Laws and principles governing fluid flow in porous media

  • Natalia Kovalchuk
  • Constantinos HadjistassouEmail author
Regular Article
Part of the following topical collections:
  1. Flowing Matter, Problems and Applications


Currently, it is impossible to imagine the petroleum industry without utilising numerical simulation methods for reservoir analysis and production. Investigating the petroleum reservoir performance calls for a comprehensive understanding of the physical processes that govern flow transport in porous media. Irrespective of the goals of the analysis whether pertaining to core investigations, reservoir simulation and planning of enhanced recovery methods, flow processes obey the same physical laws. In this paper, the basic laws and principles describing fluid flow and flow patterns manifesting in subsurface porous media are discussed. Appreciating the applicability and limitations of the physical laws allows us to develop and employ modelling methods for flow behaviour analysis and reservoir performance prediction which is the main goal of petroleum engineering. Concluding, we present the black-oil model, the compositional model and the complex models as applied to petroleum field applications.

Graphical abstract


Topical issue: Flowing Matter, Problems and Applications 


  1. 1.
    A.M. Amao, Mathematical model for Darcy Forchheimer flow with applications to well performance analysis, Thesis, Texas Tech University, 2007Google Scholar
  2. 2.
    C.W. Hall, Laws and Models: Science, Engineering, and Technology (CRC Press, 1999)Google Scholar
  3. 3.
    F.W. Constant, Fundamental Laws of Physics (Addison-Wesley, 1963)Google Scholar
  4. 4.
    F.W. Constant, Fundamental Principles of Physics (Addison-Wesley, 1967)Google Scholar
  5. 5.
    M.K. Das, P.P. Mukherjee, K. Muralidhar, Modeling Transport Phenomena in Porous Media with Applications (Springer, 2017)Google Scholar
  6. 6.
    L. Wang, L.-P. Wang, Z. Guo, J. Mi, Int. J. Heat Mass Transfer 82, 357 (2015)CrossRefGoogle Scholar
  7. 7.
    C.Y. Wang, P. Cheng, Adv. Heat Transfer 30, 93 (1997)CrossRefGoogle Scholar
  8. 8.
    C.Y. Wang, W.B. Gu, B.Y. Liaw, J. Electrochem. Soc. 145, 3407 (1998)CrossRefGoogle Scholar
  9. 9.
    C. Bringedal, Modeling of heat transfer in porous media in the context of geothermal energy extraction, Thesis, University of Bergen, 2015. Google Scholar
  10. 10.
    V. Gurau, H. Liu, S. Kakac, AIChE J. 44, 2410 (1998)CrossRefGoogle Scholar
  11. 11.
    V. Lampe, Modelling fluid flow and heat transport in fractured porous media, Thesis, University of Bergen, 2013Google Scholar
  12. 12.
    W.G. Gray, C.T. Miller, Introduction to the Thermodynamically Constrained Averaging Theory for Porous Medium Systems (Springer, 2014)Google Scholar
  13. 13.
    X. Peng, Y. Liu, B. Liang, Z. Du, PLoS ONE 12, 177 (2017)Google Scholar
  14. 14.
    M. Ohlberger, B. Schweizer, Modelling of interfaces in unsaturated porous media, in Dynamical Systems and Differential Equations, AIMS Proceedings 2007, Proceedings of the 6th AIMS International Conference, Poitiers, France, 2007, Conference Publications 2007, 2007 (Special) pp. 794-803,
  15. 15.
    M. Dejam, H. Hassanzadeh, Z. Chen, Water Resour. Res. 53, 8187 (2017)ADSCrossRefGoogle Scholar
  16. 16.
    S. Liu, J.H. Maslyah, Chem. Eng. Commun. 148, 653 (1996)CrossRefGoogle Scholar
  17. 17.
    A. Dybbs, R.V. Edwards, A New Look at Porous Media Fluid Mechanics -- Darcy to Turbulent (Springer, 1984) pp. 199--256Google Scholar
  18. 18.
    C.S. Slichter, The motions of underground waters, Water Supply Paper No. 67 (Washington Government Printing Office, 1902)Google Scholar
  19. 19.
    L. Bloshanskaya, A. Ibragimov, F. Siddiqui, M.Y. Soliman, J. Porous Media 20, 769 (2017)CrossRefGoogle Scholar
  20. 20.
    W. Sobieski, A. Trykozko, Tech. Sci. 17, 321 (2014)Google Scholar
  21. 21.
    H. Teng, T.S. Zhao, Chem. Eng. Sci. 55, 2727 (2000)CrossRefGoogle Scholar
  22. 22.
    K.R. Bahoush, H.S. Kazemzadeh, Mech. Eng. 16, 159 (2009)Google Scholar
  23. 23.
    H.-C. Chan, W.C. Huang, J.-M. Leu, C.-J. Lai, Int. J. Heat Fluid Flow 28, 1157 (2007)CrossRefGoogle Scholar
  24. 24.
    Ø. Fevang, K. Singh, C.H. Whitson, Guidelines for choosing compositional and black-oil models for volatile oil and gas-condensate reservoirs, in SPE Annual Technical Conference and Exhibition, Conference Proceedings (Society of Petroleum Engineers, 2000)Google Scholar
  25. 25.
    J. Haukas, Compositional reservoir simulation with emphasis on the IMPSAT formulation, University of Bergen, 2006Google Scholar
  26. 26.
    Z. Chen, SIAM J. Numer. Anal. 38, 489 (2000)MathSciNetCrossRefGoogle Scholar
  27. 27.
    G. Qin, R.E. Ewing, Z. Chen, SIAM J. Appl. Math. 60, 747 (2000)MathSciNetCrossRefGoogle Scholar
  28. 28.
    A.H. Alizadeh, M. Piri, Rev. Geophys. 52, 468 (2014)ADSCrossRefGoogle Scholar
  29. 29.
    O.O. Duru, R.N. Horne, SPE Reserv. Eval. Eng. 13, 873 (2010)CrossRefGoogle Scholar
  30. 30.
    S. Yin, M.B. Dusseault, L. Rothenburg, Int. J. Numer. Anal. Methods Geomech. 33, 449 (2009)CrossRefGoogle Scholar
  31. 31.
    C. Guo, M. Wei, H. Liu, PLoS ONE 10, e0143649 (2015)CrossRefGoogle Scholar

Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Marine and Carbon LabUniversity of NicosiaNicosiaCyprus

Personalised recommendations