Asymptotic approximation of long-time solution for low-temperature filtration combustion |
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Authors: | Grigori Chapiro Alexei A Mailybaev Aparecido J de Souza Dan Marchesin Johannes Bruining |
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Institution: | 1.UFJF,Juiz de Fora,Brazil;2.IMPA,Rio de Janeiro,Brazil;3.Moscow State University,Moscow,Russia;4.UFCG,Campina Grande,Brazil;5.TU Delft,Delft,the Netherlands |
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Abstract: | 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. |
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