共查询到20条相似文献，搜索用时 421 毫秒
1.
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
2.
Contrast in capillary pressure of heterogeneous permeable media can have a significant effect on the flow path in two-phase immiscible flow. Very little work has appeared on the subject of capillary heterogeneity despite the fact that in certain cases it may be as important as permeability heterogeneity. The discontinuity in saturation as a result of capillary continuity, and in some cases capillary discontinuity may arise from contrast in capillary pressure functions in heterogeneous permeable media leading to complications in numerical modeling. There are also other challenges for accurate numerical modeling due to distorted unstructured grids because of the grid orientation and numerical dispersion effects. Limited attempts have been made in the literature to assess the accuracy of fluid flow modeling in heterogeneous permeable media with capillarity heterogeneity. The basic mixed finite element (MFE) framework is a superior method for accurate flux calculation in heterogeneous media in comparison to the conventional finite difference and finite volume approaches. However, a deficiency in the MFE from the direct use of fractional flow formulation has been recognized lately in application to flow in permeable media with capillary heterogeneity. In this work, we propose a new consistent formulation in 3D in which the total velocity is expressed in terms of the wetting-phase potential gradient and the capillary potential gradient. In our formulation, the coefficient of the wetting potential gradient is in terms of the total mobility which is smoother than the wetting mobility. We combine the MFE and discontinuous Galerkin (DG) methods to solve the pressure equation and the saturation equation, respectively. Our numerical model is verified with 1D analytical solutions in homogeneous and heterogeneous media. We also present 2D examples to demonstrate the significance of capillary heterogeneity in flow, and a 3D example to demonstrate the negligible effect of distorted meshes on the numerical solution in our proposed algorithm. 相似文献
3.
《Advances in water resources》2005,28(7):671-687
Block heterogeneities have an important influence on macroscale two-phase flow and transport in porous media. Applying a vertex-centered finite volume method, we first focus on a physically correct representation of the processes at the interface between different materials, i.e. of capillary equilibrium enforcing a discontinuity in saturation. Second, we will compare different linearization schemes in the Newton iterations in order to improve the efficiency of the numerical simulator. 相似文献
4.
基于前一篇文章中得到的关于三维层状孔隙介质中弹性波场的积分形式半解析解,本文通过离散波数法开展了数值模拟.将全空间均匀孔隙介质中单力点源和爆炸点源作用下弹性波场的解析解和我们的数值模拟结果进行对比,发现两者是完全一致的.而在一个两层半空间模型下的数值模拟,验证了固相位移Green函数的9组空间互易性情况.通过以上两种对比检验,验证了半解析解理论公式、数值模拟方法以及相应程序代码的正确性和可靠性.随后利用敏感度分析研究了不同的介质参数变化对爆炸点源在界面上会产生的反射波场的影响.通过垂直地震剖面模型的数值模拟,发现弹性波场能很好地反映孔隙介质物理性质的变化,同时也讨论了动力协调这一孔隙介质中的特殊现象.我们发展的基于半解析解的数值模拟方法可以为三维层状孔隙介质中弹性波传播特征的研究提供一种可供选择的有效工具和手段. 相似文献
5.
《Advances in water resources》1999,23(3):199-216
This paper is concerned with the fast resolution of nonlinear and linear algebraic equations arising from a fully implicit finite volume discretization of two-phase flow in porous media. We employ a Newton-multigrid algorithm on unstructured meshes in two and three space dimensions. The discretized operator is used for the coarse grid systems in the multigrid method. Problems with discontinuous coefficients are avoided by using a newly truncated restriction operator and an outer Krylov-space method. We show an optimal order of convergence for a wide range of two-phase flow problems including heterogeneous media and vanishing capillary pressure in an experimental way. Furthermore, we present a data parallel implementation of the algorithm with speedup results. 相似文献
6.
《Advances in water resources》1998,21(5):351-362
Flow and displacement of non-Newtonian fluids in porous media occurs in many subsurface systems, related to underground natural resource recovery and storage projects, as well as environmental remediation schemes. A thorough understanding of non-Newtonian fluid flow through porous media is of fundamental importance in these engineering applications. Considerable progress has been made in our understanding of single-phase porous flow behavior of non-Newtonian fluids through many quantitative and experimental studies over the past few decades. However, very little research can be found in the literature regarding multi-phase non-Newtonian fluid flow or numerical modeling approaches for such analyses.For non-Newtonian fluid flow through porous media, the governing equations become nonlinear, even under single-phase flow conditions, because effective viscosity for the non-Newtonian fluid is a highly nonlinear function of the shear rate, or the pore velocity. The solution for such problems can in general only be obtained by numerical methods.We have developed a three-dimensional, fully implicit, integral finite difference simulator for single- and multi-phase flow of non-Newtonian fluids in porous/fractured media. The methodology, architecture and numerical scheme of the model are based on a general multi-phase, multi-component fluid and heat flow simulator — TOUGH2. Several rheological models for power-law and Bingham non-Newtonian fluids have been incorporated into the model. In addition, the model predictions on single- and multi-phase flow of the power-law and Bingham fluids have been verified against the analytical solutions available for these problems, and in all the cases the numerical simulations are in good agreement with the analytical solutions. In this presentation, we will discuss the numerical scheme used in the treatment of non-Newtonian properties, and several benchmark problems for model verification.In an effort to demonstrate the three-dimensional modeling capability of the model, a three-dimensional, two-phase flow example is also presented to examine the model results using laboratory and simulation results existing for the three-dimensional problem with Newtonian fluid flow. 相似文献
7.
Discontinuous Galerkin methods for advective transport in single-continuum models of fractured media
Birgitte Eikemo Knut-Andreas Lie Geir Terje Eigestad Helge K. Dahle 《Advances in water resources》2009
Accurate simulation of flow and transport processes in fractured rocks requires that flow in fractures and shear zones to be coupled with flow in the porous rock matrix. To this end, we will herein consider a single-continuum approach in which both fractures and the porous rock are represented as volumetric objects, i.e., as cells in an unstructured triangular grid with a permeability and a porosity value associated with each cell. Hence, from a numerical point of view, there is no distinction between flow in the fractures and the rock matrix. This enables modelling of realistic cases with very complex structures. To compute single-phase advective transport in such a model, we propose to use a family of higher-order discontinuous Galerkin methods. Single-phase transport equations are hyperbolic and have an inherent causality in the sense that information propagates along streamlines. This causality is preserved in our discontinuous Galerkin discretization. We can therefore use a simple topological sort of the graph of discrete fluxes to reorder the degrees-of-freedom such that the discretized linear system gets a lower block-triangular form, from which the solution can be computed very efficiently using a single-pass forward block substitution. The accuracy and utility of the resulting transport solver is illustrated through several numerical experiments. 相似文献
8.
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
9.
In this paper we extend to three-phase flow the nonequilibrium formalism proposed by Barenblatt and co-workers for two-phase porous media flow. The underlying idea is to include nonequilibrium effects by introducing a pair of effective water and gas saturations, which are linked to the actual saturations by a local evolution equation. We illustrate and analyze how nonequilibrium effects lead to qualitative and quantitative differences in the solution of the three-phase flow equations. 相似文献
10.
Oversampling techniques are often used in porous media simulations to achieve high accuracy in multiscale simulations. These methods reduce the effect of artificial boundary conditions that are imposed in computing local quantities, such as upscaled permeabilities or basis functions. In the problems without scale separation and strong non-local effects, the oversampling region is taken to be the entire domain. The basis functions are computed using single-phase flow solutions which are further used in dynamic two-phase simulations. The standard oversampling approaches employ generic global boundary conditions which are not associated with actual flow boundary conditions. In this paper, we propose a flow based oversampling method where the actual two-phase flow boundary conditions are used in constructing oversampling auxiliary functions. Our numerical results show that the flow based oversampling approach is several times more accurate than the standard oversampling method. We provide partial theoretical explanation for these numerical observations. 相似文献
11.
本文利用优化的25点频率-空间域有限差分算法对基于BISQ模型双相各向同性介质中的地震波进行了数值模拟.通过与经典的Biot模型理论模拟结果进行对比,分析了Biot流动（宏观流体流动）和Squirt流动（微观流体流动）耦合作用对地震波在孔隙介质中传播特性的影响.数值模拟在地震频段进行,结果显示：在理想相界和黏滞相界情况下,Squirt流动机制都比Biot流动机制产生了更大的速度频散和能量衰减.其中,在Biot流动和Squirt流动耦合作用下的快P波的速度和振幅小于仅考虑Biot流动影响下快P波速度和振幅,而且慢P波的衰减也更加强烈.本文还研究了地震波在双层双相各向同性介质分界面处的反射和透射特征,双相介质中波的反射与透射现象类似于单相介质的情况.模拟结果表明,利用优化25点频率-空间域有限差分法模拟双相孔隙介质中的地震波场是可行的,这为开展双相孔隙介质全波形反演问题的研究提供了可能. 相似文献
12.
《Advances in water resources》2003,26(4):373-394
Richards’ equation (RE) is commonly used to model flow in variably saturated porous media. However, its solution continues to be difficult for many conditions of practical interest. Among the various time discretizations applied to RE, the method of lines (MOL) has been used successfully to introduce robust, accurate, and efficient temporal approximations. At the same time, a mixed-hybrid finite element method combined with an adaptive, higher order time discretization has shown benefits over traditional, lower order temporal approximations for modeling single-phase groundwater flow in heterogeneous porous media. Here, we extend earlier work for single-phase flow and consider two mixed finite element methods that have been used previously to solve RE using lower order time discretizations with either fixed time steps or empirically based adaption. We formulate the two spatial discretizations within a MOL context for the pressure head form of RE as well as a fully mass-conservative version. We conduct several numerical experiments for both spatial discretizations with each formulation, and we compare the higher order, adaptive time discretization to a first-order approximation with formal error control and adaptive time step selection. Based on the numerical results, we evaluate the performance of the methods for robustness and efficiency. 相似文献
13.
14.
在电缆地层测试器的测量过程中，油水两相共渗的情况普遍存在，此时其测量过程的数学模型是非线性的耦合场问题，无法用解析方法求解.加上测量中存在抽吸探针与地层、井筒接触面几何形状复杂、探针与地层尺寸相差悬殊等问题，使得应用渗流力学中较为成熟的有限差分方法求解数学模型也不能获得理想的结果.本文应用适合于处理复杂几何形状计算的有限元方法，根据地层测试器测试过程中油水两相渗流的数学模型，首次建立了地层测试器测量油水两相渗流的有限元模型，给出了验证和求解的实例.运用本文所建立的计算模型可以更准确地模拟测试过程中压力和饱和度随时间和空间变化的情况,为正确使用地层测试器提供指导. 相似文献
15.
Pore-scale forces have a significant effect on the macroscopic behaviour of multiphase flow through porous media. This paper studies the effect of these forces using a new volume-of-fluid based finite volume method developed for simulating two-phase flow directly on micro-CT images of porous media. An analytical analysis of the relationship between the pore-scale forces and the Darcy-scale pressure drops is presented. We use this analysis to propose unambiguous definitions of Darcy-scale viscous pressure drops as the rate of energy dissipation per unit flow rate of each phase, and then use them to obtain the relative permeability curves. We show that this definition is consistent with conventional laboratory/field measurements by comparing our predictions with experimental relative permeability. We present single and two-phase flow simulations for primary oil injection followed by water injection on a sandpack and a Berea sandstone. The two-phase flow simulations are presented at different capillary numbers which cover the transition from capillary fingering at low capillary numbers to a more viscous fingering displacement pattern at higher capillary numbers, and the effect of capillary number on the relative permeability curves is investigated. Overall, this paper presents a new finite volume-based methodology for the detailed analysis of two-phase flow directly on micro-CT images of porous media and upscaling of the results to the Darcy scale. 相似文献
16.
《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
17.
《Geofísica Internacional》2014,53(1):59-75
A two-phase (water and oil) flow model in a homogeneous porous media is studied, considering immiscible and incompressible displacement. This model is numerically solved using the Finite Volume Method (FVM) and we compare four numerical schemes for the approximation of fluxes on the faces of the discrete volumes. We describe briefly how to obtain the mathematical and computational models applying axiomatic formulations and generic programming. Two strategies of parallelization are implemented in order to reduce the execution time. We study distributed (cluster of CPUs) and shared (Graphics Processing Units) memory architectures. A performance comparison of these two architectures is done along with an analysis of the four numerical schemes, for a water-flooding five-spot pattern model. 相似文献
18.
A systematic numerical method has been presented to investigate the constitutive relationships between two-phase flow properties of horizontal fractures and aperture distributions. Based on fractal geometry, single rough-walled fractures are generated numerically by modified successive random addition (SRA) method and then aperture distributions with truncated Gaussian distribution are formed by shear displacement between lower and upper surfaces. (The truncated Gaussian distribution is used to describe aperture evolution under different normal stresses.) According to the assumption of two-dimensional porous media and local parallel plate model, invasion percolation approach is employed to model the two-phase flow displacement (imbibition) in generated horizontal fractures, in which capillary forces are dominant over viscous and gravity forces. For truncated Gaussian distributions, constitutive relationships from numerical simulation are compared to closed-form relationships and a good agreement is obtained. The simulation results indicate strong phase interference with the sum of two phase relative permeability values being less than one in the intermediate saturations. It is found that fracture properties related to residual saturations depend on spatial correlation of aperture distributions. Based on the simulation results, we proposed an empirical relationship between the fracture residual-saturation-rated parameters and the corresponding aperture distributions. 相似文献
19.
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
20.
Developing robust and efficient numerical solution methods for Richards' equation (RE) continues to be a challenge for certain problems. We consider such a problem here: infiltration into unsaturated porous media initially at static conditions for uniform and non-uniform pore size media. For ponded boundary conditions, a sharp infiltration front results, which propagates through the media. We evaluate the resultant solution method for robustness and efficiency using combinations of variable transformation and adaptive time-stepping methods. Transformation methods introduce a change of variable that results in a smoother solution, which is more amenable to efficient numerical solution. We use adaptive time-stepping methods to adjust the time-step size, and in some cases the order of the solution method, to meet a constraint on nonlinear solution convergence properties or a solution error criterion. Results for three test problems showed that adaptive time-stepping methods provided robust solutions; in most cases transforming the dependent variable led to more efficient solutions than untransformed approaches, especially as the pore-size uniformity increased; and the higher-order adaptive time integration method was robust and the most efficient method evaluated. 相似文献