Ind. Eng. Chem. Res. 1996,34,613-618
613
Mass Transfer in Countercurrent Packed Columns: Application to Supercritical COz Extraction of Terpenes Pedro C. SimBes,* Henrique A. MatosJ Paulo J. Carmelo, Edmundo Gomes de AzevedoJ and Manuel Nunes da Ponte Faculdade de Cihcias e Tecnologia, Universidade Nova de Lisboa, 2825 Monte de Caparica, Portugal
Mass transfer in a countercurrent column, filled with structured gauze packing, was measured for the separation of a mixture of terpenes (d-limonenell,8-cineole) by supercritical carbon dioxide, at 313 and 318 K and pressures up to 9 MPa. The extraction efficiency was determined in terms of the overall mass transfer coefficient, KLU. Operating lines for this process had a n appreciable curvature due to a high miscibility of the two contacting phases. The real slope of these lines had to be estimated. Available mass transfer models for packed columns predicted efficiencies diverging to a great extent from the experimental results.
Introduction Supercritical fluid extraction (SFE) is an alternative separation method to more conventional processes such as liquid extraction and distillation. However, up to now, few works have been devoted to the investigation of the efficiency of countercurrent packed columns under supercritical conditions from a mass transfer point of view (Peter et al., 1978; Rathkamp et al., 1987; Seibert et al., 1988; Czech and Peter, 1990; de Haan and de Graauw, 1991; Lim et al., 1991; Brunner et al., 1991; Bernad et al., 1993). For this reason, we have initiated a study to characterize the performance of a continuous SFE bench-scale apparatus in the processing of relatively complex mixtures. In this paper we report mass transfer results for the separation of a mixture of two terpenes of similar volatilities (d-limonene/l,8-cineole) by supercritical carbon dioxide. The feasibility of applying SFE to the purification of eucalyptus oil was also analyzed as this oil can be modeled by the given terpene mixture. The mass transfer process of this system is characterized by operating lines with a severe curvature. Design equations used in former SFE studies assume the linearity of these lines, so several other procedures were tested in this work in order to evaluate the real shape of the operating lines.
Experimental Section The experiments were performed in the apparatus schematically shown in Figure 1. The extraction column EC, with a 2.4 cm i.d. and a length of 1m, is packed with CY-laboratory Sulzer gauze packing. The surface area, a,,of the packing is 890 m2/m3with a void fraction, E = 0.90. These values were taken from the literature (de Haan and de Graauw, 1991) as no information was made available by the manufacturer. The geometrical dimensions of the packing used by the former authors compared more closely with our laboratory packing than other data reported in the literature (Hufton et al., 1988). The column was operated in a countercurrent way, with the liquid feed entering at the top of the column, by means of a Lewa high-pressure metering pump MPL, and the less dense carbon dioxide a t the bottom. A metering valve MVL and a back-pressure regulator BPRLwere used to control the feed flow rate +
Permanent address: Centro de Quimica Estrutural, In-
stituto Superior TBcnico, 1096 Lisboa, Portugal.
and pressure. The solvent stream is pumped by a diaphragm compressor C to the desired extraction pressure and preheated before entering the EC by flowing through a heat exchanger HEI. The remaining raffinate, with a considerable amount of solubilized carbon dioxide, is drawn off from the bottom of the column. The extract phase, with the dissolved solutes, leaves the EC at the top and flows through a second heat exchanger HEII, where it is heated, and through the expansion valve V6, which reduces the pressure before entering a second column (the separation column, SC, similar to the previous one). The solutes are precipitated and collected at the bottom of the SC (valve V7). The regenerated carbon dioxide leaves the separation column at the top and is recirculated through C to the bottom of the EC. Fresh solvent is added t o this stream by a liquid piston pump PP to compensate for losses in the sampling operation. Both columns are maintained at the desired temperatures by a water heating jacket. The expansion valve, the feed entrance tube, and the raffinate exit valve are provided with heating tapes. Solvent flow rate is measured with the help of a Coriolis force type mass flow meter MFM and the liquid feed flow rate by weighing. Sampling devices are provided at the top and bottom of both columns. Sampling is performed by expanding a certain amount of volume of each stream to atmospheric pressure. The precipitated solutes are weighed and their composition analyzed by gas chromatography; the collected gas is measured with a calibrated wet gas meter. During a run, the composition of the exiting streams in the EC were measured until the stationary state was reached. The separation column, operating a t a pressure of 4 MPa, has shown a regeneration efficiency higher than 96% in removing the solubilized terpenes from the extract stream. Global and partial mass balances t o the extraction column were checked by the amount of terpenes collected in the bottom of the two columns and are accurate up to 97%. The carbon dioxide used was 99.995 mol % pure and supplied by Air Liquide. d-Limonene, 97 mol % pure, was supplied by Merck, and the 1,8-cineole, 97 mol % pure, was supplied by Socidestilda.
Results The feed was the same for all the experiments, containing 78.8 wt % cineole and 21.2 wt % limonene.
0888-588519512634-0613$09.0010 0 1995 American Chemical Society
614 Ind. Eng. Chem. Res., Vol. 34,No. 2, 1995
3
'
MPL
i
1
HE111
v
.
e
\#
-
'
.
A
1 1 :
V
Table 1. Mass Transfer Performance of the Packed Column at 313 K and Different Conditions of Pressure (Pd)and Solvent-to-FeedRatio (GIL)
3F
run
/
0.2
Pext (MPa) GIL ylimanene extract x 103 (wt %)
Y
XrafEnate co,
(wt%)
x IO6 (kg/s) Nfimonene x lO'(kg/s) extraction yield, q (%) Ncineole
K~ 0.05 !
240
260
280 300 density of C02 (Kg/m3)
I
220
Figure 2. Extract stream composition in limonene (mass %) as a function of the density of carbon dioxide (kg/m3): W, T = 313 K, G I L = 11; A, T = 313 K, G I L = 13; *, T = 318 K, G I L = 11.
Runs were performed at two temperatures, 313 and 318 K, and a t several pressures up t o the critical point. The feed flow rate was held constant for all the experiments, only the solvent flow rate being changed. Feasibility of the Process. The possibility of purifying eucalyptus oil by SFE (separating the main impurity, the d-limonene, from 1,8-cineole)was evaluated by measuring the selectivity and capacity of the solvent at different conditions of pressure, temperature, and solvent-to-feed ratio (GIL). Solvent loading, expressed as mass fraction of d-limonene in the outlet gas phase, is shown in Figure 2 as a function of the density of carbon dioxide. Higher amounts of terpenes are
103 (s-1)
1
2
3
4
5
7.70 13.2 0.09
7.71 11.5 0.10
7.89 13.2 0.11
7.91 11.5 0.12
8.00 11.5 0.13
48.3 2.31 6.72 5.6
2.09 6.38 5.2
49.7 2.72 7.93 6.4
2.43 7.53 6.3
55.4 2.64 7.98 6.6 1.84
Table 2. Mass Transfer Performance of the Packed Column at 318 K and Different Conditions of Pressure (Pea)and Solvent-to-FeedRatio (GIL). run 6 7 Pext (MPa) 8.59 8.82 GIL 11.5 11.0 extract 0.16 0.22 Ylimonene x 103 (wt %) 50.2 xratXnate co, (wt%) Ncineole x I O 6 (kds) 3.90 5.04 Nlimonene x 10' (kds) 1.04 1.44 extraction yield, Q, (%) 8.5 11.0 KMZx 103 (s-1) 13.71
dissolved in the extract phase as the density of solvent increases. The use of higher gas-phase flow rates lowers the solvent capacity due t o a shorter contact time between the two coexisting phases in the column. Measured loadings are shown in Tables 1 and 2, respectively, at 313 and 318 K. The selectivity of carbon
Ind. Eng. Chem. Res., Vol. 34, No. 2, 1995 615 Table 3. Vapor-Liquid Equilibrium for the Ternary System CO&Z-Limonene/l,8-Cineole. x and y Are the Mass Fraction Compositions of the Liquid and Gas Phases, Respectively COZ cineole P(MPa) T(K) X Y X Y 0.9926 0.1719 0.0056 8.0 313 0.7770 0.1018 0.0179 8.8 318 0.8687 0.9766
0.91 7.6
0
6.4 P / MPa
0.0
J
Figure 3. Selectivity of carbon dioxide toward d-limonene as a function of pressure and temperature of extraction and solventto-feed ratio (GIL):,. T = 313 K,GIL = 11;A, T = 313 K,GIL = 13;*, T = 318 K,GIL =11.
dioxide toward d-limonene was calculated by taking the quotient of the ratios between the compositions of d-limonene and 1,8-cineole in the extract stream (gas phase exiting the extraction column) and in the liquid feed stream: Slimicin
- (Y1im’Ycin)extract -
(1)
(xlim/xcin)feed
The experimental results, given in Figure 3, reveal a low selectivity of the solvent toward the d-limonene indicating that an economically advantageous separation process will not be feasible at these conditions. The calculated values for the extraction yield, p, are also given in Tables 1 and 2.
Mass Transfer Performance. Operating Line. The extraction efficiency of the packed column was characterized by the overall mass transfer coefficient, Km (a is the interfacial area per unit volume of packing over which mass transfer occurs, a parameter usually unknown). The equation used for the calculation of KN is expressed as follows:
where fi = NJCN, with Ni the mass flux of component i transferred between the two phases. 2 is the packing height and L the mass flow rate of the liquid phase; x i is the mass fraction of component i in the liquid phase at a certain point of the column and x i * is the respective equilibrium composition of i . Equation 2 takes into account the simultaneous diffusion of all components (through parameter f i ) and the variation of the flow rate of each phase along the extraction column (Treybal, 1981). The present system is characterized by the nonnegligible flux of carbon dioxide diffusing in the opposite direction to the diffusion of the two terpenes (shown by the high values reported for the mass fraction of carbon dioxide in the raffinate stream, Tables 1 and 2). This remarkably changes the flow rate of each phase along the column. The design equation (2)-i being the desired component, d-limonene-is integrated over the packed height, 2, by considering material balance information (i.e.,the liquid- and vapor-phase compositions along the packing height) and equilibrium data in terms of two curves, the
equilibrium and operating lines. The correction parameter, fi, is considered to be constant in order to simplify the integration and calculated by the mass balances of each component over the column. The equilibrium line is obtained from phase equilibrium results. Data for CO2 cineole limonene and the corresponding binaries were given by Azevedo et al. (1988) and Matos et al. (1989). However, the precision of their ternary data, especially the cineolellimonene ratio, was not sufficient for a good definition of the equilibrium line in our column, due to the small quantities taken in their sampling process. In this work, we used one of the apparatuses described by those authors, but with a bigger equilibrium cell, so that larger quantities could be sampled. Equilibrium data was measured for the ternary system for two different conditions (313 K and 8.0 MPa and 318 K and 8.8 MPa) at the same overall composition of the feed used in the mass transfer experiments. They are reported in Table 3. The operating line relates the composition of streams in contact with each other along the column a t steady state conditions. It is evaluated by solving the global and partial (limonene) mass balances over the column height. Characterized by an appreciable miscibility of the two coexistence phases it is expected that our operating line will have a pronounced curvature. No experimental data was available on the concentration profile of the two streams, and we also question the experimental feasibility to obtain this data, as severe flux deformation and entrainament may occur, distorting the concentration profiles along the column. As a consequence, our operating lines had to be estimated. Several different considerations were tried in this way. Input variables were the experimental compositions and flows of the two phases at column ends. We required as an additional condition that the mass flows of each component in a given phase should vary in a monotonous way with the packing height. First, we assumed the linearity of the operating curve (constant slope). Negative mass flows for the two phases were obtained when solving the global and partial mass balances, indicating that the former assumption was inaccurate for the terpene system. The assumption of the hypothetical existence of equilibrium stages along the packing height, in analogy with multistage countercurrent processes (King, 1980, chapter 6), was unsuitable in our case, as the number of theoretical stages of the column was less than 1(Figure 4). Some points ( x i y i ) were then arbitrarily chosen between the terminal ends of the line, and for each case, the mass balance in limonene was solved. The calculated results are indicated in Table 4 and, for run 5, shown in Figure 4 together with the respective equilibrium line, which was considered linear in the dilute concentration range where separation takes place. Two different assumptions were also considered relating the mass flows of each phase: a linear relation (i) between
+
+
616 Ind. Eng. Chem. Res., Vol. 34, No. 2, 1995
f Equilibrium line
0,211
0,212
0,215
0,214
0,213
0,216
lim. '('lime cin. 1 for the separation process at 313 K and 8.0 MPa and equilibrium line (-1. X
+
Figure 4. Operating line (-W-)
Table 4. Operating Line: Mass Fractions in a Solvent-Free Basis and Mass Flows (kg/s) of &Limonene at Several Points between the End Points of the Extraction Column 8.0MPa, 313 K 8.8MPa, 318 K Xi Ni L~ 107 G; x lo6 xi Yi L~ 107 Gi x lo6 Arbitrarily Chosen Points 0.0 0.210 0.0 1.161 0.0 0.212 0.0 1.137 0.212 2.72 3.07 0.211 1.188 1.167 0.172 0.213 4.59 0.2115 1.275 1.182 0.217 11.36 0.205 0.214 8.07 0.2119 1.299 0.220 13.80 1.217 0.2225 0.2149 1.218 8.18 0.2120 1.307 0.2205 14.61 0.2240 0.2150 L; versus x; Linear 1.137 0.0 0.21 0.0 1.161 0.0 0.212 0.0 1.234 0.21137 7.31 1.164 2.73 0.211 0.1679 0.213 0.21721 10.96 1.191 5.45 0.2115 1.271 0.2064 0.214 0.2227 0.21995 13.88 1.216 7.91 0.2119 1.300 0.2149 0.2205 14.61 8.18 0.212 1.307 0.224 1.218 0.2150 G versus Y Linear 0.21 0.0 1.161 0.0 0.0 1.137 0.0 0.212 0.2111 0.212 1.296 13.53 0.190 1.197 6.06 0.2130 0.2116 0.217 1.303 14.16 0.205 1.206 6.96 0.2138 0.2119 0.22 1.306 14.55 0.2225 1.217 8.08 0.2149 0.212 0.2205 1.307 14.61 1.218 8.18 0.215 0.2240
Li and xi and (ii)between G and yi. The obtained results are also presented in Table 4. The estimated curves are relatively similar, due to the very narrow range in compositions of the liquid stream (in a solvent-free basis), which is a result of the low selectivity of the process. The upper end of the operating line at 313 K (Figure 4), corresponding to the enriched section of the column, shows an almost constant slope, as the solvent stream becomes saturated with the terpenes; the range of possible values (xiryi) to draw the line in this section was extremely limited as only some of them gave reasonable results (that is, in agreement with the monotonous shape of the L and G flows). The slope (Gi/ Li)of the curve shows an abrupt increase in the lower end of the column as the gas stream entering the column starts to dissolve appreciable amounts of terpenes. Preliminary results obtained in our column for a different system (the deacidification of olive oil by supercritical carbon dioxide, where selectivity is relatively high) have shown appreciable differences in the shape of the estimated operating lines according to the method being used (Carmelo et al., 1993). Mass Transfer Coefficients. The overall coefficients, &a, were calculated only for runs 5 and 7, for
which phase equilibrium data was available, and are presented in Tables 1 and 2. These results are of the same order of magnitude as other data published in the literature for packed columns operating at supercritical conditions (Rathkamp et al., 1987; Bernad et al., 19931, for the extraction of alcohols from aqueous solutions by supercritical carbon dioxide. The appreciable magnitude of our coefficients is explained by the small differences of the extract compositions in limonene f y i ) to the correspondent equilibrium values (see Figure 41, as the extraction pressures in these runs are very close to the critical point of each isotherm. The higher density of the solvent in run 7 compared to run 5 should account for the higher overall coefficient obtained in the first case. Mass Transfer Models. Our results were compared with those of several different mass transfer models available in the literature for supercritical and gas absorption packed columns. As no data were taken on the hydrodynamic behavior of this system, we have chosen four models based on different assumptions regarding the hydrodynamics. A schematic view of the structured gauze packing, developed initially for distillation conditions by Bravo et al. (19851, was used in all
Ind. Eng. Chem. Res., Vol. 34, No. 2, 1995 617 models t o define an equivalent diameter, deg, of the packing. Two of the models assume the available surface packing to be completely wetted by the dispersed phase. Seibert et al. (19881, by applying a model for packed columns under high-pressure conditions, considered the gas phase to preferentially wet the packing surface instead of forming spherical drops. A mass transfer equation applicable to laminar flow parallel to flat surfaces was used:
(3) Bravo et al. (1985) (and in a subsequent work, de Haan and de Graauw, 1991) developed a model for structured packings under distillation conditions where the liquid phase is dispersed in thin films that wets the gauze packing surface. The gas side mass transfer coefficient is predicted from the correlation for wettedwall columns proposed by Sherwood and Gilliland (1934). The film coefficient for the liquid phase is based on the penetration theory of Higbie (Treybal, 1981) assuming the liquid flow pattern to be approximated by a laminar film flowing down a vertical plate. In the same way as the former model they considered the complete wetting of the packing surface. This consideration will strongly depend on the hydrodynamic and physical properties (surface tension) of a given system. For this reason, two other models based on the concept of partial wetted packing area were tested on our system. Onda et al. (1968) developed a model for gas absorption processes, regarding the liquid phase as dispersed in a thin film that covered only partially the packed surface; they used the wetted area as a geometric parameter to determine the Reynolds number for the liquid phase:
-
a, -
Akman and Sun01(1991) suggested the use of the last correlation, together with a set of equations developed separately by Ramm (19531, and applied these equations to a combined process of supercritical extraction and adsorption on activated carbon. The required physical properties of the two phases were estimated at the operating conditions of pressure, temperature, and composition where no experimental data was available in the literature. The viscosity of pure carbon dioxide was taken from Stephan and Lucas (1979). The viscosities of pure liquid d-limonene and 1,E-cineole a t atmospheric pressure (Medeiros et al., 1993) were extrapolated to the working pressures by a correlation (Reid et al., 1987); the vapor- and liquidphase viscosities were then estimated from the pure component values by the correlation method of Grunberg and Nissan (Reid et al., 1987). The diffusion coefficient of limonene in the liquid phase was estimated by the Wilke-Chang equation (19551, whereas for the vapor phase we used an empirical equation proposed by Catchpole et al. (1994). The density of the liquid phase was estimated by the Peng-Robinson equation of state; the vapor-phase density, as only a relatively small amount of terpenes were dissolved in the carbon dioxide, was considered to be equal to the respective solvent density (IUPAC tables, Angus et al., 1976). The estimated overall mass transfer coefficients are presented in Table 5. They deviate from the experi-
Table 6. Estimated Overall Mass Transfer Coefficient, x 109 (8-l) model run5 run 7 Seibert et al., 1988 19.62 17.1 5.45 4.56 Bravo et al., 1985 Onda et al., 1968 3.94 2.97 Akman, 1991-Ramm, 1953 0.64 0.44
Km
mental coefficients in some of the models by an order of magnitude. The predicted influence of pressure and temperature on KLUis also different from the experimentally observed. We attribute this t o a less accurate estimation of the physical properties of both phases. For instance, the partial wetted area is very dependent on the surface tension of the mixture, assumed here to be equal to the value for pure 1,8-cineole. If we consider a variation of this property with pressure (Hiller et al. (1990) report a decrease in the surface tension of mixtures of fatty acids with supercritical solvents as the critical pressure of the mixture is reached) the last two models (Onda et al. and Akman-Ramm) will predict an inverse behavior for KLU. Due to a limited pump capacity, the liquid flow rate was kept relatively low in these experiments (about 5.7 x kg/s); the hydrodynamics of our column should then be characterized by a liquid phase dispersed in thin films covering only partially the surface area of the gauze packing (visual confirmation of this behavior is at the present impossible on our column).
Conclusions The mass transfer efficiency in the separation of a mixture of two terpenes by a countercurrent packed column under supercritical conditions was investigated in this work by calculating the overall mass transfer coefficient, KLU. As this system is characterized by an appreciable mixing of the two phases, the resulting operating line has a pronounced curvature. Several procedures were taken to estimate the shape of these lines, as no experimental data was available on the concentration profile of each component along the packed height. The estimated curves appear to be sensibly similar. Experimental KLLZvalues were relatively high, due to the approach t o equilibrium of the extract composition in limonene. The applicability of mass transfer models, available in the literature, to the separation of natural oils by SFE was also examined, as these models were until now limited in their application to the separation of simple mixtures and not to more complex mixtures. The predicted mass transfer coefficients deviate considerably from the experimental ones, probably due t o a poor estimation of the physical properties of the gas and liquid phases, at conditions near the critical points of the mixture. The development of a model for such mixtures will demand an accurate estimate of the surface area of the packing effectively used for transport and the determination of experimental data on physical properties and hydrodynamics of the mixing phases in the packed column.
Acknowledgment Financial support from A.I.D., Washington, DC, and EuroArs TBcnica, Lisbon, is gratefully acknowledged.
Nomenclature a = interfacial area per unit volume of packing, m2/m3 a, = wetted area of the packing, m2/m3
618 Ind. Eng. Chem. Res., Vol. 34, No. 2, 1995
a, = specific surface area of the packing, m2/m3 cin = 1,8-cineole
de, = equivalent diameter of the packing, m D = diffusion coefficient, m2/s g = acceleration of gravity, 9.81 d s 2 G = mass flow rate of gas phase, kg/s i = component
KL = overall mass transfer coefficient based
on the liquid phase, m l s k G = film mass transfer coefficient in the gas phase, m/s k L = film mass transfer coefficient in the liquid phase, m/s 1 = length parameter, m L = mass flow rate of the liquid phase, kg/s L’ = liquid mass velocity, kg/s.m2 lim = d-limonene = equilibrium distribution coefficient Ni = m a s s flow rate of component i, kg/s P = pressure, Pa S = column cross-section area, m2 Sbdcin
= selectivity of carbon dioxide toward d-limonene
T = temperature, K u = velocity, m l s x = mass fraction of component i in the liquid phase x* = mass fraction of component i in the liquid phase that is in equilibrium with the component i in the gas phase y = mass fraction of component i in the gas phase Z = height of packing, m Greek Letters E
= porosity
7 = viscosity, Pds p = extraction yield Q = density, kg/m3 u = surface tension, N/m
Dimensionless Numbers Fq = Froude n u m b e r (a$ 2/ge) Re’l = Reynolds number (L’/asvl) We1 = Weber number (L’2/asue)
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Carmelo, P. J.; SimBes, P. C.; Nunes da Ponte, M. Modeling of Mass Transfer in Supercritical Countercurrent Extraction Columns: Application to Olive Oils. Chem. Biochem. Eng. Q. 1993, 8 (11, 5-9. Czech, B.; Peter, S. Efficiency of different packings in countercurrent near-critical fluid extraction. In Proceedings of the Zd International Symposium on High Pressure Chemical Engineering, Erlangen, Germany; DECHEMA Chemische Technik und Biotechnologie e.v.: Frankfurt am Main, Germany, 1990; pp 419-424. de Haan, A. B.; de Graauw, J. Mass Transfer in Supercritical Extraction Columns with Structured Packings for Hydrocarbon Processing. Znd. Eng. Chem. Res. 1991, 30, 2463-2470. Hiller, N.; Schiemann, H.; Weidner, E.; Peter, S. Surface Tension and wetting in systems with a near-critical component. In Proceedings of the Zd International Symposium on High Pressure Chemical Engineering, Erlangen, Germany; DECHEMA Chemische Technik und Biotechnologie e.v.: Frankfurt am Main, Germany, 1990; pp 251-254. HuRon, J. R.; Bravo, J. L.; Fair, J. R. Scale-up of Laboratory Data for Distillation Columns Containing Corrugated Metal-Type Structured Packing. Znd. Eng. Chem. Res. 1988,27,2096-2100. King, C. J. Separation Processes, 2nd ed.; McGraw-Hill: New York, 1980. Lim, S.; Lim, G. B.; Rizvi, S. S. H. Continuous Supercritical COz Processing of Milk Fat. In Proceedings ofthe Znd International Symposium on Supercritical Fluids, Boston; MCHugh,M. A., Ed.; Johns Hopkins University: Baltimore, 1991; pp 292-296. Matos, H. A.; de Azevedo, E. G.; SimBes, P. C.; Carrondo, M. T.; Nunes da Ponte, M. Phase Equilibria of Natural Flavours and Supercritical Solvents. Fluid Phase Equilib. 1989,52,357-364. Medeiros, A. G.; Sousa, A. T.; Nieto de Castro, C. A. Density and Viscosity of Terpene Mixtures. In Proceedings of the 13th European Conference on Thermophysical Properties, Lisbon, Portugal; Nieto de Castro, C., Ed.; Faculdade de Cihcias, Universidade de Lisboa: Lisbon, Portugal, 1991; PS6-27, 565. Onda, K.; Takeuchi, H.; Okumoto, Y. Mass Transfer Coefficients between Gas and Liquid Phases in Packed Columns. J . Chem. Eng. Jpn. 1968,1, 56-62. Peter, S.;Brunner, G.; Riha, R. Economic Aspects of the Separation of Substances by Means of Compressed Gases in Countercurrent Processes. Ger. Chem. Eng. 1978, 1 , 26-30. Ra”, W. M. Absorptionsprozesse in der chemischen Technik; VEB Verlag: Berlin, 1953. Rathkamp, P. J.; Bravo, J. L.; Fair, J. R. Evaluation of Packed Columns in Supercritical Processes. Solvent Eztr. Zon Ezch. 1987,5 (31, 367-391. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4thed.; McGraw-Hill: New York, 1987. Seibert, A. F.; Moosberg, D. G.; Bravo, J. L.; Johnston, K. P. Spray, Sieve Tray and Packed High Pressure Extraction ColumnsDesign and Analysis. In Proceedings of the lstInternational Symposium on Supercritical Fluids, Nice, France; Perrut, M., Ed.; Societe Francaise de Chemie: Nice, France, 1988; pp 561570. Sherwood, T. K.; Gilliland, E. R. Diffusion of Vapours into Air Streams. Znd. Eng. Chem. 1934,26, 516. Stephan, K.; Lucas, K. Viscosity of Dense Fluids; Plenum Press: New York, 1979. Treybal, R. E. Mass-Transfer Operations, 3rd ed.; McGraw-Hill: New York, 1981. Wilke, C. R.; Chang, P. Correlation of Diffusion Coefficients in Dilute Solutions. AlChE J . 1965, 1 (21, 264-270. Received for review December 2 , 1993 Revised manuscript received October 7, 1994 Accepted October 27, 1994@ IE930615N
Abstract published in Advance ACS Abstracts, January 15, 1995. @
