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The solubility of two monoterpenes in supercritical carbon dioxide
Fluid Phase Equilibria, 85 (1993) 285-300 Elsevier Science Publishers B.V., Amsterdam
285
The solubility of two monoterpenes carbon dioxide
in supercritical
Miroslav Richter ’ and Helena Sovova * Institute of Chemical Process Fundamentals, 16.5 02 Prague 6-Suchdol (Czech Republic) (Received
March
16, 1992; accepted
Czech Academy
of Sciences,
in final form September
21, 1992)
ABSTRACT Richter, M. and Sovova, H., 1993. The solubility of two monoterpenes carbon dioxide. Fluid Phase Equilibria, 85: 285-300.
in supercritical
The solubilities in supercritical CO, of two terpenes, cc-pinene as a representative of the monoterpene hydrocarbons and cis-verbenol as one of the oxygenated terpenes, have been measured at temperatures from 40 to 55°C and pressures from 5 to 12 MPa using a dynamic flow apparatus, which was tested by measuring the solubilities of naphthalene in compressed carbon dioxide. The experimental solubility data were correlated using a compressed gas model with the Peng-Robinson equation of state and empirical equations based on the dependence of the concentration of solute on the density of pure solvent. The unknown critical properties of both monoterpenes were estimated using the Joback contribution method. The vapour pressure of cis-verbenol was determined by the modified Watson method. The optimum conditions for the supercritical fluid extraction of both monoterpenes were determined.
INTRODUCTION
In addition to steam distillation and liquid extraction, supercritical fluid extraction is used to obtain various valuable components of plants for the food and pharmaceutical industries (Parkinson and Johnson, 1989). Conventional distillation methods involve higher temperatures which result in decomposition of heat-labile substances. Conventional extraction methods involve chemical solvents which, even in residual quantities, are of concern from the standpoint of toxicity to consumers of the end products. Supercritical extraction, however, is performed at relatively low temperatures and involves the use of fluids which can be separated from the end products by simple physical means. It is a semicontinuous process with the dense gas
*
Corresponding
author. Research Czech Republic.
’ Present address: Labem,
0378-3812/93/$06.00
0
Institute
of Inorganic
1993 - Elsevier
Chemistry,
Science Publishers
RevoluEni
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286
M. Richter and H. SovovLi 1 Fluid Phase Equilibria
85 (1993) 285-300
recycling between the extractor, where it flows through a fixed bed of solid vegetable material, and the separator, where it is separated from the extract after expansion. A solubility difference of several orders of magnitude can be achieved by an appropriate adjustment of pressure and temperature in the extractor and in the separator. Carbon dioxide is a preferred supercritical solvent, since it is non-toxic, non-flammable, environmentally acceptable and relatively inexpensive, and its critical point allows extraction at relatively low temperatures. The solubility dependence of the extracted components on pressure and temperature forms the basis for the design of the conditions in the extractor and separator. Terpenes, components of essential oils, show the highest CO, solubilities among the vegetable substances. The solubility dependences have been published for some of them: limonene (Stahl and Gerard, 1985; Di Giacomo et al., 1989; Brandani et al., 1990; Matos et al., 1989), citral (Di Giacomo et al., 1989; Brandani et al., 1990), carvone, anethole, eugenol, caryophyllene and valeranone (Stahl and Gerard, 1985), menthol (Maier and Stephan, 1984) and 1,8-cineole (Matos et al., 1989). Results for phase equilibria in a ternary system limonene-citral-CO, have also been reported (Mathias et al., 1986; Kalra et al., 1987; Di Giacomo et al., 1989; Brandani et al.. 1990). This paper presents carbon dioxide solubility data for two monoterpenes: cc-pinene, one of the most frequently occurring terpenes, and cis-verbenol, an oxygenated terpene. Solubilities of naphthalene in dense carbon dioxide measured during the testing of the apparatus for solubility measurements are also reported.
EXPERIMENTAL
An apparatus similar to that of Johnston and Eckert ( 1981) was used for the measurement of the solubilities (see Fig. 1). Carbon dioxide from the pressure cylinder (1) was charged through a tube with a molecular sieve into the diaphragm compressor (2). The compressed CO? was stored in a surge tank to dampen any pressure fluctuations. It was bled into the system from a spring-loaded regulator (3) controlling the pressure to within + 0.03 MPa. The compressed gas reached the temperature of the bath (4) in an immersed capillary (5) and then equilibrated with the solute in the saturator (6). The pressure at the saturator inlet was measured using a tensometer calibrated to +0.02 MPa and the temperature in the saturator was assumed to be equal to the bath temperature controlled to within +O.l “C. After saturation, the loaded solvent was expanded to atmospheric pressure through a metering valve (7). The solute separated from the gaseous CO2 and accumulated in a glass U-tube or coil immersed in a mixture of ethanol and dry ice, the collector (8). The amount of solute-free gas was measured in a ther-
287
M. Richter and H. Sovovri I Fluid Phase Equilibria 85 (1993) 285-300
I... &IL)_ L
3 Fig. 1. Schematic
diagram
2
of the dynamic
1
flow apparatus
for measuring
solubilities.
mostatted calibrated glass vessel, the eudiometer (9), where it displaced silicone oil saturated with COz. The saturator was a high pressure column with an internal volume of 12 cm3. At higher solubilities, 2 or 3 such columns were connected in series. Each of the columns contained 2-3 g of the solute. The solid solute was mixed with glass beads 1 mm in diameter. In the case of liquid a-pinene, glass wool was wetted with the solute and a layer of glass beads was placed above it to prevent entrainment of liquid drops. The complication of precipitation in the valve was overcome by its design. It was electrically heated to compensate for the heat consumption during gas expansion and had a long stem with a small angle, allowing precise control of low flow rates. The path of the expanded gas in it was direct and short. Three eudiometers of volumes 0.26, 0.53 and 1.1 1 were used. The lower the range of the measured solubilities, the larger was the eudiometer used. The apparatus was first flushed with low pressure CO?, then the pressure in the saturator was increased to the required value and, after thermal equilibrium within the constant-temperature bath was reached, the flow rate of CO, was adjusted by the metering valve to one standard litre per hour. This flow rate was found to be satisfactory in ensuring that solubiliry equilibrium was achieved in the gas at the exit of the saturator. A sufficient amount of extract was initially collected in a waste trap until equilibrium within the saturator had been attained; then a tared collector was substituted and the gas flowing through it started filling up the eudiometer. A run was completed by removing the collector after the volume of CO, was equal to the volume of the eudiometer used. The amount of collected solute was found from the weight gain in the collector, or, for solubilities lower than
M. Richter and H. Sovovci / Fluid Phase Equilibria
288
85 (1993) 285-300
y = 0.005, ph o t ometrically after dissolving the solute in a known amount of liquid solvent. The solubility was calculated from the amounts of the collected solute and of the gas. Three measurements were carried out for each set of conditions. The reproducibility of the solubility measurements was better than 5%, except for solubilities lower than y = 2 x 10p3. The carbon dioxide used in this work was more than 99.9% pure as supplied by Chemical Works Litvinov. The minimum purity of the a-pinene supplied by AG Fluka Chemie was 97%. cis-Verbenol, obtained by oxidation of a-pinene, was more than 99% pure. Naphthalene was recrystallized and its purity was checked by measurement of its melting point. The value of 80.3”C agrees well with the literature data (Reid et al., 1987). Propanol and cyclohexanol, the solvents used for photometry and supplied by Lachema, were of p.a. purity. RESULTS
The solubility values for naphthalene in CO2 measured at 35°C 45°C and 55°C agree to within better than 2% with the data of Tsekhanskaya et al. ( 1964). Also the agreement with the data of McHugh and Paulaitis ( 1980) is satisfactory (see Fig. 2).
A
Y.103
0 0
.
12
@
P
8
6
8
10
12
14
16
P /MPa Fig. 2. Solubility of naphthalene in CO, at 35°C; ( 1964); A, McHugh and Paulaitis ( 1980).
n , this work; 0, Tsekhanskaya
et al.
1
4.63 4.73 4.90 4.93 5.27 5.27 5.30 5.36 5.73 5.80 5.89 5.99 6.07 6.49 6.52 6.69 6.69 6.86 6.91 7.05 7.16 7.26 7.30 7.34 7.37 7.44 7.48 7.54 7.55 7.74
1.35 1.42 1.16 1.43 1.45 1.42 1.51 1.54 1.95 1.96 2.18 2.00 2.06 2.39 2.37 2.21 2.27 2.75 2.75 2.30 2.10 2.78 2.98 3.40 3.72 3.41 4.13 4.47 3.80 (19.05)
3.36 3.36 3.86 4.23 4.27 4.86 5.15 6.04 6.85 7.67 8.15 8.17 8.63 8.64 8.85 8.87 9.04 9.05 9.16 9.16 9.20 9.28 9.29
P (MPa)
y X 103
P ( MPa)
2.40 2.62 2.18 2.13 2.27 2.27 2.57 2.53 3.14 4.22 5.78 6.10 7.32 7.46 8.15 8.01 9.51 9.31 10.42 9.88 10.82 (48.19) (47.28)
y x 103
for cc-pinene in dense carbon
50°C
solubilities
40°C
Experimental
TABLE
dioxide
3.25 4.00 4.01 5.19 5.25 6.13 6.16 6.91 6.96 7.53 8.00 8.10 8.15 8.56 8.95 8.98 9.20 9.29 9.60 9.71 9.71 9.75 9.77 9.87
P (MPa)
55°C
2.62 2.92 2.82 2.97 3.08 3.27 3.35 3.48 3.63 4.70 5.19 5.47 5.86 6.53 7.18 7.20 8.26 9.17 15.04 12.35 15.70 17.23 (28.18) (87.00)
y x 103 22.7 25.0 27.4 27.4 27.5 30.0 30.4 35.0 40.0 50.0 55.0 62.0
t (“C)
6.14 MPa
10.41 2.82 1.88 1.84 1.63 1.34 1.39 1.49 1.86 2.63 3.30 4.24
y x 103 37.9 38.6 40.0 42.7 44.7 44.7 48.3 48.3 50.0 55.0 62.0 62.1
t (“C)
7.65 MPa
31.93 16.40 9.50 5.23 4.53 4.58 4.20 4.13 3.90 4.47 4.65 4.93
y x lo3
290
M. Richter and H. SovovLi / Fluid Phase Equilibria
85 (1993) 285-300
The experimental solubility data for liquid a-pinene in supercritical carbon dioxide at 40°C 50°C and 55°C together with two isobars in the subcritical region are presented in Table 1. These data were compared with the phase equilibrium data measured using the static method (PavliCek and Richter, 1993). The agreement of the results obtained by both methods is illustrated in Fig. 3. Larger differences are observed only close to the critical point of the mixture where the dynamic method yields higher values of solubility. These are caused by partial entrainment of the liquid phase from the saturator owing to the extremely small difference in the densities of both phases. These data, indicated in Table 1 in parentheses, were not taken into account in the evaluation of solubilities. The experimental solubility data for solid cis-verbenol in supercritical CO, at 40°C 50°C and 55°C are given in Table 2. Its solubility is one order of magnitude lower than that of cr-pinene and the data are more scattered. In Fig. 4, the solubilities in CO? of cr-pinene and cis-verbenol measured at 50°C are compared with the solubilities of other monoterpenes available in the literature. Of these, a-pinene is the most soluble, limonene and cineole are less soluble, and menthol, cis-verbenol and citral have the lowest solubilities in C02. The conditions suitable for supercritical fluid extraction and for the separation of the extract from carbon dioxide are determined from the solubility data. Over the temperature range 40-55°C the pressure in the extractor should be adjusted to 8- 10 MPa for a-pinene and to 9- 13 MPa for cis-verbenol, with the higher pressures corresponding to the higher
20 Y.103
. 0
15
-
10
: (j’
:
5
c
t,
Y
,r” *
.
l/
lo.*
0 3
5
Fig. 3. CO, solubilities the static method (0).
7
PlMPa
’
for cc-pinene at 50°C measured
by the dynamic
method
(0)
and by
M. Richter and H. Sovov6 1 Fluid Phase Equilibria 85 (1993) 285-300 TABLE
291
2
Experimental
solubilities
40°C
for cis-verbenol
in dense carbon
50°C
dioxide 55°C
P (MPa)
y x 103
P (MPa)
y x 103
P ( MPa)
y x 103
5.09 5.11 6.07 6.08 6.94 7.01 7.06 7.51 7.58 8.12 8.15 8.27 8.28 8.31 8.39 8.40 8.56 8.58 8.63 9.07 9.10 9.85 9.91 10.71 10.94
0.06 0.05 0.14 0.13 0.26 0.21 0.23 0.65 0.63 1.15 1.13 1.39 1.18 1.14 2.57 3.12 3.62 4.42 5.63 20.62 20.25 27.30 29.60 52.30 53.00
5.14 5.16 6.13 6.13 6.30 7.17 7.17 7.71 7.72 8.08 8.08 8.46 8.54 8.86 8.92 9.36 9.46 9.49 9.15 10.33 10.37 10.54 10.60 10.87 10.94 11.84 12.84 12.98
0.14 0.13 0.18 0.16 0.20 0.42 0.41 0.65 0.68 1.11 1.04 0.70 0.83 1.07 0.96 2.01 1.99 2.63 2.72 4.08 5.39 10.75 11.64 12.46 12.64 30.90 47.20 46.40
5.16 6.20 6.22 7.38 7.43 8.28 8.28 8.89 8.89 9.69 9.71 9.76 10.71 10.77 11.25 12.06 12.21 13.10 13.52 13.78
0.12 0.26 0.17 0.44 0.43 0.75 0.84 0.90 0.94 1.08 1.02 1.72 4.64 5.35 10.52 12.55 13.27 28.60 35.20 38.50
temperatures. The pressure in the separator is limited by the suction pressure of the CO, pump. According to the solubility isobars for a-pinene, the temperature close to 30°C is recommended at 6 MPa. These conditions are also suitable for the separation of cis-verbenol from C02. The CO2 solubility data for binary systems cannot, however, be used to evaluate the extractive fractionation of two terpenes directly, as is demonstrated by the following experiment. Several measurements of CO2 solubilities at 40°C were carried out for a liquid mixture of a-pinene and cis-verbenol at a molar ratio of 4: 1. The amount of solutes trapped in the collector was determined from its weight and their ratio by gas chromatography. The results are shown in Fig. 5. While the value of the solubility for
M. Richter and H. SovovLi 1 Fluid Phase Equilibria 8.5 (1993) 285-300
292
10
P /MPa
14
12
Fig. 4. CO, solubilities for monoterpenes at 50°C; n , cc-pinene; Cl, cis-verbenol (this work); 0, limonene (Di Giacomo et al., 1989); 0, limonene (Matos et al., 1989); LI, cineole (Mates et al., 1989); +, methanol (Maier and Stephan, 1984); +, citral (Di Giacomo et al., 1989).
loo : Y.103
10
-
/, /
.
/
/
l-
/ 0 * . -6
oo_
/ ,
/
-
7
PIMPa
8
Fig. 5. Vapour-phase composition of the ternary system cc-pinene-cis-verbenol-CO, with 4: 1 mole ratio of cr-pinene and cis-verbenol in the liquid phase: 0, a-pinene; 0, cis-verbenol. CO, solubilities in the binary systems a-pinene-CO, (-) and cis-verbenol-CO, (- - -). All data at 40°C.
M. Richter and H. Sovovci / Fluid Phase Equilibria 85 (1993) 285-300
293
a-pinene in the ternary and binary systems was identical, within experimental error, the solubility of cis-verbenol increased in the presence of a-pinene, which acted as entrainer. MODELLING OF SOLUBILITIES
Two approaches were applied in the mathematical treatment of the experimental data. In the first one the solubilities were correlated with carbon dioxide density according to several equations found in the literature. The density of CO;! was calculated using the Bender equation of state (Knaff and Schhinder, 1987). In the second approach, the compositions of the equilibrated phases were modelled using the Peng-Robinson equation of state. As the dynamic flow method of solubility measurement does not give the necessary information about the composition of the condensed phase, this approach was applied to the solid-gas systems only, using the assumption that the gas does not dissolve in the solid. For the a-pineneCO2 system, equilibrium data measured by the static method had to be added to the data presented in Table 1 and the results of this evaluation will be presented elsewhere (PavliEek and Richter, 1993). The relative standard deviation of the solubilities 0.5
s = (l/N)
[
5 (Ywal-Yr,exp)2/YLp
r=l
1
(1)
was the objective function used to fit the experimental data. Correlations of solubility with CO2 density Chrastil (1982) derived the equation c =d“exp(a/T+b)
(2)
on the basis of the assumption that one molecule of a solute associates on average with k molecules of a gas. The parameter ti = AH/R is related to the heat of vaporization and solvation, his a constant, c is the concentration of the solute in grams per litre (g 1-l) of the gas, and d is the density of the pure gas, also in g l- ‘. According to the Chrastil equation, the log-log relationship between solubility and density should be linear up to relatively high solute concentrations (100-200 g 1-l). The solubilities measured in this work fulfil this condition only partially: the solubilities for naphthalene deviate from it at the lowest COZ densities, and the log-log solubility versus density curves are concave both for a-pinene and for cis-verbenol. The results calculated using the Chrastil equation are summarized in Table 3. Adachi and Lu (1983) modified the Chrastil equation, introducing a density dependent association number: c = d’, +&fe# exp(ii/T + 6) (3)
M. Richter and H. Sovowi 1 F&id Phase Equilibria
294 TABLE
85 (1993) 285-300
3
Correlations
of solubilities
with solvent
density
6
d
k
s WI
(K) Chrastil equation u-Pinene cis-Verbenol Naphthalene
- 5406.0 - 2423.0 - 5405.0
6.309 - 16.374 -4.759
a
b
2.173 4.280 3.859 et
W Adachi-Lu a-Pinene cis-Verbenol Naphthalene
23.5 30.6 12.2 e, x 10’
e,x106
Ug-‘)
(I2 0
s (%I
16.0 25.2 8.2
equation
E factor cis-Verbenol
-4020.0 -2663.0 - 5567.0
13.410 - 12.759 13.650
- 0.659 3.741 0.009
3.975 -0.235 2.799
- 3.487 0.956 - 1.705
u
P
0
s
(deg-‘)
(W
50.0
2.3886
0.7818
-0.0191
25.6
The results of fitting the solubility data with eqn. (3) are also reported in Table 3, where the agreement has improved, especially for the a-pineneCO2 system (see Fig. 6). It is convenient to combine the non-idealities in the gas phase in the enhancement factor E, such that it describes the actual solubility divided by the ideal solubility P”/P: E = yP/P”
(4)
In the solid-supercritical solvent system, the logarithm of the enhancement factor is often proportional to the density of the pure solvent. Schmitt and Reid (1985) suggested the following correlation for the E factor: log E = a(d/d,)
+ p + c(t - tref)
(5)
where d/d, is the reduced solvent density and t,r is a suitable reference temperature. The results of correlating the CO, solubilities for cis-verbenol using eqns. (4) and (5) are listed in Table 3. The vapour pressure values, P”, used in the calculations are given in Table 4. Only the data measured above the cross-over pressure, 7.5 MPa, where the solubility isotherms converge, were taken into account. The solubilities measured at lower pressures would
295
50
loo
d)gC’
300
Fig. 6. Corelation of ct-pinene solubility in COz. Experimental: Model: -, Chrastil equation; - - -, Adachi-Lu equation.
A. 40°C; 0, 50°C; a, 55°C.
TABLE 4 Properties of the solutes and CO, a-Pinene (CIOHH) iI& (g mol-‘) T, (K) P, WPa) V, ( cm3 mol-‘) w Tb
W
136.24 630.6 2.89 484.5 0.312 429.4
cis-Verbenol (CtoH,,O)
Naphthalene (C&a)
COZ
152.24 680.0 3.08 502.5 0.729 497.15
128.17 748.4 4.05 410.0 0.302 491.1
44.01 304.2 7.38 94.0 0.239 194.7
29.38 _ 70.58 _ 159.68
-
P” (Pa)
308.15 313.15 318.15 323.15 328.15
K K K K K
_ 1440.0 _ 2386.0 3001.1
41.8 92.2 133.7
-
be overestimated by this correlation. The standard deviation of this correlation from the experimental data is comparable with the deviation of the Adachi-Lu equation, The experimental solubilities of naphthaiene do not obey eqn. (5) as the values of the proportionality coefhcient a calculated from the individual isotherms differ.
M. Richterand H. Sovotxi 1 FluidPhaseEqu~~~br~ 8.5(1993) 285-300
296
Pfiase equilibrium
At the phase equilibrium, the condition of equal fugacities in both phases ff
=ff"
is fulfilled for each component
i. The fugacity of the pure solid is given by
f:=P;CDF(IT;P;) exp p (v/AT)
dP
[S p,s The fugacity in the gas phase is
1
(7)
fi = y,@P
(8)
The fugacity coefficients Qp,were derived from the Peng-Robinson of state p-
--- RT V-b
qv+tb)
a(T) +b(V-b)
equation
(9)
using the critical properties PC, Tc and the acentric factor w listed in Table 4. The data in Table 4 were obtained as follows. The critical properties T,, PC and V, for the terpenes were estimated using the Joback group-contribution method (Reid et al., 1987); for naphthalene and COZ they were found from the literature (Reid et al., 1987), as were the boiling points of a-pinene (Weast and Astle, 1982), cis-verbenol (Beilstein, 1949) and naphthalene (Reid et al., 1987, p. 721), and the acentric factors for naphthalene (Reid et al., 1987, p. 721) and CO, (Reid et al., 1987, p. 667). The acentric factors for a-pinene and cis-verbenol were calculated according to the definition (Reid et al., 1987) w = -lOg(PS)T,=0.7 - 1
(10)
The vapour pressure of naphthalene was interpolated from the published data (T~me~ans, 1950, pp. 177, 178; Timmermans, 1965, p. 130), as was that of cc-pinene (Timmermans, 1965, p. 177). The vapour pressure of cis-verbenol was determined by the modified Watson method (Lyman et al,, 1982). For the mixtures, the mixing rules and the corresponding combination rules a = i
i=l
UiJ =
jJyjyia, j=l
( 1 - ~~,)(U~iU~)l”
b = i
i
(11)
yiyjb,
i=lJ=l
b, = ( l -
PtJNIbii +
bjj)/2
(12)
were chosen. The interaction parameter ki2 and the size parameter /3r2were determined by a regression method minimizing the relative standard deviation of solubilities. Their values are listed in Table 5. The phase equilibrium
297
TABLE 5 Modelling of solid-gas
phase equilibria by the Peng-Robinson
35°C Naphthalene ;::
0 0.088
S (%)
9.9
45°C
00.081
55°C
00.049
equation of state 55%
-0.193 -0.032 15.8
11.7
28.5
40°C
50°C
55°C
40°C
5Q”C
0.143 0 33.4
0.136 0 24.7
0.139 0 26.1
0.084 -0.116 25.0
0.084 -0.102 18.3
Fig. 7. CQ2 solubifity of cis-verbenol according to the Peng-Robinson equation of state. with k,, = 0.084 and /II2 = -0.116 Experimental: n , 40°C; 0, 50°C; A, 55°C. Model: -, at 4O”C, with k,, = 0.084 and plz = -0.102 at 5O”C, with k,, = 0.139 and plz = 0 at 55°C.
of naphthalene-CO, was modelled with sufficient accuracy using only the interaction parameter k 122except for the 55°C isotherm. For ck-verbenol, the data measured at 40°C and SOT were better fitted with both parameters klz and fif2, but no improvement was achieved by introducing the parameter PI2 for the 55°C isotherm. The agreement between the experimental and calculated CO, solubilities for cis-verbenol is illustrated in Fig. 7.
M. Richter and H. Sovovri / Fluid Phase Equilibria 85 (1993) 285-300
298 CONCLUSION
Solubility data for cc-pinene, cis-verbenol and naphthalene in CO2 were measured and correlated with solvent density. The three-parameter Chrastil equation assumes a linear log-log dependence of solubility on the density of CO?. The data for terpenes which deviate substantially from this rule were better correlated by the five-parameter modified equation suggested by Adachi and Lu. The CO2 solubilities for cis-verbenol measured above the cross-over pressure P = 7.5 MPa were well described by the correlation of the enhancement factor with CO, density. From the solubilities of cis-verbenol and naphthalene, the interaction parameters of the mixing rules for the Peng-Robinson equation of state were evaluated on the assumption that CO? does not dissolve in the solid. Using one interaction parameter, the relative standard deviation of the model from the experimental data is comparable with that of the Chrastil the Peng-Robinson equation with the equation. For cis-verbenol-CO*, two interaction parameters k 12 and & fits the experimental solubilities better than the Adachi-Lu equation. To predict the solubility of mixtures in supercritical C02, the mutual interactions of individual components must be taken into account. In the presence of a more soluble component, the concentration of the less soluble component in the vapour phase can increase considerably. This was the case with the system a-pinene-cis-verbenol-CO,. Contrary to expectations based on the binary equilibria, the extraction of cis-verbenol was faster, but the extractive fractionation of the mixture, based on the difference between the solubilities, was less efficient. The solubility data were used to determine the most suitable operating condition for the extraction of terpenes with supercritical COz. Over the temperature range 40-55°C the pressure in the extractor should be adjusted to 8-10 MPa for a-pinene and to 9-13 MPa for cis-verbenol, with the higher pressures corresponding to the higher temperatures. The temperature close to 30°C should be adjusted in the separator at 6 MPa for both terpenes. LIST OF SYMBOLS
a _ ;:
6 i e19 e2, e3
E
equation-of-state attractive parameter parameter in density correlations equation-of-state parameter parameter in density correlations gas-phase concentration solvent density parameters in the Adachi-Lu correlation enhancement factor
299
fugacity
association number binary interaction parameter molecular weight pressure vapour pressure reduced pressure ( = P/P?) gas constant refative standard d~v~a~~~ tern~ra~~ (“C) absolute tern~era~~~ ( Kj boiling point (K) reduced temperature ( = yJl/;Tc) molar volume gas-phase mole fraction
C
exl? eal
8 s
critical point experimental c;akzcnfated
gas phase solid phase, saturation
300
M. Richter and H. Sovovci / Fluid Phase Equilibria
85 (1993) 285-300
Chrastil, J., 1982. Solubility of solids and liquids in supercritical gases. J. Phys. Chem., 86: 3016-3021. Di Giacomo, G., Brandani, V., Del Re, G. and Mucciante, V., 1989. Solubility of essential oil components in compressed supercritical carbon dioxide. Fluid Phase Equilibria, 52: 405-411. Johnston, K.P. and Eckert, C.A., 1981. An analytical Carnahan-Starling-van der Waals model for solubility of hydrocarbon solids in supercritical fluids. AIChE J., 27: 773-779. Kalra, H., Chung, S.Y.-K. and Chen, C.-J., 1987. Phase equilibrium data for supercritical extraction of lemon flavors and palm oils with carbon dioxide. Fluid Phase Equilibria, 36: 263-278. Knaff, G. and Schltinder, E.U., 1987. Mass transfer for dissolving solids in supercritical carbon dioxide. Part I: Resistance of the boundary layer. Chem. Eng. Process., 21: 151-162. Lyman, V.J., Reehl, W.F. and Rosenblatt, D.H., 1982. Handbook of Chemical Property Estimation Methods. McGraw-Hill, New York. Maier, M. and Stephan, K., 1984. Eine neue Apparatur zur Messung der Lijslichkeit von organischen Stoffen in hochverdichteten Gasen. Chem. Ing. Tech., 56: 222-223. Mathias, P.M., Copeman, T.W. and Prausnitz, J.M., 1986. Phase equilibria for supercritical extraction of lemon flavors and palm oils with carbon dioxide. Fluid Phase Equilibria, 29: 545-554. Matos, H.A., de Azevedo, E.G., Simoes, P.C., Carrondo, M.T. and da Ponte, M.N., 1989. Phase equilibria of natural flavours and supercritical solvents. Fluid Phase Equilibria, 52: 357-364. McHugh, M. and Paulaitis, M.E., 1980. Solid solubilities of naphthalene and biphenyl in supercritical carbon dioxide. J. Chem. Eng. Data, 25: 326-329. Parkinson, G. and Johnson, E., 1989. Supercritical processes win CPI acceptance. Chem. Eng. Int. Ed., 96(7): 35-39. PavliCek, J. and Richter, M., 1993. High-pressure vapour-liquid equilibrium in the carbon dioxide-a-pinene system. Fluid Phase Equilibria, in press. Reid, R.C., Prausnitz, J.M. and Sherwood, T.K., 1987. The Properties of Gases and Liquids, 4th Edn. McGraw-Hill, New York. Schmitt, W.J. and Reid, R.C., 1985. In: J.M.L. Penninger, M. Radosz, M.A. McHugh and V.J. Krukonis (Eds.), Supercritical Fluid Technology. Elsevier, Amsterdam, p. 123. Stahl, E. and Gerard, D., 1985. Solubility behaviour and fractionation of essential oils in dense carbon dioxide. Perfumer & Flavorist, 10 (April/May): 29-37. Timmermans, J., 1950. Physico-chemical Constants of Pure Organic Compounds, Vol. I. Elsevier, Amsterdam. Timmermans, J., 1965. Physico-chemical Constants of Pure Organic Compounds, Vol. II. Elsevier, Amsterdam. Tsekhanskaya, J.V., Jomtiev, M.B. and Mushkina, E.V., 1964. Rastvorimostj naftalina v etilene i dvuokisi ugleroda pod davlenijem. Zh. Prikl. Khim., 38: 2166-2171. Weast, R.C. and Astle, M.J. (Eds.), 1982. CRC Handbook of Chemistry and Physics, 62nd edn., CRC Press, Boca Raton, FL.
285
The solubility of two monoterpenes carbon dioxide
in supercritical
Miroslav Richter ’ and Helena Sovova * Institute of Chemical Process Fundamentals, 16.5 02 Prague 6-Suchdol (Czech Republic) (Received
March
16, 1992; accepted
Czech Academy
of Sciences,
in final form September
21, 1992)
ABSTRACT Richter, M. and Sovova, H., 1993. The solubility of two monoterpenes carbon dioxide. Fluid Phase Equilibria, 85: 285-300.
in supercritical
The solubilities in supercritical CO, of two terpenes, cc-pinene as a representative of the monoterpene hydrocarbons and cis-verbenol as one of the oxygenated terpenes, have been measured at temperatures from 40 to 55°C and pressures from 5 to 12 MPa using a dynamic flow apparatus, which was tested by measuring the solubilities of naphthalene in compressed carbon dioxide. The experimental solubility data were correlated using a compressed gas model with the Peng-Robinson equation of state and empirical equations based on the dependence of the concentration of solute on the density of pure solvent. The unknown critical properties of both monoterpenes were estimated using the Joback contribution method. The vapour pressure of cis-verbenol was determined by the modified Watson method. The optimum conditions for the supercritical fluid extraction of both monoterpenes were determined.
INTRODUCTION
In addition to steam distillation and liquid extraction, supercritical fluid extraction is used to obtain various valuable components of plants for the food and pharmaceutical industries (Parkinson and Johnson, 1989). Conventional distillation methods involve higher temperatures which result in decomposition of heat-labile substances. Conventional extraction methods involve chemical solvents which, even in residual quantities, are of concern from the standpoint of toxicity to consumers of the end products. Supercritical extraction, however, is performed at relatively low temperatures and involves the use of fluids which can be separated from the end products by simple physical means. It is a semicontinuous process with the dense gas
*
Corresponding
author. Research Czech Republic.
’ Present address: Labem,
0378-3812/93/$06.00
0
Institute
of Inorganic
1993 - Elsevier
Chemistry,
Science Publishers
RevoluEni
86, 400 60 Usti nad
B.V. All rights reserved
286
M. Richter and H. SovovLi 1 Fluid Phase Equilibria
85 (1993) 285-300
recycling between the extractor, where it flows through a fixed bed of solid vegetable material, and the separator, where it is separated from the extract after expansion. A solubility difference of several orders of magnitude can be achieved by an appropriate adjustment of pressure and temperature in the extractor and in the separator. Carbon dioxide is a preferred supercritical solvent, since it is non-toxic, non-flammable, environmentally acceptable and relatively inexpensive, and its critical point allows extraction at relatively low temperatures. The solubility dependence of the extracted components on pressure and temperature forms the basis for the design of the conditions in the extractor and separator. Terpenes, components of essential oils, show the highest CO, solubilities among the vegetable substances. The solubility dependences have been published for some of them: limonene (Stahl and Gerard, 1985; Di Giacomo et al., 1989; Brandani et al., 1990; Matos et al., 1989), citral (Di Giacomo et al., 1989; Brandani et al., 1990), carvone, anethole, eugenol, caryophyllene and valeranone (Stahl and Gerard, 1985), menthol (Maier and Stephan, 1984) and 1,8-cineole (Matos et al., 1989). Results for phase equilibria in a ternary system limonene-citral-CO, have also been reported (Mathias et al., 1986; Kalra et al., 1987; Di Giacomo et al., 1989; Brandani et al.. 1990). This paper presents carbon dioxide solubility data for two monoterpenes: cc-pinene, one of the most frequently occurring terpenes, and cis-verbenol, an oxygenated terpene. Solubilities of naphthalene in dense carbon dioxide measured during the testing of the apparatus for solubility measurements are also reported.
EXPERIMENTAL
An apparatus similar to that of Johnston and Eckert ( 1981) was used for the measurement of the solubilities (see Fig. 1). Carbon dioxide from the pressure cylinder (1) was charged through a tube with a molecular sieve into the diaphragm compressor (2). The compressed CO? was stored in a surge tank to dampen any pressure fluctuations. It was bled into the system from a spring-loaded regulator (3) controlling the pressure to within + 0.03 MPa. The compressed gas reached the temperature of the bath (4) in an immersed capillary (5) and then equilibrated with the solute in the saturator (6). The pressure at the saturator inlet was measured using a tensometer calibrated to +0.02 MPa and the temperature in the saturator was assumed to be equal to the bath temperature controlled to within +O.l “C. After saturation, the loaded solvent was expanded to atmospheric pressure through a metering valve (7). The solute separated from the gaseous CO2 and accumulated in a glass U-tube or coil immersed in a mixture of ethanol and dry ice, the collector (8). The amount of solute-free gas was measured in a ther-
287
M. Richter and H. Sovovri I Fluid Phase Equilibria 85 (1993) 285-300
I... &IL)_ L
3 Fig. 1. Schematic
diagram
2
of the dynamic
1
flow apparatus
for measuring
solubilities.
mostatted calibrated glass vessel, the eudiometer (9), where it displaced silicone oil saturated with COz. The saturator was a high pressure column with an internal volume of 12 cm3. At higher solubilities, 2 or 3 such columns were connected in series. Each of the columns contained 2-3 g of the solute. The solid solute was mixed with glass beads 1 mm in diameter. In the case of liquid a-pinene, glass wool was wetted with the solute and a layer of glass beads was placed above it to prevent entrainment of liquid drops. The complication of precipitation in the valve was overcome by its design. It was electrically heated to compensate for the heat consumption during gas expansion and had a long stem with a small angle, allowing precise control of low flow rates. The path of the expanded gas in it was direct and short. Three eudiometers of volumes 0.26, 0.53 and 1.1 1 were used. The lower the range of the measured solubilities, the larger was the eudiometer used. The apparatus was first flushed with low pressure CO?, then the pressure in the saturator was increased to the required value and, after thermal equilibrium within the constant-temperature bath was reached, the flow rate of CO, was adjusted by the metering valve to one standard litre per hour. This flow rate was found to be satisfactory in ensuring that solubiliry equilibrium was achieved in the gas at the exit of the saturator. A sufficient amount of extract was initially collected in a waste trap until equilibrium within the saturator had been attained; then a tared collector was substituted and the gas flowing through it started filling up the eudiometer. A run was completed by removing the collector after the volume of CO, was equal to the volume of the eudiometer used. The amount of collected solute was found from the weight gain in the collector, or, for solubilities lower than
M. Richter and H. Sovovci / Fluid Phase Equilibria
288
85 (1993) 285-300
y = 0.005, ph o t ometrically after dissolving the solute in a known amount of liquid solvent. The solubility was calculated from the amounts of the collected solute and of the gas. Three measurements were carried out for each set of conditions. The reproducibility of the solubility measurements was better than 5%, except for solubilities lower than y = 2 x 10p3. The carbon dioxide used in this work was more than 99.9% pure as supplied by Chemical Works Litvinov. The minimum purity of the a-pinene supplied by AG Fluka Chemie was 97%. cis-Verbenol, obtained by oxidation of a-pinene, was more than 99% pure. Naphthalene was recrystallized and its purity was checked by measurement of its melting point. The value of 80.3”C agrees well with the literature data (Reid et al., 1987). Propanol and cyclohexanol, the solvents used for photometry and supplied by Lachema, were of p.a. purity. RESULTS
The solubility values for naphthalene in CO2 measured at 35°C 45°C and 55°C agree to within better than 2% with the data of Tsekhanskaya et al. ( 1964). Also the agreement with the data of McHugh and Paulaitis ( 1980) is satisfactory (see Fig. 2).
A
Y.103
0 0
.
12
@
P
8
6
8
10
12
14
16
P /MPa Fig. 2. Solubility of naphthalene in CO, at 35°C; ( 1964); A, McHugh and Paulaitis ( 1980).
n , this work; 0, Tsekhanskaya
et al.
1
4.63 4.73 4.90 4.93 5.27 5.27 5.30 5.36 5.73 5.80 5.89 5.99 6.07 6.49 6.52 6.69 6.69 6.86 6.91 7.05 7.16 7.26 7.30 7.34 7.37 7.44 7.48 7.54 7.55 7.74
1.35 1.42 1.16 1.43 1.45 1.42 1.51 1.54 1.95 1.96 2.18 2.00 2.06 2.39 2.37 2.21 2.27 2.75 2.75 2.30 2.10 2.78 2.98 3.40 3.72 3.41 4.13 4.47 3.80 (19.05)
3.36 3.36 3.86 4.23 4.27 4.86 5.15 6.04 6.85 7.67 8.15 8.17 8.63 8.64 8.85 8.87 9.04 9.05 9.16 9.16 9.20 9.28 9.29
P (MPa)
y X 103
P ( MPa)
2.40 2.62 2.18 2.13 2.27 2.27 2.57 2.53 3.14 4.22 5.78 6.10 7.32 7.46 8.15 8.01 9.51 9.31 10.42 9.88 10.82 (48.19) (47.28)
y x 103
for cc-pinene in dense carbon
50°C
solubilities
40°C
Experimental
TABLE
dioxide
3.25 4.00 4.01 5.19 5.25 6.13 6.16 6.91 6.96 7.53 8.00 8.10 8.15 8.56 8.95 8.98 9.20 9.29 9.60 9.71 9.71 9.75 9.77 9.87
P (MPa)
55°C
2.62 2.92 2.82 2.97 3.08 3.27 3.35 3.48 3.63 4.70 5.19 5.47 5.86 6.53 7.18 7.20 8.26 9.17 15.04 12.35 15.70 17.23 (28.18) (87.00)
y x 103 22.7 25.0 27.4 27.4 27.5 30.0 30.4 35.0 40.0 50.0 55.0 62.0
t (“C)
6.14 MPa
10.41 2.82 1.88 1.84 1.63 1.34 1.39 1.49 1.86 2.63 3.30 4.24
y x 103 37.9 38.6 40.0 42.7 44.7 44.7 48.3 48.3 50.0 55.0 62.0 62.1
t (“C)
7.65 MPa
31.93 16.40 9.50 5.23 4.53 4.58 4.20 4.13 3.90 4.47 4.65 4.93
y x lo3
290
M. Richter and H. SovovLi / Fluid Phase Equilibria
85 (1993) 285-300
The experimental solubility data for liquid a-pinene in supercritical carbon dioxide at 40°C 50°C and 55°C together with two isobars in the subcritical region are presented in Table 1. These data were compared with the phase equilibrium data measured using the static method (PavliCek and Richter, 1993). The agreement of the results obtained by both methods is illustrated in Fig. 3. Larger differences are observed only close to the critical point of the mixture where the dynamic method yields higher values of solubility. These are caused by partial entrainment of the liquid phase from the saturator owing to the extremely small difference in the densities of both phases. These data, indicated in Table 1 in parentheses, were not taken into account in the evaluation of solubilities. The experimental solubility data for solid cis-verbenol in supercritical CO, at 40°C 50°C and 55°C are given in Table 2. Its solubility is one order of magnitude lower than that of cr-pinene and the data are more scattered. In Fig. 4, the solubilities in CO? of cr-pinene and cis-verbenol measured at 50°C are compared with the solubilities of other monoterpenes available in the literature. Of these, a-pinene is the most soluble, limonene and cineole are less soluble, and menthol, cis-verbenol and citral have the lowest solubilities in C02. The conditions suitable for supercritical fluid extraction and for the separation of the extract from carbon dioxide are determined from the solubility data. Over the temperature range 40-55°C the pressure in the extractor should be adjusted to 8- 10 MPa for a-pinene and to 9- 13 MPa for cis-verbenol, with the higher pressures corresponding to the higher
20 Y.103
. 0
15
-
10
: (j’
:
5
c
t,
Y
,r” *
.
l/
lo.*
0 3
5
Fig. 3. CO, solubilities the static method (0).
7
PlMPa
’
for cc-pinene at 50°C measured
by the dynamic
method
(0)
and by
M. Richter and H. Sovov6 1 Fluid Phase Equilibria 85 (1993) 285-300 TABLE
291
2
Experimental
solubilities
40°C
for cis-verbenol
in dense carbon
50°C
dioxide 55°C
P (MPa)
y x 103
P (MPa)
y x 103
P ( MPa)
y x 103
5.09 5.11 6.07 6.08 6.94 7.01 7.06 7.51 7.58 8.12 8.15 8.27 8.28 8.31 8.39 8.40 8.56 8.58 8.63 9.07 9.10 9.85 9.91 10.71 10.94
0.06 0.05 0.14 0.13 0.26 0.21 0.23 0.65 0.63 1.15 1.13 1.39 1.18 1.14 2.57 3.12 3.62 4.42 5.63 20.62 20.25 27.30 29.60 52.30 53.00
5.14 5.16 6.13 6.13 6.30 7.17 7.17 7.71 7.72 8.08 8.08 8.46 8.54 8.86 8.92 9.36 9.46 9.49 9.15 10.33 10.37 10.54 10.60 10.87 10.94 11.84 12.84 12.98
0.14 0.13 0.18 0.16 0.20 0.42 0.41 0.65 0.68 1.11 1.04 0.70 0.83 1.07 0.96 2.01 1.99 2.63 2.72 4.08 5.39 10.75 11.64 12.46 12.64 30.90 47.20 46.40
5.16 6.20 6.22 7.38 7.43 8.28 8.28 8.89 8.89 9.69 9.71 9.76 10.71 10.77 11.25 12.06 12.21 13.10 13.52 13.78
0.12 0.26 0.17 0.44 0.43 0.75 0.84 0.90 0.94 1.08 1.02 1.72 4.64 5.35 10.52 12.55 13.27 28.60 35.20 38.50
temperatures. The pressure in the separator is limited by the suction pressure of the CO, pump. According to the solubility isobars for a-pinene, the temperature close to 30°C is recommended at 6 MPa. These conditions are also suitable for the separation of cis-verbenol from C02. The CO2 solubility data for binary systems cannot, however, be used to evaluate the extractive fractionation of two terpenes directly, as is demonstrated by the following experiment. Several measurements of CO2 solubilities at 40°C were carried out for a liquid mixture of a-pinene and cis-verbenol at a molar ratio of 4: 1. The amount of solutes trapped in the collector was determined from its weight and their ratio by gas chromatography. The results are shown in Fig. 5. While the value of the solubility for
M. Richter and H. SovovLi 1 Fluid Phase Equilibria 8.5 (1993) 285-300
292
10
P /MPa
14
12
Fig. 4. CO, solubilities for monoterpenes at 50°C; n , cc-pinene; Cl, cis-verbenol (this work); 0, limonene (Di Giacomo et al., 1989); 0, limonene (Matos et al., 1989); LI, cineole (Mates et al., 1989); +, methanol (Maier and Stephan, 1984); +, citral (Di Giacomo et al., 1989).
loo : Y.103
10
-
/, /
.
/
/
l-
/ 0 * . -6
oo_
/ ,
/
-
7
PIMPa
8
Fig. 5. Vapour-phase composition of the ternary system cc-pinene-cis-verbenol-CO, with 4: 1 mole ratio of cr-pinene and cis-verbenol in the liquid phase: 0, a-pinene; 0, cis-verbenol. CO, solubilities in the binary systems a-pinene-CO, (-) and cis-verbenol-CO, (- - -). All data at 40°C.
M. Richter and H. Sovovci / Fluid Phase Equilibria 85 (1993) 285-300
293
a-pinene in the ternary and binary systems was identical, within experimental error, the solubility of cis-verbenol increased in the presence of a-pinene, which acted as entrainer. MODELLING OF SOLUBILITIES
Two approaches were applied in the mathematical treatment of the experimental data. In the first one the solubilities were correlated with carbon dioxide density according to several equations found in the literature. The density of CO;! was calculated using the Bender equation of state (Knaff and Schhinder, 1987). In the second approach, the compositions of the equilibrated phases were modelled using the Peng-Robinson equation of state. As the dynamic flow method of solubility measurement does not give the necessary information about the composition of the condensed phase, this approach was applied to the solid-gas systems only, using the assumption that the gas does not dissolve in the solid. For the a-pineneCO2 system, equilibrium data measured by the static method had to be added to the data presented in Table 1 and the results of this evaluation will be presented elsewhere (PavliEek and Richter, 1993). The relative standard deviation of the solubilities 0.5
s = (l/N)
[
5 (Ywal-Yr,exp)2/YLp
r=l
1
(1)
was the objective function used to fit the experimental data. Correlations of solubility with CO2 density Chrastil (1982) derived the equation c =d“exp(a/T+b)
(2)
on the basis of the assumption that one molecule of a solute associates on average with k molecules of a gas. The parameter ti = AH/R is related to the heat of vaporization and solvation, his a constant, c is the concentration of the solute in grams per litre (g 1-l) of the gas, and d is the density of the pure gas, also in g l- ‘. According to the Chrastil equation, the log-log relationship between solubility and density should be linear up to relatively high solute concentrations (100-200 g 1-l). The solubilities measured in this work fulfil this condition only partially: the solubilities for naphthalene deviate from it at the lowest COZ densities, and the log-log solubility versus density curves are concave both for a-pinene and for cis-verbenol. The results calculated using the Chrastil equation are summarized in Table 3. Adachi and Lu (1983) modified the Chrastil equation, introducing a density dependent association number: c = d’, +&fe# exp(ii/T + 6) (3)
M. Richter and H. Sovowi 1 F&id Phase Equilibria
294 TABLE
85 (1993) 285-300
3
Correlations
of solubilities
with solvent
density
6
d
k
s WI
(K) Chrastil equation u-Pinene cis-Verbenol Naphthalene
- 5406.0 - 2423.0 - 5405.0
6.309 - 16.374 -4.759
a
b
2.173 4.280 3.859 et
W Adachi-Lu a-Pinene cis-Verbenol Naphthalene
23.5 30.6 12.2 e, x 10’
e,x106
Ug-‘)
(I2 0
s (%I
16.0 25.2 8.2
equation
E factor cis-Verbenol
-4020.0 -2663.0 - 5567.0
13.410 - 12.759 13.650
- 0.659 3.741 0.009
3.975 -0.235 2.799
- 3.487 0.956 - 1.705
u
P
0
s
(deg-‘)
(W
50.0
2.3886
0.7818
-0.0191
25.6
The results of fitting the solubility data with eqn. (3) are also reported in Table 3, where the agreement has improved, especially for the a-pineneCO2 system (see Fig. 6). It is convenient to combine the non-idealities in the gas phase in the enhancement factor E, such that it describes the actual solubility divided by the ideal solubility P”/P: E = yP/P”
(4)
In the solid-supercritical solvent system, the logarithm of the enhancement factor is often proportional to the density of the pure solvent. Schmitt and Reid (1985) suggested the following correlation for the E factor: log E = a(d/d,)
+ p + c(t - tref)
(5)
where d/d, is the reduced solvent density and t,r is a suitable reference temperature. The results of correlating the CO, solubilities for cis-verbenol using eqns. (4) and (5) are listed in Table 3. The vapour pressure values, P”, used in the calculations are given in Table 4. Only the data measured above the cross-over pressure, 7.5 MPa, where the solubility isotherms converge, were taken into account. The solubilities measured at lower pressures would
295
50
loo
d)gC’
300
Fig. 6. Corelation of ct-pinene solubility in COz. Experimental: Model: -, Chrastil equation; - - -, Adachi-Lu equation.
A. 40°C; 0, 50°C; a, 55°C.
TABLE 4 Properties of the solutes and CO, a-Pinene (CIOHH) iI& (g mol-‘) T, (K) P, WPa) V, ( cm3 mol-‘) w Tb
W
136.24 630.6 2.89 484.5 0.312 429.4
cis-Verbenol (CtoH,,O)
Naphthalene (C&a)
COZ
152.24 680.0 3.08 502.5 0.729 497.15
128.17 748.4 4.05 410.0 0.302 491.1
44.01 304.2 7.38 94.0 0.239 194.7
29.38 _ 70.58 _ 159.68
-
P” (Pa)
308.15 313.15 318.15 323.15 328.15
K K K K K
_ 1440.0 _ 2386.0 3001.1
41.8 92.2 133.7
-
be overestimated by this correlation. The standard deviation of this correlation from the experimental data is comparable with the deviation of the Adachi-Lu equation, The experimental solubilities of naphthaiene do not obey eqn. (5) as the values of the proportionality coefhcient a calculated from the individual isotherms differ.
M. Richterand H. Sovotxi 1 FluidPhaseEqu~~~br~ 8.5(1993) 285-300
296
Pfiase equilibrium
At the phase equilibrium, the condition of equal fugacities in both phases ff
=ff"
is fulfilled for each component
i. The fugacity of the pure solid is given by
f:=P;CDF(IT;P;) exp p (v/AT)
dP
[S p,s The fugacity in the gas phase is
1
(7)
fi = y,@P
(8)
The fugacity coefficients Qp,were derived from the Peng-Robinson of state p-
--- RT V-b
qv+tb)
a(T) +b(V-b)
equation
(9)
using the critical properties PC, Tc and the acentric factor w listed in Table 4. The data in Table 4 were obtained as follows. The critical properties T,, PC and V, for the terpenes were estimated using the Joback group-contribution method (Reid et al., 1987); for naphthalene and COZ they were found from the literature (Reid et al., 1987), as were the boiling points of a-pinene (Weast and Astle, 1982), cis-verbenol (Beilstein, 1949) and naphthalene (Reid et al., 1987, p. 721), and the acentric factors for naphthalene (Reid et al., 1987, p. 721) and CO, (Reid et al., 1987, p. 667). The acentric factors for a-pinene and cis-verbenol were calculated according to the definition (Reid et al., 1987) w = -lOg(PS)T,=0.7 - 1
(10)
The vapour pressure of naphthalene was interpolated from the published data (T~me~ans, 1950, pp. 177, 178; Timmermans, 1965, p. 130), as was that of cc-pinene (Timmermans, 1965, p. 177). The vapour pressure of cis-verbenol was determined by the modified Watson method (Lyman et al,, 1982). For the mixtures, the mixing rules and the corresponding combination rules a = i
i=l
UiJ =
jJyjyia, j=l
( 1 - ~~,)(U~iU~)l”
b = i
i
(11)
yiyjb,
i=lJ=l
b, = ( l -
PtJNIbii +
bjj)/2
(12)
were chosen. The interaction parameter ki2 and the size parameter /3r2were determined by a regression method minimizing the relative standard deviation of solubilities. Their values are listed in Table 5. The phase equilibrium
297
TABLE 5 Modelling of solid-gas
phase equilibria by the Peng-Robinson
35°C Naphthalene ;::
0 0.088
S (%)
9.9
45°C
00.081
55°C
00.049
equation of state 55%
-0.193 -0.032 15.8
11.7
28.5
40°C
50°C
55°C
40°C
5Q”C
0.143 0 33.4
0.136 0 24.7
0.139 0 26.1
0.084 -0.116 25.0
0.084 -0.102 18.3
Fig. 7. CQ2 solubifity of cis-verbenol according to the Peng-Robinson equation of state. with k,, = 0.084 and /II2 = -0.116 Experimental: n , 40°C; 0, 50°C; A, 55°C. Model: -, at 4O”C, with k,, = 0.084 and plz = -0.102 at 5O”C, with k,, = 0.139 and plz = 0 at 55°C.
of naphthalene-CO, was modelled with sufficient accuracy using only the interaction parameter k 122except for the 55°C isotherm. For ck-verbenol, the data measured at 40°C and SOT were better fitted with both parameters klz and fif2, but no improvement was achieved by introducing the parameter PI2 for the 55°C isotherm. The agreement between the experimental and calculated CO, solubilities for cis-verbenol is illustrated in Fig. 7.
M. Richter and H. Sovovri / Fluid Phase Equilibria 85 (1993) 285-300
298 CONCLUSION
Solubility data for cc-pinene, cis-verbenol and naphthalene in CO2 were measured and correlated with solvent density. The three-parameter Chrastil equation assumes a linear log-log dependence of solubility on the density of CO?. The data for terpenes which deviate substantially from this rule were better correlated by the five-parameter modified equation suggested by Adachi and Lu. The CO2 solubilities for cis-verbenol measured above the cross-over pressure P = 7.5 MPa were well described by the correlation of the enhancement factor with CO, density. From the solubilities of cis-verbenol and naphthalene, the interaction parameters of the mixing rules for the Peng-Robinson equation of state were evaluated on the assumption that CO? does not dissolve in the solid. Using one interaction parameter, the relative standard deviation of the model from the experimental data is comparable with that of the Chrastil the Peng-Robinson equation with the equation. For cis-verbenol-CO*, two interaction parameters k 12 and & fits the experimental solubilities better than the Adachi-Lu equation. To predict the solubility of mixtures in supercritical C02, the mutual interactions of individual components must be taken into account. In the presence of a more soluble component, the concentration of the less soluble component in the vapour phase can increase considerably. This was the case with the system a-pinene-cis-verbenol-CO,. Contrary to expectations based on the binary equilibria, the extraction of cis-verbenol was faster, but the extractive fractionation of the mixture, based on the difference between the solubilities, was less efficient. The solubility data were used to determine the most suitable operating condition for the extraction of terpenes with supercritical COz. Over the temperature range 40-55°C the pressure in the extractor should be adjusted to 8-10 MPa for a-pinene and to 9-13 MPa for cis-verbenol, with the higher pressures corresponding to the higher temperatures. The temperature close to 30°C should be adjusted in the separator at 6 MPa for both terpenes. LIST OF SYMBOLS
a _ ;:
6 i e19 e2, e3
E
equation-of-state attractive parameter parameter in density correlations equation-of-state parameter parameter in density correlations gas-phase concentration solvent density parameters in the Adachi-Lu correlation enhancement factor
299
fugacity
association number binary interaction parameter molecular weight pressure vapour pressure reduced pressure ( = P/P?) gas constant refative standard d~v~a~~~ tern~ra~~ (“C) absolute tern~era~~~ ( Kj boiling point (K) reduced temperature ( = yJl/;Tc) molar volume gas-phase mole fraction
C
exl? eal
8 s
critical point experimental c;akzcnfated
gas phase solid phase, saturation
300
M. Richter and H. Sovovci / Fluid Phase Equilibria
85 (1993) 285-300
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