Phase Equilibrium for the Extraction of Squalene from Shark Liver Oil

The interaction parameters required were very small, which suggests that previously reported deficiencies in the modeling of phase equilibria for comp...
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Ind. Eng. Chem. Res. 1997, 36, 3762-3768

SEPARATIONS Phase Equilibrium for the Extraction of Squalene from Shark Liver Oil Using Supercritical Carbon Dioxide Owen J. Catchpole* and Jan-Christian von Kamp Industrial Research Limited, P.O. Box 31-310, Lower Hutt, New Zealand

Phase equilibrium data were required for extracting squalene from shark liver oil which contains triglycerides and glyceryl ethers as the other major components. Vapor/liquid equilibrium for the binary system squalene/carbon dioxide was measured over the pressure range 100-250 bar and temperature range 313-333 K using a continuous-packed column method. The solubility of squalene in the vapor phase was correlated using a simple density-based equation. Phase equilibria for both squalene/carbon dioxide and a model triglyceride/carbon dioxide system were correlated using the Peng-Robinson equation of state. The Peng-Robinson attraction and repulsion parameters for carbon dioxide were optimized to reproduce known carbon dioxide density at a given temperature and pressure. Using this approach it was possible to accurately correlate vapor/liquid equilibria and phase densities for both carbon dioxide/squalene and carbon dioxide/triglyceride binary systems and predict vapor/liquid equilibria and phase densities for the three-component mixture over the same temperature and pressure range as the experimental data. The interaction parameters required were very small, which suggests that previously reported deficiencies in the modeling of phase equilibria for components with widely varying sizes may be due to the inaccurate attraction and repulsion parameters used for the light (carbon dioxide) component. Introduction Squalene (C30H50) is a highly unsaturated thermally unstable and light-sensitive hydrocarbon that appears in concentrations of 50-70% by weight in the livers of certain deep sea sharks (Tsujimoto, 1932; Hilditch and Williams, 1964). Squalene is also present in lower concentrations in some natural plant oils such as olive, corn, peanut, and rapeseed oils (Sonntag, 1979). Squalene is a popular health food tonic in some countries, where its reputed properties include enhanced oxygenation of the blood, anticancer, and increased longevity for the user (Gopakumar and Thankappan, 1986). It is also used in several cosmetic applications as a carrier for lipid-soluble components, as it can enter the skin easily, and in the manufacture of squalane (Winholz, 1976). The remainder of the shark liver oil is usually made up of triglycerides and glyceryl ethers as the other major components, with small concentrations of pristane and free fatty acids which give rise to an objectionable odor (Tsujimoto, 1932; Hilditch and Williams, 1964). Since the end use of squalene is in food and pharmaceutical applications, the use of organic solvent extraction is undesirable. The partial separation of squalene from other shark liver oil components without the use of organic solvents has been reported using the method of cold saponification (conversion of triglycerides to soaps), followed by repeated centrifugation and thermal crystallization (Salmonowicz and Krawzczak-Krogulecka, 1981). Squalene has been extracted from olive oil by combinations of urea complexation, saponification, and fractional distillation (Serra Massia and Martinez * Author to whom correspondence is addressed. Phone: ++64 4 5690 000. Fax ++64 4 5690 132. E-mail: o.catchpole@ irl.cri.nz. S0888-5885(97)00224-8 CCC: $14.00

Moreno, 1981). Separation of the shark liver oil components using carbon dioxide is attractive as no additional chemicals are required nor are the triglyceride fractions converted into soaps or thermally degraded. High-pressure liquid/vapor equilibrium for the binary system squalene/carbon dioxide has not been reported and is the subject of this work. Predicted phase equilibrium for the three-component mixture of carbon dioxide, squalene, and triglyceride is also addressed, as are the liquid-phase densities of these mixtures. Phase equilibrium data have been presented for pure and mixed triglycerides in carbon dioxide (Geana and Steiner, 1995; Bharath et al., 1992, 1993; Klein and Schulz, 1989). Phase equilibrium data have also recently been reported for triglyceride-rich mixtures containing small quantities of squalene and fatty acids (Stodlt et al., 1996; Simo˜es and Brunner, 1996). This work covers the whole concentration range for binary mixtures of squalene and triglycerides. Theoretical Section Phase Equilibrium. The most popular approaches to correlating solubilities of low volatility solutes in supercritical carbon dioxide are the empirical density based correlation of Chrastil (Chrastil, 1982) and cubic equation of state such as the Peng-Robinson equation of state (Peng and Robinson, 1976). The Chrastil correlation takes the form:

ln S ) k ln F + F + G/T

(1)

The symbols are given in the Nomenclature section. The correlation can only be used for the vapor-phase concentration of solute in carbon dioxide and gives no information on the liquid-phase composition. The Peng© 1997 American Chemical Society

Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3763

Robinson equation of state is (Peng and Robinson, 1976):

am RT (V - bm) V(V + bm) + bm(V - bm)

P)

(2)

parameter ac (J m3 mol-2) b (m3 mol-1) Tc (K) Pc (bar) MW (g mol-1) f(ω) kij lij C (m3 mol-1)

with the usual mixing rules:

am )

∑i ∑j xixj(aiaj)0.5(1 - kij)

(3)

bm )

∑i ∑j xixj

(bi + bj) (1 - lij) 2

(4)

and kij ) lij ) 0 when i ) j. In theory this equation can be used to correlate the composition of both liquid and vapor phases for any number of components. When phase equilibrium is achieved, the fugacity/pressure ratio for component i in each phase is equal. Phase equilibrium is calculated from an equation of state via the fugacity coefficient, which for the Peng-Robinson equation with the mixing rules given by eqs 3 and 4 is as follows (Kwak and Mansoori, 1986):

ln(φ) )

A

∑j xjbij - bm

{

x8B

(Z - 1) - ln(Z - B) -

bm

}[

∑j xjaij ∑j xjbij - bm

2

am

bm

ln

]

Z + 2.414B

Z - 0.414B

(5)

carbon dioxide (1)

squalene (2)

(6)

For squalene, Tc and f(ω) were optimized to give the

C54 triglyceride (3)

see Appendix A1 24.2918 63.9460 see Appendix A1 6.5906 × 10-4 1.2538 × 10-3 not required 716.5 1043.8 not required 7.0326 5.385 44.01 410.7 890.2 not required 3.2916 2.2961 0 0.05278 0.0420 0 0 0.0370 see Appendix A2 -1.9803 × 10-4 -3.2980 × 10-4

least-squares error between the vapor pressure as calculated using the Peng-Robinson equation and the reported vapor-pressure data (Heilbron et al., 1926; Windholz, 1976). The a and b parameters for the triglyceride fraction were estimated using the equations presented in Geana and Steiner (1995), with the assumption that the average molecular weight corresponded to a triglyceride with 54 carbon atoms (C54). The parameter values for ac, b, Tc, MW, f(ω), kij, and lij that were used in the phase equilibrium calculations are given in Table 1 for carbon dioxide, squalene, and C54 triglyceride. Phase Densities. Cubic equations of state are known to give inaccurate prediction of supercritical fluid and liquid-phase densities (Reid et al., 1987). The predictive performance can be improved by correcting the predicted molar volume with a component-specific correction factor C (Peneloux and Rauzy, 1982; Mathias et al., 1989):

Vcorr ) V + C

In the original derivation of the equation (Peng and Robinson, 1976), the a and b parameters are related to the critical properties and acentric factor of the component in question. Use of the original a and b parameters for predicting the density of pure carbon dioxide using cubic equations of state results in large errors in the near-critical region (Reid et al., 1987) and will thus give large errors in the prediction of the density of the mixtures. Accurate prediction of the liquid-phase density is important for packed-column separation of squalene from triglycerides (Catchpole et al., 1997). The separation must be carried out in a region where there is a small difference between the vapor- and liquidphase densities to achieve high solubility of squalene but a sufficient density difference to avoid flooding. In this work, the a and b parameters for carbon dioxide were optimized at each pressure and temperature condition so that the density and fugacity to pressure ratio matches that predicted from the IUPAC equation of state for carbon dioxide (Angus et al., 1978), as shown in Appendix 1. The a and b parameters for squalene were estimated using the method of Dohrn and Brunner (Dohrn and Brunner, 1991). This method requires an estimate of the normal boiling point and the density of the liquid at 20 °C. The normal boiling point was estimated by fitting an Antoinne type vapor pressure equation to reported vapor pressure data (Heilbron et al., 1926; Windholz, 1976) and then extrapolating to the boiling point. The temperature and acentric factor dependence of the a parameter for squalene and triglyceride was modeled as follows:

ai ) a[1 + f(ω){1 - xT/Tc}]2

Table 1. Optimized Peng-Robinson Parameters for CO2, Squalene, and C54 Triglyceride

C)

∑i xiCi

(7) (8)

where V is the molar volume predicted by the PengRobinson equation of state, and Vcorr is the corrected molar volume for the liquid phase. In this work, the a and b parameters for carbon dioxide have been optimized to fit the density and fugacity/pressure ratio, and so the correction term CCO2 is zero. Correction factors for squalene and C54 triglyceride were obtained by calculating the molar volume for phase equilibrium of the pure component at a temperature at which liquid density figures were available (typically 293-298 K) and then correcting this volume to reproduce the literature density figure. The calculation method is described further in Appendix 1. Corrections to the vapor-phase molar volume due to the presence of squalene and C54 triglyceride were deemed unnecessary due to the very low concentrations of these components. Experimental Section The solubility determinations were carried out in the apparatus shown schematically in Figure 1. The basic apparatus consisted of a high-pressure compressor for supplying supercritical carbon dioxide, a packed column with three temperature-controlled sections, a highpressure piston pump for the supply of the liquid squalene, and a separation vessel contained in a temperature-controlled water bath for the recovery of squalene. The apparatus is similar to that described for carrying out mass-transfer measurements on shark liver oil at a laboratory scale (Catchpole and von Kamp, 1996). The experiments were performed by passing supercritical carbon dioxide upward through the packed

3764 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997

Figure 1. Schematic of the experimental apparatus.

column at the fractionation pressure, which was controlled to (0.5 bar by a backpressure regulator, and the fractionation temperature(s), which was controlled to (0.5 °C by the temperature controllers. At the same time, liquid squalene was pumped into the top of the column by a plunger pump at a known volumetric rate. The volumetric rate was measured by the change in volume with time in the calibrated feed burette. The raffinate was collected from the bottom of the column at regular time intervals through valve S3. The carbon dioxide and dissolved squalene passed into the separation stage, which was maintained at a pressure of 30 bar. Squalene was recovered at regular time intervals from this vessel through valve S1. Carbon dioxide left the separation vessel through another pressure reduction valve, where the pressure was reduced to atmospheric. The carbon dioxide then flowed through a flow totalizer and rotameter to determine the volume and thus mass of gas that passed through over the same regular time interval. The solubility was thus calculated as the mass of squalene recovered over the mass of carbon dioxide that passed through the flow totalizer over the given time period. All solubility determinations were carried out using a fixed mass flow rate of carbon dioxide and at least a 2-fold excess of squalene required to achieve saturation. For determination of the liquidphase concentration of carbon dioxide in solute, the raffinate was collected in a further separation vessel through a pressure reduction valve S3 at the base of the column. The pressure was allowed to build up to 20 bar in the vessel before carbon dioxide was flashed off for a given time period. Valve S3 was then shut, the pressure reduced to atmospheric, and the squalene recovered from the bottom valve on the separator. The carbon dioxide that was flashed off was vented through a dry test meter to give the volume of carbon dioxide that had been present in the liquid phase at high pressure. The time period for sampling was short enough to ensure that there was still liquid in the bottom of the column. Using up all the liquid was indicated by a rapid increase in pressure in the collection vessel. The use of a continuous-packed column method to measure solubility in carbon dioxide does not appear to be widely practiced, although Lahiere and Fair (1987) used a continuous-flow method to obtain alcohol/water/

CO2 distribution coefficients. Therefore, considerable effort was expended to ensure the reliability of the results. Possible sources of error were identified as too small a density difference between squalene and carbon dioxide, leading to carry over; insufficient squalene flow rate to achieve saturation; variation of apparent solubility with carbon dioxide flow rate; and insufficient packed height to achieve saturation. Apparent solubilities were measured at 200 bar and 313 K, where there was a lowdensity difference between CO2 and squalene. The measurements were carried out at a fixed carbon dioxide mass flow rate and increasing squalene flow rate. The measurements were constant as the squalene/carbon dioxide ratio was varied from the minimum to achieve saturation until a critical ratio of around 2 times the normal 2-fold ratio was reached. Beyond this ratio, squalene was carried out of the column without dissolving. At pressures greater than 200 bar and 313 K, no reliable results were achieved as the density difference was too small. Apparent solubilities at 175 bar and 313 K using fixed oil to carbon dioxide ratios and carbon dioxide flow rates lower and greater than the standard flow rate were also carried out. The solubility measurements were constant over a wide carbon dioxide flow rate range until a critical flow rate of around 4 times the standard flow rate was reached. At this flow rate, the apparent solubility decreased, possibly due to poor contacting between the carbon dioxide and oil. All measurements were performed with squalene to carbon dioxide ratios and carbon dioxide flow rates less than the critical values. Squalene solubilities were also determined at a packed height two-thirds of the normal packed height over the whole pressure and temperature range. There was no deviation in the measured values from those at the full packed height. Squalene solubility in carbon dioxide in the gas phase and carbon dioxide solubility in the liquid phase were determined over the pressure and temperature ranges 100-250 bar and 313-333 K, respectively. At least six measurements of the solubility were made per experiment at a given temperature and pressure. Selected temperature and pressure combinations were selected at random and repeated, to check the reproducibility of the measurements, which were found to vary by less than 5% of the mean value. The experimental error for the solubility of squalene in carbon dioxide was estimated to be (0.05 g/kg of carbon dioxide and that for carbon dioxide in squalene (0.005 weight fraction. Results and Discussion Binary Mixture Phase Equilibrium and Solubility. The solubility of pure squalene in supercritical carbon dioxide was measured over the temperature and pressure ranges 313-333 K and 100-250 bar, respectively. To our knowledge, the solubility of squalene in supercritical CO2 has not been reported in the literature. The solubility ranged from a minimum of 0.1 g/kg of CO2 at 333 K and 100 bar to 35.4 g/kg at 323 K and 250 bar. The mole fractions of squalene in carbon dioxide in the gas and liquid phases are given in Table 2. The solubility of squalene in the gas phase was correlated using both eqs 1 and 2. The fit of eq 1 as compared to the experimental data is shown in Figure 2. All points shown in Figure 2 are the average values of at least six measurements. The variation in the individual measurements was less than 5% of the average value. The best-fit correlation is given as follows:

Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3765

Figure 2. Solubility of squalene in carbon dioxide as a function of density and temperature.

Figure 3. Liquid and vapor mass fractions for the squalene/ carbon dioxide system: lines, Peng-Robinson predictions; points, experimental data.

Table 2. Phase Equilibrium Data for Carbon Dioxide (1)/Squalene (2) temperature, K

pressure, bar

vapor mole fraction

liquid mole fraction

313

100 125 150 175 200 100 125 150 175 200 225 250 100 125 150 175 200 225 250

0.99950 0.99889 0.99833 0.99778 0.99724 0.99994 0.99943 0.99879 0.99814 0.99748 0.99680 0.99600 0.99999 0.99985 0.99933 0.99873 0.99799 0.99713 0.99631

0.77088 0.78398 0.79217

323

333

0.81452

0.74664 0.78398 0.80742 0.82131

2993.72 + 5.68 ln F T

(9)

Figure 4. Liquid and vapor mass fractions for the C54 triglyceride/carbon dioxide system: comparison of literature data with predictions from the Peng-Robinson equation of state.

The solubility behavior follows that of other lipid compounds with low volatility such as fatty acids, triglycerides, and tocopherols (Chrastil, 1982; del Valle et al., 1989). The vapor/liquid equilibrium of the binary squalene/carbon dioxide mixture was also well correlated by the Peng-Robinson equation using only one binary interaction parameter kij and the optimized a and b parameters for carbon dioxide, as shown in Figure 3 for temperatures of 313 and 333 K. The phase equilibrium for triglycerides using C54 as a typical component was also effectively correlated using the Peng-Robinson equation with optimized parameters for carbon dioxide, as shown in Figure 4 for the same temperatures. To obtain the best fit, it was necessary to use a second binary interaction parameter, lij. The best-fit values of a, b, kij, and lij are listed in Table 1. The model fit was also compared against the experimental vapor/liquid equilibrium data for rapeseed oil in carbon dioxide (Geana and Steiner, 1995; Klein and Schulz, 1989) and sesame seed oil in carbon dioxide (Bharath et al., 1992). The interaction parameters for both binary systems are

very small even though there is a very large difference in size between the light component, carbon dioxide, and the heavy component, squalene or C54 triglyceride. This suggests that previously reported deficiencies (Mu¨hlbauer and Raal, 1995) in the modeling of mixtures with components that differ greatly in size may be due to the choice of attraction (a) and repulsion (b) parameters for the light component. This is not surprising as the Peng-Robinson equation does not accurately predict density at supercritical conditions for carbon dioxide using standard a and b parameters. For both binary systems, carbon dioxide is the main component on a molar basis in both the vapor and liquid phases. However, the phase equilibrium calculations for both systems have only been carried out over the relatively narrow temperature and pressure range relevant to this work, and the fit may not be so good outside the region of interest. Ternary Phase Equilibrium. The Peng-Robinson equation was used to predict phase equilibrium for the three-component mixture C54 triglyceride/squalene/

ln S ) -25.53 -

3766 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997

Figure 5. Liquid and vapor phase mole fraction of squalene at selected temperature and pressure combinations: points, PengRobinson predictions; lines, linear regressions.

Figure 6. Mass fractions in the liquid and vapor phase and equilibrium coefficients for squalene on a carbon dioxide free basis.

carbon dioxide and calculate separation factors for squalene/C54 triglyceride. Interaction parameters kij and lij for the interaction between squalene (component i) and C54 triglyceride (component j) were assumed to be zero. Predicted vapor and liquid equilibrium mole fractions for squalene in the C54 triglyceride/squalene/ carbon dioxide system are shown for selected temperatures and pressures in Figure 5. The liquid mole fractions equate to discrete mass fractions of squalene on a carbon dioxide free basis ranging from 0 to 1. It is interesting to note that the equilibrium relationship is nearly linear, as shown by the regression lines included in Figure 5. The mass fraction of carbon dioxide dissolved in the liquid phase at a given temperature and pressure stays almost constant even when the squalene mass fraction varies from 0 to 1 (on a carbon dioxide free basis). The predicted vapor and liquid mass fractions of squalene for the same system are plotted on a carbon dioxide free basis in Figure 6. Also included in Figure 6 is the equilibrium coefficient K (mass fraction of squalene in the vapor phase over the mass fraction

Figure 7. Saturated and pure component liquid and vapor phase densities at 313 K as a function of pressure.

in the liquid phase on a carbon dioxide free basis). The selectivity toward squalene is best at low pressure and low mass fraction of squalene. The solubility of triglycerides decreases more sharply with decreasing pressure than squalene, and so the increase in selectivity is to be expected. The equilibrium coefficient decreases as the temperature and vapor-phase density increase, although it is still sufficiently high at the highest temperature and pressure combination of 250 bar and 333 K to enable easy separation of the two components. Densities of the Liquid and Vapor Phases. The predicted liquid-phase density of squalene saturated with carbon dioxide and the vapor-phase density of carbon dioxide saturated with squalene are shown as a function of pressure at 313 K in Figure 7. The densities of pure liquid squalene and pure carbon dioxide are included for comparison. The pure liquid density was calculated using the Peng-Robinson equation. The pure liquid density increases slightly with pressure, as the liquid is nearly incompressible. The carbon dioxide density was calculated using the IUPAC equation of state (Angus et al., 1978). The saturated vapor-phase density is slightly more dense than that of pure carbon dioxide over the pressure range 70-125 bar. As has been shown by other workers, the enhancement in vapor-phase density near the critical pressure of carbon dioxide can be important for free convection mass transfer (Lim et al., 1990; Mu¨ller and Este´vez, 1990). The saturated liquid-phase density increases slightly with pressure as an increasing mass of carbon dioxide is dissolved over the pressure range 1-80 bar and then flattens out. The pure liquid and vapor densities cross over at around 220 bar, while the saturated densities cross over at a higher pressure, thus enabling the solubility to be determined. As the temperature increases at constant pressure, the density difference between the saturated liquid and vapor phases increases. The liquid-phase densities of carbon dioxide/ squalene/C54 mixtures at a fixed mass fraction of squalene (on a carbon dioxide free basis) show a pressure dependence similar to that of saturated liquid squalene. The density increases as the concentration of carbon dioxide increases and then flattens out as the carbon dioxide content also flattens out. The liquid-

Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3767

phase density of the ternary mixture decreases as the squalene content increases at a fixed temperature and pressure. Conclusions High-pressure vapor/liquid equilibrium data for the squalene/carbon dioxide binary system were measured in a packed column over the temperature range 313333 K and pressure range 100-250 bar. The solubility of squalene in carbon dioxide was correlated using a simple density-based equation. The phase equilibrium of the binary systems squalene/carbon dioxide and C54 triglyceride and ternary phase equilibrium for the system squalene/C54 triglyceride/carbon dioxide were predicted over the same temperature and pressure ranges using the Peng-Robinson equation of state. The attraction and repulsion parameters for carbon dioxide were optimized at each temperature and pressure to enable accurate density predictions to be made for the liquid and vapor phases. Nomenclature a ) Peng-Robinson attraction parameter ) Rac A ) aP/(RT)2 b ) Peng-Robinson repulsion parameter ) βRTc/Pc B ) bP/RT C ) volume correction factor (m3 mol-1) f ) fugacity (Pa) F ) empirical constant in density correlation G ) empirical constant in density correlation (K) k ) Peng-Robinson attraction interaction parameter K ) equilibrium distribution coefficient (g/g) l ) Peng-Robinson repulsion interaction parameter P ) pressure (Pa) R ) universal gas constant S ) solubility of solute in the gas phase (g/kg) T ) temperature (K) V ) molar volume (m3 mol-1) x ) liquid-phase mole fraction y ) vapor-phase mole fraction Z ) compressibility ) PV/RT

Z3 - Z2(1 - B) + Z(A - 3B2 - 2B) - AB + B2 + B3 ) 0 (A1) ln(f/P) ) (Z - 1) - ln(Z - B) -

Z + 2.414B A ln x8B Z - 0.414B (A2)

[

]

Equation A1 can be rearranged to give A in terms of B and Z:

A)

Z3 - Z2(1 - B) - Z(2B - 3B2) + B2 + B3 B-Z

(A3)

An iterative solution for A and B was obtained by using the IUPAC prediction for Z in eqs A2 and A3 and adjusting the value of B (which gives A from eq A3) until the least-squares error given by eq A4 was minimized:

δ)

[

]

{ln(f/P)PR - ln(f/P)IUPAC}2 {ln(f/P)IUPAC}2

1/2

(A4)

The values for a and b were then calculated from the final A and B values. Appendix A2. Determination of Volumetric Correction Factors C for Squalene and C54 Triglyceride When the vapor pressure is well below the boiling point at atmospheric pressure, the vapor-phase behavior is similar to that of a perfect gas; i.e., both the compressibility factor, ZV, and the fugacity/pressure ratio are equal to 1. The liquid-phase value for Z is required at a temperature at which the density is known to obtain the volumetric correction factor C. This requires an estimate of the vapor pressure P which gives rise to a fugacity/pressure ratio of 1 for the liquid phase. Solution of eq A1 to obtain the liquid-phase compressibility ZL can be problematic at low pressures due to rounding errors. However, all terms containing cubic factors become negligible, and ZL is then obtained from a simple quadratic expression:

Greek Characters

A - 2B - x(A - 4B)2 - 8B2 2

R ) Peng-Robinson parameter ) 0.45724[1 + f(ω)(1 xTr)]2 β ) Peng-Robinson constant ) 0.07780 φ ) fugacity coefficient ) f/yP F ) density (kg m-3) ω ) acentric factor

The difference between the calculated molar volume obtained from ZL and the actual molar volume obtained from literature data is the volume correction factor C.

Subscripts

Literature Cited

c ) critical i ) component i j ) component j

Angus, S.; Armstrong, B.; de Reuck, K. M. International Thermodynamic Tables of the Fluid State: Carbon Dioxide; Pergammon Press: Oxford, U.K., 1978. Bharath, R.; Inomata, H.; Adschiri, T.; Arai, K. Phase Equilibrium Study for the Separation and Fractionation of Fatty Oil Components using Supercritical Carbon Dioxide. Fluid Phase Equilib. 1992, 81, 307-320. 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, 188-192. Catchpole, O. J.; von Kamp, J.-C. Extraction of Squalene from Shark Liver Oil. Proc. Chemeca 96 (ISBN 0 85825 658 4) 1996, 1, 65-70. Catchpole, O. J.; von Kamp, J.-C.; Grey, J. B. Extraction of Squalene from Shark Liver Oil in a Packed Column using Supercritical Carbon Dioxide. Ind. Eng. Chem. Res. 1997, in press.

Appendix A1. Determination of Peng-Robinson a and b Parameters The a and b parameters for carbon dioxide at a given temperature and pressure were determined by minimizing the least-squares error between the Peng-Robinson and IUPAC equation of state compressibility Z and logarithm of the fugacity to pressure ratio f/P. For the Peng-Robinson equation of state, the compressibility and fugacity/pressure ratio are obtained from eqs A1 and A2 respectively:

ZL )

3768 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 Chrastil, J. Solubility of Solids and Liquids in Supercritical Gases. J. Phys. Chem. 1982, 86, 3016-3021. del Valle, J. M.; Aguilera, J. M. An Improved Equation for Predicting the Solubility of Vegetable Oils in Supercritical CO2. Ind. Eng. Chem. Res. 1989, 27, 1551-1553. Dohrn, R.; Brunner, G. Correlations for the Pure Component Parameters of the Peng-Robinson Equation of State. Proc. 2nd Int. Symp. Supercrit. Fluids 1991, 471-474. Geana, D.; Steiner, R. Calculation of Phase Equilibrium in Supercritical Extraction of C54 Triglyceride (Rapeseed Oil). J. Supercrit. Fluids 1995, 8, 107-118. Gopakumar, K.; Thankappan, T. K. Squalene, its Source, Uses and Industrial Applications. Seafood Export J. 1986, March, 17. Heilbron, I. M.; Kamm, E. D.; Owens, W. M. The Unsaponifiable Matter from the Oils of Elasmobranch Fish. Part I. A Contribution to the Study of the Constitution of Squalene (Spinacene). J. Chem. Soc. 1926, 1630-1644. Hilditch, T. P.; Williams, P. N. The Chemical Constitution of Natural Fats; Chapman & Hall: London, 1964; pp 34-79. Klein, T.; Schulz, S. Measurement and Model Prediction of Vapour-Liquid Equilibria of Mixtures of Rapeseed Oil and Supercritical Carbon Dioxide. Ind. Eng. Chem. Res. 1989, 28, 1073-1081. Kwak, T. Y.; Mansoori, G. A. Van der Waals Mixing Rules for Cubic Equations of State. Applications for Supercritical Fluid Extraction Modelling. Chem. Eng. Sci. 1986, 41, 1303-1309. Lahiere, R. J.; Fair, J. R. Mass-Transfer Efficiencies of Column Contactors in Supercritical Extraction Service. Ind. Eng. Chem. Res. 1987, 26, 2086-2092. Lim, G.-B.; Holder, G. D.; Shah, Y. T. Mass Transfer in Gas-Solid Systems at Supercritical Conditions. J. Supercrit. Fluids 1990, 3, 186-197. Mathias, P. M.; Naheiri, T.; Oh, E. M. A Density Correction for the Peng Robinson Equation of State. Fluid Phase Equilib. 1989, 47, 77-87. Mu¨hlbauer, A. L.; Raal, J. D. Computation and Thermodynamic Interpretation of High-Pressure Vapour-Liquid Equilibrium: a Review. Chem. Eng. J. 1995, 60, 1-29.

Mu¨ller, E. A.; Este´vez, L. A. Mixing Expansivities and Grashof Numbers in Supercritical Fluids Using Cubic Equations-ofState. J. Supercrit. Fluids 1990, 3, 136-142. Peneloux, A.; Rauzy, E. A Consistent Correction for RedlichKwong-Soave Volumes. Fluid Phase Equilib. 1982, 8, 7-23. Peng, D.-Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976, 15 (1), 59-64. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids; McGraw-Hill: New York, 1987; pp 44-45. Salmonowicz, J.; Krawczak-Krogulecka, W. Possibilities for Complex Use of Liver Oil of some Species of Sharks. Zesz. Probl. Postepow Nauk Roln. 1981, 211, 207-210. Serra Massia, A.; Martinez Moreno, J. M. Squalene Recovery during the Physical Refining of Olive Oil. Grasas Aceites 1981, 32 (5), 313-317. Simo˜es, P. C.; Brunner, G. Multicomponent Phase Equilibria of an Extra-Virgin Olive Oil in Supercritical Carbon Dioxide. J. Supercrit. Fluids 1996, 9, 75-81. Sonntag, N. O. V. Structure and Composition of Fats and Oils. In Baileys Industrial Oil and Fat Products, 4th ed.; Swern, D., Ed.; John Wiley and Sons: New York, 1979; Vol. 1, pp 67-69. Stodlt, J.; Saure, C.; Brunner, G. Phase Equilibria of Fat Compounds with Supercritical Carbon Dioxide. Fluid Phase Equilib. 1996, 116, 399-406. Tsujimoto, M. The Liver Oils of Elasmobranch Fish. J. Sci. Chem. Ind. (Trans.) 1932, 317-323. Winholz, M. The Merck Index; Merck and Co., Inc.: New York, 1976; Vol. 9, pp 1133-1134.

Received for review March 17, 1997 Revised manuscript received June 9, 1997 Accepted June 11, 1997X IE970224Z

X Abstract published in Advance ACS Abstracts, August 1, 1997.