共查询到20条相似文献，搜索用时 39 毫秒
1.
Modern geostatistical techniques allow the generation of high-resolution heterogeneous models of hydraulic conductivity containing millions to billions of cells. Selective upscaling is a numerical approach for the change of scale of fine-scale hydraulic conductivity models into coarser scale models that are suitable for numerical simulations of groundwater flow and mass transport. Selective upscaling uses an elastic gridding technique to selectively determine the geometry of the coarse grid by an iterative procedure. The geometry of the coarse grid is built so that the variances of flow velocities within the coarse blocks are minimum. Selective upscaling is able to handle complex geological formations and flow patterns, and provides full hydraulic conductivity tensor for each block. Selective upscaling is applied to a cross-bedded formation in which the fine-scale hydraulic conductivities are full tensors with principal directions not parallel to the statistical anisotropy of their spatial distribution. Mass transport results from three coarse-scale models constructed by different upscaling techniques are compared to the fine-scale results for different flow conditions. Selective upscaling provides coarse grids in which mass transport simulation is in good agreement with the fine-scale simulations, and consistently superior to simulations on traditional regular (equal-sized) grids or elastic grids built without accounting for flow velocities. 相似文献
2.
Multiscale mixed/mimetic methods on corner-point grids 总被引：1，自引：0，他引：1
Multiscale simulation is a promising approach to facilitate direct simulation of large and complex grid models for highly
heterogeneous petroleum reservoirs. Unlike traditional simulation, approaches based on upscaling/downscaling, multiscale methods
seek to solve the full flow problem by incorporating subscale heterogeneities into local discrete approximation spaces. We
consider a multiscale formulation based on a hierarchical grid approach, where basis functions with subgrid resolution are
computed numerically to correctly and accurately account for subscale variations from an underlying (fine-scale) geomodel
when solving the global flow equations on a coarse grid. By using multiscale basis functions to discretise the global flow
equations on a (moderately sized) coarse grid, one can retain the efficiency of an upscaling method and, at the same time,
produce detailed and conservative velocity fields on the underlying fine grid. For pressure equations, the multiscale mixed
finite-element method (MsMFEM) has been shown to be a particularly versatile approach. In this paper, we extend the method
to corner-point grids, which is the industry standard for modelling complex reservoir geology. To implement MsMFEM, one needs
a discretisation method for solving local flow problems on the underlying fine grids. In principle, any stable and conservative
method can be used. Here, we use a mimetic discretisation, which is a generalisation of mixed finite elements that gives a
discrete inner product, allows for polyhedral elements, and can (easily) be extended to curved grid faces. The coarse grid
can, in principle, be any partition of the subgrid, where each coarse block is a connected collection of subgrid cells. However,
we argue that, when generating coarse grids, one should follow certain simple guidelines to achieve improved accuracy. We
discuss partitioning in both index space and physical space and suggest simple processing techniques. The versatility and
accuracy of the new multiscale mixed methodology is demonstrated on two corner-point models: a small Y-shaped sector model
and a complex model of a layered sedimentary bed. A variety of coarse grids, both violating and obeying the above mentioned
guidelines, are employed. The MsMFEM solutions are compared with a reference solution obtained by direct simulation on the
subgrid. 相似文献
3.
Knut–Andreas Lie Stein Krogstad Ingeborg Skjelkv?le Ligaarden Jostein Roald Natvig Halvor M?ll Nilsen B?rd Skaflestad 《Computational Geosciences》2012,16(2):297-322
Accurate geological modelling of features such as faults, fractures or erosion requires grids that are flexible with respect
to geometry. Such grids generally contain polyhedral cells and complex grid-cell connectivities. The grid representation for
polyhedral grids in turn affects the efficient implementation of numerical methods for subsurface flow simulations. It is
well known that conventional two-point flux-approximation methods are only consistent for K-orthogonal grids and will, therefore, not converge in the general case. In recent years, there has been significant research
into consistent and convergent methods, including mixed, multipoint and mimetic discretisation methods. Likewise, the so-called
multiscale methods based upon hierarchically coarsened grids have received a lot of attention. The paper does not propose
novel mathematical methods but instead presents an open-source Matlab? toolkit that can be used as an efficient test platform for (new) discretisation and solution methods in reservoir simulation.
The aim of the toolkit is to support reproducible research and simplify the development, verification and validation and testing
and comparison of new discretisation and solution methods on general unstructured grids, including in particular corner point
and 2.5D PEBI grids. The toolkit consists of a set of data structures and routines for creating, manipulating and visualising
petrophysical data, fluid models and (unstructured) grids, including support for industry standard input formats, as well
as routines for computing single and multiphase (incompressible) flow. We review key features of the toolkit and discuss a
generic mimetic formulation that includes many known discretisation methods, including both the standard two-point method
as well as consistent and convergent multipoint and mimetic methods. Apart from the core routines and data structures, the
toolkit contains add-on modules that implement more advanced solvers and functionality. Herein, we show examples of multiscale
methods and adjoint methods for use in optimisation of rates and placement of wells. 相似文献
4.
5.
Knut-Andreas Lie Jostein R. Natvig Stein Krogstad Yahan Yang Xiao-Hui Wu 《Computational Geosciences》2014,18(3-4):357-372
A Dirichlet–Neumann representation method was recently proposed for upscaling and simulating flow in reservoirs. The DNR method expresses coarse fluxes as linear functions of multiple pressure values along the boundary and at the center of each coarse block. The number of flux and pressure values at the boundary can be adjusted to improve the accuracy of simulation results and, in particular, to resolve important fine-scale details. Improvement over existing approaches is substantial especially for reservoirs that contain high-permeability streaks or channels. As an alternative, the multiscale mixed finite-element (MsMFE) method was designed to obtain fine-scale fluxes at the cost of solving a coarsened problem, but can also be used as upscaling methods that are flexible with respect to geometry and topology of the coarsened grid. Both methods can be expressed in mixed-hybrid form, with local stiffness matrices obtained as “inner products” of numerically computed basis functions with fine-scale sub-resolution. These basis functions are determined by solving local flow problems with piecewise linear Dirichlet boundary conditions for the DNR method and piecewise constant Neumann conditions for MsMFE. Adding discrete pressure points in the DNR method corresponds to subdividing faces in the coarse grid and hence increasing the number of basis functions in the MsMFE method. The methods show similar accuracy for 2D Cartesian cases, but the MsMFE method is more straightforward to formulate in 3D and implement for general grids. 相似文献
6.
Hussein Mustapha 《Computational Geosciences》2011,15(3):385-397
We present G23FM, a mesh generation tool for discretizing two- and three-dimensional complex fractured geological media. G23FM
includes different techniques to generate finite element grids that maintain the geometric integrity of input surfaces, and
geologic data and produce optimal triangular/tetrahedral grids for flow and transport simulations. G23FM generates grid for
two-dimensional cross-sections, represents faults and fractures, for three-dimensional fractured media, and has the capability
of including finer grids. Different examples are presented to illustrate some of the main features of G23FM. 相似文献
7.
贴体网格有限差分正演模拟算法不仅能够精确模拟任意起伏地形下的波场特征,且计算效率较高,是一种很有应用前景的处理西部复杂地表问题的方法;然而,目前求解波动方程时常用的同位网格和标准交错网格,在处理贴体网格起伏地表正演模拟时存在诸多问题。为此,将全交错网格引入到曲线坐标系下,避免了标准交错网格的插值误差和同位网格中奇偶失联引起的高频振荡现象,提高了模拟精度,减小了算法实现的复杂度。在自由边界条件实施时,采用牵引力镜像法计算速度分量,速度自由边界条件配合紧致交错差分格式更新应力分量,得到了较好的效果。随后,重点研究了贴体全交错网格正演模拟算法的影响因素,考虑了网格正交性、网格间距和网格拼接等的影响,并取得了如下认识：算法对网格的正交性没有过分要求;网格间距的突变会引起虚假反射的产生;不同类型的网格拼接对模拟结果不会造成明显的影响。 相似文献
8.
建立了一套大尺度格栅紊流试验系统,格栅进行有别于传统垂向模式的横向振动,采用粒子图像测速技术(Particle Image Velocimetry,PIV)测量流速。对瞬时流速的检验表明,该系统产生的紊流场具有较强的随机性和统计规律性。均方根流速在格栅片附近变化较大,在两片格栅中间处趋于稳定,纵向均方根流速明显大于垂向均方根流速,二者比值在1.5~2.0之间,接近天然明渠紊流。雷诺应力在距格栅越近处波动越大,随着距格栅距离的增加而减小,至两片格栅中间处雷诺应力基本为0。时间和长度积分尺度在格栅片处最小,随着距格栅距离的增加而线性增加,至两片格栅中间处达到最大值。流速能谱呈现Kolmogorov理论的-5/3次方规律。本系统生成的紊流场的统计规律与传统的垂向振动格栅紊流较为一致,但纵向和垂向的紊动强度更接近实际,为后续紊流中泥沙和污染物等运动机理的研究奠定了基础。 相似文献
9.
In this paper, we study newly developed methods for linear elasticity on polyhedral meshes. Our emphasis is on applications of the methods to geological models. Models of subsurface, and in particular sedimentary rocks, naturally lead to general polyhedral meshes. Numerical methods which can directly handle such representation are highly desirable. Many of the numerical challenges in simulation of subsurface applications come from the lack of robustness and accuracy of numerical methods in the case of highly distorted grids. In this paper, we investigate and compare the Multi-Point Stress Approximation (MPSA) and the Virtual Element Method (VEM) with regard to grid features that are frequently seen in geological models and likely to lead to a lack of accuracy of the methods. In particular, we look at how the methods perform near the incompressible limit. This work shows that both methods are promising for flexible modeling of subsurface mechanics. 相似文献
10.
Emil M. Constantinescu Adrian Sandu Gregory R. Carmichael 《Computational Geosciences》2008,12(2):133-151
We discuss an adaptive resolution system for modeling regional air pollution based on the chemical transport model STEM. The
grid adaptivity is implemented using the generic adaptive mesh refinement tool Paramesh, which enables the grid management
operations while harnessing the power of parallel computers. The computational algorithm is based on a decomposition of the
domain, with the solution in different subdomains being computed with different spatial resolutions. Various refinement criteria
that adaptively control the fine grid placement are analyzed to maximize the solution accuracy while maintaining an acceptable
computational cost. Numerical experiments in a large-scale parallel setting (~0.5 billion variables) confirm that adaptive
resolution, based on a well-chosen refinement criterion, leads to the decrease in spatial error with an acceptable increase
in computational time. Fully dynamic grid adaptivity for air quality models is relatively new. We extend previous work on
chemical and transport modeling by using dynamically adaptive grid resolution. Advantages and shortcomings of the present
approach are also discussed. 相似文献
11.
在构建全国国土空间规划体系的新时代背景下, 地质工作如何有效支撑服务国土空间规划成为地质工作转型升级的新命题。我国地质成果在国土空间规划领域的应用程度与发达国家还存在明显差距, 主要原因在于地质调查精度和信息集成程度不足, 而且在体制机制和技术层面都存在与规划行业的脱节。通过深度参与《上海市国土空间生态修复规划》编制, 我们进一步发现地质工作的应用价值被普遍低估, 地质工作的技术路径难以契合规划行业思路, 传统地质成果表达方式也难以引起社会关注。为解决这些问题, 建议加强重点规划区地质调查和信息集成, 通过法律法规明确国土空间规划必须考虑的地质要素, 畅通地质信息获取渠道, 构建支撑国土空间规划的地质评价标准体系。在操作层面, 建议进一步开展以需求为导向的主动宣传, 构建问题导向、简单易行的技术路径, 强化空间导向、聚焦重点的成果表达形式。 相似文献
12.
在构建全国国土空间规划体系的新时代背景下,地质工作如何有效支撑服务国土空间规划成为地质工作转型升级的新命题。我国地质成果在国土空间规划领域的应用程度与发达国家还存在明显差距,主要原因在于地质调查精度和信息集成程度不足,而且在体制机制和技术层面都存在与规划行业的脱节。通过深度参与《上海市国土空间生态修复规划》编制,我们进一步发现地质工作的应用价值被普遍低估,地质工作的技术路径难以契合规划行业思路,传统地质成果表达方式也难以引起社会关注。为解决这些问题,建议加强重点规划区地质调查和信息集成,通过法律法规明确国土空间规划必须考虑的地质要素,畅通地质信息获取渠道,构建支撑国土空间规划的地质评价标准体系。在操作层面,建议进一步开展以需求为导向的主动宣传,构建问题导向、简单易行的技术路径,强化空间导向、聚焦重点的成果表达形式。 相似文献
13.
We present a fully implicit formulation of coupled flow and geomechanics for fractured three-dimensional subsurface formations. The Reservoir Characterization Model (RCM) consists of a computational grid, in which the fractures are represented explicitly. The Discrete Fracture Model (DFM) has been widely used to model the flow and transport in natural geological porous formations. Here, we extend the DFM approach to model deformation. The flow equations are discretized using a finite-volume method, and the poroelasticity equations are discretized using a Galerkin finite-element approximation. The two discretizations—flow and mechanics—share the same three-dimensional unstructured grid. The mechanical behavior of the fractures is modeled as a contact problem between two computational planes. The set of fully coupled nonlinear equations is solved implicitly. The implementation is validated for two problems with analytical solutions. The methodology is then applied to a shale-gas production scenario where a synthetic reservoir with 100 natural fractures is produced using a hydraulically fractured horizontal well. 相似文献
14.
Eirik Keilegavlen Jeremy E. Kozdon Bradley T. Mallison 《Computational Geosciences》2012,16(4):1021-1042
The governing equations for multiphase flow in porous media have a mixed character, with both nearly elliptic and nearly hyperbolic variables. The flux for each phase can be decomposed into two parts: (1) a geometry- and rock-dependent term that resembles a single-phase flux; and (2) a mobility term representing fluid properties and rock–fluid interactions. The first term is commonly discretized by two- or multipoint flux approximations (TPFA and MPFA, respectively). The mobility is usually treated with single-point upstream weighting (SPU), also known as dimensional or donor cell upstream weighting. It is well known that when simulating processes with adverse mobility ratios, SPU suffers from grid orientation effects. An important example of this, which will be considered in this work, is the displacement of a heavy oil by water. For these adverse mobility ratio flows, the governing equations are unstable at the modeling scale, rendering a challenging numerical problem. These challenges must be addressed in order to avoid systematic biasing of simulation results. In this work, we present a framework for multidimensional upstream weighting for multiphase flow with buoyancy on general two-dimensional grids. The methodology is based on a dual grid, and the resulting transport methods are provably monotone. The multidimensional transport methods are coupled with MPFA methods to solve the pressure equation. Both explicit and fully implicit approaches are considered for time integration of the transport equations. The results show considerable reduction of grid orientation effects compared to SPU, and the explicit multidimensional approach allows larger time steps. For the implicit method, the total number of non-linear iterations is also reduced when multidimensional upstream weighting is used. 相似文献
15.
This paper presents a finite-volume method for hexahedral multiblock grids to calculate multiphase flow in geologically complex reservoirs. Accommodating complex geologic and geometric features in a reservoir model (e.g., faults) entails non-orthogonal and/or unstructured grids in place of conventional (globally structured) Cartesian grids. To obtain flexibility in gridding as well as efficient flow computation, we use hexahedral multiblock grids. These grids are locally structured, but globally unstructured. One major advantage of these grids over fully unstructured tetrahedral grids is that most numerical methods developed for structured grids can be directly used for dealing with the local problems. We present several challenging examples, generated via a commercially available tool, that demonstrate the capabilities of hexahedral multiblock gridding. Grid quality is discussed in terms of uniformity and orthogonality. The presence of non-orthogonal grid and full permeability tensors requires the use of multi-point discretization methods. A flux-continuous finite-difference (FCFD) scheme, previously developed for stratigraphic hexahedral grid with full-tensor permeability, is employed for numerical flow computation. We extend the FCFD scheme to handle exceptional configurations (i.e. three- or five-cell connections as opposed to the regular four), which result from employing multiblock gridding of certain complex objects. In order to perform flow simulation efficiently, we employ a two-level preconditioner for solving the linear equations that results from the wide stencil of the FCFD scheme. The individual block, composed of cells that form a structured grid, serves as the local level; the higher level operates on the global block configuration (i.e. unstructured component). The implementation uses an efficient data structure where each block is wrapped with a layer of neighboring cells. We also examine splitting techniques [14] for the linear systems associated with the wide stencils of our FCFD operator. We present three numerical examples that demonstrate the method: (1) a pinchout, (2) a faulted reservoir model with internal surfaces and (3) a real reservoir model with multiple faults and internal surfaces. 相似文献
16.
The purpose of this paper is to collect, clarify, augment and modify the authors' previous work on the subject of finite strain compatibility. The derivations of the fundamental equations are reviewed so that the geometric meaning of each step can be explained. Besides providing a basis for the geological interpretations of the equations, these derivations also lead to a useful new form of the strain compatibility equations.We begin by showing that compatibility is a geometric property of continuous and smooth coordinate grids, and we derive and explain the coordinate grid compatibility equations. We then use the fact that every finite deformation may be described by two coordinate grids to derive finite strain compatibility equations in principal coordinates and Cartesian coordinates. The resulting strain compatibility equations are not easily solved for general strain fields in any coordinate system. Nonetheless, we show that many common geological strain patterns have simple geometries for which the compatibility equations can be interpreted. For example, if a deformation has constant strain in one direction, as most shear zones do, then compatibility provides an iterative method for determining the strain throughout the deformed region if the strain is initially known at any one point. Some of the other strain geometries to which we apply compatibility in this paper include simple shear, inhomogeneous pure shear, parallel and similar folding. 相似文献
17.
Richards方程在非饱和渗流模拟及其他相关领域应用广泛。在数值求解过程中,可以采用有限差分方法进行数值离散并迭代求解,为了获得较可靠的数值解,常规的均匀网格空间步长往往是较小的。在一些不利数值条件下,如入渗于干燥土壤,迭代计算费时甚至精度也不能得到很好改善。因此,文章提出Chebyshev空间网格改进方法,结合有限差分方法对Richards方程进行数值离散以获得线性方程组,并通过经典的Picard迭代方法进行迭代求解线性方程组以得到Richards方程的数值解。通过均质土和分层土2个不利情况下的非饱和渗流算例,又结合模型解析解和软件Hydrus-1D,对比研究了改进网格方法与均匀网格方法获得数值解的精度。结果表明,提出的Chebyshev网格方法相较于传统的均匀网格,可以在较少的节点数下获得较高的数值精度,又具有较小的计算开销,有较好的应用前景。 相似文献
18.
Improved and enhanced oil recovery methods require sophisticated simulation tools to predict the injected flow pass together with the chemical reactions inside it. One approach is application of higher-order numerical schemes to avoid excessive numerical diffusion that is very typical for transport processes. In this work, we provide a first step towards higher-order schemes applicable on general polyhedral and corner-point grids typically used in reservoir simulation. We compare three possible approaches of linear reconstruction and slope limiting techniques on a variety of different meshes in two and three spatial dimensions and discuss advantages and disadvantages. 相似文献
19.
We propose a methodology, called multilevel local–global (MLLG) upscaling, for generating accurate upscaled models of permeabilities
or transmissibilities for flow simulation on adapted grids in heterogeneous subsurface formations. The method generates an
initial adapted grid based on the given fine-scale reservoir heterogeneity and potential flow paths. It then applies local–global
(LG) upscaling for permeability or transmissibility [7], along with adaptivity, in an iterative manner. In each iteration of MLLG, the grid can be adapted where needed to reduce
flow solver and upscaling errors. The adaptivity is controlled with a flow-based indicator. The iterative process is continued
until consistency between the global solve on the adapted grid and the local solves is obtained. While each application of
LG upscaling is also an iterative process, this inner iteration generally takes only one or two iterations to converge. Furthermore,
the number of outer iterations is bounded above, and hence, the computational costs of this approach are low. We design a
new flow-based weighting of transmissibility values in LG upscaling that significantly improves the accuracy of LG and MLLG
over traditional local transmissibility calculations. For highly heterogeneous (e.g., channelized) systems, the integration
of grid adaptivity and LG upscaling is shown to consistently provide more accurate coarse-scale models for global flow, relative
to reference fine-scale results, than do existing upscaling techniques applied to uniform grids of similar densities. Another
attractive property of the integration of upscaling and adaptivity is that process dependency is strongly reduced, that is,
the approach computes accurate global flow results also for flows driven by boundary conditions different from the generic
boundary conditions used to compute the upscaled parameters. The method is demonstrated on Cartesian cell-based anisotropic
refinement (CCAR) grids, but it can be applied to other adaptation strategies for structured grids and extended to unstructured
grids. 相似文献
20.
Estimation of residual fluxes in estuarine cross sections is a very important procedure to establish, among others aspects, residence time of contaminants, circulation pattern, and sediment transport dynamics. However, the analytical procedure to obtain such values is not trivial and is presented in detail, demonstrating the importance of the grid-cell area as a weighting element in the calculation of spatial averages. The procedure is tested with four different grid designs and it is shown that grids with proportional columns and rows are the only ones that do not introduce statistical noise in the estimation of the residual fluxes. The four designs are also tested with data from a cross section of the Bahía Blanca Estuary (Argentina), results again show that the proportional columns and rows grid provide the best approach in calculating residual fluxes. 相似文献