Asymptotic approximation of long-time solution for low-temperature filtration combustion
- 145 Downloads
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.
KeywordsFiltration combustion Traveling wave Singular perturbation Low-temperature oxidation Asymptotic expansions
Mathematics Subject Classifications (2010)80A25 76S05
Unable to display preview. Download preview PDF.
- 4.Aldushin, A., Seplyarsky, B.: Propagation of exothermic reaction in a porous-medium during gas blowing. Sov. Phys. Dokl. 23, 483–485 (1978)Google Scholar
- 6.Chapiro, G.: Gas-solid combustion in insulated porous media. Ph.D. thesis, IMPA, http://www.preprint.impa.br (2009)
- 7.Chapiro, G., Hime, G., Mailybaev, A., Marchesin, D., de Souza, A.: Global asymptotic effects of the structure of combustion waves in porous media. In: Hyperbolic Problems: Theory, Numerics, and Applications: Plenary and Invited Talks: Twelfth International Conference on Hyperbolic Problems, 9–13 June 2008, vol. 67, pp. 487–496. AMS (2009)Google Scholar
- 8.Chapiro, G., Mailybaev, A.A., Marchesin, D., Souza, A.: Singular perturbation in combustion waves for gaseous flow in porous media. In: Proceedings of XXVI CILAMCE, 19–21 October. Guarapari, Brazil (2005)Google Scholar
- 9.Chapiro, G., Marchesin, D.: Non-diffusive combustion waves in insulated porous media. BJPG 2(2), 18–28 (2008)Google Scholar
- 11.Freitag, N., Verkoczy, B.: Low-temperature oxidation of oils in terms of SARA fractions: why simple reaction models don’t work. In: Canadian International Petroleum Conference, Calgary, Alberta (2003)Google Scholar
- 18.Wasow, W.: Asymptotic Expansions for Ordinary Differential Equations. Dover, New York (2002)Google Scholar