Fundando-se em argumentos de equilíbrio e estabilidade termodinâmica, a solubilidade de soluto em um solvente é definida pelo limiar de existência da mistura como sistema homogêneo. De fato, entende-se tal grandeza sobre a coexistência de fases. A noção de solubilidade apresentada é desenvolvida através de modelos simples, que incluem resultados na rede bem como a extensão do modelo de van der Waals ao caso de duas componentes. Desta extrai-se uma condição genérica à observação de mínimos na solubilidade incidente sobre a topologia de seu diagrama de fases e de evidente correspondência física. / Concerning the equilibrium and stability in thermodynamics, the solubility of solute in a solvent is defined as the threshold of the mixture existing as a homogeneous system. Indeed, such quantity meets its meaning when understood on the coexistence surface. The idea of solubility presented is developed following the discussion of simple models, including results on the lattice as well as the van der Waals model extended to include two components. From these results we extract a general condition which connects the occurence of a minimum in solubility to the topological structure of the phase diagram.

The knowledge of the phase behaviour of heavy oils and bitumen is important in order to understand the phenomenon of coke formation. Computation of their phase behaviour, using an equation of state, faces problems due to their complex composition. Hence n-alkane binaries of polyaromatic hydrocarbons are used to approximate the phase behaviour of heavy oils and bitumen. Appropriate values of binary interaction parameters are required for an equation of state to predict the correct phase behaviour of these model binary fluids. This thesis deals with fitting of the binary interaction parameter for the Peng-Robinson equation of state using landmarks in the binary phase space such as K- and L-points. A K- or an L-point is a point in the phase space where two phases become critical in the presence of another phase in equilibrium. An algorithm to calculate K- and L-points using an equation of state was developed. The variation of calculated K- and L-points with respect to the binary interaction parameter was studied and the results were compared with the experimental data in the literature. The interaction parameter was then fitted using the best match of experimental results with the computed ones. The binary interaction parameter fitted using a K- or an L-point was then used to predict the P-T projection of the binary system in phase space. Also, the qualitative effect of the binary interaction parameter on the P-T projection was studied. A numerical and thermodynamic study of the algorithm was done. Numerical issues like the initial guesses, convergence criterion and numerical techniques were studied and the thermodynamic constraints in the generalization of the algorithm are discussed. It was observed that the binary interaction parameter not only affects the location of K- and L-points in the phase space but also affects the calculation procedure of K- and L-points. Along with the propane binaries of polyaromatic hydrocarbons, K- and L-points were also calculated for systems like methane binaries of higher n-alkanes and the ethane + ethanol binary. In the case of the ethane + ethanol system, K- and L-points, matching the experimental results were calculated with different values of the binary interaction parameter. But the Peng-Robinson equation of state was unable to predict the correct type of phase behaviour using any value of the binary interaction parameter. The Peng-Robinson equation of state was able to predict the correct type of phase behaviour with the binary interaction parameter, fitted using K- and/or L-points for methane + n-alkane systems. The systems studied were the methane binaries of n-pentane, n-hexane and n-heptane. For the propane binaries of polyaromatic hydrocarbons, no value of the binary interaction parameter was able to predict the K-point with a good accuracy. The binary interaction parameter which gave the best possible results for a K-point failed to predict the correct type of phase behaviour. The binary interaction parameter fitted using the P-T projection enabled the Peng-Robinson equation of state to give a qualitative match for the high pressure complex phase behaviour of these systems. Solid phase equilibria were not taken into consideration.

The knowledge of the phase behaviour of heavy oils and bitumen is important in order to understand the phenomenon of coke formation. Computation of their phase behaviour, using an equation of state, faces problems due to their complex composition. Hence n-alkane binaries of polyaromatic hydrocarbons are used to approximate the phase behaviour of heavy oils and bitumen. Appropriate values of binary interaction parameters are required for an equation of state to predict the correct phase behaviour of these model binary fluids. This thesis deals with fitting of the binary interaction parameter for the Peng-Robinson equation of state using landmarks in the binary phase space such as K- and L-points. A K- or an L-point is a point in the phase space where two phases become critical in the presence of another phase in equilibrium. An algorithm to calculate K- and L-points using an equation of state was developed. The variation of calculated K- and L-points with respect to the binary interaction parameter was studied and the results were compared with the experimental data in the literature. The interaction parameter was then fitted using the best match of experimental results with the computed ones. The binary interaction parameter fitted using a K- or an L-point was then used to predict the P-T projection of the binary system in phase space. Also, the qualitative effect of the binary interaction parameter on the P-T projection was studied. A numerical and thermodynamic study of the algorithm was done. Numerical issues like the initial guesses, convergence criterion and numerical techniques were studied and the thermodynamic constraints in the generalization of the algorithm are discussed. It was observed that the binary interaction parameter not only affects the location of K- and L-points in the phase space but also affects the calculation procedure of K- and L-points. Along with the propane binaries of polyaromatic hydrocarbons, K- and L-points were also calculated for systems like methane binaries of higher n-alkanes and the ethane + ethanol binary. In the case of the ethane + ethanol system, K- and L-points, matching the experimental results were calculated with different values of the binary interaction parameter. But the Peng-Robinson equation of state was unable to predict the correct type of phase behaviour using any value of the binary interaction parameter. The Peng-Robinson equation of state was able to predict the correct type of phase behaviour with the binary interaction parameter, fitted using K- and/or L-points for methane + n-alkane systems. The systems studied were the methane binaries of n-pentane, n-hexane and n-heptane. For the propane binaries of polyaromatic hydrocarbons, no value of the binary interaction parameter was able to predict the K-point with a good accuracy. The binary interaction parameter which gave the best possible results for a K-point failed to predict the correct type of phase behaviour. The binary interaction parameter fitted using the P-T projection enabled the Peng-Robinson equation of state to give a qualitative match for the high pressure complex phase behaviour of these systems. Solid phase equilibria were not taken into consideration.

13C NMR spectroscopic analysis was carried out to clarify the formed hydrate structure in specific conditions on hydrate phase diagram of ternary methane, neohexane, and water system. The obtained NMR spectra at three different conditions suggested that both structure I and H were formed simultaneously and coexisted at 273.6 K and 50 bar. But, for both conditions of 273.6 K, 25 bar and 283.1 K, 50 bar the formed hydrate was identified as structure H only. These results showed that the pure CH4 hydrate of structure I was formed and coexisted with mixed CH4+neohexane hydrate of structure H in low temperature and high pressure region after passing through the phase boundary of pure CH4 hydrate. We have examined the structure coexistence at 273.6 K and 50 bar with other structure H formers of isopentane, methylcyclopentane, and methylcyclohexane. In case of isopentane, the obtained NMR spectrum showed that structure I and H coexisted and the amount of methane molecules in structure I was two times as many as in cages of structure H. However, there were no resonance lines of structure I when methylcyclohexane formed structure H with methane molecules.

Lactic acid is a fermentation-derived organic acid used in a wide range of industries, such as food processing and pharmaceuticals. Its market is expected to expand due to the worldwide concern for the environment, as it is an essential feedstock for biodegradable polymers. However, fermentation product is a very dilute, multicomponent aqueous solution. Subsequent separation, purification and concentration of organic acids is difficult because of high affinity of the acids for water. Reactive extraction is a viable alternative to classical separation techniques. Amine extractants dissolved in organic diluents are suitable agents with reasonable ranges of viscosity and density of the solvent phase. The product is obtained in an organic phase after reactive extraction. The aim of this study is to obtain equilibrium data of back extraction of lactic acid into appropriate aqueous solutions from the organic phase. Aqueous solutions of NaCl, NaOH, Na2SO4, NaNO3 and Na2CO3 were examined as back extractant in various initial concentrations (0.005 &ndash / 3 M). The organic phase consists of tri-n-octylmethylammonium lactate (TOMA(La)) dissolved in either oleyl alcohol or octanol with initial concentrations between 0.1 and 0.3 M. According to results of the experiments, the level of back extraction generally increased with increasing initial salt concentration in aqueous phase and decreased with increasing initial TOMA(La) concentration in organic phase. For all salts investigated, considerable levels of back extraction were obtained. NaOH was considered as the most suitable back extractant among the salts investigated since it exhibits higher distribution coefficients, regenerates tri-n-octylmethylammonium hydroxide (TOMAOH) in the organic phase and has no adverse effect on fermentation medium when forward and backward extraction steps are coupled with the fermentation. The effect of diluent type of TOMA(La) was also investigated during the experiments and it was concluded that octanol is a better diluent since it gives higher equilibrium distribution coefficients in addition to its higher solvating power and lower viscosity. The present work is a part of a comprehensive research program aiming to collect data and develop knowledge for the design of an industrial reactive extraction process coupling forward and backward extraction of lactic acid in a single unit and integrating fermentation and product separation. The kinetic parameters should be obtained as the next step for the design of such a process.

Biodiesel is a fuel derived from renewable sources as vegetable oils and animal fat and can be obtained from transesterification reaction. This process involves reacting vegetable oil with alcohol in the presence of a catalyst, followed by a purification step. The focus of this study was to determine the binodal curve and the tie lines for ternary mixtures of biodiesel from castor oil-ethanol-glycerin. The liquid-liquid equilibrium data will assist the purifying of the final product from transesterification reaction. The binodal curves were determined at 30 °C, 45 °C and 60 °C, and the tie lines were obtained for the system at 30 °C. The parameters used to determine the tie lines were the viscosity and density, instead of gas chromatography, traditionally used to determine the composition of the phases. The tie lines to the system of castor oil biodiesel - ethanol - glycerin at 30 °C obtained from the viscosity of the rich phase in biodiesel and the rich phase in glycerin, showed satisfactory results, providing data of phases composition. However, when using the density, the results were inconsistent with the observed data in the literature. / Biodiesel é um combustível derivado de fontes renováveis como óleos vegetais e gordura animal e pode ser obtido a partir da reação de transesterificação. Este processo consiste em reagir o óleo vegetal com álcool seguida por uma etapa de purificação. O foco deste trabalho foi à obtenção das curvas binodais e a determinação das linhas de amarração para o sistema ternário biodiesel de mamona- etanol-glicerina, visando obter resultados de equilíbrio líquido-líquido que possam auxiliar a etapa de purificação do produto final da reação de transesterificação. As curvas binodais foram determinadas a temperatura de 30 ºC, 45 ºC e 60 ºC, e as linhas de amarração foram obtidas para o sistema a 30 °C. Os parâmetros utilizados para a determinação das linhas de amarração foram à viscosidade e a densidade, ao invés da cromatografia gasosa, tradicionalmente utilizada para determinação da composição das fases. A determinação das linhas de amarração para o sistema biodiesel de mamona-etanol-glicerina a 30 °C, através da viscosidade da fase rica em glicerina e da fase rica em biodiesel, apresentaram resultados satisfatórios, fornecendo dados bem caracterizados do sistema. No entanto, quando da utilização da densidade das fases, os resultados não apresentaram coerência com os dados observados na literatura.

Fundando-se em argumentos de equilíbrio e estabilidade termodinâmica, a solubilidade de soluto em um solvente é definida pelo limiar de existência da mistura como sistema homogêneo. De fato, entende-se tal grandeza sobre a coexistência de fases. A noção de solubilidade apresentada é desenvolvida através de modelos simples, que incluem resultados na rede bem como a extensão do modelo de van der Waals ao caso de duas componentes. Desta extrai-se uma condição genérica à observação de mínimos na solubilidade incidente sobre a topologia de seu diagrama de fases e de evidente correspondência física. / Concerning the equilibrium and stability in thermodynamics, the solubility of solute in a solvent is defined as the threshold of the mixture existing as a homogeneous system. Indeed, such quantity meets its meaning when understood on the coexistence surface. The idea of solubility presented is developed following the discussion of simple models, including results on the lattice as well as the van der Waals model extended to include two components. From these results we extract a general condition which connects the occurence of a minimum in solubility to the topological structure of the phase diagram.

Fundando-se em argumentos de equilíbrio e estabilidade termodinâmica, a solubilidade de soluto em um solvente é definida pelo limiar de existência da mistura como sistema homogêneo. De fato, entende-se tal grandeza sobre a coexistência de fases. A noção de solubilidade apresentada é desenvolvida através de modelos simples, que incluem resultados na rede bem como a extensão do modelo de van der Waals ao caso de duas componentes. Desta extrai-se uma condição genérica à observação de mínimos na solubilidade incidente sobre a topologia de seu diagrama de fases e de evidente correspondência física. / Concerning the equilibrium and stability in thermodynamics, the solubility of solute in a solvent is defined as the threshold of the mixture existing as a homogeneous system. Indeed, such quantity meets its meaning when understood on the coexistence surface. The idea of solubility presented is developed following the discussion of simple models, including results on the lattice as well as the van der Waals model extended to include two components. From these results we extract a general condition which connects the occurence of a minimum in solubility to the topological structure of the phase diagram.

Orientador: Maria Angela de Almeida Meireles / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia de Alimentos / Made available in DSpace on 2018-08-25T04:15:24Z (GMT). No. of bitstreams: 1 Debien_IsabelCristinadoNascimento_D.pdf: 14354516 bytes, checksum: 30a73e64c77ed62ec9c96b7c5a8067b0 (MD5) Previous issue date: 2014 / Resumo: O presente projeto de doutorado foi desenvolvido em duas etapas: (1) Estudo da extração com fluido supercrítico e com líquido pressurizado dos ecdisteróides do Ginseng brasileiro (Pfaffia glomerata) e (2) Estudo do equilíbrio de fases de sistemas complexos. Etapa 1: Espécies do gênero Pfaffia são popularmente conhecidas como substituto do gênero Panax devido a sua morfologia e propriedades bioativas semelhantes. Dentre as espécies do gênero Pfaffia, a Pfaffia glomerata, popularmente conhecida como Ginseng brasileiro, se destaca devido à presença de ecdisteróides. Comercialmente, esse composto é obtido através de métodos convencionais de extração sólido-líquido, onde uma grande quantidade de solvente é utilizada. Atualmente, há um crescente interesse por métodos de extração que agridam menos o meio ambiente, como é o caso da extração com fluido supercrítico (SFE) e com líquido pressurizado (PLE) que possibilitam a extração de compostos bioativos utilizando altas temperaturas e pressões com menor consumo de solvente. Nessa etapa do trabalho os objetivos foram: (a) realizar um estudo preliminar da extração com fluido supercrítico da beta-ecdisona das raízes de Ginseng brasileiro (Pfaffia glomerata). Foram avaliados os efeitos da pressão (20 e 30 MPa) e quantidade de cossolvente utilizada (15, 75 e 90 % de etanol) no comportamento da curva global de extração (OEC) e no teor de beta-ecdisona no extrato. Usando dióxido de carbono (CO2): etanol (EtOH) (85:15, v/v) como solvente a 20 MPa, maiores quantidade de beta-ecdisona foram obtidas em um menor tempo de processo. O aumento da proporção de etanol na mistura (cossolvente) resultou no aumento do rendimento da extração e do teor de beta-ecdisona em relação a quantidade de matéria-prima; (b) realizar um estudo da extração com líquido pressurizado da beta-ecdisona das raízes de Ginseng brasileiro. Foram avaliados os efeitos da temperatura (333 ¿ 393 K), pressão (8 ¿ 30 MPa) e do solvente (EtOH e EtOH : H2O (80:20 v/v)) no rendimento global, atividade antioxidante e teor de beta-ecdisona dos extratos. O aumento da temperatura ocasionou o aumento do rendimento global, chegando a 25 % (base seca). Assim, pode-se concluir que aumentando a temperatura a seletividade do solvente diminui, uma vez que ocorre a coextração de outros compostos além dos ecdisteróides. Extratos com maior atividade antioxidante foram obtidos quando o solvente de extração é a mistura EtOH: H2O (80:20, v/v). Quando o EtOH puro foi usado como solvente uma maior recuperação de beta-ecdisona foi obtida. Cerca de 5 % de beta-ecdisona nos extratos foi obtida usando etanol a 393 K, enquanto a pressão não afetou significativamente. Assim a melhor condição de extração em termos do teor de beta-ecdisona (393 K, 8 MPa e etanol como solvente) foi selecionada para a realização do estudo cinético. Na OEC foi possível observar que na primeira hora de extração aproximadamente 70 % do total do rendimento e 74 % do total de massa de beta-ecdisona foi obtido. O custo de manufatura foi avaliado na condição da cinética, onde foram obtidos maiores teores de beta-ecdisona quanto maior a capacidade do extrator. Os custos de manufatura, tanto em relação a quantidade de extrato quanto em relação a quantidade de beta-ecdisona recuperada no processo de PLE, foram 14 e 8 vezes maiores do que os obtidos no processo de SFE, respectivamente. Etapa 2: Polímeros biodegradáveis tem recebido maior atenção devido ao seu potencial para aplicações na área médica e na indústria de alimentos, dentre eles o poli (L-lactídeo) (PLA) principalmente por causa da sua biocompatibilidade e características sustentáveis. Ao longo dos últimos anos, a síntese de tais biopolímeros pela reação de polimerização utilizando a técnica de abertura do anel aromático catalisada enzimaticamente em fluidos comprimidos tem se mostrado bastante promissora. O objetivo nessa etapa do trabalho foi medir os dados de equilíbrio de fases dos sitemas L-ácido láctico + (propano + etanol) e L-ácido láctico + (CO2 + etanol). Os experimentos foram realizados numa célula de equilíbrio de fases com visualização utilizando o método estático sintético, em temperaturas de 323,15 a 353,15 K e pressões até 25 MPa, mantendo constante a fração mássica de etanol:CO2 (ou propano) de 1:9. Para o sistema L-ácido láctico + (propano + etanol) foram observadas as transições líquido-vapor, líquido-líquido e líquido-líquido-vapor, enquanto que para o sistema L-ácido láctico + (CO2 + etanol) foram observadas somente as transições líquido-líquido. Os resultados mostraram que o sistema L-ácido láctico + (propano + etanol) apresenta transições do tipo UCST (Upper Critical Solution Temperature) e um UCEP (Upper Critical End Point), enquanto o sistema L-ácido láctico + (CO2 + etanol) apresenta um comportamento do tipo LCST (Lower Critical Solution Temperature). Foi realizada a modelagem termodinâmica dos dados experimentais obtidos utilizando a equação de estado de Peng-Robinson com regra de mistura quadrática de van der Waals (PR-vdW2) e com regra de mistura de Wong-Sandler (PR-WS). Os resultados mostraram que os modelos PR-vdW2 e PR-WS foram capazes de representar satisfatoriamente o comportamento de fases do sistema L-ácido láctico + (dióxido de carbono + etanol). Entretanto, para o sistema L-ácido láctico + (propano + etanol), o modelo PR-vdW2 não foi capaz de descrever apropriadamente o seu comportamento / Abstract: The doctoral project is being developed in two steps: (1) Supercritical fluid and pressurized liquid extraction study of Brazilian ginseng (Pfaffia glomerata) ecdysteroids and (2) Phase equilibrium data of complex systems. Step 1: Species of the genus Pfaffia are popularly known as substitute for Panax due their similar morphology and bioactive properties. Among them, Pfaffia glomerata has received special attention due the presence of ecdysteroids. Commercially, this compound is obtained by conventional solid-liquid extraction methods, that is, using large quantities of solvents. Nowadays, more environmentally friend methods are preferred, like supercritical fluid (SFE) and pressurized liquid extraction (PLE) that enables extraction of bioactive compounds under high temperatures and pressures. The aim of this step of work is: (a) preliminary study the supercritical fluid extraction of Brazilian ginseng (Pfaffia glomerata) ecdysteroids. The effects of pressure (20 and 30 MPa) and cosolvent amount (10, 15, 75 and 90 % of Ethanol) on the behavior of overall extraction curve (OEC) and content of beta-ecdysone were studied. The larger amounts of beta-ecdysone were obtained in shorter processing time using CO2: EtOH (85:15, v/v) as extracting solvent at 20 MPa. The higher proportion of EtOH in the mixture leads an increase an extraction yield and an increase a beta-ecdysone content relative a raw material amount. (b) study the pressurized liquid extraction of Brazilian ginseng (Pfaffia glomerata) ecdysteroids. The effects of temperature (333 ¿ 393 K), pressure (8 ¿ 30 MPa) and solvent [ethanol and ethanol:water (80:20 v/v)] on the global yield extraction, antioxidant activity and beta-ecdysone content of the extracts from Brazilian ginseng (Pfaffia glomerata) roots were studied. The extraction global yield increased with the increase in temperature (333 ¿ 393 K) reaching up to 25 % (dry basis). As the temperature increased the selectivity of the extracting solvent decreased promoting the co-extraction of other compounds besides the ecdysteroids. The use of EtOH:H2O (80:20 v/v) as extracting solvent produced extracts with the highest antioxidant activity. The recovery of beta-ecdysone was maximized when EtOH was used, besides fractions containing up to 5 % of beta-ecdysone were obtained using this solvent at 393 K, while pressure did not affect it. Thus the better extraction condition in terms of beta-ecdysone was selected (393 K, 8 MPa and ethanol as extracting solvent) and the kinetic extraction study was realized. From the overall extraction curve obtained it was possible to verify that in the first hour of extraction approximately 70 % of the total yield and 74 % of the total beta-ecdysone mass are obtained. The cost of manufacturing (COM) was evaluated in the kinetic condition in which was obtained the highest beta-ecdysone content; the increase of the extractor capacity significantly decreased the COM. The COMs for the crude extract and beta-ecdysone obtained by this novel process were 14-fold and 8-fold lower than that for the SFE process, respectively. Step 2: Biodegradable polymers has received increased attention due to their potential applications in medicine and food industry, with highlights to poly (L-lactic acid) (PLA) mainly because of its biocompatibility and resorbable features. Over the last years, synthesis of such biopolymer by enzyme-catalyzed ring-opening polymerization of L-lactic acid in compressed fluids has been considered a promising route over. The aim of this step of work is to report phase equilibrium data (cloud points) of L-lactic acid + (propane + ethanol) and L-lactic acid + (carbon dioxide + ethanol). Phase equilibrium experiments were conducted in a variable-volume view cell employing the static synthetic method, from 323.15 K to 353.15 K and pressures up to 25 MPa, keeping constant the mass ratio of ethanol to CO2 or propane at 1:9. For the (propane + ethanol) + L-lactic acid it was observed vapor-liquid, liquid-liquid and vapor-liquid-liquid, while for (carbon dioxide + ethanol) + L-lactic acid only liquid-liquid type transitions were recorded. Results show that the system (propane + ethanol) + L-lactic acid present UCST (Upper Critical Solution Temperature) transition type and an UCEP (Upper Critical End Point), whereas the system (carbon dioxide + ethanol) + L-lactic acid exhibit LCST (Lower Critical Solution Temperature) behavior. The experimental data were modeled using the Peng-Robinson equation of state with the classical van der Waals quadratic mixing rule (PR-vdW2) and with the Wong-Sandler mixing rule (PR-WS). It is shown that the PR-vdW2 and PR-WS models were both able to satisfactorily represent the phase behavior of the system L-lactic acid + (carbon dioxide + ethanol). However, for the system L-lactic acid + (propane + ethanol), the PR-vdW2 model was not able to appropriately describe its phase behavior / Doutorado / Engenharia de Alimentos / Doutora em Engenharia de Alimentos

Orientador: Reginaldo Guirardello / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Química / Made available in DSpace on 2018-08-19T12:38:06Z (GMT). No. of bitstreams: 1 Cunico_LarissaPeixoto_M.pdf: 3845396 bytes, checksum: d8e7fc1418bed93fc9777451bc5ab2e5 (MD5) Previous issue date: 2012 / Resumo: A demanda mundial por energia cresce a cada ano. Essa demanda pode atingir níveis que os recursos atuais de combustíveis fósseis não podem sustentar. Neste contexto, os biocombustíveis surgem como uma fonte crescente de energia primária, aumentando a oportunidade de pesquisa e desenvolvimento de tecnologia a níveis animadores. Uma importante questão relacionada com o desenvolvimento destes biocombustíveis é o equilíbrio de fases entre seus componentes. Este trabalho investiga o equilíbrio líquido-vapor (ELV) de sistemas binários e o equilíbrio líquido-líquido (ELL) de sistemas ternários e quaternários, além do equilíbrio líquido-líquido-vapor (ELLV) de sistemas ternários, compostos por óleo vegetal, álcool, glicerina e éster, envolvidos na produção do biodiesel. O modelo desenvolvido também é capaz de predizer o equilíbrio químico e de fases para vários tipos de óleos vegetais na produção de biodiesel. Para tanto houve a necessidade da estimativa das propriedades físicas destes vários componentes e uma busca por métodos de predição através de contribuição de grupos foi realizada para as propriedades físicas não encontradas na literatura. A minimização da energia de Gibbs foi utilizada para calcular cada fase presente em uma determinada condição de pressão e temperatura, assim como a composição de cada fase prevista. A equação de estado de Soave-Redlich-Kwong (SRK-EOS) com a regra de mistura de van der Waals de dois parâmetros ajustáveis (VdW-2) foi empregada. O software GAMS® 23.1.3 (General Algebraic System Model) combinado com o solver CPLEX foi utilizado para resolver numericamente o modelo matemático. Através de discretização das frações molares, a modelagem do problema pode ser desenvolvida na forma de uma programação linear. Os dados experimentais foram representados de forma satisfatória por estes modelos e utilizando SRK-EOS obteve-se desvio absoluto médio e tempo computacional para sistemas binários, ternários e quaternários respectivamente de 1,03%, 1,39% e 1,30% e 0,17s, 27s e 6s, para os sistemas utilizando metanol. Já para os sistemas que utilizam etanol, o desvio absoluto médio e tempo computacional para sistemas binários e ternários são respectivamente de 0,64% e 2,10% e 0,14s e 26s / Abstract: The worldwide energy demand increases every year. This demand will reach levels that cannot be supplied by current conventional fossil fuel resources. In this context, biofuels arise as a growing primary source of energy, raising research opportunities and encouraging technology development. An important technical issue related to biofuels development is the phase equilibrium among their components. This work investigates the vapor-liquid equilibrium (VLE) and liquid-liquid equilibrium (LLE) of binary, ternary and quaternary systems composed by vegetable oil, alcohol, glycerol and ester, involved in biodiesel production. The Gibbs energy minimization was used to calculate the amount of each phase present in a particular condition of pressure and temperature, as well as the composition of each phase predicted. The Soave-Redlich-Kwong (SRK) equation of state with van der Waals mixing rule, with two adjustable parameters (vdW-2) was employed. The GAMS® 23.2.1 (General Algebraic Model System) in combination with the solver CPLEX was used to tackle the large and complex mathematical models. The minimization of the Gibbs energy was done using a discretized procedure, so that the problem could be solved as a linear programming approach. The proposed model is also used to predict the chemical and phase equilibrium for eight types of vegetable oils in biodiesel production. For this purpose it was necessary to estimate the physical properties of these various components and a search for methods of prediction by group contribution was made to physical properties not found in the literature. The experimental data were correlated quite well by the Soave-Redlich-Kwong (SRK) equation of state, with absolute medium deviations and computational time for binary, ternary and quaternary systems using methanol as a compound of: 0.83% and 0.17s, 1.39% and 27s and 1.30% and 6s, respectively. Using ethanol as a compound, the absolute medium deviations and computational time for binary and ternary systems of: 0,64%, 2,10% , 0,14s and 26s / Mestrado / Desenvolvimento de Processos Químicos / Mestre em Engenharia Química