4990
Ind. Eng. Chem. Res. 2001, 40, 4990-4997
Partitioning of Ethyl Acetate, Maltol, Glucose, and Fructose to Liquid Phases of the Carbon Dioxide + Water + 1-Propanol System Till Adrian, Jo1 rg Freitag, and Gerd Maurer* Lehrstuhl fu¨ r Technische Thermodynamik, Universita¨ t Kaiserslautern, Postfach 3049, D-67653 Kaiserslautern, Germany
This investigation reports on a thermodynamic phenomenon that can be observed in aqueous solutions of hydrophilic organic solvents: A completely miscible binary liquid mixture of water and an organic solvent, e.g., 1-propanol, can reveal a liquid-phase split, when it is pressurized with a “near-critical” gas, i.e., a gas near its critical temperature. This phase split phenomenon is briefly explained and new experimental data are presented for the partitioning of some natural products (ethyl acetate, D-fructose, D-glucose, and maltol) on, at near-critical pressures, coexisting liquid phases of a three-phase vapor-liquid-liquid equilibrium in the ternary system carbon dioxide + water + 1-propanol. In addition to the experimental data, a semiempirical approach for the correlation of the partition coefficients is shortly outlined. As the partition coefficients significantly deviate from unity, this phase equilibrium phenomenon can be applied for a new mild high-pressure liquid-liquid extraction process for natural products. Introduction Liquid-liquid extraction is a widely used unit operation for the recovery of sensitive products from aqueous solutions. A successful extraction process for, e.g., natural products, requires an extraction environment comprising ambient temperature, nontoxic water-like solvents, specific pH, and ionic strength. A search for such new water-like, mild liquid-liquid extraction media led Wendland et al.1 to propose completely watermiscible solvents, such as ethanol and propanol, for a novel liquid-liquid extraction process between a waterrich liquid phase and a hydrophilic organic solvent-rich liquid phase. This proposal was based on a thermodynamic phenomenon first reported by Elgin and Weinstock2 for the dehydration of many types of organic solvents. Elgin and Weinstock2 discovered that a mixture of water, and, at ambient temperature and pressure completely water-soluble, organic solvent can be forced to split into two liquid phases by pressurization with a “near-critical” gas, i.e., a gas near its critical temperature. To take advantage of this phenomenon as a basis for a new mild liquid-liquid extraction process, the basic phase split phenomenon in ternary systems nearcritical gas + water + hydrophilic organic solvent had to be studied more intensively than Elgin and Weinstock2 did and the extraction of model compounds out of either liquid-phase had to be studied, too. In recent years, the liquid-phase split phenomenon in ternary systems of near-critical carbon dioxide (CO2) + water + hydrophilic organic solvent was studied intensively, cf. Adrian et al.3 The studies comprise measurements of ternary high-pressure phase equilibrium and modeling with an equation of state (EoS). In addition to the basic phase equilibrium phenomenon, research on the partitioning of natural product model compounds on coexisting water-like liquid phases was started. First, experimental results for the partitioning * To whom correspondence should be addressed. E-mail:
[email protected]; phone: +49-631-2052410; fax: +49631-2053835.
of carbohydrates in ternary system carbon dioxide + water + hydrophilic organic solvent were reported by Pfohl et al.4,5 Recently, Adrian et al.6-8 reported a set of experimental data for the partitioning of vanillin and caffeine on coexisting liquid phases in the ternary system carbon dioxide + water + acetone and for the partitioning of eight natural product model compounds in the ternary system carbon dioxide + water + 1-propanol. A process for extraction and separation of cardiac glycosides was discussed by Adrian et al.8 Correlations of partitioning measurements were reported by Pfohl et al.4 and Adrian et al.7 This paper extends the studies on partitioning of natural product model compounds on coexisting liquid phases in the ternary system carbon dioxide + water + 1-propanol. It reports experimental data on the partitioning of carbohydrates D-fructose and D-glucose, as well as model compounds ethyl acetate and maltol, on coexisting liquid phases in the ternary system carbon dioxide + water +1-propanol at 313 and 333 K. The experimental results presented here show that the phase equilibrium phenomenon discussed is applicable for isolation of natural products from aqueous solutions, in case of maltol and ethyl acetate, and for purification of aqueous solutions containing D-fructose and D-glucose. The experimental results are correlated using a combination of EoS approach and UNIQUAC excess Gibbs energy approach. The correlation gives the partition coefficient with an average relative deviation of around 10%. Experimental Procedures Materials. Carbon dioxide (purity > 0.9995 mol mol-1) was obtained from TV Kohlensa¨ure, Ludwigshafen, Germany. Deionized water was bidistilled before use. All other chemicals were purchased from Merck, Darmstadt, Germany. They were used as supplied: 1-propanol (purity > 0.995 kg kg-1), ethyl acetate (purity > 0.995 kg kg-1), D-fructose (purity > 0.99 kg kg-1), D-glucose (purity > 0.995 kg kg-1), and maltol/ 3-hydroxy-2-methyl-4H-pyran-4-one (purity > 0.99 kg kg-1).
10.1021/ie000980w CCC: $20.00 © 2001 American Chemical Society Published on Web 09/27/2001
Ind. Eng. Chem. Res., Vol. 40, No. 22, 2001 4991
Figure 2. Phase behavior of the ternary system carbon dioxide + water + 1-propanol at about 333 K.
Figure 1. Schematic drawing of the measurement apparatus.
Apparatus. Figure 1 shows a schematic drawing of the apparatus applied in this research that functions according to the static-analytical method for phase equilibrium determination. It is basically the same as described by Wendland et al.1 in an experimental investigation of the high-pressure multiphase equilibrium of the ternary system carbon dioxide + water + 2-propanol. The equipment consists of a cylindrical highpressure view cell with sapphire windows and two external sample loops for circulating the coexisting liquid phases. The composition of the phase-forming low-boiling components (i.e., carbon dioxide, water, and 1-propanol) in a liquid phase is determined by gas chromatography (GC). For the present investigation, that apparatus was modified to enable the analysis of high boiling natural product model compounds by high performance liquid chromatography (HPLC), using a pressure proof UV/Vis detector. For further details see Adrian.9 Experimental Uncertainties. The uncertainty of the experimental results is less than ( 0.05 K for temperature, and ( 5 and ( 10 kPa for pressures below and above 10 MPa, respectively. The error in density measurements is generally below ( 2 g dm-3. The relative error in the GC-analysis for the determination of the mole fractions of carbon dioxide, water, and 1-propanol is less than 2% except for very small concentrations. In that region, the minimum absolute error of about 0.0025 mol mol-1 limits the accuracy. The relative error in the HPLC-analysis for a natural product concentration (g dm-3) in a liquid phase is e 4.1% for ethyl acetate, e 7.6% for D-fructose, e 6.8% for D-glucose, and e 1.2% for maltol. Basic Phase Split Phenomenon. Figure 2 summarizes the liquid-phase split phenomenon in the ternary system carbon dioxide + water + 1-propanol at about 333 K and different pressures. A basic knowledge of it is crucial for the understanding of the experimental results and their correlation. The lower triangular diagram on the left side of Figure 2 shows the phase behavior at ambient pressure. There, a vapor-liquid equilibrium (VL) is observed extending from the carbon dioxide + water to the carbon dioxide + 1-propanol binary system.
Raising the pressure at constant temperature near the critical pressure of carbon dioxide results in a liquidphase split and, consequently, in the formation of a three-phase vapor-liquid-liquid equilibrium (VLL), existing between a water-rich liquid (L1), an organic solvent-rich liquid (L2), and a carbon dioxide-rich gas (V). The resulting ternary phase behavior is demonstrated in the upper triangular diagram on the left side of Figure 2. The extent of the high-pressure three-phase equilibrium is restricted to a region between a lower (LCEP) and an upper critical endpoint (UCEP). This is demonstrated on the right side of Figure 2, where for a constant temperature (333 K) several triangular diagrams are arranged to form a prism. In that prism, the pressure increases from bottom to top. It can be recognized that the three-phase region originates at a lower critical endpoint (LCEP) pressure of the critical line (L1 ) L2) at 333 K: pLCEP ) 9.75 MPa. In this case, both liquid phases of the three-phase equilibrium are critical and coexist with a vapor phase. At higher pressures, the three-phase equilibrium VL1L2 exists in a wide composition range. With increasing pressure, the compositions of L1 and V in three-phase equilibrium change little, but the composition of L2 is shifted toward the vapor phase. At the critical point (CP) of the vaporliquid equilibrium of the binary system carbon dioxide + 1-propanol, a second critical line (L2 ) V) appears. Finally, the three-phase equilibrium disappears, when the liquid L2 and the vapor V in three-phase equilibrium become identical at a certain pressure. That pressure coincides with the upper critical endpoint (UCEP) of the (L2 ) V) critical line at 333 K: pUCEP ) 16.74 MPa. At higher pressures, a single two-phase liquid-liquid equilibrium is observed between a water-rich and a carbon dioxide-rich phase at liquidlike densities. That is the region of supercritical extraction. The present work does not deal with supercritical extraction but with liquid-liquid equilibria existing at pressures near the critical pressure of the applied gas and between the lower and the upper critical endpoints: pLCEP < p < pUCEP. The experiments particularly deal with the partitioning of natural products on both liquid phases L1 and L2 of three-phase equilibrium VL1L2 as this can be the basis for a new near-critical liquid-liquid extraction process. For a more detailed review of the phase behavior of ternary systems, carbon dioxide + water + hydrophilic
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Table 1. Experimental Results for the Partitioning of Ethyl Acetate (Ea) to Coexisting Liquid Phases L1 and L2 in High Pressure VL1L2 Equilibrium of Carbon Dioxide (CO2) + Water (W) + 1-Propanol (1POH) 313.15 K L1 MPa
L2 g/dm3
mol/mol
p
xCO2
xW
x1POH
7.099 7.599 8.099 9.100 10.10 11.10 12.10 13.10 14.10
0.036 0.033 0.031 0.031 0.032 0.032 0.032 0.033 0.033
0.883 0.901 0.909 0.912 0.910 0.912 0.912 0.912 0.913
0.080 0.066 0.059 0.057 0.057 0.056 0.056 0.055 0.054
103‚x
Ea
0.104 0.065 0.047 0.038 0.035 0.033 0.031 0.030 0.029
g/dm3
mol/mol
cEa
F
xCO2
xW
x1POH
0.393 0.256 0.188 0.153 0.143 0.134 0.125 0.123 0.118
963 967 967 972 976 976 978 982 983
0.141 0.198 0.267 0.301 0.331 0.359 0.392 0.421 0.474
0.608 0.516 0.428 0.395 0.369 0.343 0.317 0.289 0.253
0.251 0.286 0.305 0.303 0.300 0.298 0.291 0.289 0.272
103‚x
Ea
0.602 0.678 0.739 0.687 0.688 0.684 0.688 0.728 0.742
cEa
F
1.47 1.50 1.51 1.38 1.36 1.32 1.31 1.36 1.36
897 886 880 880 878 873 874 872 870
333.15 K L1 MPa
L2 g/dm3
mol/mol
g/dm3
mol/mol
p
xCO2
xW
x1POH
103‚xEa
cEa
F
xCO2
xW
x1POH
103‚xEa
cEa
F
10.10 11.10 12.10 13.10 14.10 15.10 16.10
0.042 0.037 0.035 0.036 0.037 0.037 0.037
0.873 0.894 0.902 0.903 0.905 0.906 0.907
0.084 0.069 0.062 0.061 0.059 0.057 0.056
0.146 0.093 0.074 0.051 0.046 0.042 0.038
0.537 0.358 0.291 0.199 0.181 0.166 0.151
948 959 963 961 965 966 962
0.143 0.211 0.272 0.314 0.342 0.398 0.467
0.629 0.522 0.440 0.398 0.373 0.322 0.267
0.228 0.266 0.287 0.287 0.284 0.280 0.266
0.755 0.917 0.985 0.799 0.807 0.839 0.835
1.89 2.04 2.03 1.59 1.57 1.57 1.49
890 877 873 863 861 853 835
Table 2. Experimental Results for the Partitioning of Maltol (Ml) to Coexisting Liquid Phases L1 and L2 in High Pressure VL1L2 Equilibrium of Carbon Dioxide + Water + 1-Propanol 313.15 K L1 MPa
L2 g/dm3
mol/mol
g/dm3
mol/mol
p
xCO2
xW
x1POH
103‚xMl
cMl
F
xCO2
xW
x1POH
103‚xMl
cMl
F
7.099 7.600 8.097 8.598 9.099 10.10 11.10 12.10 13.06 14.10
0.037 0.035 0.033 0.033 0.031 0.032 0.032 0.033 0.034 0.032
0.880 0.895 0.905 0.906 0.912 0.912 0.911 0.910 0.908 0.914
0.083 0.071 0.063 0.062 0.057 0.056 0.057 0.057 0.057 0.053
0.070 0.031 0.032 0.027 0.032 0.025 0.023 0.044 0.021 0.045
0.379 0.174 0.180 0.154 0.187 0.143 0.133 0.251 0.120 0.264
961 965 968 968 970 968 970 971 972 983
0.127 0.181 0.246 0.276 0.300 0.323 0.352 0.384 0.404 0.477
0.639 0.549 0.459 0.431 0.402 0.375 0.356 0.329 0.319 0.258
0.234 0.271 0.295 0.293 0.298 0.302 0.293 0.287 0.276 0.265
0.178 0.109 0.128 0.111 0.138 0.105 0.095 0.179 0.083 0.175
0.647 0.359 0.386 0.328 0.396 0.295 0.264 0.493 0.228 0.464
900 890 880 880 874 873 873 874 874 872
333.15 K L1 MPa
L2 g/dm3
mol/mol
g/dm3
mol/mol
p
xCO2
xW
x1POH
103‚xMl
cMl
F
xCO2
xW
x1POH
103‚xMl
cMl
F
10.10 11.10 12.05 13.10 14.10 15.10 16.06
0.044 0.040 0.039 0.038 0.040 0.039 0.038
0.869 0.887 0.891 0.899 0.897 0.902 0.907
0.087 0.073 0.070 0.063 0.063 0.059 0.055
0.071 0.051 0.045 0.048 0.052 0.054 0.057
0.369 0.279 0.248 0.267 0.291 0.304 0.319
948 956 958 959 956 958 954
0.140 0.201 0.245 0.294 0.331 0.383 0.461
0.637 0.539 0.484 0.429 0.392 0.345 0.284
0.223 0.260 0.271 0.278 0.277 0.272 0.255
0.165 0.157 0.145 0.167 0.183 0.197 0.202
0.599 0.509 0.446 0.492 0.525 0.542 0.523
894 879 875 874 870 861 839
organic solvent, and a detailed description of the phase behavior of the here applied ternary system, see Adrian et al.3,10 Experimental Results Experiments comprise the determination of partition coefficients of natural product model compounds in coexisting liquid phases of the three-phase VL1L2 equilibrium in the ternary system carbon dioxide + water + 1-propanol at 313 and 333 K. The chosen natural
products belong to groups of different chemical nature: and D-glucose are carbohydrates, and ethyl acetate is an ester having a characteristic fruity odor, being used, e.g., as artificial essence. Maltol is a heterocyclic hydrocarbon, found, e.g., in pine needles and chicory. Experiments with ethyl acetate and maltol were restricted to concentrations of about one gram of solute per kilogram feed solution. Thus, the natural product concentrations in coexisting liquid phases are so small that experimental results for the partition coefficient
D-fructose
Ind. Eng. Chem. Res., Vol. 40, No. 22, 2001 4993 Table 3. Experimental Results for the Partitioning of D-Fructose (Fr) to Coexisting Liquid Phases L1 and L2 in High Pressure VL1L2 Equilibrium of Carbon Dioxide + Water + 1-Propanol 313.15 K L1 MPa
L2 g/dm3
mol/mol
p
xCO2
xW
x1POH
103‚x
7.059 8.098 9.598 11.10 13.10
0.033 0.032 0.032 0.032 0.032
0.886 0.899 0.902 0.902 0.904
0.073 0.061 0.059 0.057 0.056
8.59 8.33 8.06 8.18 7.81
Fr
g/dm3
mol/mol
cFr
F
xCO2
xW
x1POH
103‚x
66 66 64 66 63
997 999 1002 1008 1010
0.173 0.292 0.350 0.423 0.499
0.529 0.384 0.331 0.274 0.219
0.296 0.323 0.318 0.302 0.281
2.68 1.22 0.91 0.73 0.56
Fr
cFr
F
12 4.9 3.5 2.7 2.0
888 874 870 868 867
333.15 K L1 MPa
L2 g/dm3
mol/mol
g/dm3
mol/mol
p
xCO2
xW
x1POH
103‚xFr
cFr
F
xCO2
xW
x1POH
103‚xFr
cFr
F
9.558 10.10 11.10 12.10 14.10
0.043 0.039 0.037 0.037 0.037
0.858 0.874 0.884 0.890 0.892
0.093 0.080 0.073 0.066 0.064
6.32 6.42 5.86 7.00 7.19
46 48 45 54 56
967 974 979 985 988
0.139 0.183 0.222 0.299 0.370
0.615 0.533 0.485 0.395 0.322
0.243 0.282 0.293 0.305 0.307
2.86 2.09 1.22 1.04 0.68
14 9.5 5.3 4.2 2.6
897 884 876 866 860
Table 4. Experimental Results for the Partitioning of D-Glucose (Gl) to Coexisting Liquid Phases L1 and L2 in High Pressure VL1L2 Equilibrium of Carbon Dioxide + Water + 1-Propanol 313.25 K L1 MPa
L2 g/dm3
mol/mol
p
xCO2
xW
x1POH
103‚x
7.060 8.100 9.578 11.10 13.10
0.036 0.033 0.033 0.030 0.035
0.883 0.904 0.906 0.914 0.904
0.078 0.060 0.059 0.051 0.058
3.52 3.28 2.58 4.37 4.03
Gl
g/dm3
mol/mol
cGl
F
xCO2
xW
x1POH
103‚x
27 27 21 36 33
979 988 993 996 996
0.162 0.282 0.343 0.400 0.477
0.551 0.400 0.343 0.293 0.239
0.286 0.318 0.314 0.307 0.283
0.96 0.36 0.20 0.27 0.19
Gl
cGl
F
4.5 1.5 0.80 1.0 0.70
898 881 877 875 872
333.15 K L1 MPa
L2 g/dm3
mol/mol
p
xCO2
xW
x1POH
103‚x
9.439 10.10 11.04 12.04 14.10
0.055 0.041 0.038 0.037 0.041
0.828 0.873 0.887 0.894 0.889
0.115 0.082 0.071 0.065 0.066
2.14 4.50 4.29 4.03 3.87
Gl
g/dm3
mol/mol
cGl
F
xCO2
xW
x1POH
103‚x
15 34 33 32 30
948 970 975 977 975
0.123 0.204 0.251 0.303 0.389
0.649 0.490 0.441 0.387 0.312
0.227 0.305 0.308 0.309 0.298
1.02 1.25 0.66 0.41 0.23
are considered to agree with the infinite dilution partition coefficient within experimental uncertainty. However, during experiments with the investigated carbohydrates, the feed concentration was 30-fold higher than during ethyl acetate experimentssabout 50 g of solute per kg of aqueous feed solution. This was because for HPLC detection a pressure proof UV/Vis detector was used, and the UV/Vis absorbency of carbohydrates is very low, so the carbohydrate feed concentration had to be increased. The experimental results for partitioning of the single natural products ethyl acetate, maltol, D-fructose, and D-glucose on coexisting liquid phases in the system carbon dioxide + water + 1-propanol at elevated pressures and temperatures of 313 and 333 K are summarized in Tables 1-4. The results comprise the composition of the coexisting liquid phases given as mole fractions, the concentration (c) of a natural product model compound k in a liquid phase, and the overall mass densities (F) of each of the coexisting liquid phases. Figures 3 and 4 show a comparison between previously measured (cf. Adrian et al.10) compositions of
Gl
cGl
F
5.4 5.4 2.7 1.62 0.86
903 879 871 863 854
coexisting fluid phases in three-phase equilibrium VL1L2 in the ternary system carbon dioxide + water + 1-propanol and new experimental results. Figure 3 shows a plot of the system pressure over the mole fraction of carbon dioxide in coexisting fluid phases VL1L2 at 313 K. For quaternary systems, the mole fraction of carbon dioxide on a (natural product) free basis is plotted. Figure 4 shows a plot of system pressure over the densities of coexisting fluid phases VL1L2 at 313 K. From both figures, it can be concluded that only during carbohydrate partitioning measurements the underlying three-phase equilibrium was significantly influenced. The reason for this is that the carbohydrate measurements were not performed at (nearly) infinite dilution (cf. above). For a better understanding of the partitioning measurements, the results for the partition coefficients are also shown in Figures 5 to 8. There, the partition coefficient of a solute k (K(c) k ) is defined as the ratio of the concentration of solute k (ck, in g dm-3) in the organic solvent-rich phase L2 and in the aqueous phase L1:
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Figure 3. Three-phase equilibrium VL1L2 in ternary/quaternary system carbon dioxide + water + 1-propanol + (natural product) at 313 K: Mole fraction of carbon dioxide on a (natural product)free basis in coexisting fluid phases: O, phase-forming ternary system, i.e., without partitioned substances (Adrian et al.10) as well as with partitioned ethyl acetate or maltol; 4, with D-fructose; 0, with D-glucose. The size of the symbols represents the experimental uncertainties. (L2) (L1) K(c) k ) ck /ck
Figure 4. Three-phase equilibrium VL1L2 in ternary/quaternary system carbon dioxide + water + 1-propanol + (natural product) at 313 K: Densities of coexisting phases: O, phase-forming ternary system, i.e., without partitioned substances (Adrian et al.10) as well as with partitioned ethyl acetate or maltol; 4, with D-fructose; 0, with D-glucose. The size of the symbols represents the experimental uncertainties.
(1)
To facilitate a comparison for both temperatures (313 and 333 K) in a single diagram, K(c) k is plotted versus a reduced pressure Π. That reduced pressure is a normalized distance to the pressure at the lower critical endpoint LCEP:
Π)
p - pLCEP pUCEP - pLCEP
(2)
pLCEP and pUCEP were both taken from the phaseforming ternary system carbon dioxide + water + 1-propanol; at 313 K: pLCEP ) 6.78 MPa, pUCEP ) 15.00 MPa; at 333 K: pLCEP ) 9.75 MPa, pUCEP ) 16.74 MPa, cf. Adrian et al.10 At p ) pLCEP, where (L1 ) L2), the infinite dilution partition coefficient (Kk(c),∞) becomes unity:
) lim K(c) K(c),∞ k k ) 1 ck f 0
(3)
whereas at p ) pUCEP, K(c),∞ * 1, as (L1 * L2), but k (L2 ) V). The infinite dilution partition coefficient of ethyl acetate (cf. Figure 5) rises with increasing pressure and reaches a maximum of about 11 at 313 K and about 9 at 333 K. The infinite dilution partition coefficient of maltol (cf. Figure 6) first, increases with increasing pressure, runs through a maximum and slightly drops afterward. This maximum is about 2.2 at 313 K and about 1.6 at 333 K.
Figure 5. Infinite dilution partition coefficient K(c),∞ of ethyl acetate (Ea) in coexisting liquid phases of three-phase equilibrium VL1L2 in carbon dioxide + water + 1-propanol system at 313 and 333 K as a function of reduced pressure Π ) (p - pLCEP)/(pUCEP pLCEP). The size of the symbols represents the experimental uncertainties, unless otherwise indicated.
The partition coefficients of both investigated carbohydrates decrease with increasing pressure and reach a minimum value of around 0.03 for both investigated temperatures (cf. Figures 7 and 8). Adding substantial amounts of carbohydrates to the ternary system significantly influenced the appearance of the three-phase equilibrium (cf. above), this can be seen as well in Figure 7 as in Figure 8, where at 333 K coexisting liquid phases were observed at pressures below the LCEP of the ternary phase-forming system (i.e., at Π < 0). As all investigated natural product model compounds show partition coefficients differing remarkably from unity, partitioning of those solutes on coexisting liquid phases, created by pressurizing an aqueous 1-propanol solution with carbon dioxide, might allow for, e.g., extraction and purification of valuable natural products in downstream processing in biotechnology.
Ind. Eng. Chem. Res., Vol. 40, No. 22, 2001 4995
Figure 6. Infinite dilution partition coefficient K(c),∞ of maltol (Ml) in coexisting liquid phases of three-phase equilibrium VL1L2 in carbon dioxide + water + 1-propanol system at 313 and 333 K as a function of reduced pressure Π ) (p - pLCEP)/(pUCEP - pLCEP). The size of the symbols represents the experimental uncertainties.
Figure 9. Projection of experimental “L1L2-tie-lines” of the three phase equilibrium VL1L2 at 333 K of the carbon dioxide + water + 1-propanol ternary system into a triangular composition diagram. Table 5. UNIQUAC Size (ri) and Surface (qi) Parameters component i
ri
qi
carbon dioxidea waterb 1-propanolb ethyl acetateb D-fructoseb D-glucoseb maltolc
1.3000 0.9200 3.2499 3.4786 8.4608 8.4600 3.8754
0.982 1.400 3.128 3.116 8.404 8.400 3.048
a Taken from Holderbaum and Gmehling.13 b Calculated according to UNIFAC, cf. Hansen et al.14 c Calculated according to Bondi.15
Figure 7. Partition coefficient K(c) of D-fructose (Fr) in coexisting liquid phases of three-phase equilibrium VL1L2 in carbon dioxide + water + 1-propanol system at 313 and 333 K as a function of reduced pressure Π ) (p - pLCEP)/(pUCEP - pLCEP). The size of the symbols represents the experimental uncertainties.
Figure 8. Partition coefficient K(c) of D-glucose (Gl) in coexisting liquid phases of three-phase equilibrium VL1L2 in carbon dioxide + water + 1-propanol system at 313 and 333 K as a function of reduced pressure Π ) (p - pLCEP)/(pUCEP - pLCEP). The size of the symbols represents the experimental uncertainties.
Correlation of Partition Coefficients. Correlation of partition coefficient measurements was performed according to the procedure described recently by Adrian et al.7 The procedure combines an equation of state (EoS) for describing the high-pressure VLL equilibrium of the phase-forming ternary system carbon dioxide + water + 1-propanol, with an excess Gibbs energy (GE) approach as typically used to correlate liquid-liquid equilibrium data at low pressures. Basically, the approach originates from the following observation: The projection of different so-called “liquidliquid tie-lines” of VL1L2 high-pressure equilibrium at different pressures but the same temperature (cf. Figure 2, right side) into a single triangular composition diagram, looks very much like a “common”, isothermal,
low-pressure liquid-liquid equilibrium. Such a projection is shown in Figure 9 for the VL1L2 high-pressure equilibrium of carbon dioxide + water + 1-propanol at 333 K. The experimental results shown cover pressures from 10.1 MPa (“tie-line” (a)), i.e., near the lower critical endpoint LCEP, to 16.1 MPa (tie-line (b)), i.e., near the upper critical endpoint UCEP. Assessing Figure 9 and lacking other possibilities to model natural product partitioning (cf. Adrian et al.7), the idea was born to model the natural product partitioning with a combination of the GE approach and EoS. Thus, the derived correlation procedure consists of the following three steps: (i) Correlation of the ternary high-pressure multiphase VL1L2 equilibrium using the Peng-Robinson equation of state, to determine the pressure for the isothermal VL1L2 equilibrium. (ii) Correlation of liquid-liquid tie-lines of VL1L2 high-pressure equilibrium in the ternary system carbon dioxide + water + 1-propanol with an UNIQUAC GE approach. (iii) Correlation of natural product partition coefficient between coexisting liquid phases, defined on mole (L2) (L1) E fraction scale, K(x) k ) xk /xk , using UNIQUAC G approach, only taking into account the condition of isoactivity for natural product k in both liquid phases. Some details on the correlation step with the PengRobinson EoS are summarized in the appendix. For the correlation steps with the UNIQUAC GE approach,11,12 the UNIQUAC size (ri) and surface (qi) parameters are summarized in Table 5 and the binary UNIQUAC interaction parameters amn are given in Table 6. The correlation results for the infinite dilution partition coefficient K(x),∞ for ethyl acetate and maltol and k the results for the partition coefficient K(x) for Dk fructose and D-glucose are summarized in Table 7. The relative differences between the calculations and the experiments amount up to about 10%. From thermodynamics, the approach used to correlate the experimental results is not completely consistent but
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Ind. Eng. Chem. Res., Vol. 40, No. 22, 2001
Table 6. Calculated Binary UNIQUAC Interaction Parameters (amn) component (n) carbon dioxide
water
1-propanol
component (m)
amn/K
anm/K
amn/K
anm/K
amn/K
anm/K
water 1-propanol ethyl acetate D-fructose D-glucose maltol
555.4 330.7 265.0 5548 -221.0 -83.52
397.6 -125.6 -1535 -291.9 -111.5 -830.1
48.92 -293.2 -233.2 -55.21 -9.717
140.6 -1456 190.2 -3424 -1211
258.5 3545 -31.82 -142.0
-2221 -215.8 -2952 -878.7
Table 7. Mean Relative Deviation between Calculated and Experimental Results for the Partition Coefficient of Some Natural Products
Table 8. Pure Component Parameters for Calculations with the Peng-Robinson Equation of Statea
natural product k
(x) 100 ∆K(x) k /Kk
component
Tc K
pc MPa
m
n
ethyl acetate maltol D-fructose D-glucose
1.7 5.4 3.4 10.2
carbon dioxide 1-propanol water
304.1 536.8 647.3
7.38 5.17 22.05
0.6877 1.1505 0.8893
0.3813 0.8075 0.0151
a
provides a reasonable estimate for inter- as well as extrapolation of the experimental data. For further information on correlation procedure, see Adrian9 as well as Adrian et al.7 Conclusion A completely miscible mixture of water and a hydrophilic solvent, such as 1-propanol, can be forced to split into two hydrophilic liquid phases by pressurization with carbon dioxide near its critical temperature. Experimental results for the partitioning of some natural product model compounds (ethyl acetate, maltol, D-fructose, and D-glucose) on the coexisting hydrophilic liquid phases show that this phase equilibrium phenomenon might be applicable for, e.g., isolation of natural products from aqueous solutions in a high-pressure liquidliquid extraction process. Experimental data for partition coefficients can be correlated with an accuracy of about 10% using a combined model of EoS and GE approach. The phase equilibrium phenomenon allows for a design of a novel high-pressure separation process, either applied in a mixer-settler battery or in a countercurrent column. Acknowledgment
Taken from Melhem et al.18
Table 9. Binary Interaction Parameters for Correlation of VL1L2 Equilibrium with the Peng-Robinson Equation of State Plus Panagiotopoulos and Reid Mixing Rulea component (i)
component (j)
kij
kji
carbon dioxide carbon dioxide water
water 1-propanol 1-propanol
0.0434 0.0395 -0.1599
-0.0479 0.0509 -0.1588
a
Taken from Adrian et al.3
In the ternary mixture, bmix is calculated according to N
bmix )
xi b i ∑ i)1
bi ) 0.07780
(5)
RTc pc
(6)
The attractive interaction parameter amix for the ternary mixture is described by a mixing rule proposed by Panagiotopoulos and Reid:17 N N
amix )
∑ ∑(1 - Kij)xixjxaiaj i)1 j)1
(7)
with
Financial support of this work by Deutsche Forschungsgemeinschaft, Bad Godesberg, Germany, is gratefully acknowledged. Furthermore, the authors express their thanks to TV Kohlensa¨ure, Ludwigshafen, Germany, for generously supplying carbon dioxide free of charge.
Kij ) kij - (kij - kji)xi
(8)
Kii ) 0
(9)
and
a of a pure component is described as usual: Appendix Correlation Procedure DetailssModeling of a Ternary High-Pressure Phase Equilibrium with the Peng-Robinson EoS. Calculations were performed with the Peng-Robinson equation of state (Peng and Robinson16)
p)
a(T) RT v - b v(v + b) + b(v - b)
(4)
ai(T) ) Ri(T)ai(Tc)
(10)
R2Tc2 a(Tc) ) 0.45724 pc
(11)
with
and
( ) ( x)
ln R(T) ) m 1 where the attractive interaction is taken into account by parameter a, and b is the covolume.
T +n 1Tc
according to Melhem et al.18
T Tc
2
(12)
Ind. Eng. Chem. Res., Vol. 40, No. 22, 2001 4997
Pure component parameters are summarized in Table 8 and the results of a correlation for the binary interaction parameters kij are given in Table 9. It should be mentioned that the parameters had to be fitted to ternary data (cf. Adrian et al.3), and therefore, they may not be a good choice for describing the vapor-liquid equilibrium of the binary systems. Nomenclature a ) UNIQUAC parameter, Peng-Robinson EoS parameter b ) Peng-Robinson EoS parameter c ) concentration (g dm-3) CP ) critical point EoS ) equation of state GC ) gas chromatography GE ) excess Gibbs energy HPLC ) high-performance liquid chromatography i ) component j ) component K ) partition coefficient kij, Kij ) binary interaction parameters of components i and j L ) liquid phase LCEP ) lower critical endpoint m ) parameter for the calculation of R(T) n ) parameter for the calculation of R(T) N ) number of components p ) pressure pH ) power of hydrogen q ) UNIQUAC surface parameter r ) UNIQUAC size parameter R ) universal gas constant T ) temperature UCEP ) upper critical endpoint UNIQUAC ) unified quasi chemical method UV/Vis ) ultraviolet to visible v ) molar volume V ) vapor phase x ) mole fraction Greek R ) temperature dependent parameter for the calculation of a(T) ∆ ) difference Π ) reduced pressure F ) density Subscripts 1 ) liquid phase 1 (water-rich) 2 ) liquid phase 2 (solvent-rich) c ) critical CO2 ) carbon dioxide Ea ) ethyl acetate Fr ) D-fructose Gl ) D-glucose i ) component j ) component k ) natural product LCEP ) lower critical endpoint of (L1 ) L2) critical line m ) component mix ) mixture Ml ) maltol n ) component 1POH ) 1-propanol UCEP ) upper critical endpoint (L2 ) V) critical line W ) water
Superscripts ∞ ) infinite dilution (c) ) concentration scale (Li) ) liquid-phase i (x) ) mole fraction scale
Literature Cited (1) Wendland, M.; Hasse, H.; Maurer, G. Multiphase highpressure equilibria of carbon dioxide-water-2-propanol. J. Supercrit. Fluids 1993, 6, 211. (2) Elgin, J. C.; Weinstock, J. J. Phase equilibrium at elevated pressures in ternary systems of ethylene and water with organic liquids. Salting out with a supercritical gas. J. Chem. Eng. Data 1959, 4, 3. (3) Adrian, T.; Wendland, M.; Hasse, H.; Maurer, G. Highpressure multiphase behaviour of ternary systems carbon dioxidewater-polar solvent: review and modelling with the PengRobinson equation of state. J. Supercrit. Fluids 1998, 12, 185. (4) Pfohl, O.; Timm, J.; Dohrn, R.; Brunner, G. Measurement and correlation of vapour-liquid-liquid equilibria in the glucose + acetone + water + carbon dioxide system. Fluid Phase Equilib. 1996, 124, 221. (5) Pfohl, O.; Petersen, J.; Dohrn, R.; Brunner, G. Partitioning of carbohydrates in the vapour-liquid-liquid region of the 2-propanol+water+carbon dioxide system. J. Supercrit. Fluids 1997, 10, 95. (6) Adrian, T.; Freitag, J.; Maurer, G. High-pressure multiphase equilibria in aqueous systems of carbon dioxide, a hydrophilic organic solvent and biomolecules. Fluid Phase Equilib. 1999, 158160, 685 (7) Adrian, T.; Freitag, J.; Maurer, G. Partitioning of some biomolecules at high pressures to aqueous/organic liquid-liquid phases of the carbon dioxide + water + 1-propanol system. J. Supercrit. Fluids 2000, 17, 197. (8) Adrian, T.; Freitag, J.; Maurer, G. A novel high-pressure liquid-liquid extraction process for downstream processing in biotechnology: extraction of cardiac glycosides. Biotechnol. Bioeng. 2000, 69, 559. (9) Adrian, T. Hochdruck-Mehrphasengleichgewichte in Gemischen aus Kohlendioxid, Wasser, einem wasserlo¨ slichen organischen Lo¨ sungsmittel und einem Naturstoff; Ph.D. Dissertation, University of Kaiserslautern, Kaiserslautern, Germany, 1997. (10) Adrian, T.; Oprescu, S.; Maurer, G. Experimental investigation of the multiphase high-pressure equilibria of carbon dioxide-water-(1-propanol). Fluid Phase Equilib. 1997, 132, 187. (11) Abrams, D. S.; Prausnitz, J. M. Statistical thermodynamics of liquid mixtures: a new expression for the excess Gibbs energy of partly or completely miscible systems. AICHE J. 1975, 21, 116. (12) Maurer, G.; Prausnitz, J. M. On the derivation and extension of the UNIQUAC equation. Fluid Phase Equilib. 1978, 2, 91. (13) Holderbaum, T.; Gmehling, J. PSRK: a group contribution equation of state based on UNIFAC. Fluid Phase Equilib. 1991, 70, 251. (14) Hansen, H. K.; Rasmussen, P.; Fredenslund, A.; Schiller, M.; Gmehling, J. Vapour-liquid equilibria by UNIFAC group contribution. 5th Revision and extension. Ind. Eng. Chem. Res. 1991, 30, 2352. (15) Bondi, A. Physical Properties of Molecular Crystals, Liquids and Gases; Wiley: New York, 1968. (16) Peng, D.-Y.; Robinson, D. B. A new two-constant equation of state. Ind. Eng. Chem. Fundam. 1976, 15, 59. (17) Panagiotopoulos, A. Z.; Reid, R. C. Multiphase highpressure equilibria in ternary systems. Fluid Phase Equilib. 1986, 29, 525. (18) Melhem, G. A.; Saini, R.; Goodwin, B. M. A modified PengRobinson equation of state. Fluid Phase Equilib. 1989, 47, 189.
Received for review November 17, 2000 Accepted August 1, 2001 IE000980W
