A Global Optimization Approach to Grid Generation

Farmer, Chris L.; Heath, D.E.; Moody, Ryan

doi:10.2118/21236-ms

Cited by 31 publications

(9 citation statements)

References 5 publications

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“…In fact, for large heterogeneous models, a computational grid should be constructed by addressing the heterogeneities. Permeability-based grid generation has been investigated before (Garcia et al 1992;Farmer et al 1991;Li et al 1995;Qi et al 2001), where the underlying idea is to preserve key fi ne-grid heterogeneities in the coarse grid by refi ning areas of high permeability variation. The technique is commonly used because it does not entail any fl ow simulation.…”

Section: Application Of Bga In Coarse-grid Generationmentioning

confidence: 99%

Unstructured-Coarse-Grid Generation Using Background-Grid Approach

Evazi

Mahani

2010

SPE Journal

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Reservoir flow simulation involves subdivision of the physical domain into a number of gridblocks. This is best accomplished with optimized gridpoint density and a minimized number of gridblocks, especially for coarse-grid generation from a fine-grid geological model.In any coarse-grid generation, proper distribution of gridpoints, which form the basis of numerical gridblocks, is a challenging task. We show that this can be achieved effectively by a novel grid-generation approach based on a background grid that stores gridpoint spacing parameters.Spacing parameter (L) can be described by Poisson's equationwhere the local density of gridpoints is controlled by a variable source term (G); see Eq. 1. This source term can be based on different gridpoint density indicators, such as permeability variations, fluid velocity, or their combination (e.g., vorticity) where they can be extracted from the reference fine grid. Once a background grid is generated, advancing-front triangulation (AFT) and then Delaunay tessellation are invoked to form the final (coarse) gridblocks. The algorithm produces grids varying smoothly from high-to low-density gridpoints, thus minimizing use of grid-smoothing and -optimization techniques. This algorithm is quite flexible, allowing choice of the gridding indicator, hence providing the possibility of comparing the grids generated with different indicators and selecting the best.In this paper, the capabilities of approach in generation of unstructured coarse grids from fine geological models are illustrated using 2D highly heterogeneous test cases. Flexibility of algorithm to gridding indicator is demonstrated using vorticity, permeability variation, and velocity. Quality of the coarse grids is evaluated by comparing their two-phase-flow simulation results to those of fine grid and uniform coarse grid. Results demonstrate the robustness and attractiveness of the approach, as well as relative quality/performance of grids generated by using different indicators.

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Section: Application Of Bga In Coarse-grid Generationmentioning

confidence: 99%

Unstructured-Coarse-Grid Generation Using Background-Grid Approach

Evazi

Mahani

2010

SPE Journal

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“…The discrete nature of the geostatistical grid leads to complications in calculating the partial derivatives. An example of a nonlinear optimization approach not requiring partial derivatives uses simulated annealing (Farmer, Heath, and Moody, 1991). A different approach can be taken by noting that, unlike many optimization problems, adjusting a node only has a local effect; heterogeneity is inherently a local phenomenon.…”

Section: Geostatistical Adaptive Grid (Gag)mentioning

confidence: 99%

An adaptive grid technique for minimizing heterogeneity of cells or elements

Robey

1995

Math Geol

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KEY WORDS: adaptive grid, heterogeneity, upscaling. ~TRODUCTIONGeologic materials are inherently heterogeneous, but there is much structure in the heterogeneity. Geostatistical methods are becoming more adept at capturing these heterogeneous structures. Such methods allow a description of a domain in a relatively fine degree of detail, even if consisting of millions of nodes. Flow modeling typically is carried out on a coarser grid. Despite the coarser grid, it is important to capture the geologic structure because otherwise the detail provided by the geostatistical methods (or other similar techniques) are not retained in the flow model. An adaptive grid allows the coarser flow grid to resolve more of the geologic features without increasing the number of cells or elements relative to a uniform grid. This type of adaptivity is termed R-type for redistribution of node points.As a result of the heterogeneity, hydrologic properties have different statistical distributions for different scales. Usually the property values are available at lab scale and are generated for a simulation using geostatistical or statistical rReceived 23 December 1994; accepted 14 March 1995. "Spectra Research Institute, 1613 University Blvd., NE, Albuquerque, New Mexico 87102-1710.

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“…Generally speaking, coarse grid generation, upscaling calculation and descritization technique are three complimentary components in coarse scale simulation. Generation of suitable coarse grid is as important as employing a suitable upscaling/homogenization and descritization technique [19][20][21][22][23][24][25][26][27][28] . In many cases the best choice of a coarse grid can reduce numerical dispersion and the need for two-phase upscaling, e.g.…”

Section: Introductionmentioning

confidence: 99%

A Quantitative and Qualitative Comparison of Coarse Grid Generation Techniques for Numerical Simulation of Flow in Heterogeneous Porous Media

Qomi

Mahani

Firoozabadi³

2009

SPE Reservoir Simulation Symposium

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Applying upscaling techniques is an undeniable demand in reservoir simulation, considering the difference between level of details in a geological model and level of details that can be handled by reservoir simulators. Upscaling reservoir model involves first constructing a coarse grid by employing gridding algorithms and then computing average properties for coarse grid blocks. Although various techniques have been proposed for each of these steps, one has to be aware of strengths and weaknesses of each technique before attempting to apply them. In this paper, we focus on different gridding methods and evaluate their performances. Three main grid generation techniques are considered: permeability-based (PB), flow-based (FB), and vorticity-based (VB) gridding. We apply all three methods to some 2D heterogeneous models and simulate two-phase flow on the constructed grids. Then we compare their obtained global and local results. Fluid cuts at producer is employed as global performance indicator and saturation distribution error as local indicator. We show that FB and VB gridding, which are dynamic methods, are superior to PB gridding, which is a static method. Based on this analysis, we then concentrate on FB and VB griddings and investigate their performances in greater details. While FB gridding uses fluid velocity as grid blocks density indicator, VB gridding combines velocity and permeability variation in gridding according to its definition and takes advantages of both. Therefore, although performance of FB and VB griddings are comparable in many cases, VB has benefit of producing coarse grid blocks with more uniform permeability and fluid properties distribution. This in turn yields more accurate global and local results and reduces application of sophisticated upscaling techniques and full-tensor permeability upscaling.

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A Global Optimization Approach to Grid Generation

Cited by 31 publications

References 5 publications

Unstructured-Coarse-Grid Generation Using Background-Grid Approach

Unstructured-Coarse-Grid Generation Using Background-Grid Approach

An adaptive grid technique for minimizing heterogeneity of cells or elements

A Quantitative and Qualitative Comparison of Coarse Grid Generation Techniques for Numerical Simulation of Flow in Heterogeneous Porous Media

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