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Reactive Flows in Porous Media: The Reaction-Infiltration Instability

  • John Chadam
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 114)

Abstract

In this note we summarize some recent results of reactive flows in porous media for which the fluid/solid reaction can increase the porosity/permeability of the medium. The phenomenon is modelled by a coupled system of nonlinear ordinary and partial differential equations for which a global existence and uniqueness theorem is stated. As a physically relevant parameter tends to zero the problem converges to a moving free boundary problem. The shape stability of planar reaction interfaces is discussed in this context using local bifurcation analysis. Numerical results are presented to show the complexity of the possible evolving reaction interfaces.

Keywords

Reaction Interface Global Existence Reactive Flow Reactive Fluid Porosity Change 
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References

  1. [1]
    Chadam J., Hettmer J., Merino E., Moore C., Ortoleva P. Geochemical self-organization I: Feedback mechanisms and modelling approach. Amer. J. Sci., 287:977–1007, 1987.Google Scholar
  2. [2]
    Chadam J., Merino E., Ortoleva P., Sen A. Self-organization in water-rock inter-action systems II: The reaction-infiltrate instability. Amer. J. Sci., 287:1008–1040, 1987.CrossRefGoogle Scholar
  3. [3]
    Chadam J., Ortoleva P., Peirce A. Stability of reactive flows in porous media: Coupled porosity and viscosity changes. SIAM J. Appl. Math., 51:684–692, 1991.CrossRefGoogle Scholar
  4. [4]
    Chadam J., Ortoleva P., Sen A. Reactive percolation instability. IMA J. Appl. Math., 36:207–220, 1987.CrossRefGoogle Scholar
  5. [5]
    Chen W., Ortoleva P. Reaction front fingering in carbonate-cemented sandstones. Earth-Sci. Rev., 29:183–198, 1990.Google Scholar
  6. [6]
    Collet J.-F. Construction of weak solutions in a two-dimensional domain for a problem arising in hydrogeology. PhD thesis, Indiana University, 1992.Google Scholar
  7. [7]
    Saffman P. G., Taylor G.I. The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc. Roy. Soc. London Ser. A, 245:312–329, 1958.CrossRefGoogle Scholar
  8. [8]
    Xin J., Peirce A., Chadam J., Ortoleva P. Reactive flows in layered porous media II. The shape instability of the reaction interface. SIAM J. Appl. Math. To appear.Google Scholar

Copyright information

© Springer Basel AG 1993

Authors and Affiliations

  • John Chadam
    • 1
  1. 1.The Fields InstituteWaterlooCanada

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