Computational Geosciences

, Volume 16, Issue 3, pp 799–808 | Cite as

Asymptotic approximation of long-time solution for low-temperature filtration combustion

  • Grigori Chapiro
  • Alexei A. Mailybaev
  • Aparecido J. de Souza
  • Dan Marchesin
  • Johannes Bruining
Original Paper


There is a renewed interest in using combustion for the recovery of medium viscosity oil. We consider the combustion process when air is injected into the porous medium containing some fuel and inert gas. Commonly the reaction rate is negligible at low temperatures, hence the possibility of oxygen breakthrough. In this case, the oxygen gets in contact with the fuel in the downstream zone leading to slow reaction. We focus on the case when the reaction is active for all temperatures, but heat losses are negligible. For a combustion model that includes heat and mass balance equations, we develop a method for calculating the wave profile in the form of an asymptotic expansion and derive its zero- and first-order approximations. This wave profile appears to be different from wave profiles analyzed in other papers, where only the reaction at the highest temperatures was taken into account. The combustion wave has a long decaying tail. This tail is hard to observe in the laboratory because heat losses must be very small for the long tail to form. Numerical simulations were performed in order to validate our asymptotic formulae.


Filtration combustion Traveling wave Singular perturbation Low-temperature oxidation Asymptotic expansions 

Mathematics Subject Classifications (2010)

80A25 76S05 


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Grigori Chapiro
    • 1
  • Alexei A. Mailybaev
    • 2
    • 3
  • Aparecido J. de Souza
    • 4
  • Dan Marchesin
    • 2
  • Johannes Bruining
    • 5
  1. 1.UFJFJuiz de ForaBrazil
  2. 2.IMPARio de JaneiroBrazil
  3. 3.Moscow State UniversityMoscowRussia
  4. 4.UFCGCampina GrandeBrazil
  5. 5.TU DelftDelftthe Netherlands

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