Ind. Eng. Chem. Res. 2009, 48, 1551–1555
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Calculation of Solubilities for Systems Containing Multiple Non-Volatile Solutes and Supercritical Carbon Dioxide Beatriz P. Nobre,† Rui L. Mendes,† Eduardo M. Queiroz,‡ Fernando P. Pessoa,‡ Jose´ P. Coelho,*,§ and Anto´nio F. Palavra| INETI Departamento de Energias RenoVa´Veis, DER Estrada do Pac¸o do Lumiar, Edif. Solar XXI, 1649-038 Lisboa, Portugal, DEQ/EQ/UFRJ, Sl. 209, Bl. E, Ilha do Funda˜o, CEP 21949-900, Rio de Janeiro, Brazil, ISEL, Chemical Engineering and Biotechnology Research Center, Rua Conselheiro Emı´dio NaVarro, 1, 1959-007 Lisboa, Portugal, and Centro de Quı´mica Estrutural, Complexo Interdisciplinar, Instituto Superior Te´cnico, AVenida RoVisco Pais, 1049-001 Lisboa, Portugal
Most of the investigations on thermodynamic modeling of solid solubility in supercritical fluids are limited to pure nonvolatile solutes. Even with a presence of solid mixtures, it is considered that the different solids in the mixture behave as if they were alone, that is, they do not interact. Results in the literature show that this is true if the molecules of the solutes have symmetry, both in size or polarity. The aim of this work is to present solubility experimental data of a solid mixture (β-carotene/bixin) and supercritical carbon dioxide and to propose a thermodynamic model in order to describe this very asymmetric system. The proposed model is based on the Peng-Robinson equation of state and depends on the critical properties and the binary interaction parameters. The binary interaction parameters between carbon dioxide and β-carotene and between carbon dioxide and bixin were obtained from binary experimental data. For the solid mixture and carbon dioxide the model considers interactions between the solids in the solid phase and relaxes the constraint of equal interaction parameters between the solutes. A new set of experimental data on the solubility in supercritical CO2 of a mixture of bixin and β-carotene (1:1, wt) measured at 40 and 60 °C and pressures up to 350 bar is presented, and its behavior is well described by the proposed model, with a deviation of 18.2% and 44.6% for β-carotene and bixin, respectively, opposed to the model without any solid interaction, which poorly describes the available experimental data (approximately 70% average deviation). This model may be used for solid mixtures even when the solids melt. 1. Introduction Annatto (Bixa orellana) is a tropical tree whose seeds produce pigments that have widespread use in the food industry, namely for coloring butter, margarine, cheese, oils, and sauces, with hues ranging from yellow to red.1 Bixin, the structural formula of which can be seen in Figure 1, is a carotenoid of molecular weight 394.0 g/mol found only in the seeds of annatto (2-3% wt), and chemically it is the monomethyl ester of the dicarboxylic acid norbixin.2 That compound is one of the main natural coloring materials3 that easily degrades when exposed to light but is less sensitive to heat (stable up to 125 °C).4 While bixin is soluble in oils upon heating, another important pigment found in annatto seeds, norbixin, is soluble in water and insoluble in supercritical CO2.5 β-Carotene, the structural formula of which is also seen in Figure 1, is a carotenoid of high molecular weight, 536.9 g/mol, with colors ranging from light orange to dark red. It appears largely distributed in plants (carrots, tomatoes, annatto, etc.), fungi, and algae. This compound has important applications as provitamin A, antioxidant, and coloring material. Measurement of solid and liquid solubilities in supercritical fluids continues to be an important part of supercritical fluid (SCF) research. Despite the extensive progress that has occurred, equations of state (EOS) and related models used to describe * To whom correspondence should be addressed. E-mail:
[email protected]. † DER Estrada do Pac¸o do Lumiar. ‡ DEQ/EQ/UFRJ. § Chemical Engineering and Biotechnology Research Center. | Instituto Superior Te´cnico.
supercritical fluid phase behavior are still not capable of being completely predictive across all solute-SCF systems.6 Supercritical CO2 extraction of pigments from annatto seeds has been reported5,7,8 as well as a few data on bixin solubility in the same supercritical solvent.5,9 Recent data of β-carotene solubility in CO2 has also appeared.10-13 The importance of solubility studies in supercritical fluids of mixtures of two solid compounds has been emphasized,14 with a review of many examples already studied. The presence of a second solute can alter the solubility obtained in binary systems of solid-supercritical fluid; for instance, the solubility is enhanced in the case of naphthalene and benzoic acid mixtures in supercritical CO215 and hydroxybenzoic acid isomers mixtures in the same supercritical solvent,16 but it is lowered in mixtures of β-carotene and capsaicin with supercritical carbon dioxide, in which the latter compound showed lower solubility than in the corresponding binary system.17 No experimental data on
Figure 1. Structural formulas of cis-bixin (A) and all-trans-β-carotene (B).
10.1021/ie8006352 CCC: $40.75 2009 American Chemical Society Published on Web 12/23/2008
1552 Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009
Figure 2. UV-visible spectra of bixin and of a mixture (50:50, weight) of bixin and β-carotene in chloroform: 1, starting bixin; 2, bixin after purification with supercritical CO2; 3, bixin and β-carotene mixture; P, peak; V, valley.
the solubility of β-carotene and bixin as a solid mixture in supercritical carbon dioxide was found in the literature. The aim of this work is to present solubility experimental data of a very asymmetric system consisting of β-carotene and bixin as a solid mixture and supercritical carbon dioxide at several conditions of pressure and temperature, and a thermodynamic model is proposed to describe this system. This system was chosen because both carotenoids are present in annatto seeds.
in which the solid precipitates. At the end of the run this wool, the inside of the three-way valve, and the expansion tubing are washed with chloroform (Merck, p.a.) containing 0.2% wt of BHT. After the working pressure and temperature were reached, the system was allowed to equilibrate for 1 h and a purge was carried out passing 10 L (expanded carbon dioxide) through the solute bed, at a low flow rate [0.1-0.2 L (STP)/min], to ensure the saturation of the lines following the equilibrium cell. After the purges, the solubility measurements were then performed. Several gas flow rates between 0.1 and 0.7 L/min were tested to assess their influence on the equilibrium. It was verified that the equilibrium was maintained using these values, so for most of the measurements a flow rate of 0.2 L/min was chosen. The concentration of bixin in chloroform was determined by spectrophotometry (Hitachi U-2000) measuring the absorbance at 501 nm. The concentrations of β-carotene and bixin mixtures in the same solvent were determined also by spectrophotometry in two steps. At first, the relative proportion of each carotenoid was determined by measuring the absorbance in the peak (P) and in the valley (V) of the spectrum, as can be seen in Figure 2. The ratio of the absorbances in the peak and valley was found to be a linear function of the relative proportion of each carotenoid. Second, the absorbance of the mixture was measured at 501 nm and the concentration of the individual carotenoids determined. 3. Thermodynamic Model
2. Experimental Section Solubility data of β-carotene and/or bixin in supercritical carbon dioxide were presented at the Second International Symposium on High Pressure Systems.18 To measure these data, bixin (90% purity, supplied by Universidade Federal do Rio de Janeiro, Brazil, through a joint project) and β-carotene (Sigma, 95% purity, type 1) were used. In each experiment, 4 g of solid was mixed with glass beads and enclosed in the pressure vessel between two layers of glass wool. In experiments with the solid mixture, 2 g of each solid were used. Before the solubility measurements, either β-carotene or bixin were further purified by passing several hundred liters (expanded basis) of CO2 and CO2 modified with 5% ethanol, respectively, at a pressure of 200 bar and a temperature of 50 °C. In Figure 2 are shown the UV-visible spectra in chloroform of bixin before purification (curve 1) and after purification (curve 2) and of a mixture of β-carotene and bixin (curve 3). The flow type apparatus used allows pressures and temperatures up to 400 bar and 80 °C and was already described in a previous paper.19 The same apparatus was used to measure the solubility of β-carotene in supercritical CO2 and in supercritical ethane.10 During the solubility experiments, the liquid CO2 (99.995% purity, Air Liquid) flows from a cylinder to the equilibrium vessel, through a metering pump, which compresses the fluid to the working pressure at the temperature of a water bath. The pressure is controlled by a back-pressure regulator, and the fluid before reaching the extractor passes through a coil (heat exchanger). The supercritical fluid is expanded to atmospheric pressure in a three-way valve, and the solutes are collected in a cooled glass U-tube. Gas flow rate is monitored through a rotameter, and the total carbon dioxide volume is measured with a wet test meter. The solutes are recovered, with chloroform, from the U-tube, and to ensure an integral recovery of the compound, the first branch of the tube is filled with glass wool
The following are assumptions of the thermodynamic model in this work: (i) the supercritical phase is a dense gas phase, (ii) the solubility of the gas in the solid phase can be neglected, (iii) one-component solid phase is considered a pure solid phase, and (iv) a solid mixture is considered to behave like a very heavy liquid phase and there is interaction between its components. With the assumption iv will be possible to take into account the impact of the partial melting of the solids on the solubility enhancement in mixed-solid and supercritical fluid systems. Under these conditions, the solubility of a solid (y1), considering one-component solid phase, in the supercritical fluid phase is calculated using y1 )
[
sat P1sat φ1sat V sat m (P - P1 ) exp P φ^ G RT 1
]
(1)
where the gas phase is indicated by the superscript G and the solid phase by the superscript S; y1 is the molar fraction of pure solid in the gas phase, the superscript sat represents the saturation condition, Psat represents the sublimation pressure, sat is the molar volume of solid. and Vm Considering the solid mixture, the solubility of each solid in the gas phase (yi) is given by yi )
φ^ iS φ^ iG
xi
(2)
where the superscript S indicates solid mixture phase and the subscript i one of the solids. The thermodynamic model is based on the Peng-Robinson cubic equation of state (PR EOS)20 P)
a RT V - b (V + C1b)(V + C2b)
(3)
Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009 1553
where P is the absolute pressure, T is the absolute temperature, R is the gas universal constant, a is the energy parameter, and b is the covolume parameter, which can be obtained by RTci b ) bi ) 0.45725 Pci
(5)
a ) ai ) a[1 + Ki(1 - Tri1⁄2)]2
(6)
Ki ) 0.37464 + 1.54226wi - 0.26992wi2
(7)
Tri ) T/Tci
(8)
C1 ) 1 + √2, C2 ) 1 - √2
(9)
Tc is the critical temperature, Pc is the critical pressure, w is the acentric factor, Tr is the reduce temperature, C1 and C2 constants. The cubic form of the PR EOS for the compressibility factor, z, is z3 - (1 - B)z2 + (A - 3B2 - 2B)z - (AB - B2 - B3) ) 0
(10)
where aP R2T2
(11)
bP RT For mixtures, the mixing rules are given by B)
b ) bm ) a ) am )
(12)
∑∑zzb
(13)
∑∑zza
(14)
i j ij
i
j
i j ij
i
j
where m represents mixture, j or i designates a component, and the summation is over all the components presents in the mixture. The parameters aij and bij are given through the following combination rule: aij ) (aiaj)1⁄2(1 - kij)
(15)
1 bij ) (bi + bj)(1 - Lij) 2
(16)
where kiI ) 0, Lij ) Lji, and Lii ) 0. Moreover, kij ) kji only when i or j represents the carbon dioxide. The fugacity coefficient (φˆi) of the component i in the mixture, from the PR EOS, is given by ln(φ^ i) )
bi (z - 1) - ln(z - B) + bm A bi 2 b a √ m m 2 2B
[
∑za
]
j ij
j
Pc (bar) Tc (K) w Tb (K) sat Vm (cm3/mol)a
(4)
R2Tci2 a ) 0.7780 Pci
A)
Table 1. Physical Properties of β-Carotene
(17) [ zz +- RB βB ]
ln
4. Results and Discussion In Figure 2 is shown the spectrum (in chloroform) of the starting bixin for the solubility studies. The absorption maxima were found to be 470 and 501 nm. Some degradation was apparent, because there was absorption below 400 nm. In the same figure is shown the spectrum of bixin after being submitted to the supercritical CO2, and the absorbance at 400 nm is proportionally lower than that shown by the starting bixin.
a
Joback method14
present work
6.1 1481.1 0.4844 1209.6 536.5
10.0 648.0 0.4110 536.5
21
Experimental value.
It was already reported that the presence of impurities or degradation compounds in carotenoid samples can affect the obtained solubility values in supercritical fluids, and the necessity to eliminate these interfering compounds was already emphasized.10,13 So, for the solubility measurements of bixin in supercritical CO2, a similar methodology to clean the samples was carried out. The sample used for these studies was submitted to supercritical CO2 at 200 bar and 50 °C. The mole fraction obtained was monitored along with the volume of CO2 used, decreasing monotonously. To increase the cleaning rate of the bixin, a mixture of CO2 and ethanol (5%, mol) replaced the CO2. The process was ended when the values of the solubility became reproducible (within 3%). The solubility in supercritical CO2 of a mixture of bixin and β-carotene (1:1, wt) was measured at 40 and 60 °C and pressures up to 350 bar. While the ratio of solubilities between β-carotene andbixin,whendeterminedinthebinarysystemsolute-supercritical CO2, is about 4 and 6 (mole fraction) at 40 and 60 °C, respectively, for the conditions of pressure studied, these values decreased on average to 1 and 3 when the solubilities are measured in the ternary system solid mixture-supercritical CO2. There is a great increase in solubility of the bixin in mixture, with values near those of the more soluble compound, corresponding to an average solubility enhancement14 of 263%. On the other hand, the solubility of β-carotene is practically the same in both binary and ternary systems (with an average enhancement of 6%, which can be within the experimental error). This effect could be explained in terms of an entrainment effect, in a similar manner to cosolvent systems, in which the more soluble solute modifies the solvent properties of the supercritical carbon dioxide.14 Experimental data were published in the literature for the system β-carotene-carbon dioxide.10 For the systems bixincarbon dioxide and β-carotene-bixin-carbon dioxide, they were measured in the present bilateral cooperation project (Brazil-Portugal).18 It is verified from the experimental data that the bixin solubility in the ternary system, with the presence of β-carotene, is higher than that in the binary system, bixin-carbon dioxide, while the β-carotene solubilities are similar in both systems. The increase of the bixin solubility is from 2.5 to 5.5 times in the same conditions of temperature and pressure. To calculate the solubility, it is necessary to know the physical properties of β-carotene and bixin, which were not available. Therefore, the Joback group contribution (CG) method was used to estimate the critical properties,21 but the results show that it is not possible to adjust adequately the solubility data. Then, the critical properties and the acentric factor were reestimated with the interaction parameters by assuming as the objective function the minimization of the deviation between calculated and experimental results. Tables 1 and 2 show the physical properties calculated using the Joback method21 and the values obtained in this work for β-carotene and for bixin, respectively, where Tb is the boiling temperature. The interaction parameters kij and the sublimation pressures for the components, β-carotene and bixin, were estimated by
1554 Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009 Table 2. Physical Properties of Bixin
Pc (bar) Tc (K) w Tb (K) Vm (cm3/mol)a a
Joback method14
present work
10.9 1244.1 0.9289 1012.1 407.38
18.5 946.0 1.2301 407.38
21
Calculated by the Rackett method.
Table 3. Estimated Interaction Parameters, Sublimation Pressures and Deviations for the System CO2-β-Carotene Considering the Parameters without and with Temperature Dependence temp (°C)
kij
Psub × 1015 (bar)
deviations (%)
40 50 60 40 50 60
-0.43678 -0.43678 -0.43678 -0.40826 -0.43680 -0.49249
0.90225 7.57610 34.89241 2.14732 7.57610 10.61991
5.0 6.8 24.5 3.6 6.8 13.0
Table 4. Estimated Interaction Parameters, Sublimation Pressures and Deviations for the System CO2-Bixin Considering the Parameters without and with Temperature Dependence temp (°C)
kij
Psub × 1015 (bar)
deviations (%)
40 50 60 40 50 60
0.15267 0.15267 0.15267 0.18574 0.15267 0.16711
1.25846 7.44967 46.67926 5.85674 7.44967 80.57884
10.9 4.2 7.9 6.9 4.2 6.9
minimizing the deviations between the calculated and the experimental binary data, considering Lij ) 0. Two strategies were adopted. In the first one, the interaction parameter was considered temperature-independent, while in the second one the parameter was considered temperature-dependent. The values of parameters and deviations from solubility experimental data can be seen in Tables 3 and 4 for the binary systems CO2-βcarotene and CO2-bixin, respectively. The results demonstrate that even with the same value of the interaction parameter, for the several temperatures, the representation of experimental data is good (mean deviation of 10%). In Figures 3 and 4 are represented the calculated and experimental solubility results for β-carotene and bixin, respectively, in the binary systems, using the respective constant interaction parameters (temperature-independent parameters).
Figure 4. Experimental data (], ∆) and data calculated by the model (s) for CO2-bixin.
Figure 5. Experimental data (O, 0) and β-carotene solubility data calculated by the model (s) for the system CO2-bixin-β-carotene, at 40 and 60 °C.
Figure 6. Experimental data (], ∆) and bixin solubility data calculated by the model (s) for the system CO2-bixin-β-carotene, at 40 and 60 °C.
Figure 3. Experimental data (], ∆) and data calculated by the model (s) for CO2-β-carotene.
The model with symmetric interaction parameters was also tested to represent the ternary system with the interaction parameter between β-carotene (2) and bixin (3) obtained using ternary experimental data. The results show that this model
Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009 1555
cannot represent well this system, leading to a mean deviation of 70% in relation to experimental data, so the present model is proposed considering the interaction between solids in the solid phase, which is considered to behave like a liquid. The composition of the solid phase must be informed. Its molar composition for the experimental data was 42.37% for β-carotene and 57.63% for bixin. The interaction parameters were obtained and their values are k23 ) -1.9899 and k32 ) -1.1897, leading to a deviation of 18.2% for β-carotene and 44.6% for bixin (Figures 5 and 6, respectively). The parameter Lij between bixin and β-carotene does not affect or enhance significantly the calculated data, so it is assumed to equal zero. It is also worthwhile to remember that the values of the interaction parameters between CO2 and each solid are maintained equal to those obtained from the respective binary systems. 5. Conclusion The solubility in supercritical CO2 of a mixture of bixin and β-carotene (1:1, wt) was measured at 40 and 60 °C and pressures up to 350 bar. There is a great increase in solubility of the bixin in the mixture. On the other hand, the solubility of β-carotene is practically the same in both binary and ternary systems. The system containing two solids (β-carotene and bixin) and supercritical carbon dioxide is very complex and the nonideallity happens due to the difference among the sizes of the molecules and their polarities. The proposed model is based on the Peng-Robinson equation of state and then is very dependent on the critical properties and binary interaction parameters. New values for critical properties and saturation pressure are presented for β-carotene and bixin. The binary interaction parameters between carbon dioxide and β-carotene and between carbon dioxide and bixin were obtained from binary experimental data presented in the literature. For the solid mixture of β-carotene and bixin, the model without any solid interaction poorly describes the available experimental data (approximately 70% average deviation). Then, a model considering interaction between the solids in the solid phase and relaxing the constraint of equal interaction parameters between the solutes was tested and was able to better describe the experimental data behavior, with a deviation of 18.2% and 44.6% for β-carotene and bixin, respectively. Literature Cited (1) McKeown, G. G.; Mark, E. The composition of oil-soluble annatto food colours. J AOAC 1962, 45, 761–766. (2) Preston, H. D.; Rickard, M. D. Extraction and chemistry of annatto. Food Chem. 1980, 5, 47–56. (3) Scotter, M. J.; Thorpe, S. A.; Reynolds, S. L.; Wilson, L. A.; Strutt, P. R. Characterization of the principal colouring components of annatto
using high performance liquid chromatography with photodiode-array detection. Food Addit. Contam. 1994, 11, 301–315. (4) McKeown, G. G. Bixin powder production in conical spouted bed units. J. AOAC 1963, 46, 790–796. (5) Degnan, A. J.; Von Elbe, J. H.; Hartel, R. W. Extraction of annatto seed pigment by supercritical carbon dioxide. J. Food Sci. 1991, 56, 1655– 1659. (6) Garnier, S.; Neau, E.; Alessi, P.; Cortesi, A.; Kikic, I. Modelling solubility of solids in supercritical fluids using fusion properties. Fluid Phase Equilib. 1991, 491, 158–160. (7) Chao, R. R.; Mulvaney, S. J.; Sanson, D. R.; Hsieh, F. H.; Tempesta, M. S. Supercritical CO2 extraction of annatto (Bixa orellana) pigments and some characteristics of the color extracts. J. Food Sci. 1991, 56, 80–83. (8) Anderson, S. G.; Nair, M. G.; Chandra, A.; Morrisson, E. Supercritical fluid carbon dioxide extraction of annatto seeds and quantification of trans-bixin by high pressure liquid chromatography. Phytochem. Anal. 1997, 8, 247–249. (9) Jay, A. J.; Steytler, M.; Knights, M. Spectrophotometric studies of food colors in near-critical carbon dioxide. J. Supercrit. Fluids 1991, 4, 131–141. (10) Mendes, R. L.; Nobre, B. P.; Coelho, J. P.; Palavra, A. F. Solubility of β-carotene in supercritical carbon dioxide and ethane. J. Supercrit. Fluids 1999, 16, 99–106. (11) Cocero, M. J.; Gonza´lez, S.; Pe´rez, S.; Alonso, E. Supercritical extraction of unsaturated products. Degradation of β-carotene in supercritical extraction processes. J. Supercrit. Fluids 2000, 19, 39–44. (12) Hansen, B. N.; Harvey, A. H.; Coelho, J. A. P.; Palavra, A. M. F.; Bruno, T. J. Solubility of capsaicin and β-carotene in supercritical carbon dioxide and in halocarbons. J. Chem. Eng. Data 2001, 5, 1054–1058. (13) Sovova´, H.; Stateva, R. P.; Galushko, A. A. Solubility of β-carotene in supercritical CO2 and the effect of entrainers. J. Supercrit. Fluids 2001, 21, 195–203. (14) Lucien, F. P.; Foster, N. R. Solubilities of solid mixtures in supercritical carbon dioxide: A review. J. Supercrit. Fluids 2000, 17, 111– 134. (15) Kurnik, R. T.; Reid, R. C. Solubility of solid mixtures in supercritical fluids. Fluid Phase Equilib. 1982, 8, 93–105. (16) Lucien, F. P.; Foster, N. R. Solubilities of mixed hydroxybenzoic acid isomers in supercritical carbon dioxide. J. Chem. Eng. Data 1998, 43, 726–731. (17) Skerget, M.; Knez, Z. Solubility of binary solid mixture β-carotenecapsaicin in dense CO2. J. Agric. Food Chem. 1997, 45, 2066–2069. (18) Nobre, B. P.; Queiroz, E. M.; Pessoa, F. L. P.; Coelho, J. P.; Palavra, A. F.; Mendes, R. L. Solubility of bixin and bixin/β-carotene mixtures in supercritical carbon dioxide. Chemical Engineering Transactions 2002, 2, 391–396. (19) Mendes, R. L.; Coelho, J. P.; Fernandes, H. L.; Marrucho, I. J.; Cabral, J. M. S.; Novais, J. M.; Palavra, A. F. Applications of supercritical CO2 extraction to microalgae and plants. J. Chem. Tech. Biotechnol. 1995, 62, 53–59. (20) Peng, D. Y.; Robinson, D. B. A new two-constant equation of state. Ind. Eng. Chem. Fundam. 1976, 15, 59–64. (21) Reid, R. C.; Prausnitz, J. M., Sherwood, T. K. The Properties of Gases and Liquids, 3rd ed.; McGraw Hill, New York, 1986.
ReceiVed for reView April 19, 2008 ReVised manuscript receiVed October 28, 2008 Accepted November 10, 2008 IE8006352
