A produção de petróleo no pré-sal pode ser associada a contaminantes como o CO2. As plataformas instaladas neste polo possuem o sistema de remoção de CO2 usando permeação em membrana polimérica, que separa a corrente de gás em uma pobre em CO2 e outra rica neste. Este trabalho propõe um modelo para simulação da separação de gases utilizando permeador de gases do tipo espiral em contra-corrente. Este modelo utiliza equações baseadas em fenômenos de transporte e termodinâmica, tais como: comportamento real dos gases, variação da permeância com temperatura, transferência de calor dentro do equipamento e efeito Joule-Thomson. A validação foi feita utilizando dados da literatura para separações isotérmicas e dados obtidos em permeador instalado em plataforma de petróleo. Utilizou-se metodologia de reconciliação de dados e agrupamento para tratamento dos dados industriais, o que permitiu maior eficiência na reconciliação dos parâmetros do modelo. A partir da modelagem proposta determinaram-se os parâmetros de processos mais relevantes, permitindo a simulação de condições operacionais diferentes das utilizadas na regressão e a verificação da influência da variação de cada uma das condições operacionais. / The production of oil in pre-salt field is associated with contaminants such as CO2. The rigs installed in this field have a CO2 removal system using permeation on polymer membrane, which separates the gas stream in a stream with low CO2 content and another one with high CO2 content. This paper proposes a model for simulation of gas separation using spiral type permeator of gases in countercurrent flow. This model uses equations based on transport and thermodynamic phenomena such as: real behavior of gases, permeance dependence with temperature, heat transfer inside the equipment and Joule-Thomson effect. The validation was performed using literature data for isothermal separations and data from permeator installed on the oil rig. Was used data reconciliation methodology and clusterization for treatment of industrial data, allowing more efficient reconciliation of the model parameters. From the proposed model were determined the most relevant process parameters, allowing the simulation of operating conditions different than those used in the regression and verification of the influence of the change of each of the operating conditions.

Dans divers domaines de la physique, certains phénomènes sont modélisés par des systèmes hyperboliques non-conservatifs. En particulier, dans le domaine de la physique des plasmas, dont l'un des champs d'application majeur est la Fusion par Confinement Inertiel, le système d'Euler bi-température, modélisant les phénomènes de transport de particules chargées, en est un exemple. La difficulté de l'étude de ces systèmes réside dans la présence de termes non-conservatifs, qui empêchent la définition classique des solutions faibles. Pour parvenir à une définition de ce type de solutions, on a recours à l'emploi de systèmes cinétiques sous-jacents. Dans ce manuscrit, on s'intéresse à l'étude numérique de ces systèmes cinétiques pour la résolution du système d'Euler bi-température.Ce manuscrit se divise en deux parties. La première partie contient l'étude numérique du système d'Euler bi-température. Dans un premier chapitre, on résout numériquement les équations en dimension 1 d'espace par le biais d'un système sous-jacent issu de la physique des plasmas: le système de Vlasov-BGK-Ampère. On présente une méthode numérique préservant l'asymptotique pour ce système sous-jacent et on montre, par des simulations numériques, que le schéma limite obtenu donne des résultats consistants avec Euler bi-température. Dans un second chapitre, on résout le même modèle en dimension 2 d'espace par un système sous-jacent de type BGK discret. On démontre une inégalité d'entropie pour les solutions issues du modèle sous-jacent, ainsi qu'une inégalité discrète de dissipation d'entropie pour le schéma.Dans la deuxième partie de ce manuscrit, on s'intéresse au développement de méthodes numériques pour quelques modèles cinétiques. On considère ici le cas des écoulements raréfiés de mélanges de gaz, dans l'optique d'une application aux cas des plasmas. Premièrement, on présente un schéma cinétique adaptatif et dynamique en vitesse pour les gaz inertes. Par l'emploi de lois de conservation discrètes, la solution est approchée sur un ensemble de vitesses discrètes local et dynamique. Dans un second temps, on propose une extension de cette méthode visant à améliorer les performances de celle-ci. Puis, ces deux versions de la méthode sont comparées à la méthode classique sur grille fixe uniforme sur une série de cas tests.Enfin, dans le dernier chapitre, on propose une méthode numérique pour la résolution d'une extension de ces équations, prenant en compte la présence de réactions chimiques au sein du mélange. Le contexte considéré est celui des réactions chimiques bi-moléculaires réversibles lentes. La méthode proposée, de type implicite-explicite, est linéaire, stable et conservative. / In various domains of physics, several phenomena can be modeled via the use of nonconservative hyperbolic systems. In particular, in plasma physics, in the process of developping and understanding the phenomena leading to Inertial Confinement Fusion, the bi-temperature Euler sytem can be used to model particle transport phenomena in a plasma. The difficulty of the mathematical study of such systems dwells in the presence of so-called non-conservative products, which prevent the classical definition of weak solutions via distribution theory. To attempt to define these quantities, it is useful to supplement the hyperbolic system with an underlying kinetic model. In this work, the objective is the numerical study of such kinetic systems in order to solve the bi-temperature Euler system.This manuscript is split in two parts. The first one contains the study of the bi-temperature Euler system. In the first chapter, this system in dimension 1 is solved by the use of an underlying kinetic model sprung from plasma physics: the Vlasov-BGK-Ampère system. An asymptotic-preserving numerical method is introduced, and it is shown that the scheme obtained in the limit is consistant with a scheme for teh bi-temperature Euler system. In the following chapter, the same hyperbolic model in dimension 2 is studied, this time via a discrete-BGK type underlying model. An entropy inequality is proved for solutions coming from the kinetic model, as well as a discrete entropy dissipation inequality.In the second part of the manuscript, we are interested in the development of numerical schemes for gas mixture rarefied flows. Firstly, an adaptive kinetic scheme is introduced for inert gas mixtures. By the use of discrete conservation laws, the solution is approximated on a set of discrete velocities that depends on space, time and species. Secondly, an extension of the method is proposed in order to improve the efficiency of the first method. Finally, the two methods are compared to the classical fixed grid method on a series of test cases.In the last chapter, a numerical method is proposed for rarefied flows of reacting mixtures. The setting considered is the case of slow bimolecular reversible chemical reactions. The method introduced is an explicit-implicit treatment of the relaxation operator, which is shown to be stable, linear and conservative.

A produção de petróleo no pré-sal pode ser associada a contaminantes como o CO2. As plataformas instaladas neste polo possuem o sistema de remoção de CO2 usando permeação em membrana polimérica, que separa a corrente de gás em uma pobre em CO2 e outra rica neste. Este trabalho propõe um modelo para simulação da separação de gases utilizando permeador de gases do tipo espiral em contra-corrente. Este modelo utiliza equações baseadas em fenômenos de transporte e termodinâmica, tais como: comportamento real dos gases, variação da permeância com temperatura, transferência de calor dentro do equipamento e efeito Joule-Thomson. A validação foi feita utilizando dados da literatura para separações isotérmicas e dados obtidos em permeador instalado em plataforma de petróleo. Utilizou-se metodologia de reconciliação de dados e agrupamento para tratamento dos dados industriais, o que permitiu maior eficiência na reconciliação dos parâmetros do modelo. A partir da modelagem proposta determinaram-se os parâmetros de processos mais relevantes, permitindo a simulação de condições operacionais diferentes das utilizadas na regressão e a verificação da influência da variação de cada uma das condições operacionais. / The production of oil in pre-salt field is associated with contaminants such as CO2. The rigs installed in this field have a CO2 removal system using permeation on polymer membrane, which separates the gas stream in a stream with low CO2 content and another one with high CO2 content. This paper proposes a model for simulation of gas separation using spiral type permeator of gases in countercurrent flow. This model uses equations based on transport and thermodynamic phenomena such as: real behavior of gases, permeance dependence with temperature, heat transfer inside the equipment and Joule-Thomson effect. The validation was performed using literature data for isothermal separations and data from permeator installed on the oil rig. Was used data reconciliation methodology and clusterization for treatment of industrial data, allowing more efficient reconciliation of the model parameters. From the proposed model were determined the most relevant process parameters, allowing the simulation of operating conditions different than those used in the regression and verification of the influence of the change of each of the operating conditions.

Clean post-discharge nitrogen plasma and nitrogen plasma with different traces have been focus of scientists for more than 50 years and there were published many articles on theme active discharge, post-discharge, processes and reactions. It is possible to create kinetic models from all these information and then calculate concentrations of elements in atomic form. This diploma thesis is focused on measuring of concentration of atomic nitrogen for different conditions (decay time, pressure, admixture). The titration method by nitric oxide in post-discharge was used to determinate of concentration of atomic nitrogen. All experimental results were obtained by the optical emission spectroscopy. Optical emission spectra were taken in the range of 300-600 nm. DC discharge was created in a quartz tube in a flowing regime. The flowing regime was chosen for this experiment because of better time resolution of decay time, order in milliseconds. Decay time was in the range of 16 – 82 ms for individual experiments. Nitrogen flow was 400 mln/min. Nitrogen oxide flow was in the range of 0-10 mln/min and it was added at the selected post-discharge time. Trace of methane was 0,006 % of the whole volume. Total gas pressure was set on values from 500 to 4000 Pa. The output of discharge was set on constant value of current 150 mA and the output has changed according to the amount of pressure. Nitrogen first positive, second positive and first negative spectral systems, NO spectral system and NO2* spectral system were recognized in all measured spectra. Absolute concentration of atomic nitrogen was specified by the method of titration of NO. Traces of methane increase dissociation of molecular nitrogen and therefore increase the concentration of atomic nitrogen. This thesis brings new results into longtime research of moon Titan and new results into study of processes in nitrogen-methane plasma.