Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho objetiva a construção de estruturas robustas e computacionalmente eficientes para a solução do problema de deposição de parafinas do ponto de vista do equilíbrio sólido-líquido. São avaliados diversos modelos termodinâmicos para a fase líquida: equação de estado de Peng-Robinson e os modelos de coeficiente de atividade de Solução Ideal, Wilson, UNIQUAC e UNIFAC. A fase sólida é caracterizada pelo modelo Multisólido. A previsão de formação de fase sólida é inicialmente prevista por um teste de estabilidade termodinâmica. Posteriormente, o sistema de equações não lineares que caracteriza o equilíbrio termodinâmico e as equações de balanço material é resolvido por três abordagens numéricas: método de Newton multivariável, método de Broyden e método Newton-Armijo. Diversos experimentos numéricos foram conduzidos de modo a avaliar os tempos de computação e a robustez frente a diversos cenários de estimativas iniciais dos métodos numéricos para os diferentes modelos e diferentes misturas. Os resultados indicam para a possibilidade de construção de arcabouços computacionais eficientes e robustos, que podem ser empregados acoplados a simuladores de escoamento em dutos, por exemplo. / The objective of this work is to develop robust and computationally efficient frameworks devoted to the solution of the problem of paraffin deposition, from the point of view of the solid-liquid equilibrium. In this scenario, several thermodynamic models will be evaluated to the description of the behavior of the liquid phase: the Peng-Robinson cubic equation of state and the activity coefficient models of Ideal Solution, Wilson, UNIQUAC and UNIFAC. The solid phase is characterized by the Multisolid model. The formation of the solid phase is initially predicted by a thermodynamic stability test. Subsequently, the nonlinear algebraic system that describes the thermodynamic equilibrium and the material balance equations is solved by three numerical approaches: the multivariable Newton method, the Broyden method and the Newton-Armijo method. Several numerical experiments were conducted in order to evaluate computation times and robustness facing several scenarios of initial estimates of the numerical methods for various models and mixtures. The results indicate the possibility of construction of efficient and robust computational frameworks which can be used coupled with fluid flow simulators, for instance.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho objetiva a construção de estruturas robustas e computacionalmente eficientes para a solução do problema de deposição de parafinas do ponto de vista do equilíbrio sólido-líquido. São avaliados diversos modelos termodinâmicos para a fase líquida: equação de estado de Peng-Robinson e os modelos de coeficiente de atividade de Solução Ideal, Wilson, UNIQUAC e UNIFAC. A fase sólida é caracterizada pelo modelo Multisólido. A previsão de formação de fase sólida é inicialmente prevista por um teste de estabilidade termodinâmica. Posteriormente, o sistema de equações não lineares que caracteriza o equilíbrio termodinâmico e as equações de balanço material é resolvido por três abordagens numéricas: método de Newton multivariável, método de Broyden e método Newton-Armijo. Diversos experimentos numéricos foram conduzidos de modo a avaliar os tempos de computação e a robustez frente a diversos cenários de estimativas iniciais dos métodos numéricos para os diferentes modelos e diferentes misturas. Os resultados indicam para a possibilidade de construção de arcabouços computacionais eficientes e robustos, que podem ser empregados acoplados a simuladores de escoamento em dutos, por exemplo. / The objective of this work is to develop robust and computationally efficient frameworks devoted to the solution of the problem of paraffin deposition, from the point of view of the solid-liquid equilibrium. In this scenario, several thermodynamic models will be evaluated to the description of the behavior of the liquid phase: the Peng-Robinson cubic equation of state and the activity coefficient models of Ideal Solution, Wilson, UNIQUAC and UNIFAC. The solid phase is characterized by the Multisolid model. The formation of the solid phase is initially predicted by a thermodynamic stability test. Subsequently, the nonlinear algebraic system that describes the thermodynamic equilibrium and the material balance equations is solved by three numerical approaches: the multivariable Newton method, the Broyden method and the Newton-Armijo method. Several numerical experiments were conducted in order to evaluate computation times and robustness facing several scenarios of initial estimates of the numerical methods for various models and mixtures. The results indicate the possibility of construction of efficient and robust computational frameworks which can be used coupled with fluid flow simulators, for instance.

Made available in DSpace on 2014-12-17T15:01:30Z (GMT). No. of bitstreams: 1 JessicaCSLM_DISSERT.pdf: 2011571 bytes, checksum: 8e087d35d6e4c83d4f7eda24cd8d3e57 (MD5) Previous issue date: 2012-09-21 / Anhydrous ethanol is used in chemical, pharmaceutical and fuel industries. However, current processes for obtaining it involve high cost, high energy demand and use of toxic and pollutant solvents. This problem occurs due to the formation of an azeotropic mixture of ethanol + water, which does not allow the complete separation by conventional methods such as simple distillation. As an alternative to currently used processes, this study proposes the use of ionic liquids as solvents in extractive distillation. These are organic salts which are liquids at low temperatures (under 373,15 K). They exhibit characteristics such as low volatility (almost zero/ low vapor ), thermal stability and low corrosiveness, which make them interesting for applications such as catalysts and as entrainers. In this work, experimental data for the vapor pressure of pure ethanol and water in the pressure range of 20 to 101 kPa were obtained as well as for vapor-liquid equilibrium (VLE) of the system ethanol + water at atmospheric pressure; and equilibrium data of ethanol + water + 2-HDEAA (2- hydroxydiethanolamine acetate) at strategic points in the diagram. The device used for these experiments was the Fischer ebulliometer, together with density measurements to determine phase compositions. The experimental data were consistent with literature data and presented thermodynamic consistency, thus the methodology was properly validated. The results were favorable, with the increase of ethanol concentration in the vapor phase, but the increase was not shown to be pronounced. The predictive model COSMO-SAC (COnductor-like Screening MOdels Segment Activity Coefficient) proposed by Lin & Sandler (2002) was studied for calculations to predict vapor-liquid equilibrium of systems ethanol + water + ionic liquids at atmospheric pressure. This is an alternative for predicting phase equilibrium, especially for substances of recent interest, such as ionic liquids. This is so because no experimental data nor any parameters of functional groups (as in the UNIFAC method) are needed / O etanol anidro tem ampla aplica??o em ind?strias qu?mica, farmac?utica e de combust?veis. No entanto, os processos atuais para a sua obten??o envolvem custo elevado, alta demanda de energia e a utiliza??o de solventes t?xicos e poluentes. Esse problema ocorre devido ? forma??o de aze?tropo na mistura etanol + ?gua, n?o permitindo a separa??o completa por m?todos convencionais tais como destila??o simples. Como uma alternativa aos processos atualmente utilizados, este estudo prop?e a utiliza??o de l?quidos i?nicos como agentes na destila??o extrativa. Trata-se de sais org?nicos l?quidos a baixas temperaturas (abaixo de 373,15 K). Suas caracter?sticas, tais como baixa volatilidade (press?o de vapor muito baixa), estabilidade t?rmica e baixa corrosividade os tornam interessantes para aplica??es como catalisadores e solventes. Neste trabalho, dados experimentais de press?o de vapor de etanol e ?gua puros na faixa de press?o de 20 a 101 kPa, assim como dados de equil?brio l?quido-vapor(ELV) do sistema etanol + ?gua a press?o atmosf?rica, e dados de equil?brio do sistema etanol + ?gua + 2-HDEAA (acetato de 2-hidrodietanolamina) foram obtidos em pontos estrat?gicos do diagrama. O dispositivo usado para esses experimentos foi o ebuliometro de Fischer, juntamente com medidas de densidade para determinar a composi??o das fases. Os dados obtidos apresentaram coer?ncia com dados da literatura e consist?ncia termodin?mica, desta forma, a metodologia foi devidamente validada. Os resultados foram favor?veis, com o aumento da concentra??o de etanol na fase vapor, por?m o aumento n?o demonstrou ser elevado. O modelo preditivo COSMO-SAC (COnductor-like Screening MOdels Segment Activity Coefficient), desenvolvido por Lin e Sandler (2002), foi aplicado para os c?lculos de predi??o de Equil?brio L?quido-Vapor do sistema etanol + ?gua com l?quido i?nico a press?o atmosf?rica. Essa ? uma alternativa para a previs?o do equil?brio de fases, especialmente para subst?ncias de interesse recente, tais como l?quidos i?nicos, uma vez que nem dados experimentais, nem par?metros de grupos funcionais (como no m?todo UNIFAC) s?o necess?rios

A precipitação e cristalização de proteínas são operações unitárias amplamente utilizadas na indústria biotecnológica. A formação de precipitado nestas operações é muitas vezes atingida por meio da adição de um sal que diminui a solubilidade da proteína, ou seja, o chamado fenômeno de saltingout. A principal informação para o estudo da precipitação e da cristalização é o diagrama de fases, em que a solubilidade da proteína é apresentada em função das variáveis do sistema (temperatura, pH, concentração de sal). Outra medida importante é o segundo coeficiente virial, que é uma medida indireta da interação intermolecular. A combinação de ambas as informações é fundamental para a identificação das condições em que fases cristalina ou amorfa são obtidas. O equilíbrio sólido-líquido da lisozima de clara de ovo de galinha em soluções aquosas contendo sais biodegradáveis (succinato de sódio, citrato de sódio e tartarato de sódio) foi estudado por meio da determinação da solubilidade da proteína e do segundo coeficiente virial em função da força iônica. Os dados experimentais do segundo coeficiente virial em função da força iônica foram medidos por meio de cromatografia de autointeração. Estes dados foram correlacionados por modelos apropriados. As informações de solubilidade e do segundo coeficiente virial da proteína foram combinadas para gerar condições experimentais adequadas na identificação da janela de cristalização, i.e., as condições em que uma fase cristalina é obtida. Uma matriz do tipo placa de cultivo foi usada para os experimentos de cristalização. Os resultados experimentais mostraram que as regiões das fases cristalina e amorfa no diagrama de fases são funções simultâneas do segundo coeficiente virial, como parâmetro termodinâmico, e da supersaturação, como parâmetro cinético. Os três sais foram capazes de induzir o efeito salting-out, sendo o succinato de sódio o sal mais eficaz na diminuição da solubilidade da lisozima, seguido pelo tartarato de sódio e pelo citrato de sódio. No caso da lisozima, cristais foram obtidos em soluções de succinato de sódio e tartarato de sódio, e as condições nas quais a fase cristalina é formada foram identificadas; no entanto, para o citrato de sódio somente fase amorfa foi observada. Em conjunto, estes resultados mostram que estes sais biodegradáveis são agentes precipitantes promissores. / The precipitation and crystallization of proteins are unit operations widely used in the biotechnology industry. The formation of a solid phase in these operations is often achieved by adding a salt that lowers the protein solubility, the so-called salting-out phenomenon. The key information to study precipitation or crystallization is the phase diagram, in which the solubility of a protein is presented as a function of system variables (temperature, pH, salt concentration). Another important parameter is the second virial coefficient, which is an indirect measure of intermolecular interactions. The combination of both kinds of information is fundamental to identify the conditions in which crystal and amorphous phases can be formed. The solid-liquid equilibrium of hen egg-white lysozyme in aqueous solutions containing biodegradable salts, viz., sodium citrate, sodium tartrate and sodium succinate, was studied by determining both the protein solubility and the second virial coefficient as a function of ionic strength. Experimental data for second viral coefficient as a function of ionic strength were obtained through self-iteration chromatography. These data were correlated by appropriate models. The protein solubility and the second virial coefficient information were combined to generate adequate experimental conditions to identify the so-called crystallization slot, i.e., the conditions in which a crystalline solid phase is obtained. A plate matrix disposition was used for the crystallization experiments. The experimental results show that the crystal and amorphous regions in the phase diagram depend simultaneously on the second virial coefficient, as a thermodynamic parameter, and on the supersaturation ratio, as a kinetic parameter. All these salts were able to induce salting-out, being sodium succinate the most effective one in decreasing lysozyme solubility, followed by sodium tartrate and sodium citrate. For lysozyme in sodium succinate and sodium tartrate solutions, the conditions for which a crystal phase is formed were identified; however, for sodium citrate only amorphous solid phases were observed.! Overall, these results show that these biodegradable salts are promising precipitating agents.

L'objectif de ce travail est l'étude de la solubilité d'un principe actif hydrophobe modèle, le diazépam, dans un solvant binaire d'intérêt pour la lyophilisation industrielle, le mélange eau + tert-butanol. Un modèle décrivant la dépendance du volume d'excès du solvant vis-à-vis de sa composition et de sa température a été validé à partir de données mesurées au cours de ce travail et de données de la littérature. Les variations de diverses propriétés partielles d'excès issues de ce modèle en fonction de la composition du solvant et de sa température ont été interprétées en termes d'interactions moléculaires et d'arrangements structuraux. Ensuite, la solubilité du diazépam dans le solvant a été mesurée en fonction de sa composition et de sa température. La masse volumique des phases liquides saturées ainsi que les propriétés thermophysiques des cristaux de principe actif originels et des phases solides en excès issues des équilibres solide-liquide ont été déterminées. Les propriétés thermodynamiques caractéristiques du processus de dissolution du diazépam en condition d'équilibre ont été obtenues à partir de la dépendance de sa solubilité vis-à-vis de la température. À partir de ces données, les propriétés thermodynamiques d'excès du diazépam dans les différents mélanges saturés ont été calculées et les forces responsables de la variation de la solubilité du principe actif avec la composition du solvant ont été identifiées. Enfin, la capacité de deux modèles d'enthalpie libre d'excès, le modèle de Scatchard-Hildebrand combiné ou non au modèle de Flory-Huggins, à corréler les données expérimentales de solubilité a été évaluée et comparée / The aim of this work is to investigate the solubility behavior of a hydrophobic model drug, diazepam, in a binary solvent of industrial interest for freeze-drying, the water + tert-butyl alcohol mixture. Firstly, a model describing the dependence of the excess volume of the solvent on both composition and temperature was validated from experimental data obtained during this work and literature data. This model was used to derive expressions for excess partial thermodynamic quantities and their variations with respect to composition and temperature were discussed in terms of molecular interactions and structural arrangements in solution. Secondly, the solubility of diazepam in neat solvents and different binary solvent mixtures was determined. The density of drug-saturated mixtures was also determined as well as the thermophysical properties of original diazepam crystals and excess solid phases from solid-liquid equilibria. The thermodynamic properties relative to the dissolution process of the drug under saturation condition were obtained from solubility temperature dependence using van’t Hoff plots. From these, the excess partial thermodynamic properties of diazepam in saturated mixtures were computed and the forces driving the drug solubility variation with respect to the solvent composition were identified. Finally, two excess Gibbs energy models, the Scatchard-Hildebrand and combined Scatchard-Hildebrand/Flory-Huggins models were tested to represent the solubility data. Their capabilities in correlating the dependence of the drug solubility on both the solvent composition and temperature were evaluated and compared

Nous avons développé une méthode de contributions de groupes permettant d'estimer, en fonction de la température, le coefficient d'interaction binaire (kij) de l'équation d'état de Peng Robinson. Notre approche rend cette équation d'état prédictive. Douze groupes sont définis et il est possible d'estimer les kij pour n'importe quel mélange renfermant des alcanes, des aromatiques, des naphtènes et du CO2. Les diagrammes de phase et lieux des points critiques des systèmes binaires sont bien prédits par le modèle baptisé PPR78 (Predictive 1978, Peng Robinson equation of state). Ce modèle permet également de traiter efficacement les mélanges multiconstituants comme les pétroles bruts et les gaz naturels. A l'aide d'une cellule haute pression, des mesures d'équilibres liquide - vapeur ont été réalisées pour la première fois sur deux systèmes binaires : CO2 méthylcyclopentane et CO2 isopropylcyclohexane. Des mesures ont également été faites sur un mélange renfermant du CO2 et cinq hydrocarbures / A group contribution method allowing the estimation of the temperature dependent binary interaction parameter (kij) for the Peng Robinson equation of state is proposed. Doing so, a new predictive thermodynamic model is born. Twelve groups are defined and it is now possible to estimate the kij for any mixture containing alkanes, aromatics, naphthenes and CO2, whatever the temperature. The model, called PPR78 (Predictive 1978, Peng Robinson equation of state), gives a good description of the phase diagrams and critical locus of binary systems. This predictive model can be successfully employed for the simulation of many mixtures such as natural gases and petroleum fluids. Using a high pressure visual cell, vapor liquid equilibria measurements were made for two binary systems: CO2 methylcyclopentane and CO2 isopropylcyclohexane. For these two systems, no literature data were available. Finally, we measured bubble and dew points on a five component hydrocarbon mixture in the presence of CO2

La gazéification de la biomasse par voie thermochimique constitue une ressource en énergie renouvelable ayant un grand potentiel de développement. Parmi les différentes techniques possibles, la voie cogénération Chaleur/bio-SNG (Substitute Natural Gaz) est proche de la maturité technologique. Un des verrous technologique de cette technologie est l’élimination des goudrons contenu dans le gaz issu du gazéifieur. Le présent travail de recherche constitue une contribution à la levée de ce verrou. La technique d’élimination des goudrons par lavage au moyen d’un solvant non miscible à l’eau ayant été sélectionnée pour un pilote de démonstration, le présent travail de recherche s’est principalement focalisé sur l’acquisition de données d’équilibre bi et triphasique des composés modèles des goudrons - eau – solvant de lavage. De telles données sont en effet indispensable pour la mise au point du modèle thermodynamique permettant la modélisation et l’optimisation du lavage. Les analyses des phases liquides en équilibre on été réalisées par CPG-FID ou CPG-SM. Dans certains cas les niveaux de concentration étaient particulièrement faibles. Les concentrations réciproque obtenues et les coefficients de partage qui s’en déduisent vérifie respectivement la corrélation empirique de Hands et la relation de Van’t Hoff. L’équilibre liquide-liquide-vapeur des binaires eau – solvant de lavage ont été étudiés par la méthode statique. Les concentrations des phases en équilibres ont été corrélées par les modèles NRTL et UNIQUAC au moyen du logiciel commercial ‘Simulis Thermodynamic’. Les paramètres d’interaction ainsi ajustés permettent une bonne restitution des données expérimentales. / Gasification of biomass is a promising thermochemical renewable energy resource. Among all biomass conversion processes, gasification by heat cogeneration / bio-SNG (Substitute Natural Gas) is the promising one. But still, one of the deadlocks to be raised is the reduction of the high level of tar present in the product gas. The objective of this work is to perform a data base which will be useful at the operation of tar removal from aqueous medium. The present work has mainly focused on the acquisition of bi and triphasic equilibrium data model molecules of tars - water - washing solvent. Such data are indeed essential for the development of the thermodynamic model for the modeling and the optimization of the washing process. Analyses of liquid phases in equilibrium have been performed by GC-FID or GC-MS. In some cases the concentration levels were particularly low (up to 10-10 mole fraction of anthracene in the aqueous phase). Reciprocal concentrations obtained and the partition coefficients which are deduced from the empirical correlation satisfy each of Hands and the Van't Hoff relationship. Liquid-liquid-vapor equilibrium of binary systems (water-extracting solvent) was studied with the static method. The concentrations of the phases in equilibrium were correlated by the NRTL and UNIQUAC models using the commercial software 'Thermodynamic Simulis'. The interaction parameters adjusted allow a good reproduction of experimental data.

No description available.

La prédiction de valeurs de tension interfaciale des fluides est capitale dans de nombreuses applications industrielles. Les techniques de simulation moléculaire et l’évolution rapide des moyens de calcul intensif permettent depuis quelques années de prédire des valeurs de tension interfaciale pour des systèmes complexes. Des travaux concernant des équilibres liquide / vapeur des corps purs SO2, O2, N2 et Ar montrent que les modèles choisi pour chaque molécule peuvent influencer la qualité des prédictions de tension interfaciale. Des simulations d’équilibres gaz acide / alcane de type CO2 / n-butane, CO2 / n-décane et H2S / n-pentane ont ensuite été réalisées. Elles ont mis en évidence l’efficacité des méthodes de simulation de type Monte Carlo pour la prédiction des tensions interfaciales pour de tels systèmes. L’étude de systèmes ternaires H2O / N2+CH4 et H2O / CO2+H2S a par ailleurs montré que le recourt à la dynamique moléculaire pouvait faciliter l’équilibration des systèmes simulés, rendant plus efficace la prédiction des tensions interfaciales. L’étude d’équilibres liquide / vapeur de saumures de chlorure de sodium a permis de mettre en évidence l’efficacité de certains potentiels non-polarisables pour la prédiction de l’évolution de la tension interfaciale avec la molarité de sel. Les modèles polarisables de type core-shell choisis ne permettent de prédire ni les masses volumiques, ni les tensions interfaciales. Enfin, l’étude d’équilibres eau / alcane en présence de sel ou de méthanol a montré que les méthodes de dynamique moléculaire permettaient de prédire quantitativement des valeurs de tension interfaciale pour ce type d’interface. L’effet de l’alcool abaissant la tension interfaciale a bien été observé, tout comme son placement préférentiel à l’interface. / The prediction of interfacial tension of fluids is critical for many industrial applications. Advances in molecular simulation, and the recent evolution of supercomputing calculations allow for some years to predict the values of interfacial tension for complex systems. A work involving liquid / vapor equilibrium of pure compounds SO2, O2, N2 and Ar show that the models used can impact the quality of the prediction. Simulations of acid gas / alkane equilibrium such CO2 / n-butane, CO2 / n-decane or H2S / n-pentane were then performed. They have demonstrated the performance of methods of Monte Carlo simulations for the reproduction of interfacial tensions for such system. The study of ternary systems H2O / N2+CH4 and H2O / CO2+H2S has also shown that using molecular dynamics could help the equilibration of the simulated systems. The study of liquid / vapor equilibrias of sodium chloride brines show that certain non-polarizable models perform very well to predict the changes in the interfacial tension with the molarity of salt. The core-shell polarizable models based on the Drude oscillator model chosen did not allow to predict brines densities and the interfacial tensions. Finally, the study of water / alkane equilibria in the presence of salt or methanol showed that the molecular dynamics methods allow to predict quantitatively interfacial tension values for this kinds of interfaces. The effect of alcohol lowering the interfacial tension has been observed : this small surfactant populate the interfacial region at weak concentration.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O objetivo do presente trabalho é apresentar um estudo sobre o equilíbrio de fases sólido-líquido-vapor para hidratos de metano. A análise do equilíbrio trifásico sólido-líquido-vapor tem encontrado diversas aplicações para sistemas hidrocarboneto-água, uma vez que permite, por exemplo, a determinação da região de estabilidade de hidratos de metano e hidratos de gás natural. Inicialmente foi feita uma pesquisa sobre o estado da arte no que diz respeito ao comportamento termodinâmico e equilíbrio de fases de hidratos. Foram implementados os modelos apresentados por Ballard (2002) e Zhang et al. (2005). A proposta de Zhang et al. (2005) é aplicável para equilíbrios de fases a temperaturas abaixo de 300 K. Sua abordagem combinou a teoria de van der Waals e Platteeuw para a fase hidrato com a equação do estado de Peng-Robinson (1976) modificada por Stryjek e Vera (1986) para ambas as fases fluidas (fase vapor e fase aquosa). A abordagem de Ballard (2000) considerou a distorção do hidrato do seu estado padrão, o que fornece uma exata composição do hidrato e melhora a previsão da formação dos hidratos a altas pressões. Ao esclarecer a mudança de volume no hidrato, o raio da gaiola do hidrato é uma função do seu volume. Com isso, Ballard propôs uma nova abordagem considerando tal variação de volume e gerou um equilíbrio de fases em uma rotina de flash multifásico através da minimização da energia livre de Gibbs. Assim, o presente trabalho apresenta as abordagens de Zhang et al. (2005) e Ballard (2002) para o comportamento termodinâmico de hidratos e faz uma análise e comparação entre eles. Para resolver o problema do flash computacionalmente, foi utilizada a ferramenta lsqnonlin (built-in do software MATLAB). O lsqnonlin é um algoritmo baseado no método de Levenberg-Marquadt. / The objective of the present work is to present a study of solid-vapor-liquid three-phase equilibrium for methane hydrates. The analysis of three-phase equilibrium has several applications for water-hydrocarbon systems, since it permits, for example, determination of stability region for methane hydrates and natural gas hydrates. We have started seeking in literature about the state-of-art for thermodynamic behaviour and phase equilibrium for hydrates. And then the models proposed by Ballard (2002) and Zhang et al. (2005) were implemented. Zhang et al. (2005) have proposed a phase equilibrium for single-guest gas hydrates at temperatures below 300 K. Their approach has combined the van der WaalsPlatteeuw theory for the hydrate phase and the PengRobinson equation of state for both fluid phases (vapor and aqueous phase) (1976) modified by Stryjek and Vera (1986). Ballards (2000) approach has allowed the hydrate distortion from its standard state and has gave a more accurate composition of the hydrate and has improved hydrate formation predictions at high pressures. As a direct result of accounting for a changing hydrate volume, the cage radii were functions of the hydrate volume. Thus, Ballard have proposed the hydrate phase equilibrium by Gibbs energy minimization in a multi-phase flash routine. Thus, this work presents the Zhang et al. (2005) and Ballards (2002) approaches for hydrate thermodynamic behavior and makes an analysis and comparison of them. To compute the flash problem, we use the tool lsqnonlin (built-in of MATLAB software). The algorithm lsqnonlin is based on the Levenberg-Marquadt method.