共查询到20条相似文献，搜索用时 31 毫秒
1.
An efficient and accurate numerical model for multicomponent compressible single-phase flow in fractured media is presented. The discrete-fracture approach is used to model the fractures where the fracture entities are described explicitly in the computational domain. We use the concept of cross flow equilibrium in the fractures. This will allow large matrix elements in the neighborhood of the fractures and considerable speed up of the algorithm. We use an implicit finite volume (FV) scheme to solve the species mass balance equation in the fractures. This step avoids the use of Courant–Freidricks–Levy (CFL) condition and contributes to significant speed up of the code. The hybrid mixed finite element method (MFE) is used to solve for the velocity in both the matrix and the fractures coupled with the discontinuous Galerkin (DG) method to solve the species transport equations in the matrix. Four numerical examples are presented to demonstrate the robustness and efficiency of the proposed model. We show that the combination of the fracture cross-flow equilibrium and the implicit composition calculation in the fractures increase the computational speed 20–130 times in 2D. In 3D, one may expect even a higher computational efficiency. 相似文献
2.
Various numerical methods have been used in the literature to simulate single and multiphase flow in fractured media. A promising approach is the use of the discrete-fracture model where the fracture entities in the permeable media are described explicitly in the computational grid. In this work, we present a critical review of the main conventional methods for multiphase flow in fractured media including the finite difference (FD), finite volume (FV), and finite element (FE) methods, that are coupled with the discrete-fracture model. All the conventional methods have inherent limitations in accuracy and applications. The FD method, for example, is restricted to horizontal and vertical fractures. The accuracy of the vertex-centered FV method depends on the size of the matrix gridcells next to the fractures; for an acceptable accuracy the matrix gridcells next to the fractures should be small. The FE method cannot describe properly the saturation discontinuity at the matrix–fracture interface. In this work, we introduce a new approach that is free from the limitations of the conventional methods. Our proposed approach is applicable in 2D and 3D unstructured griddings with low mesh orientation effect; it captures the saturation discontinuity from the contrast in capillary pressure between the rock matrix and fractures. The matrix–fracture and fracture–fracture fluxes are calculated based on powerful features of the mixed finite element (MFE) method which provides, in addition to the gridcell pressures, the pressures at the gridcell interfaces and can readily model the pressure discontinuities at impermeable faults in a simple way. To reduce the numerical dispersion, we use the discontinuous Galerkin (DG) method to approximate the saturation equation. We take advantage of a hybrid time scheme to alleviate the restrictions on the size of the time step in the fracture network. Several numerical examples in 2D and 3D demonstrate the robustness of the proposed model. Results show the significance of capillary pressure and orders of magnitude increase in computational speed compared to previous works. 相似文献
3.
We propose a novel computational method for the efficient simulation of two-phase flow in fractured porous media. Instead of refining the grid to capture the flow along the faults or fractures, we represent the latter as immersed interfaces, using a reduced model for the flow and suitable coupling conditions. We allow for non matching grids between the porous matrix and the fractures to increase the flexibility of the method in realistic cases. We employ the extended finite element method for the Darcy problem and a finite volume method that is able to handle cut cells and matrix-fracture interactions for the saturation equation. Moreover, we address through numerical experiments the problem of the choice of a suitable numerical flux in the case of a discontinuous flux function at the interface between the fracture and the porous matrix. A wrong approximate solution of the Riemann problem can yield unphysical solutions even in simple cases. 相似文献
4.
《Advances in water resources》2005,28(7):729-744
In this paper, we discuss the local discontinuous Galerkin (LDG) method applied to elliptic flow problems and give details on its implementation, focusing specifically on the case of piecewise linear approximating functions. The LDG method is one a family of discontinuous Galerkin (DG) methods proposed for diffusion models. These DG methods allow for very general hp finite element meshes, and produce locally conservative fluxes which can be used in coupling flow with transport. The drawback to DG methods, when compared to their continuous counterparts, is the number of degrees of freedom required to compute the solution. This motivates a coupled approach, discussed herein, where the solution is allowed to be continuous or discontinuous on a node-by-node basis. This coupled approximation is locally conservative in regions where the numerical solution is discontinuous. Numerical results for fully discontinuous, continuous and coupled discontinuous/continuous solutions are given, where we compare solution accuracy, matrix condition numbers and mass balance errors for the various approaches. 相似文献
5.
In general, the accuracy of numerical simulations is determined by spatial and temporal discretization levels. In fractured porous media, the time step size is a key factor in controlling the solution accuracy for a given spatial discretization. If the time step size is restricted by the relatively rapid responses in the fracture domain to maintain an acceptable level of accuracy in the entire simulation domain, the matrix tends to be temporally over-discretized. Implicit sub-time stepping applies smaller sub-time steps only to the sub-domain where the accuracy requirements are less tolerant and is most suitable for problems where the response is high in only a small portion of the domain, such as within and near the fractures in fractured porous media. It is demonstrated with illustrative examples that implicit sub-time stepping can significantly improve the simulation efficiency with minimal loss in accuracy when simulating flow and transport in fractured porous media. The methodology is successfully applied to density-dependent flow and transport simulations in a Canadian Shield environment, where the flow and transport is dominated by discrete, highly conductive fracture zones. 相似文献
6.
The effect of fracture network geometry on free convection in fractured rock is studied using numerical simulations. We examine the structural properties of fracture networks that control the onset and strength of free convection and the patterns of density-dependent flow. Applicability of the equivalent porous medium approach (EPM) is also tested, and recommendations are given, for which situations the EPM approach is valid. To date, the structural properties of fracture networks that determine free convective flow are examined only in few, predominantly simplified regular fracture networks. We consider fracture networks containing continuous, discontinuous, orthogonal and/or inclined discrete fractures embedded in a low-permeability rock matrix. The results indicate that bulk permeability is not adequate to infer the occurrence and magnitude of free convection in fractured rock. Fracture networks can inhibit or promote convection depending on the fracture network geometry. Continuous fracture circuits are the crucial geometrical feature of fracture networks, because large continuous fracture circuits with a large vertical extent promote convection. The likelihood of continuous fracture circuits and thus of free convection increases with increasing fracture density and fracture length, but individual fracture locations may result in great deviances in strength of convection between statistically equivalent fracture networks such that prediction remains subject to large uncertainty. 相似文献
7.
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. 相似文献
8.
Variable-density groundwater flow and solute transport in porous media containing nonuniform discrete fractures 总被引：1，自引：0，他引：1
Variations in fluid density can greatly affect fluid flow and solute transport in the subsurface. Heterogeneities such as fractures play a major role for the migration of variable-density fluids. Earlier modeling studies of density effects in fractured media were restricted to orthogonal fracture networks, consisting of only vertical and horizontal fractures. The present study addresses the phenomenon of 3D variable-density flow and transport in fractured porous media, where fractures of an arbitrary incline can occur. A general formulation of the body force vector is derived, which accounts for variable-density flow and transport in fractures of any orientation. Simulation results are presented that show the verification of the new model formulation, for the porous matrix and for inclined fractures. Simulations of variable-density flow and solute transport are then conducted for a single fracture, embedded in a porous matrix. The simulations show that density-driven flow in the fracture causes convective flow within the porous matrix and that the high-permeability fracture acts as a barrier for convection. Other simulations were run to investigate the influence of fracture incline on plume migration. Finally, tabular data of the tracer breakthrough curve in the inclined fracture is given to facilitate the verification of other codes. 相似文献
9.
The structure of macroporous or aggregated soils and fractured rocks is generally so complex that it is impractical to measure the geometry at the microscale (i.e., the size and the shape of soil aggregates or rock matrix blocks, and the myriad of fissures or fractures), and use such data in geometry-dependent macroscale flow and transport models. This paper analyzes a first-order type dual-porosity model which contains a geometry-dependent coefficient, β, in the mass transfer term to macroscopically represent the size and shape of soil or rock matrix blocks. As a reference, one- and two-dimensional geometry-based diffusion models were used to simulate mass transport into and out of porous blocks of defined shapes. Estimates for β were obtained analytically for four different matrix block geometries. Values for β were also calculated by directly matching analytical solutions of the diffusion models for a number of selected matrix block geometries to results obtained with the first-order model assuming standard boundary conditions. Direct matching improved previous results for cylindrical macropore geometries, especially when relatively small ratios between the outer soil mantle and the radius of the inner cylinder were used. Results of our analysis show that β is closely related to the ratio of the effective surface area available for mass transfer, and the soil matrix volume normalized by the effective characteristic length of the matrix system. Using values of β obtained by direct matching, an empirical function is derived to estimate macroscopic geometry coefficients from medium properties which in principle are measurable. The method permits independent estimates of β, thus allowing the dual-porosity approach eventually to be applied to media with complex and mixed types of structural geometry. 相似文献
10.
We present advances in compositional modeling of two-phase multi-component flow through highly complex porous media. Higher-order methods are used to approximate both mass transport and the velocity and pressure fields. We employ the Mixed Hybrid Finite Element (MHFE) method to simultaneously solve, to the same order, the pressure equation and Darcy's law for the velocity. The species balance equation is approximated by the discontinuous Galerkin (DG) approach, combined with a slope limiter. In this work we present an improved DG scheme where phase splitting is analyzed at all element vertices in the two-phase regions, rather than only as element averages. This approximation is higher-order than the commonly employed finite volume method and earlier DG approximations. The method reduces numerical dispersion, allowing for an accurate capture of shock fronts and lower dependence on mesh quality and orientation. Further new features are the extension to unstructured grids and support for arbitrary permeability tensors (allowing for both scalar heterogeneity, and shear anisotropy). The most important advancement in this work is the self-consistent modeling of two-phase multi-component Fickian diffusion. We present several numerical examples to illustrate the powerful features of our combined MHFE–dg method with respect to lower-order calculations, ranging from simple two component fluids to more challenging real problems regarding CO2 injection into a vertical domain saturated with a multi-component petroleum fluid. 相似文献
11.
Numerical simulations of variable-density flow and solute transport have been conducted to investigate dense plume migration for various configurations of 2D fracture networks. For orthogonal fractures, simulations demonstrate that dispersive mixing in fractures with small aperture does not stabilize vertical plume migration in fractures with large aperture. Simulations in non-orthogonal 2D fracture networks indicate that convection cells form and that they overlap both the porous matrix and fractures. Thus, transport rates in convection cells depend on matrix and fracture flow properties. A series of simulations in statistically equivalent networks of fractures with irregular orientation show that the migration of a dense plume is highly sensitive to the geometry of the network. If fractures in a random network are connected equidistantly to the solute source, few equidistantly distributed fractures favor density-driven transport. On the other hand, numerous fractures have a stabilizing effect, especially if diffusive transport rates are high. A sensitivity analysis for a network with few equidistantly distributed fractures shows that low fracture aperture, low matrix permeability and high matrix porosity impede density-driven transport because these parameters reduce groundwater flow velocities in both the matrix and the fractures. Enhanced molecular diffusion slows down density-driven transport because it favors solute diffusion from the fractures into the low-permeability porous matrix where groundwater velocities are smaller. For the configurations tested, variable-density flow and solute transport are most sensitive to the permeability and porosity of the matrix, which are properties that can be determined more accurately than the geometry and hydraulic properties of the fracture network, which have a smaller impact on density-driven transport. 相似文献
12.
含裂缝多孔介质渗透率预测是非常规油气资源勘探开发的一个紧迫问题.现有多孔介质岩石物理模型通常利用圆形孔管模拟宏观岩石孔隙空间,难以定量描述软孔隙/裂缝在压力作用下的闭合情况,缺乏裂缝/孔隙间流量交换的连通机制.本文提出含三维裂缝/软孔隙网络多孔介质模型,将储层岩石裂缝/软孔隙表示为椭圆截面微管,建立了周期性压力作用下微观裂缝流量表达式,通过网络模型和流量守恒条件,得到含有三维裂缝/软孔隙网络的多孔介质渗透率计算方法.数值算例表明,预测结果与实验数据分布范围吻合很好,能够给出不同类型岩心对应孔隙纵横比的分布图.三维裂缝/软孔隙网络模型建立了宏观可观测量与裂缝参数之间关系,能够定量分析岩石渗透率随裂缝体密度、纵横比、孔隙流体类型和围压等因素的变化规律,为复杂条件下储层渗透率预测提供了一种有效方法. 相似文献
13.
《Advances in water resources》2002,25(1):67-84
A discontinuous Galerkin (DG) finite element method is described for the two-dimensional, depth-integrated shallow water equations (SWEs). This method is based on formulating the SWEs as a system of conservation laws, or advection–diffusion equations. A weak formulation is obtained by integrating the equations over a single element, and approximating the unknowns by piecewise, possibly discontinuous, polynomials. Because of its local nature, the DG method easily allows for varying the polynomial order of approximation. It is also “locally conservative”, and incorporates upwinded numerical fluxes for modeling problems with high flow gradients. Numerical results are presented for several test cases, including supercritical flow, river inflow and standard tidal flow in complex domains, and a contaminant transport scenario where we have coupled the shallow water flow equations with a transport equation for a chemical species. 相似文献
14.
The geochemical computer model PHREEQC can simulate solute transport in fractured bedrock aquifers that can be conceptualized as dual-porosity flow systems subject to one-dimensional advective-dispersive transport in the bedrock fractures and diffusive transport in the bedrock matrix. This article demonstrates how the physical characteristics of such flow systems can be parameterized for use in PHREEQC, it provides a method for minimizing numerical dispersion in PHREEQC simulations, and it compares PHREEQC simulations with results of an analytical solution. The simulations assumed a dual-porosity conceptual model involving advective-reactive-dispersive transport in the mobile zone (bedrock fracture) and diffusive-reactive transport in the immobile zone (bedrock matrix). The results from the PHREEQC dual-porosity transport model that uses a finite-difference approach showed excellent agreement compared with an analytical solution. 相似文献
15.
《Advances in water resources》2004,27(2):129-140
The discontinuous spectral Galerkin method uses a finite-element discretization of the groundwater flow domain with basis functions of arbitrary order in each element. The independent choice of the basis functions in each element permits discontinuities in transmissivity in the flow domain. This formulation is shown to be of high order accuracy and particularly suitable for accurately calculating the flow field in porous media. Simulations are presented in terms of streamlines in a bidimensional aquifer, and compared with the solution calculated with a standard finite-element method and a mixed finite-element method. Numerical simulations show that the discontinuous spectral Galerkin approximation is more efficient than the standard finite-element method (in computing fluxes and streamlines/pathlines) for a given accuracy, and it is more accurate on a given grid. On the other hand the mixed finite-element method ensures the continuity of the fluxes at the cell boundaries and it is particular efficient in representing complicated flow fields with few mesh points. Simulations show that the mixed finite-element method is superior to the discontinuous spectral Galerkin method producing accurate streamlines even if few computational nodes are used. The application of the discontinuous Galerkin method is thus of interest in groundwater problems only when high order and extremely accurate solutions are needed. 相似文献
16.
Bioremediation in Fractured Rock: 1. Modeling to Inform Design,Monitoring, and Expectations 
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下载免费PDF全文 Claire R. Tiedeman Allen M. Shapiro Paul A. Hsieh Thomas E. Imbrigiotta Daniel J. Goode Pierre J. Lacombe Mary F. DeFlaun Scott R. Drew Carole D. Johnson John H. Williams Gary P. Curtis 《Ground water》2018,56(2):300-316
Field characterization of a trichloroethene (TCE) source area in fractured mudstones produced a detailed understanding of the geology, contaminant distribution in fractures and the rock matrix, and hydraulic and transport properties. Groundwater flow and chemical transport modeling that synthesized the field characterization information proved critical for designing bioremediation of the source area. The planned bioremediation involved injecting emulsified vegetable oil and bacteria to enhance the naturally occurring biodegradation of TCE. The flow and transport modeling showed that injection will spread amendments widely over a zone of lower‐permeability fractures, with long residence times expected because of small velocities after injection and sorption of emulsified vegetable oil onto solids. Amendments transported out of this zone will be diluted by groundwater flux from other areas, limiting bioremediation effectiveness downgradient. At nearby pumping wells, further dilution is expected to make bioremediation effects undetectable in the pumped water. The results emphasize that in fracture‐dominated flow regimes, the extent of injected amendments cannot be conceptualized using simple homogeneous models of groundwater flow commonly adopted to design injections in unconsolidated porous media (e.g., radial diverging or dipole flow regimes). Instead, it is important to synthesize site characterization information using a groundwater flow model that includes discrete features representing high‐ and low‐permeability fractures. This type of model accounts for the highly heterogeneous hydraulic conductivity and groundwater fluxes in fractured‐rock aquifers, and facilitates designing injection strategies that target specific volumes of the aquifer and maximize the distribution of amendments over these volumes. 相似文献
17.
We present a method to determine equivalent permeability of fractured porous media. Inspired by the previous flow-based upscaling methods, we use a multi-boundary integration approach to compute flow rates within fractures. We apply a recently developed multi-point flux approximation Finite Volume method for discrete fracture model simulation. The method is verified by upscaling an arbitrarily oriented fracture which is crossing a Cartesian grid. We demonstrate the method by applying it to a long fracture, a fracture network and the fracture network with different matrix permeabilities. The equivalent permeability tensors of a long fracture crossing Cartesian grids are symmetric, and have identical values. The application to the fracture network case with increasing matrix permeabilities shows that the matrix permeability influences more the diagonal terms of the equivalent permeability tensor than the off-diagonal terms, but the off-diagonal terms remain important to correctly assess the flow field. 相似文献
18.
19.
Jostein R. Natvig Knut&#x;Andreas Lie Birgitte Eikemo Inga Berre 《Advances in water resources》2007,30(12):2424-2438
We consider a discontinuous Galerkin scheme for computing transport in heterogeneous media. An efficient solution of the resulting linear system of equations is possible by taking advantage of a priori knowledge of the direction of flow. By arranging the elements in a suitable sequence, one does not need to assemble the full system and may compute the solution in an element-by-element fashion. We demonstrate this procedure on boundary-value problems for tracer transport and time-of-flight. 相似文献
20.
This paper presents and compares several numerical solutions of the coupled system of Navier–Stokes and Darcy equations. The schemes are based on combinations of the finite element method and the discontinuous Galerkin method. Accuracy and robustness of the methods are investigated for heterogeneous porous media. The importance of local mass conservation for filtration problems is also discussed. 相似文献