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Abstract

Summary

Discrete representations of highly heterogeneous porous media require high-resolution models, which are computationally expensive to simulate. Model reduction through upscaling is an effective way to accelerate flow simulations. Although single-grid upscaling techniques can provide accurate results for the pressure field, they may fail to capture the details of the saturation distribution when highly coarsened models are used.

One approach to address this issue is to use the coarse grid only for the pressure solution, and the original fine grid for transport solutions. Such procedures, commonly referred to as multiscale methods, have been extensively investigated in the reservoir simulation community. In this work we present a new dual-grid model that shares many similarities with existing finite-volume-based multiscale methods. Our dual-grid approach is, however, formulated as an extension of our previously developed aggregation-based upscaling procedure.

First, a coarse model is constructed for the pressure solution. The main flow parameters for this model are the transmissibilities between adjacent coarse (aggregated) cells. These are obtained using a flow-based upscaling procedure that (typically) requires two or three global fine-grid pressure solutions. The pressure fields constructed for transmissibility upscaling are used not only to evaluate the coarse transmissibility, but also to extract a fine-grid flux profile for each coarse (aggregated) interface. In the second step, fine-grid fluxes are calculated for the transport equation.

This is done locally within each coarse aggregate by solving a pressure equation with flux boundary conditions. These fluxes are determined by scaling the profile for each interface to match the coarse rate provided by the pressure solution. The overall procedure is implemented for unstructured fine and coarse grids. Examples involving two-phase flow in heterogeneous and fractured two-dimensional models are presented. Numerical results demonstrate the capabilities and flexibility of the overall methodology.

© EAGE Publications BV
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/content/papers/10.3997/2214-4609.201802264
2018-09-03
2024-04-26

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References

  1. Bosma, S., Hajibeygi, H., Tene, M. and Tchelepi, H.
    [2017] Multiscale finite volume method for discrete fracture modeling on unstructured grids (MS-DFM). Journal of Computational Physics, 351, 164–.
     [Google Scholar]
  2. Chen, Y., Durlofsky, L., Gerritsen, M. and Wen, X.
    [2003] A coupled local-global upscaling approach for simulating flow in highly heterogeneous formations. Advances in Water Resources, 26(10), 1041–1060.
     [Google Scholar]
  3. Efendiev, Y., Ginting, V., Hou, T. and Ewing, R.
    [2006] Accurate multiscale finite element methods for two-phase flow simulations. Journal of Computational Physics, 220(1), 155–174.
     [Google Scholar]
  4. Farmer, C.
    [2002] Upscaling: Areview. International Journal for Numerical Methods in Fluids, 40(1–2), 63–78.
     [Google Scholar]
  5. Gautier, Y., Blunt, M. and Christie, M.
    [1999] Nested gridding and streamline-based simulation for fast reservoir performance prediction. Computational Geosciences, 3(3–4), 295–320.
     [Google Scholar]
  6. Hajibeygi, H. and Jenny, P.
    [2011] Adaptive iterative multiscale finite volume method. Journal of Computational Physics, 230(3), 628–643.
     [Google Scholar]
  7. Hou, T. and Wu, X.H.
    [1997] A multiscale finite element method for elliptic problems in composite materials and porous media. Journal of Computational Physics, 134(1), 169–189.
     [Google Scholar]
  8. Hui, M.H., Karimi-Fard, M., Mallison, B. and Durlofsky, L.
    [2018] A general modeling framework for simulating complex recovery processes in fractured reservoirs at different resolutions. SPE Journal, 23(2), 598–613.
     [Google Scholar]
  9. Jenny, P., Lee, S. and Tchelepi, H.
    [2003] Multi-scale finite-volume method for elliptic problems in subsurface flow simulation. Journal of Computational Physics, 187(1), 47–67.
     [Google Scholar]
  10. Karimi-Fard, M. and Durlofsky, L.
    [2016] A general gridding, discretization, and coarsening methodology for modeling flow in porous formations with discrete geological features. Advances in Water Resources, 96, 372–.
     [Google Scholar]
  11. Karimi-Fard, M., Durlofsky, L. and Aziz, K.
    [2004] An efficient discrete-fracture model applicable for general-purpose reservoir simulators. SPE Journal, 9(2), 227–236.
     [Google Scholar]
  12. Kippe, V., Aarnes, J. and Lie, K.A.
    [2008] A comparison of multiscale methods for elliptic problems in porous media flow. Computational Geosciences, 12(3), 377–398.
     [Google Scholar]
  13. Kunze, R. and Lunati, I.
    [2012] An adaptive multiscale method for density-driven instabilities. Journal of Computational Physics, 231(17), 5557–5570.
     [Google Scholar]
  14. Lee, S., Wolfsteiner, C. and Tchelepi, H.
    [2008] Multiscale finite-volume formulation for multiphase flow in porous media: Black oil formulation of compressible, three-phase flow with gravity. Computational Geosciences, 12(3), 351–366.
     [Google Scholar]
  15. Lunati, I. and Lee, S.
    [2009] An operator formulation of the multiscale finite-volume method with correction function. Multiscale Modeling and Simulation, 8(1), 96–109.
     [Google Scholar]
  16. Moyner, O. and Lie, K.A.
    [2016] A multiscale restriction-smoothed basis method for high contrast porous media represented on unstructured grids. Journal of Computational Physics, 304, 71–.
     [Google Scholar]
  17. Shah, S., Moyner, O., Tene, M., Lie, K.A. and Hajibeygi, H.
    [2016] The multiscale restriction smoothed basis method for fractured porous media (F-MsRSB). Journal of Computational Physics, 318, 57–.
     [Google Scholar]
  18. Zhou, H. and Tchelepi, H.
    [2008] Operator-based multiscale method for compressible flow. SPE Journal, 13(2), 267–273.
     [Google Scholar]
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An Unstructured Dual-Grid Model For Flow In Fractured And Heterogeneous Porous Media
Conference Proceedings 2018, 1 (2018); https://doi.org/10.3997/2214-4609.201802264
/content/papers/10.3997/2214-4609.201802264
/content/papers/10.3997/2214-4609.201802264
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