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1.
This paper presents a fracture mapping (FM) approach combined with the extended finite element method (XFEM) to simulate coupled deformation and fluid flow in fractured porous media. Specifically, the method accurately represents the impact of discrete fractures on flow and deformation, although the individual fractures are not part of the finite element mesh. A key feature of FM‐XFEM is its ability to model discontinuities in the domain independently of the computational mesh. The proposed FM approach is a continuum‐based approach that is used to model the flow interaction between the porous matrix and existing fractures via a transfer function. Fracture geometry is defined using the level set method. Therefore, in contrast to the discrete fracture flow model, the fracture representation is not meshed along with the computational domain. Consequently, the method is able to determine the influence of fractures on fluid flow within a fractured domain without the complexity of meshing the fractures within the domain. The XFEM component of the scheme addresses the discontinuous displacement field within elements that are intersected by existing fractures. In XFEM, enrichment functions are added to the standard finite element approximation to adequately resolve discontinuous fields within the simulation domain. Numerical tests illustrate the ability of the method to adequately describe the displacement and fluid pressure fields within a fractured domain at significantly less computational expense than explicitly resolving the fracture within the finite element mesh. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
2.
Chiara Biscarini 《Landslides》2010,7(2):117-124
This paper describes the application of detailed computational fluid dynamics (CFD) to simulate the formation and propagation
of waves generated by the impact of landslide material with water. The problem is schematised as a multiphase–multicomponent
fluid flow: compressible air, water and transported alluvial material. The landslide simulation is performed by means of a
hybrid approach: as a rigid solid body slipping down along an inclined slope until it starts penetrating the water body. The
CFD model solves the Navier–Stokes equations with the RNG k-ɛ turbulence closure scheme and the volume of fluid multiphase
method, which maintains the interface as a sharp front. The governing equations are solved using the commercial CFD code,
FLUENT. The computed results are compared with experimental data reported in the literature. The model is then applied to
simulate the 1958 Lituya bay Tsunami event with a 2D a simplified geometry and the results are compared to others found in
literature. 相似文献
3.
Fluid injection–induced tensile opening is modeled using an extended finite volume method (XFVM). An embedded fracture strategy is used for the flow problem, that is, the fractures are discretized using finite volume segments without resolving the grid around them. Further, the discontinuities across fractures are modeled using special basis functions. The fracture openings due to enhanced fluid pressure and the associated shear slip due to traction free boundary condition on the fracture segments are both modeled using these special discontinuity basis functions. Mass transfer between fractures and matrix is modeled using the pressure difference. The enhancement of fracture storativity due to tensile opening leads to stronger coupling between flow and mechanics. An iterative scheme relying on the fixed-stress approach for fractures, which conserves the stress dependent terms over each iteration of the flow problem, has been introduced. Tensile opening has been simulated for single fractures embedded in two- and three-dimensional matrices. The convergence criterion for sequentially implicit fixed-stress scheme for fractures embedded in elastic media is established and has been validated numerically. Further, for 2D simulations, the effect of the matrix permeability for fracture propagation due to tensile opening has been studied. 相似文献
4.
An Approach for Modeling Rock Discontinuous Mechanical Behavior Under Multiphase Fluid Flow Conditions 总被引：1，自引：0，他引：1
Peng-Zhi Pan Jonny Rutqvist Xia-Ting Feng Fei Yan 《Rock Mechanics and Rock Engineering》2014,47(2):589-603
In this paper, the two computer codes TOUGH2 and RDCA (for “rock discontinuous cellular automaton”) are integrated for coupled hydromechanical analysis of multiphase fluid flow and discontinuous mechanical behavior in heterogeneous rock. TOUGH2 is a well-established code for geohydrological analysis involving multiphase, multicomponent fluid flow and heat transport; RDCA is a numerical model developed for simulating the nonlinear and discontinuous geomechanical behavior of rock. The RDCA incorporates the discontinuity of a fracture independently of the mesh, such that the fracture can be arbitrarily located within an element, while the fluid pressure calculated by TOUGH2 can be conveniently applied to fracture surfaces. We verify and demonstrate the coupled TOUGH–RDCA simulator by modeling a number of simulation examples related to coupled multiphase flow and geomechanical processes associated with the deep geological storage of carbon dioxide—including modeling of ground surface uplift, stress-dependent permeability, and the coupled multiphase flow and geomechanical behavior of fractures intersecting the caprock. 相似文献
5.
E. Karimzade M. Sharifzadeh H. R. Zarei K. Shahriar M. Cheraghi Seifabad 《Arabian Journal of Geosciences》2017,10(9):206
Groundwater flow is a major issue in underground opening in fractured rocks. Because of finding the fracture connectivity, contribution of each fracture in flow, and fracture connectivity to excavation boundary, the prediction of water flow to underground excavations is difficult. Simulation of fracture characteristics and spatial distribution is necessary to obtain realistic estimation of inflow quantity to tunnel and underground excavations. In this research, a computer code for three-dimensional discrete fracture network modeling of water inflow into underground excavations was developed. In this code, the fractures are simulated as ellipsoid while geometrical properties of the fractures are reproduced using a stochastic method. Properties such as the size, orientation, and density of the fractures are modeled by their respective probability distributions, which are obtained from field measurements. According to the fracture condition, the flow paths in rock mass are determined. The flow paths are considered as channels with rectangular sections in which channel width and fracture aperture determine geometry of channel section. Inflow into excavation is predicted ignoring matrix permeability and considering the hydrogeological conditions. To verify presented model, simulation results were compared to a part of the Cheshmeh-Roozieh water transfer tunnel in Iran. The results obtained from this research are in good agreement with the field data. Thus, the average of the predicted inflow has just an approximation error equal to 17.8%, and its standard deviation is 8.6 l/s, which is equal to 21% of the observed value that demonstrates low dispersion of the predicted values. 相似文献
6.
Diffusion-controlled development of silica-undersaturated domains in felsic granulites of the Bohemian Massif (Variscan belt of Central Europe) 总被引：2，自引：0，他引：2
Lucie Tajčmanová Jiří Konopásek James A. D. Connolly 《Contributions to Mineralogy and Petrology》2007,153(2):237-250
Plagioclase rims around metastable kyanite crystals appear during decompression of high-pressure felsic granulites from the
high-grade internal zone of the Bohemian Massif (Variscan belt of Central Europe). The development of the plagioclase corona
is a manifestation of diffusion-driven transfer of CaO and Na2O from the surrounding matrix and results in isolation of kyanite grains from the quartz- and K-feldspar-bearing matrix. This
process establishes Si-undersaturated conditions along the plagioclase–kyanite interface, which allow crystallization of spinel
during low-pressure metamorphism. The process of the plagioclase rim development is modeled thermodynamically assuming local
equilibrium. The results combined with textural observations enable estimation of equilibration volume and diffusion length
for Na and Ca that extends ∼400–450 and ∼450–550 μm, respectively, around each kyanite crystal. Low estimated bulk diffusion
coefficients suggest that the diffusion rate of Ca and Na is controlled by low diffusivity of Al across the plagioclase rim. 相似文献
7.
We derive a macroscopic model for single-phase, incompressible, viscous fluid flow in a porous medium with small cavities called vugs. We model the vuggy medium on the microscopic scale using Stokes equations within the vugular inclusions, Darcy's law within the porous rock, and a Beavers–Joseph–Saffman boundary condition on the interface between the two regions. We assume periodicity of the medium and obtain uniform energy estimates independent of the period. Through a two-scale homogenization limit as the period tends to zero, we obtain a macroscopic Darcy's law governing the medium on larger scales. We also develop some needed generalizations of the two-scale convergence theory needed for our bimodal medium, including a two-scale convergence result on the Darcy–Stokes interface. The macroscopic Darcy permeability is computable from the solution of a cell problem. An analytic solution to this problem in a simple geometry suggests that: (1) flow along vug channels is primarily Poiseuille with a small perturbation related to the Beavers–Joseph slip, and (2) flow that alternates from vug to matrix behaves as if the vugs have infinite permeability. 相似文献
8.
Anna Nissen Eirik Keilegavlen Tor Harald Sandve Inga Berre Jan Martin Nordbotten 《Computational Geosciences》2018,22(2):451-467
In simulation of fluid injection in fractured geothermal reservoirs, the characteristics of the physical processes are severely affected by the local occurence of connected fractures. To resolve these structurally dominated processes, there is a need to develop discretization strategies that also limit computational effort. In this paper, we present an upscaling methodology for geothermal heat transport with fractures represented explicitly in the computational grid. The heat transport is modeled by an advection-conduction equation for the temperature, and solved on a highly irregular coarse grid that preserves the fracture heterogeneity. The upscaling is based on different strategies for the advective term and the conductive term. The coarse scale advective term is constructed from sums of fine scale fluxes, whereas the coarse scale conductive term is constructed based on numerically computed basis functions. The method naturally incorporates the coupling between solution variables in the matrix and in the fractures, respectively, via the discretization. In this way, explicit transfer terms that couple fracture and matrix solution variables are avoided. Numerical results show that the upscaling methodology performs well, in particular for large upscaling ratios, and that it is applicable also to highly complex fracture networks. 相似文献
9.
In this paper, a numerical model to predict flow‐induced shear failure along pre‐existing fractures is presented. The framework is based on a discrete fracture representation embedded in a continuum describing the damaged matrix. A finite volume method is used to compute both flow and mechanical equilibrium, whereas specifically tailored basis functions are used to account for the physics at discontinuities. The failure criterion is based on a maximum shear strength limit, which changes with varying compressive stress on the fracture manifold. The displacements along fracture manifolds are obtained such that force balance is achieved under conditions, where shear stress of the failing fracture segment is constrained to the maximum shear strength at the segment. Simultaneously, the fluid pressure is computed independently of the shear slip. A relaxation model approach is used to obtain the maximum shear limit on the fracture manifold, which leads to grid convergence. 相似文献
10.
The dual-porosity model is usually employed to simulate the flow in fractured reservoirs. However, its original form for the multiphase flow does not consider the displacement effect under macropressure gradient. Especially for the incompressible multiphase flow, it predicts zero transfer term between fracture and matrix, which is unreasonable. To improve this, a modified double-porosity model is proposed for incompressible two-phase flow, in which the displacement effect is considered and the corresponding shape factor is derived. For the anisotropic case, the shape factor of displacement depends upon the velocity direction. The accuracy and the efficiency of the proposed dual-porosity model are indicated through numerical tests. 相似文献
11.
Cubic law with aperture-length correlation: implications for network scale fluid flow 总被引：2，自引：2，他引：0
Christian Klimczak Richard A. Schultz Rishi Parashar Donald M. Reeves 《Hydrogeology Journal》2010,18(4):851-862
Previous studies have computed and modeled fluid flow through fractured rock with the parallel plate approach where the volumetric flow per unit width normal to the direction of flow is proportional to the cubed aperture between the plates, referred to as the traditional cubic law. When combined with the square root relationship of displacement to length scaling of opening-mode fractures, total flow rates through natural opening-mode fractures are found to be proportional to apertures to the fifth power. This new relationship was explored by examining a suite of flow simulations through fracture networks using the discrete fracture network model (DFN). Flow was modeled through fracture networks with the same spatial distribution of fractures for both correlated and uncorrelated fracture length-to-aperture relationships. Results indicate that flow rates are significantly higher for correlated DFNs. Furthermore, the length-to-aperture relations lead to power-law distributions of network hydraulic conductivity which greatly influence equivalent permeability tensor values. These results confirm the importance of the correlated square root relationship of displacement to length scaling for total flow through natural opening-mode fractures and, hence, emphasize the role of these correlations for flow modeling. 相似文献
12.
We consider the modeling and simulation of compositional two-phase flow in a porous medium, where one phase is allowed to
vanish or appear. The modeling of Marchand et al. (in review) leads to a nonlinear system of two conservation equations. Each
conservation equation contains several nonlinear diffusion terms, which in general cannot be written as a function of the
gradients of the two principal unknowns. Also the diffusion coefficients are not necessarily explicit local functions of them.
For the generalised mixed finite elements approximation, Lagrange multipliers associated to each principal unknown are introduced,
the sum of the diffusive fluxes of each component is explicitly eliminated and the static condensation leads to a “global”
nonlinear system of equations only in the Lagrange multipliers also including complementarity conditions to cope with vanishing
or appearing phases. After time discretisation, this system can be solved at each time step using a semi-smooth Newton method.
The static condensation involves “local” nonlinear systems of equations associated to each element, solved also by a semismooth
Newton method. The algorithm is successfully applied to 1D and 2D examples of water–hydrogen flow involving gas phase appearance
and disappearance. 相似文献
13.
This paper presents the development of a discrete fracture model of fully coupled compressible fluid flow, adsorption and geomechanics to investigate the dynamic behaviour of fractures in coal. The model is applied in the study of geological carbon dioxide sequestration and differs from the dual porosity model developed in our previous work, with fractures now represented explicitly using lower-dimensional interface elements. The model consists of the fracture-matrix fluid transport model, the matrix deformation model and the stress-strain model for fracture deformation. A sequential implicit numerical method based on Galerkin finite element is employed to numerically solve the coupled governing equations, and verification is completed using published solutions as benchmarks. To explore the dynamic behaviour of fractures for understanding the process of carbon sequestration in coal, the model is used to investigate the effects of gas injection pressure and composition, adsorption and matrix permeability on the dynamic behaviour of fractures. The numerical results indicate that injecting nonadsorbing gas causes a monotonic increase in fracture aperture; however, the evolution of fracture aperture due to gas adsorption is complex due to the swelling-induced transition from local swelling to macro swelling. The change of fracture aperture is mainly controlled by the normal stress acting on the fracture surface. The fracture aperture initially increases for smaller matrix permeability and then declines after reaching a maximum value. When the local swelling becomes global, fracture aperture starts to rebound. However, when the matrix permeability is larger, the fracture aperture decreases before recovering to a higher value and remaining constant. Gas mixtures containing more carbon dioxide lead to larger closure of fracture aperture compared with those containing more nitrogen. 相似文献
14.
Methods reported in the literature for rock fracture simulations include approaches based on stochastic geometry, multiple-point
statistics and a combination of geostatistics for fracture density and object-based modelling for fracture geometries. The
advantages and disadvantages of each of these approaches are discussed with examples. By way of review, the authors begin
with the geostatistical indicator simulation method, based on the truncated–Gaussian algorithm; this is followed by multiple-point
statistical simulation and then the stochastic geometry approach, which is based on marked point process simulation. A new
approach, based on pluriGaussian structural simulation, is then introduced. The new approach incorporates in the simulation
the spatial correlation between different sets of fractures, which in general, is very difficult, if not impossible, to accomplish
in the three methods reviewed. Each simulation method is summarised together with detailed simulation procedures for each.
A published two-dimensional fracture dataset is used as a means of assessing the performance of each simulation method and
of demonstrating the concepts discussed in the text. 相似文献
15.
Najla Frih Vincent Martin Jean Elizabeth Roberts Ali Saada 《Computational Geosciences》2012,16(4):1043-1060
We consider a model for fluid flow in a porous medium with a fracture. In this model, the fracture is treated as an interface between subdomains, on which specific equations have to be solved. In this article, we analyze the discrete problem, assuming that the fracture mesh and the subdomain meshes are completely independent, but that the geometry of the fracture is respected. We show that despite this nonconformity, first-order convergence is preserved with the lowest-order Raviart–Thomas(-Nedelec) mixed finite elements. Numerical simulations confirm this result. 相似文献
16.
Numerical approximation based on different forms of the governing partial differential equation can lead to significantly
different results for two-phase flow in porous media. Selecting the proper primary variables is a critical step in efficiently
modeling the highly nonlinear problem of multiphase subsurface flow. A comparison of various forms of numerical approximations
for two-phase flow equations is performed in this work. Three forms of equations including the pressure-based, mixed pressure–saturation
and modified pressure–saturation are examined. Each of these three highly nonlinear formulations is approximated using finite
difference method and is linearized using both Picard and Newton–Raphson linearization approaches. Model simulations for several
test cases demonstrate that pressure based form provides better results compared to the pressure–saturation approach in terms
of CPU_time and the number of iterations. The modification of pressure–saturation approach improves accuracy of the results.
Also it is shown that the Newton–Raphson linearization approach performed better in comparison to the Picard iteration linearization
approach with the exception for in the pressure–saturation form. 相似文献
17.
Jonny Rutqvist Deborah Barr Jens T. Birkholzer Kiyoshi Fujisaki Olaf Kolditz Quan-Sheng Liu Tomoo Fujita Wenqing Wang Cheng-Yuan Zhang 《Environmental Geology》2009,57(6):1347-1360
This paper presents an international, multiple-code, simulation study of coupled thermal, hydrological, and mechanical (THM)
processes and their effect on permeability and fluid flow in fractured rock around heated underground nuclear waste emplacement
drifts. Simulations were conducted considering two types of repository settings (1) open emplacement drifts in relatively
shallow unsaturated volcanic rock, and (2) backfilled emplacement drifts in deeper saturated crystalline rock. The results
showed that for the two assumed repository settings, the dominant mechanism of changes in rock permeability was thermal–mechanically
induced closure (reduced aperture) of vertical fractures, caused by thermal stress resulting from repository-wide heating
of the rock mass. The magnitude of thermal–mechanically induced changes in permeability was more substantial in the case of
an emplacement drift located in a relatively shallow, low-stress environment where the rock is more compliant, allowing more
substantial fracture closure during thermal stressing. However, in both of the assumed repository settings in this study,
the thermal–mechanically induced changes in permeability caused relatively small changes in the flow field, with most changes
occurring in the vicinity of the emplacement drifts. 相似文献
18.
This study was based on the discrete fracture model to investigate the influence of fracture parameters on the solute transport
in the fractured rocks of andesite in Lan-Yu island, Taiwan. In the simulation cases, the centers of fractures, fracture lengths
and apertures were assumed to have Poisson’s distribution, negative exponential distribution and lognormal distribution, respectively.
With the above assumptions, constructing the discrete fracture model became practicable. Using the mass-balance equation with
specified boundary conditions, the flow field in the rock was solved. Then particles were released under the flow field. Monte
Carlo method was used assuming that the amount of particles was proportional to the flow rates to get the particle accumulated
percentage breakthrough curve and to estimate the dispersion coefficient. On the basis of the discrete fracture model, it
was possible to evaluate the property of dispersion behavior of andesite in Lan-Yu Island with flow and transport mechanism.
Properties of the dispersion behavior such as the relation between distance and traveling-time (ln〈r
2〉 and ln 〈t〉), anisotropic behavior, and the overall dispersion coefficient in a fracture network were characterized: the slope value
of ln〈r
2〉 and ln〈t〉 was 1.64 an indication of non-Fickian dispersion, the particles dispersion along the flow (D11) was bigger than that perpendicular
to the flow (D22), and the dispersion coefficient by this study was 0.91 m comparing the value 1 m from Sauty’s method. 相似文献
19.
The paper deals with two-dimensional (2D) numerical modelling of hydro-fracking (hydraulic fracturing) in rocks at the meso-scale. A numerical model was developed to characterize the properties of fluid-driven fractures in rocks by combining the discrete element method (DEM) with computational fluid dynamics (CFD). The mechanical behaviour of the rock matrix was simulated with DEM and the behaviour of the fracturing fluid flow in newly developed and pre-existing fractures with CFD. The changes in the void geometry in the rock matrix were taken into account. The initial 2D hydro-fracking simulation tests were carried out for a rock segment under biaxial compression with one injection slot in order to validate the numerical model. The qualitative effect of several parameters on the propagation of a hydraulic fracture was studied: initial porosity of the rock matrix, dynamic viscosity of the fracking fluid, rock strength and pre-existing fracture. The characteristic features of a fractured rock mass due to a high-pressure injection of fluid were realistically modelled by the proposed coupled approach.
相似文献20.
Naturally fractured mine pillars provide an excellent example of the importance of accurately determining rock mass strength.
Failure in slender pillars is predominantly controlled by naturally occurring discontinuities, their influence diminishing
with increasing pillar width, with wider pillars failing through a combination of brittle and shearing processes. To accurately
simulate this behaviour by numerical modelling, the current analysis incorporates a more realistic representation of the mechanical
behaviour of discrete fracture systems. This involves realistic simulation and representation of fracture networks, either
as individual entities or as a collective system of fracture sets, or a combination of both. By using an integrated finite
element/discrete element–discrete fracture network approach it is possible to study the failure of rock masses in tension
and compression, along both existing pre-existing fractures and through intact rock bridges, and incorporating complex kinematic
mechanisms. The proposed modelling approach fully captures the anisotropic and inhomogeneous effects of natural jointing and
is considered to be more realistic than methods relying solely on continuum or discontinuum representation. The paper concludes
with a discussion on the development of synthetic rock mass properties, with the intention of providing a more robust link
between rock mass strength and rock mass classification systems. 相似文献