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A Multiscale Method Coupling Network and Continuum Models in Porous Media II—Single- and Two-Phase Flows

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Advances in Applied Mathematics, Modeling, and Computational Science

Part of the book series: Fields Institute Communications ((FIC,volume 66))

Abstract

We present a numerical multiscale method for coupling mass conservation laws at the continuum scale with a discrete, pore scale network model for two-phase flow in porous media. Our previously developed single-phase flow algorithm is extended to two-phase flows, for the situations in which the saturation profile go through a sharp transition from fully saturated to almost unsaturated states. Our method evaluates the continuum equation by simulations using small representative networks centering at different physical locations, and thereby computes the effective dynamics of the two phase flow at the continuum scale. On the other hand, the initial and boundary data for the network simulations are determined by the variables used in the continuum model. We present numerical results for single-phase flows with nonlinear flux-pressure dependence, as well as two-phase flows.

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Acknowledgements

Chu and Tsai are partially supported by NSF DMS-0714612, and NSF DMS-0914840.

Author information

Authors and Affiliations

  1. Department of Mathematics, The University of Texas at Austin, Austin, TX, 78712, USA

    Jay Chu, Björn Engquist & Richard Tsai

  2. ICES, The University of Texas at Austin, Austin, TX, 78712, USA

    Björn Engquist & Richard Tsai

  3. Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, TX, 78712, USA

    Maša Prodanović

  4. CPGE, The University of Texas at Austin, Austin, TX, 78712, USA

    Maša Prodanović

Authors
  1. Jay Chu
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  2. Björn Engquist
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  3. Maša Prodanović
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  4. Richard Tsai
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Corresponding author

Correspondence to Jay Chu .

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Editors and Affiliations

  1. , Department of Mathematics, Wilfrid Laurier University, University Avenue West 75, Waterloo, N2L 3C5, Ontario, Canada

    Roderick Melnik

  2. , Dept. of Physics and Computer Science, Wilfrid Laurier University, University Avenue West 75, Waterloo, N2L 3C5, Canada

    Ilias S. Kotsireas

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Chu, J., Engquist, B., Prodanović, M., Tsai, R. (2013). A Multiscale Method Coupling Network and Continuum Models in Porous Media II—Single- and Two-Phase Flows. In: Melnik, R., Kotsireas, I. (eds) Advances in Applied Mathematics, Modeling, and Computational Science. Fields Institute Communications, vol 66. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-5389-5_7

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