions about the transport processes. Verification tests show that
Pfunt, Helena; Houben, Georg; Himmelsbach, Thomas
2016-09-01
Gas production from shale formations by hydraulic fracturing has raised concerns about the effects on the quality of fresh groundwater. The migration of injected fracking fluids towards the surface was investigated in the North German Basin, based on the known standard lithology. This included cases with natural preferential pathways such as permeable fault zones and fracture networks. Conservative assumptions were applied in the simulation of flow and mass transport triggered by a high pressure boundary of up to 50 MPa excess pressure. The results show no significant fluid migration for a case with undisturbed cap rocks and a maximum of 41 m vertical transport within a permeable fault zone during the pressurization. Open fractures, if present, strongly control the flow field and migration; here vertical transport of fracking fluids reaches up to 200 m during hydraulic fracturing simulation. Long-term transport of the injected water was simulated for 300 years. The fracking fluid rises vertically within the fault zone up to 485 m due to buoyancy. Progressively, it is transported horizontally into sandstone layers, following the natural groundwater flow direction. In the long-term, the injected fluids are diluted to minor concentrations. Despite the presence of permeable pathways, the injected fracking fluids in the reported model did not reach near-surface aquifers, either during the hydraulic fracturing or in the long term. Therefore, the probability of impacts on shallow groundwater by the rise of fracking fluids from a deep shale-gas formation through the geological underground to the surface is small.
Directory of Open Access Journals (Sweden)
Qingdong Zeng
2015-10-01
Full Text Available Fluid-solid coupling is ubiquitous in the process of fluid flow underground and has a significant influence on the development of oil and gas reservoirs. To investigate these phenomena, the coupled mathematical model of solid deformation and fluid flow in fractured porous media is established. In this study, the discrete fracture model (DFM is applied to capture fluid flow in the fractured porous media, which represents fractures explicitly and avoids calculating shape factor for cross flow. In addition, the extended finite element method (XFEM is applied to capture solid deformation due to the discontinuity caused by fractures. More importantly, this model captures the change of fractures aperture during the simulation, and then adjusts fluid flow in the fractures. The final linear equation set is derived and solved for a 2D plane strain problem. Results show that the combination of discrete fracture model and extended finite element method is suited for simulating coupled deformation and fluid flow in fractured porous media.
Haluch, Anna; Rybak-Ostrowska, Barbara; Konon, Andrzej
2017-04-01
Knowledge of the anisotropy of rock fabric, geometry and distribution of the natural fault and fracture network play a crucial role in the exploration for unconventional hydrocarbon recourses. Lower Paleozoic rocks from Pomerania within the Polish part of Peri-Baltic Basin, as prospective sequences, can be considered a laboratory for analysis of fault and fracture arrangement in relation to the mineral composition of the host rocks. A microstructural study of core samples from five boreholes in Pomerania indicate that the Silurian succession in the study area is predominantly composed of claystones and mudstones interbedded with thin layers of tuffites. Intervals with a high content of detrital quartz or diagenetic silica also occur. Most of the Silurian deposits are abundant in pyrite framboids forming layers or isolated small concretions. Early diagenetic carbonate concretions are also present. The direction and distribution of natural faults and fractures have resulted not only from paleostress. Preliminary study reveals that the fault and fracture arrangement is related to the mechanical properties of the host rocks that depend on their fabric and mineralogical composition: subvertical fractures in mudstones and limestones show steeper dips than those within the more clayey intervals; bedding-parallel fractures occur within organic-rich claystones and along the boundaries between different lithologies; tuffites and radiolaria-bearing siliceous mudstones are more brittle and show denser nets of fractures or wider mineral apertures; and, fracture refraction is observed at competence contrast or around spherical concretions. The fault and fracture mineralization itself is prone to the heterogenity of the rock profile. Thus, fractures infilled with calcite occur in all types of the studied rocks, but mineral growth is syntaxial within marly mudstones because of chemical uniformity, and antitaxial within sillicous mudstones. Fractures infilled with quartz are
Risk Assessment in Fractured Clayey Tills - Which Modeling Tools?
DEFF Research Database (Denmark)
Chambon, Julie Claire Claudia; Bjerg, Poul Løgstrup; Binning, Philip John
2012-01-01
assessment is challenging and the inclusion of the relevant processes is difficult. Furthermore the lack of long-term monitoring data prevents from verifying the accuracy of the different conceptual models. Further investigations based on long-term data and numerical modeling are needed to accurately......The article presents different tools available for risk assessment in fractured clayey tills and their advantages and limitations are discussed. Because of the complex processes occurring during contaminant transport through fractured media, the development of simple practical tools for risk...
Coupled THMC modelling of single fractures in novaculite and granite for DECOVALEX-2015
Bond, A.; Chittenden, N.; Fedors, R. W.; Lang, P. S.; McDermott, C.; Neretnieks, I. E.; Pan, P.; Šembara, J.; Brusky, I.; Watanabe, N.; Lu, R.; Yasuhara, H.
2015-12-01
The host rock immediately surrounding a nuclear waste repository has the potential to undergo a complex set of physical and chemical processes starting from construction of the facility until many years after completion. Understanding the relevant processes of fracture evolution may be key to supporting the attendant safety arguments for such a facility. In the present phase of the international research project DECOVALEX, the experimental work of Yasuhara et al [1,2] has been examined, wherein artificial fractures in novaculite and granite are subject to a mechanical confining pressure, variable fluid flows and different applied temperatures. Differential pressures across the samples were measured to determine permeability and hence hydraulic aperture evolution, while at the same time the chemical composition of the outflows were continually sampled. For the novaculite experiments, the fracture surfaces' topography were characterised using a high-resolution laser profilometer (see Figure 1), and post-experimental characterisation of the aperture was performed using a Wood's metal fracture cast. This paper presents a synthesis of the ongoing work of six separate research teams. A range of approaches are presented including 2D and 3D high resolution coupled THMC models. Homogenised 'single compartment' models of the fracture have also been adopted, attempting to upscale the processes so that they could be used in larger network or effective continuum models. Particular attention is given to the competing roles of aqueous geochemistry, pressure solution, stress corrosion and pure mechanics in order to reproduce the experimental observations. The results of the work show that while good, physically plausible representations of the experiment can be obtained, there is considerable uncertainty in the relative importance of the various processes and that the parameterisation of these processes can be closely linked to the physical interpretation of the fracture surface
Blessent, Daniela; Jørgensen, Peter R; Therrien, René
2014-01-01
We used the FRAC3Dvs numerical model (Therrien and Sudicky 1996) to compare the dual-porosity (DP), equivalent porous medium (EPM), and discrete fracture matrix diffusion (DFMD) conceptual models to predict field-scale contaminant transport in a fractured clayey till aquitard. The simulations show that the DP, EPM, and DFMD models could be equally well calibrated to reproduce contaminant breakthrough in the till aquitard for a base case. In contrast, when groundwater velocity and degradation rates are modified with respect to the base case, the DP method simulated contaminant concentrations up to three orders of magnitude different from those calculated by the DFMD model. In previous simulations of well-characterized column experiments, the DFMD method reproduced observed changes in solute transport for a range of flow and transport conditions comparable to those of the field-scale simulations, while the DP and EPM models required extensive recalibration to avoid high magnitude errors in predicted mass transport. The lack of robustness with respect to variable flow and transport conditions suggests that DP models and effective porosity EPM models have limitations for predicting cause-effect relationships in environmental planning. The study underlines the importance of obtaining well-characterized experimental data for further studies and evaluation of model key process descriptions and model suitability. © 2013, National Groundwater Association.
Internet Network Resource Information Model
Institute of Scientific and Technical Information of China (English)
陈传峰; 李增智; 唐亚哲; 刘康平
2002-01-01
The foundation of any network management systens is a database that con-tains information about the network resources relevant to the management tasks. A networkinformation model is an abstraction of network resources, including both managed resources andmanaging resources. In the SNMP-based management framework, management information isdefined almost exclusively from a "device" viewpoint, namely, managing a network is equiva-lent to managing a collection of individual nodes. Aiming at making use of recent advances indistributed computing and in object-oriented analysis and design, the Internet management ar-chitecture can also be based on the Open Distributed Processing Reference Model (RM-ODP).The purpose of this article is to provide an Internet Network Resource Information Model.First, a layered management information architecture will be discussed. Then the Internetnetwork resource information model is presented. The information model is specified usingObject-Z.
Complex Networks in Psychological Models
Wedemann, R. S.; Carvalho, L. S. A. V. D.; Donangelo, R.
We develop schematic, self-organizing, neural-network models to describe mechanisms associated with mental processes, by a neurocomputational substrate. These models are examples of real world complex networks with interesting general topological structures. Considering dopaminergic signal-to-noise neuronal modulation in the central nervous system, we propose neural network models to explain development of cortical map structure and dynamics of memory access, and unify different mental processes into a single neurocomputational substrate. Based on our neural network models, neurotic behavior may be understood as an associative memory process in the brain, and the linguistic, symbolic associative process involved in psychoanalytic working-through can be mapped onto a corresponding process of reconfiguration of the neural network. The models are illustrated through computer simulations, where we varied dopaminergic modulation and observed the self-organizing emergent patterns at the resulting semantic map, interpreting them as different manifestations of mental functioning, from psychotic through to normal and neurotic behavior, and creativity.
2008-12-01
well, then a Euclidean distance would be appropriate. The quadratic assignment procedure ( QAP ) (Krackhardt, 1987) could be used to compare the...Networks. Journal of Applied Psychology, 71(1): 50-55. Krackhardt, D. (1987). QAP Partialling as a Test of Spuriousness. Social Networks, 9, 171-186
Joint geophysical and flow inversion to characterize fracture networks in subsurface systems
Mudunuru, M K; Makedonska, N; Chen, T
2016-01-01
Subsurface applications including geothermal, geological carbon sequestration, oil and gas, etc., typically involve maximizing either the extraction of energy or the storage of fluids. Characterizing the subsurface is extremely complex due to heterogeneity and anisotropy. Due to this complexity, there are uncertainties in the subsurface parameters, which need to be estimated from multiple diverse as well as fragmented data streams. In this paper, we present a non-intrusive joint inversion framework, for integrating data from geophysical and flow sources to constraint subsurface Discrete Fracture Networks (DFN). In this approach, we first estimate bounds on the statistics for the DFN fracture orientations using microseismic data. These bounds are estimated through a combination of a focal mechanism (physics-based approach) and clustering analysis (statistical approach) of seismic data. Then, the fracture lengths are constrained based on the flow data. The efficacy of this multi-physics based joint inversion is...
Assortative model for social networks
Catanzaro, Michele; Caldarelli, Guido; Pietronero, Luciano
2004-09-01
In this Brief Report we present a version of a network growth model, generalized in order to describe the behavior of social networks. The case of study considered is the preprint archive at cul.arxiv.org. Each node corresponds to a scientist, and a link is present whenever two authors wrote a paper together. This graph is a nice example of degree-assortative network, that is, to say a network where sites with similar degree are connected to each other. The model presented is one of the few able to reproduce such behavior, giving some insight on the microscopic dynamics at the basis of the graph structure.
Felici, Fabrizio; Alemanni, Annalisa; Bouacida, Djamil; de Montleau, Pierre
2016-10-01
Fault arrays and natural fractures distribution strongly influence subsurface fluids migration, trapping and production. It is critical to develop methodologies that can be used to accurately characterize reservoir volumes as present-day exploration and appraisal campaigns become increasingly focused on tight or low porosity reservoirs. A common method used to model the distribution and intensity of subsurface fracture sets is the Discrete Fracture Network (DFN) technique. Shortcomings of the DFN technique include the evaluation of fracture attributes, computational aspects in the case of large fields, and most importantly issues related to upscaling. Thus, the aim of this work is to present a simplified methodology for fractured reservoir characterization based on the distribution of fracture intensity as a continuous property. Fracture intensity was calculated from image well-logs data and then distributed in the reservoir according to specific fracture drivers. The case study is related to a large appraisal gas field located in the Illizi Basin, Southern Algeria, where Late Ordovician glacial deposits are the primary reservoir levels, in which the presence of faults and fractures strongly enhance well performances. The final fracture intensity model was obtained by implementing a workflow in a commonly used commercial geomodeling software and calibrated by means of well test data analysis. The implemented methodology is a useful tool for large fractured reservoir characterization when DFN technique is hardly applicable for computational reasons or the level of uncertainty does not support a performing discrete analysis.
Model of Fracture, Friction, and Wear Phenomena of Porous Iron
Directory of Open Access Journals (Sweden)
A. A. Shatsov
2011-01-01
Full Text Available Mechanical and tribotechnical features of powdered materials are strongly influenced by pore volume, fracture character, impurities, alloying, concentration inhomogeneity, friction conditions, and other factors. Pores also have influence on acceleration of diffusion processes and reduce undercooled austenite resistance. Annealed in hydrogen, ultra pure iron powder was used to study porous iron features. Toughness fracture and tribotechnical features had nonmonotonic dependence from porosity different from all known dependences got from technical iron powders. Researches brought out the fact that in process of porosity reduction by pressing and annealing cycles, the average dimension of porous is changed. According to the analysis of porous structure were created models of friction, wear, and fracture of pure porous iron.
Developing Personal Network Business Models
DEFF Research Database (Denmark)
Saugstrup, Dan; Henten, Anders
2006-01-01
on the 'state of the art' in the field of business modeling. Furthermore, the paper suggests three generic business models for PNs: a service oriented model, a self-organized model, and a combination model. Finally, examples of relevant services and applications in relation to three different cases......The aim of the paper is to examine the issue of business modeling in relation to personal networks, PNs. The paper builds on research performed on business models in the EU 1ST MAGNET1 project (My personal Adaptive Global NET). The paper presents the Personal Network concept and briefly reports...... are presented and analyzed in light of business modeling of PN....
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.
Network models in anatomical systems.
Esteve-Altava, Borja; Marugán-Lobón, Jesús; Botella, Héctor; Rasskin-Gutman, Diego
2011-01-01
Network theory has been extensively used to model the underlying structure of biological processes. From genetics to ecology, network thinking is changing our understanding of complex systems, specifically how their internal structure determines their overall behavior. Concepts such as hubs, scale-free or small-world networks, common in the complexity literature, are now used more and more in sociology, neurosciences, as well as other anthropological fields. Even though the use of network models is nowadays so widely applied, few attempts have been carried out to enrich our understanding in the classical morphological sciences such as in comparative anatomy or physical anthropology. The purpose of this article is to introduce the usage of network tools in morphology; specifically by building anatomical networks, dealing with the most common analyses and problems, and interpreting their outcome.
Fracture Mechanical Markov Chain Crack Growth Model
DEFF Research Database (Denmark)
Gansted, L.; Brincker, Rune; Hansen, Lars Pilegaard
1991-01-01
On the basis of the B-model developed in [J. L. Bogdanoff and F. Kozin, Probabilistic Models of Cumulative Damage. John Wiley, New York (1985)] a new numerical model incorporating the physical knowledge of fatigue crack propagation is developed. The model is based on the assumption that the crack...
Telecommunications network modelling, planning and design
Evans, Sharon
2003-01-01
Telecommunication Network Modelling, Planning and Design addresses sophisticated modelling techniques from the perspective of the communications industry and covers some of the major issues facing telecommunications network engineers and managers today. Topics covered include network planning for transmission systems, modelling of SDH transport network structures and telecommunications network design and performance modelling, as well as network costs and ROI modelling and QoS in 3G networks.
Leptin Influences Healing in the Sprague Dawley Rat Fracture Model
Liu, Pengcheng; Cai, Ming
2017-01-01
Background Leptin plays a crucial role in bone metabolism, and its level is related to bone callus formation in the fracture repair process. The objective of this study was to evaluate the effect of recombinant leptin on the healing process of femoral fractures in rats. Material/Methods Forty-eight male Sprague Dawley (SD) rats with an average body weight of 389 g (range: 376–398 g) and an average age of 10 weeks were included in this animal research, and all rats were randomly divided into two major groups. Then standardized femur fracture models were implemented in all SD rats. Rats in the control group were treated with only 0.5 mL of physiological saline, and rats in the experimental group were treated with recombinant leptin 5 μg/kg/d along with the same 0.5 mL of physiological saline for 42 days intraperitoneally. At the same time, each major group was evenly divided into three parallel subgroups for each parallel bone evaluation separately at the second, fourth, and sixth weeks. Each subgroup included eight rats. Results The total radiological evaluation results showed that the healing progress of femoral fracture in the experimental group was superior to that in the control group from the fourth week. At the sixth week, experimental group rats began to present significantly better femoral fracture healing progress than that of the control group rats. Results of biomechanics show the ultimate load (N) and deflection ultimate load (mm) of the experimental group rats was significantly increased compared with that of the control group rats from the fourth week. Conclusions Our results suggest that leptin may have a positive effect on SD rat femur fracture healing. PMID:28088810
Brittle fracture phase-field modeling of a short-rod specimen
Energy Technology Data Exchange (ETDEWEB)
Escobar, Ivana [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Tupek, Michael R. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Bishop, Joseph E. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-09-01
Predictive simulation capabilities for modeling fracture evolution provide further insight into quantities of interest in comparison to experimental testing. Based on the variational approach to fracture, the advent of phase-field modeling achieves the goal to robustly model fracture for brittle materials and captures complex crack topologies in three dimensions.
Campus network security model study
Zhang, Yong-ku; Song, Li-ren
2011-12-01
Campus network security is growing importance, Design a very effective defense hacker attacks, viruses, data theft, and internal defense system, is the focus of the study in this paper. This paper compared the firewall; IDS based on the integrated, then design of a campus network security model, and detail the specific implementation principle.
Implicit level set algorithms for modelling hydraulic fracture propagation.
Peirce, A
2016-10-13
Hydraulic fractures are tensile cracks that propagate in pre-stressed solid media due to the injection of a viscous fluid. Developing numerical schemes to model the propagation of these fractures is particularly challenging due to the degenerate, hypersingular nature of the coupled integro-partial differential equations. These equations typically involve a singular free boundary whose velocity can only be determined by evaluating a distinguished limit. This review paper describes a class of numerical schemes that have been developed to use the multiscale asymptotic behaviour typically encountered near the fracture boundary as multiple physical processes compete to determine the evolution of the fracture. The fundamental concepts of locating the free boundary using the tip asymptotics and imposing the tip asymptotic behaviour in a weak form are illustrated in two quite different formulations of the governing equations. These formulations are the displacement discontinuity boundary integral method and the extended finite-element method. Practical issues are also discussed, including new models for proppant transport able to capture 'tip screen-out'; efficient numerical schemes to solve the coupled nonlinear equations; and fast methods to solve resulting linear systems. Numerical examples are provided to illustrate the performance of the numerical schemes. We conclude the paper with open questions for further research. This article is part of the themed issue 'Energy and the subsurface'.
Theory and modelling of diamond fracture from an atomic perspective.
Brenner, Donald W; Shenderova, Olga A
2015-03-28
Discussed in this paper are several theoretical and computational approaches that have been used to better understand the fracture of both single-crystal and polycrystalline diamond at the atomic level. The studies, which include first principles calculations, analytic models and molecular simulations, have been chosen to illustrate the different ways in which this problem has been approached, the conclusions and their reliability that have been reached by these methods, and how these theory and modelling methods can be effectively used together.
Modarres, Reza; Ouarda, Taha B. M. J.; Vanasse, Alain; Orzanco, Maria Gabriela; Gosselin, Pierre
2014-07-01
Changes in extreme meteorological variables and the demographic shift towards an older population have made it important to investigate the association of climate variables and hip fracture by advanced methods in order to determine the climate variables that most affect hip fracture incidence. The nonlinear autoregressive moving average with exogenous variable-generalized autoregressive conditional heteroscedasticity (ARMA X-GARCH) and multivariate GARCH (MGARCH) time series approaches were applied to investigate the nonlinear association between hip fracture rate in female and male patients aged 40-74 and 75+ years and climate variables in the period of 1993-2004, in Montreal, Canada. The models describe 50-56 % of daily variation in hip fracture rate and identify snow depth, air temperature, day length and air pressure as the influencing variables on the time-varying mean and variance of the hip fracture rate. The conditional covariance between climate variables and hip fracture rate is increasing exponentially, showing that the effect of climate variables on hip fracture rate is most acute when rates are high and climate conditions are at their worst. In Montreal, climate variables, particularly snow depth and air temperature, appear to be important predictors of hip fracture incidence. The association of climate variables and hip fracture does not seem to change linearly with time, but increases exponentially under harsh climate conditions. The results of this study can be used to provide an adaptive climate-related public health program and ti guide allocation of services for avoiding hip fracture risk.
Phase structure within a fracture network beneath a surface pond: Field experiment
Energy Technology Data Exchange (ETDEWEB)
GLASS JR.,ROBERT J.; NICHOLL,M.J.
2000-05-09
The authors performed a simple experiment to elucidate phase structure within a pervasively fractured welded tuff. Dyed water was infiltrated from a surface pond over a 36 minute period while a geophysical array monitored the wetted region within vertical planes directly beneath. They then excavated the rock mass to a depth of {approximately}5 m and mapped the fracture network and extent of dye staining in a series of horizontal pavements. Near the pond the network was fully stained. Below, the phase structure immediately expanded and with depth, the structure became fragmented and complicated exhibiting evidence of preferential flow, fingers, irregular wetting patterns, and varied behavior at fracture intersections. Limited transient geophysical data suggested that strong vertical pathways form first followed by increased horizontal expansion and connection within the network. These rapid pathways are also the first to drain. Estimates also suggest that the excavation captured from {approximately}10% to 1% or less of the volume of rock interrogated by the infiltration slug and thus the penetration depth could have been quite large.
Prediction models of prevalent radiographic vertebral fractures among older men.
Schousboe, John T; Rosen, Harold R; Vokes, Tamara J; Cauley, Jane A; Cummings, Steven R; Nevitt, Michael C; Black, Dennis M; Orwoll, Eric S; Kado, Deborah M; Ensrud, Kristine E
2014-01-01
No studies have compared how well different prediction models discriminate older men who have a radiographic prevalent vertebral fracture (PVFx) from those who do not. We used area under receiver operating characteristic curves and a net reclassification index to compare how well regression-derived prediction models and nonregression prediction tools identify PVFx among men age ≥65 yr with femoral neck T-score of -1.0 or less enrolled in the Osteoporotic Fractures in Men Study. The area under receiver operating characteristic for a model with age, bone mineral density, and historical height loss (HHL) was 0.682 compared with 0.692 for a complex model with age, bone mineral density, HHL, prior non-spine fracture, body mass index, back pain, grip strength, smoking, and glucocorticoid use (p values for difference in 5 bootstrapped samples 0.14-0.92). This complex model, using a cutpoint prevalence of 5%, correctly reclassified only a net 5.7% (p = 0.13) of men as having or not having a PVFx compared with a simple criteria list (age ≥ 80 yr, HHL >4 cm, or glucocorticoid use). In conclusion, simple criteria identify older men with PVFx and regression-based models. Future research to identify additional risk factors that more accurately identify older men with PVFx is needed.
Directory of Open Access Journals (Sweden)
N.V. Grygorieva
2017-06-01
Full Text Available Background. Vertebral fractures are one of the severe complications of systemic osteoporosis, which lead to the low-back pain, decrease or loss of efficiency and increase of mortality in older people. FRAX and dual-energy X-ray absorptiometry (DXA are important methods in determining major osteoporotic fractures risk, including vertebral fractures. Materials and methods. We studied the parameters of Ukrainian model of FRAX in women depending on the presence of vertebral fractures. 652 patients aged 40–89 years examined at the Ukrainian Scientific Medical Center of Osteoporosis were divided into two groups: the first one — 523 women without any previous fractures, the second one — 129 patients with previous vertebral fractures. The assessment of bone mineral density (BMD was performed using DXA (Prodigy, General Electric. The 10-year probability of major osteoporotic fractures (FRAX-MOF and hip fractures (FRAX-HF has been determined using Ukrainian model of FRAX according to two methods — with body mass index (FRAXBMI and BMD. Results. According the distribution of FRAXBMI-MOF parameters in women depending on the presence of vertebral fractures, it was found that index of FRAXBMI-MOF was less than 20 % (the limit indicated as the criterion for treatment initiation in US guidelines in 100 and 100 % of subjects, respectively. The indices of FRAX BMD-HF were less than 3 % (the limit for starting treatment in US guidelines in 95 and 55 % of women, respectively. It was shown the significant moderate correlation between the indices of two methods in all groups for both parameters of the algorithm — FRAX-MOF and FRAX-HF. Conclusions. The study of the age-specific features of FRAX in women depending on the presence of vertebral fractures showed a significant increase in the risks for both major osteoporotic and hip fractures, regardless of the used technique (with BMI or BMD in women with vertebral fractures or without any fractures. Our
Neural network modeling of emotion
Levine, Daniel S.
2007-03-01
This article reviews the history and development of computational neural network modeling of cognitive and behavioral processes that involve emotion. The exposition starts with models of classical conditioning dating from the early 1970s. Then it proceeds toward models of interactions between emotion and attention. Then models of emotional influences on decision making are reviewed, including some speculative (not and not yet simulated) models of the evolution of decision rules. Through the late 1980s, the neural networks developed to model emotional processes were mainly embodiments of significant functional principles motivated by psychological data. In the last two decades, network models of these processes have become much more detailed in their incorporation of known physiological properties of specific brain regions, while preserving many of the psychological principles from the earlier models. Most network models of emotional processes so far have dealt with positive and negative emotion in general, rather than specific emotions such as fear, joy, sadness, and anger. But a later section of this article reviews a few models relevant to specific emotions: one family of models of auditory fear conditioning in rats, and one model of induced pleasure enhancing creativity in humans. Then models of emotional disorders are reviewed. The article concludes with philosophical statements about the essential contributions of emotion to intelligent behavior and the importance of quantitative theories and models to the interdisciplinary enterprise of understanding the interactions of emotion, cognition, and behavior.
Nonequilibrium model on Apollonian networks.
Lima, F W S; Moreira, André A; Araújo, Ascânio D
2012-11-01
We investigate the majority-vote model with two states (-1,+1) and a noise parameter q on Apollonian networks. The main result found here is the presence of the phase transition as a function of the noise parameter q. Previous results on the Ising model in Apollonian networks have reported no presence of a phase transition. We also studied the effect of redirecting a fraction p of the links of the network. By means of Monte Carlo simulations, we obtained the exponent ratio γ/ν, β/ν, and 1/ν for several values of rewiring probability p. The critical noise q{c} and U were also calculated. Therefore, the results presented here demonstrate that the majority-vote model belongs to a different universality class than equilibrium Ising model on Apollonian network.
Algebraic Statistics for Network Models
2014-02-19
AFRL-OSR-VA-TR-2014-0070 (DARPA) Algebraic Statistics for Network Models SONJA PETROVIC PENNSYLVANIA STATE UNIVERSITY 02/19/2014 Final Report...DARPA GRAPHS Phase I Algebraic Statistics for Network Models FA9550-12-1-0392 Sonja Petrović petrovic@psu.edu1 Department of Statistics Pennsylvania...Department of Statistics, Heinz College , Machine Learning Department, Cylab Carnegie Mellon University 1. Abstract This project focused on the family of
Joshi, Nitin; Ojha, C. S. P.; Sharma, P. K.
2012-10-01
In this study a conceptual model that accounts for the effects of nonequilibrium contaminant transport in a fractured porous media is developed. Present model accounts for both physical and sorption nonequilibrium. Analytical solution was developed using the Laplace transform technique, which was then numerically inverted to obtain solute concentration in the fracture matrix system. The semianalytical solution developed here can incorporate both semi-infinite and finite fracture matrix extent. In addition, the model can account for flexible boundary conditions and nonzero initial condition in the fracture matrix system. The present semianalytical solution was validated against the existing analytical solutions for the fracture matrix system. In order to differentiate between various sorption/transport mechanism different cases of sorption and mass transfer were analyzed by comparing the breakthrough curves and temporal moments. It was found that significant differences in the signature of sorption and mass transfer exists. Applicability of the developed model was evaluated by simulating the published experimental data of Calcium and Strontium transport in a single fracture. The present model simulated the experimental data reasonably well in comparison to the model based on equilibrium sorption assumption in fracture matrix system, and multi rate mass transfer model.
A model for fracturation in the Loyalty Islands
Bogdanov, Igor; Huaman, David; Thovert, Jean-François; Genthon, Pierre; Adler, Pierre M.
2007-10-01
The Loyalty Islands are a series of limestone karstified islands that are currently uplifted and deformed on the elastic bulge of the Australian plate before its subduction at the Vanuatu trench (SW Pacific). These islands have been extensively surveyed for geology and hydrogeology, and fracturation maps have been produced which indicate a major direction N110±35°. This fracture orientation is analytically modeled as resulting from the elastic deformation of the Australian lithosphere before its subduction. First, the vertical deflection around a circular subduction zone is determined. Second, a point force is introduced which accounts for the first stages of a collision between the Loyalty ridge and this circular subduction zone. This model yields principal stress orientations and elevations of the islands in fair agreement with real data.
Microfluidic Investigation of Oil Mobilization in Shale Fracture Networks at Reservoir Conditions
Porter, M. L.; Jimenez-Martinez, J.; Carey, J. W.; Viswanathan, H. S.
2015-12-01
Investigations of pore-scale fluid flow and transport phenomena using engineered micromodels has steadily increased in recent years. In these investigations fluid flow is restricted to two-dimensions allowing for real time visualization and quantification of complex flow and reactive transport behavior, which is difficult to obtain in other experimental systems. One drawback to these studies is the use of engineered materials that do not faithfully represent the rock properties (e.g., porosity, wettability, roughness, etc.) encountered in subsurface formations. In this work, we describe a unique high pressure (up to 1500 psi) and temperature (up to 80 °C) microfluidics experimental system in which we investigate fluid flow and transport in geo-material (e.g., shale, Portland cement, etc.) micromodels. The use of geo-material micromodels allows us to better represent fluid-rock interactions including wettability, chemical reactivity, and nano-scale porosity at conditions representative of natural subsurface environments. Here, we present experimental results in fracture systems with applications to hydrocarbon mobility in hydraulically fractured shale. Complex fracture network patterns are derived from 3D x-ray tomography images of actual fractures created in shale rock cores. We use both shale and glass micromodels, allowing for a detailed comparison between flow phenomena in the different materials. We discuss results from two-phase huff-and-puff experiments involving N2 and n-Decane, as well as three-phase displacement experiments involving supercritical CO2, brine, and n-Decane.
Institute of Scientific and Technical Information of China (English)
Zhang Ru; Ai Ting; Li Hegui; Zhang Zetian; Liu Jianfeng
2013-01-01
In current research, a series of triaxial tests, which were employed to simulate three typical mining lay-outs (i.e., top-coal caving, non-pillar mining and protected coal seam mining), were conducted on coal by using MTS815 Flex Test GT rock mechanics test system, and the fracture networks in the broken coal samples were qualitatively and quantitatively investigated by employing CT scanning and 3D reconstruc-tion techniques. This work aimed at providing a detail description on the micro-structure and fracture-connectivity characteristics of rupture coal samples under different mining layouts. The results show that: (i) for protected coal seam mining layout, the coal specimens failure is in a compression-shear manner and oppositely, (ii) the tension-shear failure phenomenon is observed for top-coal caving and non-pillar mining layouts. By investigating the connectivity features of the generated fractures in the direction of r1 under different mining layouts, it is found that the connectivity level of the fractures of the samples corresponding to non-pillar mining layout was the highest.
Tecklenburg, Jan; Neuweiler, Insa; Carrera, Jesus; Dentz, Marco
2016-05-01
We study modeling of two-phase flow in highly heterogeneous fractured and porous media. The flow behaviour is strongly influenced by mass transfer between a highly permeable (mobile) fracture domain and less permeable (immobile) matrix blocks. We quantify the effective two-phase flow behavior using a multirate rate mass transfer (MRMT) approach. We discuss the range of applicability of the MRMT approach in terms of the pertinent viscous and capillary diffusion time scales. We scrutinize the linearization of capillary diffusion in the immobile regions, which allows for the formulation of MRMT in the form of a non-local single equation model. The global memory function, which encodes mass transfer between the mobile and the immobile regions, is at the center of this method. We propose two methods to estimate the global memory function for a fracture network with given fracture and matrix geometry. Both employ a scaling approach based on the known local memory function for a given immobile region. With the first method, the local memory function is calculated numerically, while the second one employs a parametric memory function in form of truncated power-law. The developed concepts are applied and tested for fracture networks of different complexity. We find that both physically based parameter estimation methods for the global memory function provide predictive MRMT approaches for the description of multiphase flow in highly heterogeneous porous media.
DEFF Research Database (Denmark)
Mosthaf, Klaus; Rosenberg, L.; Balbarini, Nicola
approaches have been developed to describe contaminant transport in fractured media, such as the discrete fracture (with various fracture geometries), equivalent porous media (with and without anisotropy), and dual porosity models. However, these modeling concepts are not well tested for limestone geologies...... of field data is the determination of relevant hydraulic properties and interpretation of aqueous and solid phase contaminant concentration sampling data. Traditional water sampling has a bias towards fracture sampling, however concentrations in the limestone matrix are needed for assessing contaminant...
Osinga, S.; Pizzocolo, F.; Veer, E.F. van der; Heege, J.H. ter
2016-01-01
Fractured rocks play an important role in many types of petroleum and geo-energy operations. From fractured limestone reservoirs to unconventionals, understanding the geomechanical behaviour and the dynamically coupled (dual) permeability system is paramount for optimal development of these systems.
Elasto-viscoplastic phase field modelling of anisotropic cleavage fracture
Shanthraj, P.; Svendsen, B.; Sharma, L.; Roters, F.; Raabe, D.
2017-02-01
A finite-strain anisotropic phase field method is developed to model the localisation of damage on a defined family of crystallographic planes, characteristic of cleavage fracture in metals. The approach is based on the introduction of an undamaged configuration, and the inelastic deformation gradient mapping this configuration to a damaged configuration is microstructurally represented by the opening of a set of cleavage planes in the three fracture modes. Crack opening is modelled as a dissipative process, and its evolution is thermodynamically derived. To couple this approach with a physically-based phase field method for brittle fracture, a scalar measure of the overall local damage is introduced, whose evolution is determined by the crack opening rates, and weakly coupled with the non-local phase field energy representing the crack opening resistance in the classical sense of Griffith. A finite-element implementation of the proposed model is employed to simulate the crack propagation path in a laminate and a polycrystalline microstructure. As shown in this work, it is able to predict the localisation of damage on the set of pre-defined cleavage planes, as well as the kinking and branching of the crack resulting from the crystallographic misorientation across the laminate boundary and the grain boundaries respectively.
Contaminated open fracture and crush injury:a murine model
Institute of Scientific and Technical Information of China (English)
Shawn R Gilbert; Justin Camara; Richard Camara; Lynn Duffy; Ken Waites; Hyunki Kim; Kurt Zinn
2015-01-01
Modern warfare has caused a large number of severe extremity injuries, many of which become infected. In more recent conflicts, a pattern of co-infection with Acinetobacter baumannii and methicillin-resistant Staphylococcus aureus has emerged. We attempted to recreate this pattern in an animal model to evaluate the role of vascularity in contaminated open fractures. Historically, it has been observed that infected bones frequently appear hypovascular, but vascularity in association with bone infection has not been examined in animal models. Adult rats underwent femur fracture and muscle crush injury followed by stabilization and bacterial contamination with A. baumannii complex and methicillin-resistant Staphylococcus aureus. Vascularity and perfusion were assessed by microCT angiography and SPECT scanning, respectively, at 1, 2 and 4 weeks after injury. Quantitative bacterial cultures were also obtained. Multi-bacterial infections were successfully created, with methicillin-resistant S. aureus predominating. There was overall increase in blood flow to injured limbs that was markedly greater in bacteria-inoculated limbs. Vessel volume was greater in the infected group. Quadriceps atrophy was seen in both groups, but was greater in the infected group. In this animal model, infected open fractures had greater perfusion and vascularity than non-infected limbs.
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
Advances in theoretical models of network science
Institute of Scientific and Technical Information of China (English)
FANG Jin-qing; BI Qiao; LI Yong
2007-01-01
In this review article, we will summarize the main advances in network science investigated by the CIAE Group of Complex Network in this field. Several theoretical models of network science were proposed and their topological and dynamical properties are reviewed and compared with the other models. Our models mainly include a harmonious unifying hybrid preferential model, a large unifying hybrid network model, a quantum interference network, a hexagonal nanowire network, and a small-world network with the same degree. The models above reveal some new phenomena and findings, which are useful for deeply understanding and investigating complex networks and their applications.
Structure learning for Bayesian networks as models of biological networks.
Larjo, Antti; Shmulevich, Ilya; Lähdesmäki, Harri
2013-01-01
Bayesian networks are probabilistic graphical models suitable for modeling several kinds of biological systems. In many cases, the structure of a Bayesian network represents causal molecular mechanisms or statistical associations of the underlying system. Bayesian networks have been applied, for example, for inferring the structure of many biological networks from experimental data. We present some recent progress in learning the structure of static and dynamic Bayesian networks from data.
Current approaches to gene regulatory network modelling
Directory of Open Access Journals (Sweden)
Brazma Alvis
2007-09-01
Full Text Available Abstract Many different approaches have been developed to model and simulate gene regulatory networks. We proposed the following categories for gene regulatory network models: network parts lists, network topology models, network control logic models, and dynamic models. Here we will describe some examples for each of these categories. We will study the topology of gene regulatory networks in yeast in more detail, comparing a direct network derived from transcription factor binding data and an indirect network derived from genome-wide expression data in mutants. Regarding the network dynamics we briefly describe discrete and continuous approaches to network modelling, then describe a hybrid model called Finite State Linear Model and demonstrate that some simple network dynamics can be simulated in this model.
Network model of security system
Directory of Open Access Journals (Sweden)
Adamczyk Piotr
2016-01-01
Full Text Available The article presents the concept of building a network security model and its application in the process of risk analysis. It indicates the possibility of a new definition of the role of the network models in the safety analysis. Special attention was paid to the development of the use of an algorithm describing the process of identifying the assets, vulnerability and threats in a given context. The aim of the article is to present how this algorithm reduced the complexity of the problem by eliminating from the base model these components that have no links with others component and as a result and it was possible to build a real network model corresponding to reality.
A new transient network model for associative polymer networks
Wientjes, R.H.W.; Jongschaap, R.J.J.; Duits, M.H.G.; Mellema, J.
1999-01-01
A new model for the linear viscoelastic behavior of polymer networks is developed. In this model the polymer system is described as a network of spring segments connected via sticky points (as in the Lodge model). [Lodge, A. S., “A network theory of flow birefringence and stress in concentrated poly
DEFF Research Database (Denmark)
Bisdom, Kevin; Bertotti, Giovanni; Nick, Hamid
2016-01-01
Predicting equivalent permeability in fractured reservoirs requires an understanding of the fracture network geometry and apertures. There are different methods for defining aperture, based on outcrop observations (power law scaling), fundamental mechanics (sublinear length-aperture scaling...
A large deformation viscoelastic model for double-network hydrogels
Mao, Yunwei; Lin, Shaoting; Zhao, Xuanhe; Anand, Lallit
2017-03-01
We present a large deformation viscoelasticity model for recently synthesized double network hydrogels which consist of a covalently-crosslinked polyacrylamide network with long chains, and an ionically-crosslinked alginate network with short chains. Such double-network gels are highly stretchable and at the same time tough, because when stretched the crosslinks in the ionically-crosslinked alginate network rupture which results in distributed internal microdamage which dissipates a substantial amount of energy, while the configurational entropy of the covalently-crosslinked polyacrylamide network allows the gel to return to its original configuration after deformation. In addition to the large hysteresis during loading and unloading, these double network hydrogels also exhibit a substantial rate-sensitive response during loading, but exhibit almost no rate-sensitivity during unloading. These features of large hysteresis and asymmetric rate-sensitivity are quite different from the response of conventional hydrogels. We limit our attention to modeling the complex viscoelastic response of such hydrogels under isothermal conditions. Our model is restricted in the sense that we have limited our attention to conditions under which one might neglect any diffusion of the water in the hydrogel - as might occur when the gel has a uniform initial value of the concentration of water, and the mobility of the water molecules in the gel is low relative to the time scale of the mechanical deformation. We also do not attempt to model the final fracture of such double-network hydrogels.
Characterization of fracture processes by continuum and discrete modelling
Kaliske, M.; Dal, H.; Fleischhauer, R.; Jenkel, C.; Netzker, C.
2012-09-01
A large number of methods to describe fracture mechanical features of structures on basis of computational algorithms have been developed in the past due to the importance of the topic. In this paper, current and promising numerical approaches for the characterization of fracture processes are presented. A fracture phenomenon can either be depicted by a continuum formulation or a discrete notch. Thus, starting point of the description is a micromechanically motivated formulation for the development of a local failure situation. A current, generalized method without any restriction to material modelling and loading situation in order to describe an existing crack in a structure is available through the material force approach. One possible strategy to simulate arbitrary crack growth is based on an adaptive implementation of cohesive elements in combination with the standard discretization of the body. In this case, crack growth criteria and the determination of the crack propagation direction in combination with the modification of the finite element mesh are required. The nonlinear structural behaviour of a fibre reinforced composite material is based on the heterogeneous microstructure. A two-scale simulation is therefore an appropriate and effective way to take into account the scale differences of macroscopic structures with microscopic elements. In addition, fracture mechanical structural properties are far from being sharp and deterministic. Moreover, a wide range of uncertainties influence the ultimate load bearing behaviour. Therefore, it is evident that the deterministic modelling has to be expanded by a characterization of the uncertainty in order to achieve a reliable and realistic simulation result. The employed methods are illustrated by numerical examples.
Numerical modeling of concrete hydraulic fracturing with extended finite element method
Institute of Scientific and Technical Information of China (English)
REN QingWen; DONG YuWen; YU TianTang
2009-01-01
The extended finite element method (XFEM) is a new numerical method for modeling discontinuity.Research about numerical modeling for concrete hydraulic fracturing by XFEM is explored. By building the virtual work principle of the fracture problem considering water pressure on the crack surface, the governing equations of XFEM for hydraulic fracture modeling are derived. Implementation of the XFEM for hydraulic fracturing is presented. Finally, the method is verified by two examples and the advan-tages of the XFEM for hydraulic fracturing analysis are displayed.
Numerical modeling of concrete hydraulic fracturing with extended finite element method
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The extended finite element method (XFEM) is a new numerical method for modeling discontinuity. Research about numerical modeling for concrete hydraulic fracturing by XFEM is explored. By building the virtual work principle of the fracture problem considering water pressure on the crack surface, the governing equations of XFEM for hydraulic fracture modeling are derived. Implementation of the XFEM for hydraulic fracturing is presented. Finally, the method is verified by two examples and the advan- tages of the XFEM for hydraulic fracturing analysis are displayed.
Fracture surfaces of heterogeneous materials: A 2D solvable model
Katzav, E.; Adda-Bedia, M.; Derrida, B.
2007-05-01
Using an elastostatic description of crack growth based on the Griffith criterion and the principle of local symmetry, we present a stochastic model describing the propagation of a crack tip in a 2D heterogeneous brittle material. The model ensures the stability of straight cracks and allows for the study of the roughening of fracture surfaces. When neglecting the effect of the nonsingular stress, the problem becomes exactly solvable and yields analytic predictions for the power spectrum of the paths. This result suggests an alternative to the conventional power law analysis often used in the analysis of experimental data.
Directory of Open Access Journals (Sweden)
Isa Kolo
2016-01-01
Full Text Available A coupled elastic-plasticity-damage constitutive model, AK Model, is applied to predict fracture propagation in rocks. The quasi-brittle material model captures anisotropic effects and the distinct behavior of rocks in tension and compression. Calibration of the constitutive model is realized using experimental data for Carrara marble. Through the Weibull distribution function, heterogeneity effect is captured by spatially varying the elastic properties of the rock. Favorable comparison between model predictions and experiments for single-flawed specimens reveal that the AK Model is reliable and accurate for modelling fracture propagation in rocks.
A physical model study of effect of fracture aperture on seismic wave
Institute of Scientific and Technical Information of China (English)
2008-01-01
Based on Hudson’s theoretical hypothesis of equivalent fracture model,inserting aligned round chips in solid model can simulate fractured media. The effect of fractures on the propagation of P and S waves can be observed by changing the fracture thickness. The base model is made of epoxy resin,and the material of fractures is a kind of low-velocity mixture containing silicon rubber. With constant diameter and number of fractures in each model,one group of models can be formed through changing the thickness of fracture. These models have the same fracture density. By using the ultrasonic pulse transmission method,the experiment records time and waveform of P and S waves in the direction parallel and perpendicular to the fracture orientation. The result shows that,with the same fracture density,changing fracture aperture will affect both velocity and amplitude of P and S waves,and the effect on P-wave amplitude is much greater than that on the velocity. Moreover,the variation in velocity of S wave is more obvious in the slow shear wave (S2),while the variation in amplitude is more obvious in the fast shear wave (S1). These properties of wave propagation are useful for seismic data processing and interpretation.
Energy Technology Data Exchange (ETDEWEB)
La Pointe, Paul R. [Golder Associate Inc., Redmond, WA (United States); Olofsson, Isabelle; Hermanson, Jan [Golder Associates AB, Uppsala (Sweden)
2005-04-01
different high and low fracture intensity intervals in order to capture the variation of this parameter in the model volume. The fracture intensity P32 has been derived by means of simulations for each rock domain and each fracture type, and is expressed as a mean value, and if possible standard deviation and span. The uncertainty in the model has been quantified: for the different geometrical parameters by providing ranges of variations and studying relevant distribution models, by conducting sensitivity analysis on some input data: the effect of truncation of lineaments at the border of the regional model volume and the impact of truncation in outcrop mapping. An alternative conceptual model is under study which is based on the identified deterministic deformation zones, and not on lineaments. An important issue using this model is the bias of information and the limited amount of structures. The current DFN model still contains significant uncertainties which need to be resolved in order to be able to produce a final site DFN model. Three main issues are listed below: The definition of the subhorizontal fracture set in terms of geological processes and tectonics. The size distribution is a critical issue for the hydrogeology of the site. The variation of the fracture intensity by rock domain has been identified but the variation pattern and the spatial distribution within an individual domain are still sufficiently unpredictable that the fracture network permeability structure within a rock domain is uncertain from a conceptual perspective, not just a data uncertainty perspective. Moreover, many rock domains have not yet been sampled by boreholes or outcrops, and thus their fracture properties remain highly uncertain. Validation of the DFN models will require resolution of these two issues, and may also require the drilling of highly inclined or horizontal boreholes. Near-vertical boreholes and the mapping protocol to only map fracture traces in outcrop greater than 0
Full 3-D numerical modeling of borehole electric image logging and the evaluation model of fracture
Institute of Scientific and Technical Information of China (English)
2008-01-01
A full 3-D finite element method numerical modeling program is written based on the principle and technical specification of borehole electric image well logging tool. The response of well logging is computed in the formation media model with a single fracture. The effect of changing fracture aperture and resistivity ratio to the logging response is discussed. The identification ability for two parallel fractures is also present. A quantitative evaluation formula of fracture aperture from borehole electric image logging data is set up. A case study of the model well is done to verify the accuracy of the for-mula. The result indicates that the formula is more accurate than the foreign one.
Continuous and Discontinuous Modelling of Fracture in Concrete Using FEM
Tejchman, Jacek
2013-01-01
The book analyzes a quasi-static fracture process in concrete and reinforced concrete by means of constitutive models formulated within continuum mechanics. A continuous and discontinuous modelling approach was used. Using a continuous approach, numerical analyses were performed using a finite element method and three different enhanced continuum models: isotropic elasto-plastic, isotropic damage and anisotropic smeared crack one. The models were equipped with a characteristic length of micro-structure by means of a non-local and a second-gradient theory. So they could properly describe the formation of localized zones with a certain thickness and spacing and a related deterministic size effect. Using a discontinuous FE approach, numerical results of cracks using a cohesive crack model and XFEM were presented which were also properly regularized. Finite element analyses were performed with concrete elements under monotonic uniaxial compression, uniaxial tension, bending and shear-extension. Concrete beams un...
Finite element model of the Jefferson fracture: comparison with a cadaver model
Bozkus, Hakan; Karakas, Askin; Hancı, Murat; Uzan, Mustafa; Bozdag, Ergun; Sarıoglu, Ali
2001-01-01
This study tries to explain the reason why the Jefferson fracture is a burst fracture, using two different biomechanical models: a finite element model (FEM) and a cadaver model used to determine strain distribution in C1 during axial static compressive loading. For the FEM model, a three-dimensional model of C1 was obtained from a 29-year-old healthy human, using axial CT scans with intervals of 1.0 mm. The mesh model was composed of 8200 four-noded isoparametric tetrahedrons and 37,400 soli...
DEFF Research Database (Denmark)
Bisdom, Kevin; Bertotti, Giovanni; Nick, Hamid
2016-01-01
on subsurface fracture aperture, which is essential for quantifying porosity and permeability. Apertures are difficult to obtain from either outcropping or subsurface data and are therefore often based on fracture size or scaling relationships, but these do not consider the orientation and spatial distribution...
Target-Centric Network Modeling
DEFF Research Database (Denmark)
Mitchell, Dr. William L.; Clark, Dr. Robert M.
In Target-Centric Network Modeling: Case Studies in Analyzing Complex Intelligence Issues, authors Robert Clark and William Mitchell take an entirely new approach to teaching intelligence analysis. Unlike any other book on the market, it offers case study scenarios using actual intelligence repor....... Working through these cases, students will learn to manage and evaluate realistic intelligence accounts.......In Target-Centric Network Modeling: Case Studies in Analyzing Complex Intelligence Issues, authors Robert Clark and William Mitchell take an entirely new approach to teaching intelligence analysis. Unlike any other book on the market, it offers case study scenarios using actual intelligence......, and collaborative sharing in the process of creating a high-quality, actionable intelligence product. The case studies reflect the complexity of twenty-first century intelligence issues by dealing with multi-layered target networks that cut across political, economic, social, technological, and military issues...
A numerical model of hydro-thermo-mechanical coupling in a fractured rock mass
Energy Technology Data Exchange (ETDEWEB)
Bower, K.M.
1996-06-01
Coupled hydro-thermo-mechanical codes with the ability to model fractured materials are used for predicting groundwater flow behavior in fractured aquifers containing thermal sources. The potential applications of such a code include the analysis of groundwater behavior within a geothermal reservoir. The capability of modeling hydro-thermo systems with a dual porosity, fracture flow model has been previously developed in the finite element code, FEHM. FEHM has been modified to include stress coupling with the dual porosity feature. FEHM has been further developed to implicitly couple the dependence of fracture hydraulic conductivity on effective stress within two dimensional, saturated aquifers containing fracture systems. The cubic law for flow between parallel plates was used to model fracture permeability. The Bartin-Bandis relationship was used to determine the fracture aperture within the cubic law. The code used a Newton Raphson iteration to implicitly solve for six unknowns at each node. Results from a model of heat flow from a reservoir to the moving fluid in a single fracture compared well with analytic results. Results of a model showing the increase in fracture flow due to a single fracture opening under fluid pressure compared well with analytic results. A hot dry rock, geothermal reservoir was modeled with realistic time steps indicating that the modified FEHM code does successfully model coupled flow problems with no convergence problems.
Fundamental study of crack initiation and propagation. [Computer model of ductile fracture
Energy Technology Data Exchange (ETDEWEB)
Norris, D.M. Jr.; Reaugh, J.E.; Moran, B.; Quinones, D.F.; Wilkins, M.L.
1977-12-21
Objective is to determine the fracture toughness of A533B-1 steel by computer modeling Charpy V-notch tests. A computer model of ductile fracture was developed that predicts fracture initiation. The model contains a set of material-dependent parameters obtained by computer simulations of small specimen tests. The computer calculations give detailed stress and strain histories up to the time of fracture, which are used to determine the model parameter values. The calibrated fracture model, that correctly predicts fracture initiation (and initiation energy) in the Charpy specimen, may then be used to simulate tests of accepted fracture-toughness specimens and hence obtain fracture toughness. The model parameters were calibrated to predict fracture in four different test specimens: two different notched-tension specimens, a simple tension specimen, and a precracked compact-tension specimen. The model was then used in a computer simulation of the Charpy V-notch specimen to initiate and advance a flat fracture. Results were compared with interrupted Charpy tests. Calibration of the model for two additional heat treatments of A533B-1 steel is in progress.
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
Investigations led for several years at Laxemar and Forsmark reveal the large heterogeneity of geological formations and associated fracturing. This project aims at reinforcing the statistical DFN modeling framework adapted to a site scale. This leads therefore to develop quantitative methods of characterization adapted to the nature of fracturing and data availability. We start with the hypothesis that the maximum likelihood DFN model is a power-law model with a density term depending on orientations. This is supported both by literature and specifically here by former analyses of the SKB data. This assumption is nevertheless thoroughly tested by analyzing the fracture trace and lineament maps. Fracture traces range roughly between 0.5 m and 10 m - i e the usual extension of the sample outcrops. Between the raw data and final data used to compute the fracture size distribution from which the size distribution model will arise, several steps are necessary, in order to correct data from finite-size, topographical and sampling effects. More precisely, a particular attention is paid to fracture segmentation status and fracture linkage consistent with the DFN model expected. The fracture scaling trend observed over both sites displays finally a shape parameter k{sub t} close to 1.2 with a density term (alpha{sub 2d}) between 1.4 and 1.8. Only two outcrops clearly display a different trend with k{sub t} close to 3 and a density term (alpha{sub 2d}) between 2 and 3.5. The fracture lineaments spread over the range between 100 meters and a few kilometers. When compared with fracture trace maps, these datasets are already interpreted and the linkage process developed previously has not to be done. Except for the subregional lineament map from Forsmark, lineaments display a clear power-law trend with a shape parameter k{sub t} equal to 3 and a density term between 2 and 4.5. The apparent variation in scaling exponent, from the outcrop scale (k{sub t} = 1.2) on one side, to
Energy Technology Data Exchange (ETDEWEB)
Almansouri, Hani [Purdue University; Foster, Benjamin [Purdue University; Kisner, Roger A [ORNL; Polsky, Yarom [ORNL; Bouman, Charlie [Purdue University
2016-01-01
This paper documents our progress developing an ultrasound phased array system in combination with a model-based iterative reconstruction (MBIR) algorithm to inspect the health of and characterize the composition of the near-wellbore region for geothermal reservoirs. The main goal for this system is to provide a near-wellbore in-situ characterization capability that will significantly improve wellbore integrity evaluation and near well-bore fracture network mapping. A more detailed image of the fracture network near the wellbore in particular will enable the selection of optimal locations for stimulation along the wellbore, provide critical data that can be used to improve stimulation design, and provide a means for measuring evolution of the fracture network to support long term management of reservoir operations. Development of such a measurement capability supports current hydrothermal operations as well as the successful demonstration of Engineered Geothermal Systems (EGS). The paper will include the design of the phased array system, the performance specifications, and characterization methodology. In addition, we will describe the MBIR forward model derived for the phased array system and the propagation of compressional waves through a pseudo-homogenous medium.
(Environmental and geophysical modeling, fracture mechanics, and boundary element methods)
Energy Technology Data Exchange (ETDEWEB)
Gray, L.J.
1990-11-09
Technical discussions at the various sites visited centered on application of boundary integral methods for environmental modeling, seismic analysis, and computational fracture mechanics in composite and smart'' materials. The traveler also attended the International Association for Boundary Element Methods Conference at Rome, Italy. While many aspects of boundary element theory and applications were discussed in the papers, the dominant topic was the analysis and application of hypersingular equations. This has been the focus of recent work by the author, and thus the conference was highly relevant to research at ORNL.
A Two-Scale Reduced Model for Darcy Flow in Fractured Porous Media
Chen, Huangxin
2016-06-01
In this paper, we develop a two-scale reduced model for simulating the Darcy flow in two-dimensional porous media with conductive fractures. We apply the approach motivated by the embedded fracture model (EFM) to simulate the flow on the coarse scale, and the effect of fractures on each coarse scale grid cell intersecting with fractures is represented by the discrete fracture model (DFM) on the fine scale. In the DFM used on the fine scale, the matrix-fracture system are resolved on unstructured grid which represents the fractures accurately, while in the EFM used on the coarse scale, the flux interaction between fractures and matrix are dealt with as a source term, and the matrix-fracture system can be resolved on structured grid. The Raviart-Thomas mixed finite element methods are used for the solution of the coupled flows in the matrix and the fractures on both fine and coarse scales. Numerical results are presented to demonstrate the efficiency of the proposed model for simulation of flow in fractured porous media.
AVAZ inversion for fracture weakness parameters based on the rock physics model
Chen, Huaizhen; Yin, Xingyao; Qu, Shouli; Zhang, Guangzhi
2014-12-01
Subsurface fractures within many carbonates and unconventional resources play an important role in the storage and movement of fluid. The more reliably the detection of fractures could be performed, the more finely the reservoir description could be made. In this paper, we aim to propose a method which uses two important tools, a fractured anisotropic rock physics effective model and AVAZ (amplitude versus incident and azimuthal angle) inversion, to predict fractures from azimuthal seismic data. We assume that the rock, which contains one or more sets of vertical or sub-vertical fractures, shows transverse isotropy with a horizontal axis of symmetry (HTI). Firstly, we develop one improved fractured anisotropic rock physics effective model. Using this model, we estimate P-wave velocity, S-wave velocity and fracture weaknesses from well-logging data. Then the method is proposed to predict fractures from azimuthal seismic data based on AVAZ inversion, and well A is used to verify the reliability of the improved rock physics effective model. Results show that the estimated results are consistent with the real log value, and the variation of fracture weaknesses may detect the locations of fractures. The damped least squares method, which uses the estimated results as initial constraints during the inversion, is more stable. Tests on synthetic data show that fracture weaknesses parameters are still estimated reasonably with moderate noise. A test on real data shows that the estimated results are in good agreement with the drilling.
Directory of Open Access Journals (Sweden)
Cristina Eller-Vainicher
Full Text Available BACKGROUND: It is known that bone mineral density (BMD predicts the fracture's risk only partially and the severity and number of vertebral fractures are predictive of subsequent osteoporotic fractures (OF. Spinal deformity index (SDI integrates the severity and number of morphometric vertebral fractures. Nowadays, there is interest in developing algorithms that use traditional statistics for predicting OF. Some studies suggest their poor sensitivity. Artificial Neural Networks (ANNs could represent an alternative. So far, no study investigated ANNs ability in predicting OF and SDI. The aim of the present study is to compare ANNs and Logistic Regression (LR in recognising, on the basis of osteoporotic risk-factors and other clinical information, patients with SDI≥1 and SDI≥5 from those with SDI = 0. METHODOLOGY: We compared ANNs prognostic performance with that of LR in identifying SDI≥1/SDI≥5 in 372 women with postmenopausal-osteoporosis (SDI≥1, n = 176; SDI = 0, n = 196; SDI≥5, n = 51, using 45 variables (44 clinical parameters plus BMD. ANNs were allowed to choose relevant input data automatically (TWIST-system-Semeion. Among 45 variables, 17 and 25 were selected by TWIST-system-Semeion, in SDI≥1 vs SDI = 0 (first and SDI≥5 vs SDI = 0 (second analysis. In the first analysis sensitivity of LR and ANNs was 35.8% and 72.5%, specificity 76.5% and 78.5% and accuracy 56.2% and 75.5%, respectively. In the second analysis, sensitivity of LR and ANNs was 37.3% and 74.8%, specificity 90.3% and 87.8%, and accuracy 63.8% and 81.3%, respectively. CONCLUSIONS: ANNs showed a better performance in identifying both SDI≥1 and SDI≥5, with a higher sensitivity, suggesting its promising role in the development of algorithm for predicting OF.
Triple Medium Physical Model of Post Fracturing High-Rank Coal Reservoir in Southern Qinshui Basin
Institute of Scientific and Technical Information of China (English)
Shiqi Liu; Shuxun Sang; Qipeng Zhu; Jiefang Zhang; Hefeng Gao; Huihu Liu; Lixing Lin
2015-01-01
In this paper, influences on the reservoir permeability, the reservoir architecture and the fluid flow pattern caused by hydraulic fracturing are analyzed. Based on the structure and production fluid flow model of post fracturing high-rank coal reservoir, Warren-Root Model is improved. A new physical model that is more suitable for post fracturing high-rank coal reser-voir is established. The results show that the width, the flow conductivity and the permeability of hydraulic fractures are much larger than natural fractures in coal bed reservoir. Hydraulic frac-ture changes the flow pattern of gas and flow channel to wellbore, thus should be treated as an independent medium. Warrant-Root Model has some limitations and can’t give a comprehensive interpretation of seepage mechanism in post fracturing high-rank coal reservoir. Modified War-rant-Root Model simplifies coal bed reservoir to an ideal system with hydraulic fracture, ortho-gonal macroscopic fracture and cuboid matrix. Hydraulic fracture is double wing, vertical and symmetric to wellbore. Coal bed reservoir is divided into cuboids by hydraulic fracture and fur-ther by macroscopic fractures. Flow behaviors in coal bed reservoir are simplified to three step flows of gas and two step flows of water. The swap mode of methane between coal matrix and macroscopic fractures is pseudo steady fluid channeling. The flow behaviors of methane to well-bore no longer follow Darcy’s Law and are mainly affected by inertia force. The flow pattern of water follows Darcy’s Law. The new physical model is more suitable for post fracturing high-rank coal reservoir.
Quasi-Brittle Fracture Modeling of Preflawed Bitumen Using a Diffuse Interface Model
Directory of Open Access Journals (Sweden)
Yue Hou
2016-01-01
Full Text Available Fundamental understandings on the bitumen fracture mechanism are vital to improve the mixture design of asphalt concrete. In this paper, a diffuse interface model, namely, phase-field method is used for modeling the quasi-brittle fracture in bitumen. This method describes the microstructure using a phase-field variable which assumes one in the intact solid and negative one in the crack region. Only the elastic energy will directly contribute to cracking. To account for the growth of cracks, a nonconserved Allen-Cahn equation is adopted to evolve the phase-field variable. Numerical simulations of fracture are performed in bituminous materials with the consideration of quasi-brittle properties. It is found that the simulation results agree well with classic fracture mechanics.
Micromechanical modeling of damage and fracture of unidirectional fiber reinforced composites
DEFF Research Database (Denmark)
Mishnaevsky, Leon; Brøndsted, Povl
2009-01-01
An overview of methods of the mathematical modeling of deformation, damage and fracture in fiber reinforced composites is presented. The models are classified into five main groups: shear lag-based, analytical models, fiber bundle model and its generalizations, fracture mechanics based and contin...
Glaessgen, Edward H.; Saether, Erik; Phillips, Dawn R.; Yamakov, Vesselin
2006-01-01
A multiscale modeling strategy is developed to study grain boundary fracture in polycrystalline aluminum. Atomistic simulation is used to model fundamental nanoscale deformation and fracture mechanisms and to develop a constitutive relationship for separation along a grain boundary interface. The nanoscale constitutive relationship is then parameterized within a cohesive zone model to represent variations in grain boundary properties. These variations arise from the presence of vacancies, intersticies, and other defects in addition to deviations in grain boundary angle from the baseline configuration considered in the molecular dynamics simulation. The parameterized cohesive zone models are then used to model grain boundaries within finite element analyses of aluminum polycrystals.
CNEM: Cluster Based Network Evolution Model
Directory of Open Access Journals (Sweden)
Sarwat Nizamani
2015-01-01
Full Text Available This paper presents a network evolution model, which is based on the clustering approach. The proposed approach depicts the network evolution, which demonstrates the network formation from individual nodes to fully evolved network. An agglomerative hierarchical clustering method is applied for the evolution of network. In the paper, we present three case studies which show the evolution of the networks from the scratch. These case studies include: terrorist network of 9/11 incidents, terrorist network of WMD (Weapons Mass Destruction plot against France and a network of tweets discussing a topic. The network of 9/11 is also used for evaluation, using other social network analysis methods which show that the clusters created using the proposed model of network evolution are of good quality, thus the proposed method can be used by law enforcement agencies in order to further investigate the criminal networks
Fracture development around deep underground excavations: Insights from FDEM modelling
Directory of Open Access Journals (Sweden)
Andrea Lisjak
2014-12-01
Full Text Available Over the past twenty years, there has been a growing interest in the development of numerical models that can realistically capture the progressive failure of rock masses. In particular, the investigation of damage development around underground excavations represents a key issue in several rock engineering applications, including tunnelling, mining, drilling, hydroelectric power generation, and the deep geological disposal of nuclear waste. The goal of this paper is to show the effectiveness of a hybrid finite-discrete element method (FDEM code to simulate the fracturing mechanisms associated with the excavation of underground openings in brittle rock formations. A brief review of the current state-of-the-art modelling approaches is initially provided, including the description of selecting continuum- and discontinuum-based techniques. Then, the influence of a number of factors, including mechanical and in situ stress anisotropy, as well as excavation geometry, on the simulated damage is analysed for three different geomechanical scenarios. Firstly, the fracture nucleation and growth process under isotropic rock mass conditions is simulated for a circular shaft. Secondly, the influence of mechanical anisotropy on the development of an excavation damaged zone (EDZ around a tunnel excavated in a layered rock formation is considered. Finally, the interaction mechanisms between two large caverns of an underground hydroelectric power station are investigated, with particular emphasis on the rock mass response sensitivity to the pillar width and excavation sequence. Overall, the numerical results indicate that FDEM simulations can provide unique geomechanical insights in cases where an explicit consideration of fracture and fragmentation processes is of paramount importance.
Evaluation of modeling approaches to simulate contaminant transport in a fractured limestone aquifer
DEFF Research Database (Denmark)
Mosthaf, Klaus; Fjordbøge, Annika Sidelmann; Broholm, Mette Martina
contaminant transport in fractured media, such as discrete fracture, equivalent porous media, and dual continuum models. However, these modeling concepts are not well tested for real limestone geologies. Our goal is therefore to develop, evaluate and compare approaches for modeling transport of contaminants...... data is the determination of relevant hydraulic properties and interpretation of aqueous and solid phase contaminant concentration sampling data. Traditional water sampling has a bias towards fracture sampling; however, concentrations in the limestone matrix are needed for assessing contaminant rebound...
Biological transportation networks: Modeling and simulation
Albi, Giacomo
2015-09-15
We present a model for biological network formation originally introduced by Cai and Hu [Adaptation and optimization of biological transport networks, Phys. Rev. Lett. 111 (2013) 138701]. The modeling of fluid transportation (e.g., leaf venation and angiogenesis) and ion transportation networks (e.g., neural networks) is explained in detail and basic analytical features like the gradient flow structure of the fluid transportation network model and the impact of the model parameters on the geometry and topology of network formation are analyzed. We also present a numerical finite-element based discretization scheme and discuss sample cases of network formation simulations.
Pirolo, Joseph M; Behn, Anthony W; Abrams, Geoffrey D; Bishop, Julius A
2015-09-01
Both medial and anterolateral plate applications have been described for the treatment of distal tibia fractures, each with distinct advantages and disadvantages. The objective of this study was to compare the biomechanical properties of medial and anterolateral plating constructs used to stabilize simulated varus and valgus fracture patterns of the distal tibia. In 16 synthetic tibia models, a 45° oblique cut was made to model an Orthopedic Trauma Association type 43-A1.2 distal tibia fracture in either a varus or valgus injury pattern. Each fracture was then reduced and plated with a precontoured medial or anterolateral distal tibia plate. The specimens were biomechanically tested in axial and torsional loading, cyclic axial loading, and load to failure. For the varus fracture pattern, medial plating showed less fracture site displacement and rotation and was stiffer in both axial and torsional loading (Ptibia fractures.
Numerical modeling of the effects of roughness on flow and eddy formation in fractures
Directory of Open Access Journals (Sweden)
Scott Briggs
2017-02-01
Full Text Available The effect of roughness on flow in fractures was investigated using lattice Boltzmann method (LBM. Simulations were conducted for both statistically generated hypothetical fractures and a natural dolomite fracture. The effect of increasing roughness on effective hydraulic aperture, Izbash and Forchheimer parameters with increasing Reynolds number (Re ranging from 0.01 to 500 was examined. The growth of complex flow features, such as eddies arising near the fracture surface, was directly associated with changes in surface roughness. Rapid eddy growth above Re values of 1, followed by less rapid growth at higher Re values, suggested a three-zone nonlinear model for flow in rough fractures. This three-zone model, relating effective hydraulic conductivity to Re, was also found to be appropriate for the simulation of water flow in the natural dolomite fracture. Increasing fracture roughness led to greater eddy volumes and lower effective hydraulic conductivities for the same Re values.
Calculation of Forming Limits for Sheet Metal using an Enhanced Continuous Damage Fracture Model
Nguyen, Ngoc-Trung; Kim, Dae-Young; Kim, Heon Young
2011-08-01
An enhanced continuous damage fracture model was introduced in this paper to calculate forming limits of sheet metal. The fracture model is a combination of a fracture criterion and a continuum damage constitutive law. A modified McClintock void growth fracture criterion was incorporated with a coupled damage-plasticity Gurson-type constitutive law. Also, by introducing a Lode angle dependent parameter to define the loading asymmetry condition, the shear effect was phenomenologically taken into account. The proposed fracture model was implemented using user-subroutines in commercial finite element software. The model was calibrated and correlated by the uniaxial tension, shear and notched specimens tests. Application of the fracture model for the LDH tests was discussed and the simulation results were compared with the experimental data.
Ising model for distribution networks
Hooyberghs, H; Giuraniuc, C; Van Schaeybroeck, B; Indekeu, J O
2012-01-01
An elementary Ising spin model is proposed for demonstrating cascading failures (break-downs, blackouts, collapses, avalanches, ...) that can occur in realistic networks for distribution and delivery by suppliers to consumers. A ferromagnetic Hamiltonian with quenched random fields results from policies that maximize the gap between demand and delivery. Such policies can arise in a competitive market where firms artificially create new demand, or in a solidary environment where too high a demand cannot reasonably be met. Network failure in the context of a policy of solidarity is possible when an initially active state becomes metastable and decays to a stable inactive state. We explore the characteristics of the demand and delivery, as well as the topological properties, which make the distribution network susceptible of failure. An effective temperature is defined, which governs the strength of the activity fluctuations which can induce a collapse. Numerical results, obtained by Monte Carlo simulations of t...
Modeling of Fracture Toughness of Electroless Nickel （EN） Coatings
Institute of Scientific and Technical Information of China (English)
K.Zangeneh; S.M.Monir-vaghefi; F.Ashrafizadeh
2004-01-01
In the present reserch, a model has been proposed for estimate fracture toughness of Nickel-phosphorus (EN) layers. For this purpose, high phosphorus (9%) EN coatings with thicknesses of 6, 12, 24, 36 and 48μm were applied on steel substrates and then treated as conventional process. Fracture toughness of coatings was obtained using Vickers indentation method. It is found that fracture toughness increses as coating thickness reduces. Effect of coating thickness on fracture toughness was exhibited by various models. Evaluation of models revealed good agreement between of proposed model (Kc=f(t,t2)) and experimental data.
Thermally induced fractures: A field proven analytical model
Energy Technology Data Exchange (ETDEWEB)
Detienne, J.L.; Creusot, M.; Kesslar, N. [and others
1995-12-31
Thermally Induced Fracturing (TIF) during water injection is a well-established phenomenon. TIF modelling implies solving simultaneously equations which are dealt with separately in conventional petroleum engineering applications. Combining these equations leads to very complex computer programs. This has led to the requirement for the simple model which is presented in this paper. Coupling analytical expressions representing each of these phenomena, rather than the basic physical equations, has led to a computer program which can be run on a modem desk-top computer. This program has successfully matched the daily wellhead pressure and injection rate over a period of 3 to 5 years, for injection wells in complex sandstone/dolomite reservoirs. The model can be used for injection well monitoring as well as in a predictive mode when planning new water injection projects. The algorithm is sufficiently simple to be implemented in a conventional reservoir simulator.
Review of permeability evolution model for fractured porous media
Institute of Scientific and Technical Information of China (English)
Jianjun Ma
2015-01-01
The ability to capture permeability of fractured porous media plays a significant role in several engi-neering applications, including reservoir, mining, petroleum and geotechnical engineering. In order to solve fluid flow and coupled flow-deformation problems encountered in these engineering applications, both empirical and theoretical models had been proposed in the past few decades. Some of them are simple but still work in certain circumstances;others are complex but also need some modifications to be applicable. Thus, the understanding of state-of-the-art permeability evolution model would help researchers and engineers solve engineering problems through an appropriate approach. This paper summarizes permeability evolution models proposed by earlier and recent researchers with emphasis on their characteristics and limitations.
Nonparametric Bayesian Modeling of Complex Networks
DEFF Research Database (Denmark)
Schmidt, Mikkel Nørgaard; Mørup, Morten
2013-01-01
Modeling structure in complex networks using Bayesian nonparametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This article provides a gentle introduction to nonparametric Bayesian modeling of complex networks: Using...... for complex networks can be derived and point out relevant literature....
Stress analysis of fracture of atherosclerotic plaques: crack propagation modeling.
Rezvani-Sharif, Alireza; Tafazzoli-Shadpour, Mohammad; Kazemi-Saleh, Davood; Sotoudeh-Anvari, Maryam
2016-12-09
Traditionally, the degree of luminal obstruction has been used to assess the vulnerability of atherosclerotic plaques. However, recent studies have revealed that other factors such as plaque morphology, material properties of lesion components and blood pressure may contribute to the fracture of atherosclerotic plaques. The aim of this study was to investigate the mechanism of fracture of atherosclerotic plaques based on the mechanical stress distribution and fatigue analysis by means of numerical simulation. Realistic models of type V plaques were reconstructed based on histological images. Finite element method was used to determine mechanical stress distribution within the plaque. Assuming that crack propagation initiated at the sites of stress concentration, crack propagation due to pulsatile blood pressure was modeled. Results showed that crack propagation considerably changed the stress field within the plaque and in some cases led to initiation of secondary cracks. The lipid pool stiffness affected the location of crack formation and the rate and direction of crack propagation. Moreover, increasing the mean or pulse pressure decreased the number of cycles to rupture. It is suggested that crack propagation analysis can lead to a better recognition of factors involved in plaque rupture and more accurate determination of vulnerable plaques.
Size effect on brittle and ductile fracture of two-dimensional interlinked carbon nanotube network
Jing, Yuhang; Aluru, N. R.
2017-09-01
The mechanical properties of two-dimensional (2D) interlinked carbon nanotube (CNT) network are investigated using ab initio calculation and molecular dynamics simulations (MD) with Reaxff force field. The simulation results show that bulk 2D interlinked CNT network has good mechanical properties along the axial direction which can be comparable to that of single-walled CNT and graphene, but has better ductility along the radial direction than single-walled CNT and graphene. In addition, the mechanical properties of 2D interlinked CNT network ribbon along the radial direction depend strongly on the size of the ribbon. The Young's modulus and Poisson's ratio decrease as the size increases while the fracture strain increases with the size increasing. By analyzing the atomic structural (both bond length and atomic von Mises stress) evolution of the ribbons, the mechanism of a brittle-to-ductile transition is revealed. The exploration of the mechanical properties of the 2D interlinked CNT network paves the way for application of the relevant devices that can benefit from the high Young's modulus, high tensile strength, and good ductility.
Energy Technology Data Exchange (ETDEWEB)
Paul Meakin; Alexandre Tartakovsky
2009-07-01
In the subsurface fluids play a critical role by transporting dissolved minerals, colloids and contaminants (sometimes over long distances), by mediating dissolution and precipitation processes and enabling chemical transformations in solution and at mineral surfaces. Although the complex geometries of fracture apertures, fracture networks and pore spaces may make it difficult to accurately predict fluid flow in saturated (single-phase) subsurface systems, well developed methods are available. The simulation of multiphase fluid flow in the subsurface is much more challenging because of the large density and/or viscosity ratios found in important applications (water/air in the vadose zone, water/oil, water/gas, gas/oil and water/oil/gas in oil reservoirs, water/air/non-aqueous phase liquids (NAPL) in contaminated vadose zone systems and gas/molten rock in volcanic systems, for example). In addition, the complex behavior of fluid-fluid-solid contact lines, and its impact on dynamic contact angles, must also be taken into account, and coupled with the fluid flow. Pore network models and simple statistical physics based models such as the invasion percolation and diffusion-limited aggregation models have been used quite extensively. However, these models for multiphase fluid flow are based on simplified models for pore space geometries and simplified physics. Other methods such a lattice Boltzmann and lattice gas models, molecular dynamics, Monte Carlo methods, and particle methods such as dissipative particle dynamics and smoothed particle hydrodynamics are based more firmly on first principles, and they do not require simplified pore and/or fracture geometries. However, they are less (in some cases very much less) computationally efficient that pore network and statistical physics models. Recently a combination of continuum computation fluid dynamics, fluid-fluid interface tracking or capturing and simple models for the dependence of contact angles on fluid velocity
Energy Technology Data Exchange (ETDEWEB)
Meakin, Paul; Tartakovsky, Alexandre M.
2009-01-01
In the subsurface fluids play a critical role by transporting dissolved minerals, colloids and contaminants (sometimes over long distances), by mediating dissolution and precipitation processes and enabling chemical transformations in solution and at mineral surfaces. Although the complex geometries of fracture apertures, fracture networks and pore spaces may make it difficult to accurately predict fluid flow in saturated (single-phase) subsurface systems, well developed methods are available. The simulation of multiphase fluid flow in the subsurface is much more challenging because of the large density and/or viscosity ratios found in important applications (water/air in the vadose zone, water/oil, water/gas, gas/oil and water/oil/gas in oil reservoirs, water/air/non-aqueous phase liquids (NAPL) in contaminated vadose zone systems and gas/molten rock in volcanic systems, for example). In addition, the complex behavior of fluid-fluid-solid contact lines, and its impact on dynamic contact angles, must also be taken into account, and coupled with the fluid flow. Pore network models and simple statistical physics based models such as the invasion percolation and diffusion-limited aggregation models have been used quite extensively. However, these models for multiphase fluid flow are based on simplified models for pore space geometries and simplified physics. Other methods such a lattice Boltzmann and lattice gas models, molecular dynamics, Monte Carlo methods, and particle methods such as dissipative particle dynamics and smoothed particle hydrodynamics are based more firmly on first principles, and they do not require simplified pore and/or fracture geometries. However, they are less (in some cases very much less) computationally efficient that pore network and statistical physics models. Recently a combination of continuum computation fluid dynamics, fluid-fluid interface tracking or capturing and simple models for the dependence of contact angles on fluid velocity
A triple-continuum approach for modeling flow and transportprocesses in fractured rock
Energy Technology Data Exchange (ETDEWEB)
Wu, Yu-Shu; Liu, H.H.; Bodvarsson, G.S; Zellmer, K .E.
2001-08-31
This paper presents a triple-continuum conceptual model forsimulating flow and transport processes in fractured rock. Field datacollected from the unsaturated zone of Yucca Mountain, a repository siteof high-level nuclear waste, show a large number of small-scalefractures. The effect of these small fractures has not been considered inprevious modeling investigations within the context of a continuumapproach. A new triple-continuum model (consisting of matrix,small-fracture, and large-fracture continua) has been developed toinvestigate the effect of these small fractures. This paper derives themodel formulation and discusses the basic triple-continuum behavior offlow and transport processes under different conditions, using bothanalytical solutions and numerical approaches. The simulation resultsfrom the site-scale model of the unsaturated zone of Yucca Mountainindicate that these small fractures may have an important effect onradionuclide transport within the mountain
Sanford, Ward E.
2016-11-01
The trend of decreasing permeability with depth was estimated in the fractured-rock terrain of the upper Potomac River basin in the eastern USA using model calibration on 200 water-level observations in wells and 12 base-flow observations in subwatersheds. Results indicate that permeability at the 1-10 km scale (for groundwater flowpaths) decreases by several orders of magnitude within the top 100 m of land surface. This depth range represents the transition from the weathered, fractured regolith into unweathered bedrock. This rate of decline is substantially greater than has been observed by previous investigators that have plotted in situ wellbore measurements versus depth. The difference is that regional water levels give information on kilometer-scale connectivity of the regolith and adjacent fracture networks, whereas in situ measurements give information on near-hole fractures and fracture networks. The approach taken was to calibrate model layer-to-layer ratios of hydraulic conductivity (LLKs) for each major rock type. Most rock types gave optimal LLK values of 40-60, where each layer was twice a thick as the one overlying it. Previous estimates of permeability with depth from deeper data showed less of a decline at modeling results. There was less certainty in the modeling results deeper than 200 m and for certain rock types where fewer water-level observations were available. The results have implications for improved understanding of watershed-scale groundwater flow and transport, such as for the timing of the migration of pollutants from the water table to streams.
Sanford, Ward E.
2017-03-01
The trend of decreasing permeability with depth was estimated in the fractured-rock terrain of the upper Potomac River basin in the eastern USA using model calibration on 200 water-level observations in wells and 12 base-flow observations in subwatersheds. Results indicate that permeability at the 1-10 km scale (for groundwater flowpaths) decreases by several orders of magnitude within the top 100 m of land surface. This depth range represents the transition from the weathered, fractured regolith into unweathered bedrock. This rate of decline is substantially greater than has been observed by previous investigators that have plotted in situ wellbore measurements versus depth. The difference is that regional water levels give information on kilometer-scale connectivity of the regolith and adjacent fracture networks, whereas in situ measurements give information on near-hole fractures and fracture networks. The approach taken was to calibrate model layer-to-layer ratios of hydraulic conductivity (LLKs) for each major rock type. Most rock types gave optimal LLK values of 40-60, where each layer was twice a thick as the one overlying it. Previous estimates of permeability with depth from deeper data showed less of a decline at modeling results. There was less certainty in the modeling results deeper than 200 m and for certain rock types where fewer water-level observations were available. The results have implications for improved understanding of watershed-scale groundwater flow and transport, such as for the timing of the migration of pollutants from the water table to streams.
Taal-van Koppen, J.K.J.
2008-01-01
Fractured reservoirs are notoriously difficult to characterize because the resolution of seismic data is too low to detect fractures whereas borehole data is detailed but sparse. Therefore, outcrops can be of great support in gaining knowledge of the three-dimensional geometry of fracture networks,
Mathematical Modelling Plant Signalling Networks
Muraro, D.
2013-01-01
During the last two decades, molecular genetic studies and the completion of the sequencing of the Arabidopsis thaliana genome have increased knowledge of hormonal regulation in plants. These signal transduction pathways act in concert through gene regulatory and signalling networks whose main components have begun to be elucidated. Our understanding of the resulting cellular processes is hindered by the complex, and sometimes counter-intuitive, dynamics of the networks, which may be interconnected through feedback controls and cross-regulation. Mathematical modelling provides a valuable tool to investigate such dynamics and to perform in silico experiments that may not be easily carried out in a laboratory. In this article, we firstly review general methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This mathematical analysis of sub-cellular molecular mechanisms paves the way for more comprehensive modelling studies of hormonal transport and signalling in a multi-scale setting. © EDP Sciences, 2013.
Liu, Yong-gang; Zuo, Li-xin; Pei, Guo-xian; Dai, Ke; Sang, Jing-wei
2013-08-20
To explore the establishment of Schatzker classification digital model of tibial plateau fractures and its application in virtual surgery. Proximal tibial of one healthy male volunteer was examined with 64-slice spiral computed tomography (CT). The data were processed by software Mimics 10.01 and a model of proximal tibia was reconstructed. According to the Schatzker classification criteria of tibial plateau fractures, each type of fracture model was simulated.Screen-captures of fracture model were saved from different directions.Each type of fracture model was exported as video mode.Fracture model was imported into FreeForm modeling system.With a force feedback device, a surgeon could conduct virtual fracture operation simulation.Utilizing the GHOST of FreeForm modeling system, the software of virtual cutting, fracture reduction and fixation was developed.With a force feedback device PHANTOM, a surgeon could manipulate virtual surgical instruments and fracture classification model and simulate surgical actions such as assembly of surgical instruments, drilling, implantation of screw, reduction of fracture, bone grafting and fracture fixation, etc. The digital fracture model was intuitive, three-dimensional and realistic and it had excellent visual effect.Fracture could be observed and charted from optional direction and angle.Fracture model could rotate 360 ° in the corresponding video mode. The virtual surgical environment had a strong sense of reality, immersion and telepresence as well as good interaction and force feedback function in the FreeForm modeling system. The user could make the corresponding decisions about surgical method and choice of internal fixation according to the specific type of tibial plateau fracture as well as repeated operational practice in virtual surgery system. The digital fracture model of Schatzker classification is intuitive, three-dimensional, realistic and dynamic. The virtual surgery systems of Schatzker classifications make
Random Boolean network models and the yeast transcriptional network
Kauffman, Stuart; Peterson, Carsten; Samuelsson, Björn; Troein, Carl
2003-12-01
The recently measured yeast transcriptional network is analyzed in terms of simplified Boolean network models, with the aim of determining feasible rule structures, given the requirement of stable solutions of the generated Boolean networks. We find that for ensembles of generated models, those with canalyzing Boolean rules are remarkably stable, whereas those with random Boolean rules are only marginally stable. Furthermore, substantial parts of the generated networks are frozen, in the sense that they reach the same state regardless of initial state. Thus, our ensemble approach suggests that the yeast network shows highly ordered dynamics.
Cohesive zone modelling of interface fracture near flaws in adhesive joints
DEFF Research Database (Denmark)
Hansen, Peter Feraren; Jensen, Henrik Myhre
2004-01-01
A cohesive zone model is suggested for modelling of interface fracture near flaws in adhesive joints. A shear-loaded adhesive joint bonded with a planar circular bond region is modelled using both the cohesive zone model and a fracture mechanical model. Results from the models show good agreement...... of crack propagation on the location and shape of the crack front and on the initial joint strength. Subsequently, the cohesive zone model is used to model interface fracture through a planar adhesive layer containing a periodic array of elliptical flaws. The effects of flaw shape are investigated, as well...... on the fracture process zone width relative to the flaw dimensions. It is also seen that with increasing fracture process zone width, the strength variation with the flaw shape decreases, however, the strength is effected over a wider range of propagation, (C) 2004 Elsevier Ltd. All rights reserved....
Plant Growth Models Using Artificial Neural Networks
Bubenheim, David
1997-01-01
In this paper, we descrive our motivation and approach to devloping models and the neural network architecture. Initial use of the artificial neural network for modeling the single plant process of transpiration is presented.
Generalization performance of regularized neural network models
DEFF Research Database (Denmark)
Larsen, Jan; Hansen, Lars Kai
1994-01-01
Architecture optimization is a fundamental problem of neural network modeling. The optimal architecture is defined as the one which minimizes the generalization error. This paper addresses estimation of the generalization performance of regularized, complete neural network models. Regularization...
Directory of Open Access Journals (Sweden)
Ma Geng
2014-12-01
Full Text Available The existing reservoir stimulating technologies are only applicable to hard coal but helpless for soft coal, which is one of the main factors hindering the CBM industrialization in China. Therefore, it is urgent to develop a universal stimulating technology which can increase the permeability in various coal reservoirs. Theoretical analysis and field tests were used to systematically analyze the mechanical mechanisms causing the formation of various levels and types of fractures, such as radial tensile fractures, peripheral tensile fractures, and shear fractures in hydraulic fracturing, and reveal the mechanism of permeability enhancement by fracture network stimulating in surrounding beds and coal reservoirs. The results show that multi-staged perforation fracturing of horizontal wells, hydraulic-jet staged fracturing, four-variation hydraulic fracturing and some auxiliary measures are effective technical approaches to fracture network stimulation, especially the four-variation hydraulic fracturing can stimulate the fracture network in vertical and cluster wells. It is concluded that the fracture network stimulating technology for surrounding beds has significant advantages, such as safe drilling operation, strong stimulation effect, strong adaptability to stress-sensitive and velocity-sensitive beds, and is suitable for coal reservoirs of any structure. Except for the limitation in extremely water-sensitive and high water-yield surrounding beds, the technology can be universally used in all other beds. The successful industrial tests in surface coal bed methane and underground coal mines gas extraction prove that the theory and technical system of fracture network stimulating in surrounding beds and coal reservoirs, as a universally applicable measure, will play a role in the CBM development in China.
Scalable Capacity Bounding Models for Wireless Networks
Du, Jinfeng; Medard, Muriel; Xiao, Ming; Skoglund, Mikael
2014-01-01
The framework of network equivalence theory developed by Koetter et al. introduces a notion of channel emulation to construct noiseless networks as upper (resp. lower) bounding models, which can be used to calculate the outer (resp. inner) bounds for the capacity region of the original noisy network. Based on the network equivalence framework, this paper presents scalable upper and lower bounding models for wireless networks with potentially many nodes. A channel decoupling method is proposed...
A mechanism-based approach to modeling ductile fracture.
Energy Technology Data Exchange (ETDEWEB)
Bammann, Douglas J.; Hammi, Youssef; Antoun, Bonnie R.; Klein, Patrick A.; Foulk, James W., III; McFadden, Sam X.
2004-01-01
Ductile fracture in metals has been observed to result from the nucleation, growth, and coalescence of voids. The evolution of this damage is inherently history dependent, affected by how time-varying stresses drive the formation of defect structures in the material. At some critically damaged state, the softening response of the material leads to strain localization across a surface that, under continued loading, becomes the faces of a crack in the material. Modeling localization of strain requires introduction of a length scale to make the energy dissipated in the localized zone well-defined. In this work, a cohesive zone approach is used to describe the post-bifurcation evolution of material within the localized zone. The relations are developed within a thermodynamically consistent framework that incorporates temperature and rate-dependent evolution relationships motivated by dislocation mechanics. As such, we do not prescribe the evolution of tractions with opening displacements across the localized zone a priori. The evolution of tractions is itself an outcome of the solution of particular, initial boundary value problems. The stress and internal state of the material at the point of bifurcation provides the initial conditions for the subsequent evolution of the cohesive zone. The models we develop are motivated by in-situ scanning electron microscopy of three-point bending experiments using 6061-T6 aluminum and 304L stainless steel, The in situ observations of the initiation and evolution of fracture zones reveal the scale over which the failure mechanisms act. In addition, these observations are essential for motivating the micromechanically-based models of the decohesion process that incorporate the effects of loading mode mixity, temperature, and loading rate. The response of these new cohesive zone relations is demonstrated by modeling the three-point bending configuration used for the experiments. In addition, we survey other methods with the potential
Finite element model of the Jefferson fracture: comparison with a cadaver model.
Bozkus, H; Karakas, A; Hanci, M; Uzan, M; Bozdag, E; Sarioglu, A C
2001-06-01
This study tries to explain the reason why the Jefferson fracture is a burst fracture, using two different biomechanical models: a finite element model (FEM) and a cadaver model used to determine strain distribution in C1 during axial static compressive loading. For the FEM model, a three-dimensional model of C1 was obtained from a 29-year-old healthy human, using axial CT scans with intervals of 1.0 mm. The mesh model was composed of 8200 four-noded isoparametric tetrahedrons and 37,400 solid elements. The material properties of the cortical bone of the vertebra were assessed according to the previous literature and were assumed to be linear isotropic and homogeneous for all elements. Axial static compressive loads were applied at between 200 and 1200 N. The strain and stress (maximum shear and von Mises) analyses were determined on the clinically relevant fracture lines of anterior and posterior arches. The results of the FEM were compared with a cadaver model. The latter comprised the C1 bone of a cadaver placed in a methylmethacrylate foam. Axial static compressive loads between 200 and 1200 N were applied by an electrohydraulic testing machine. Strain values were measured using strain gauges, which were cemented to the bone where the clinically relevant fracture lines of the anterior and posterior arches were located. As a result, compressive strain was observed on the outer surface of the anterior arch and inferior surface of the posterior arch. In addition, there was tensile strain on the inner surface of the anterior arch and superior surface of the posterior arch. The strain values obtained from the two experimental models showed similar trends. The FEM analysis revealed that maximum strain changes occurred where the maximum shear and von Mises stresses were concentrated. The changes in the C1 strain and stress values during static axial loading biomechanically prove that the Jefferson fracture is a burst fracture.
Wang, Ding; Qu, Shou-Li; Ding, Ping-Bo; Zhao, Qun
2017-03-01
The presence of bedding-parallel fractures at any scale in a rock will considerably add to its compliance and elastic anisotropy. Those properties will be more significantly affected when there is a relatively high degree of connectivity between the fractures and the corresponding interconnected pores. This contribution uses linear poroelasticity to reveal the characteristics of the full frequency-dependent compliance of an infinitely extended fracture model assuming the periodicity of the fractured structures. The fracture compliance tensor is complex-valued due to the wave-induced fluid flow between fractures and pores. The interaction between the adjacent fractures is considered under fluid mass conservation throughout the whole pore space. The quantitative effects of fracture (volume) density (the ratio between fracture thickness and spacing) and host rock porosity are analyzed by the diffusion equation for a relatively low-frequency band. The model in this paper is equivalent to the classical dry linear slip model when the bulk modulus of fluid in the fractures tends to zero. For the liquid-filled case, the model becomes the anisotropic Gassmann's model and sealed saturated linear slip model at the low-frequency and high-frequency limits, respectively. Using the dynamic compliance definition, we can effectively distinguish the saturating fluids in the fractures with the same order magnitude of bulk modulus (e.g., water and oil) using the compliance ratio method. Additionally, the modified dynamic model can be simplified as acceptable empirical formulas if the strain on the fractures induced by the incoming waves is small enough.
Brand Marketing Model on Social Networks
Directory of Open Access Journals (Sweden)
Jolita Jezukevičiūtė
2014-04-01
Full Text Available The paper analyzes the brand and its marketing solutions onsocial networks. This analysis led to the creation of improvedbrand marketing model on social networks, which will contributeto the rapid and cheap organization brand recognition, increasecompetitive advantage and enhance consumer loyalty. Therefore,the brand and a variety of social networks are becoming a hotresearch area for brand marketing model on social networks.The world‘s most successful brand marketing models exploratoryanalysis of a single case study revealed a brand marketingsocial networking tools that affect consumers the most. Basedon information analysis and methodological studies, develop abrand marketing model on social networks.
Multi-scale modeling of inter-granular fracture in UO2
Energy Technology Data Exchange (ETDEWEB)
Chakraborty, Pritam [Idaho National Lab. (INL), Idaho Falls, ID (United States); Zhang, Yongfeng [Idaho National Lab. (INL), Idaho Falls, ID (United States); Tonks, Michael R. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Biner, S. Bulent [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2015-03-01
A hierarchical multi-scale approach is pursued in this work to investigate the influence of porosity, pore and grain size on the intergranular brittle fracture in UO2. In this approach, molecular dynamics simulations are performed to obtain the fracture properties for different grain boundary types. A phase-field model is then utilized to perform intergranular fracture simulations of representative microstructures with different porosities, pore and grain sizes. In these simulations the grain boundary fracture properties obtained from molecular dynamics simulations are used. The responses from the phase-field fracture simulations are then fitted with a stress-based brittle fracture model usable at the engineering scale. This approach encapsulates three different length and time scales, and allows the development of microstructurally informed engineering scale model from properties evaluated at the atomistic scale.
Image-based modeling of the flow transition from a Berea rock matrix to a propped fracture
Sanematsu, P.; Willson, C. S.; Thompson, K. E.
2013-12-01
In the past decade, new technologies and advances in horizontal hydraulic fracturing to extract oil and gas from tight rocks have raised questions regarding the physics of the flow and transport processes that occur during production. Many of the multi-dimensional details of flow from the rock matrix into the fracture and within the proppant-filled fracture are still unknown, which leads to unreliable well production estimations. In this work, we use x-ray computed micro tomography (XCT) to image 30/60 CarboEconoprop light weight ceramic proppant packed between berea sandstone cores (6 mm in diameter and ~2 mm in height) under 4000 psi (~28 MPa) loading stress. Image processing and segmentation of the 6 micron voxel resolution tomography dataset into solid and void space involved filtering with anisotropic diffusion (AD), segmentation using an indicator kriging (IK) algorithm, and removal of noise using a remove islands and holes program. Physically-representative pore network structures were generated from the XCT images, and a representative elementary volume (REV) was analyzed using both permeability and effective porosity convergence. Boundary conditions were introduced to mimic the flow patterns that occur when fluid moves from the matrix into the proppant-filled fracture and then downstream within the proppant-filled fracture. A smaller domain, containing Berea and proppants close to the interface, was meshed using an in-house unstructured meshing algorithm that allows different levels of refinement. Although most of this domain contains proppants, the Berea section accounted for the majority of the elements due to mesh refinement in this region of smaller pores. A finite element method (FEM) Stokes flow model was used to provide more detailed insights on the flow transition from rock matrix to fracture. Results using different pressure gradients are used to describe the flow transition from the Berea rock matrix to proppant-filled fracture.
Effect of leptin on bone metabolism in rat model of traumatic brain injury and femoral fracture
Institute of Scientific and Technical Information of China (English)
WANG Lei; YUAN Ji-shan; ZHANG Hong-xi; DING Hua; TANG Xing-guo; WEI Yong-zhong
2011-01-01
Objective: To observe serum and callus leptin expression within the setting of fracture and traumatic brain injury (TBI).Methods: Atotal of 64 male SD rats were randomized equally into 4 groups: nonoperated group, TBI group, fraeture group, and fracture+TBI group. Rats were sacrificed at 2, 4, 8 and 12 weeks after fracture+TBI. Serum leptin was detected using radioimmunoassay, and callus formation was measured radiologically. Callus leptin was analyzed by immunohistochemistry.Results: Serum ieptin levels in the fracture group, TBI group and combined fracture+TBI group were all significantly increased compared with control group at the 2 week time-point (P＜0.05). Serum leptin in the combined fracture +TBI group was significantly higher than that in the fracture and TBI groups at 4 and 8 weeks after injury (P＜0. 05).The percentage of leptin-positive cells in the fracture+TBI callus and callus volume were significantly higher than those in the fracture-only group (P＜0.01).Conclusions: We demonstrated elevated leptin expression within healing bone especially in the first 8 weeks in a rat model of fracture and TBI. A close association exists between leptin levels and the degree of callus formation in fractures.
Modeling of Immiscible, Two-Phase Flows in a Natural Rock Fracture
Energy Technology Data Exchange (ETDEWEB)
Crandall, Dustin; Ahmadi, Goodarz; Smith, Duane H
2009-01-01
One potential method of geologically sequestering carbon dioxide (CO2) is to inject the gas into brine-filled, subsurface formations. Within these low-permeability rocks, fractures exist that can act as natural fluid conduits. Understanding how a less viscous fluid moves when injected into an initially saturated rock fracture is important for the prediction of CO2 transport within fractured rocks. Our study examined experimentally and numerically the motion of immiscible fluids as they were transported through models of a fracture in Berea sandstone. The natural fracture geometry was initially scanned using micro-computerized tomography (CT) at a fine volume-pixel (voxel) resolution by Karpyn et al. [1]. This CT scanned fracture was converted into a numerical mesh for two-phase flow calculations using the finite-volume solver FLUENT® and the volume-of-fluid method. Additionally, a translucent experimental model was constructed using stereolithography. The numerical model was shown to agree well with experiments for the case of a constant rate injection of air into the initially water-saturated fracture. The invading air moved intermittently, quickly invading large-aperture regions of the fracture. Relative permeability curves were developed to describe the fluid motion. These permeability curves can be used in reservoir-scale discrete fracture models for predictions of fluid motion within fractured geological formations. The numerical model was then changed to better mimic the subsurface conditions at which CO2 will move into brine saturated fractures. The different fluid properties of the modeled subsurface fluids were shown to increase the amount of volume the less-viscous invading gas would occupy while traversing the fracture.
Pizzati, Mattia; Cavozzi, Cristian; Magistroni, Corrado; Storti, Fabrizio
2016-04-01
Fracture density pattern predictions with low uncertainty is a fundamental issue for constraining fluid flow pathways in thrust-related anticlines in the frontal parts of thrust-and-fold belts and accretionary prisms, which can also provide plays for hydrocarbon exploration and development. Among the drivers that concur to determine the distribution of fractures in fold-and-thrust-belts, the complex kinematic pathways of folded structures play a key role. In areas with scarce and not reliable underground information, analogue modelling can provide effective support for developing and validating reliable hypotheses on structural architectures and their evolution. In this contribution, we propose a working method that combines analogue and numerical modelling. We deformed a sand-silicone multilayer to eventually produce a non-cylindrical thrust-related anticline at the wedge toe, which was our test geological structure at the reservoir scale. We cut 60 serial cross-sections through the central part of the deformed model to analyze faults and folds geometry using dedicated software (3D Move). The cross-sections were also used to reconstruct the 3D geometry of reference surfaces that compose the mechanical stratigraphy thanks to the use of the software GoCad. From the 3D model of the experimental anticline, by using 3D Move it was possible to calculate the cumulative stress and strain underwent by the deformed reference layers at the end of the deformation and also in incremental steps of fold growth. Based on these model outputs it was also possible to predict the orientation of three main fractures sets (joints and conjugate shear fractures) and their occurrence and density on model surfaces. The next step was the upscaling of the fracture network to the entire digital model volume, to create DFNs.
Ductile Fracture of AHSS Sheets under Multi-axial Loading: Experiments and Modeling
Dunand, M.; Mohr, D.
2011-08-01
Fracture experiments on TRIP-assisted steel sheets covering a wide range of stress states (from shear to equibiaxial tension) are performed to create a comprehensive experimental database to calibrate and evaluate the shear-modified Gurson model (Nielsen and Tvergaard, 2010) and the Modified Mohr-Coulomb (MMC) fracture model (Bai and Wierzbicki, 2010). The experimental program includes notched tensile tests as well as fracture experiments on butterfly-shaped specimens under combined tension and shear loading. Both phenomenological fracture models are physics-inspired and take the effect of the first and third stress tensor invariants into account in predicting the onset of ductile fracture. The MMC model is based on the assumption that the initiation of fracture is determined by a critical stress state, while the shear-modified Gurson model assumes void growth as the governing mechanism. The model accuracy is quantified based on the predictions of the displacements to fracture for experiments which have not been used for calibration. It is found that the MMC model predictions agree well with all experiments (less than 4% error), while less accurate predictions are observed for the shear-modified Gurson model. A comparison of plots of the strain to fracture as a function of the stress triaxiality and the normalized third invariant reveals significant differences between the two models except within the vicinity of stress states that have been used for calibration.
Fracture of Carbon Nanotube - Amorphous Carbon Composites: Molecular Modeling
Jensen, Benjamin D.; Wise, Kristopher E.; Odegard, Gregory M.
2015-01-01
Carbon nanotubes (CNTs) are promising candidates for use as reinforcements in next generation structural composite materials because of their extremely high specific stiffness and strength. They cannot, however, be viewed as simple replacements for carbon fibers because there are key differences between these materials in areas such as handling, processing, and matrix design. It is impossible to know for certain that CNT composites will represent a significant advance over carbon fiber composites before these various factors have been optimized, which is an extremely costly and time intensive process. This work attempts to place an upper bound on CNT composite mechanical properties by performing molecular dynamics simulations on idealized model systems with a reactive forcefield that permits modeling of both elastic deformations and fracture. Amorphous carbon (AC) was chosen for the matrix material in this work because of its structural simplicity and physical compatibility with the CNT fillers. It is also much stiffer and stronger than typical engineering polymer matrices. Three different arrangements of CNTs in the simulation cell have been investigated: a single-wall nanotube (SWNT) array, a multi-wall nanotube (MWNT) array, and a SWNT bundle system. The SWNT and MWNT array systems are clearly idealizations, but the SWNT bundle system is a step closer to real systems in which individual tubes aggregate into large assemblies. The effect of chemical crosslinking on composite properties is modeled by adding bonds between the CNTs and AC. The balance between weakening the CNTs and improving fiber-matrix load transfer is explored by systematically varying the extent of crosslinking. It is, of course, impossible to capture the full range of deformation and fracture processes that occur in real materials with even the largest atomistic molecular dynamics simulations. With this limitation in mind, the simulation results reported here provide a plausible upper limit on
Contaminant transport in fracture networks with heterogeneous rock matrices. The Picnic code
Energy Technology Data Exchange (ETDEWEB)
Barten, Werner [Paul Scherrer Inst., CH-5232 Villigen PSI (Switzerland); Robinson, Peter C. [QuantiSci Limited, Henley-on-Thames (United Kingdom)
2001-02-01
different timescales. To account for one-dimensional matrix diffusion into homogeneous planar or cylindrical rock layers, analytical relations in the Laplace domain are used. To deal with one-dimensional or two-dimensional matrix diffusion into heterogeneous rock matrices, a finite-element method is embedded. The capability of the code for handling two-dimensional matrix diffusion is - to our knowledge - unique in fracture network modelling. To ensure the reliability of the code, which merges methods from graph theory, Laplace transformation, finite-element methods, analytical and algebraic transformations and a convolution to calculate complex radionuclide transport processes over a large and diverse application range, implementation of the code and careful verification have been alternated for iterative improvement and especially the elimination of bugs. The internal mathematical structure of PICNIC forms the basis of the verification strategy. The code is verified in a series of seven steps with increasing complexity of the rock matrix. Calculations for single nuclides and nuclide decay chains are carefully tested and analysed for radionuclide transport in single legs, in pathways and in networks. Different sources and boundary conditions are considered. Quantitative estimates of the accuracy of the code are derived from comparisons with analytical solutions, cross-comparisons with other codes and different types of self -consistency tests, including extended testing of different refinements of the embedded finite- element method for different rock matrix geometries. The geosphere barrier efficiency is a good single indicator of the code accuracy. Application ranges with reduced accuracy of the code are also considered. For one-dimensional matrix diffusion into homogeneous and heterogeneous rock matrices, cross-comparisons with other codes are performed. For two-dimensional matrix diffusion, however, no code for cross-comparison is available. Consequently, the
Energy Technology Data Exchange (ETDEWEB)
Olofsson, Isabelle; Simeonov, Assen [Swedish Nuclear Fuel and Waste Manageme nt Co., Stockholm (Sweden); Stephens, Michael [Geological Survey of Sweden (SGU), U ppsala (Sweden); Follin, Sven [SF GeoLogic AB, Taeby (Sweden); Nilsson, Ann-Chatrin [G eosigma AB, Uppsala (Sweden); Roeshoff, Kennert; Lindberg, Ulrika; Lanaro, Flavio [Bergbygg konsult AB, Haesselby (Sweden); Fredriksson, Anders; Persson, Lars [Golder Associat es AB (Sweden)
2007-04-15
The Swedish Nuclear Fuel and Waste Management Company (SKB) is undertaking site characterization at two different locations, Forsmark and Simpevarp/Laxemar, with the objective of siting a final waste repository at depth for spent nuclear fuel. The programme is built upon the development of site descriptive models after each data freeze. This report describes the first attempt to define fracture domains for the Forsmark site modelling in stage 2.2. Already during model version 1.2 at Forsmark, significant spatial variability in the fracture pattern was observed. The variability appeared to be so significant that it provoked the need for a subdivision of the model volume for the treatment of geological and hydrogeological data into sub-volumes. Subsequent analyses of data collected up to data freeze 2.1 led to a better understanding of the site and a concept for the definition of fracture domains based on geological characteristics matured. The main objectives of this report are to identify and describe fracture domains at the site on the basis of geological data and to compile hydrogeological, hydrogeochemical and rock mechanics data within each fracture domain and address the implications of this integration activity. On the basis of borehole data, six fracture domains (FFM01-FFM06) have been recognized inside and immediately around the candidate volume. Three of these domains (FFM01, FFM02 and FFM06) lie inside the target volume for a potential repository in the northwestern part of the candidate area, and need to be addressed in the geological DFN modelling work. The hydrogeological data support the subdivision of the bedrock into fracture domains FFM01, FFM02 and FFM03. Few or no data are available for the other three domains. The hydrogeochemical data also support the subdivision into fracture domains FFM01 and FFM02. Since few data are available from the bedrock between deformation zones inside FFM03, there is little information on the hydrogeochemical
Modeling and characterization of interfacial adhesion and fracture
Yao, Qizhou
2000-09-01
The loss of interfacial adhesion is mostly seen in the failure of polymer adhesive joints. In addition to the intrinsic physical attraction across the interface, the interfacial adhesion strength is believed to highly depend on a number of factors, such as adhesive chemistry/structure, surface topology, fracture pattern, thermal and elastic mismatch across the interface. The fracture failure of an adhesive joint involves basically three aspects, namely, the intrinsic interfacial strength, the driving force for fracture and other energy dissipation. One may define the intrinsic interfacial strength as the maximum value of the intrinsic interfacial adhesion. The total work done by external forces to the component that contains the interface is partitioned into two parts. The first part is consumed by all other energy dissipation mechanisms (plasticity, heat generation, viscosity, etc.). The second part is used to debond the interface. This amount should equal to the intrinsic adhesion of the interface according to the laws of conservation of energy. It is clear that in order to understand the fundamental physics of adhesive joint failure, one must be able to characterize the intrinsic interfacial adhesion and be able to identify all the major energy dissipation mechanisms involved in the debonding process. In this study, both physical and chemical adhesion mechanisms were investigated for an aluminum-epoxy interface. The physical bonding energy was estimated by computing the Van de Waals forces across the interface. A hydration model was proposed and the associated chemical bonding energy was calculated through molecular simulations. Other energy dissipation mechanisms such as plasticity and thermal residual stresses were also identified and investigated for several four-point bend specimens. In particular, a micromechanics based model was developed to estimate the adhesion enhancement due to surface roughness. It is found that for this Al-epoxy system the major
Numerical modelling of single-phase flow in rough fractures with contacts
Olkiewicz, Piotr; Dabrowski, Marcin
2017-04-01
Fracture flow may dominate in rocks with low porosity and it can accompany both industrial and natural processes. Typical examples of such processes are natural flows in crystalline rocks and industrial flows in oil and gas production systems or hydraulic fracturing. Fracture flow provides an important mechanism for transporting mass and energy. The distribution of the apertures of fracture and contact area are the key parameters with regard to the fracture transmissivity. We use the method of correlated random fields [Mourzenko, 1996] to generate synthetic fracture geometry in 3D. The flow of an incompressible Newtonian viscous fluid in geological formation can be approximated by the Stokes, the Stokes-Brinkman or the Reynolds models. We use our own implementation of the finite element method based on MILAMIN [Dabrowski, 2008] to solve governing partial differential equation over domain. We compare the Stokes, the Stokes-Brinkamn and the Reynolds models for fracture flow based on systematic numerical simulations for a wide range of geometric parameters. Mismatch between the Reynolds and the Stokes models becomes significant with increasing fracture roughness or contact area. The Stokes-Brinkman model is more accurate than Reynolds models due to additional Laplacian term, which allows to fulfil no-slip boundary condition. We present condition when the Reynolds and the Stokes-Brinkman models are valid. In the last three decades many authors used the Reynolds equation for studying fracture flow because of its simplicity. We recommend using the Stokes-Brinkman model for fracture flow, which allows to fulfil no-slip boundary condition on asperities boundary and is more accurate for rough fractures than the Reynolds model.
Modeling of fracture of protective concrete structures under impact loads
Energy Technology Data Exchange (ETDEWEB)
Radchenko, P. A., E-mail: radchenko@live.ru; Batuev, S. P.; Radchenko, A. V.; Plevkov, V. S. [Tomsk State University of Architecture and Building, Tomsk, 634003 (Russian Federation)
2015-10-27
This paper presents results of numerical simulation of interaction between a Boeing 747-400 aircraft and the protective shell of a nuclear power plant. The shell is presented as a complex multilayered cellular structure consisting of layers of concrete and fiber concrete bonded with steel trusses. Numerical simulation was performed three-dimensionally using the original algorithm and software taking into account algorithms for building grids of complex geometric objects and parallel computations. Dynamics of the stress-strain state and fracture of the structure were studied. Destruction is described using a two-stage model that allows taking into account anisotropy of elastic and strength properties of concrete and fiber concrete. It is shown that wave processes initiate destruction of the cellular shell structure; cells start to destruct in an unloading wave originating after the compression wave arrival at free cell surfaces.
Network Bandwidth Utilization Forecast Model on High Bandwidth Network
Energy Technology Data Exchange (ETDEWEB)
Yoo, Wucherl; Sim, Alex
2014-07-07
With the increasing number of geographically distributed scientific collaborations and the scale of the data size growth, it has become more challenging for users to achieve the best possible network performance on a shared network. We have developed a forecast model to predict expected bandwidth utilization for high-bandwidth wide area network. The forecast model can improve the efficiency of resource utilization and scheduling data movements on high-bandwidth network to accommodate ever increasing data volume for large-scale scientific data applications. Univariate model is developed with STL and ARIMA on SNMP path utilization data. Compared with traditional approach such as Box-Jenkins methodology, our forecast model reduces computation time by 83.2percent. It also shows resilience against abrupt network usage change. The accuracy of the forecast model is within the standard deviation of the monitored measurements.
Comparison of GTN Model and XFEM for Fracture Mechanics Analysis
Energy Technology Data Exchange (ETDEWEB)
Lee, Sung Jun; Chang, Yoon Suk [Kyung Hee University, Youngin (Korea, Republic of)
2014-10-15
The simulation of discontinuities such as stationary and growing cracks by conventional finite element(FE) method is limited for bulk materials due to the necessity of computationally expensive remeshing process and high mesh densities. Accordingly, several advanced finite element techniques have been introduced to model crack propagation without remeshing. However, there are still many modeling uncertainties relating to arbitrary discontinuities in respect of accuracy and efficiency. In order to overcome this problem, eXtended Finite Element Method(XFEM) which allows the presence of discontinuities in elements by enriching degrees of freedom(DOF) with special displacement function was developed by Belytschko and Black. In this paper, the XFEM was applied to tensile tests for API X65 steel to implement crack simulation based on fracture mechanics analyses and verify through the comparison with the preceding study using Gurson-Tvergaard-Needleman (GTN) model. In this paper, a comprehensive numerical analyses were carried out to verify an adequacy of the XFEM by comparing its results with those obtained from experiments and GTN model. The XFEM has an efficiency due to the accessibility to the corresponding parameters such as cohesive strength, cohesive energy and critical separation. Also, visualization of crack simulation has an advantage compared to the GTN model. In these respects, the XFEM can be widely used in industrial fields and further analyses for bulk materials are needed.
Zhanghua Lian; Ying Zhang; Xu Zhao; Shidong Ding; Tiejun Lin
2015-01-01
Multi-stage SRV fracturing in horizontal wells is a new technology developed at home and abroad in recent years to effectively develop shale gas or low-permeability reservoirs, but on the other hand makes the mechanical environment of fracturing strings more complicated at the same time. In view of this, based on the loading features of tubing strings during the multi-stage fracturing of a horizontal well, mechanical models were established for three working cases of multiple packer setting, ...
Modelling of excavation depth and fractures in rock caused by tool indentation
Energy Technology Data Exchange (ETDEWEB)
Kou Shaoquan; Tan Xiangchun; Lindqvist, P.A. [Luleaa Univ. of Technology (Sweden)
1997-10-01
The hydraulic regime after excavation in the near-field rock around deposition holes and deposition tunnels in a spent nuclear fuel repository is of concern for prediction of the saturation process of bentonite buffer and tunnel backfill. The hydraulic condition of main interest in this context is a result of the fracture network that is caused by the excavation. Modelling of the excavation disturbed zone in hard rocks caused by mechanical excavation has been carried out in the Division of Mining Engineering since 1993. This report contains an overview of the work conducted. The mechanical excavation is reasonably simplified as an indentation process of the interaction between rigid indenters and rocks. A large number of experiments have been carried out in the laboratory, and the results used for identifying crushed zones and fracture systems in rock under indentation are presented based on these experiments. The indentation causes crushing and damage of the rock and results in a crushed zone and a cracked zone. The indenter penetrates the rock with a certain depth when the force is over a threshold value relevant to the rock and tool. Outside the cracked zone there are basically three systems of cracks: median cracks, radial cracks, and side cracks. Fully developed radial cracks on each side of the indented area can connect with each other and join with median crack. This forms the so-called radial/median crack system. The influence of the mechanical properties of the rock is discussed based on our conceptual model, and the main factors governing the indentation event are summarised. The cracked zone is dealt with by an analytical fracture model. The side crack is simulated by applying the boundary element method coupled with fracture mechanics. Functional relationships are established relating either the indentation depth or the length of radial/median cracks to the various quantities characterising the physical event, namely the shape and the size of the
Fracture network of the Ferron Sandstone Member of the Mancos Shale, east-central Utah, USA
Condon, S.M.
2003-01-01
The fracture network at the outcrop of the Ferron Sandstone Member of the Mancos Shale was studied to gain an understanding of the tectonic history of the region and to contribute data to studies of gas and water transmissivity related to the occurrence and production of coal-bed methane. About 1900 fracture readings were made at 40 coal outcrops and 62 sandstone outcrops in the area from Willow Springs Wash in the south to Farnham dome in the north of the study area in east-central Utah.Two sets of regional, vertical to nearly vertical, systematic face cleats were identified in Ferron coals. A northwest-striking set trends at a mean azimuth of 321??, and a northeast-striking set has a mean azimuth of 55??. Cleats were observed in all coal outcrops examined and are closely spaced and commonly coated with thin films of iron oxide.Two sets of regional, systematic joint sets in sandstone were also identified and have mean azimuths of 321?? and 34??. The joints of each set are planar, long, and extend vertically to nearly vertically through multiple beds; the northeast-striking set is more prevalent than the northwest-striking set. In some places, joints of the northeast-striking set occur in closely spaced clusters, or joint zones, flanked by unjointed rock. Both sets are mineralized with iron oxide and calcite, and the northwest-striking set is commonly tightly cemented, which allowed the northeast-striking set to propagate across it. All cleats and joints of these sets are interpreted as opening-mode (mode I) fractures. Abutting relations indicate that the northwest-striking cleats and joints formed first and were later overprinted by the northeast-striking cleats and joints. Burial curves constructed for the Ferron indicate rapid initial burial after deposition. The Ferron reached a depth of 3000 ft (1000 m) within 5.2 million years (m.y.), and this is considered a minimum depth and time for development of cleats and joints. The Sevier orogeny produced southeast
Ekofisk chalk: core measurements, stochastic reconstruction, network modeling and simulation
Energy Technology Data Exchange (ETDEWEB)
Talukdar, Saifullah
2002-07-01
This dissertation deals with (1) experimental measurements on petrophysical, reservoir engineering and morphological properties of Ekofisk chalk, (2) numerical simulation of core flood experiments to analyze and improve relative permeability data, (3) stochastic reconstruction of chalk samples from limited morphological information, (4) extraction of pore space parameters from the reconstructed samples, development of network model using pore space information, and computation of petrophysical and reservoir engineering properties from network model, and (5) development of 2D and 3D idealized fractured reservoir models and verification of the applicability of several widely used conventional up scaling techniques in fractured reservoir simulation. Experiments have been conducted on eight Ekofisk chalk samples and porosity, absolute permeability, formation factor, and oil-water relative permeability, capillary pressure and resistivity index are measured at laboratory conditions. Mercury porosimetry data and backscatter scanning electron microscope images have also been acquired for the samples. A numerical simulation technique involving history matching of the production profiles is employed to improve the relative permeability curves and to analyze hysteresis of the Ekofisk chalk samples. The technique was found to be a powerful tool to supplement the uncertainties in experimental measurements. Porosity and correlation statistics obtained from backscatter scanning electron microscope images are used to reconstruct microstructures of chalk and particulate media. The reconstruction technique involves a simulated annealing algorithm, which can be constrained by an arbitrary number of morphological parameters. This flexibility of the algorithm is exploited to successfully reconstruct particulate media and chalk samples using more than one correlation functions. A technique based on conditional simulated annealing has been introduced for exact reproduction of vuggy
MODELS FOR NETWORK DYNAMICS - A MARKOVIAN FRAMEWORK
LEENDERS, RTAJ
1995-01-01
A question not very often addressed in social network analysis relates to network dynamics and focuses on how networks arise and change. It alludes to the idea that ties do not arise or vanish randomly, but (partly) as a consequence of human behavior and preferences. Statistical models for modeling
Modelling delay propagation within an airport network
Pyrgiotis, N.; Malone, K.M.; Odoni, A.
2013-01-01
We describe an analytical queuing and network decomposition model developed to study the complex phenomenon of the propagation of delays within a large network of major airports. The Approximate Network Delays (AND) model computes the delays due to local congestion at individual airports and capture
Modelling delay propagation within an airport network
Pyrgiotis, N.; Malone, K.M.; Odoni, A.
2013-01-01
We describe an analytical queuing and network decomposition model developed to study the complex phenomenon of the propagation of delays within a large network of major airports. The Approximate Network Delays (AND) model computes the delays due to local congestion at individual airports and
A system dynamics model for communications networks
Awcock, A. J.; King, T. E. G.
1985-09-01
An abstract model of a communications network in system dynamics terminology is developed as implementation of this model by a FORTRAN program package developed at RSRE is discussed. The result of this work is a high-level simulation package in which the performance of adaptive routing algorithms and other network controls may be assessed for a network of arbitrary topology.
Ju, Yang; Zhang, Qingang; Zheng, Jiangtao; Chang, Chun; Xie, Heping
2017-02-01
The irregular morphology of single rock fracture significantly influences subsurface fluid flow and gives rise to a complex and unsteady flow state that typically cannot be appropriately described using simple laws. Yet the fluid flow in rough fractures of underground rock is poorly understood. Here we present a numerical method and experimental measurements to probe the effect of fracture roughness on the properties of fluid flow in fractured rock. We develop a series of fracture models with various degrees of roughness characterized by fractal dimensions that are based on the Weierstrass-Mandelbrot fractal function. The Lattice Boltzmann Method (LBM), a discrete numerical algorithm, is employed for characterizing the complex unsteady non-Darcy flow through the single rough fractures and validated by experimental observations under the same conditions. Comparison indicates that the LBM effectively characterizes the unsteady non-Darcy flow in single rough fractures. Our LBM model predicts experimental measurements of unsteady fluid flow through single rough fractures with great satisfactory, but significant deviation is obtained from the conventional cubic law, showing the superiority of LBM models of single rough fractures.
Fractal model and Lattice Boltzmann Method for Characterization of Non-Darcy Flow in Rough Fractures
Ju, Yang; Zhang, Qingang; Zheng, Jiangtao; Chang, Chun; Xie, Heping
2017-02-01
The irregular morphology of single rock fracture significantly influences subsurface fluid flow and gives rise to a complex and unsteady flow state that typically cannot be appropriately described using simple laws. Yet the fluid flow in rough fractures of underground rock is poorly understood. Here we present a numerical method and experimental measurements to probe the effect of fracture roughness on the properties of fluid flow in fractured rock. We develop a series of fracture models with various degrees of roughness characterized by fractal dimensions that are based on the Weierstrass-Mandelbrot fractal function. The Lattice Boltzmann Method (LBM), a discrete numerical algorithm, is employed for characterizing the complex unsteady non-Darcy flow through the single rough fractures and validated by experimental observations under the same conditions. Comparison indicates that the LBM effectively characterizes the unsteady non-Darcy flow in single rough fractures. Our LBM model predicts experimental measurements of unsteady fluid flow through single rough fractures with great satisfactory, but significant deviation is obtained from the conventional cubic law, showing the superiority of LBM models of single rough fractures.
Biomechanical analysis of four types of internal fixation in subtrochanteric fracture models.
Wang, Jie; Ma, Xin-long; Ma, Jian-xiong; Xing, Dan; Yang, Yang; Zhu, Shao-wen; Ma, Bao-yi; Chen, Yang; Feng, Rui; Jia, Hao-bo; Yu, Jing-tao
2014-05-01
To compare the biomechanical properties of four types of internal fixation (proximal femoral nail [PFN], dynamic hip screw [DHS], dynamic condylar screw [DCS], and proximal femoral locking plate [PFLP]) for different types of subtrochanteric fractures. Thirty-two antiseptic femurs were randomly divided into four groups. After internal fixation had been implanted, different types of subtrochanteric fracture models were produced and each tested under vertical, torsional and vertical damage loads. The stiffness ratio of PFN in each fracture model and failure load were the highest in the four groups; however, the torsional stiffness ratio was the lowest. Tension strain ratios of DHS and DCS on the lateral side became compression strain ratios with restoration of the medial fragment. The stiffness ratio of DHS was lower than PFLP in each fracture model, torsional stiffness ratio was the highest in fracture models II to V and the failure load was lower only than PFN. The stiffness ratio and failure load of DCS were both the lowest, torsional stiffness ratio was similar to PFLP's in fracture models II to V. The stiffness ratio of PFLP was only lower than PFN's in each fracture model, but the failure load was lower than DHS's. Four types of internal fixation achieve better stabilities for type I subtrochanteric fractures. PFN and PFLP produce reliable stability in type IIIA subtrochanteric fractures. If the medial buttress is restored, DCS can be considered. For type IV subtrochanteric fractures, only PFN provides stable fixation. PFLP is suitable for comminuted fractures with large fragments. © 2014 Chinese Orthopaedic Association and Wiley Publishing Asia Pty Ltd.
Homogenization of intergranular fracture towards a transient gradient damage model
Sun, G.; Poh, L. H.
2016-10-01
This paper focuses on the intergranular fracture of polycrystalline materials, where a detailed model at the meso-scale is translated onto the macro-level through a proposed homogenization theory. The bottom-up strategy involves the introduction of an additional macro-kinematic field to characterize the average displacement jump within the unit cell. Together with the standard macro-strain field, the underlying processes are propagated onto the macro-scale by imposing the equivalence of power and energy at the two scales. The set of macro-governing equations and constitutive relations are next extracted naturally as per standard thermodynamics procedure. The resulting homogenized microforce balance recovers the so-called 'implicit' gradient expression with a transient nonlocal interaction. The homogenized gradient damage model is shown to fully regularize the softening behavior, i.e. the structural response is made mesh-independent, with the damage strain correctly localizing into a macroscopic crack, hence resolving the spurious damage growth observed in many conventional gradient damage models. Furthermore, the predictive capability of the homogenized model is demonstrated by benchmarking its solutions against reference meso-solutions, where a good match is obtained with minimal calibrations, for two different grain sizes.
Comparison of Measured and Modelled Hydraulic Conductivities of Fractured Sandstone Cores
Baraka-Lokmane, S.; Liedl, R.; Teutsch, G.
- A new method for characterising the detailed fracture geometry in sandstone cores is presented. This method is based on the impregnation of samples with coloured resin, without significant disturbance of the fractures. The fractures are made clearly visible by the resin, thus allowing the fracture geometry to be examined digitally. In order to model the bulk hydraulic conductivity, the samples are sectioned serially perpendicular to the flow direction. The hydraulic conductivity of individual sections is estimated by summing the contribution of the matrix and each fracture from the digital data. Finally, the hydraulic conductivity of the bulk sample is estimated by a harmonic average in series along the flow path. Results of this geometrical method are compared with actual physical conductivity values measured from fluid experiments carried out prior to sectioning. The predicted conductivity from the fracture geometry parameters (e.g., fracture aperture, fracture width, fracture length and fracture relative roughness all measured using an optical method) is in good agreement with the independent physical measurements, thereby validating the approach.
Tecklenburg, Jan; Carrera, Jesus; Dentz, Marco
2016-01-01
We study modeling of two-phase flow in highly heterogeneous fractured and porous media. The flow behaviour is strongly influenced by mass transfer between a highly permeable (mobile) fracture domain and less permeable (immobile) matrix blocks. We quantify the effective two-phase flow behaviour using a multirate rate mass transfer (MRMT) approach. We discuss the range of applicability of the MRMT approach in terms of the pertinent viscous and capillary diffusion time scales. We scrutinize the linearization of capillary diffusion in the immobile regions, which allows for the formulation of MRMT in the form of a non-local single equation model. The global memory function, which encodes mass transfer between the mobile and the immobile regions, is at the center of this method. We propose two methods to estimate the global memory function for a fracture network with given fracture and matrix geometry. Both employ a scaling approach based on the known local memory function for a given immobile region. With the firs...
Network models in epidemiology: an overview
Lloyd, Alun L.; Valeika, Steve
In this chapter we shall discuss the development and use of network models in epidemiology. While network models have long been discussed in the theoretical epidemiology literature, they have recently received a large amount of attention amongst the statistical physics community. This has been fueled by the desire to better understand the structure of social and large-scale technological networks, and the increases in computational power that have made the simulation of reasonably-sized network models a feasible proposition. A main aim of this review is to bridge the epidemiologic and statistical physics approaches to network models for infectious diseases, highlighting the important contributions made by both research communities.
Modeling gene regulatory networks: A network simplification algorithm
Ferreira, Luiz Henrique O.; de Castro, Maria Clicia S.; da Silva, Fabricio A. B.
2016-12-01
Boolean networks have been used for some time to model Gene Regulatory Networks (GRNs), which describe cell functions. Those models can help biologists to make predictions, prognosis and even specialized treatment when some disturb on the GRN lead to a sick condition. However, the amount of information related to a GRN can be huge, making the task of inferring its boolean network representation quite a challenge. The method shown here takes into account information about the interactome to build a network, where each node represents a protein, and uses the entropy of each node as a key to reduce the size of the network, allowing the further inferring process to focus only on the main protein hubs, the ones with most potential to interfere in overall network behavior.
Eight challenges for network epidemic models
Directory of Open Access Journals (Sweden)
Lorenzo Pellis
2015-03-01
Full Text Available Networks offer a fertile framework for studying the spread of infection in human and animal populations. However, owing to the inherent high-dimensionality of networks themselves, modelling transmission through networks is mathematically and computationally challenging. Even the simplest network epidemic models present unanswered questions. Attempts to improve the practical usefulness of network models by including realistic features of contact networks and of host–pathogen biology (e.g. waning immunity have made some progress, but robust analytical results remain scarce. A more general theory is needed to understand the impact of network structure on the dynamics and control of infection. Here we identify a set of challenges that provide scope for active research in the field of network epidemic models.
An evolutionary model of social networks
Ludwig, M.; Abell, P.
2007-07-01
Social networks in communities, markets, and societies self-organise through the interactions of many individuals. In this paper we use a well-known mechanism of social interactions — the balance of sentiment in triadic relations — to describe the development of social networks. Our model contrasts with many existing network models, in that people not only establish but also break up relations whilst the network evolves. The procedure generates several interesting network features such as a variety of degree distributions and degree correlations. The resulting network converges under certain conditions to a steady critical state where temporal disruptions in triangles follow a power-law distribution.
Energy Technology Data Exchange (ETDEWEB)
Michael L. Wiggins; Raymon L. Brown; Faruk Civan; Richard G. Hughes
2002-12-31
For many years, geoscientists and engineers have undertaken research to characterize naturally fractured reservoirs. Geoscientists have focused on understanding the process of fracturing and the subsequent measurement and description of fracture characteristics. Engineers have concentrated on the fluid flow behavior in the fracture-porous media system and the development of models to predict the hydrocarbon production from these complex systems. This research attempts to integrate these two complementary views to develop a quantitative reservoir characterization methodology and flow performance model for naturally fractured reservoirs. The research has focused on estimating naturally fractured reservoir properties from seismic data, predicting fracture characteristics from well logs, and developing a naturally fractured reservoir simulator. It is important to develop techniques that can be applied to estimate the important parameters in predicting the performance of naturally fractured reservoirs. This project proposes a method to relate seismic properties to the elastic compliance and permeability of the reservoir based upon a sugar cube model. In addition, methods are presented to use conventional well logs to estimate localized fracture information for reservoir characterization purposes. The ability to estimate fracture information from conventional well logs is very important in older wells where data are often limited. Finally, a desktop naturally fractured reservoir simulator has been developed for the purpose of predicting the performance of these complex reservoirs. The simulator incorporates vertical and horizontal wellbore models, methods to handle matrix to fracture fluid transfer, and fracture permeability tensors. This research project has developed methods to characterize and study the performance of naturally fractured reservoirs that integrate geoscience and engineering data. This is an important step in developing exploitation strategies for
On the Fictitious Crack Model of Concrete Fracture
DEFF Research Database (Denmark)
Brincker, Rune; Dahl, Henrik
in the fracture zone is discussed, and an alternative energy formulation is given and males it possible to distinguish between stable and unstable situations. The reformulated sub-structure method is implemented on computer in a way that makes it possible to use a multilinear stress......-crack-opening-displacement relation for the material in the fracture zone, and some qualitative results are given....
The model of social crypto-network
Directory of Open Access Journals (Sweden)
Марк Миколайович Орел
2015-06-01
Full Text Available The article presents the theoretical model of social network with the enhanced mechanism of privacy policy. It covers the problems arising in the process of implementing the mentioned type of network. There are presented the methods of solving problems arising in the process of building the social network with privacy policy. It was built a theoretical model of social networks with enhanced information protection methods based on information and communication blocks
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.
Implementation of a flaw model to the fracturing around a vertical shaft
CSIR Research Space (South Africa)
Van de Steen, B
2003-04-01
Full Text Available This paper investigates whether a micromechanical model developed to investigate the relation between the basic failure processes at grain-scale and the macroscopic failure pattern can be applied to model the fracturing around large...
Rose, David M; Sutter, Edward G; Mears, Simon C; Gupta, Rohit R; Belkoff, Stephen M
2010-11-01
The purpose of our study was to biomechanically compare, under cyclic loading conditions, fracture site motion, humeral head collapse, and intra-articular hardware penetration in simulated 3-part osteoporotic proximal humeral fractures stabilized with 1 of 2 locking-plate constructs. We performed fixation on simulated 3-part proximal humeral fractures in 10 pairs of cadaveric osteoporotic humeri with a Hand Innovations S3 Proximal Humerus Plate (S3 plate) or an LCP Proximal Humerus Plate (LCP plate; 1 each for each pair). The specimens were potted, mounted on a materials testing machine, and subjected to 5000 cycles of abduction in the scapular plane, loading through the supraspinatus tendon. Interfragmentary displacement at 2 virtual points (the most medial aspect of the calcar and the most superior aspect of the osteotomy line between the greater tuberosity and humeral head) was measured using an optical tracking system. Humeral head rotation was also measured. We used a generalized linear latent and mixed model to check for an effect of cyclic loading and treatment on the parameters of interest (significance, P fracture site motion, it is unknown whether the magnitude of the motion is clinically significant.
A dynamic network model for interbank market
Xu, Tao; He, Jianmin; Li, Shouwei
2016-12-01
In this paper, a dynamic network model based on agent behavior is introduced to explain the formation mechanism of interbank market network. We investigate the impact of credit lending preference on interbank market network topology, the evolution of interbank market network and stability of interbank market. Experimental results demonstrate that interbank market network is a small-world network and cumulative degree follows the power-law distribution. We find that the interbank network structure keeps dynamic stability in the network evolution process. With the increase of bank credit lending preference, network clustering coefficient increases and average shortest path length decreases monotonously, which improves the stability of the network structure. External shocks are main threats for the interbank market and the reduction of bank external investment yield rate and deposits fluctuations contribute to improve the resilience of the banking system.
Modeling Diagnostic Assessments with Bayesian Networks
Almond, Russell G.; DiBello, Louis V.; Moulder, Brad; Zapata-Rivera, Juan-Diego
2007-01-01
This paper defines Bayesian network models and examines their applications to IRT-based cognitive diagnostic modeling. These models are especially suited to building inference engines designed to be synchronous with the finer grained student models that arise in skills diagnostic assessment. Aspects of the theory and use of Bayesian network models…
Modeling Diagnostic Assessments with Bayesian Networks
Almond, Russell G.; DiBello, Louis V.; Moulder, Brad; Zapata-Rivera, Juan-Diego
2007-01-01
This paper defines Bayesian network models and examines their applications to IRT-based cognitive diagnostic modeling. These models are especially suited to building inference engines designed to be synchronous with the finer grained student models that arise in skills diagnostic assessment. Aspects of the theory and use of Bayesian network models…
A novel computer algorithm for modeling and treating mandibular fractures: A pilot study.
Rizzi, Christopher J; Ortlip, Timothy; Greywoode, Jewel D; Vakharia, Kavita T; Vakharia, Kalpesh T
2017-02-01
To describe a novel computer algorithm that can model mandibular fracture repair. To evaluate the algorithm as a tool to model mandibular fracture reduction and hardware selection. Retrospective pilot study combined with cross-sectional survey. A computer algorithm utilizing Aquarius Net (TeraRecon, Inc, Foster City, CA) and Adobe Photoshop CS6 (Adobe Systems, Inc, San Jose, CA) was developed to model mandibular fracture repair. Ten different fracture patterns were selected from nine patients who had already undergone mandibular fracture repair. The preoperative computed tomography (CT) images were processed with the computer algorithm to create virtual images that matched the actual postoperative three-dimensional CT images. A survey comparing the true postoperative image with the virtual postoperative images was created and administered to otolaryngology resident and attending physicians. They were asked to rate on a scale from 0 to 10 (0 = completely different; 10 = identical) the similarity between the two images in terms of the fracture reduction and fixation hardware. Ten mandible fracture cases were analyzed and processed. There were 15 survey respondents. The mean score for overall similarity between the images was 8.41 ± 0.91; the mean score for similarity of fracture reduction was 8.61 ± 0.98; and the mean score for hardware appearance was 8.27 ± 0.97. There were no significant differences between attending and resident responses. There were no significant differences based on fracture location. This computer algorithm can accurately model mandibular fracture repair. Images created by the algorithm are highly similar to true postoperative images. The algorithm can potentially assist a surgeon planning mandibular fracture repair. 4. Laryngoscope, 2016 127:331-336, 2017. © 2016 The American Laryngological, Rhinological and Otological Society, Inc.
Semi-analytical model of cross-borehole flow experiments for fractured medium characterization
Roubinet, D.; Irving, J.; Day-Lewis, F. D.
2014-12-01
The study of fractured rocks is extremely important in a wide variety of research fields where the fractures and faults can represent either rapid access to some resource of interest or potential pathways for the migration of contaminants in the subsurface. Identification of their presence and determination of their properties are critical and challenging tasks that have led to numerous fracture characterization methods. Among these methods, cross-borehole flowmeter analysis aims to evaluate fracture connections and hydraulic properties from vertical-flow-velocity measurements conducted in one or more observation boreholes under forced hydraulic conditions. Previous studies have demonstrated that analysis of these data can provide important information on fracture connectivity, transmissivity, and storativity. Estimating these properties requires the development of analytical and/or numerical modeling tools that are well adapted to the complexity of the problem. Quantitative analysis of cross-borehole flowmeter experiments, in particular, requires modeling formulations that: (i) can be adapted to a variety of fracture and experimental configurations; (ii) can take into account interactions between the boreholes because their radii of influence may overlap; and (iii) can be readily cast into an inversion framework that allows for not only the estimation of fracture hydraulic properties, but also an assessment of estimation error. To this end, we present a new semi-analytical formulation for cross-borehole flow in fractured media that links transient vertical-flow velocities measured in one or a series of observation wells during hydraulic forcing to the transmissivity and storativity of the fractures intersected by these wells. Our model addresses the above needs and provides a flexible and computationally efficient semi-analytical framework having strong potential for future adaptation to more complex configurations. The proposed modeling approach is demonstrated
The Shear Mechanisms of Natural Fractures during the Hydraulic Stimulation of Shale Gas Reservoirs
Directory of Open Access Journals (Sweden)
Zhaobin Zhang
2016-08-01
Full Text Available The shearing of natural fractures is important in the permeability enhancement of shale gas reservoirs during hydraulic fracturing treatment. In this work, the shearing mechanisms of natural fractures are analyzed using a newly proposed numerical model based on the displacement discontinuities method. The fluid-rock coupling system of the model is carefully designed to calculate the shearing of fractures. Both a single fracture and a complex fracture network are used to investigate the shear mechanisms. The investigation based on a single fracture shows that the non-ignorable shearing length of a natural fracture could be formed before the natural fracture is filled by pressurized fluid. Therefore, for the hydraulic fracturing treatment of the naturally fractured shale gas reservoirs, the shear strength of shale is generally more important than the tensile strength. The fluid-rock coupling propagation processes of a complex fracture network are simulated under different crustal stress conditions and the results agree well with those of the single fracture. The propagation processes of complex fracture network show that a smaller crustal stress difference is unfavorable to the shearing of natural fractures, but is favorable to the formation of complex fracture network.
NUMERICAL MODELING FOR POSITIVE AND INVERSE PROBLEMS OF 3-D SEEPAGE IN DOUBLE FRACTURED MEDIA
Institute of Scientific and Technical Information of China (English)
ZHOU Zhi-fang; GUO Geng-xin
2005-01-01
Three-dimensional seepage in double fractured media was modeled in this paper.The determination of hydraulic conductivity tensor of rock mass is a vital problem for the sea water intrusion or sea water encroachment and seepage of fissured medium.According to the geological and hydrogeological conditions for the 2nd-stage construction of the Three Gorges Project (TGP), the physical and mathematical models for the groundwater movement through the 3D double fractured media of rock mass during construction were established in this paper.Based on discontinuity-control inverse theory, some related parameters of double fractured media were inversed with flux being the known quantity and calibration of water table the objective function.Synchronously, the seepage field of the construction region was systematically analyzed and simulated, the results of which exhibit that the double fractured media model of fracture water can comprehensively and correctly describe the geological and hydrogeological conditions in the construction region.
Energy Technology Data Exchange (ETDEWEB)
Charoenwongsa, S.; Kazemi, H.; Miskimins, J.; Fakcharoenphol [Colorado School of Mines, Golden, CO (United States)
2010-07-01
A fully coupled geomechanics flow model was used to assess how the changes in pore pressure and temperature influence rock stresses in tight gas reservoirs. The finite difference method was used to develop simulations for phases, components, and thermal stresses. A wave component was used to model the propagation of the strain displacement front as well as changes in stress with time. Fluid and heat flow volumes were modelled separately from rock formation properties. The influence of hydraulic fracturing on stress distributions surrounding the fracture was investigated as well as the effect of filter cake and filtrate. Results of the study showed that significant changes in shear stresses near hydraulic fractures occur as a result of hydraulic fracture face displacement perpendicular to the fracture face. While temperature effects also caused changes in stress distributions, changes in pore pressure did not significantly impact shear stresses as the filtrate did not travel very far into the reservoir. 17 refs., 17 figs.
A phase-field model for ductile fracture at finite strains and its experimental verification
Ambati, Marreddy; Kruse, Roland; De Lorenzis, Laura
2016-01-01
In this paper, a phase-field model for ductile fracture previously proposed in the kinematically linear regime is extended to the three-dimensional finite strain setting, and its predictions are qualitatively and quantitatively compared with several experimental results, both from ad-hoc tests carried out by the authors and from the available literature. The proposed model is based on the physical assumption that fracture occurs when a scalar measure of the accumulated plastic strain reaches a critical value, and such assumption is introduced through the dependency of the phase-field degradation function on this scalar measure. The proposed model is able to capture the experimentally observed sequence of elasto-plastic deformation, necking and fracture phenomena in flat specimens; the occurrence of cup-and-cone fracture patterns in axisymmetric specimens; the role played by notches and by their size on the measured displacement at fracture; and the sequence of distinct cracking events observed in more complex specimens.
Bayesian Network Webserver: a comprehensive tool for biological network modeling.
Ziebarth, Jesse D; Bhattacharya, Anindya; Cui, Yan
2013-11-01
The Bayesian Network Webserver (BNW) is a platform for comprehensive network modeling of systems genetics and other biological datasets. It allows users to quickly and seamlessly upload a dataset, learn the structure of the network model that best explains the data and use the model to understand relationships between network variables. Many datasets, including those used to create genetic network models, contain both discrete (e.g. genotype) and continuous (e.g. gene expression traits) variables, and BNW allows for modeling hybrid datasets. Users of BNW can incorporate prior knowledge during structure learning through an easy-to-use structural constraint interface. After structure learning, users are immediately presented with an interactive network model, which can be used to make testable hypotheses about network relationships. BNW, including a downloadable structure learning package, is available at http://compbio.uthsc.edu/BNW. (The BNW interface for adding structural constraints uses HTML5 features that are not supported by current version of Internet Explorer. We suggest using other browsers (e.g. Google Chrome or Mozilla Firefox) when accessing BNW). ycui2@uthsc.edu. Supplementary data are available at Bioinformatics online.
Virtual fracture reduction of the acetabulum using a rigid body biomechanical model
Boudissa, Mehdi; Chabanas, Matthieu; Oliveri, Hadrien; Tonetti, Jérôme
2014-01-01
International audience; Acetabular fractures are a challenge in orthopaedic surgery. A simple rigid body biomechanical model of the hip is proposed to simulate the fracture reduction. The action of surgical tools can be simulated interactively, which enables clinicians to evaluate different strategies for a better surgical planning.
Wassing, B.B.T.; Wees, J.D. van; Fokker, P.A.
2012-01-01
We developed a coupled code to obtain a better understanding of the role of pore pressure changes in causing fracture reactivation and seismicity during EGS. We implemented constitutive models for fractures in a continuum approach, which is advantageous because of the ease of integration in existing
Numerical investigations of rib fracture failure models in different dynamic loading conditions.
Wang, Fang; Yang, Jikuang; Miller, Karol; Li, Guibing; Joldes, Grand R; Doyle, Barry; Wittek, Adam
2016-01-01
Rib fracture is one of the most common thoracic injuries in vehicle traffic accidents that can result in fatalities associated with seriously injured internal organs. A failure model is critical when modelling rib fracture to predict such injuries. Different rib failure models have been proposed in prediction of thorax injuries. However, the biofidelity of the fracture failure models when varying the loading conditions and the effects of a rib fracture failure model on prediction of thoracic injuries have been studied only to a limited extent. Therefore, this study aimed to investigate the effects of three rib failure models on prediction of thoracic injuries using a previously validated finite element model of the human thorax. The performance and biofidelity of each rib failure model were first evaluated by modelling rib responses to different loading conditions in two experimental configurations: (1) the three-point bending on the specimen taken from rib and (2) the anterior-posterior dynamic loading to an entire bony part of the rib. Furthermore, the simulation of the rib failure behaviour in the frontal impact to an entire thorax was conducted at varying velocities and the effects of the failure models were analysed with respect to the severity of rib cage damages. Simulation results demonstrated that the responses of the thorax model are similar to the general trends of the rib fracture responses reported in the experimental literature. However, they also indicated that the accuracy of the rib fracture prediction using a given failure model varies for different loading conditions.
Strong Local-Nonlocal Coupling for Integrated Fracture Modeling
Energy Technology Data Exchange (ETDEWEB)
Littlewood, David John [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Silling, Stewart A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Mitchell, John A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Seleson, Pablo D. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Bond, Stephen D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Parks, Michael L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Turner, Daniel Z. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Burnett, Damon J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ostien, Jakob [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Gunzburger, Max [Florida State Univ., Tallahassee, FL (United States)
2015-09-01
Peridynamics, a nonlocal extension of continuum mechanics, is unique in its ability to capture pervasive material failure. Its use in the majority of system-level analyses carried out at Sandia, however, is severely limited, due in large part to computational expense and the challenge posed by the imposition of nonlocal boundary conditions. Combined analyses in which peridynamics is em- ployed only in regions susceptible to material failure are therefore highly desirable, yet available coupling strategies have remained severely limited. This report is a summary of the Laboratory Directed Research and Development (LDRD) project "Strong Local-Nonlocal Coupling for Inte- grated Fracture Modeling," completed within the Computing and Information Sciences (CIS) In- vestment Area at Sandia National Laboratories. A number of challenges inherent to coupling local and nonlocal models are addressed. A primary result is the extension of peridynamics to facilitate a variable nonlocal length scale. This approach, termed the peridynamic partial stress, can greatly reduce the mathematical incompatibility between local and nonlocal equations through reduction of the peridynamic horizon in the vicinity of a model interface. A second result is the formulation of a blending-based coupling approach that may be applied either as the primary coupling strategy, or in combination with the peridynamic partial stress. This blending-based approach is distinct from general blending methods, such as the Arlequin approach, in that it is specific to the coupling of peridynamics and classical continuum mechanics. Facilitating the coupling of peridynamics and classical continuum mechanics has also required innovations aimed directly at peridynamic models. Specifically, the properties of peridynamic constitutive models near domain boundaries and shortcomings in available discretization strategies have been addressed. The results are a class of position-aware peridynamic constitutive laws for
Energy Technology Data Exchange (ETDEWEB)
Lee, Youho, E-mail: euo@kaist.ac.kr; Lee, Jeong Ik, E-mail: jeongiklee@kaist.ac.kr; NO, Hee Cheon, E-mail: hcno@kaist.ac.kr
2016-03-15
Highlights: • Use of constant heat transfer coefficient for fracture analysis is not sound. • On-time heat transfer coefficient should be used for thermal fracture prediction. • ∼90% of the actual fracture stresses were predicted with the on-time transient h. • Thermal-hydraulic codes can be used to better predict brittle cladding fracture. • Effects of surface oxides on thermal shock fracture should be accounted by h. - Abstract: This study presents the importance of coherency in modeling thermal-hydraulics and mechanical behavior of a solid for an advanced prediction of cladding thermal shock fracture. In water quenching, a solid experiences dynamic heat transfer rate evolutions with phase changes of the fluid over a short quenching period. Yet, such a dynamic change of heat transfer rates has been overlooked in the analysis of thermal shock fracture. In this study, we are presenting quantitative evidence against the prevailing use of a constant heat transfer coefficient for thermal shock fracture analysis in water. We conclude that no single constant heat transfer could suffice to depict the actual stress evolution subject to dynamic fluid phase changes. Use of the surface temperature dependent heat transfer coefficient will remarkably increase predictability of thermal shock fracture of brittle materials. The presented results show a remarkable stress prediction improvement up to 80–90% of the actual stress with the use of the surface temperature dependent heat transfer coefficient. For thermal shock fracture analysis of brittle fuel cladding such as oxidized zirconium-based alloy or silicon carbide during LWR reflood, transient subchannel heat transfer coefficients obtained from a thermal-hydraulics code should be used as input for stress analysis. Such efforts will lead to a fundamental improvement in thermal shock fracture predictability over the current experimental empiricism for cladding fracture analysis during reflood.
Wang, Ruifei; Song, Hongqing; Tang, Hewei; Wang, Yuhe; Killough, John; Huang, Gang
2016-01-01
Permeability variation in tight channel sand formation makes an important role in gas production. Based on the features of channel sand formation, a mathematical model has been established considering anisotropy of permeability. The analytical solutions were derived for productivity of both vertical wells and vertically fractured wells. Simulation results show that, gas production rate of anisotropic channel sand formation is less than that of isotropic formation. For vertically fractured well, artificial fracture direction, drainage radius, permeability ratio and fracture half-length have considerable influence on production rate. The optimum fracture direction should be deviated less than π/8 from the maximum permeability direction (or the channel direction). In addition, the analytical model was verified by in situ measured data. The research provides theoretical basis for the development of tight channel sand gas reservoirs.
Olsson, P. A. T.; Kese, K.; Kroon, M.; Alvarez Holston, A.-M.
2015-06-01
In this work we report the results of an ab initio study of the transgranular fracture toughness and cleavage of brittle zirconium hydrides. We use the Griffith-Irwin relation to assess the fracture toughness using calculated surface energy and estimated isotropic Voigt-Reuss-Hill averages of the elastic constants. The calculated fracture toughness values are found to concur well with experimental data, which implies that fracture is dominated by cleavage failure. To investigate the cleavage energetics, we model the decohesion process. To describe the interplanar interaction we adopt Rose’s universal binding energy relation, which is found to reproduce the behaviour accurately. The modelling shows that the work of fracture and ductility decreases with increasing hydrogen content.
Bayesian estimation of the network autocorrelation model
Dittrich, D.; Leenders, R.T.A.J.; Mulder, J.
2017-01-01
The network autocorrelation model has been extensively used by researchers interested modeling social influence effects in social networks. The most common inferential method in the model is classical maximum likelihood estimation. This approach, however, has known problems such as negative bias of
Object Oriented Modeling Of Social Networks
Zeggelink, Evelien P.H.; Oosten, Reinier van; Stokman, Frans N.
1996-01-01
The aim of this paper is to explain principles of object oriented modeling in the scope of modeling dynamic social networks. As such, the approach of object oriented modeling is advocated within the field of organizational research that focuses on networks. We provide a brief introduction into the f
Agent-based modeling and network dynamics
Namatame, Akira
2016-01-01
The book integrates agent-based modeling and network science. It is divided into three parts, namely, foundations, primary dynamics on and of social networks, and applications. The book begins with the network origin of agent-based models, known as cellular automata, and introduce a number of classic models, such as Schelling’s segregation model and Axelrod’s spatial game. The essence of the foundation part is the network-based agent-based models in which agents follow network-based decision rules. Under the influence of the substantial progress in network science in late 1990s, these models have been extended from using lattices into using small-world networks, scale-free networks, etc. The book also shows that the modern network science mainly driven by game-theorists and sociophysicists has inspired agent-based social scientists to develop alternative formation algorithms, known as agent-based social networks. The book reviews a number of pioneering and representative models in this family. Upon the gi...
Liao, F; Huang, Z.
2015-01-01
Open Access funded by Engineering and Physical Sciences Research Council under a Creative Commons license. A robust finite element procedure for modelling the localised fracture of reinforced concrete beams at elevated temperatures is developed. In this model a reinforced concrete beam is represented as an assembly of 4-node quadrilateral plain concrete, 3-node main reinforcing steel bar, and 2-node bond-link elements. The concrete element is subdivided into layers for considering the temp...
Development of an Animal Model of Thoracolumbar Burst Fracture-Induced Acute Spinal Cord Injury
2016-07-01
AWARD NUMBER: W81XWH-14-2-0013 TITLE: DEVELOPMENT OF AN ANIMAL MODEL OF THORACOLUMBAR BURST FRACTURE-INDUCED ACUTE SPINAL CORD INJURY...4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER DEVELOPMENT OF AN ANIMAL MODEL OF THORACOLUMBAR BURST FRACTURE-INDUCED ACUTE SPINAL CORD INJURY 5b. GRANT...Rodent research has led to many advances in SCI treatment, but successful clinical translation remains limited. Here we describe a large animal model
Development of an Animal Model of Thoracolumbar Burst Fracture Induced Acute Spinal Cord Injury
2015-05-01
AWARD NUMBER: W81XWH-14-2-0013 TITLE: DEVELOPMENT OF AN ANIMAL MODEL OF THORACOLUMBAR BURST FRACTURE- INDUCED ACUTE SPINAL CORD INJURY...2015 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER DEVELOPMENT OF AN ANIMAL MODEL OF THORACOLUMBAR BURST FRACTURE-INDUCED ACUTE SPINAL CORD INJURY 5b...controlled spinal cord impactor for use in large animal models of SCI in order to more reliably recreate the human injury. A custom designed spinal cord
Energy Technology Data Exchange (ETDEWEB)
1980-09-01
Nineteen papers were presented at the workshop on modeling thermohydrologic flow in fractured masses. This workshop was a result of the interest currently being given to the isolation of nuclear wastes in geologic formations. Included in these proceedings are eighteen of the presentations, one abstract and summaries of the panel discussions. The papers are listed under the following categories: introduction; overviews; fracture modelings; repository studies; geothermal models; and recent developments. Eighteen of the papers have been abstracted and indexed.
Fluid Compressibility Effects during Hydraulic Fracture: an Opportunity for Gas Fracture Revival
Mighani, S.; Boulenouar, A.; Moradian, Z.; Evans, J. B.; Bernabe, Y.
2015-12-01
Hydraulic fracturing results when internal pore pressure is increased above a critical value. As the fracture extends, the fluid flows to the crack tip. The fracturing process depends strongly on the physical properties of both the porous solid and the fluid (e.g. porosity and elastic moduli for the solid, viscosity and compressibility for the fluid). It is also affected by the in-situ stress and pore pressure conditions. Here, we focus on the effect of fluid properties on hydraulic fracturing under conventional triaxial loading. Cylinders of Solnhofen limestone (a fine-grained, low permeability rock) were prepared with a central borehole through which different pressurized fluids such as oil, water or argon, were introduced. Preliminary experiments were performed using a confining pressure of 5 MPa and axial stress of 7 MPa. Our goal was to monitor fracture extension using strain gauges, acoustic emissions (AE) recording and ultrasonic velocity measurements. We also tried to compare the data with analytical models of fracture propagation. Initial tests showed that simple bi-wing fractures form when the fracturing fluid is relatively incompressible. With argon as pore fluid, a complex fracture network was formed. We also observed that the breakdown pressure was higher with argon than with less compressible fluids. After fracturing occurred, we cycled fluid pressure for several times. During the first cycles, re-opening of the fracture was associated with additional propagation. In general, it took 4 cycles to inhibit further propagation. Analytical models suggest that initial fractures occurring with compressible fluids tend to stabilize. Hence, formation and extension of additional fractures may occur, leading to a more complex morphology. Conversely, fractures formed by incompressible fluids remain critically stressed as they extend, thus producing a simple bi-wing fracture. Using compressible fracturing fluids could be a suitable candidate for an efficient
Edge exchangeable models for network data
Crane, Harry
2016-01-01
Exchangeable models for vertex labeled graphs cannot replicate the large sample behaviors of sparsity and power law degree distributions observed in many network datasets. Out of this mathematical impossibility emerges the question of how network data can be modeled in a way that reflects known empirical behaviors and respects basic statistical principles. We address this question by observing that edges, not vertices, act as the statistical units in most network datasets, making a theory of edge labeled networks more natural for most applications. Within this context we introduce the new invariance principle of {\\em edge exchangeability}, which unlike its vertex exchangeable counterpart can produce networks with sparse and/or power law structure. We characterize the class of all edge exchangeable network models and identify a particular two parameter family of models with suitable theoretical properties for statistical inference. We discuss issues of estimation from edge exchangeable models and compare our a...
Evaluation of fracture models through pressurized-thermal-shock testing
Energy Technology Data Exchange (ETDEWEB)
Pugh, C.E.; Bryan, R.H.; Bass, B.R.; Nanstad, R.K.
1988-01-01
Two multiple-transient pressurized-thermal-shock experiments (PTSEs) have been conducted under the NRC-sponsored Heavy-Section Steel Technology (HSST) program. The first test (PTSE-1) employed an SA-508 class 2 steel with high Charpy upper-shelf energy level and a relatively high brittle-to-ductile transition temperature. The second test (PTSE-2) used a 2 1/4 Cr-1 Mo steel (SA-387 grade 22) that had been given a special heat treatment to yield a low Charpy upper-shelf energy level and attendant low tearing resistance. Each experiment included two combined thermal and pressure transients that give rise to propagation and arrest of an initial long flaw that extended about 10% through the thick wall of the test cylinder. Both materials exhibited the ability to inhibit crack propagation by warm prestressing, high initiation toughness values and high crack-arrest toughness values. Cleavage initiation and arrest are modeled well by available fracture theories. However, calculations of ductile tearing based on resistance curves did not consistently predict the observed tearing.