-The tangent plane criterion has become important for a correct solution evaluation phase and chemical of equilibrium problem. This method, applicable to single and multiphase systems, is mainly used for a single equation of state modeling all phases involved. The present work is mainly concerned with the application of interval analysis methods for global energy minimization in high-pressure phase stability problems. Two approaches are applied: (i) the Gibbs free energy global minimization under conditions of constant temperature and pressure and (ii) the Helmholtz free energy density global minimization under conditions of constant temperature and volume. Five case studies, one ternary and four binary systems, are analyzed in connection with the Peng-Robinson equation of state (PREOS) model. Five more case studies, for the CO 2 + trans-2-hexen-1-ol system at high pressures, are used to compare different methods of phase equilibrium calculation with the approach using interval analysis. Finally, a complex system, clove oil + CO 2 , is analyzed. The results indicate that the interval analysis method is robust and reliable for all the problems studied.

Tobacco dependence is characterised as a chronic, relapsing disorder that typically requires multiple quit attempts before successful, long-term abstinence is achieved (Steinberg, Foulds, Richardson, Burke, & Shah, 2006). Best practice, evidence-based treatment includes multiple-session counselling and pharmacotherapy, or the combination of both (Fiore et al., 2008). The field has moved past the notion that tobacco dependence is simply a bad habit, a vice, or a moral deficiency that can be overcome by willpower or education alone (Mars & Ling, 2008). However, the language used in discussing treatment has not always been consistent with this evidence. Some words and phrases used lend themselves to varied meanings, and could lead to significant misunderstanding not only among professionals in the field, but also among the general public (O'Brien, 2010; Davis, 1992; Perkins, 1999; Hughes, 2013). In this paper, we discuss some commonly used, problematic terminology, and suggest more appropriate terms (Table 1).

This work describes a method to predict the solubility of essential oils in supercritical carbon dioxide. The method is based on the formulation proposed in 1979 by Asselineau, Bogdanic and Vidal. The Peng-Robinson and Soave-Redlich-Kwong cubic equations of state were used with the van der Waals mixing rules with two interaction parameters. Method validation was accomplished calculating orange essential oil solubility in pressurized carbon dioxide. The solubility of orange essential oil in carbon dioxide calculated at 308.15 K for pressures of 50 to 70 bar varied from 1.7± 0.1 to 3.6± 0.1 mg/g. For same the range of conditions, experimental solubility varied from 1.7± 0.1 to 3.6± 0.1 mg/g. Predicted values were not very sensitive to initial oil composition.
Este trabalho descreve uma metodologia para o cálculo da solubilidade de óleos essenciais em dióxido de carbono a altas pressões baseada na formulação proposta em 1979 por Asselineau, Bogdanic e Vidal. Foram utilizadas as equações cúbicas de estado de Peng-Robinson e Soave-Redlich-Kwong com regras de mistura de van der Waals com dois parâmetros de interação. O cálculo da solubilidade do óleo essencial de laranja em dióxido de carbono pressurizado foi usado para validação do método. A solubilidade calculada a 308,15 K para pressões entre 50 e 70 bar variou entre 1,5 e 4,1 mg/g. Valores experimentais para as mesmas condições variam entre 1,7± 0.1 a 3,6± 0.1 mg/g. Os valores preditos não são muito sensíveis à composição inicial do óleo essencial

One of the most important byproducts of the orange juice industry is the oil phase. This is a mixture of terpenes, alcohols, and aldehydes, dissolved in approximately 96% limonene. To satisfactorily use oil phase as an ingredient in the food and cosmetics industries separation of the limonene is required. One possibility is to use a fixed bed of silica gel to remove the light or aroma compounds from the limonene. The aroma substances are then extracted from the bed of silica gel using supercritical carbon dioxide. This work deals with the modeling of the desorption step of the process using mass balance equations coupled with the Langmuir equilibrium isotherm. Data taken from the literature for the overall extraction curves were used together with empirical correlations to calculate the concentration profile of solute in the supercritical phase at the bed outlet. The system of equations was solved by the finite volume technique. The overall extraction curves calculated were in good agreement with the experimental ones

The generalized maximum likelihood method was used to determine binary interaction parameters between carbon dioxide and components of orange essential oil. Vapor-liquid equilibrium was modeled with Peng-Robinson and Soave-Redlich-Kwong equations, using a methodology proposed in 1979 by Asselineau, Bogdanic and Vidal. Experimental vapor-liquid equilibrium data on binary mixtures formed with carbon dioxide and compounds usually found in orange essential oil were used to test the model. These systems were chosen to demonstrate that the maximum likelihood method produces binary interaction parameters for cubic equations of state capable of satisfactorily describing phase equilibrium, even for a binary such as ethanol/CO2. Results corroborate that the Peng-Robinson, as well as the Soave-Redlich-Kwong, equation can be used to describe phase equilibrium for the following systems: components of essential oil of orange/CO2.
Foi empregado o método da máxima verossimilhança generalizado para determinação de parâmetros de interação binária entre os componentes do óleo essencial de laranja e dióxido de carbono. Foram usados dados experimentais de equilíbrio líquido-vapor de misturas binárias de dióxido de carbono e componentes do óleo essencial de laranja. O equilíbrio líquido-vapor foi modelado com as equações de Peng-Robinson e de Soave-Redlich-Kwong usando a metodologia proposta em 1979 por Asselineau, Bogdanic e Vidal. A escolha destes sistemas teve como objetivo demonstrar que o método da máxima verosimilhança produz parâmetros de interação binária, para equações cúbicas de estado capazes de descrever satisfatoriamente até mesmo o equilíbrio para o binário etanol/CO2. Os resultados comprovam que tanto a equação de Peng-Robinson quanto a de Soave-Redlich-Kwong podem ser empregadas para descrever o equilíbrio de fases para o sistemas: componentes do óleo essencial de laranja/CO2