400
Ind. Eng. Chem. Res. 1992,31,400-404
Solubility of Fatty Acid Esters in Supercritical Carbon Dioxide K. Keat Liong, Neil R. Foster,* and Simon S. T. Ting School of Chemical Engineering and Industrial Chemistry, University of New South Wales, P.O.Box 1, Kensington 2033,Australia
The solubilities of the ethyl esters of C181, C203, C204, and C22:6 (oleic acid, eicosatrienoic acid, arachidonic acid, and cis-4,7,10,13,16,19-docosahexaenoic acid, respectively) in supercritical carbon dioxide were measured in the temperature range 313-373 K and at pressures between 90 and 250 bar. Measurements were obtained using a continuous flow saturation apparatus. Modeling of the experimental data waa carried out using the Peng-Robinson equation and an empirical density-based correlation. Introduction There is some evidence relating the level of consumption of essential fatty acids (EFAs) with the risk of developing coronary heart disease. In particular, all-cis4,7,10,13,16,19-docosahexaenoicacid (DHA) is one such EFA which has attracted enormous public interest because of its therapeutic effects on human health. DHA is one of the major fatty acid constituents present in fish oil. In order to confirm the claim of therapeutic activity of the components, it is necessary to be able to concentrate this fatty acid from natural products. There is considerable potential in using supercritical fluid (SCF) technology to effect the concentration and separation of these fatty acids or their esters. However, the design of such an extraction process requires accurate experimental equilibrium data. In particular, pure component solubility data are required prior to designing an extraction process as they provide an indication of the rate of extraction and hence the optimum process size for a given throughput. The incentive for the present study is a lack of appropriate data for design purposes. In this study, the solubility isotherms of the ethyl esters of DHA (C22:6), arachidonic acid (C204), eicosatrienoic acid (C203), and oleic acid (C181) in supercritical carbon dioxide were determined in the temperature range 313-373 K, for pressures between 90 bar and 250 bar. The measurements were obtained using a continuous flow saturation apparatus. Modeling of the experimental data was carried out using the Pew-Robinson equation of state and an empirical density-baaed correlation. Experimental Section A continuous flow saturation technique was used to measure the solubility of the fatty acid ethyl esters in supercritical carbon dioxide. An attempt was made to use the recirculation technique employed by Adams et al. (1988); however, the pump (Alltech, Model No. BBB-4-2) used for recirculation regularly developed leaks across the plunger seals, which led to considerable errors in the solubility data obtained. Due to this problem, subsequent experiments relied on the adjustment of the flow rates of the SCF to ensure that equilibrium was established between the solute and the fluid. Material. The ethyl ester solutes were obtained from Sigma Chemicals (99% purity). The purity of the liquid carbon dioxide used was 99.8%. Equipment and Procedure. A schematic diagram of the continuous flow saturation apparatus is shown in Figure 1. The apparatus consisted primarily of a syringe pump (Isco, Model No. LC-5000), a heating coil, two equilibrium cells,a cold trap for sample collection, and a wet gas meter (Alexander Wright & Co., Model DM3A). The heating coil and the equilibrium cells were immersed
in a constant-temperature water bath, controlled to an accuracy of f0.1 "C with a heater/circulator (Thermoline Unistat). The syringe pump was capable of delivery pressures up to 300 bar and delivery rates between 1.5 and 400 mL/h (liquid carbon dioxide basis). The liquid carbon dioxide was directed to the preheater coil to enable the fluid to reach the desired extraction temperature. Upon leaving the heating coil, the carbon dioxide was passed through the equilibrium cells. One of the equilibrium cella was a 200-mm length of 19-mm-0.d. stainless steel tubing, while the other was a visual cell (Jerguson, Model No. 13-R-32). The first equilibrium cell was packed with alternate layers of fiiter paper (cut up into small strip) to suspend the liquid solute and with glass beads (2-mm 0.d.) to facilitate efficient fluid-liquid contact. The second equilibrium cell, fitted with 15-mm thick borosilicate windows on both faces, allowed visual observation of the phase behavior of the carbon dioxide-ester systems during extraction and provided a means by which the operator could ensure that entrainment of the liquid solute was not occurring. The solute-laden fluid phase was then passed through a needle valve (Whitey, Model No. SS-31-RS4),at which point the mixture was expanded to atmospheric pressure. The needle valve was also used to adjust the total pressure of the system. The liquid solute which precipitated as a result of the loss in the solvent power of the carbon dioxide was collected in a cold trap. The gaseous carbon dioxide was then passed through a calibrated wet gas meter and the total flow of the gas measured. In order to confirm that equilibrium solubility was being measured, the experiment was conducted at various flow rates between 6 and 18 mL/h (liquid carbon dioxide basis). The temperature of the system was monitored using a Type K thermocouple, and the system pressure was monitored by a pressure transducer (3504 strain gauge type) mounted on the head of the syringe pump. Another pressure transducer (Druck PDCR 610) was placed at the exit of the equilibrium cells to ensure that the pressure drop across the system was negligible. The overall error was *0.2 "C for temperature and k0.5 bar for pressure. The amount of solute collected during each run was measured gravimetrically on a balance (Mettler AE200), accurate to f0.1 mg. Results and Discussion Saturation of the solute in the fluid stream at a given pressure and temperature was confirmed by running the solubility experiments at a number of different solvent flow rates. The flow rate was initially set at 18 mL/h (liquid carbon dioxide flow rate) and was decreased subsequently to 12 and 6 mL/h. It was found that the solubility data
0888-588519212631-04oO$O3.oO/O 0 1992 American Chemical Society
Ind. Eng. Chem. Res., Vol. 31,No. 1, 1992 401
a
96 TO V.mt
Q
1I
9.
IO.
I
Figure 1. Schematic diagram of the continuous flow saturation apparatus: (1)syringe pump; (2)heating coil; (3)heater/circulator; (4)equilibrium cell; (5)Jerguson gauge; (6)thermocouple; (7)regulating valve; (8) cold trap; (9) wet gas meter.
1.000E-04
t'
d
I
1
50
0
100
150
200
Pressure (bar) Figure 3. Solubility of various esters in supercritical carbon dioxide as a function of pressure at 313 K.
333K, C20:3
1
" h
n
0
e
PP
/.;"
0.004
1
r
0
20
40
80
80
100
120
140
Pressure (bar) Figure 2. Solubility of C181 esters in carbon dioxide as a function of pressure.
for each of these flow rates were consistent to within *3 % . The solubility of oleic acid methyl ester has been measured previously (Wu et d,1988,Inomata et d., 1989,Zou et al., 1990). A comparison of the solubility isotherms as a function of pressure obtained by the above-mentioned workers for oleic acid methyl ester with that of the oleic acid ethyl ester obtained in thiswork is presented in Figure 2. It was evident that the results obtained in this study and those obtained by Wu et al. (1988),and Inomata et al. (1989),showed similar trends. The lower solubility observed for the ethyl esters as compared to the methyl esters was probably a result df the lower vapor pressure of the former. However, the results obtained by Zou et al. (1990)showed a distinct deviation from the trends observed, in that the solubility was significantly higher. It is possible that the high degree of solubility obtained was a result of entrainment of the solute in the fluid phase. The evidence for this explanation is that although the model (Mlich-Kwong equation of state with the mixing rules of Panagiotopoulos and Reid (1987)used by Zou et al. (1990))fitted the liquid phase data well, a significant error resulted when the fluid-phase data were correlated. The solubilities of C181,C203,C204,and DHA ethyl esters as a function of pressure at 313 K are presented in Figure 3. The greater solubility of the shorter chain esters was consistent with the higher solute vapor pressures and therefore waa not unexpected. The effect of pressure followed the expected trend of inmasing solubility with an isothermal increase in pressure in all cases. This can be explained in terms of the specific interactions between the solute and solvent molecules. As the system pressure was increased, the carbon dioxide density increased accordingly. This resulted in a decrease in the intermolecular mean distance of the carbon dioxide molecules, thereby increasing the specific interactions between the solute and solvent molecules.
0 0
200
400
800
800
1000
Density (g/l) Figure 4. Solubility of C203 and C204 ethyl esters as a function of carbon dioxide density.
-e
0
200
400
800
800
1000
Density (g/I) Figure 5. Solubility of C22:6 ethyl ester as a function of carbon dioxide density.
The effect of supercritical carbon dioxide density on the solubilities of C203 and C204 ethyl esters and DHA ethyl ester is presented in Figures 4 and 5, respectively. The data show that solubilities are in the range of 0.02-0.8mol % for densities between 330 and 810 g/L. Each solubility data point represents an average of three trials. With the exception of runs conducted at 373 K, where the deviations are approximately 7% ,the individual measurements differed by less than 4%. The larger degree of uncertainty observed at 373 K was a result of difficulties in controlling the experimental temperature and the low densities (and hence low solute solubilities) of the carbon dioxide at these conditions. The effeds of carbon dioxide density, presented in Figures 4 and 5,show that once the solvent density exceeded a threshold limit of approximately 500 g/L, the solubilities were observed to increase strongly with density.
402 Ind. Eng. Chem. Res., Vol. 31, No. 1, 1992
Again, this can be attributed to the existence of strong attractive forces between the solute and the surrounding solvent molecules. A log-log plot of the effect of the density of carbon dioxide on the solubility of DHA ethyl ester is presented in Figure 6. As for all the esters studied in this work, the logarithm of the solubility was found to be a hear function of the logarithm of the density of the solvent. Another factor affecting the solubility of the esters in supercritical carbon dioxide is the system temperature, which influences both the solvent density (hence the intermolecular interactions in the fluid phase) and the solute vapor pressure. At a given density, the solubilities were also observed to increase with temperature. This was not unexpected as the vapor pressure effect is more dominant at higher temperatures in supercritical fluid extraction. The effect of the degree of unsaturation of the esters on the solubility is also shown in Figure 3. It was observed that the solubility of the C203 ethyl ester (three double bonds) was approximately 8% higher than for the C204 ethyl ester (four double bonds) over the range of pressures examined. Data Correlation. The experimentally determined solubility data were correlated using both the Peng-Robinson equation of state with the van der Waals mixing rules and a density-based correlation. Modeling with the Peng-Robinson Equation of State. The use of cubic equations of state to determine the fugacity coefficients and, subsequently, the solubilities of liquids in SCFs has been satisfactorily accomplished in previous studies (Kinget al., 1983;Wu et al., 1988; Inomata et al., 1989). In this study, the experimental solubility data were modeled using the Peng-Robinson equation of state with the van der Waals mixing rules. Peng-Robinson equation a p = - -RT V - b V2+2bV-b2 where 0.45724R2T: a= ~TR,(J) PC (Y(TR,(J) = [I 4- m(1 - TR'/')]' m = 0.37464 + 1.54226~- 0.269920~ 0.0778ORTc b= PC
Van der Waals mixing rules
where ajj = ( I - kij)(ujaj)lI2 b,j =
bi
+ bj
2
The constants a and b were evaluated from the critical properties for both the solute and the solvent. This represents a major limitation of the equation-of-state approach, for while the critical and vapor pressure data for the solvent are readily available, they are rarely available for the liquid solutes studied. For many eaters, the normal
-
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313K
-
323K 333K
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r
-a
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,c d
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i
1 0 0 0 E - 0 5 __ 100
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Density ( g A )
Figure 6. Solubility of C226 ethyl ester aa a function of carbon dioxide density (ln-ln). Table I. Interaction Parameters for the Peng-Robinson Equation for the Estedarbon Dioxide Systems ethyl ester temp/K kIp ethyl ester temp/K K12 DHA 313 0.097 C203 313 0.089 323 0.057 333 0.076 333 0.062 373 0.049 373 0.050
boiling temperature, Th,and the critical properties such as P,, T,, and V, must be estimated, therefore introducing additional uncertainties to the model. In this investigation, the boiling point and critical properties of the esters were estimated from the group contribution methods of Lydersen (Lyman, 1982) and Joback (Reid et al., 1987). The acentric factors were estimated from vapor pressure data at a reduced temperature of 0.7. Another limitation of the equation-of-state approach is that the binary interaction parameter, kI2, needs to be estimated. This interaction parameter is basically a fitting parameter which forces the equation-of-state model to more accurately fit the experimental data. The interaction parameters in this study were determined by minimizing the s u m of squares of differences between the experimentally obtained solubility data and t h w predicted using the Peng-Robinson equation of state. The interaction parameters so determined are presented in Table I. A comparison between the experimental solubility data and predicted results is shown in Figure 7. The Pew-Robinson equation provided only a qualitative representation of the experimental solubility data, as can be observed from Figure 7. This observation is consistent with those of previous researchers (Schmitt, 1984), who found that the Peng-Robinson equation underpredicted solubilities at low pressures but overpredicted at high pressures. The ability of a particular equation of state to accurately predict experimental solubility data often depends upon the mixing rules used (Eckert et al., 1983). It is expected that an improved fit of the experimental data could be achieved with the introduction of additional mixing rules. However it was not within the scope of this study to fuUy investigate the effect of the mixing rules on the performance of the Peng-Robinson equation. Density-BasedCorrelation. A density-based model developed by Chrastil (1982) was used to correlate the experimental data. While it would be more correct to employ the true density (in this discussion, references to density pertain to pure carbon dioxide density) of the binary system in the calculations, this would involve extensive experimentation. However, useful results can be obtained when approximations are made with pure carbon
Ind. Eng. Chem. Res., Vol. 31, No. 1, 1992 403 SO0 kll kii
-
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150
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100 -
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I 0.90
0.984
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1
Mole Fraction Carbon Dioxide Figure 7. Solubility of C22:6 and C203 ethyl esters in supercritical carbon dioxide: a comparison with the values predicted with the Peng-Robinson equation.
011 100
1000
Density (g/l)
Figure 8. Solubility of ethyl esters in supercritical carbon dioxide at 313 K: correlated using the Chrastil model.
".
n rI
I
1000
100
011
A
0
0.01
8-
100
1000
Density (g/l)
Figure 10. Solubility of the C226 ethyl ester in supercriticalcarbon dioxide: correlated using the Chrastil model. Table 11. Number of Molecules in a Solvato Complex As Determined from the Plot of In (Solubility) veraun In (Density) ethyl molecules in regression eeter solvato complex coeff temp/K C181 313 9.39 0.999 C203 313 7.15 0.999 C203 6.15 333 0.998 C203 373 0.994 8.04 C204 0.999 7.11 313 C22:6 8.42 313 0.996 7.72 C22:6 323 0.999 C226 0.998 7.62 333 C226 373 0.999 6.72
Density (g/l)
Figure 9. Solubility of the C203 ethyl ester in supercritical carbon dioxide: correlated using the Chrastil model.
dioxide densities, as was shown in the model proposed by Chrastil (1982). The Chrastil model was based on the postulate that the association between the solute and solvent molecules resulta in the formation of a solvato complex. The expression by Chrastil (1982) is written in the form as shown in eq 4. Therefore, a plot of the logarithm of solute solubility
c = pK exp(
9 + J.>
(4)
as a function of the logarithm of solvent density should
yield a straight line of slope equal to the total number of molecules involved in the solvato complex. The logarithm of the solubilities of the ethyl esters plotted as a function of the logarithm of carbon dioxide density are presented in Figures 8-10. The linearity provided by the above model was excellent, with regression coefficients (R2) of 0.994 or better. With the exception of the solubility data of the C203 ethyl ester a t 373 K, the slope of the solubility isotherms was found to decrease with increasing temperature, which also suggested that the number of molecules involved in the solvato complex decreased with an increase in temperature. The values obtained for the number of molecules per complex are listed in Table 11.
404 Ind. Eng. Chem. Res., Vol. 31, No. 1,1992
This finding is not consistent with the observations of Chrastil (1982), who obtained straight and parallel lines (which indicates that the number of molecules involved in the solvato complex is independent of both pressure and temperature) for systems studied at different temperatures. Straight but nonparallel lines, as obtained in this investigation, are indicative of solvato complexes whose size varies with changes in temperature but are unaffected by changes in pressure. The correlation proposed by Chrastil(1982) has several advantages over the more traditional cubic equation-ofstate approach. The most apparent advantage is the smaller number of parameters that need to be evaluated. Also, the model is superior in its correlation over the range of pressures and temperatures studied. However, there is some doubt as to the physical sigvalue determined for the solvato comnificance of the plex. The values of K observed for each ethyl ester-carbon dioxide system in this study, along with those determined by Chrastil (1982), indicate that there is no relationship between the number of molecules involved in the solvato complex and the shape, size, or type of the solute molecule. Although the form of equation proposed by Chrastil (1982) was useful in correlating existing solubility data, the justification for straight-line behavior is probably not as simple as proposed. Conclusion A continuous flow saturation apparatus was used to measure the solubilities of the ethyl esters of oleic acid (C18:1), eicosatrienoic acid (C20:3), arachidonic acid (C204), and docosahexaenoic acid (C22:6, DHA) in supercritical carbon dioxide. The solubilities were determined at temperatures between 313 and 373 K for carbon dioxide densities ranging from 330 to 810 g/L. Solubilities for the shortest chain ethyl ester (C18:l) examined were in the range of 0.3-2.2 mol %, whereas those observed for the longest chain ester (DHA) were considerably lower, 0.02-0.1 mol %, for similar experimental conditions. The effect of the degree of unsaturation of the esters on solubility in supercritical carbon dioxide was also examined. Although the solubility of the C203 ester was approximately 8% higher than that for C20:4 esters, the difference in solubility was small when compared to differences in solubilities according to chain length. The results therefore suggest that it is possible to fractionate fatty acid esters from a multicomponent mixture according to their chain length and, to a much lesser extent, according to the degree of unsaturation. The experimental study of the solubilities of the ethyl esters in supercritical carbon dioxide has also enabled the applicability of theoretical models to be examined. In particular, the Peng-Robinson equation of state and a density-based model proposed by Chrastil (1982) were tested. The Peng-Robinson equation was found to provide only a qualitative representation of the experimental solubility data. This is consistent with the observations of Schmitt (1984), who found that the Peng-Robinson equation underpredicted solubilities at low pressures but overpredicted a t high pressures. The solubility data were found to follow the form of the relationship proposed by Chrastil (1982). However, the slope of the solubility isotherms was observed to decrease with increasing temperature. This finding is in contrast with those observed by Chrastil (1982), who obtained parallel solubility isotherms for systems studied at dif-
ferent temperatures. Although the model proposed by Chrastil(1982) was useful in correlating existing data, the justification for straight-line behavior is probably not as straightforward as proposed. In addition, there is some doubt as to the physical significance of the value of the solvato complex K determined. Nomenclature C = concentration of the solute in the gas k = interaction parameter P = pressure R = universal gas constant T = temperature V = molar volume Subscripts
b = boiling R = reduced c = critical i = component i j = component j Greek Characters
a, + = empirical constants in the Chrastil model
w = p K
acentric factor
= density = constant, representing the average number of solvent
molecules present in the solvato complex Registry No. C18:l ethyl ester, 111-62-6;C203 ethyl ester, 99660-95-4;C20:4 ethyl ester, 1808-26-0;DHA ethyl ester, 81926-94-5;COz,124-38-9.
Literature Cited Adams, W. R.; Zollweg, J. A.; Streett, W. B.; Rizvi, S. S. H. New Apparatus for Measurement of Supercritical Fluid-Liquid Phase Equilibria. AIChE J. 1988,34, 1387. Chrastil, J. Solubility of Solids and Liquids in Supercritical Carbon Dioxide. J. Phys. Chem. 1982,86, 3016. Eckert, C. A.; Ziger, D. H.; Johnston, K. P.; Kim, S. Solute Partial Molar Volumes in Supercritical Fluids. J. Phys. Chem. 1983,90, 2738. Inomata, H.; Kondo, T.; Hirohama, S.; Arai, K.; Suzuki, Y.; Konno, M. Vapour-Liquid Equilibria for Binary Mixtures of Carbon Dioxide and Fatty Acid Methyl Esters. Fluid Phase Equilib. 1989, 46, 41. King, M. B.; Alderson, D. L.; Fallah, F. H.; Kassim, D. M.; Kassim, K. M.; Sheldon, J. R.; Mahmud, R. S. Some Vapour/Liquid and Vapour/Solid Equilibrium Measurements of Relevance for Supercritical Extraction Operations, and Their Correlation. In Chemical Engineering at Supercritical Fluid Conditions; Paulaitis, M. E., Penninger, J. M. L., Gray, R. D., Jr., Davidson, P., Eds.; Ann Arbor Science: Ann Arbor, MI, 1983;p 31. Lyman, W. J. Handbook of Chemical Property Estimation Methods; McGraw-Hill: New York, 1982;Chapter 12,pp 1-55. Panagiotopolous, A. Z.; Reid, R. C. High Pressure Phase Equilibria in Ternary Fluid Mixtures. ACS Symp. Ser. 1987,329,115. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1987; pp 12-14. Schmitt, W. J. The Solubility of Monofunctional Organic Compounds in Chemically Diverse Supercritical Fluids. Ph.D. Dissertation, Massachusetts Institute of Technology, 19M. Wu, A. H.; Stammer, A.; Prausnitz, J. M. Extraction of Fatty Acid Methyl Esters with Supercritical Carbon Dioxide. Proceedings of the International Symposium on Supercritical Fluids, Nice, France; Institut National Polytechnique de Lorraine: Vendoeuvre Cedes, France, 1988,p 107. 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, 23. Receiued for reuiew May 16, 1991 Accepted August 26, 1991
