A nonuniform coarsening approach for the scale-up of displacement processes in heterogeneous porous media

Durlofsky, Louis J.; Jones, Richard C.; Milliken, William J.

doi:10.1016/s0309-1708(96)00053-x

Cited by 183 publications

(110 citation statements)

References 16 publications

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“…If we want to employ smooth boundary conditions, e.g., piecewise linear, then the coarse grid should preferably be chosen so that we "minimize" the presence of strong heterogeneous features that penetrate the grid-block interfaces. This might suggest the use of flexible gridding schemes like the nonuniform coarsening approach proposed by Durlofsky et al, [12]. The non-uniform coarsening technique, which generates grids that are finely gridded in high flow regions, was developed because it was acknowledged that it is important to model the high flow regions in porous media flow correctly in order to produce reliable production scenarios.…”

Section: Implementational Issuesmentioning

confidence: 99%

Multiscale Domain Decomposition Methods for Elliptic Problems with High Aspect Ratios

Aarnes

Hou

2002

Acta Mathematicae Applicatae Sinica, English Series

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Abstract. In this paper we study domain decomposition methods for solving some elliptic problem arising from flows in heterogeneous porous media. Due to the multiple scale nature of the elliptic coefficients arising from the heterogeneous formations, the construction of efficient domain decomposition methods for these problems requires a coarse solver which is adaptive to the fine scale features, [4]. We propose the use of a multiscale coarse solver based on a finite volume -finite element formulation. The resulting domain decomposition methods seem to induce a convergence rate nearly independent of the aspect ratio of the extreme permeability values within the substructures. A rigorous convergence analysis based on the Schwarz framework is carried out, and we demonstrate the efficiency and robustness of the preconditioner through numerical experiments which include problems with multiple scale coefficients, as well as problems with continuous scales.

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Section: Implementational Issuesmentioning

confidence: 99%

Multiscale Domain Decomposition Methods for Elliptic Problems with High Aspect Ratios

Aarnes

Hou

2002

Acta Mathematicae Applicatae Sinica, English Series

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“…Previous approaches for the coarse scale modeling of transport in heterogeneous oil reservoirs include the use of pseudo relative permeabilities [3,7,31,32], the application of nonuniform or flow-based coarse grids [12], and the use of volume averaging and higher moments [10,16,17]. Our methodology for subgrid upscaling of the hyperbolic (or convection dominated) equations uses volume averaging techniques.…”

Section: Upscaled Modeling In Multiphase Flow Applicationsmentioning

confidence: 99%

“…This kind of technique in conjunction with the upscaling of absolute permeability is commonly used in applications (e.g., [12,11,10]). The difference of our approach is that the coupling of the small scales is performed through the finite volume element formulation of the global problem and the small scale information of the velocity field can be easily recovered.…”

Section: Fine and Coarse Scale Modelsmentioning

confidence: 99%

Upscaled modeling in multiphase flow applications

Ginting¹,

Ewing²,

Efendiev³

et al. 2004

Mat. apl. comput.

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“…Durlofsky et al [23] introduced an upscaling method whereby a grid of finer resolution is used in the regions of high fluid velocities, but upscaled, homogenized description is utilized for the rest of the flow domain. Similar to the DM method, in Durlofsky et al's approach, the relative permeabilities are not upscaled.…”

Section: Introductionmentioning

confidence: 99%

Upscaling of the permeability by multiscale wavelet transformations and simulation of multiphase flows in heterogeneous porous media

Rasaei

Sahimi

2008

Comput Geosci

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We describe a new approach for simulation of multiphase flows through heterogeneous porous media, such as oil reservoirs. The method, which is based on the wavelet transformation of the spatial distribution of the single-phase permeabilities, incorporates in the upscaled computational grid all the relevant data on the permeability, porosity, and other important properties of a porous medium at all the length scales. The upscaling method generates a nonuniform computational grid which preserves the resolved structure of the geological model in the near-well zones as well as in the high-permeability sectors and upscales the rest of the geological model. As such, the method is a multiscale one that preserves all the important information across all the relevant length scales. Using a robust front-detection method which eliminates the numerical dispersion by a high-order total variation diminishing method (suitable for the type of nonuniform upscaled grid that we generate), we obtain highly accurate results with a greatly reduced computational cost. The speedup in the computations is up to over three orders of magnitude, depending on the degree of heterogeneity of the model. To demonstrate the accuracy and efficiency of our methods, five distinct models (including one with fractures) of heterogeneous porous media are considered, and two-phase flows in the models are studied, with and without the capillary pressure.

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A nonuniform coarsening approach for the scale-up of displacement processes in heterogeneous porous media

Cited by 183 publications

References 16 publications

Multiscale Domain Decomposition Methods for Elliptic Problems with High Aspect Ratios

Multiscale Domain Decomposition Methods for Elliptic Problems with High Aspect Ratios

Upscaled modeling in multiphase flow applications

Upscaling of the permeability by multiscale wavelet transformations and simulation of multiphase flows in heterogeneous porous media

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