La nucléation, la croissance et la dissociation des hydrates de gaz au voisinage d’un ménisque eau – gaz dans des capillaires de verre sont étudiées par vidéo-microscopie et spectroscopie Raman à température, pression, mouillabilité et géométrie du substrat contrôlées. Dans ce travail, deux hydrates simples de structure I (hydrate de CO2 et hydrate de CH4), deux hydrates simples de structure II (N2 et Cyclopentane) et un hydrate double (cyclopentane + CO2) sont examinés. En baissant la température bien au-dessous de 0 °C, i.e., sous un fort sous-refroidissement, tous ces hydrates, excepté l’hydrate de cyclopentane, nucléent sans que la glace soit formée. L’hydrate forme d’abord une croûte polycristalline sur le ménisque eau-molécule invitée (guest). Ensuite, il se propage rapidement à partir de ce ménisque dans l’eau sous forme de fibres ou dendrites et le long de la paroi capillaire sous forme d’une croûte fine et polycristalline appelée ”halo”. Sur un substrat hydrophile, ce halo avance du côté de la phase invitée, alimenté par une couche d’eau entre le halo et la paroi interne du capillaire. Symétriquement, sur un verre hydrophobe (traité au silane), le halo et une couche de la phase invitée se propagent du côté eau. Aucun halo n’est observé sur un substrat de mouillabilité intermédiaire. La croissance et la morphologie du halo d’hydrate et l’épaisseur de sa couche sous-jacente d’eau (ou de phase invitée) dépendent fortement du sous-refroidissement. Grâce au faible volume du capillaire utilisé et à la vitesse rapide de refroidissement, la limite de métastabilité de l’hydrate de CO2 est approchée pour différentes pressions et mouillabilité. Le régime des faibles sous-refroidissements est également étudié : une nouvelle morphologie d’hydrate de CO2 est découverte pour des sous-refroidissements inférieurs à 0,5 °C, constituée d’un cristal creux, générée au niveau du ménisque eau – guest et avançant du côté guest le long du verre, alimenté par une épaisse couche d’eau prise en sandwich entre le verre et ce cristal. Une nouvelle procédure est proposée pour détermination des conditions d’équilibre des hydrates de gaz dans une large plage de température et de pression, y compris l’extension métastable de la ligne triphasique (eau liquide – hydrate – guest) jusqu’à des températures bien inférieures à 0 °C. Enfin, les mécanismes par lesquels le CO2 et le cyclopentane agissent en synergie pour former l’hydrate de structure II sont discutés. / The nucleation, growth and dissociation of gas hydrate across a water – gas meniscus in glass capillaries are investigated by means of video-microscopy and confocal Raman spec- troscopy under controlled temperature, pressure, cooling rate and substrate wettability and geometry. Structure I and II hydrates are examined, with the following guest molecules: CO2, CH4, N2, cyclopentane, and cyclopentane + CO2. By lowering the temperature well below 0 °C, i.e., under strong subcooling, all these hydrates but the cyclopentane hydrate nucleate without forming ice on the liquid water – guest meniscus, which is rapidly covered with a polycrystalline crust. The hydrate then propagates from this meniscus as fast-growing fibers or dendrites in bulk water and as a thin polycrystalline crust, or halo, along the capillary wall. On water-wet substrates, this halo advances on the guest side of the meniscus, fed by a water layer sandwiched between the halo and glass. Symmetrically, on guest-wet (silane-treated) glass, the halo and an underlying guest layer grow on the water side of the interface. No halo is observed on intermediate-wet glass. The hydrate halo growth and morphology and the thickness of its underlying water (or guest) layer strongly depend on subcooling. Thanks to the small capillary volume and the rapid temperature descent, the metastability limit of CO2 hydrate is approached for various pressures and substrate wettabilities. The low subcooling regime is investigated as well: a novel CO2 hydrate morphology is discovered for subcoolings below 0.5 °C, which consist of a hollow hydrate crystal originating from the water – guest meniscus and advancing on the guest side along glass, fed by a thick water layer sandwiched between glass and this crystal. A new procedure is proposed to determine gas hydrate dissociation conditions in a large temperature and pressure range, including the metastable extension of the three-phase (liquid water – hydrate - guest) down to temperatures well below 0 °C. Finally, the mechanisms by which CO2 and cyclopentane synergistically act to form the structure II hydrate are discussed.

The availability of high quality thermodynamic data on solid solutions and compounds present in multicomponent systems assists in optimizing processing parameters for synthesis, and in evaluating stability domains and materials compatibility under different conditions. Several oxide systems of technological interest, for which thermodynamic data was either not available or is inconsistent were selected for study. Thermodynamic properties of phases present in the binary systems Nb-O and Ta-O were measured in the temperature range from 1000 to 1300 K using solid state electrochemical cells based on (Y2O3) ThO2 as the electrolyte. Based on these measurements and more recent data on heat capacity and phase transitions reported in the literature, Gibbs energy of formation for NbO, NbO2, NbO2.422, Nb2O5-x and Ta2O5 were reassessed. Significant improvements in the data for NbO2, Nb2O5 and Ta2O5 are suggested. The pseudo binary system MoO2-TiO2 was investigated because of the inconsistency between the phase diagram and thermodynamic properties of the solid solution reported in the literature. Based on new electrochemical measurements, a new improved phase diagram for the system MoO2-TiO2, incorporating recently discovered monoclinic to tetragonal phase transition in MoO2 at 1533 K, is presented. Isothermal section of the phase diagram for the ternary systems Cr-Rh-O and Ta-Rh-O and thermodynamic properties of ternary oxides CrRhO3 and TaRhO4 were measured for the first time in the temperature range from 900 to 1300 K. Phase relations for these systems have been computed as a function of oxygen potential at fixed temperature and as a function of temperature at selected oxygen partial pressures. Metal-spinel-corundum three-phase equilibrium in the Ni-Al-Cr-O system at 1373 K has been explored because of its relevance to high temperature corrosion of super alloys. The Gibbs energy of mixing of spinel solid solution was derived from the tie-line data and is compared with the values calculated from cation distribution models. An oxygen potential diagram is developed for the decomposition of spinel solid solution to nickel and corundum solid solution at 1373 K under reducing conditions. The high temperature thermodynamic properties of the phases present in quaternary systems Ca-Co-Al-O and Ca-Cu-Ti-O have been measured by solid state electrochemical cells based on stabilized zirconia. Gibbs energies of formation of the quaternary oxides Ca3CoAl4O10 in the temperature range from 1150 to1500 K and CaCu3Ti4O12 in the range from 900 to 1350 K are presented. Chemical potential diagrams have been computed for the system Al2O3-CaO-CoO at 1500 K. The oxygen potential corresponding to the decomposition of the complex perovskite CaCu3Ti4O12 (CCTO) has been calculated as a function of temperature from the emf of the cell. The effect of the oxygen partial pressure on the phase relations in the pseudo-ternary system CaO-(CuO/Cu2O)-TiO2 at 1273 K has been evaluated. The phase diagrams are useful for the control of the secondary phases that form during synthesis of CCTO, a material exhibiting colossal dielectric response.

Die ternären Systeme Ti/P/Te, Ce/P/Te und Si/P/Te wurden in der vorliegenden Dissertation hinsichtlich der Existenz neuer Verbindungen untersucht. Diese Verbindungen wurden insbesondere in Bezug auf ihre thermochemischen Eigenschaften charakterisiert. Durch Kombination von experimentellen Untersuchungen und thermodynamischen Modellierungen der ablaufenden Festkörper-Gasphasen-Gleichgewichte konnten die Synthesen der neuen Verbindungen optimiert werden. Abschließend erfolgte zudem die physikalische und kristallographische Charakterisierung der gefundenen Phosphidtelluride.

The knowledge of phase equilibrium is essential for the planning and realisation of separation processes in chemical engineering. In this work an equipment for measurement of precise isothermal vapour–liquid equilibria (VLE) using the dynamic method was developed. The pool of experimental data for cyclohexylamine was extended significantly. Isothermal VLE were measured in 3 binary and 4 ternary systems, liquid-liquid equilibria (LLE) were measured in 4 ternary systems and in one quarternary system, in each case for two temperatures, whereas in 2 ternary systems and in the quarternary system even liquid-liquid-liquid equilibria (LLLE) occur. Furthermore, activity coefficients at infinite dilution in 4 binary systems and excess molar volumes in 7 binary systems have been estimated. Binary VLE and LLE data of the components water, octane, cyclohexylamine and aniline of this work and data from literature were fitted with the activity coefficient models NRTL and UNIQUAC, as well as with the equations of state Elliott-Suresh-Donohue (ESD) and Perturbed-Chain-Statistical Associating Fluid Theory (PC-SAFT) which contain both a term to consider explicit hydrogen bonds. In addition, the predictive capabilities of the equations of state (EoS) were investigated. With parameters obtained by simultaneous fitting of VLE and, if available, LLE data similar results with the models NRTL and UNIQUAC could be obtained. Each time the deviations for the vapour pressure were lower than 3 % and lower than 2 % in vapour phase composition. The deviations, in three out of the six systems for vapour pressure and vapour phase composition, were larger with the ESD-EoS than with the activity coefficient models. NRTL, UNIQUAC and ESD delivered similar results with the simultaneously fitted parameters for the LLE, whereas the deviations were lower than 5 %. Comparable results were delivered by the ESD-EoS and PC-SAFT for the fitting and the prediction in the investigated binary systems. Also a fitting for NRTL, UNIQUAC and ESD was carried out, but only to one data set. The intention was to show the effect of parameterization on prediction in ternary systems. Predictions were made for VLE and LLE in ternary systems of the above mentioned components, solely with interaction parameters fitted to binary data. For the models NRTL, UNIQUAC und ESD predictions of simultaneously and separately fitted parameters are presented. It is shown that with parameters simultaneously fitted to several data sets significantly better results could be obtained compared to the parameters separately fitted to a single data set. Additionally, for the equations of state ESD and PC-SAFT predictions for the LL(L)E in ternary systems are compared, but here only with separately fitted parameters. For three out of the four investigated ternary systems a too large miscibility gap is calculated with the models NRTL, UNIQUAC and ESD. In the system water+octane+aniline good results could be obtained for the prediction of the LLLE. In summary the equations of state deliver similar results. In the systems water+octane+CHA and octane+CHA+aniline also too large two phase regions were delivered. Better predictions could be obtained in the systems water+octane+aniline and water+CHA+aniline. The forecasts of the VLE in the ternary systems are good with the simultaneously fitted parameters. The deviations for the vapour phase compositions are as for the vapour pressures under 6 %. Larger deviations occur for the system water+octane+aniline only. As evaluation result for the thermodynamic models can be mentioned that the activity coefficient models NRTL and UNIQUAC deliver somewhat better results for the fitting of the binary data than the equations of state ESD and PC-SAFT however, with a larger number of adjustable parameters. The prediction of the VLE is satisfactorily in the ternary systems and with similar quality of all considered models. Larger deviations occur for the prediction of the LL(L)E in the ternary systems. The results of the ESD-EoS were, with one exception, each time better than those of the activity coefficient models. There is no significant difference between the prediction of the ternary systems for the ESD-EoS and the PC-SAFT.

Polyhalite is an abundant distributed mineral in rock salt formations, and considered to respond as a natural heavy metal sink because the Mg2+ ion can be substituted by other bivalent metal ions like Mn2+, Co2+, Ni2+, Cu2+ and Zn2+. One of the quantities needed to predict mineral solubilities in multi-electrolyte solutions is the solubility constant Ksol. Since polyhalite forms slowly over months or years at 298 K, the solid-liquid phase equilibria experiments were accomplished at 313 K. Enthalpies of dissolution were measured and used to extrapolate lnKsol from 313 K to 298 K. Pitzer’s equations have been applied to describe activities of solute and water, with Pitzer parameters estimated from experimental data. The solubility constants for the polyhalites were applied to calculate the solubility equilibria in the quaternary systems K+, M2+, Ca2+ / SO42- // H2O (M = Mg, Mn, Co, Cu, Zn) at 298 K and 313 K, and in case of Mg-polyhalite also in the hexary system Na+, K+, Mg2+, Ca2+ / Cl-, SO42- // H2O.

Specific Interactions in Carbon Dioxide + Polymer Systems Anupama Kasturirangan 163 Pages Directed by Dr. Amyn S. Teja Weak complex formation in CO2 + polymer and CO2 + copolymer systems containing C=O and C-F groups was quantified using in situ FTIR spectroscopy. The enthalpy of interaction thus obtained was directly incorporated into a lattice model and compressibility effects were accounted for via ratio of free volumes in modified segment number. CO2 + fluropolymer phase behavior could be correlated within experimental error (AAD of about 2%) using the new model, a task that has been beyond the capability of published models and it was also possible to predict phase equilibria of CO2 + PLGA copolymer systems with a single parameter obtained by fitting cloud point behavior in a reference system (CO2 + PLA in this case).New data on sorption equilibria in several CO2 + PLGA systems were obtained using a quartz crystal microbalance (QCM) and new data on Tg depression in the CO2 + PLA system were also obtained using a high pressure DSC method and used to demonstarte that model parameters are valid over extended pressure ranges. The new compressible lattice model developed is thus able to correlate cloud points, sorption equilibria, glass transition temperatures, and melting points using a single parameter. The model is therefore likely to be beneficial in many applications involving CO2 + polymer systems including drug delivery and encapsulation, polymer coating, and membranes for natural gas separations.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Métodos de otimização que utilizam condições de otimalidade de primeira e/ou segunda ordem são conhecidos por serem eficientes. Comumente, esses métodos iterativos são desenvolvidos e analisados à luz da análise matemática do espaço euclidiano n-dimensional, cuja natureza é de caráter local. Consequentemente, esses métodos levam a algoritmos iterativos que executam apenas as buscas locais. Assim, a aplicação de tais algoritmos para o cálculo de minimizadores globais de uma função não linear,especialmente não-convexas e multimodais, depende fortemente da localização dos pontos de partida. O método de Otimização Global Topográfico é um algoritmo de agrupamento, que utiliza uma abordagem baseada em conceitos elementares da teoria dos grafos, a fim de gerar bons pontos de partida para os métodos de busca local, a partir de pontos distribuídos de modo uniforme no interior da região viável. Este trabalho tem dois objetivos. O primeiro é realizar uma nova abordagem sobre método de Otimização Global Topográfica, onde, pela primeira vez, seus fundamentos são formalmente descritos e suas propriedades básicas são matematicamente comprovadas. Neste contexto, propõe-se uma fórmula semi-empírica para calcular o parâmetro chave deste algoritmo de agrupamento, e, usando um método robusto e eficiente de direções viáveis por pontos-interiores, estendemos o uso do método de Otimização Global Topográfica a problemas com restrições de desigualdade. O segundo objetivo é a aplicação deste método para a análise de estabilidade de fase em misturas termodinâmicas,o qual consiste em determinar se uma dada mistura se apresenta em uma ou mais fases. A solução deste problema de otimização global é necessária para o cálculo do equilíbrio de fases, que é um problema de grande importância em processos da engenharia, como, por exemplo, na separação por destilação, em processos de extração e simulação da recuperação terciária de petróleo, entre outros. Além disso, afim de ter uma avaliação inicial do potencial dessa técnica, primeiro vamos resolver 70 problemas testes, e então comparar o desempenho do método proposto aqui com o solver MIDACO, um poderoso software recentemente introduzido no campo da otimização global. / Optimization methods that use optimality conditions of first and/or second order are known to be efficient. Commonly, such iterative methods are developed and analyzed in the light of knowledge concerning the mathematical analysis in n-dimensional Euclidean spaces, whose nature is of local character. Consequently, these methods lead to iterative algorithms that perform only local searches. Thus, the application of such algorithms to the calculation of global minimizers of a non-linear function, especially non-convex and multimodal, depends strongly on the location of the starting points. The Topographical Global Optimization method is a clustering algorithm, which uses an ingenious approach based on elementary concepts of graph theory, in order to generate good starting points for local search methods, from points distributed uniformly in the interior of the feasible set. The purpose of this work is two-fold. The first is a revisit to the Topographical Global Optimization method, where, for the first time, its foundations are formally described and its basic properties are mathematically proven. In this context, we propose a semi-empirical formula for computing the key parameter of this clustering algorithm, and, using a robustand efficient direction interior-point method, we extend the use of the Topographical Global Optimization method to problems with inequality constraints. The second objective is the application of this method to the phase stability analysis of mixtures, a difficult and important global optimization problem of the chemical engineering thermodynamics. Furthermore, in order to have an initial assessment of the power of this technique,first we solve 70 test problems, and then compare the performance of the method considered here with the MIDACO solver, a powerful software recently introduced in the field of global optimization.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Métodos de otimização que utilizam condições de otimalidade de primeira e/ou segunda ordem são conhecidos por serem eficientes. Comumente, esses métodos iterativos são desenvolvidos e analisados à luz da análise matemática do espaço euclidiano n-dimensional, cuja natureza é de caráter local. Consequentemente, esses métodos levam a algoritmos iterativos que executam apenas as buscas locais. Assim, a aplicação de tais algoritmos para o cálculo de minimizadores globais de uma função não linear,especialmente não-convexas e multimodais, depende fortemente da localização dos pontos de partida. O método de Otimização Global Topográfico é um algoritmo de agrupamento, que utiliza uma abordagem baseada em conceitos elementares da teoria dos grafos, a fim de gerar bons pontos de partida para os métodos de busca local, a partir de pontos distribuídos de modo uniforme no interior da região viável. Este trabalho tem dois objetivos. O primeiro é realizar uma nova abordagem sobre método de Otimização Global Topográfica, onde, pela primeira vez, seus fundamentos são formalmente descritos e suas propriedades básicas são matematicamente comprovadas. Neste contexto, propõe-se uma fórmula semi-empírica para calcular o parâmetro chave deste algoritmo de agrupamento, e, usando um método robusto e eficiente de direções viáveis por pontos-interiores, estendemos o uso do método de Otimização Global Topográfica a problemas com restrições de desigualdade. O segundo objetivo é a aplicação deste método para a análise de estabilidade de fase em misturas termodinâmicas,o qual consiste em determinar se uma dada mistura se apresenta em uma ou mais fases. A solução deste problema de otimização global é necessária para o cálculo do equilíbrio de fases, que é um problema de grande importância em processos da engenharia, como, por exemplo, na separação por destilação, em processos de extração e simulação da recuperação terciária de petróleo, entre outros. Além disso, afim de ter uma avaliação inicial do potencial dessa técnica, primeiro vamos resolver 70 problemas testes, e então comparar o desempenho do método proposto aqui com o solver MIDACO, um poderoso software recentemente introduzido no campo da otimização global. / Optimization methods that use optimality conditions of first and/or second order are known to be efficient. Commonly, such iterative methods are developed and analyzed in the light of knowledge concerning the mathematical analysis in n-dimensional Euclidean spaces, whose nature is of local character. Consequently, these methods lead to iterative algorithms that perform only local searches. Thus, the application of such algorithms to the calculation of global minimizers of a non-linear function, especially non-convex and multimodal, depends strongly on the location of the starting points. The Topographical Global Optimization method is a clustering algorithm, which uses an ingenious approach based on elementary concepts of graph theory, in order to generate good starting points for local search methods, from points distributed uniformly in the interior of the feasible set. The purpose of this work is two-fold. The first is a revisit to the Topographical Global Optimization method, where, for the first time, its foundations are formally described and its basic properties are mathematically proven. In this context, we propose a semi-empirical formula for computing the key parameter of this clustering algorithm, and, using a robustand efficient direction interior-point method, we extend the use of the Topographical Global Optimization method to problems with inequality constraints. The second objective is the application of this method to the phase stability analysis of mixtures, a difficult and important global optimization problem of the chemical engineering thermodynamics. Furthermore, in order to have an initial assessment of the power of this technique,first we solve 70 test problems, and then compare the performance of the method considered here with the MIDACO solver, a powerful software recently introduced in the field of global optimization.

Made available in DSpace on 2014-12-17T15:01:24Z (GMT). No. of bitstreams: 1 DivalBGN_DISSERT.pdf: 2637921 bytes, checksum: 83fbea74e9888e52417cea5286defdaa (MD5) Previous issue date: 2010-12-22 / Crude oil is a complex liquid mixture of organic and inorganic compounds that are dominated by hydrocarbons. It is a mixture of alkanes from the simplest to more complex aromatic compounds that are present derivatives such as gasoline, diesel, alcohol, kerosene, naphtha, etc.. These derivatives are extracted from any oil, however, only with a very high quality, in other words, when the content of hydrocarbons of low molecular weight is high means that production of these compounds is feasible. The American Petroleum Institute (API) developed a classification system for the various types of oil. In Brazil, the quality of most of the oil taken from wells is very low, so it is necessary to generate new technology to develop best practices for refining in order to produce petroleum products of higher commercial value. Therefore, it is necessary to study the thermodynamic equilibrium properties of its derivative compounds of interest. This dissertation aims to determine vapor-liquid equilibrium (VLE) data for the systems Phenilcyclohexane - CO2, and Cyclohexane - Phenilcyclohexane - CO2 at high pressure and temperatures between 30 to 70oC. Furthermore, comparisons between measured VLE experimental data from this work and from the literature in relation to the Peng- Robinson molecular thermodynamic model, using a simulation program SPECS IVCSEP v5.60 and two adjustable interaction parameters, have been performed for modeling and simulation purposes. Finally, the developed apparatus for determination of phase equilibrium data at high pressures is presented / O petr?leo bruto ? uma complexa mistura l?quida de compostos org?nicos e inorg?nicos em que predominam os hidrocarbonetos, desde os alcanos mais simples at? os arom?ticos mais complexos. Nessa mistura encontram-se presentes derivados como gasolina, diesel, ?lcool, querosene, nafta, g?soleos, etc., estes derivados s?o extra?dos de qualquer petr?leo, por?m, somente os com uma qualidade bastante elevada, ou seja, com teor de hidrocarbonetos de baixo peso molecular alto s?o realmente vi?veis a produ??o destes compostos. A American Petroleum Institute (API) desenvolveu um sistema de classifica??o dos tipos de petr?leo. No Brasil a qualidade da maioria dos petr?leos retirado dos po?os ? muito baixa, sendo assim, ? necess?rio obter novos conhecimentos a fim de desenvolver melhores pr?ticas de refino com o intuito de produzir derivados de petr?leo de alto valor comercial. Para isso se faz necess?rio o estudo de equil?brio termodin?mico de seus derivados. Esta disserta??o de mestrado consiste em determinar dados de equil?brio l?quido-vapor dos sistemas Fenilciclohexano - CO2 e Fenilciclohexano - Ciclohexano e CO2 a alta press?o e temperaturas entre 30 a 70 graus Celsius. Compara??es entres os dados experimentais de equil?brio liquidovapor encontrados no laborat?rio e na literatura foram realizadas em rela??o aos valores obtidos pelo modelo termodin?mico molecular de Peng-Robinson usando o programa computacional SPECS IVCSEP v5.60, com dois par?metros de intera??o ajust?veis, para fins de modelagem e simula??o. Al?m disso, ? apresentado o desenvolvimento de um equipamento de alta press?o no laborat?rio para determina??o de dados de equil?brio de fases

Orientador: Reginaldo Guirardello / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica / Made available in DSpace on 2018-08-10T21:52:58Z (GMT). No. of bitstreams: 1 Rocha_StellaAlonso_M.pdf: 1447122 bytes, checksum: 284050671a884fad6a344a1b77527d60 (MD5) Previous issue date: 2008 / Resumo: Esse trabalho é de caráter teórico e computacional e tem como objetivo o estudo e aplicação de técnicas de otimização para cálculo do equilíbrio sólido-líquido de misturas graxas binárias de origem natural, utilizando dois métodos: um problema de Programação Não-linear, implementado no software GAMS e o outro, uma análise de equações fazendo uso das condições de Kuhn-Tucker. O cálculo do equilíbrio de fases baseia-se na minimização da energia livre de Gibbs do sistema. Para a representação termodinâmica das misturas são utilizados modelos termodinâmicos capazes de representar as fases líquida e sólida. As misturas estudadas são compostas por ácidos graxos e triglicerídeos, as quais foram divididas conforme as características dos compostos utilizados: ácidos graxos saturados, insaturados e triglicerídeos, com diferentes combinações de compostos. A modelagem das fases foi desenvolvida gradativamente, inicialmente consideraram-se as fases ideais, posteriormente a fase líquida foi modelada pela equação de Margules 2-sufixos, com a fase sólida permanacendo ideal, e por fim a fase sólida foi descrita pela equação de SLAUGHTER & DOHERTY e a líquida continou a ser modelada por Margules 2-sufixos. Os modelos desenvolvidos nesse trabalho são classificados como modelos de programação não-linear convexa, o que garante a busca pelo mínimo global. Assim, quando aplicados à linguagem de programação GAMS, utilizando o solver CONOPT, ou quando utilizando as equações encontradas analiticamente, através de microcomputadores, os resultados obtidos garantem que a mínima energia livre de Gibbs foi encontrada e que a mistura está em equilíbrio. Os resultados encontrados foram comparados com os dados medidos por ROLEMBERG (2002), pela técnica DSC, apresentando uma satisfatória proximidade entre eles / Abstract: This work has a theorical and computational character which objective is the study and aplication of optimization technique for the solid-liquid equilibria calculation of binary fat mixtures with natural origin. Two methods was used: One Nonlienar Program problem,an algorithm using the software GAMS and the other, analysis of equations that use the Kuhn-Tucker constrains applied in softwares which can execute conventionals calculation, like Microsoft Excel. The calculation of phasee equilibria is based on the minimization of Gibbs free energy of the sistem. The termodynamic representation of mixtures use models which can represent liquid and solid phases. The mixtures are composed for fat acids and triglycerides which are divided on three characteristics: saturated fatty acids, unsatureted fatty acids and trigycerides with differents combination among themselves. The phases¿ modeling was developed starting for phases on ideal state. In the second step, the solid phase was considered ideal and the liquid phase was modeled using the Margules Model. At the end, it was used the Slaughter & Doherty equation to modeling the solid phase and the Margules Model continued to be used for the liquid phase. The models developed in this work are nonliner programming and convex equations, these characteristics are the proof that the optimal point found is the global optimum. So using the methods propoused in this work, the results, certainly are the minim Gibbs free energy and the compound are in equilibrium. The results founded were compared with experimental data for ROLEMBERG (2002), that were obtained with DSC technique, with satisfactory proximity among them / Mestrado / Desenvolvimento de Processos Químicos / Mestre em Engenharia Química