Asymptotic approximation of long time solution for low temperature filtration combustion
Johannes Bruining | Chapiro, Grigori | Mailybaev, Alexei | de Souza , Aparecido | Marchesin, Dan
Filtration combustion | traveling wave | Singular perturbation | Low temperature oxidation | Asymptotic expansions
There is renewed interest using combustion for the recovery of medium viscosity oil. We consider the combustion process when air in 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. For applications in the field this assumption may fail due to low-temperature oxidation reactions, which are relatively fast at low temperatures, as well as due to very small heat losses. 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 profiles appears to be different from wave profiles analyzed in other papers, where only the reaction at highest temperatures was taken into account. The combustion wave has a long decaying tail in the field, but not in the laboratory. This is so because heat losses must be very small for the long tail to form. Numerical simulations were performed in order to validate our asymptotic formulae.