2463
I n d . Eng. Chem. Res. 1991,30, 2463-2470 Acta Chem. Scand. 1960,14 (7),1475-1484. Albright, R. L. Porous Polymer as an Anchor for Catalysis. React. Polym. 1986,4,155-174. Alexandratos, S. D.; Kaiser, P. T. Molecular Recognition by Polymer-Supported Reagents Defined through Linear Free-Energy Relationship Studies. Ind. Eng. Chem. Res. 1990,29,1306-1312. Breck, D.W. Zeolite Molecular Sieves; Wiley: New York, 1974;pp 95-96. Broughton, D. B.; Neuzil, W.; Pharis, J. M.; Brearly, C. S. The Parex Process for the Recovery of Paraxylene. Chem. Eng. Prog. 1970, 66 (9),70-75. Collins, J. J. Where to use Molecular Sieves. Chem. Eng. Prog. 1968, 64 (8),66-71. Faust, S. D.; Aly, 0. M. Adsorption Processes for Waste Treatment; Butterworth: Boston, 1987;pp 167-283. Gordon, J. E. On the Correlation of Hydrogen Bridging Equilibria with Acidity. J. Org. Chem. 1961,26, 738-745. Hemminger, W.; Hohne, G. Calorimetry: Fundamentals and RQCtice; Verlag Chemie: Weinheim, Germany, 1984; pp 167-233. Jencks, W. P. Catalysis in Chemistry and Enzymology; Dover Publications: New York, 1987;pp 323-350. Maity, N.; Payne, G. F. Adsorption from Aqueous Solutions Based on a Combination of Hydrogen Bonding and Hydrophobic Interactions. Langmuir 1991,7 , 1247-1254. Melander, W.; Campbell, D. E.; Horvath, Cs. Enthalpy-Entropy Compensation in Reversed-Phase Chromatography. J. Chromatogr. 1978,158,215-225. Norde, W.; Lyklema, J. The Adsorption of Plasma Albumin and
Bovine Pancreas Ribonuclease at Negatively Charged Polystyrene Surfaces: Part V. Microcalorimetry. J. Colloid Interface Sci. 1978,66,295-302. Payne, G. F.; Ninomiya, Y. Selective Adsorption of Solutes Based on Hvdroeen Bonding. Sen. Sci. Technol. 1990, 25 (11&12), 11171112< Payne, G. F.; Payne, N. N.; Ninomiya, Y.;Shuler, M. L. Adsorption of Non-polar Solutes onto Neutral Polymeric Sorbents. Sep. Sci. Technol. 1989,24,(5&6), 453-465. Pimentel, G. C.; McClellan, A. L. The Hydrogen Bond; W. H. Freeman: San Francisco, 1960. Ramette, R. W. Solution Calorimetry in the Advanced Laboratory. J. Chem. Educ. 1984,61 (l),76-77. Rouquerol, J.; Partyka, S. Adsorption of Surfactants on Rocks: Microcalorimetric Approach Applied to Tertiary Oil Recovery. J. Chen. Technol. Biotechnol. 1981,31,584-592. Ruthven, D. M. Principles of Adsorption and Adsorption Processes; Wiley: New York, 1984;pp 2-27. Sircar, S.; Myers, A. L. Liquid Adsorption Operations: Equilibrium, Kinetics, Column Dynamics and Applications. Sep. Sci. Technol. 1986,21 (6&7), 535-562. Woodburn, K. B.;Lee, L. S.; Rao, P. S. C.; Delfino, J. J. Comparison of Sorption Energetics for Hydrophobic Organic Chemicals by Synthetic and Natural Sorbents from Methanol/Water Solvent Mixtures. Enuiron. Sci. Technol. 1989,23,407-413. I
.
Received for review April 9, 1991 Accepted July 8,1991
Mass Transfer in Supercritical Extraction Columns with Structured Packings for Hydrocarbon Processing Andre B. de Haan* and Jan de Graauw Laboratory for Process Equipment, Delft University of Technology, Leeghwaterstraat 44, 2628 CA, Delft, T h e Netherlands
A mass-transfer model for structured packings under supercritical extraction conditions based on a model for structured packings under distillation conditions has been developed. Correlations were used to determine the required physical properties. The model was tested by measuring the height equivalent to a theoretical plate (HETP) of laboratory gauze packing in a column of 3.5-cm internal diameter for the system hexadecane/2-methylnaphthalene/carbon dioxide. Comparison of the measured and calculated HETP as a function of pressure, temperature, composition, and extraction factor showed that the mass-transfer model can be used to predict the mass-transfer efficiency of a laboratory gauze packing with reasonable accuracy. Furthermore, it was demonstrated how the developed model can be used to evaluate the effect of scale-up on the mass-transfer efficiency.
Introduction In a previous paper the results of a study on the separation of alkanes and aromatics with supercritical carbon dioxide were reported (de Haan and de Graauw, 1990). It was concluded that supercritical carbon dioxide can only be used for specific applications where high-boiling alkanes and aromatics are to be separated on basis of their relative volatility. To design supercritical extraction columns for the separation of liquid hydrocarbon mixtures such as alkanes and aromatics, not only thermodynamic data but also mass-transfer data must be available. In the past few years much attention has been paid to the performance of packed columns under supercritical extraction conditions (Brunner, 1985; Brunner and Kreim, 1986; Bunzenberger and Marr, 1988; Daurelle et al., 1988; Ender and Peter, 1989; Mizandjian and Massie, 1988; Lahiere and Fair, 1987;Lahiere et al., 1987;Rathkamp et al., 1987; Seibert and Moosberg, 1988; Seibert et al., 1988). It has been shown that high mass-transfer rates can be achieved in supercritical extraction systems compared to conventional liquid extraction systems. In most of these
studies the extraction of an aqueous feed with supercritical carbon dioxide was used because h d l y any carbon dioxide dissolves in aqueous solutions. The columns were always operated and modeled as bubble columns with carbon dioxide as the dispersed phase since only solvent-to-feed ratios around 1 kg/kg were required and because it was expected that the main resistance to mass transfer would be located in the aqueous liquid phase. When a hydrocarbon mixture is contacted with carbon dioxide at high pressures, a completely different situation arises compared to aqueous systems because a large amount of carbon dioxide dissolves in the liquid hydrocarbon phase (de Haan and de Graauw, 1990) and complete miscibility occurs at relatively low pressures. Therefore, the physical properties of the liquid phase change tremendously with pressure and it is questionable whether the main resistance to mass transfer will be located in the liquid phase. This paper reports the results of a study on the mass transfer in a countercurrent laboratory column of 3.5-cm internal diameter, equipped with a laboratory gauze packing, operating under supercritical
0S88-5885/91/2630-2463~~2.50/00 1991 American Chemical Society
2464 Ind. Eng. Chem. Res., Vol. 30, No. 11, 1991 F l o w channel c r o s s - s e c t i o n
Triangular cross-section Direction of bulk v a p o u r flow Vapour f l o w direction Vapour f l o w direction bottom sheet top sheet
'k
Diamond o r s q u a r e shaoed cross-section
F l o w channel a r r a n g e m e n t
V a p o u r f l o w channel
Direction o f liquid f l o w
C g h t - l e f t mixing b e t w e e n s h e e r s
Figure 1. View of structured packing showing orientation and flow between adjacent corrugated sheets.
extraction conditions. We have chosen to operate the column as a high-pressurecountercurrent stripping column with carbon dioxide as the continuous phase because solvent-to-feed ratios larger than 4 kg/kg were required to achieve a nonequilibrium situation. Experiments were performed with the model system hexadecane/2-methylnaphthalene/carbon dioxide (de Haan and de Graauw, 1990) at different pressures and temperatures. These experiments were modeled with a mass-transfer model for supercritical extraction columns equipped with structured packings, which is described in the following paragraphs. This model is based on a model developed for structured packings under distillation conditions by Bravo et al. (1985). Mass-Transfer Model The structure of the used laboratory gauze packing is illustrated in Figure 1. It is seen that the packing consists of adjacent corrugated sheets with flow channels at an angle of 45O from the horizontal. After entering the bottom of the column, the supercritical vapor phase flows up through these flow channels, moving through a cross section that alternates between the shapes of a triangle and a twisted diamond, as illustrated in Figure 2. Since half of the diamond-shaped cross section belongs to another flow channel, the velocity of the vapor phase through the channels remains constant. The liquid phase is fed to the top of the column and will be spread into thin liquid films covering almost all the available surface area. This good liquid spreading is due to the gauze structure of the packing that promotes capillary action. In our model we assumed that the liquid phase flows down nearly vertically and can therefore be approximated with a laminar film flowing down a vertical plate. With this simplified hydraulic model of the vapor and liquid flows through the structured packing, it is possible to develop a mass-transfer model for structured packings under supercritical extraction conditions. First the dimensions of the packing that are required for the calculation of the effective vapor and liquid velocities are discussed. Hereafter the effective vapor and liquid velocities are calculated and used together with the packing dimensions for the determination of the vapor- and liquidphase mass-transfer coefficients. Finally the conventional relationships for distillation are used to calculate the
Figure 2. Flow channel geometry. Table I. Dimensions of the Used Laboratory Gauze Packing and Industrial (Bravo et al., 1985; Hufton et al., 1988) Sulzer BX Gauze Packing dimension lab ind dimension lab ind 6.4 11.0 Dmlumn, cm 3.5 >20 b, mm t 0.90 0.90 s, mm 5.0 7.7 6.7 0, deg 45 d,,mm 3.9 60 1030 600 P, m/m2 up, m2/m3 890 500 h, m m 4.0 6.4
HETP (height equivalent to a theoretical plate) of the structured packing. The required physical properties were estimated with correlations as discussed in the subsequent paragraphs. Packing Dimensions. First an equivalent diameter of a flow channel must be defined. The dimensions of flow channels in a structured packing are shown in Figure 2. For the triangular cross section, the available perimeter per unit of cross-sectional area is 4s + 2b - -1 pt=-bh rht The available perimeter per unit of cross-sectional area for the corresponding diamond-shaped opening is
An arithmetic average of these two perimeters is taken to calculate the available perimeter per unit of cross-sectional area:
(3) This hydraulic radius is used to calculate the equivalent diameter of a packing channel: 4bh de, = 4rh = (4) 4s + b The characteristic dimensions of the used laboratory gauze packing and industrial Sulzer BX packing are listed in Table I. Effective Vapor and Liquid Velocities. When the thickness of the liquid film is small compared to the thickness of the packing sheets, the effective vapor velocity through the channels is related to the superficial vapor velocity by the following relationship:
Ind. Eng. Chem. Res., Vol. 30, No. 11, 1991 2465 (5) where 8 is the angle of inclination of the channel with respect to the horizontal. The effective liquid velocity is approximated by the surface velocity of a laminar film flowing down a vertical plate (McGabe et al., 1985):
capillary action. To determine the heights of transfer units, we used the conventional relationships for distillation: HTUV = u v , / b p (13) (14)
HTUl = u l , * / k l a p
The height of an overall transfer unit and the height equivalent to a theoretical plate were calculated from HTU,, = HTU, (mV/L)HTUI = HTU, + E(HTU1) (15) In E HETP = HTU,, (16) E-1
+
where r = L / P A , (kg/(s*mperimeter)) and A, = column cross-sectional area (m'). The thickness of the film 6 is given by (McGabe et al., 1985) (7)
Vapor-Phase Mass-Transfer Coefficient. Bravo et al. (1985) estimated the vapor-phase mass-transfer coefficient from the relation for wetted wall columns: Sh = 0.034Reo.8S~0.33
(8)
where
Sh = k,d,/D, Re = (Pv(uv,ett + ul,etf)deq)/~v s c = ?v/PvDv Compared to distillation, however, the velocity of the vapor phase through the packing channels in supercritical extraction columns will be about 100 times lower (cm/s instead of m/s) as a result of its liquidlike density. Therefore, the enhancement of the vapor-phase mass-transfer coefficient caused by entrance effects resulting in a not fully developed boundary layer will be much less under supercritical extraction conditions. For this reason we used the relation for mass transfer under turbulent pipe flow conditions to estimate the vapor-phase mass-transfer coefficient (McGabe et al., 1985):
Sh = 0.023Re0*8S~0.33 (9) where Sh, Re, and Sc are defined the same as in (8). Liquid-Phase Mass-Transfer Coefficient. For short contacting times Higbie's penetration theory (McGabe et al., 1985) can be used to calculate the mass-transfer coefficient in the laminar liquid film: kl
= 2(Di/*t)'/'
FO < 0.10
(10)
where
FO = D$/46' If the contacting time t is taken as the residence time for vertical liquid flow between corrugation changes, (10) becomes
Fo < 0.10
(11)
When the penetration depth becomes larger than the film thickness, the liquid-phase mass-transfer coefficient becomes constant. In that case we used penetration into a flat plate of thickness 26 to approximate the mass-transfer coefficient in the liquid film (Beek and Muttzal, 1975): kl = 2.46(01/6) FO > 0.10 (12) Heights of Transfer Units. For gauze packing it is well-known (Bravo et al., 1985) that the available packing surface is completely wetted by the liquid film due to
Estimation of Physical Properties To calculate the mass-transfer coefficients in the vapor and liquid phases, viscosities, densities, and diffusion coefficients under supercritical extraction conditions are required. We have chosen to use correlations (Reid et al., 1987) for their estimation because no experimental data are available in the literature. Viscosity, The viscosities of pure liquid hexadecane and 2-methylnaphthalene at atmospheric pressure (Evans, 1938a,b) were extrapolated to the operating pressures by means of the following correction (Reid et al., 1987): ?p _ -- 1 + ~ ~ ( p / 2 . 1 1 8 p , ) ~ ~ (17) ?1 1+ C 3 4 P / P J where cl, cz, and c3 are functions of the reduced temperature of the component (Reid et al., 1987). At supercritical extraction conditions the hydrocarbon mixture contains a considerable amount of carbon dioxide and significant amounts of the hydrocarbons are dissolved in the supercritical carbon dioxide (de Haan and de Graauw, 1990). The vapor- and liquid-phase viscosities were estimated from the viscosities of the pure components with the method of Gunberg and Nissan (Reid et al., 1987): In om/(mPa-s) = Exi In vi/(mPa.s) + CCxixjGij (18) I
i#j
In (18), x i is the mole fraction of component i and Gij is an interaction parameter that is calculated from a group contribution method (Reid et al., 1987). The viscosity of pure carbon dioxide as a function of pressure and temperature was taken from the literature (Ulebin and Makarushkin, 1976). Figure 3 illustrates the effect of pressure on the liquidand vapor-phase viscosities for a binary mixture of hexadecane and carbon dioxide at 50 "C. The calculated curves exhibit the same behavior as measured for several binary mixtures of fatty acids and carbon dioxide (Peter et al., 1987; Peter and Jakob, 1988). Density. The densities of pure hexadecane and 2methylnaphthalene as a function of temperature (Evans, 1938a,b) and the density of pure carbon dioxide as a function of temperature and pressure (Angus and Armstrong, 1976) are available in the literature. Measured liquid-phase densities for binary mixtures of several hydrocarbons and carbon dioxide (Gasem et al., 1989; Peter et al., 1987; Peter and Jakob, 1988; Zarah et al., 1974) showed that the density of the liquid phase is nearly independent of the dissolved amount of carbon dioxide and the pressure. This carbon dioxide free hydrocarbon mixture density was estimated from (Coulson et al., 1983) (19) where MWi is the molecular weight and ui is the molar
2466 Ind, Eng. Chem. Res., Vol. 30, No. 11,1991
i
\ 10-9
0.100
5 OOC
(m P a . s l
0
50
-
1 -
100
150 P (bar1
Figure 4. Diffusion coefficients of carbon dioxide and hexadecane at infinite dilution in the vapor and liquid phase of the binary system hexadecane and carbon dioxide a t 50 O C , calculated with the Stokes-Einstein equation. 0
50
-
Solvent
150
100
P (bar1
nakj-up rolrcnt
Figure 3. Calculated liquid (top) and vapor (bottom) phase viscoeity as a function of pressure for the binary system hexadecane and carbon dioxide a t 50 "C. Table 11. Estimated Effective Hard-Sphere Diameters and Critical Volumes for the Substances under Present Study component di, m u,,O ms/kmol carbon dioxide 2.13 0.094 2-methylnaphthalene 6.32 0.470 hexadecane 9.03 0.958 a
Vent
Reid e t ai., 1987.
volume of component i. The density of the vapor phase appeared to be nearly equal to the pure carbon dioxide density (Gasem et al., 1989; Zarah et al., 1974). Diffusion Coefficients. Reasonably accurate estimates of diffusion Coefficients in liquids and supercritical fluids can be obtained with the Stokes-Einstein equation (Debenedetti and Reid, 1985,1986; Jakob et al., 1987; Wells and Foster, 1988): Di = kT/(3s7,dJ (20) where Dj is the diffusion coefficient of a spherical molecule i of diameter di in a continuum of viscosity qm, (18), and temperature T, when no slip exists between the particle and the continuum. The hard-sphere diameters (Table 11) were estimated from the molecular volume at the critical point (Sun, 1986): dj/(m) X 1O'O = 13.01~,'/~/(m~/kmol) - 3.78 (21) Figure 4 shows the calculated effect of pressure on the liquid- and vapor-phase diffusion coefficients a t infinite dilution of hexadecane and carbon dioxide molecules in a binary mixture of hexadecane and carbon dioxide at 50 "C. These diffusion coefficients were calculated with the Stokes-Einstein equation taking into account only the effect of composition on the vapor- and liquid-phase viscosity and ignoring the effect of composition on the binary diffusion coefficients. It is seen that the carbon dioxide molecules will always diffuse much faster than the hexadecane molecules. A t high pressures the liquid- and vapor-phase diffusion coefficients tend to approach each
raftln*te
I
Figure 5. Flowsheet of the supercritical extraction equipment: (1) storage vessel; (2) pump; (3) heat exchanger; (4) column; (5)separator; (6) condensor; (7) COzstorage vessel; (8) pump; (9) heat exchanger; (10) separator; (11)wet gas meter.
other due to the decrease of the liquid-phase viscosity and the increased vapor-phase viscosity (Figure 3).
Experimental Section A simplified flowsheet of the used equipment is shown in Figure 5. The extraction column (4), with an internal diameter of 3.5 cm and a length of 1m, was equipped with laboratory gauze packing (bed height 60 cm) and operated as a stripping column. The feed (1)entered the top of the column at extraction pressure (2) and extraction temperature (3). The remaining raffmte, containing considerableamounts (20-50 wt 90) of carbon dioxide, was drawn off from the bottom of the column and expanded to 1bar. A wet gas meter (11) was used to measure the amount of dissolved carbon dioxide, and the raffinate was periodically drawn off from the raffinate collection vessel (10). The supercritical carbon dioxide was fed to the bottom of the column at extraction pressure (8) and extraction temperature (9) and left the top of the column saturated with the dissolved extract. The pressure was reduced below the critical pressure of carbon dioxide (50-60 bar) to condense the extract in the separator. This extract was
Ind. Eng. Chem. Res., Vol. 30,No. 11, 1991 2467 OS( 0.50
HETP (ml 8001:
t
YZHN
150 bar
y'"""Ho
YE
0.25
0.25
0 0
0
Figure 6. Graphical determination of the number of theoretical plates from a solvent-free selectivity diagram.
periodically drawn off. The amount of carbon dioxide in which the extract was dissolved was calculated from the carbon dioxide flow to the column, measured with a Micro Motion mass flowmeter, by a carbon dioxide mass balance over the column. Fresh carbon dioxide was added to the evaporating carbon dioxide from the separator to compensate for losses in the raffinate. Hereafter the gaseous carbon dioxide was condensed before the pressure was increased again to the extraction pressure (8). Unless stated otherwise, all the experiments reported in this section were performed with a feed containing 25 w t % 2-methylnaphthalene and 75 wt % hexadecane. The experiments were carried out at several solvent-to-feed ratios. Visual observation through sapphire windows in the column showed that the wed laboratory gauze packing was always wetted by the liquid hydrocarbon phase. High solvent-to-feed ratios, where 30-70% of the feed was extracted, were used to measure the number of theoretical plates in the used laboratory column. A refractometer was used to measure the composition of the solvent-free feed, raffinate, and extract. The relative variance of the measured weight fractions of the separate components in the vapor and the liquid phase appeared to be about 5%. The number of theoretical plates was determined graphically from the experiments by a selectivity diagram construction on a solvent-free basis (Larian, 1959; Pratt, 1983). The equilibrium data required for the construction of the equilibrium line were measured by pinching the column and can be found elsewhere (de Haan and de Graauw, 1990; de Haan, 1991). A typical example of the constructed diagrams is shown in Figure 6. It is seen that in the equilibrium first stage the slope of the solvent-free operating line changes dramatically because the solvent becomes saturated with hexadecane and 2-methylnaphthalene. In the subsequent stages the slope of the solvent-free operating line remains approximately constant because the measurements were conducted in a small composition range. The obtained mass-transfer data used for this paper are listed elsewhere (de Haan, 1991). The hexadecane, >99% purity, and the 2-methylnaphthalene, >96% purity, were products from MERCKSchuchardt. Hoek-Loos supplied the >99.99% pure carbon dioxide. All these materials were used without further purification.
0.5
-E
1.0
Figure 7. Measured (0 = 150 bar, = 175 bar) and calculated HETP as a function of pressure and the extraction factor with a constant solvent-free feed (75wt % HD and 25 wt % 2MN) of 0.80 kg/h at 80 "C.
Results In the proposed mass-transfer model the HETP was calculated assuming that the component with the smallest diffusion coefficient (hexadecane) was controlling the mass-transfer rate. The diffusion coefficient of hexadecane in the liquid and the vapor phase was assumed to be nearly equal to the Stokes-Einstein diffusion coefficient at infinite dilution because at the used pressures the vapor as well as the liquid phase contain large amounts of dissolved carbon dioxide. Figure 7 shows the effect of pressure on the measured and calculated HETP as a function of the extraction factor at a solvent-free feed of 0.80 kg/h at 80 "C. When the pressure is increased from 150 to 175 bar, the HETP at extraction factors larger than 0.5 is lowered from approximately 30 cm to approximately 17 cm. At 200 bar the HETP decreases further to about 9 cm. This substantial change of the HETP with pressure results mainly from the large increase of the 2-methylnaphthalene and hexadecane distribution coefficients (de Haan and de Graauw, 1990). This means that smaller amounts of solvent are required to achieve the same extraction factor and lower superficial vapour velocities are obtained. Increasing the pressure will also increase the viscosity of the supercritical phase and decrease the diffusivity of the hexadecane and 2-methylnaphthalene molecules. Therefore the decrease in HTU, will be less than expected from the increase in distribution coefficients alone. Although not visible in figure 7,this effect of pressure on the diffusivities showed itself quite clearly during the calculation of the curves that agree quite well with the experimental data. Furthermore, it appeared that the calculated HTUl contributes less than 5 % to the HETP and that the HETP is therefore completely determined by the HTU, and the extraction factor. Figure 8 shows for different pressures the measured and the calculated HETP as a function of the extraction factor at a solvent-free feed of 0.85 kg/h and 50 OC. The effect of temperature on the HETP is illustrated when the curves at a constant carbon dioxide density of 600 kg/m3 (200 bar, 80 "C from Figure 7 and 125 bar, 50 OC from Figure 8) are compared. It is seen that for extraction factors larger than 0.5 the HETP decreases from aproximately 18 cm at 50 OC to approximately 9 cm at 80 "C. It is clear that a part of this decrease results from higher diffusivities of the hexadecane and 2-methylnaphthalenemolecules at higher temperatures. However, increasing the temperature at constant carbon dioxide densities also increases the dis-
2468 Ind. Eng. Chem. Res., Vol. 30, No. 11,1991 0.5 i
HETP
~
800C 175 bar
Imi
1
:
t I
0 254 -
125 tiar
b
150 bar
/
/
I
0 1
-E
05
0
10
0
Figure 8. Measured (0 = 125 bar) and calculated HETP as a function of pressure and the extraction factor with a constant solvent-free feed (75 wt % HD and 25 wt % 2MN) of 0.85 kg/h a t 50 OC.
HETP 800C
0.25
04 0
I
0.5
x~HN
'O
-(Figure 9. Measured (0 150 bar, S/F = 16.1; = 175 bar, S/F = 6.6) and calculated HETP as a function of pressure and the ratio of 2-methylnaphthalene to hexadecane in the liquid phase with a constant solvent-free feed of 0.80 kg/h at 80 O C .
tribution coefficients of hexadecane and 2-methylnaphthalene (de Haan and de Graauw, 1990). Therefore, the required amount of solvent to achieve the same extraction factor will be less and the HETP will decrease even more. Furthermore, it can be seen from Figure 8 that the calculated curve at 50 O C and 125 bar is also in reasonable agreement with the experimental data. Finally, it is interesting to study the variation of the HETP with the vapor- and liquid-phase composition. In the mass-transfer model it appeared that the Reynolds number of the vapor phase depends on the effective velocities of the gas as well as the liquid phase. The physical properties of the vapor phase will depend only slightly on its composition because only small amounts ( 20 cm) on the HETP for a constant superficial liquid velocity of 0.54 mm/s and a feed with 75 w t % HD and 25 wt % 2MN.
Scale-up Considerations When laboratory tests have shown the viability of a desired separation with a supercritical solvent, a reliable and consistent method must be used to scale-up successfully to industrial-size columns (d, > 20 cm). The proposed mass-transfer model can be used to evaluate the effect of packing dimensions (Table I) on the HETP as illustrated by Figure 10. For equal superficial vapor and liquid velocities the HETP in an industrial column, equipped with industrial Sulzer BX gauze packing instead of the used laboratory packing, may be expected to be about 1.5 times higher due to the combination of a smaller specific surface area of the industrial packing with a higher vapor-phase mass-transfer coefficient. This higher masstransfer coefficient is caused by the higher Reynolds numbers in the industrial Sulzer BX packing. Another important parameter is the maximum capacity at which a column can be operated. At supercritical extraction conditions, the interaction between the vapor and the liquid phase will be completely different from distillation conditions. Therefore, experimental data on flooding points are essential to determine the maximum capacity of a supercritical extraction column. Unfortunately, no experimental data on flooding under supercritical extraction conditions are available in the literature and our laboratory equipment is not suited for the determination of these flooding conditions. When the maximum capacity of a column is known, the proposed mass-transfer model can be used to evaluate the effect of increasing the flow rates on the HETP. This is illustrated in Figure 11,where the calculated effect of the liquid flow rates on the HETP is shown as a function of the extraction factor for Sulzer BX gauze packing in an industrial-scale supercritical extraction column. It is clear that the HETP increases at higher liquid flow rates because a higher superficial vapor velocity is required to obtain the same extraction factor. From the calculations it appeared that the superficial vapor velocity increases more rapidly than the vapor-phase mass-transfer coefficient, resulting in a higher HETP. Conclusions The mass-transfer efficiency of a structured laboratory gauze packing for the separation of hydrocarbon mixtures with supercritical carbon dioxide has been studied. During this study experiments were performed with the model
Ind. Eng. Chem. Res., Vol. 30, No. 11, 1991 2469 g = acceleration of gravity = G = interaction parameter
0.50U=,I
HETP
1.63 m m / s
lml
t 0.25-
175 b a r
04
0
0.5
-E
1.0
Figure 11. Calculated effect of liquid load on the HETP of industrial Sulzer BX packing (d, > 20 cm) for a feed of 75 wt % HD and 25 wt % 2MN.
system hexadecane/2-methylnaphthalene/carbondioxide at various pressures, temperatures, and extraction factors in a laboratory column with an internal diameter of 3.5 cm. A mass-transfer model has been developed in which the vapor-phase mass-transfer coefficient was calculated from the relation for mass transfer during turbulent flow in pipes. The liquid-phase mass-transfer coefficient was approximated with penetration into a laminar liquid film that completely wetted the available surface area of the gauze packing. Correlations were used to estimate the physical properties required for the calculation of the vapor- and liquid-phase mass-transfer coefficients. Comparison of the calculated and measured HETP as a function of pressure, temperature, composition, and extraction factor showed that the proposed mass-transfer model can be used to predict the mass-transfer efficiency of a laboratory gauze packing, used for the separation of liquid hydrocarbon mixtures with supercritical carbon dioxide, with a reasonable accuracy. It appeared that, when the column was operated as a stripping column, the main resistance to mass transfer was located in the supercritical vapor phase. The proposed mass-transfer model can also be used to evaluate the effect of scale-up to industrial columns (d, > 20 cm). It was calculated that for equal superficial vapor and liquid velocities the HETP in an industrial column, equipped with Sulzer BX gauze packing, will be about 1.5 times higher compared to the HETP in the used laboratory column.
Acknowledgment We thank C. van Keppel, C. E. Langedijk, and A. Das for performing the calculations and experiments reported in this paper during their graduation period at the Delft University of Technology. Thanks are due to Z. Olujic and A. Bos of our laboratory for their helpful suggestions for the preparation of this paper. Financial support for this project was provided by Unilever, Shell, DSM, RDM, Aerofako, and Heineken.
Nomenclature a = specific surface area (m2m-9 A = cross-sectional area (m2) b = channel base (m) c = constant d = diameter (m) D = diffusion coefficient (m2 8-l) E = extraction factor ( m V / L )
9.81 m s - ~
h = channel height (m) HETP = height equivalent to a theoretical plate (m) HTU = height of a transfer unit (m) k = mass-transfer coefficient (m 8-l) J K-' k = Boltzmann's constant = 1.381 X L = liquid mass velocity (kg s-l m-2) m = distribution coefficient (kg kg-'1 MW = molecular weight (kg kmol-') P = perimeter (m m-2) p = pressure (bar) r = radius (m) s = channel side (m) t = contact time ( 8 ) T = temperature (K) u = velocity (m s-l) u = molar volume (m3 kmol-') V = vapor mass velocity (kg s-l m-9 x , X = liquid mole, weight fraction y, Y = vapour mole, weight fraction
Greek Letters r = liquid flow based on perimeter (kg s-l m-9 6 = film thickness (m) c = porosity 7 = viscosity (Pa s-') p = density (kg m-3) 8 = angle of channel with respect to horizontal (deg) w = acentric factor Super- and Subscripts 1-atlbar 2MN = 2-methylnaphthalene c = critical d = diamond shape eff = effective eq = equivalent h = hydraulic HD = hexadecane i , j = component 1 = liquid phase m = mixture ov = overall p = at required pressure r = reduced s = superficial t = triangular v = vapor phase Dimensionless Numbers Fo = Fourier number = Dt/462 Re = Reynolds number = pud/v Sc = Schmidt number = q/pD Sh = Sherwood number = k d / D Registry No. Hexadecane, 544-76-3;2-methylnaphthalene, 1321-94-4.
Literature Cited Angus, S.; Armstrong, B. IUPAC International Thermodynamic Tables of the Fluid State: Carbon Dioxide; Pergamon Press: Oxford, 1976; pp 326-347. Beek. W. J.: Muttzal, K. M. K. TrQnSpOrtPhenomena; Wiley: New York, 1975; pp 161-164.
Bravo. J. L.: Rocha, J. A.: Fair, J. R. Mass Transfer in Gauze Packings. Hydrocardon Kocess. 1985, 64 (I), 91-95. Brunner, G. Mass Transfer in Gas Extraction. In Supercritical Fluid Technology, Process Technology Proceedings; Penninger, J. M. L., Radosz, M., McHugh, M. A., Krukonis, V. J., Eds.; Elsevier: Amsterdam, 1985; Vol. 3, pp 245-261. Brunner, G.; Kreim, K. Separation of Ethanol from Aqueous Solutions by Gas Extraction. Ger. Chem. Eng. 1986,9, 246-250. Bunzenberger, G.; Marr, R. Counter Current High Pressure Extraction in Aqueous Systems. In Proceedings of the Znternutionul
2470
Ind. E n g . Chem. Res. 1991,30, 2470-2476
Symposium on Supercritical Fluids; Perrut, M., Ed.; 1988;pp 613-618. Coulson, J. M.; Richardson, J. F.; Sinnott, R. K. Chemical Engineering Vol. 6 Design; Pergamon Press: Oxford, 1983; pp 238-239. Daurelle, T.; Barth, D.; Perrut, M. Supercritical Fluid Extraction: Mass Transfer in a Counter Current Packed Column. In Proceedings of the International Symposium on Supercritical Fluids; Perrut, M., Ed.; 1988;pp 571-580. Debenedetti, P. G.; Reid, R. C. Binary Diffusion in Supercritical Fluids. In Supercritical Fluid Technology, Process Technology Proceedings; Penninger, J. M. L., Radosz, M., McHugh, M. A., Krukonis, V. J., Eds.; Elsevier: .Amsterdam, 1985; Vol. 3, pp 225-244. Debenedetti, P. G.; Reid, R. C. Diffusion and Mass Transfer in Supercritical Fluids. AIChE J. 1986,32 (12),2034-2046. de Haan, A. B. Supercritical Fluid Extraction of Liquid Hydrocarbon Mixtures. Ph.D. Dissertation, Delft University of Technology, 1991. de Haan, A. B.; de Graauw, J. Separation of Alkanes and Aromatics with Supercritical Carbon Dioxide. Sep. Sci. Technol. 1990,25 (13-151,1993-2006. Ender, U.;Peter, S. Verbesserung des Stoffaustausches bei der Uberkritischen Fluid-Extraktion durch Druckpulsation. Chem.-Ing.-Tech. 1989,61 (4),324-326. Evans, E. B. The Viscosities of Hydrocarbons, Part 1-111. J. Inst. Pet. Technol. 1938a,24, 38-53. Evans, E. B. The Viscosities of Hydrocarbons, Part VI1 and VIII. J. Inst. Pet. Technol. 1938b,24,537-553. Gasem, K. A. M.; Dickson, K. B.; Dulcamare, P. B.; Nagarajan, N.; Robinson Jr., R. L. Equilibrium Phase Compositions, Phase Densities and Interfacial Tensions for C02 + Hydrocarbon Systems. 5. C02 + Tetradecane. J. Chem. Eng. Data 1989,34(21, 191-195. Hufton, J. R.; Bravo, J. L.; Fair, J. R. Scale-up of Laboratory Data for Distillation Columns Containing Corrugated Metal-Type Structured Packing. Ind. Eng. Chem. Res. 1988,27,2096-2100. Jakob, H.; Seekamp, M.; Peter, S. Zum Stoffubergang beim Losen von Stoffen mit hoher Molmasse in uberkritischen Extractionsmitteln. Chem.-Ing.-Tech. 1987,59 (7),572-574. Lahiere, R. J.; Fair, J. R. Mass-Transfer Efficiencies of Column Contactors in Supercritical Extraction Service. Ind. Eng. Chem. Res. 1987,26,2086-2092. Lahiere, R.J.; Humphrey, J. L.; Fair, J. R. Mass Transfer in Countercurrent Supercritical Extraction. Sep. Sci. Technol. 1987,22 (2&3), 379-393.
Larian, M. G. Fundamentals of Chemical Engineering Operations; Constable and Company L T D London, 1959;pp 449-452. McGabe, W. L.; Smith, J. C.; Harriot, P. Unit Operations of Chemical Engineering, 4th ed.; McGraw-Hill: New York, 1985. Mizandjian, J. L.; Massie, J. F. Performance of a Packed Contactor in Supercritical COz Countercurrent Extraction. In Proceedings of the International Symposium on Supercritical Fluids; Perrut, M., Eds.; 1988;pp 661-667. Peter, S.; Jakob, H. Viscosity of Coexisting Phases a t Supercritical Fluid Extraction. In Proceedings of the International Symposium on Supercritical Fluids; Perrut, M., Ed.; 1988;pp 303-310. Peter, S.; Weidner, E.; Jakob, H. Die Viskositat koexistierender Phasen bei der uberkritischen Fluidextraktion. Chem.-hg.-Tech. 1987,59 (l),59-62. Pratt, H.R. C. Computation of Stagewise and Differential Contactors: Plug Flow. In Handbook of Solvent Extraction; Lo, T. C., Baird, M. H. I., Hanson, C., Eds.; Wiley: New York, 1983;pp 160-161. Rathkamp, P. J.; Bravo, J. L.; Fair, J. R. Evaluation of Packed Columns in Supercritical Extraction Processes. Solv. Extr. Ion Ex&. 1987,5 (3),367-391. Reid, R. C.;Prausnitz, J. M.; Poling, B. E. The Properties of Gases & Liquids, 4th ed.; McGraw-Hill: New York, 1987. Seibert, A. F.; Moosberg, D. G. Performance of Spray, Sieve Tray, and Packed Contactors for High Pressure Extraction. Sep. Sci. Technol. 1988,23(12&13), 2049-2063. 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 International Symposium on Supercritical Fluids; Perrut, M., Ed.; 1988; pp 561-570. Sun, S. Tracer Diffusion in Dense Fluids up to the Supercritical Region. Dissertation, 1986;Available Univ. Microfilms Intl., Order No. DA8615303. Ulebin, S. A.; Makarushkin, V. I. Teploenergetika 1976,(6),65-69. Wells, P. A.; Foster, N. R. DIffusion in Supercritical Fluids. In Proceedings of the International Symposium on Supercritical Fluids; Perrut, M., Ed.; 1988; pp 319-326. Zarah, B. Y.; Luks, K. D.; Kohn, J. P. Phase Equilibria Behavior of Carbon Dioxide in Binary and Ternary Systems. J. Chem. Eng. Data 1974,19 (4),349-354. Received for review February 4, 1991 Revised manuscript received June 26, 1991 Accepted July 17,1991
Extraction of Lysozyme Using Reversed Micellar Solution: Distribution Equilibrium and Extraction Rates Takumi Kinugasa, Shin-Ichiro Tanahashi, and Hiroshi Takeuchi* Department of Chemical Engineering, Nagoya University, Chikusa-ku, Nagoya, 464-01, Japan
Studies were made of the extraction of lysozyme from aqueous KCl media with an isooctane solution containing Aerosol OT (AOT). The distribution equilibrium of the protein between the aqueous and the organic phases was explained in terms of two effects: an electrostatic interaction between the charged proteins and AOT headgroups, and a size exclusion effect due to water pool of the reverse micelles. The amount of water solubilized into the surfactant solution was correlated with both concentrations of the salt and AOT. It was found that the micellar solution saturated with proteins has a limiting content that depends on only water content of the organic phase. Furthermore, rates of both the forward and backward extraction of lysozyme were examined in a stirred transfer cell. In the stripping of the protein from the micellar solution, it was found that there is a dominant resistance to leave it at the oil-water interface.
Introduction With progress in genetic engineering and cell fusion techniques, new synthesis methods of proteins have been established. However, the development of efficient methods for recovery or concentration of proteins and other biproducts from fermentation broths and cell culture media is crucial for an advance in biotechnology. Various forms of chromatography and electrophoresis are usefully
applied to purification of high-value pharmaceuticals but are expensive and difficult to scale beyond laboratory size. Usual solvent extraction can be applied to large-scale processes for separation of organic acids and amino acids; however, its application for proteins is not suitable because of denaturation in organic solvents. Most recently, a novel extraction technique using reverse micelles has been reported by Luisi et al. (1979) as an
0888-588519112630-2470$02.50/0 0 1991 American Chemical Society
