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A Study of the Effect of Inhomogeneities on Immiscible Flow in Naturally Fractured Reservoirs

  • Jim DouglasJr.
  • Jeffrey L. Hensley
  • Paulo Jorge Paes Leme
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 114)

Abstract

The so-called medium block model for two-phase, immiscible, incompressible flow in a naturally-fractured petroleum reservoir is extended to admit inhomogeneous and non-periodic physical properties in both fractures and matrix blocks. In particular, a number of block types is allowed over each point in the reservoir, along with inhomogeneous physical properties. Numerical studies are performed to analyze the dependence of the flow on these properties for both vertical cross-sections and five-spot injection.

Keywords

Relative Permeability Matrix Block Production Curve Fracture Permeability Fracture Reservoir 
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References

  1. [1]
    Arbogast T. The double porosity model for single phase flow in naturally fractured reservoirs. In Numerical Simulation in Oil Recovery, The IMA Volumes in Mathematics and its Applications 11, pages 23–45. Springer-Verlag, Berlin and New York, 1988. M. F. Wheeler, ed.CrossRefGoogle Scholar
  2. [2]
    Arbogast T., Douglas J., Hornung U. Modeling of naturally fractured petroleum reservoirs by formal homogenization techniques. In Frontiers in Pure and Applied Mathematics, pages 1–19. Elsevier, Amsterdam, 1991. R. Dautray, ed.Google Scholar
  3. [3]
    Aziz K. and Settari T. Petroleum Reservoir Simulation. Applied Science Publishers, London, 1979.Google Scholar
  4. [4]
    Barenblatt G. I., Zheltov I. R, Kochina I. N. Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks. J. Appl. Math, and Mech., 24:1286–1303, 1960.CrossRefGoogle Scholar
  5. [5]
    Chavent G., Jaffré J. Mathematical Models and Finite Elements for Reservoir Simulation. North-Holland, Amsterdam, 1986.Google Scholar
  6. [6]
    de Swaan A. Theory of waterflooding in fractured reservoirs. Soc. Petroleum Engr. J., 18:117–122, 1978.Google Scholar
  7. [7]
    Douglas J., Jr., Arbogast T. Dual porosity models for flow in naturally fractured reservoirs. In Dynamics of Fluids in Hierarchical Porous Formations, pages 177–221. Academic Press, London, 1990. J. H. Cushman, ed.Google Scholar
  8. [8]
    Douglas J., Jr., Arbogast T., Paes Leme P. J., Hensley J. L., Nunes N. P. Immiscible displacement in vertically fractured reservoirs. Transport in Porous Media. To appear, 1993.Google Scholar
  9. [9]
    Douglas J., Jr., Hensley J. L., Arbogast T. A dual-porosity model for waterflooding in naturally fractured reservoirs. Computer Methods in Applied Mechanics and Engineering, 87:157–174, 1991.CrossRefGoogle Scholar
  10. [10]
    Hornung U. Applications of the homogenization method to flow and transport through porous media. In Flow and Transport in Porous Media, Singapore. Summer School, Beijing 1988, World Scientific. Xiao Shutie, ed., to appear.Google Scholar
  11. [11]
    Hornung U. Miscible displacement in porous media influenced by mobile and immobile water. Rocky Mtn. Jour. Math., 21:645–669, 1991. Corr. pages 1153–1158.CrossRefGoogle Scholar
  12. [12]
    Hornung IL, Jäger, W. Homogenization of reactive transport through porous media. In EQUADIFF 1991, Singapore. World Scientific Publishing. C. Perelló, ed., submitted 1992.Google Scholar
  13. [13]
    Hornung IL, Jäger W. A model for chemical reactions in porous media. In Complex Chemical Reaction Systems. Mathematical Modeling and Simulation, volume 47 of Chemical Physics, pages 318–334. Springer, Berlin, 1987. J. Warnatz and W. Jäger, eds.CrossRefGoogle Scholar
  14. [14]
    Hornung U., Jäger W. Diffusion, convection, adsorption, and reaction of chemicals in porous media. J. Diff. Equations, 92:199–225, 1991.CrossRefGoogle Scholar
  15. [15]
    Hornung U., Showalter R. E. Diffusion models for fractured media. Jour. Math. Anal. Appl, 147:69–80, 1990.CrossRefGoogle Scholar
  16. [16]
    Peaceman D. W. Fundamentals of Numerical Reservoir Simulation. Elsevier, New York, 1977.Google Scholar
  17. [17]
    Showalter R. E. Distributed microstructure models of porous media. This volume.Google Scholar
  18. [18]
    Vogt Ch. A homogenization theorem leading to a Volterra integro-differential equation for permeation chromotography. Preprint #155, Sonderfachbereich 123, 1982.Google Scholar
  19. [19]
    Warren J. E., Root P. J. The behavior of naturally fractured reservoirs. Soc. Petr. Eng. J., 3:245–255, 1963.Google Scholar

Copyright information

© Springer Basel AG 1993

Authors and Affiliations

  • Jim DouglasJr.
    • 1
  • Jeffrey L. Hensley
    • 2
  • Paulo Jorge Paes Leme
    • 3
    • 4
  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA
  2. 2.Center for Parallel and Scientific ComputingUniversity of TulsaTulsaUSA
  3. 3.Institute PolitécnicoUniversidade do Estado do Rio de JaneiroNova FriburgoBrazil
  4. 4.Departamento de MatemáticaPontifícia Universidade Católica do R.J.Rio de JaneiroBrazil

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