Advertisement

Viscous Fingering of Reversible Reactive Flows in Porous Media

  • Hesham Alhumade
  • Jalel Azaiez
Conference paper

Abstract

The dynamics of viscous fingering instability of miscible displacements in a homogeneous porous medium are examined in the case of flows that involve reversible chemical reactions between the displacing and displaced fluid. The flows are modeled using the continuity equation, Darcy’s law, and volume-averaged forms of the convection-diffusion-reaction equation for mass balance of a bi-molecular reaction. Numerical simulations were carried out using a Hartley transform based pseudo-spectral method combined with semi-implicit finite-difference time-stepping algorithm. The results of the simulations allowed to analyze the mechanisms of fingering instability that result from the dependence of the fluids viscosities on the concentrations of the different species, and focused on different flow scenarios. In particular, the study examined the effects of varying important parameters namely the Damkohler number that represents the ratio of the hydrodynamic and chemical characteristic time scales, and the chemical reversibility coefficient, and analyzed the resulting changes in the finger structures. The results are presented for flows with an initially stable as well as initially unstable front between the two reactants.

Keywords

Fluid mechanics Homogeneous porous media Hydrodynamics Miscible displacements Reversible chemical reaction Stability Viscous fingering 

Notes

Acknowledgements

H. Alhumade acknowledges financial support from the Ministry of higher education in Saudi Arabia. The authors would like also to acknowledge WestGrid for providing computational resources.

References

  1. 1.
    H. Alhumade, J. Azaiez, In: Reversible reactive flow displacements in homogeneous porous media, Lecture Notes in Engineering and Computer Science: Proceedings of The World Congress on Engineering 2013, WCE 2013, 3–5 July, 2013, London, pp. 1681–1686Google Scholar
  2. 2.
    H. Alhumade, J. Azaiez, Stability analysis of reversible reactive flow displacements in porous media. Chem. Eng. Sci. 101, 46–55 (2013)CrossRefGoogle Scholar
  3. 3.
    T. Bansagi, D. Horvath, A. Toth, Nonlinear interactions in the density fingering of an acidity front. J. Chem. Phys. 121, 11912–11915 (2004)CrossRefGoogle Scholar
  4. 4.
    R.N. Bracewell, The Fourier Transform and its Applications, 2nd edn. (McGraw Hill, New York, 2000)Google Scholar
  5. 5.
    B. Chopard, M. Droz, T. Karapiperis, Z. Racz, Properties of the reaction front in a reversible reaction-diffusion process. Phys. Rev. E 47, R40–R43 (1993). Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary TopicsCrossRefGoogle Scholar
  6. 6.
    A. De Wit, G.M. Homsy, Nonlinear interactions of chemical reactions and viscous fingering in porous media. Phys. Fluids 11, 949–951 (1999)CrossRefMATHGoogle Scholar
  7. 7.
    A. De Wit, G.M. Homsy, Viscous fingering in reaction-diffusion systems. J. Chem. Phys. 110, 8663–8675 (1999)CrossRefGoogle Scholar
  8. 8.
    K. Ghesmat, J. Azaiez, Miscible displacements of reactive and anisotropic dispersive flows in porous media. Tran. Porous Med. 77, 489–506 (2009)CrossRefGoogle Scholar
  9. 9.
    S. Havlin, D. Ben-Avraham, Diffusion in disordered media. Adv. Phys. 51, 187–292 (2002)CrossRefGoogle Scholar
  10. 10.
    S.H. Hejazi, J. Azaiez, Nonlinear interactions of dynamic reactive interfaces in porous media. Chem. Eng. Sci. 65, 938–949 (2010)CrossRefGoogle Scholar
  11. 11.
    G.M. Homsy, Viscous Fingering in Porous Media. Ann. Rev. Fluid Mech. 19, 271–311 (1987)CrossRefGoogle Scholar
  12. 12.
    D. Horvath, T. Bansagi, A. Toth, Orientation-dependent density fingering in an acidity front. J. Chem. Phys. 117, 4399–4402 (2002)CrossRefGoogle Scholar
  13. 13.
    M.N. Islam, J. Azaiez, Fully implicit finite difference pseudo-spectral method for simulating high mobility-ratio miscible displacements. Int. J. Num. Meth. Fluids 47, 161–183 (2005)CrossRefMATHGoogle Scholar
  14. 14.
    K.V. McCloud, J.V. Maher, Experimental perturbations to Saffman–Taylor flow. Phys. Rep. 260, 139–185 (1995)CrossRefGoogle Scholar
  15. 15.
    M. Mishra, M. Martin, A. de Wit, Miscible viscous fingering with linear adsorption on the porous matrix. Phys. Fluids 19, 1–9 (2007)CrossRefGoogle Scholar
  16. 16.
    Y. Nagatsu, T. Ueda, Effects of reactant concentrations on reactive miscible viscous fingering. Fluid. Mech. Trans. Phen. 47, 1711–1720 (2001)Google Scholar
  17. 17.
    Y. Nagatsu, T. Ueda, Effects of finger-growth velocity on reactive miscible viscous fingering. AIChE J. 49, 789–792 (2003)CrossRefGoogle Scholar
  18. 18.
    Y. Nagatsu, S. Bae, Y. Kato, Y. Tada, Miscible viscous fingering with a chemical reaction involving precipitation. Phys. Rev. E: Stat., Nonlin., Soft Matter Phys. 77, 1–4 (2008)CrossRefGoogle Scholar
  19. 19.
    H. Nasr-El-Din, K. Khulbe, V. Hornof, G. Neale, Effects of interfacial reaction on the radial displacement of oil by alkaline solutions. Revue—Institut Francais du Petrole 45, 231–244 (1990)CrossRefGoogle Scholar
  20. 20.
    T. Rica, D. Horvath, A. Toth, Density fingering in acidity fronts: Effect of viscosity. Chem. Phys. Lett. 408, 422–425 (2005)CrossRefGoogle Scholar
  21. 21.
    P. Saffman, G. Taylor, The penetration of a fluid into a porous medium or hele-shaw cell containing a more viscous liquid. Proc. R. Soc. Lond. A 245, 312–329 (1958)CrossRefMATHMathSciNetGoogle Scholar
  22. 22.
    M. Sinder, V. Sokolovsky, J. Pelleg, Reversible reaction diffusion process with initially mixed reactants: Boundary layer function approach. Phys. B: Condens. Matter 406, 3042–3049 (2011)CrossRefGoogle Scholar
  23. 23.
    M. Sinder, H. Taitelbaum, J. Pelleg, Reversible and irreversible reaction fronts in two competing reactions system. Nucl. Instrum. Methods Phys. Res. Sect. B 186, 161–165 (2002)CrossRefGoogle Scholar
  24. 24.
    C. Tan, G. Homsy, Simulation of nonlinear viscous fingering in miscible displacement. Phys. Fluids 31, 1330–1338 (1998)CrossRefGoogle Scholar
  25. 25.
    A. Zadrazil, I. Kiss, J. D’Hernoncourt, H. Sevcikova, J. Merkin, A. De Wit, Effects of constant electric fields on the buoyant stability of reaction fronts. Phys. Rev. E 71, 1–11 (2005)CrossRefGoogle Scholar
  26. 26.
    W. Zhang, Nanoscale iron particles for environmental remediation: An overview. J. Nanopart. Res. 5, 323–332 (2003)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.University of WaterlooWaterlooCanada
  2. 2.University of CalgaryCalgaryCanada

Personalised recommendations