A comparison study between an adaptive quadtree grid and uniform grid upscaling for reservoir simulation

Masoud Babaei, Ahmed H Elsheikh, Peter R. King

    Research output: Contribution to journalArticle

    Abstract

    An adaptive quadtree grid generation algorithm is developed and applied for tracer and multiphase flow in channelized heterogeneous porous media. Adaptivity was guided using two different approaches. In the first approach, wavelet transformation was used to generate a refinement field based on permeability variations. The second approach uses flow information based on the solution of an initial-time fine-scale problem. The resulting grids were compared with uniform grid upscaling. For uniform upscaling, two commonly applied methods were used: renormalization upscaling and local-global upscaling. The velocities obtained by adaptive grid and uniformly upscaled grids, were downscaled. This procedure allows us to separate the upscaling errors, on adaptive and uniform grids, from the numerical dispersion errors resulting from solving the saturation equation on a coarse grid. The simulation results obtained by solving on flow-based adaptive quadtree grids for the case of a single phase flow show reasonable agreement with more computationally demanding fine-scale models and local-global upscaled models. For the multiphase case, the agreement is less evident, especially in piston-like displacement cases with sharp frontal movement. In such cases a non-iterative transmissibility upscaling procedure for adaptive grid is shown to significantly reduce the errors and make the adaptive grid comparable to iterative local-global upscaling. Furthermore, existence of barriers in a porous medium complicates both upscaling and grid adaptivity. This issue is addressed by adapting the grid using a combination of flow information and a permeability based heuristic criterion.

    Original languageEnglish
    Pages (from-to)377-400
    Number of pages24
    JournalTransport in Porous Media
    Volume98
    Issue number2
    DOIs
    Publication statusPublished - Jun 2013

    Keywords

    • Adaptive quadtree grid
    • Permeability- and flow-based gridding
    • Renormalization upscaling
    • Local-global upscaling
    • Downscaling
    • HETEROGENEOUS POROUS-MEDIA
    • FLOW-BASED GRIDS
    • PERMEABILITY TENSORS
    • MULTISCALE METHOD
    • SUBSURFACE FLOW
    • 2-PHASE FLOW
    • SCALE-UP
    • TRANSPORT
    • MODEL
    • SCHEMES

    Cite this

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    title = "A comparison study between an adaptive quadtree grid and uniform grid upscaling for reservoir simulation",
    abstract = "An adaptive quadtree grid generation algorithm is developed and applied for tracer and multiphase flow in channelized heterogeneous porous media. Adaptivity was guided using two different approaches. In the first approach, wavelet transformation was used to generate a refinement field based on permeability variations. The second approach uses flow information based on the solution of an initial-time fine-scale problem. The resulting grids were compared with uniform grid upscaling. For uniform upscaling, two commonly applied methods were used: renormalization upscaling and local-global upscaling. The velocities obtained by adaptive grid and uniformly upscaled grids, were downscaled. This procedure allows us to separate the upscaling errors, on adaptive and uniform grids, from the numerical dispersion errors resulting from solving the saturation equation on a coarse grid. The simulation results obtained by solving on flow-based adaptive quadtree grids for the case of a single phase flow show reasonable agreement with more computationally demanding fine-scale models and local-global upscaled models. For the multiphase case, the agreement is less evident, especially in piston-like displacement cases with sharp frontal movement. In such cases a non-iterative transmissibility upscaling procedure for adaptive grid is shown to significantly reduce the errors and make the adaptive grid comparable to iterative local-global upscaling. Furthermore, existence of barriers in a porous medium complicates both upscaling and grid adaptivity. This issue is addressed by adapting the grid using a combination of flow information and a permeability based heuristic criterion.",
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    A comparison study between an adaptive quadtree grid and uniform grid upscaling for reservoir simulation. / Babaei, Masoud; Elsheikh, Ahmed H; King, Peter R.

    In: Transport in Porous Media, Vol. 98, No. 2, 06.2013, p. 377-400.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - A comparison study between an adaptive quadtree grid and uniform grid upscaling for reservoir simulation

    AU - Babaei, Masoud

    AU - Elsheikh, Ahmed H

    AU - King, Peter R.

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    N2 - An adaptive quadtree grid generation algorithm is developed and applied for tracer and multiphase flow in channelized heterogeneous porous media. Adaptivity was guided using two different approaches. In the first approach, wavelet transformation was used to generate a refinement field based on permeability variations. The second approach uses flow information based on the solution of an initial-time fine-scale problem. The resulting grids were compared with uniform grid upscaling. For uniform upscaling, two commonly applied methods were used: renormalization upscaling and local-global upscaling. The velocities obtained by adaptive grid and uniformly upscaled grids, were downscaled. This procedure allows us to separate the upscaling errors, on adaptive and uniform grids, from the numerical dispersion errors resulting from solving the saturation equation on a coarse grid. The simulation results obtained by solving on flow-based adaptive quadtree grids for the case of a single phase flow show reasonable agreement with more computationally demanding fine-scale models and local-global upscaled models. For the multiphase case, the agreement is less evident, especially in piston-like displacement cases with sharp frontal movement. In such cases a non-iterative transmissibility upscaling procedure for adaptive grid is shown to significantly reduce the errors and make the adaptive grid comparable to iterative local-global upscaling. Furthermore, existence of barriers in a porous medium complicates both upscaling and grid adaptivity. This issue is addressed by adapting the grid using a combination of flow information and a permeability based heuristic criterion.

    AB - An adaptive quadtree grid generation algorithm is developed and applied for tracer and multiphase flow in channelized heterogeneous porous media. Adaptivity was guided using two different approaches. In the first approach, wavelet transformation was used to generate a refinement field based on permeability variations. The second approach uses flow information based on the solution of an initial-time fine-scale problem. The resulting grids were compared with uniform grid upscaling. For uniform upscaling, two commonly applied methods were used: renormalization upscaling and local-global upscaling. The velocities obtained by adaptive grid and uniformly upscaled grids, were downscaled. This procedure allows us to separate the upscaling errors, on adaptive and uniform grids, from the numerical dispersion errors resulting from solving the saturation equation on a coarse grid. The simulation results obtained by solving on flow-based adaptive quadtree grids for the case of a single phase flow show reasonable agreement with more computationally demanding fine-scale models and local-global upscaled models. For the multiphase case, the agreement is less evident, especially in piston-like displacement cases with sharp frontal movement. In such cases a non-iterative transmissibility upscaling procedure for adaptive grid is shown to significantly reduce the errors and make the adaptive grid comparable to iterative local-global upscaling. Furthermore, existence of barriers in a porous medium complicates both upscaling and grid adaptivity. This issue is addressed by adapting the grid using a combination of flow information and a permeability based heuristic criterion.

    KW - Adaptive quadtree grid

    KW - Permeability- and flow-based gridding

    KW - Renormalization upscaling

    KW - Local-global upscaling

    KW - Downscaling

    KW - HETEROGENEOUS POROUS-MEDIA

    KW - FLOW-BASED GRIDS

    KW - PERMEABILITY TENSORS

    KW - MULTISCALE METHOD

    KW - SUBSURFACE FLOW

    KW - 2-PHASE FLOW

    KW - SCALE-UP

    KW - TRANSPORT

    KW - MODEL

    KW - SCHEMES

    U2 - 10.1007/s11242-013-0149-7

    DO - 10.1007/s11242-013-0149-7

    M3 - Article

    VL - 98

    SP - 377

    EP - 400

    JO - Transport in Porous Media

    JF - Transport in Porous Media

    SN - 0169-3913

    IS - 2

    ER -