Modeling the Phase Equilibrium of Soybean Oil Deodorizer Distillates

Ind. Eng. Chem. Res. 2001, 40, 1239-1243

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GENERAL RESEARCH Modeling the Phase Equilibrium of Soybean Oil Deodorizer Distillates + Supercritical Carbon Dioxide Using the Peng-Robinson EOS Marilena E. Araujo,† Ne´ lio T. Machado,† and M. Angela A. Meireles*,‡ LAOS, Departamento de Engenharia Quı´mica, UFPA, Cx. P. 8612, 66050-970 Bele´ m, Para´ , Brazil, and LASEFI, Departamento de Engenharia de Alimentos, FEA, Unicamp, Cx. P. 6121, 13083-970 Campinas, Sa˜ o Paulo, Brazil

The Peng-Robinson EOS was used to predict vapor-liquid equilibrium (VLE) of the multicomponent mixture soybean oil deodorizer distillates (SODD)/CO2. The composition of SODD from the Cia. Riograndense (RS, Brazil) was used. SODD was treated as a mixture containing fatty acids (palmitic, oleic, and linoleic), sterols (stigmasterol), tocopherols (R-tocopherol), and squalene. The interaction parameters were obtained from solubility and/or VLE data available in the literature for the binary pairs of SODD compounds/carbon dioxide. For the binary systems SODD compound i/SODD compound j, the interaction parameters were set equal to zero. The results were compared with literature data using distribution coefficients and selectivities. The selectivity was calculated by reducing the mixture to a pseudo-binary system containing a light and a heavy compound. The modeling of the system SODD/CO2 using the Peng-Robinson EOS has proven to be a powerful tool for obtaining preliminary information of VLE of complex systems and for guiding experimental vapor-liquid equilibrium measurements. Introduction The deodorization of comestible vegetable oils is required to eliminate off-flavor compounds. The deodorization that is carried out by stripping with water vapor produces a residue called oil deodorizer distillates, and in the soybean industry, it gains the name soybean oil deodorizer distillates (SODD). SODD is composed of a complex mixture of free fatty acids, triglycerides, oleins, unsaturated high-molecular-weight aldehydes, sterols, and tocopherols. Multistage supercritical gas extraction has emerged as an alternative to replace traditional separation processes, when the separation of thermally labile substances and the attainment of high-purity products is the target. Of special importance in real separation problems are phase equilibrium data of complex systems (multicomponent mixtures). In the past several years, great effort has been devoted to the development of a thermodynamic database necessary for the investigation of the extraction and fractionation of fats and oil-related compounds with supercritical CO2. However, very little data exists in the literature concerning the phase equilibrium measurements of complex systems such as fats and oils in supercritical CO2,1-3 palm oil fatty acid distillates,4,5 and soybean oil deodorizer condensates.6,7 * Author to whom correspondence should be addressed. Phone: 55 19 3788-4033. Fax: 55 19 37884027. E-mail: [email protected]. † UFPA. ‡ Fac. Eng. Alim., Unicamp.

High-pressure phase equilibrium data can be determined experimentally or predicted using thermodynamic models (equations of state). Phase equilibrium measurements for systems including a multicomponent mixture and a supercritical fluid have to be carried out over a wide range of temperatures and pressures in order to yield the mutual solubilities, compositions of coexisting phases, distribution coefficients, and separation factors, which are of fundamental importance in countercurrent extraction. The distribution coefficients described on a solvent-free basis provide information about the phase in which the components are preferably enriched and about which components are preferably enriched in the extract and in the raffinate.4,7,8 The correlation of experimental vapor-liquid equilibrium (VLE) data using equation of state (EOS) models is of special importance, as it not only provides a general view of the phase behavior of the system but also makes it possible to decrease the number of experiments.9 Therefore, EOS models are useful tools for the correlation of experimental data and for the prediction of phase equilibria. The Peng-Robinson EOS, with the van der Waals mixing rule and with combining rules for two binary interaction parameters, has been shown to give good results for the description of the vapor-liquid equilibrium of systems of lipid-related compounds with CO2.10-16 In this work, the Peng-Robinson EOS, with two parameters for the van der Waals mixing rules, was used to predict the VLE of the soybean deodorizer distillates/carbon dioxide system, as well as to provide a database for the separation analysis. The soybean

10.1021/ie0001772 CCC: $20.00 © 2001 American Chemical Society Published on Web 01/19/2001

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deodorizer distillates were lumped into a mixture consisting of fatty acids (palmitic, oleic, and linoleic acids), R-tocopherol, stigmasterol, and squalene considering the composition of the byproduct obtained from the deodorization step of the physical refining process of soybean oil at Cia. Riograndense (RS, Brazil). The predicted results were compared to the experimental VLE data available in the literature.7 The objective of this calculation was to show how a relatively simple thermodynamic model, associated with a very simplified picture of a complex system, could assist in preliminary calculations for industrial design as well as in experimental design.

Table 1. Thermophysical Properties of All Pure Compounds in Soybean Deodorizer Distillates compounds

Tc (K)

Pc (bar)

ω

M [g/g mol)]

palmitic acid oleic acid linoleic acid R-tocopherol stigmasterol squalene

780.3819 796.3419 796.0319 897.0419 848.8419 838.0619

14.6720 12.4219 12.4019 8.2019 9.2119 6.5319

1.010421 0.924522 0.776722 1.368023 1.054923 1.398523

256.43 282.47 280.45 430.69 412.00 410.73

Table 2. Experimental VLE Data of All Binary Pairs of Soybean Oil Deodorizer Distillate Compounds/CO2 Used to Compute the Binary Interaction Parameters

Thermodynamic Modeling The thermodynamic modeling of the multicomponent system soybean oil deodorizer distillates/CO2 was performed using the Peng-Robinson equation of state given as follows:

P)

a(T) RT V - b V(V + b) + b(V - b)

(1) a

The van der Waals mixing rules, with combining rules for two binary interaction parameters, are given by the equations

∑∑xixjaij bm ) ∑∑xixjbij

am )

(3) (4)

(bii + bjj) (1 - Kbij) 2

(5)

bij )

a

where Kaij and Kbij are the binary interaction parameters obtained by adjusting the vapor-liquid equilibrium data. The interaction parameters Kaij and Kbij are associated with the inability of the geometric mean combination rule of eqs 2 and 3 to describe the molecular interactions between the different species i and j. Thermophysical Properties of Pure Components of Soybean Deodorizer Distillates. The computation of vapor-liquid equilibria of multicomponent mixtures using equations of state requires information concerning the thermophysical data (critical temperature Tc, critical pressure Pc, and acentric factor ω) of all of the pure components constituting the mixture. The critical data of the pure substances can be determined experimentally or calculated using predictive methods. However, many natural compounds suffer degradation before the critical temperature is achieved, and hence, the prediction of critical data of those substances depends on the method used to perform the computation. The thermophysical properties of palmitic acid, oleic acid, linoleic acid, R-tocopherols, stigmasterol, and squalene were computed using predictive methods. The predictive methods used in the present work were those identified in the literature17,18 as the most suitable for the compounds present in SODD. Table 1 shows the predicted values for the critical properties and acentric factors for all of the compounds in soybean deodorizer distillates. Binary Interaction Parameters Vapor-liquid equilibrium data available in the literature for the binary pairs of soybean oil deodorizer

no. of experimental points

ref

palmitic acid oleic acid linoleic acid R-tocopherol stigmasterol squalene

15 17 12 20 19 17

14 13 12 25 26 27

SODD ) soybean oil deodorizer distillates.

Table 3. Computed Binary Interaction Parameters of All Binary Pairs of Soybean Oil Deodorizer Distillate Compounds/CO2

(2)

aij ) x(aiiajj)(1 - Kaij)

system SODDa compound/CO2

system SODDa compound/CO2

Kaij

Kbij

palmitic acid oleic acid linoleic acid R-tocopherol stigmasterol squalene

0.257501 0.125919 0.094511 0.089368 0.248005 0.035365

0.080401 0.054627 0.02944 0.011246 0.081330 0.018977

SODD ) soybean oil deodorizer distillates.

distillate compounds (squalene, R-tocopherol, stigmasterol, palmitic acid, oleic acid, and linoleic acid) with carbon dioxide have been used to compute the binary interaction parameters in the Peng-Robinson equation of state with the van der Waals mixing rules. Table 2 shows the source of the experimental VLE data for the binary pairs of soybean oil deodorizer distillate compounds/CO2 used to compute the binary interaction parameters Kaij and Kbij. The binary interaction parameters (Table 3) were obtained using the program EDEFlash for Windows v1.2.17 The program uses a P-T flash algorithm and the modified Simplex method.24 Depending on the available experimental data, the objective function (OF) was chosen as

(i) for VLE data n

OF )

2

∑∑

j ) 1i ) 1

[(

xe(i)

(ii) for vapor-phase data n

OF )

) (

xc(i) - xe(i)

2

∑∑

j ) 1i ) 1

[(

2

+

ye(i)

)]

yc(i) - ye(i) ye(i)

)]

yc(i) - ye(i)

2

(6)

j

2

(7)

j

For binary systems of the type SODD compound i/SODD compound j, the interaction parameters were set equal to zero. Chemical Composition of Soybean Oil Deodorizer Distillates. Thermodynamic modeling of vapor-

Ind. Eng. Chem. Res., Vol. 40, No. 4, 2001 1241 Table 4. Chemical Composition of Soybean Oil Deodorizer Distillates (TCRR, TS1, and TS2) compound

TCRR (wt %)

TS1 (wt %)

TS2 (wt %)

palmitic acid (total) oleic acid (total) linoleic acid (total) R-tocopherol stigmasterol squalene free fatty acids middle comp. (MFK) tocopherols sterols triglycerides total

17.36 14.67 36.43 8.95 17.96 4.63 100

2.12 17.09 1.10 24.16 9.72 45.81 100

2.54 11.69 1.51 31.93 8.97 43.35 99.99

liquid equilibrium in the form of P-T flash requires as input data the pure-component thermophysical properties and the binary interaction parameters. In addition, the EDEFlash program requires the molar composition of the multicomponent mixture (soybean oil deodorizer distillates) on a solvent-free basis.17,18 The soybean oil deodorizer distillates multicomponent system obtained as a byproduct of the deodorization step of the physical refining process of soybean oil at Cia. Riograndense (RS, Brazil) was lumped into three families of homologous series (total fatty acids, sterols, and tocopherols) and squalene. Table 4 shows the composition of the soybean oil deodorizer distillates obtained as a subproduct at Cia. Riograndense (RS, Brazil),28 hereafter called TCRR, and of those reported in the literature,7,29 hereafter called TS1 and TS2.

Figure 1. P-x-y diagram for the system SODD/supercritical CO2 at 343 K. Comparison between predicted (TCRR) and experimental data (TS1 and TS2).29

Results and Discussion The ability of the Peng-Robinson EOS with the van der Waals mixing rules (quadratic mixing rule, with the conventional corrected geometric mean combining rule) to predict vapor-liquid equilibria of the multicomponent system soybean oil deodorizer distillates/CO2 was evaluated.29 The computed values for the mutual solubilities, distribution coefficients, and separation factors were compared with the experimental vapor-liquid equilibrium data for the multicomponent system soybean oil deodorizer distillates/CO2 reported by Stoldt.29 Figure 1 shows the VLE (P-x-y diagram) predicted by the Peng-Robinson EOS with the van der Waals mixing rules using the composition given in Table 4 (TCRR) and the binary interaction parameters of Table 3. The VLE computation was done considering the multicomponent mixture, and afterward the results were expressed in terms of the pseudo-binary system SODD/ CO2 for ease of comparison with the literature data (TS1 and TS2).29 The results show that the thermodynamic modeling of vapor-liquid equilibrium for the soybean oil deodorizer distillates/CO2 system at 343 K described the mutual solubilities of the soybean oil deodorizer distillates/CO2 system with relative success, particularly those in the gas phase, regardless of the differences in composition between TCRR and TS1 and TS2 (Table 4). The partition coefficients of all of the components of soybean oil deodorizer distillates on a solvent-free basis are depicted in Figure 2. The results show that squalene and the fatty acids (palmitic, oleic, and linoleic acids) are enriched in the gaseous phase, whereas the sterols (stigmasterol) and tocopherols (R-tocopherol) are enriched in the liquid phase. The Ki values of the soybean

Figure 2. Partition coefficients of the soybean oil deodorizer distillate compounds (TCRR) on a solvent-free basis at 343 K.

oil deodorizer distillate compounds decrease in the following order: Ksqualene > Kfatty acids > Ktocopherols > Kstigmasterol. The distribution coefficient of squalene decreases, while the distribution coefficients of the other compounds show a tendency to increase, as the system pressure increases. This behavior is due not only to the initial concentrations of soybean oil deodorizer distillate compounds in the feed mixture but also to their chemical structures, that is, their different solubilities in the gaseous phase. Figure 3 shows the partition coefficients of soybean oil deodorizer distillate compounds (TS1) reported in the work of Stoldt,7,29 computed on a solvent-free basis. TS1 was lumped into five different families of homologous series as follows: light compounds (fatty acids), middle compounds MFK (not identified), heavy compounds SFK (triglycerides), sterols, and tocopherols. The results show that fatty acids, squalene, and the middle compounds are enriched in the gas phase, whereas the remaining components (sterols, tocopherols, and triglycerides) are enriched in the liquid phase. The Ki values of the TS1 compounds decrease in the following order: Kfatty acids > Ksqualene > KMFK > Ktocopherols > Ksterols > Ktriglycerides. A comparison between the Ki values of soybean oil deodorizer distillates reported in the work of Stoldt7,29 (TS1) and those (of TCRR) predicted by the Peng-Robinson equation with the van der Waals mix-

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ponent system of Stoldt.7,29 This is because of the differences in composition between TCRR and TS1 and TS2. The initial composition has a great effect on the phase equilibria. The heavy compounds represented by the triglycerides in TS1 and TS2 were not found in TCRR. In addition, the mass fraction of fatty acids in TCRR was much higher than those in TS1 and TS2. The higher the amount of fatty acids and the lower the amount of sterols, here represented by stigmasterol, the higher the separation factor. Conclusions

Figure 3. Partition coefficients of soybean oil deodorizer distillate compounds (TS1) on a solvent-free basis at 343 K.29

Figure 4. Separation factor RLK/HK of soybean oil deodorizer distillates (TS1, TS2, and TCRR) at 343 K.

ing rules for two binary interaction parameters at 343 K shows the great ability of the chosen EOS to describe the tendency toward separation of soybean oil deodorizer distillates in countercurrent columns using supercritical CO2 as the solvent. The only difference lies in the partition coefficients of the fatty acids and squalene, as the fatty acids in the soybean oil deodorizer distillates are more soluble than squalene in supercritical CO2, as reported in the work of Machado.5 Based on the values for the partition coefficients of the SODD compounds (TCRR), computed with the Peng-Robinson equation with the van der Waals mixing rules for two binary interaction parameters at 343 K, the multicomponent mixture was reduced to a pseudo-binary system consisting of a light component (squalene + fatty acids) and a heavy component (tocopherols + sterols). The thermodynamic feasibility of the separation of fatty acids and squalene from tocopherols and sterols in soybean oil deodorizer distillates (TCRR) at 343 K is shown in Figure 4. The results show that the separation factor RLK/HK decreases as the pressure increases, and this means that the separation becomes more difficult. This corresponds to the effect that the selectivity decreases with increasing gas load (solvent power). Figure 4 also shows the calculated values for the separation factors reported in the work of Stoldt.29 The separation factors predicted for TCRR, using the PengRobinson equation with the van der Waals mixing rules for two binary interaction parameters, are higher than those calculated using the VLE data for the multicom-

The Peng-Robinson equation of state, with the van der Waals mixing rules with two binary interaction parameters, was used to predict the phase equilibrium of the soybean oil deodorizer distillates/carbon dioxide complex system. The soybean deodorizer distillates complex system was lumped together as a mixture consisting of palmitic acid, oleic acid, linoleic acid, stigmasterol, R-tocopherols, and squalene. The initial composition was shown not to have a great effect on the prediction of the phase equilibrium. VLE equilibrium isotherms (313-353 K), predicted with the PengRobinson EOS, were comparable to those obtained experimentally for the soybean deodorizer distillates/ CO2 system. The results show that the Peng-Robinson equation of state was able to predict the mutual solubilities of the soybean deodorizer system at pressures between 20 and 35 MPa. The partition coefficients of the soybean deodorizer distillates show that fatty acids and squalene are enriched in the gaseous phase, while the remaining compounds (sterols, tocopherols) are enriched in the liquid phase. The Ki values of the soybean oil deodorizer distillates compounds (TCRR) decrease in the following order: Ksqualene > Kfatty acids > Ktocopherols > Kstigmasterol. The thermodynamic feasibility of the separation of fatty acids and squalene from tocopherols and sterols in soybean oil deodorizer distillates (TCRR) at 343 K shows that the separation factor RLK/HK decreases as the pressure increases, and this means that the separation becomes more difficult at higher pressures. The proposed methodology provided satisfactory results, if one considers the simplifications concerning the composition of soybean deodorizer distillates and that the SODD compound i/SODD compound j interaction parameters were assumed to be zero. The thermodynamic modeling of the soybean deodorizer distillates/CO2 system, using the Peng-Robinson equation of state with van der Waals mixing rules with two binary interaction parameters, has proven to be a powerful tool for providing preliminary information on the VLE of complex systems, as well as a tool for guiding experimental vapor-liquid equilibrium measurements. This information can be used to reduce the number of necessary experiments, but not to replace experimental data. Literature Cited (1) Staby, A.; Forskov, T.; Mollerup, J. Phase Equilibria of Fish Oil Fatty Acid Ethyl Esters and Sub- and Supercritical CO2. Fluid Phase Equilib. 1993, 87, 309. (2) Borch-Jensen, C.; Mollerup, J. Phase Equilibria of Fish Oil in Sub- and Supercritical Carbon Dioxide. Fluid Phase Equilib. 1997, 138, 179. (3) Franc¸ a, L. F. Estudo do Aproveitamento dos Carotenos das Fibras Resultantes da Prensagem na Indu´stria de O Ä leo de Palma,

Ind. Eng. Chem. Res., Vol. 40, No. 4, 2001 1243 pela Extrac¸ a˜o com CO2 Supercrı´tico. Ph.D. Dissertation, State University of Campinas (UNICAMP), Campinas, SP, Brazil, 1999. (4) Machado, N. T.; Brunner, G. Separation of Saturated and Unsaturated Fatty Acids from Palm Fatty Acids Distillates in Continuous Multistage Countercurrent Columns with Supercritical Carbon Dioxide as Solvent: A Process Design Methodology. Cieˆ nc. Tecnol. Aliment. 1997, 17 (4), 361 (also available at http:// www.scielo.br). (5) Machado, N. T. Fractionation of PFAD Compounds in Countercurrent Columns Using Supercritical CO2 as Solvent. Ph.D. Dissertation, Technical University of Hamburg-Harburg (TUHH), Hamburg, Germany, 1996. (6) Brunner, G.; Malchow, Th.; Sturken, K.; Gottschau, Th. Separation of Tocopherols from Deodorizer Condensates by Countercurrent Extraction with Carbon Dioxide. J. Supercrit. Fluids 1991, 4, 72. (7) Stoldt, J.; Brunner, G. Phase Equilibrium Measurement in Complex Systems of Fats, Fat Compounds and Supercritical Carbon Dioxide. Fluid Phase Equilib. 1998, 146, 269. (8) Machado, N. T.; Brunner, G. High-Pressure Vapor-Liquid Equilibria of Palm Fatty Acids Distillates-Carbon Dioxide System. Cieˆ nc. Tecnol. Aliment. 1997, 17 (4), 354 (also available at http:// www.scielo.br). (9) Brunner, G. Gas Extraction: An Introduction to Fundamentals of Supercritical Fluids and the Application to Separation Processes; Springer: New York, 1994. (10) Inomata, H.; Kondo, T.; Hirohama, S.; Arai, K.; Suzuki, Y.; Konno, M. Vapor-Liquid Equilibria for Binary Mixtures of Carbon Dioxide and Fatty Acid Methyl Esters. Fluid Phase Equilib. 1989, 46, 41. (11) Bharath, R.; Inomata, H.; Arai, K.; Shoji, K.; Noguchi, Y. Vapor-Liquid Equilibria for Binary Mixtures of Carbon Dioxide and Fatty Acid Ethyl Esters. Fluid Phase Equilib. 1989, 50, 315327. (12) Zou, M.; Yu, Z.-R.; Kashulines, P.; Rizvi, S. S. H.; Zollweg, J. A. Fluid-Liquid-Phase Equilibria of Fatty Acids and Fatty Acid Methyl Esters in Supercritical Carbon Dioxide. J. Supercrit. Fluids 1990, 3 (1), 23. (13) Yu, Z.-R.; Rizvi, S. S. H.; Zollweg, J. A. Phase Equilibria of Oleic Acid, Methyl Oleate and Anhydrous Milk Fat in Supercritical Carbon Dioxide. J. Supercrit. Fluids 1992, 5 (2), 114. (14) Bharath, R.; Yamane, S.; Inomata, H.; Adschiri, T.; Arai, K. Phase Equilibria of Supercritical CO2-Fatty Oil Component Binary Systems. Fluid Phase Equilib. 1993, 83, 183. (15) Yu, Z.-R.; Singh, B.; Rizvi, S. S. H. Solubilities of Fatty Acids, Fatty Acid Esters, Triglycerides, and Fats and Oils in Supercritical Carbon Dioxide. J. Supercrit. Fluids 1994, 7, 51. (16) Geana, D.; Steiner, R. Calculation of Phase Equilibrium in Supercritical Extraction of C54 Triglyceride (Rapeseed Oil). J. Supercrit. Fluids 1995, 8 (2), 107.

(17) Arau´jo, M. E. Estudo do Equilı´brio de Fases para Sistemas O Ä leo Vegetal/Dio´xido de Carbono Empregando a Equac¸ a˜o de Peng-Robinson. Ph.D. Dissertation, State University of Campinas (UNICAMP), Campinas, SP, Brazil, 1997. (18) Arau´jo, M. E.; Meireles, M. A. A. Improving Phase Equilibrium Calculation with Peng-Robinson EOS for Fats and Oils Related Compounds/Supercritical CO2 Systems. Fluid Phase Equilib. 2000, 169, 49. (19) Constantinou, L.; Gani, R. New Group Contribution Method for Estimating Properties of Pure Compounds. AIChE J. 1994, 40 (10), 1697. (20) Somayajulu, G. R. Estimation Procedures for Critical Constants. J. Chem. Eng. Data 1989, 34, 106. (21) Wagner, W. New Vapor-Pressure Measurements for Argon and Nitrogen and a New Method for Establishing Rational VaporPressure Equations. Cryogenics 1973, 13 (8), 470. (22) Tu, C. H. Group-Contribution Method for the Estimation of Vapor Pressures. Fluid Phase Equilib. 1994, 99, 105. (23) Constantinou, L.; Gani, R.; O’Connell, J. P. Estimation of the Acentric Factor and the Liquid Molar Volume at 298 K Using a New Group Contribution Methodology. Fluid Phase Equilib. 1995, 103, 11. (24) Nelder, J. A.; Mead, R. A Simplex Method for Function Minimization. Comput. J. 1965, 7, 308. (25) Pereira, P. J.; Gonc¸ alves, M.; Coto, B.; Gomes de Azevedo, E.; Nunes da Ponte, M. Phase Equilibria of CO2 + DL-R-tocopherol at temperatures from 292 K to 333 K and Pressures up to 26 MPa. Fluid Phase Equilib. 1993, 91, 133. (26) Wong, J. M.; Johnston, K. P. Solubilization of Biomolecules in Carbon Dioxide based Supercritical Fluids. Biotechnol. Progress 1986, 2 (1), 29. (27) Swaid, I. et al. NIR Spectroscopic Investigations on Phase Behavior of Low-Volatile Organic Substances in Supercritical Carbon Dioxide. Fluid Phase Equilib. 1985, 21, 95. (28) Augusto, M. M. M. Obtenc¸ a˜o e Caracterizac¸ a˜o de um Concentrado de Tocofero´is a partir do Destilado da Desodorizac¸ a˜o do O Ä leo de Soja. M. S. Thesis, State University of Campinas (UNICAMP), Campinas, SP, Brazil, 1988, 150. (29) Stoldt, J. Phasengleichgewichte in Komplexen Systemen aus Fetten, Fettbegleitstoffen und U ¨ berkritischem Kohlendioxid. Ph.D. Dissertation, Technical University of Hamburg-Harburg (TUHH), Hamburg, Germany, 1996.

Received for review February 7, 2000 Revised manuscript received October 31, 2000 Accepted November 6, 2000 IE0001772