共查询到20条相似文献，搜索用时 558 毫秒
1.
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
2.
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
3.
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
4.
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
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The increasing use of unstructured grids for reservoir modeling motivates the development of geostatistical techniques to
populate them with properties such as facies proportions, porosity and permeability. Unstructured grids are often populated
by upscaling high-resolution regular grid models, but the size of the regular grid becomes unreasonably large to ensure that
there is sufficient resolution for small unstructured grid elements. The properties could be modeled directly on the unstructured
grid, which leads to an irregular configuration of points in the three-dimensional reservoir volume. Current implementations
of Gaussian simulation for geostatistics are for regular grids. This paper addresses important implementation details involved
in adapting sequential Gaussian simulation to populate irregular point configurations including general storage and computation
issues, generating random paths for improved long range variogram reproduction, and search strategies including the superblock
search and the k-dimensional tree. An efficient algorithm for computing the variogram of very large irregular point sets is developed for
model checking. 相似文献
7.
Piyang Liu Gary Douglas Couples Jun Yao Zhaoqin Huang Wenhui Song Jingsheng Ma 《Computational Geosciences》2018,22(5):1187-1201
The two-scale continuum model is widely used in simulating the reactive dissolution process and predicting the optimum injection rate for carbonate reservoir acidizing treatment. The numerical methods of this model are currently based on structured grids, which are not applicable for complicated geometries. In this study, a general numerical scheme for simulating a reactive flow problem on both structured and unstructured grids is presented based on the finite volume method (FVM). The convection and diffusion terms involved in the reactive flow model are discretized by using the upwind scheme and two-point flux approximation (TPFA), respectively. The location of the centroid node inside each control volume is moved by using an optimization algorithm to make the connections with the surrounding elements as orthogonal as possible, which systematically improves the accuracy of the TPFA scheme. Additionally, in order to avoid the computational complexity resulting from the discretization of the non-linear term, the mass balance equation is only discretized in the spatial domain to get a set of ordinary differential equations (ODEs). These ODEs are coupled with the reaction equations and then solved using the numerical algorithm on ODEs. The accuracy and efficiency of the proposed method are studied by comparing the results obtained from the proposed numerical method with previous experimental and numerical results. This comparison indicates that, compared with the previous methods, the proposed method predicts the wormhole structure more accurately. Finally, the presented method is used to check the effect of the domain geometry, and it is found that the geometry of the flow domain has no effect on the optimum injection velocity, but the radial domain requires a larger breakthrough volume than the linear domain when other parameters are fixed. 相似文献
8.
Mortar Upscaling for Multiphase Flow in Porous Media 总被引：1，自引：0，他引：1
In mortar space upscaling methods, a reservoir is decomposed into a series of subdomains (blocks) in which independently constructed numerical grids and possibly different physical models and discretization techniques can be employed in each block. Physically meaningful matching conditions are imposed on block interfaces in a numerically stable and accurate way using mortar finite element spaces. Coarse mortar grids and fine subdomain grids provide two-scale approximations. In the resulting effective solution flow is computed in subdomains on the fine scale while fluxes are matched on the coarse scale. In addition the flexibility to vary adaptively the number of interface degrees of freedom leads to more accurate multiscale approximations. This methodology has been implemented in the Center for Subsurface Modeling's multiphysics multiblock simulator IPARS (Integrated Parallel Accurate reservoir Simulator). Computational experiments demonstrate that this approach is scalable in parallel and it can be applied to non-matching grids across the interface, multinumerics and multiphysics models, and mortar adaptivity. Moreover unlike most upscaling approaches the underlying systems can be treated fully implicitly. 相似文献
9.
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
10.
The problem of calculating equivalent grid block permeability tensors for heterogeneous porous media is addressed. The homogenization method used involves solving Darcy's equation subject to linear boundary conditions with flux conservation in subregions of the reservoir and can be readily applied to unstructured grids. The resulting equivalent permeability tensor is stable as defined relative to G-convergence. It is proposed to use both conforming and mixed finite elements to solve the local problems and compute approximations from above and below of the equivalent permeability, respectively. Comparisons with results obtained using periodic, pressure and no-flux boundary conditions and the renormalization method are presented. A series of numerical examples demonstrates the effectiveness of the methodology for two-phase flow in heterogeneous reservoirs. 相似文献
11.
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
12.
The problem of calculating equivalent grid block permeability tensors for heterogeneous porous media is addressed. The homogenization method used involves solving Darcy's equation subject to linear boundary conditions with flux conservation in subregions of the reservoir and can be readily applied to unstructured grids. The resulting equivalent permeability tensor is stable as defined relative to G-convergence. It is proposed to use both conforming and mixed finite elements to solve the local problems and compute approximations from above and below of the equivalent permeability, respectively. Comparisons with results obtained using periodic, pressure and no-flux boundary conditions and the renormalization method are presented. A series of numerical examples demonstrates the effectiveness of the methodology for two-phase flow in heterogeneous reservoirs. 相似文献
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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
15.
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
16.
George Shu Heng Pau John B. Bell Ann S. Almgren Kirsten M. Fagnan Michael J. Lijewski 《Computational Geosciences》2012,16(3):577-592
We describe a second-order accurate sequential algorithm for solving two-phase multicomponent flow in porous media. The algorithm
incorporates an unsplit second-order Godunov scheme that provides accurate resolution of sharp fronts. The method is implemented
within a block structured adaptive mesh refinement (AMR) framework that allows grids to dynamically adapt to features of the
flow and enables efficient parallelization of the algorithm. We demonstrate the second-order convergence rate of the algorithm
and the accuracy of the AMR solutions compared to uniform fine-grid solutions. The algorithm is then used to simulate the
leakage of gas from a Liquified Petroleum Gas (LPG) storage cavern, demonstrating its capability to capture complex behavior
of the resulting flow. We further examine differences resulting from using different relative permeability functions. 相似文献
17.
赵晓博 《物探化探计算技术》2011,33(5):517-521,463
利用Delaunay三角化这种网格非结构化方法。通过编程实现了二维模型的非结构化三角形网格剖分,并编写了中心回线法瞬变电磁2．5维有限元正演程序。与前人计算结果对比,在取得相同计算精度的情况下,与结构化网格相比,非结构化网格所需网格和节点数量大大减少,计算效率更高。通过将非结构化网格法引入到瞬变电磁2．5维正演模拟中,实现了对复杂二维地电模型的有限元数值模拟,提高了现有有限元算法的应用范围。 相似文献
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