Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Atualmente, existem modelos matemáticos capazes de preverem acuradamente as relações entre propriedades de estado; e esta tarefa é extremamente importante no contexto da Engenharia Química, uma vez que estes modelos podem ser empregados para avaliar a performance de processos químicos. Ademais, eles são de fundamental importância para a simulação de reservatórios de petróleo e processos de separação. Estes modelos são conhecidos como equações de estado, e podem ser usados em problemas de equilíbrios de fases, principalmente em equilíbrios líquido-vapor. Recentemente, um teorema matemático foi formulado (Teorema de Redução), fornecendo as condições para a redução de dimensionalidade de problemas de equilíbrios de fases para misturas multicomponentes descritas por equações de estado cúbicas e regras de mistura e combinação clássicas. Este teorema mostra como para uma classe bem definidade de modelos termodinâmicos (equações de estado cúbicas e regras de mistura clássicas), pode-se reduzir a dimensão de vários problemas de equilíbrios de fases. Este método é muito vantajoso para misturas com muitos componentes, promovendo uma redução significativa no tempo de computação e produzindo resultados acurados. Neste trabalho, apresentamos alguns experimentos numéricos com misturas-testes usando a técnica de redução para obter pressões de ponto de orvalho sob especificação de temperaturas. / Nowadays, there are mathematical models capable of predicting accurately the relationships among state properties; and this task is very important in Chemical Engineering context, since these models can be used to evaluate the performance of chemical processes. Moreover, they are of fundamental importance for oil reservoir simulation and separation processes. These models are known as equations of state and can be used in phase equilibrium problems, mainly in vapor-liquid equilibrium. Recently, a mathematical theorem was formulated (Reduction Theorem), which provides the conditions for the reduction in the dimensionality of the phase equilibrium problem for multicomponent mixtures described by cubic equations of state and classical mixing and combination rules. This theorem shows how to a well-defined class of thermodynamic models (cubic equations of state and classical mixing rules), one can reduce the dimensionality of various phase equilibrium problems. This method is very advantageous for mixtures of many components, providing a significant reduction in the computation time and producing accurate results. In this work, we presented some numerical experiments with test-mixtures using the reduction technique to obtain dew point pressures at specified temperatures.

O fator de compressibilidade (Z) de gás natural é utilizado em vários cálculos na engenharia de petróleo (avaliação de formações, perda de carga em tubulações, gradiente de pressão em poços de gás, cálculos de balanço de massa, medição de gás, compressão e processamento de gás). As fontes mais comuns de valores de Z são medições experimentais, caras e demoradas. Essa propriedade também é estimada por correlações empíricas, modelos baseados no princípio dos estados correspondentes ou equações de estado (EOS). Foram avaliadas as capacidades das EOS de Soave-Redlich-Kwong (SRK), Peng-Robinson (PR), Patel-Teja (PT), Patel-Teja-Valderrama (PTV), Schmidt-Wenzel (SW), Lawal-Lake-Silberberg (LLS) e AGA-8 para previsão desta propriedade em aproximadamente 2200 pontos de dados experimentais. Estes pontos foram divididos em quatro grupos: Grupo 1 (Presença de frações C7+, Grupo 2 (temperaturas inferiores a 258,15 K), Grupo 3 (pressões superiores a 10000 kPa) e Grupo 4 (pressões inferiores a 10000 kPa). Os cálculos utilizando as equações de estado sob diferentes esquemas de previsão de coeficientes binários de interação foram cuidadosamente investigados. Os resultados sugerem que a EOS AGA-8 apresenta os menores erros para pressões de até 70000 kPa. Entretanto, observou-se uma tendência de aumento nos desvios médios absolutos em função das concentrações de CO2 e H2S. As EOS PTV e a EOS SW são capazes de predizer o fator de compressibilidade (Z) com desvios médios absolutos entre os valores calculados e experimentais com precisão satisfatória para a maioria das aplicações, para uma variada faixa de temperatura e pressão. Este estudo também apresenta uma avaliação de 224 métodos de cálculo de Z onde foram utilizadas 8 correlações combinadas com 4 regras de mistura para estimativa de temperaturas e pressões pseudorreduzidas das amostras, junto com 7 métodos de caracterização das propriedades críticas da fração C7+, quando presente na composição do gás. Em função dos resultados são sugeridas, para diferentes tipos de sistemas, as melhores combinações de correlações com regras de mistura capazes de predizer fatores de compressibilidade (Z) com os menores erros absolutos médios relativos / The compressibility factor (Z-factor) of natural gases is necessary in many petroleum engineering calculations (evaluation of formation, pressure drop through a pipe, pressure gradient in gas wells, material balance calculations, gas metering, gas compression and processing). The most common sources of Z-factor values are experimental measurements, which are expensive and time consuming. This property is also estimated from empirical correlations, corresponding state models or equations of state (EOS) when experimental data is unavailable. Capabilities of Soave-Redlich-Kwong (SRK), Peng-Robinson (PR), Patel-Teja (PT), Patel-Teja-Valderrama (PTV), Schmidt-Wenzel (SW), Lawal-Lake-Silberberg (LLS) and AGA-8 to predict this property of 2200 data points under various schemes of binary interaction numbers are thoroughly investigated. This database was split on four groups: Group 1 (presence of hydrocarbon plus fraction - C7+), Group 2 (temperatures lower than 258.15 K), Group 3 (pressures higher than 10000 kPa) e Group 4 (pressures lower than 10000 kPa). The best results were obtained from EOS AGA-8 for pressures up to 70000 kPa. However, an increasing trend in average absolute deviations was observed as a function of CO2 e H2S concentrations. EOS PTV and EOS SW are capable to predict the compressibility factor (Z) with average absolute deviation between calculated and experimental values with satisfactory accuracy for most applications for a wide range of temperature and pressure. This study also presents an evaluation of 224 possible methods of calculating the gas compressibility factor, based on 8 correlations and corresponding state models, combined with 4 mixing rule that predict the pseudo-reduced pressure and temperatures of the mixture, that were combined with 7 methods of characterizing the plus fraction critical properties when present in the gas composition. Results suggest for different systems conditions, the best correlation and mixing rule combination capable of predicting Z-factor with the least average absolute relative error

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Atualmente, existem modelos matemáticos capazes de preverem acuradamente as relações entre propriedades de estado; e esta tarefa é extremamente importante no contexto da Engenharia Química, uma vez que estes modelos podem ser empregados para avaliar a performance de processos químicos. Ademais, eles são de fundamental importância para a simulação de reservatórios de petróleo e processos de separação. Estes modelos são conhecidos como equações de estado, e podem ser usados em problemas de equilíbrios de fases, principalmente em equilíbrios líquido-vapor. Recentemente, um teorema matemático foi formulado (Teorema de Redução), fornecendo as condições para a redução de dimensionalidade de problemas de equilíbrios de fases para misturas multicomponentes descritas por equações de estado cúbicas e regras de mistura e combinação clássicas. Este teorema mostra como para uma classe bem definidade de modelos termodinâmicos (equações de estado cúbicas e regras de mistura clássicas), pode-se reduzir a dimensão de vários problemas de equilíbrios de fases. Este método é muito vantajoso para misturas com muitos componentes, promovendo uma redução significativa no tempo de computação e produzindo resultados acurados. Neste trabalho, apresentamos alguns experimentos numéricos com misturas-testes usando a técnica de redução para obter pressões de ponto de orvalho sob especificação de temperaturas. / Nowadays, there are mathematical models capable of predicting accurately the relationships among state properties; and this task is very important in Chemical Engineering context, since these models can be used to evaluate the performance of chemical processes. Moreover, they are of fundamental importance for oil reservoir simulation and separation processes. These models are known as equations of state and can be used in phase equilibrium problems, mainly in vapor-liquid equilibrium. Recently, a mathematical theorem was formulated (Reduction Theorem), which provides the conditions for the reduction in the dimensionality of the phase equilibrium problem for multicomponent mixtures described by cubic equations of state and classical mixing and combination rules. This theorem shows how to a well-defined class of thermodynamic models (cubic equations of state and classical mixing rules), one can reduce the dimensionality of various phase equilibrium problems. This method is very advantageous for mixtures of many components, providing a significant reduction in the computation time and producing accurate results. In this work, we presented some numerical experiments with test-mixtures using the reduction technique to obtain dew point pressures at specified temperatures.

La connaissance des étoiles et des planètes denses nécessite une détermination fine du comportement thermodynamique de la matière dans ces objets. L'une des approches les plus fécondes aujourd'hui est celle des simulations ab initio, utilisant le formalisme de la physique statistique et la théorie de la fonctionnelle de la densité. Cette approche a notamment montré ses performances en reproduisant avec succès un grand nombre de résultats expérimentaux.Dans la première partie de ce travail de thèse, ces méthodes sont appliquées à l'étude des« glaces », impliquées dans des planètes telles que Uranus ou Neptune. Nous avons dans un premier temps confirmé le travail pré-existant sur le cas de l'eau (équations d'état et existence d'une phase superionique), puis nos avons étendu ces résultats aux cas de planètes plus denses, telles que les exoplanètes appelées« super-Jupiters ». Nous atteignons des limites de pression auxquelles le comportement est analytiquement connu, nous permettant de proposer un ajustement numérique pour l'eau dans une gamme de pression et température extrêmement large. Les autres glaces(méthane et ammoniac) ont seulement été étudiés dans les conditions des planètes de notre système solaire.Nous nous sommes ensuite intéressés au cas des naines blanches et à leur dynamique de refroidissement ~; il s'agit des restes d'étoiles les plus courants, et ils peuvent ainsi être utilisés comme moyen de datation de la galaxie. En particulier, la composition de ces objets conduit à des transitions de phase binaires ayant de lourdes répercussions sur leur temps de refroidissement. Nous avons investigué ce diagramme binaire à l'aide d'une méthode ab initio, et nous proposons de nouvelles stratégies numériques ainsi que des résultats confirmant partiellement les récents travaux dans le domaine. / A correct knowledge of dense stars and planets need an accurate determination of the thermodynamic behavior of matter in these objects. One of the most efficient approaches nowadays is to perform ab initio simulations, using both the statistical physics formalism and the density functionnal theory. This approach has shown its capabilities by reproducing many experimental data.In the first part of this thesis project, these methods are used to study planetary``ices'', found in planets such as Uranus or Neptun. We first confirmed the existing literature on water (equations of state and existence of a superionic phase); we then extended these results to denser planets, such as the so-called ``super-Jupiter''exoplanets. We reach very high pressures, until where the behavior is analytically established; this permitted us to construct a numerical fit for water in a very large temperature and pressure range. The other planetary ices (methane and ammonia) were thenstudied in the conditions of our solar system.We then considered white dwarves, and their cooling dynamics: they are the most usualstar remnants, so that they can be used as cosmochronometers. The composition of these objects lead to binary phase transitions, which can have important consequences on their cooling time. We used ab inition methods to investigate this binary diagram, and wesuggest new numerical strategies, leading to new results which partially confirm theprevious literature.

Neste trabalho estudaremos a existência de soluções fracas para uma classe de equações diferenciais funcionais impulsivas com retardamento dependendo do estado modeladas na forma \'x POT. PRIME\'(t) = Ax(t) + f(t;\' x IND. p(t, xt)), t \'PERTENCE A\'I = [0,a], \'x IND. 0\' =\\varphi \'PERTENCE A\' B, \'DELTA\' \'x(t IND. i) = \'I IND.i\'i(\'x IND.i\'); i = 1, ...n, onde A é o gerador infinitesimal de um \'C IND. 0\'-semigrupo compacto de operadores lineares limitados (\'T\'(t))t \'. OU =\'0 definido em um espaço de Banach X; as fun»ções \'x IND. s\' : (- \'INFIINITO\', 0] \'SETA\' X, \'x IND. s\' ( teta\') = x(s + \'teta\'), estão em um espaço de fase B descrito axiomaticamente; f : I X B \'seta\' X, \'rô\' : I X B \'SETA\' ( - \'INFINITO\', a], \'I IND. i\' : B \'SETA\'X, i=1, ...n , são funções apropriadas; 0 < \'t IND.1\' <... < \'t IND. n\' < a são n¶umeros pré-fixados e o símbolo \'DELTA\'\'ksi\'(t) = \'Ksi\'(\'t POT. + ) - \'ksi\'( \'t POT. -). / In this work we stablish the existence of mild solutions for an impulsive abstract functional differential equation with state-dependent delay described in the form \'x POT. PRIME\'(t) = Ax(t) + f(t;\' x IND. p(t, xt)), t \'BELONGS\'I = [0,a], \'x IND. 0\' =\\varphi \'IS CONTAINED\' B, \'DELTA\' \'x(t IND. i) = \'I IND.i\'i(\'x IND.i\'); i = 1, ...n, where A is the infinitesimal generator of a compact \'C IND. 0\'-semigroup of bounded linear operators (\'T\'(t))t \'. OU =\'0 defined on a Banach space X; the functions \'x IND. s\': ( - INFINito, 0] \'SETA X, \'x IND. s\'(\'teta\') , belongs to some space B described axiomatically; f : I X B \'seta\' X, \'rô\' : I X B \'SETA\' ( - \'INFINITO\', a], \'I IND. i\' : B \'SETA\'X, i=1, ...n , são funções apropriadas; 0 < \'t IND.1\' <... < \'t IND. n\' < a são n¶umeros pré-fixados e o símbolo \'DELTA\'\'ksi\'(t) = \'Ksi\'(\'t POT. + ) - \'ksi\'( \'t POT. -).

Orientador: Martin Aznar / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica / Made available in DSpace on 2018-08-05T00:40:21Z (GMT). No. of bitstreams: 1 Arce-Castillo_PedroFelipe_D.pdf: 4607592 bytes, checksum: 216de649e3febd33712f357f832e071f (MD5) Previous issue date: 2005 / Resumo: Durante a presente década, vários resultados experimentais sobre fenômenos críticos no equilíbrio de fases, tais como efeito de co-solvência, janelas de miscibilidade e regiões de duas fases LV em superfícies de três fases LLV em sistemas ternários foram obtidos experimentalmente por vários grupos de pesquisa. Estes fenômenos são de grande influência em aplicações industriais de tecnologia supercrítica ou quase crítica, já que eles são observados dentro do intervalo de pressão, temperatura e concentração onde acontecem estes processos tecnológicos. O presente trabalho de tese visou modelar computacionalmente o equilíbrio multifásico (ELL, ELV, ELLV) e predizer esses fenômenos, que acontecem perto da região crítica, em sistemas simples (CO2 + n-alcano + n-alcanol, CO2 + 2-nitrofenol + n-alcanol) e complexos, tais como polímero + CO2 + cosolvente [polipropileno (iPP) + CO2 + n-pentano; poliestireno (PS) + CO2 + ciclohexano e poli(D,L-lactida) + CO2 + dimetileter)], fazendo uso de equações de estado (EDE) não cúbicas, que possuem algum embasamento teórico, como modelos termodinâmicos. Esses modelos foram a equação da Teoria Estatística do Fluido Associado de Cadeia Perturbada (Perturbed Chain ¿ Statistical Associating Fluid Theory, PC-SAFT) e de Sanchez- Lacombe (SL). Os resultados obtidos na modelagem do equilíbrio de fases a altas pressões desses sistemas foram comparados com os obtidos pela tradicional EDE de Peng-Robinson (PR). Estes modelos termodinâmicos também foram usados na modelagem do ELV e ELL de sistemas binários compostos de copolímeros comuns e biodegradáveis com solventes a baixas e altas pressões. Cada modelo termodinâmico possui parâmetros de componente puro e um parâmetro de interação (na sua regra de cruzamento) para cada sistema binário. Em todos os modelos termodinâmicos foi usada uma regra de cruzamento convencional e uma regra de mistura de primeira ordem de van der Waals. Os parâmetros de componente puro foram obtidos ajustando por regressão os dados de pressão de vapor e do volume molar do líquido saturado para o componente simples e dados de densidade, pressão e temperatura para o polímero na fase líquida. A modelagem de cada sistema binário foi feita a partir de dados de ELL, ELV e ELLV obtendo um parâmetro de interação binária (que leva em conta as interações entre duas moléculas). A predição do comportamento de fases do sistema ternário foi feita usando os parâmetros de interação binária dos três sistemas binários envolvidos e os resultados foram comparados com os dados experimentais. A otimização foi feita usando o método modificado de Máxima Verossimilhança para determinar o ótimo global dos dois tipos de parâmetros. Em todas as modelagens do comportamento do equilíbrio multifásico dos sistemas apresentados acima, a EDE PC-SAFT teve a melhor performance em termos dos desvios relativos na pressão quando comparada à performance das EDEs SL e PR / Abstract: During the present decade, several experimental results on critical phenomena in phase equilibria, such as co-solvency effect, miscibility windows and two-phases LV regions in three phases LLV surfaces in ternary systems were obtained experimentally by several research groups. These phenomena are of great influence in industrial applications of near-critical and supercritical technology, since they are observed within the pressure, temperature and concentration intervals where these technological processes happen. The present thesis aimed for modeling computationally the phase equilibria (LLE, VLE, VLLE) and predict those phenomena that happen near to critical region in simple systems (CO2 + n-alkane + n-alkanol, CO2 + 2-nitrophenol + n-alkanol) and complex systems, such as polymer + CO2 + co-solvent [polypropylene (iPP) + CO2 + n-pentane; polystyrene (PS) + CO2 + cyclohexane and poly(D,L-lactide) + CO2 + dimethyl ether)] using non-cubic equations of state (EoS), with some theoretical base, as thermodynamic models. Those models were the Perturbed Chain - Statistical Associating Fluid Theory (PC-SAFT) and the Sanchez - Lacombe (SL) EoS. The results obtained in modeling of high-pressure phase equilibria of those systems were compared with those obtained by the traditional Peng- Robinson (PR) EoS. These thermodynamic models were also used in modeling the VLE and LLE of binary systems composed of common and biodegradable copolymers with solvents at low and high pressures. Each thermodynamic model has pure component parameters and one interaction parameter (in its combining rule) for each binary system. Conventional combining and van der Waals one-fluid mixing rules were used in all thermodynamic models. Pure component parameters were obtained by regression of liquid saturated vapor pressure and volume molar data for each simple component, and liquid density, pressure and temperature data for each polymer. The modeling of each binary system was made from LLE, VLE and VLLE data, obtaining one binary interaction parameter (which takes into account the interactions between two molecules). The prediction of phase behavior of ternary system was made using the binary interaction parameters of its three binary systems and the results were compared with experimental data. Optimization was made using the modified likelihood maximum method to determine the global optimum of the two types of parameters. In all the modeling of the multiphase equilibria behavior of the systems presented above, the PC-SAFT EoS had the best performance in terms of relative deviations in pressure when compared to performance of SL and PR EoS / Doutorado / Desenvolvimento de Processos Químicos / Doutor em Engenharia Química

Neste trabalho estudaremos a existência de soluções fracas para uma classe de equações diferenciais funcionais impulsivas com retardamento dependendo do estado modeladas na forma \'x POT. PRIME\'(t) = Ax(t) + f(t;\' x IND. p(t, xt)), t \'PERTENCE A\'I = [0,a], \'x IND. 0\' =\\varphi \'PERTENCE A\' B, \'DELTA\' \'x(t IND. i) = \'I IND.i\'i(\'x IND.i\'); i = 1, ...n, onde A é o gerador infinitesimal de um \'C IND. 0\'-semigrupo compacto de operadores lineares limitados (\'T\'(t))t \'. OU =\'0 definido em um espaço de Banach X; as fun»ções \'x IND. s\' : (- \'INFIINITO\', 0] \'SETA\' X, \'x IND. s\' ( teta\') = x(s + \'teta\'), estão em um espaço de fase B descrito axiomaticamente; f : I X B \'seta\' X, \'rô\' : I X B \'SETA\' ( - \'INFINITO\', a], \'I IND. i\' : B \'SETA\'X, i=1, ...n , são funções apropriadas; 0 < \'t IND.1\' <... < \'t IND. n\' < a são n¶umeros pré-fixados e o símbolo \'DELTA\'\'ksi\'(t) = \'Ksi\'(\'t POT. + ) - \'ksi\'( \'t POT. -). / In this work we stablish the existence of mild solutions for an impulsive abstract functional differential equation with state-dependent delay described in the form \'x POT. PRIME\'(t) = Ax(t) + f(t;\' x IND. p(t, xt)), t \'BELONGS\'I = [0,a], \'x IND. 0\' =\\varphi \'IS CONTAINED\' B, \'DELTA\' \'x(t IND. i) = \'I IND.i\'i(\'x IND.i\'); i = 1, ...n, where A is the infinitesimal generator of a compact \'C IND. 0\'-semigroup of bounded linear operators (\'T\'(t))t \'. OU =\'0 defined on a Banach space X; the functions \'x IND. s\': ( - INFINito, 0] \'SETA X, \'x IND. s\'(\'teta\') , belongs to some space B described axiomatically; f : I X B \'seta\' X, \'rô\' : I X B \'SETA\' ( - \'INFINITO\', a], \'I IND. i\' : B \'SETA\'X, i=1, ...n , são funções apropriadas; 0 < \'t IND.1\' <... < \'t IND. n\' < a são n¶umeros pré-fixados e o símbolo \'DELTA\'\'ksi\'(t) = \'Ksi\'(\'t POT. + ) - \'ksi\'( \'t POT. -).

L’étude du comportement des composantes des intérieurs planétaires dans des conditions extrêmes de pression (megabar) et température (milliers de Kelvin) est essentielle afin de construire des modèles fiables décrivant l’évolution et la structure des planètes. Dans ce travail, nous avons étudié plusieurs composantes par compression par choc laser sur les installations LULI2000 (France) et GEKKO XII (Japon).Nous avons employé des chocs décroissants pour étudier des conditions de haute-pression / haute-température. Afin d’accéder à des conditions de température modérée, nous avons utilisé des techniques de pre-compression statique (couplage compression par choc — cellules à enclumes de diamant) et dynamique (génération de doubles chocs).Nous avons étudié l’équation d’état des mélanges eau-ethanol-ammoniac et de l’eau et ammoniac purs, d’intérêt pour la description des intérieurs des planètes géantes de glace. L’étude de l’ammoniac a été particulièrement délicate en raison de sa forte réactivité et donc de la complexité du design des cibles ; nous présentons les premières données obtenues par choc laser, dans un domaine de pression jamais exploré. Les données des mélanges confirment des calculs ab initio récents basés sur une approximation de mélange linéaire.Nous avons également mesuré la réflectivité des mélanges liquides et de la silice, une composante-clé des intérieurs des planètes terrestres. Nous avons ensuite estimé la conductivité électrique — un paramètre crucial pour modéliser la génération des champs magnétiques planétaires dans les intérieurs via un mécanisme dynamo — de ces composantes.Eau, ammoniac et mélanges eau-ethanol-ammoniac affichent des réflectivités différentes, ce qui suggère que l’eau pure ne peut pas être considérée comme représentative des mélanges planétaires dans les modèles dynamo.Par ailleurs, nous avons apporté une confirmation expérimentale de calculs ab initio récents selon lesquels la conductivité de la silice n’est pas monotone le long d’une ligne isotherme pour des températures modérées.Nos données supportent des calculs qui prédisent qu’une dynamo peut avoir lieu dans les océans de magma dans des super-Terres ainsi que dans la jeune Terre. / Characterising the behaviour of planetary interiors’ components at extreme conditions (megabar pressures, temperatures of a few thousand Kelvin) is essential to build reliable models describing the evolution and structure of planets. In this thesis, we investigated various components on a wide set of conditions using laser-driven shock compression techniques at the LULI2000 (France) and GEKKO XII (Japan) facilities.Single decaying shocks were employed to study high-pressure / high-temperature states. To reach moderate-temperature conditions, closer to planetary interior profiles, we employed static and dynamic pre-compression techniques coupling Diamond Anvil Cells to shock compression and generating double shocks, respectively.We studied the equation of state of water-ethanol-ammonia mixtures and of pure liquid water and ammonia, of interest for icy giant structure models. Pure ammonia measurements have been particularly challenging due to cell design complexity in reason of its reactivity; we provide the first data obtained with laser shocks, in a pressure domain up to now unexplored. Mixtures data are in agreement with recent ab initio calculations based on the linear mixing approximation.We measured the optical reflectivity of liquid mixtures and silica, a key component of rocky planets’ interiors. From reflectivity data we estimated the electrical conductivity of such components — a crucial parameter for modelling the generation of planetary magnetic fields in the interiors via a dynamo mechanism.Water, ammonia, and water-ethanol-ammonia mixtures exhibit different reflectivity (hence conductivity) behaviours as a function of pressure and temperature. This suggests that pure water should not be used in dynamo models as representative of the icy mixtures.Moreover, we provide the first experimental confirmation of recent ab initio studies showing that the conductivity of silica along isothermal lines is not monotonic at moderate temperatures. Our data provide experimental support for the calculations predicting a dynamo action to occur in super-Earths’ and early Earth’s magma oceans.

Ce travail porte sur la contribution à la modélisation thermodynamique d'un atelier de purification d'acide acrylique. Après l'identification des principaux produits intervenant dans l'étape de purification et la collecte de leurs propriétés thermodynamiques disponibles dans la littérature, nous avons effectué une série de mesures expérimentales pour un ensemble de mélanges contenant des acides carboxyliques (en particulier : diagrammes d'équilibres liquide-liquide et équilibres liquide-vapeur, enthalpies d'excès et volumes d'excès). L'ensemble des données (nos mesures et les valeurs de la littérature) a été exploité selon deux approches de modélisation des équilibres liquide-vapeur : une approche symétrique (φ-φ) appliquée aux équations d'état de Peng-Robinson (P-R) et de PC-SAFT et une approche dissymétrique (γ-φ) appliquée aux modèles de coefficients d'activité en phase liquide NRTL, UNIQUAC et Van Laar associés à diverses équations d'état en phase vapeur (gaz parfait, Viriel, Hayden et O'Connell et Nothnagel). Nous avons finalement retenu le modèle UNIQUAC associé à la corrélation de Hayden et O'Connell en phase vapeur. Des nouveaux paramètres d'interaction ont été déterminés et conduisent à des résultats homogènes et satisfaisants en comparaison avec nos mesures expérimentales et aux données de la littérature. Ils permettent également de décrire convenablement les diagrammes d'équilibres liquide-vapeur et les volatilités relatives des mélanges étudiés / This work focuses on the contribution in the thermodynamic modeling of an acrylic acid purification unit. After identifying the main products involved in the purification step and collecting their thermodynamic properties available in the literature, we conducted a series of experimental measurements for a range of mixtures containing carboxylic acids(mainly liquid-liquid equilibrium and vapor-liquid equilibrium diagrams, excess enthalpies and excess volumes).The data set-our measurements and literature values-was used according to two approaches for modeling vapor-liquid equilibrium: a symmetric approach(φ-φ) applied to the equations of state Peng-Robinson (P-R) and PC-SAFT and an asymmetrical approach (γ-φ) applied to the models of activity coefficients in the liquid phase NRTL, UNIQUAC and Van Laar associated with various equations of state in the vapor phase(ideal gas, Viriel, Hayden O'Connell and Nothnagel). We have finally chosen the UNIQUAC thermodynamic model associated with the correlation of Hayden O'Connell in vapor phase. New binary parameters were determined and led to consistent and satisfactory results in comparison with our experimental measurements and literature data. These parameters can also be used to adequately describe the diagrams of vapor-liquid equilibrium and the relative volatilities of the mixtures studied

Ce manuscrit porte sur la modélisation et la simulation numérique d’écoulements diphasiques compressibles. Dans ce contexte, les méthodes d’interfaces diffuses sont aujourd’hui bien acceptées. Cependant, un progrès est encore attendu en ce qui concerne la précision de la capture numérique de ces interfaces. Une nouvelle méthode est développée et permet de réduire significativement cette zone de capture. Cette méthode se place dans le contexte des méthodes numériques de type “MUSCL”, très employées dans les codes de production, et sur maillages non-structurés. Ces interfaces pouvant être le lieu où une transition de phase s’opère, celle-ci est considérée au travers d’un processus de relaxation des énergies libres de Gibbs. Un nouveau solveur de relaxation à thermodynamique rapide est développé et s’avère précis, rapide et robuste y compris lors du passage vers les limites monophasiques. En outre, par rapport aux applications industrielles envisagées, une extension de la thermodynamique des phases et du mélange est nécessaire. Une nouvelle équation d’état est développée en conséquence. La formulation est convexe et est basée sur l’équation d’état “Noble-Abel-Stiffened-Gas”. Enfin, sur un autre plan la dispersion de fluides non-miscibles sous l’effet de la gravité est également abordée. Cette problématique fait apparaître de larges échelles de temps et d’espace et motive le développement d’un nouveau modèle multi-fluide de type “shallow water bi-couche”. Sa résolution numérique est également traitée / This manuscript addresses the theoretical modeling and numerical simulation of compressible two-phase flows. In this context, diffuse interface methods are now well-accepted but progress is still needed at the level of numerical accuracy regarding their capture. A new method is developed in this research work, that allows significant sharpening. This method can be placed in the framework of MUSCL-type schemes, widely used in production codes and on unstructured grids. Phase transition is addressed as well through a relaxation process relying on Gibbs free energies. A new instantaneous relaxation solver is developed and happens to be accurate, fast and robust. Moreover, in view of the intended industrial applications, an extension of the thermodynamics of the phases and of the mixture is necessary. A new equation of state is consequently developed. The formulation is convex and based on the “Noble-Abel-Stiffened-Gas” equation of state. In another context, the dispersion of non-miscible fluids under gravity effects is considered as well. This problematic involves large time and space scales and has motivated the development of a new multi-fluid model for “two-layer shallow water” flows. Its numerical resolution is treated as well