Grigori Chapiro

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

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.

Combustion waves and Riemann solutions in light porous foam

We prove the existence of traveling waves, and identify the wave sequences appearing in Riemann solutions, for a system of three evolutionary partial differential equations that models combustion of light porous foam under air injection.

Dispersive models describing mosquitoes’ population dynamics

The global incidences of dengue and, more recently, zica virus have increased the interest in studying and understanding the mosquito population dynamics. Understanding this dynamics is important for public health in countries where climatic and environmental conditions are favorable for the propagation of these diseases. This work is based on the study of nonlinear mathematical models dealing with the life cycle of the dengue mosquito using partial differential equations. We investigate the existence of traveling wave solutions using semi-analytical method combining dynamical systems techniques and numerical integration. Obtained solutions are validated through numerical simulations using finite difference schemes.

Numerical Solution of a Class of Moving Boundary Problems with a Nonlinear Complementarity Approach

Parabolic-type problems, involving a variational complementarity formulation, arise in mathematical models of several applications in Engineering, Economy, Biology and different branches of Physics. These kinds of problems present several analytical and numerical difficulties related, for example, to time evolution and a moving boundary. We present a numerical method that employs a global convergent nonlinear complementarity algorithm for solving a discretized problem at each time step. Space discretization was implemented using both the finite difference implicit scheme and the finite element method. This method is robust and efficient. Although the present method is general, at this stage we only apply it to two one-dimensional examples. One of them involves a parabolic partial differential equation that describes oxygen diffusion problem inside one cell. The second one corresponds to a system of nonlinear differential equations describing an in situ combustion model. Both models are rewritten in the quasi-variational form involving moving boundaries. The numerical results show good agreement when compared to direct numerical simulations.

Traveling wave solutions for the dispersive models describing population dynamics of Aedes aegypti

Abstract In recent decades the global incidence of dengue has grown dramatically by increased human mobility and urbanization. The study of the mosquitoes population is of great importance for public health in countries where climatic and environmental conditions are favorable for the propagation of this disease. Therefore, this work is based on the study of mathematical models dealing with the life cycle of the mosquito using partial differential equations. We investigate the existence of traveling wave solutions using semi-analytical method combining dynamical systems techniques and numerical integration. Obtained solutions are validated through direct numerical simulations using finite difference schemes. We also present initial study concerning structural stability of traveling wave solution.

Asymptotic approximation for counterflow combustion in porous media

Air injection and in situ combustion have long been considered as potential techniques for displacement and recovery of medium and heavy oil. They utilize heavy and immobile oil components as fuel producing heat and improving the recovery of upgraded crude oil. We consider a porous rock cylinder with a homogeneously distributed solid fuel, initially filled with air that is injected at constant rate on the left end of the cylinder. We assume that combustion starts at the production end and propagates upstream toward the injection end. A bimolecular reaction is assumed to take place between the injected oxygen and the solid fuel; hence, the region of reaction behaves as a source of heat as well as a sink for the oxygen and the fuel. We neglect air compressibility and heat losses. Assuming that the combustion front has a traveling wave profile, we analyze the possible wave sequences present for the counterflow combustion. Besides the analysis of the wave sequences, we apply the asymptotic expansion technique for ordinary differential equations to approximate the traveling wave profile of the combustion front. We perform numerical simulations to validate this approximation.

Analytical Study of In-situ Combustion in a Wet Porous Medium

There is a renewed interest in using combustion for the recovery of medium viscosity oil. In-situ combustion is commonly divided into zones according to the main processes occurring inside. In the downstream order they are combustion, coke, cracking, steam and light hydro-carbon zones. In this analytical study the cracking reaction and the light hydro-carbon vaporization process are neglected for simplicity. We take into account the reaction occurring between the residual petroleum coke and the oxygen contained in the injected air. We also assume the presence of small amount of immobile liquid phase, which can vaporize; this feature is useful if this study is applied to gasefication of coal containing water.

Numerical modeling of mosquito population dynamics of Aedes aegypti

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.

EM Heating-Stimulated Water Flooding for Medium–Heavy Oil Recovery

We report a study of heavy oil recovery by combined water flooding and electromagnetic (EM) heating at a frequency of 2.45 GHz used in domestic microwave ovens. A mathematical model describing this process was developed. Model equations were solved, and the solution is presented in an integral form for the one-dimensional case. Experiments consisting of water injection into Bentheimer sandstone cores, either fully water saturated or containing a model heavy oil, were also conducted, with and without EM heating. Model prediction was found to be in rather good agreement with experiments. EM energy was efficiently absorbed by water and, under dynamic conditions, was transported deep into the porous medium. The amount of EM energy absorbed increases with water saturation. Oil recovery by water flooding combined with EM heating was up to