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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.

BackgroundThe global incidences of dengue virus have increased the interest in studying and understanding the mosquito population dynamics. It is predominantly spread by Aedes aegypti in the tropical and sub-tropical countries in the world. Understanding these dynamics is important for public health in countries where climatic and environmental conditions are favorable for the propagation of these diseases. For this reason, a new model has been proposed to investigate the population dynamics of mosquitoes in a city.MethodsThe present paper discusses the numerical modeling of population dynamics of Ae. aegypti mosquitoes in an urban neighborhood of a city using the finite volume method. The model describes how populations spread through the city assisted by the wind. This model allows incorporating external factors (wind and chemical insecticides) and topography data (streets, building blocks, parks, forests and beach). The proposed model has been successfully tested in examples involving two Brazilian cities (City center, Juiz de Fora and Copacabana Beach, Rio de Janeiro).ResultsInvasion phenomena of Ae. aegypti mosquitoes have been observed in each of the simulations. It was observed that, inside the blocks, the growth of the population for both winged and aquatic phase causes an infestation of Ae. aegypti in a short time. Within the blocks the mosquito population was concentrated and diffused slowly. In the streets, there was a long-distance spread, which was influenced by wind and diffusion with a low concentration of mosquito population. The model was also tested taking into account chemical insecticides spread in two different configurations. It has been observed that the insecticides have a significant effect on the mosquito population for both winged and aquatic phases when the chemical insecticides spread more uniformly along all the streets in a neighborhood of a city.ConclusionsThe presented methodology can be employed to evaluate and to understand the epidemic risks in a specific region of the city. Moreover the model allows an increase in efficiency of the existing mosquito population control techniques and to theoretically test new methods before involving the human population.Electronic supplementary materialThe online version of this article (10.1186/s13071-018-2829-1) contains supplementary material, which is available to authorized users.

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