Advertisement

Fluid Flow in Porous Media

  • Antonio BarlettaEmail author
Chapter

Abstract

This chapter contains a discussion of the models employed to describe the fluid flow and the convection processes in a porous medium saturated by a fluid. The basic quantities, defined through an elementary representative volume scheme, are introduced. Among them, we mention the porosity and the seepage velocity field. Starting with Darcy’s law, the different formulations of the local momentum balance equation are analysed. The expressions of the local mass balance equation and of the local energy balance equation are introduced. The controversial problem of the viscous dissipation modelling for porous media with a large permeability is also outlined. The possible lack of local thermal equilibrium between the solid phase and the fluid phase is discussed, by employing a two-temperature model of the local energy balance. Finally, the seepage flow of non-Newtonian fluids in porous media is briefly surveyed relative to specific models: power-law, Bingham, and Oldroyd-B.

References

  1. 1.
    Al-Hadhrami AK, Elliott L, Ingham DB (2003) A new model for viscous dissipation in porous media across a range of permeability values. Transp Porous Media 53:117–122MathSciNetCrossRefGoogle Scholar
  2. 2.
    Alazmi B, Vafai K (2002) Constant wall heat flux boundary conditions in porous media under local thermal non-equilibrium conditions. Int J Heat Mass Transf 45:3071–3087CrossRefGoogle Scholar
  3. 3.
    Bear J (1988) Dynamics of fluids in porous media. Dover, New YorkzbMATHGoogle Scholar
  4. 4.
    Breugem WP, Rees DAS (2006) A derivation of the volume-averaged Boussinesq equations for flow in porous media with viscous dissipation. Transp Porous Media 63:1–12MathSciNetCrossRefGoogle Scholar
  5. 5.
    Christopher RH, Middleman S (1965) Power-law flow through a packed tube. Ind Eng Chem Fundam 4:422–426CrossRefGoogle Scholar
  6. 6.
    Kaviany M (2001) Principles of heat transfer in porous media, 2nd edn. Springer, New YorkzbMATHGoogle Scholar
  7. 7.
    Khuzhayorov B, Auriault JL, Royer P (2000) Derivation of macroscopic filtration law for transient linear viscoelastic fluid flow in porous media. Int J Eng Sci 38:487–504MathSciNetCrossRefGoogle Scholar
  8. 8.
    Kuznetsov AV (1998) Thermal nonequilibrium forced convection in porous media. In: Ingham DB, Pop I (eds) Transport phenomena in porous media. Pergamon Press, Oxford, pp 103–129CrossRefGoogle Scholar
  9. 9.
    Nash S, Rees DAS (2017) The effect of microstructure on models for the flow of a Bingham fluid in porous media: one-dimensional flows. Transp Porous Media 116:1073–1092MathSciNetCrossRefGoogle Scholar
  10. 10.
    Nield DA (2007) The modeling of viscous dissipation in a saturated porous medium. J Heat Transf 129:1459–1463CrossRefGoogle Scholar
  11. 11.
    Nield DA, Bejan A (2017) Convection in porous media, 5th edn. Springer, New YorkCrossRefGoogle Scholar
  12. 12.
    Pascal H (1983) Rheological behaviour effect of non-Newtonian fluids on steady and unsteady flow through a porous medium. Int J Numer Anal Methods Geomech 7:289–303CrossRefGoogle Scholar
  13. 13.
    Pearson JRA, Tardy PMJ (2002) Models for flow of non-Newtonian and complex fluids through porous media. J Non-Newtonian Fluid Mech 102:447–473CrossRefGoogle Scholar
  14. 14.
    Rees DAS (2015) Convection of a Bingham fluid in a porous medium. In: Vafai K (ed) Handbook of porous media, 3rd edn. CRC Press, Boca Raton, pp 559–595CrossRefGoogle Scholar
  15. 15.
    Rees DAS, Pop I (2005) Local thermal non-equilibrium in porous medium convection. In: Ingham DB, Pop I (eds) Transport phenomena in porous media III. Pergamon Press, Oxford, pp 147–173CrossRefGoogle Scholar
  16. 16.
    Shenoy AV (1994) Non-Newtonian fluid heat transfer in porous media. Adv Heat Transf 24:102–191Google Scholar
  17. 17.
    Straughan B (2008) Stability and wave motion in porous media. Springer, New YorkzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Industrial EngineeringAlma Mater Studiorum Università di BolognaBolognaItaly

Personalised recommendations