Traveling wave solutions for non-Newtonian foam flow in porous media

The injection and in-situ generation of foam in porous media successfully control gas mobility and improve the fluids' sweep efficiency inside porous media. Mathematical models describing this problem use two phases, foamed gas and fluid, and usually have a term for foam generation and destruction. Moreover, the non-Newtonian foam behavior is frequently modeled using the Hirasaki and Lawson's formula for foamed gas viscosity. In this paper, we detail how the traveling wave analysis can be used to estimate the propagation profiles and velocity for a range of non-Newtonian foam models in porous media at constant total superficial flow velocity. We reformulate Hirasaki and Lawson's formula in an explicit form allowing us to find traveling wave solutions for the non-Newtonian Linear Kinetic model. Comparing the solution with the one for the Newtonian version, allows us to analyze qualitatively and quantitatively the rheology of the foam flow in porous media.Comment: 20 pages, 7 figure

Numerical Validation of Analytical Estimates for Propagation of Thermal Waves Generated by Gas-Solid Combustion

Gas-solid combustion appears in many applications such as in situ combustion, which is a potential technique for oil recovery. Previous work has analyzed traveling wave solutions and obtained analytical formulas describing combustion wave temperature, velocity, and gas velocity for one-dimensional gas-solid combustion model using geometrical singular perturbation theory. In the present work these formulas are generalized. Using numerical simulation we show that they can be adapted and then applied to describe more general two-dimensional models for in situ combustion in a nonhomogeneous porous medium

NUMERICAL SIMULATION OF AN IN-SITU COMBUSTION MODEL FORMULATED AS MIXED COMPLEMENTARITY PROBLEM

The difficulty of the extraction of medium and heavy oil is its hight viscosity. One form of decreasing it consists in applying the thermal methods as steam injection or in-situ combustion. In the present work one simple model for in-situ combustion is presented. It consists of two nonlinear partial differential equations. As obtaining the analytical solutions for this type of equation is near impossible, it is necessary to make computational simulations. In fact, the solutions for in-situ combustion problem involves shock waves, which increases the difficulty of the numerical simulations. A possible way to avoid this problem is to rewrite the differential equations as one mixed nonlinear complementarity problem. In this work numerical simulations are performed using the finite difference method and a feasible directions algorithm for mixed nonlinear complementarity problem to obtain approximate solutions of the proposed model. The results are compared with ones obtained by using the Newton’s method that was used in other references

Numerical modeling of mosquito population dynamics of Aedes aegypti

Abstract Background The 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. Methods The 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). Results Invasion 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. Conclusions The 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

Additional file 1: of Numerical modeling of mosquito population dynamics of Aedes aegypti

Figure S1. An enlarged view of the center of Juiz de Fora and its surroundings. The figure shows the surroundings of the city of Juiz de Fora (Source: Google Maps). The area marked on the map (red) is shown in Fig. 2a. (DOCX 1963 kb

Additional file 2: of Numerical modeling of mosquito population dynamics of Aedes aegypti

Figure S2. An enlarged view of Copacabana in Rio de Janeiro and its surroundings. The figure shows the surroundings of the Copacabana Beach, Rio de Janeiro (Source: Google Maps). The area marked on the map (red) is shown in Fig. 3a. (DOCX 656 kb

Down-Hole Electromagnetic Heating of Deep Aquifers for Renewable Energy Storage

Electromagnetic (EM) heating is an emerging method for storing renewable energy, such as photovoltaic solar and wind electric power, into aquifers. We investigate how the captured energy increases the temperature of a prototypical deep aquifer for a six-month period and then to which extent the stored energy can be recovered during the consecutive six months. Water injected at a constant flow rate is simultaneously heated using a high-frequency electromagnetic microwave emitter operating at the water natural resonance frequency of 2.45 GHz. The coupled reservoir flow and EM heating are described using Darcy’s and the energy balance equations. The latter includes a source term accounting for the EM wave propagation and absorption, modeled separately using Maxwell’s equations. The equations are solved numerically by the Galerkin least-squares finite element method. The approach was validated using EM-heating input data obtained from controlled laboratory experiments and then was applied to the aquifer. We found that after six years of alternate storage and recovery, up to 77% of the injected energy is recovered when considering realistic heat losses estimated from field data. Even when heat losses are increased by a factor of two, up to 69% of the injected energy is recovered in this case. This shows that down-hole EM heating is a highly effective method for storing renewable energies, capable of helping to solve their inherent intermittency.Petroleum Engineerin

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 formulaeGeoscience & EngineeringCivil Engineering and Geoscience