Boundary effects in the upscaling of absolute permeability - a new approach

Terpolilli, P.; Hontans, T.

doi:10.3997/2214-4609.201406138

Cited by 9 publications

(7 citation statements)

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“…We do not give details here, but all results and proofs could be found in [22,33]. To include the result of Gallouët and Guérillot [19,20], we briefly recall their approach.…”

Section: Other Classical Methodsmentioning

confidence: 98%

Taking into account general boundary conditions in upscaling absolute permeability

Hontans

Terpolilli

2006

Comput Geosci

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Upscaling methods that need to solve local problems subject to boundary conditions are addressed in this article. We define a new upscaling method based on optimization problems, which can take into account general boundary conditions applied to local problems. The determination of upscaled permeability leads to minimizing the difference of dissipated energies (or averaged velocity) at fine and large scale. Using optimal control techniques, we obtain an effective computing algorithm that allows us to recover, with classical boundary conditions, the well-known results. The uniqueness issue is tackled for the optimization problems introduced in our approach. We show that the method is stable with respect to G-convergence, a property that establishes a link with homogenization theory, and finally, 2D numerical experiments are presented.

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“…We do not give details here, but all results and proofs could be found in [22,33]. To include the result of Gallouët and Guérillot [19,20], we briefly recall their approach.…”

Section: Other Classical Methodsmentioning

confidence: 98%

Taking into account general boundary conditions in upscaling absolute permeability

Hontans

Terpolilli

2006

Comput Geosci

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“…It is generally recognized that the main difficulty in permeability upscaling is the dependence of upscaling results on flow boundary conditions [1][2][3] , which leads to a non-unique solution. Moreover, the use of distorted gridblocks such as corner-point geometry (CPG) adds a supplementary difficulty to permeability upscaling, which has not been greatly discussed in the literature.…”

Section: Introductionmentioning

confidence: 99%

Permeability Upscaling on Corner-Point Geometry in the Near-Well Region

Ding¹

2003

Proceedings of Middle East Oil Show

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TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractIn this paper, a technique for upscaling of absolute permeability in the well vicinity on CPG (Corner-Point Geometry) gridblocks is presented. The near-well upscaling procedure is very useful for well performance prediction. It can assure the coherence of well results by using fine grid on coarse grid simulations.The near-well upscaling procedure is developed for advanced wells in 3D. Transmissibilities are upscaled from Cartesian fine grid issued from a geostatistical to CPG coarse grid used for flow simulations. To overcome the difficulty of complex geometrical intersections between fine gridblocks and coarse gridblocks, three approaches (geometrical approach, numerical approach and topological approach) are proposed and compared for flux upscaling. The topological approach, which needs a topological structure for gridblock regrouping in the vertical direction, seems the most promising. The near-well formation damage, which can be predicted using another numerical model, can also be integrated into the near-well upscaling procedure.

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“…However, the results of numerical upscaling depend greatly on boundary conditions used in fine grid simulation. Boundary effects in upscaling procedure have been greatly discussed in the literature (Christie et al, 2000;Holden et al, 2000;Terpolilli and Hontans, 2000). Optimum boundary condition is required in the numerical upscaling procedure.…”

Section: Upscaling Of Absolute Permeabilitymentioning

confidence: 99%

“…On a field scale, the flow pattern can be considered as two types: a "singular" flow pattern with high gradient pressure; and a "linear" flow pattern with low gradient pressure. Upscaling in "singular" flow region, which is usually the near-well region, is more important for well productivity calculation, while in most of the literature (Warren and Price, 1961;Begg et al, 1989;King, 1989;Durlofsky, 1991;Holden et al, 2000;Terpolilli et al, 2000), the boundary conditions correspond to the "linear" flow pattern. So, it is important to consider "singular" flow behavior in the upscaling procedure for accurate well performance calculation.…”

Section: Upscaling Of Absolute Permeabilitymentioning

confidence: 99%

“…Among the upscaled parameters, absolute permeability is by far the most important property that affects flow behaviors. Upscaling of absolute permeability is the most often considered in the literature (Warren and Price, 1961;Begg et al, 1989;King, 1989;Durlofsky, 1991;Noetinger, 1994;Christie et al, 2000;Holden et al, 2000;Terpolilli and Hontans, 2000). The main difficulty in permeability upscaling is the dependence of upscaling results on boundary conditions, which lead to a non unique solution.…”

Section: Introductionmentioning

confidence: 99%

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Near-Well Upscaling for Reservoir Simulations

Ding

2004

Oil & Gas Science and Technology - Rev. IFP

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Résumé -Mise à l'échelle au voisinage du puits pour simulations de réservoir -Les techniques de mise à l'échelle de perméabilité absolue (du modèle géologique ou géostatistique vers le modèle de simulation dynamique de réservoir) sont étudiées depuis longtemps dans la littérature. Il est généralement reconnu que la difficulté principale dans la mise à l'échelle est la dépendance des conditions aux limites, qui conduisent à des solutions non uniques. Ceci est particulièrement crucial au voisinage des puits, qui correspondent à des singularités de l'écoulement. Ainsi, à la suite d'une mauvaise mise à l'échelle de la perméabilité absolue aux abords du puits, les productivités de celui-ci, calculées par simulations en maillage fin et grossier, peuvent être très différentes. Dans cet article, nous présentons des techniques de mise à l'échelle au voisinage du puits, qui permettent d'améliorer significativement la précision de simulation en maillage grossier pour la prédiction de la productivité du puits dans un milieu hétérogène. Cette technique a été développée pour puits complexes sur un maillage corner-point geometry (CPG) en 3D. En utilisant la mise à l'échelle au voisinage du puits, les résultats aux puits obtenus par simulations en maillage grossier et en maillage fin sont équivalents. Abstract

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Boundary effects in the upscaling of absolute permeability - a new approach

Cited by 9 publications

References 0 publications

Taking into account general boundary conditions in upscaling absolute permeability

Taking into account general boundary conditions in upscaling absolute permeability

Permeability Upscaling on Corner-Point Geometry in the Near-Well Region

Near-Well Upscaling for Reservoir Simulations

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