Upscaling of Transport Equations for Multiphase and Multicomponent Flows

  • Richard Ewing
  • Yalchin Efendiev
  • Victor Ginting
  • Hong Wang
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 60)

In this paper we discuss upscaling of immiscible multiphase and miscible multicomponent flow and transport in heterogeneous porous media. The discussion presented in the paper summarizes the results of in Upscaled Modeling in Multiphase Flow Applications by Ginting et al. (2004) and in Upscaling of Multiphase and Multicomponent Flow by Ginting et al. (2006). Perturbation approaches are used to upscale the transport equation that has hyperbolic nature. Our numerical results show that these upscaling techniques give an improvement over the existing upscaled models which ignore the subgrid terms.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M.A. Christie. Upscaling for reservoir simulation. J. Pet. Tech., pages 1004–1010, 1996.Google Scholar
  2. 2.
    N.H. Darman, G.E. Pickup, and K.S. Sorbie. A comparison of two-phase dynamic upscaling methods based on fluid potentials. Comput. Geosci., 6:5–27, 2002.MATHCrossRefGoogle Scholar
  3. 3.
    C.V. Deutsch and A.G. Journel. GSLIB: Geostatistical Software Library and User’s Guide. Oxford University Press, New York, 2nd edition, 1998.Google Scholar
  4. 4.
    L.J. Durlofsky. Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media. Water Resour. Res., 27:699–708, 1991.CrossRefGoogle Scholar
  5. 5.
    L.J. Durlofsky, R.C. Jones, and W.J. Milliken. A nonuniform coarsening approach for the scale up of displacement processes in heterogeneous media. Adv. in Water Res., 20:335–347, 1997.CrossRefGoogle Scholar
  6. 6.
    Y.R. Efendiev and L.J. Durlofsky. Numerical modeling of subgrid heterogeneity in two phase flow simulations. Water Resour. Res., 38(8):1128, 2002.CrossRefGoogle Scholar
  7. 7.
    Y.R. Efendiev, L.J. Durlofsky, and S.H. Lee. Modeling of subgrid effects in coarse scale simulations of transport in heterogeneous porous media. Water Resour. Res., 36:2031–2041, 2000.CrossRefGoogle Scholar
  8. 8.
    Y.R. Efendiev, T.Y. Hou, and T. Strinopoulos. Multiscale simulations of porous media flows in flow-based coordinate. Comput. Geosci., 2006. submitted.Google Scholar
  9. 9.
    T.Y. Hou and X.H. Wu. A multiscale finite element method for elliptic problems in composite materials and porous media. J. Comput. Phys., 134:169–189, 1997.MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    P. Langlo and M.S. Espedal. Macrodispersion for two-phase, immisible flow in porous media. Adv. in Water Res., 17:297–316, 1994.CrossRefGoogle Scholar
  11. 11.
    W. Zijl and A. Trykozko. Numerical homogenization of two-phase flow in porous media. Comput. Geosci., 6(1):49–71, 2002.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Richard Ewing
    • 1
  • Yalchin Efendiev
    • 1
  • Victor Ginting
    • 2
  • Hong Wang
    • 3
  1. 1.Department of Mathematics and Institute for Scientific ComputationTexas A & M UniversityUSA
  2. 2.Department of MathematicsColorado State UniversityUSA
  3. 3.Department of MathematicsUniversity of South CarolinaColumbiaUSA

Personalised recommendations