共查询到20条相似文献，搜索用时 31 毫秒
1.
Marc G. Genton 《Mathematical Geology》1998,30(7):853-871
In the context of robust statistics, the breakdown point of an estimator is an important feature of reliability. It measures the highest fraction of contamination in the data that an estimator can support before being destroyed. In geostatistics, variogram estimators are based on measurements taken at various spatial locations. The classical notion of breakdown point needs to be extended to a spatial one, depending on the construction of most unfavorable configurations of perturbation. Explicit upper and lower bounds are available for the spatial breakdown point in the regular unidimensional case. The difficulties arising in the multidimensional case are presented on an easy example in IR2
, as well as some simulations on irregular grids. In order to study the global effects of perturbations on variogram estimators, further simulations are carried out on data located on a regular or irregular bidimensional grid. Results show that if variogram estimation is performed with a 50% classical breakdown point scale estimator, the number of initial data likely to be contaminated before destruction of the estimator is roughly 30% on average. Theoretical results confirm the previous statement on data in IRd
, d 1. 相似文献
2.
Wells are seldom modeled explicitly in large scale finite difference reservoir simulations. Instead, the well is coupled to the reservoir through the use of a well index, which relates wellbore flow rate and pressure to grid block quantities. The use of an accurate well index is essential for the detailed modeling of nonconventional wells; i.e., wells with an arbitrary trajectory or multiple branches. The determination of a well index for such problems is complicated, particularly when the simulation grid is irregular or unstructured. In this work, a general framework for the calculation of accurate well indices for general nonconventional wells on arbitrary grids is presented and applied. The method entails the use of an accurate semianalytical well model based on Green's functions as a reference single phase flow solution. This result is coupled with a finite difference calculation to provide an accurate well index for each grid block containing a well segment. The method is demonstrated on a number of homogeneous example cases involving deviated, horizontal and multilateral wells oriented skew to the grid. Both Cartesian and globally unstructured multiblock grids are considered. In all these cases, the method is shown to provide results that are considerably more accurate compared to results using standard procedures. The method is also applied to heterogeneous problems involving horizontal wells, where it is shown to be capable of approximating the effects of subgrid heterogeneity in coarse finite difference models. 相似文献
3.
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
4.
Michael G. Edwards 《Computational Geosciences》2002,6(3-4):433-452
Locally conservative flux-continuous, full-tensor, discretization schemes are presented for general unstructured grids. The schemes are control-volume distributed, where flow variables and rock properties are assigned to the polygonal control-volumes derived from the primal grid. A relationship between these finite volume schemes and the mixed finite element method is established. An extension for unstructured grids is described that leads to a general symmetric positive definite discretization matrix for both quadrilateral and triangular grids. A novel flow based gridding approach for unstructured mesh generation is also proposed for heterogeneous reservoir domains. Results computed with the flux continuous schemes on unstructured flow-based grids demonstrate the advantages of the methods. 相似文献
5.
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
6.
濮城沙三中油藏具有两个主物源,分别为NE向与SE向。油藏数值模拟需要在一套地质网格中对其进行模拟。经典的地质统计学利用变差函数描述区域化变量的空间几何结构特性。变差函数的计算是基于两点进行统计的,对其描述主要涉及方位角、变程、块金值和基台值。为了在一套模拟网格中模拟出多个物源条件下储层的分布特征,必须在不同的位置设置不同的变差函数参数。文中给出了两种方法实现这一目的:一是采用人为分区,把不同物源影响的区域分成不同的区块,分别对不同的区块设置不同的变差函数参数;二是采用变方位角,即根据不同的位置设置不同的变差函数方位角。这两种方法都实现了在一套网格中模拟具有多个物源方向的储层分布,更真实地再现了储层的空间展布特征。 相似文献
7.
Multiscale methods can in many cases be viewed as special types of domain decomposition preconditioners. The localisation
approximations introduced within the multiscale framework are dependent upon both the heterogeneity of the reservoir and the
structure of the computational grid. While previous works on multiscale control volume methods have focused on heterogeneous
elliptic problems on regular Cartesian grids, we have tested the multiscale control volume formulations on two-dimensional
elliptic problems involving heterogeneous media and irregular grid structures. Our study shows that the tangential flow approximation
commonly used within multiscale methods is not suited for problems involving rough grids. We present a more robust mass conservative
domain decomposition preconditioner for simulating flow in heterogeneous porous media on general grids. 相似文献
8.
J.D. Jansen 《Computational Geosciences》2002,6(2):195-206
This paper concerns the computation of near-well flow in numerical reservoir simulation with unstructured grids. In particular, it uses spherical trigonometry to derive analytical expressions for the flow towards a well modeled as either a number of point sources or a constant-flux line source. The expression for the point source representation is based on projections of the grid block boundaries on spheres with unit radius around the sources. The expression for the line source is based on projection on a prolate spheroid. The computation of the surface area is done through transformation to prolate spheroidal coordinates and subsequent projection on a sphere at infinity. The point source expression for a single source is exact for grid block boundaries with straight edges; the line source expression is an approximation. Both representations are fully volume conserving, such that the sum of the fluxes through the grid block boundaries surrounding a source adds up exactly to the total source flow rate. Both representations can be used to accurately model complicated wells in the form of segments. The point source representation is simpler to implement and not necessarily less accurate than the line source representation. 相似文献
9.
针对波浪数值模拟中基于矩形网格的数值方法在深水到浅水的网格间距选择与复杂边界处理上的缺陷,以及基于正交曲线网格和无结构网格的数值方法前处理工作复杂的问题,引入最近在计算力学中发展起来的无网格法——径向点插值法,对经典的双曲型缓坡方程进行空间离散,并在时间上采用四阶Adams-Bashforth-Moulton格式求解建立近岸波浪传播数学模型,通过椭圆形浅滩地形和环形河道的波浪传播计算验证,表明该无网格方法可较为有效地模拟近岸波浪的传播变形,且在处理复杂边界时具有较高的精度. 相似文献
10.
Tingting Yao 《Mathematical Geology》2004,36(4):487-506
The application of spectral simulation is gaining acceptance because it honors the spatial distribution of petrophysical properties, such as reservoir porosity and shale volume. While it has been widely assumed that spectral simulation will reproduce the mean and variance of the important properties such as the observed net/gross ratio or global average of porosity, this paper shows the traditional way of implementing spectral simulation yields a mean and variance that deviates from the observed mean and variance. Some corrections (shift and rescale) could be applied to generate geologic models yielding the observed mean and variance; however, this correction implicitly rescales the input variogram model, so the variogram resulting from the generated cases has a higher sill than the input variogram model. Therefore, the spectral simulation algorithm cannot build geologic models honoring the desired mean, variance, and variogram model simultaneously, which is contrary to the widely accepted assumption that spectral simulation can reproduce all the target statistics. However, by using Fourier transform just once to generate values at all the cells instead of visiting each cell sequentially, spectral simulation does reproduce the observed variogram better than sequential Gaussian simulation. That is, the variograms calculated from the generated geologic models show smaller fluctuations around the target variogram. The larger the generated model size relative to the variogram range, the smaller the observed fluctuations. 相似文献
11.
在煤层气排采分析及数值模拟研究中,煤储层结构的三维建模是数值模拟和结果分析的起点,具有关键作用。三维长方体等传统网格,难以表达地层的起伏变化,角点网格具有表达起伏变化地层的优势。从煤层气动态可视化的角度出发,基于角点网格建立了煤储层三维地质模型。研究了角点网格模型的数据特点及生成角点网格的方法,采用C#编程语言并结合OpenGL图形接口,开发了煤储层三维可视化软件模型,利用该模型表达了山西省沁水盆地潘庄区块的煤储层地质构造。结果表明,角点网格适用于煤储层三维模型的构建,能较好的表达煤层的结构特征。 相似文献
12.
13.
The trend toward unstructured grids in subsurface flow modeling has prompted interest in the issue of streamline or pathline tracing on unstructured grids. Streamline tracing on unstructured grids is problematic because a continuous velocity field is required for the calculation, while numerical solutions to the groundwater flow equations provide velocity in discretized form only. A method for calculating flow streamlines or pathlines from a finite-volume flow solution is presented. The method uses an unconstrained least squares method on interior cells and a constrained least squares method on boundary cells to approximate cell-centered velocities, which can then be continuously interpolated to any point in the domain of interest. Two-dimensional tests demonstrate that the method correctly reproduces uniform and corner-to-corner flow on fully unstructured grids. In three dimensions using regular hexahedral grids, the method agrees well with established semianalytical methods. Tests also demonstrate that the method produces physically realistic results on fully unstructured three-dimensional grids. 相似文献
14.
Shahid Manzoor Michael G. Edwards Ali H. Dogru Tareq M. Al-Shaalan 《Computational Geosciences》2018,22(1):195-230
Grid generation for reservoir simulation must honor classical key constraints and be boundary aligned such that control-volume boundaries are aligned with geological features such as layers, shale barriers, fractures, faults, pinch-outs, and multilateral wells. An unstructured grid generation procedure is proposed that automates control-volume and/or control point boundary alignment and yields a PEBI-mesh both with respect to primal and dual (essentially PEBI) cells. In order to honor geological features in the primal configuration, we introduce the idea of protection circles, and to generate a dual-cell feature based grid, we construct halos around key geological features. The grids generated are employed to study comparative performance of cell-centred versus cell-vertex control-volume distributed multi-point flux approximation (CVD-MPFA) finite-volume formulations using equivalent degrees of freedom. The formulation of CVD-MPFA schemes in cell-centred and cell-vertex modes is analogous and requires switching control volume from primal to dual or vice versa together with appropriate data structures and boundary conditions. The relative benefits of both types of approximation, i.e., cell-centred versus vertex-centred, are made clear in terms of flow resolution and degrees of freedom required. 相似文献
15.
为了改进计算区域离散化问题,本文利用自适应非结构化网格有限单元法求解二维地电结构下大地电磁场满足的加权余量表达式。在有限元求解电磁场的过程中,网格剖分越精细、计算精度越高,计算量也会越大。此外,结构化网格难以适应任意地形以及复杂地质构造。而自适应非结构化网格在电性变化剧烈的区域会自动加密,在电性缓变的区域则生成粗疏的网格,从而优化网格质量与数量。因此,文中引入COMSOL Multiphysics软件,以实现若干地电模型的构建及非结构化自由四边形单元网格化。将网格数据信息导入本文算法,计算大地电磁场响应,并与解析解及数值解对比。结果表明,基于非结构化网格的正演模拟精度高、适应性强,为计算区域网格化提供了新的方法。 相似文献
16.
Corner point grids is currently the standard grid representation for use in reservoir simulation. The cell faces in corner point grids are traditionally represented as bilinear surfaces where the edges between the corner points all are straight lines. This representation has the disadvantage that along faults with varying dip the cell faces on either side will not precisely match, giving overlapping cells or gaps between cells. We propose an alternative representation for the cell faces. The four vertical cell faces are still represented as bilinear surfaces, but instead of having linear edges between the cell corners along the top and bottom faces, we propose a representation of the vertical cell faces where any horizontal intersection will give a straight line, giving column faces whose shape is independent of the corner point locations of the individual grid cells. This ensures that the grid columns match up and that there are no gaps or overlapping volumes between grid cells. This representation gives a local parameterization for the whole grid column, and the top and bottom grid cell surfaces are modeled as bilinear using this parameterization. A set of local coordinates for the grid cell permits all the common grid operations like volume calculation, area calculation for cell faces, and blocking of well traces. 相似文献
17.
Sandstones of different ages provide economically significant oil, gas, and water reservoirs. In sandstones where heterogeneities are not visually obvious, it is particularly difficult to predict the location of permeability barriers and the scale at which high and low permeability zones occur, yet this is critical in providing information on hydrocarbon reservoir performance. This study uses variogram analysis to investigate spatial variation in permeability in visually homogeneous reservoir sandstone successions. Air permeability measurements were taken using unsteady state probe permeametry following regular grid schemes with centimeter spacing. Spatial variation in permeability was characterized using omnidirectional and directional variograms. This study combines variography with geological interpretation to assess the degree of heterogeneity of permeability in visually homogeneous sandstone successions. Variography indicates spatial dependence and short-range variation at 1 cm grid spacings that is not apparent at a larger 5 cm grid spacing in the visually homogeneous sandstones studied. The range of the models fitted to the variograms provide a potentially important index of spatial variability in permeability for different depositional settings including aeolian, fluvial, shallow marine, and marine/mass- flow turbidite. 相似文献
18.
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
19.
在三维模型表达中,相对于PEBI、径向(Radial)网格而言,角点网格是目前油气田开发研究比较通用的一种三维模型。它在表达复杂断块、油藏非均质性上较为突出。在油气勘探研究中,一般使用常规的面模型来进行各种定量模拟评价,这对于精度要求越来越高的油气成藏过程定量模拟与分析而言,显得精度不够。因此,基于角点网格模型的油气成藏过程的算法研究和应用在勘探评价中显得尤为重要。探讨了角点网格模型的空间信息与属性信息的管理与表达优势,讨论了如何将传统的面模型模拟算法改进成新的角点模型,研究了相应的算法,分析了其中的主要难点及解决方案,其中包括多尺度空间加密、角点网格结构及表达模型的优势、各单元网格岩性属性提取与使用、烃源岩厚度分配、运移网格间的匹配关系等问题,从三维表达、五史(构造史、热史、生烃史、排烃史及运聚史)所遇到的主要问题及解决方案进行了剖析。 相似文献
20.
Gilles Bourgault 《Mathematical Geosciences》2012,44(8):1005-1037
The likelihood of Gaussian realizations, as generated by the Cholesky simulation method, is analyzed in terms of Mahalanobis distances and fluctuations in the variogram reproduction. For random sampling, the probability to observe a Gaussian realization vector can be expressed as a function of its Mahalanobis distance, and the maximum likelihood depends only on the vector size. The Mahalanobis distances are themselves distributed as a Chi-square distribution and they can be used to describe the likelihood of Gaussian realizations. Their expected value and variance are only determined by the size of the vector of independent random normal scores used to generate the realizations. When the vector size is small, the distribution of Mahalanobis distances is highly skewed and most realizations are close to the vector mean in agreement with the multi-Gaussian density model. As the vector size increases, the realizations sample a region increasingly far out on the tail of the multi-Gaussian distribution, due to the large increase in the size of the uncertainty space largely compensating for the low probability density. For a large vector size, realizations close to the vector mean are not observed anymore. Instead, Gaussian vectors with Mahalanobis distance in the neighborhood of the expected Mahalanobis distance have the maximum probability to be observed. The distribution of Mahalanobis distances becomes Gaussian shaped and the bulk of realizations appear more equiprobable. However, the ratio of their probabilities indicates that they still remain far from being equiprobable. On the other hand, it is observed that equiprobable realizations still display important fluctuations in their variogram reproduction. The variance level that is expected in the variogram reproduction, as well as the variance of the variogram fluctuations, is dependent on the Mahalanobis distance. Realizations with smaller Mahalanobis distances are, on average, smoother than realizations with larger Mahalanobis distances. Poor ergodic conditions tend to generate higher proportions of flatter variograms relative to the variogram model. Only equiprobable realizations with a Mahalanobis distance equal to the expected Mahalanobis distance have an expected variogram matching the variogram model. For large vector sizes, Cholesky simulated Gaussian vectors cannot be used to explore uncertainty in the neighborhood of the vector mean. Instead uncertainty is explored around the n-dimensional elliptical envelop corresponding to the expected Mahalanobis distance. 相似文献