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Brazilian Journal of Chemical Engineering

Print version ISSN 0104-6632On-line version ISSN 1678-4383

Braz. J. Chem. Eng. vol.17 n.4-7 São Paulo Dec. 2000 

1Departamento de Procesos Químicos, Universidad Técnica Federico Santa María, Casilla 110 -V,
Phone: 56 32 654221 / 56 32 654258, Fax: 56 32 654478, Valparaíso - Chile
2 PLAPIQUI, UNS-CONICET, Camino, La Carrindanga, Km 7, Casilla de Correo 717,
(8000) Bahía Blanca, Argentina


(Received: October 18, 1999 ; Accepted: April 7, 2000)



Abstract - The solubility of ethane and carbon dioxide in lemon oil at elevated pressures has been measured using a variable volume cell, over temperature ranges of 298 - 308 K and 303 - 313 K, respectively, at pressures from 0.44 to 8.75 MPa. Partial liquid miscibility was not observed at any concentration measured. Molar densities of the saturated liquid mixtures are also reported. The Soave– Redlich– Kwong equation of state was used to fit experimental vapor– liquid equilibria of near critical light component– lemon oil mixtures. An appropriate representation of the experimental data was obtained by using a binary interaction parameter in the combinatorial rule for the cross energy parameter aij. The application of a quadratic mixing rule for the co– volume b with a binary interaction coefficient lij did not improve greatly the performance of the model.




The phase behavior of compressed gases in low-volatile solvents is of great interest for evaluation of the possibilities for supercritical extraction or separation of the natural products. Conventional distillation methods involve higher temperatures which result in decomposition of heat labile substances. Conventional extraction methods involve chemical solvents which, even in residual quantities, may be a source of toxicity (King and Bott, 1993).

The purpose of this study was to determine the bubble points and saturated molar liquid volumes experimentally for binary mixtures of carbon dioxide– lemon oil and ethane– lemon oil. In the temperature range considered in this work, partial liquid miscibility was not observed. The data obtained from the measurements were then correlated using the Soave– Redlich– Kwong equation of state with two adjustable binary interaction parameters. The supercritical gas phase was not considered in this study for phase equilibria analysis.



The experimental measurements were done in a variable– volume cell, with a maximum capacity of 80 ml, equipped with a window for visual observation and a movable piston. Figure 1 shows a diagram of the experimental set-up. The experimental equipment and procedure have been described in detail elsewhere (de la Fuente, 1994; de la Fuente et al, 1994). Briefly, the experimental technique consists of loading known amounts of lemon oil and light component (carbon dioxide or ethane) into the cell, which is maintained at the desired working temperature, controlled to within 0.1 K. The piston is then moved so as to decrease the volume of the cell and to pressurize the cell to bring the lemon oil/light component system into the one-phase region. After stabilization is attained, the pressure is slowly decreased by moving the piston back until a second phase (vapor or supercritical) starts to form and the bubble pressure is recorded. After this pressure has been determined at a given temperature, the procedure is repeated at a new temperature, until a pressure-temperature isopleth for the solution has been obtained. The estimated accuracy of the pressure measurements is ± 0.25 bar.



The carbon dioxide used had a purity of 99.8+ mol % (food grade), supplied by AGA. The ethane used had a purity of 99+ mol %, supplied by Matheson. The lemon oil contains about 40 components, but for phase equilibrium analysis, it is reasonable to treat it as a mixture of key components. The weight composition of the lemon oil used in this work, listed in Table 1, has been determined by gas chromatography (Lund and Bryan, 1976; Shaw, 1979; Mathias et al., 1986; Kalra et al, 1987). The chemicals were used without further purification.



The experimental results, expressed as the mass fraction of the light component in the liquid phase (w1), bubble pressures and saturated liquid volumes of carbon dioxide– lemon and ethane– lemon, over the temperature ranges of 303 – 313 K and 298 – 308 K, at pressures from 0.44 to 8.75 MPa, are reported in tables 2 and 3, respectively. These results are shown graphically in figures 2 and 3.





The accuracy of the experimental data (i.e. weight fraction of carbon dioxide and ethane in the liquid phase, bubble pressures and temperature, and molar volumes of the liquid phase) is estimated to be about 1.5 %. In the temperature range of measurement, partial liquid miscibility was not visually observed.

Information about phase equilibria, experimental data and correlation of the supercritical fluid in the liquid phase is quite scarce even for the lemon oil. Some studies have been performed on the phase behavior of supercritical CO2 and citrus oils. Stahl and Gerard (1985) studied the solubility of pure essential oil compounds in supercritical CO2. Coppella and Barton (1987) investigated the vapor– liquid equilibrium of lemon oil. Temelli (1987) studied the phase equilibria between supercritical CO2 and orange peel oil. Gomes de Azevedo et al. (1988) and Matos and Gomes de Azevedo (1989) studied the solubility of CO2 in Limonene, the major component of the lemon oil studied in this work. Figure 4 compares the bubble pressure for different systems at 313 K: CO2 –pure limonene, reported by Gomes de Azevedo et al. (1988); CO2 –orange oil, reported by Temelli (1987) with a 95 % of limonene; and this work with a 74 % limonene, all compositions are expressed in mass fraction. The agreement between the experimental result from the literature and this work is satisfactory. Gomes de Azevedo et al. (1993) have reported experimental data for the mixtures ethane– limonene from 288.15 to 308.15 K. No experimental data on the phase equilibria of ethane– lemon oil systems are available in the literature for comparison.




The Soave– Redlich– Kwong (Soave, 1972) equation of state was used to describe the phase equilibrium for mixtures of lemon oil with CO2 or ethane. The SRK EoS has been used most often owing to their firm roots in molecular theory and their simplicity (few adjustable parameters) to represent the phase behaviour of systems with components that present significant differences in molecular size and polarity. Few measurements are needed to correlate such models, and their capacity to predict high pressure solubilities and phase equilibria is often remarkable (Coorens et al., 1988; de la Fuente, 1994; de la Fuente et al., 1997, Haselow et al., 1986).

In order to apply the SRK equation, it is necessary to estimate the values of the critical temperature (Tc), critical pressure (Pc) and acentric factor (w) of lemon oil. This information is experimentally unattainable, based on a comparison of the lemon oil components' vapor pressures against their temperature of decomposition. The critical properties and acentric factor for lemon oil were therefore estimated considering a weighted mean value of Tc, Pc and w (de la Fuente, 1994) for the individual components, calculated with the Lydersen method (Reid et al., 1986) or obtained from Daubert and Danner (1989). The critical properties of the solute were not considered like adjustable parameters of the SRK equation. The values estimated for Tc, Pc and w of the lemon oil were 652.1 K, 2.77 MPa, and 0.350 respectively.

Taking into account the differences in molecular size and polarity of the components of the mixtures, a quadratic mixing rule with a binary interaction parameter lij was applied in the calculation of the co-volume b, in order to improve results (Shibata and Sandler, 1989). The classical quadratic mixing rule for a was also applied, together with an energy interaction parameter kij.




Values of the interaction parameters kij and lij were obtained by minimizing the differences between the experimental solubility () and the predicted (xi) solubilities, with the funtion S, where N is the number of data points.


The routine used to find the values of the binary interaction parameters kij and lij was based on a comercial sofware package available throughout universities and industry, Aspen Plus process simulator (1990).

Table 4 contains the values of the kij and lij interaction parameters obtained by fitting the experimental data with the SRK EoS. Also given in this table are the kij values obtained by application of a quadratic mixing rule for parameter a (Eq. 1) and the classical linear mixing rule for parameter b ().



Figures 5 and 6 show the bubble pressures predicted by the SRK equation for the CO2– lemon oil mixture at 313 K, and ethane– lemon oil mixture at 298 K, respectively.




For the CO2– lemon oil mixture, the introduction of a quadratic mixing rule for b, with a binary interaction parameter lij allows some improvement in the predictions of bubble pressure curves (Fig. 5).

If lij = 0, the curve for the bubble pressures predicted by the SRK follows a behavior similar to that mixtures of exhibiting incipient partial liquid miscibility. However, partial liquid miscibility was not observed visually in this study.

As can be infered from Figure 6, the SRK EoS with a linear parameter b, is capable of predicting the vapor-liquid equilibria for the ethane– lemon oil mixture. There are no significant differences for the values of bubble pressures between those predicted by the SRK with a quadratic or linear-mixing rule for the co– volume b.

The mixing rules applied in this work are empirical expressions, and moreover the binary intereaction parameters, are empirical corrections. Qualitatively, the parameter kij takes into account the unlike intermolecular interactions, and lij the size-ordering effects. The modeling of experimental results shows that the influence of the parameter kij is more importante that lij. It seems that the unlike intermolecular effects are more important than the size-ordering effects, for both mixtures CO2 –lemon oil and ethane– lemon oil (Peters, 1986).



The bubble points of binary mixtures and saturated molar liquid volumes of CO2 –lemon oil and ethane– lemon oil mixtures have been measured over the temperature ranges from 298 to 308 K and from 303 to 313 K, respectively, at pressures from 0.44 to 8.75 MPa. The systems do not exhibit partial liquid miscibility within the whole range of concentrations studied.

The results of phase equilibria predictions by the Soave– Redlich– Kwong equation of state indicate that the predominant effect of the molecular interactions is energetic; i.e. there are no significant differences for the values of bubble pressures predicted by the SRK with a quadratic or linear mixing rule.



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