Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-10T08:51:19.520Z Has data issue: false hasContentIssue false
  • English
  • Français

Stability of reactive interfaces in saturated porous media under gravity in the presence of transverse flows

Published online by Cambridge University Press:  16 February 2012

S. H. Hejazi  and
J. Azaiez
S. H. Hejazi
Affiliation:
Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, Calgary, Alberta, T2N 1N4, Canada
J. Azaiez*
Affiliation:
Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, Calgary, Alberta, T2N 1N4, Canada
*
†Email address for correspondence: azaiez@ucalgary.ca
Get access Rights & Permissions [Opens in a new window]

Abstract

The stability of a horizontal interface between a solution of reactant on top of another solution of reactant is analysed. A chemical product is generated at the interface as a result of a bimolecular chemical reaction . In general, all chemical components are assumed to have different densities and viscosities, and a transverse velocity is introduced parallel to the interface between the reactants. Although the transverse flow is known for its stabilizing effect in viscously unstable non-reactive systems in the presence of an injection velocity, it is shown here that it can actually destabilize an initially stable reactive front. An expression for the critical transverse velocity beyond which an initially stable interface is destabilized is derived in the case of an initial sharp interface for reactants of the same viscosity. The analysis is extended to a diffused profile, and purely buoyancy-driven flows are analysed first in the absence of viscosity contrast and then in the presence of transverse flows and viscosity contrast. Various possible density fingering scenarios are determined based on the relative contribution of each chemical component to the density profile. It is found that the chemical reaction can destabilize a buoyancy-stable initial interface by generating a non-monotonic density profile. Unlike the viscous fingering of a reactive interface, a symmetry in the stability characteristics with respect to density increase or decrease by chemical reaction product is observed in the case of chemically buoyancy-driven flows for identical reactants.

JFM classification

Interfacial Flows (free surface): Fingering instability Low-Reynolds-number flows: Hele-Shaw flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 695 , 25 March 2012 , pp. 439 - 466
Copyright
Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Almarcha, C., Trevelyan, P. M. J., Grosfils, P. & De Wit, A. 2010 Chemically driven hydrodynamic instabilities. Phys. Rev. Lett. 104 (4), 044501.CrossRefGoogle ScholarPubMed
2. Bacri, C., Salin, D. & Yortsos, Y. 1992 Analyse linéaire de la stabilité de l’écoulement de fluides miscibles en milieux poreux. C. R. Acad. Sci. Paris 314, 139–144.Google Scholar
3. Chomaz, J. M. 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357–392.Google Scholar
4. Cornell, S., Koza, Z. & Droz, M. 1995 Dynamic multiscaling of the reaction–diffusion front for . Phys. Rev. E 52 (4)3500–5.Google Scholar
5. Cross, M. & Hohenberg, P. C. 1993 Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851–1112.CrossRefGoogle Scholar
6. Ennis-King, J. & Paterson, L. 2007 Coupling of geochemical reactions and convective mixing in the long-term geological storage of carbon dioxide. Intl J. Greenh. Gas Control 1 (1), 86–93.Google Scholar
7. Galfi, L. & Racz, Z. 1988 Properties of the reaction front in an type reaction–diffusion process. Phys. Rev. A 38 (6), 3151–3154.Google Scholar
8. Gérard, T. & De Wit, A. 2009 Miscible viscous fingering induced by a simple chemical reaction. Phys. Rev. E 79 (1), 016308.Google Scholar
9. Hejazi, S. H. & Azaiez, J. 2010a Nonlinear interactions of dynamic reactive interfaces in porous media. Chem. Engng Sci. 65 (2), 938–949.Google Scholar
10. Hejazi, S. H. & Azaiez, J. 2010b Hydrodynamic instability in the transport of miscible reactive slices through porous media. Phys. Rev. E 81, 056321.Google Scholar
11. Hejazi, S. H., Trevelyan, P. M. J., Azaiez, J. & De Wit, A. 2010 Viscous fingering of a miscible reactive interface: a linear stability analysis. J. Fluid Mech. 652, 501–528.CrossRefGoogle Scholar
12. Hill, S. 1952 Channeling in packed columns. Chem. Engng Sci. 1 (6), 247–253.CrossRefGoogle Scholar
13. Homsy, G. M. 1987 Viscous fingering in porous media. Annu. Rev. Fluid Mech. 19, 271–311.Google Scholar
14. Jiang, Z. & Ebner, C. 1990 Simulation study of reaction fronts. Phys. Rev. A 42 (12), 7483–7486.CrossRefGoogle ScholarPubMed
15. Koza, Z. 1996 The long-time behaviour of initially separated reaction–diffusion systems with arbitrary diffusion constants. J. Stat. Phys. 85 (1–2), 179–191.CrossRefGoogle Scholar
16. Manickam, O. & Homsy, G. M. 1995 Fingering instabilities in vertical miscible displacement flows in porous media. J. Fluid Mech. 288, 75–102.CrossRefGoogle Scholar
17. McCloud, K. V. & Maher, J. V. 1995 Experimental perturbations to Saffman–Taylor flow. Phys. Rep. 260 (3), 139–185.CrossRefGoogle Scholar
18. Nagatsu, Y., Bae, S., Kato, Y. & Tada, Y. 2008 Miscible viscous fingering with a chemical reaction involving precipitation. Phys. Rev. E 77, 067302.Google Scholar
19. Nagatsu, Y., Kondo, Y., Kato, Y. & Tada, Y. 2009 Effects of moderate Damköhler number on miscible viscous fingering involving viscosity decrease due to a chemical reaction. J. Fluid Mech. 625, 97–124.Google Scholar
20. Nagatsu, Y., Matsuda, K., Kato, Y. & Tada, Y. 2007 Experimental study on miscible viscous fingering involving viscosity changes induced by variations in chemical species concentrations due to chemical reactions. J. Fluid Mech. 571, 475–493.Google Scholar
21. Nield, D. A. & Barletta, A. 2010 Extended Oberbeck–Boussinesq approximation study of convective instabilities in a porous layer with horizontal flow and bottom heating. Int. J. Heat Mass Transfer 53 (4), 577–585.CrossRefGoogle Scholar
22. Podgorski, T., Sostarecz, M. C., Zorman, S. & Belmonte, A. 2007 Fingering instabilities of a reactive micellar interface. Phys. Rev. E 76, 016202.Google Scholar
23. Prats, M. 1966 Effect of horizontal fluid flow on thermally induced convection currents in porous media. J. Geophys. Res. 71 (20), 4835–4839.Google Scholar
24. Rogerson, A. & Meiburg, E. 1993a Shear stabilization of miscible displacement processes in porous media. Phys. Fluids A 5 (6), 1344–1355.Google Scholar
25. Rogerson, A. & Meiburg, E. 1993b Numerical simulation of miscible displacement processes in porous media flows under gravity. Phys. Fluids A 5 (11), 2644–2660.CrossRefGoogle Scholar
26. Rongy, L., Trevelyan, P. M. J. & De Wit, A. 2008 Dynamics of reaction fronts in the presence of buoyancy-driven convection. Phys. Rev. Lett. 101 (8), 084503.CrossRefGoogle Scholar
27. Saffman, P. G. & Taylor, G. 1958 The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc. R. Soc. Lond. A 245 (1242), 312–329.Google Scholar
28. Selvam, B., Talon, L., Lesshafft, L. & Meiburg, E. 2009 Convective/absolute instability in miscible core–annular flow. Part 2. Numerical simulations and nonlinear global modes. J. Fluid Mech. 618, 323–348.Google Scholar
29. Slobod, R. L. & Caudle, B. H. 1952 X-ray shadowgrath studies of areal sweepout efficiencies. Trans. Am. Inst. Mining Met. Engrs 195, 265–270.Google Scholar
30. Tan, C. T. & Homsy, G. M. 1986 Stability of miscible displacements in porous media: rectilinear flow. Phys. Fluids 29 (11), 3549–3556.Google Scholar
31. Trevelyan, P. M. J. 2009 Higher-order large-time asymptotics for a reaction of the form . Phys. Rev. E 79 (1), 1–10.Google Scholar