2086
I n d . Eng. Chem. Res. 1987,26, 2086-2092
Frensdorff, H. K. J. Am. Chem. SOC.1971, 93(3), 600. Ghosh, N. N.; Mandal, B. M. Macromolecules 1986, 19, 19. Izatt, R. M.; Christensen, J. J. Synthetic Multidentate Macrocyclic Compounds; Academic: New York, 1978. Jayakrishnan, A,; Shah, D. 0. J . Polym. Sci., Polym. Chem. Ed. 1983, 21, 3201. Jayakrishnan, A,; Shah, D. 0. J. Appl. Polym. Sci. 1984, 29, 2937. Lee, C. Y. M.S. Thesis, University of Maryland, 1985. Pedersen, C. J. J . Am. Chem. SOC.1967, 89(26), 7017. Rasmussen, J. K. U S . Patent 4 326049, 1982. Rasmussen, J. K.; Heilman, S. M.; Toren, P. E.; Pocius, A. V.; Kotnour, T. A. J . Am. Chem. SOC.1983, 105(23),6845. Rasmussen, J. K.; Smith, H. K. Makromol. Chem. 1981a, 182, 701. 1981b, 103, 730. Rasmussen, J. K.; Smith, H. K. J . Am. Chem. SOC.
Rasmussen, J. K.; Smith, H. K. In Crown Ethers and Phase Transfer Catalysis in Polymer Science, Mathias, L. J., Carraher, C. E., Eds.; Plenum: New York, 1984; Vol. 105. Starks, C. M.; Liotta, C. Phase Transfer Catalysis;Academic: New York, 1978. Starks, C. M.; Owens, R. M. J . Am. Chem. SOC.1973, 95, 3613. Takeishi, M.; Ohkawa, H.; Hayama, S. Makromol. Chem. Rapid Commun. 1981,2,455. Weber, M’. P.; Gokel, G. W. Phase Transfer Catalysis in Organic Sjnthesis; Springer-Verlag: New York, 1977.
Received for review December 16, 1986 Revised manuscript received June 4, 1987 Accepted July 6, 1987
Mass-Transfer Efficiencies of Column Contactors in Supercritical Extraction Service Richard J. Lahiere and James R. Fair* Separations Research Program, The University of Texas at Austin, Austin, Texas 78712
The mass-transfer performance of a small-scale continuous countercurrent extractor, operating in supercritical and near-critical regions for the solvent, was investigated and characterized. Test systems were alcohol/water mixtures, and the solvent was carbon dioxide. Experiments were carried out to determine mass-transfer efficiencies of a 2.5-cm (1-in.) extraction column operating as a spray column, a sieve tray column, and a packed column. A model for predicting mass-transfer efficiencies in conventional liquid-liquid extraction was applied to the data with good success.
In recent years, the chemical engineering community has paid close attention to the use of high-pressure solvents, near or above their critical points, as extractants for separating liquid and solid mixtures at moderate temperatures. Much valuable supporting research has dealt with the characterization of solvent/mixture equilibrium and physical properties. Less attention has been directed to mass and momentum transport phenomena so crucial to commercial-scale designs. The purpose of the present work was to characterize the mass-transfer performance of a small-scale countercurrent contactor as a first step in a long-term project aimed at developing reliable models for describing the performance of supercritical extraction columns. These models would be useful in the design and simulation of high-pressure processes dealing with liquid feeds such as hazardous wastes, contaminated waters, heavy oil residues, and organic/water mixtures. Three different modes of continuous countercurrent extraction were studied: spray column, tray column, and packed column. The present paper deals primarily with the first two types. The packed column work referenced in this paper has been reported separately by Rathkamp (1986). Previous Work The advantages of supercritical processing, together with projected future applications, have been discussed by many authors (e.g., Paulaitis et al. (1983), Johnston (1984), Peter (1984), McHugh and Krukonis (1986)). In general, potential advantages of supercritical extraction include lowtemperature solvent/extract separation, favorable phase equilibria, and enhanced transport properties. There is growing literature also on solubility relationships for various solutes in supercritical solvents or cosolvent systems. Little work has been reported on the prediction and scale-up of mass-transfer efficiency performance of columns operating in supercritical extraction service. On the 0888-5885/87/2626-2086$01.50/0
other hand, there has been a significant amount of work in the area of efficiency modeling and prediction in liquid-liquid extraction. Rocha et al. (1986) have reviewed previous work in this area, with emphasis on sieve tray contactors. They have also described an improved model for predicting efficiency in sieve tray columns and have compared it with other models such as the ones by Treybal (1963, 1980), Skelland and Conger (1973), and Pilhofer (1981). It would appear reasonable to assume that the basic principles applying to models for conventional liquid-liquid extraction sieve trays and spray columns would apply also to high-pressure extraction. Studies using supercritical carbon dioxide for the removal of organic compounds in spray and tray columns have been reported by Brunner (19841, Moses and de Filippi (1984), and Brunner and Kreim (1986). While mass-transfer efficiencies were not specifically identified, it was indicated that the reported mass-transfer efficiencies were higher than those generally found in conventional liquid-liquid extraction. Tiegs (1986) and Eisenbach (1985) studied the fractionation of organic mixtures in packed and tray columns with a supercritical solvent. These authors evaluated the influence of parameters such as temperature, pressure, different internals, and the addition of cosolvents. The work by Tiegs also embraced the solvent recovery portion of the process and the optimization of the complete separation. Test Systems Three high-pressure systems were studied: liquid C02/2-propanol/water (LC/I/W), supercritical COz/ 2-propanol/water (SC/I/W), and supercritical COz/ ethanol/water (SC/E/W). One conventionalliquid-liquid extraction system, toluene/acetone/water (T/A/W), was also investigated in order to provide a base for comparison as well as to “calibrate” the experimental apparatus with respect to other equipment used previously in our laboratories for liquid extraction projects (Rocha et al., 1986). 0 1987 American Chemical Society
Ind. Eng. Chem. Res., Vol. 26, No. 10, 1987 2087 Table I. Physical Properties of Experimental Test Systems CO,/E/W, P = 102.0 atm, ProPertv T = 35 "C - - m of nonaqueous phase dispersed, w t fraction 0.064 22" =, dyn/cm MW of nonaqueous phase, g/g-mol 44.01 MW of aqueous phase, g/g-mol 19.42 p of nonaqueous phase, g/cm3 0.713 0.990 p of aqueous phase, g/cm3 0.0579 p of nonaqueous phase, cP 0.753 p of aqueous phase, cP 1.93 X lo4 D of nonaqueous phase, cm2/s D of aqueous phase, cm2/s 1.64 x 10-5
C02/I/W,
T/A/W,
CO,/I/W,
P = 102.0 atm, T = 40 "C
P = 1.0 atm, T = 25 "C
P = 81.6 atm, T = 25 "C
0.212 23" 44.01 20.12 0.603 0.990 0.0485 0.685 1.97 X 10"' 1.54 x 10-5
0.735 22.0 92.14 18.0 0.862 0.990 0.54 0.92 2.88 x 10-5 1.29 x 10-5
0.170 23" 44.01 20.12 0.774 0.990 0.0670 0.890 1.36 X lo4 1.13 x 10-5
=These values are for the CO,/water system. The recommended model (Seibert, 1986) will accurately predict the drop diameters of the ternary systems using an interficial tension of 15 dyn/cm. Sieve Tray Top View
Leeend C o a l e s c i n g Mesh
w
R e l i e f Valve
EbB H 0
8
Metering Valve Regulating Valve
I
Rupture D i s c P r e s s u r e Regulator
Vent Aqueous Feed
ps 1
I I
i$1
Brass Downcomer (Brass)
0.318cm OD
Sieve Holes
+
2.54cm
10.1 c c / s
4
Downcomer Cross-Sectional View
Carbon Dioxide Solvent
l l
OD = 0.635cm ID = 0.472cm
Vent
&@I?-
R a f t i n i t e Out
T
Figure 1. Supercritical extraction apparatus.
This paper covers only the high-pressure studies. The physical properties of the systems used are summarized in Table I. The large difference in the value of distribution coefficients between ethanol and 2-propanol is due to the higher polarity of the short-chain alcohol. The polar ethanol solute is less soluble in carbon dioxide and more soluble in water than 2-propanol and therefore has a smaller distribution coefficient in the C02/water system. These distribution coefficients were obtained experimentally by using a continuous flow method and show excellent agreement with those obtained by Gilbert (1985) and Kander (1986). Interfacial tension measurements by Hough et al. (1959) for the C02/water system were used to approximate the value of this property for our test conditions. A more accurate estimate of this property for the ternary systems was not available, but observations of the mean drop diameter in our experiments permitted a back-calculation for the interfacial tension. Values obtained in such a manner varied from 15 to 23 dyn/cm. Diffusion coefficients in the C02 phase were estimated by using the Wilke-Chang (1955) equation and applying an empirical correction factor of 0.87 to the predicted values. This factor was obtained by comparing the results of the Wilke-Chang equation with published values of diffusion coefficients for other organic compounds in supercritical C02 (Paulaitis et al., 1983).
Experimental Work A simplified flow diagram of the experimental equipment is shown in Figure 1. Figure 2 illustrates the ge-
+I+ 0.318cm
Figure 2. Sieve tray with downcomer. Table 11. Extraction Column and Sieve-Tray Geometries column diameter, cm 2.58 height, cm 121.9 cross-sectional area, cm2 5.217 sieve tray no. of trays 5 tray spacing, cm 10.16, 15.24 no. of holes 5 sieve hole diameter, cm 0.318 hole area, cm2 0.396 hole area/column area 0.0758 pitch/hole diameter ratio 2.85 downcomer diameter, cm 0.472 downcomer area, cm2 0.175 downcomer area/column area 0.0335 downcomer length, cm 8.57
ometry of the tray that was used in the sieve tray studies. This geometry represents a conventional,small-scale liquid extraction sieve tray, and its characteristics are summarized in Table 11. The only difference between the sieve tray and the spray configurations is the absence of trays in the spray column. Light- and heavy-phase fluids were fed to the column by means of positive displacement pumps. The flows were controlled by pump displacement and were monitored with high-pressure mass flow meters. The extraction temperature was controlled through heat exchange in an im-
2088 Ind. Eng. Chem. Res., Vol. 26, No. 10, 1987
mersion bath. In all cases, the temperature of both streams entering the column was the same. Temperature gradients along the column were minimized by wrapping it with heating tape and Fiberglas insulation. The operating pressure of the column was controlled by means of a back-pressure regulator, and the interface level in the column was controlled n anually with a micrometering valve operating on the raffinate stream. The extraction column used in the experiments was 2.54-cm inside diameter, fabricated from 7.62-cm X 7.62cm stainless steel bar stock and bored to the required diameter. Twelve pairs of 1.75-cm-diameterwindows were located on opposite sides of the column to permit observation of the action above and below the trays as well as the location of the interface. The inner bore of the column was smooth and circular. Sieve trays were assembled on a threaded rod which was passed through the center of the trays to f 1.m a cartridge. A Viton “0”ring around each tray provided a seal between the tray and the column wall to prevent bypassing of the process streams. Small Teflon coalescing meshes were positioned a t either end of the column to aid in disengagement and prevent entrainment into the sample points. Two tray spacings were used, 10.16 and 15.24 cm. For both spacings, five trays were employed, and in each case the distributors were positioned at the same distance from the top and bottom trays. The length of the downcomers was kept the same at the two tray spacings. For the spray column, contacting heights of 76.2 and 50.8 cm were used for the SC/I/W and SC/E/W systems, respectively.
0
P c
A
-
0 016
Experimental Results and Discussion In order to confirm the equilibrium data available in the literature, a continuous flow method was devised that used the same test column described above. When the system was run countercurrently a t solvent-to-feed ratios well below the minimum, a “pinch” point was developed at the top of the column where the exiting extract stream approached equilibrium with the feed. By altering the feed compositions for different runs, various extract compositions were obtained and an equilibrium curve was constructed. Figure 3 applies to the supercritical C02/2-
C
*’
? 0 0
0
/
?./’
0.008
111 L r
0.004
t
/ Operating Line
I
0.000
0.000
0.020
0.060
0.040
Liquid Phase (weight fraction
0.080
0.100
IPA)
Figure 3. Equilibrium measurements: supercritical carbon di. oxide/2-propanol/water system at 40 O C and 102.0 atm. 0.010
0
-
Thio Work
t Gilbert
(1985)
I
0.008
5
p.
0.006
5
0.004
I
-
i /’ 00
I
L
, , 0
0.002
n /
Experimental Procedure Details on the experimental procedure are available in the Lahiere dissertation (1986). Measurements were Iiken after steady state had been achieved as determined by constant exit stream compositions, steady flows, and stable interface level. The solvent phase was always dispersed so that COz drops would rise through the aqueous phase and the main interface would be located above the top tray. The compositions of the exiting streams were determined by gas chromatography using dual-thermal conductivity detectors; the liquid stream was analyzed “offline” by syringe injection, and the supercritical extract stream was analyzed by diverting it directly to the sampling valve in the heated chromatograph oven. Phase separation within a flowing sample was prevented by heating the line to the sampling valve. Since the system operated in a “once-through’’ mode, analysis of the feed was only required prior a t the beginning of the run, and it was assumed that the carbon dioxide (industrial grade, 99.8% purity) from the cylinders was free of solute. A typical run required 45-60 min to achieve steady state, depending on the flows employed. Composition readings were taken every 5 min, and flow rates were logged every minute. After reaching steady state, a run was continued at the preset conditions for 20-30 min before a condition was changed.
Thlo Work Kander (1986) Operating Cine
4
0.000
, , ,
, /
0.000
0.020
0.040
Aqueous Phase
0.060
0.lW
0.080
(welght fraction ethanol)
Figure 4. Equilibrium measurements: supercritical carbon dioxide/ethanol/water system at 35 ”C and 102.0 atm. 0.020
1
I points:
Experimental
/
0.000
I
I
0.000
0.020
0.040
Aqueous Phase
I
0.060
I
0.080
0.100
(weight fraction IPA)
Figure 5. Equilibrium measurements: near-critical carbon dioxide/2-propanol/water system at 25 “C and 81.6 atm.
propanol/water system (SC/I/W) and shows the intersection of the operating line with the equilibrium line for a given feed composition and solvent-to-feed ratio (below minimum). It also shows that excellent agreement with published data was obtained by using this flow method. Figures 4 and 5 show similar results for the systems supercritical CO,/ethanol/water (SC/E/W) and liquid C02/2-propanol/water (LC/I/W). Some results of the mass-transfer efficiency tests for the spray column arrangement are shown in Figure 6 in raw form as alcohol recovery fractions. The much higher recoveries experienced for 2-propanol are attributed to the higher distribution coefficient. These data were reduced
Ind. Eng. Chem. Res., Vol. 26, No. 10, 1987 2089 1.0
I
1
u.1uu
.
0.060
a
5
3
0.7
1
t
0.040
SClliW SClliW SCiEiW
+ A
Uc Uc Uc
i i
0.034 cmls 40 C 0.048 Cmis 40 C 0.048 cm/s 35 C
F
ct
* *
0.020
102.0 atm Spray Column
1.o
0.6
0.2
Dispersed
1.4
Phase Velocity, cmlsec
Figure 8. Overall volumetric mass-transfer coefficients for supercritical extraction conditions
."-
. ^ I
0 SCillW
&
40 C 102.0 atm
h:/*
0.9 -
0.8
20.0
/
I
*-*--*-*I
/"/ +
-
I
0.0
5.0
/"/"
/"
I
0.7 -
/"'
+
LCiiiW
25 C
0
SCiiiW
40 C
102.0 alm
A
SCiEiW
35 C
102.0 atm
10.0
81.6 atm
15.0
20.0
25.0
Olspersed Phase Velocity (cmls)
Figure 7. Mass-transfer efficiency, expressed as height equivalent for supercritical extraction in the to a theoretical stage (HETS), spray column. Vcconstant at 0.048 cm/s.
to heights equivalent to a theoretical stage (HETS) and are shown in Figure 7 . The HETS value relates to the more fundamental one of height of a transfer unit (HTU) through eq 1 and 2. It can be seen that the value of the distribution coefficient (m) still affects the value of HETS, thus making it an unreliable measure of mass-transfer efficiency. HETS = HTUJln X/(X - l ) ] (1) = mQdPd/(QcPc)
(2)
In order to evaluate the mass-transfer efficiency of the spray column with the equilibrium effects removed, the data were reduced to overall volumetric mass-transfer coefficients as follows KO@= u d / H T u d
SoiventiFeed Weight Ratio
Figure 9. Fractional recovery of solute under supercritical and near-critical conditions in the sieve tray column. Uc constant at 0.048 cm/s; tray spacing = 10.16 cm.
0.60
c
A A
A
e
+ * E*
c
..z
0.40
"
b c
8 0 4 A 0.00
40 C 102.0 atm 25 C 81.6 atm 35 C 102.0 atm
SClllW
LClliW SClEiW
1
I
0.0
0.2
,
I
,
I
0.4
0.6
0.8
1.0
I
1.2
I
1.4
1.6
(3) Dispersed Phase Velocity (cm/s)
and are shown in Figure 8. The points clearly fall along different lines and show Kdu to be a function of the phase velocities. If the overall mass-transfer coefficient is considered to represent the combined resistance to mass transfer from the two phases, KdU =
[
e] -1
+
(4)
it follows that the term m/ k, seems to have an influence on mass transfer. This is demonstrated by the fact that the overall mass-transfer coefficient data for the extraction of ethanol and those for the extraction of 2-propanol show a significant difference under equivalent conditions. Thus,
Figure 10. Overall stage efficiency for supercritical and near-critical conditions in the sieve tray column. U, constant at 0.048 cm/s; tray spacing = 10.16 cm.
resistance to mass transfer is present in both the dispersed supercritical phase and the continuous phase. This is an important finding since the value of the coefficient in the supercritical phase should be larger than the equivalent one for the continuous phase because of lower viscosities and higher diffusion coefficients. The small values of the distribution coefficients appear to overcome this effect. Results of the mass-transfer efficiency tests in the tray column are shown in raw form in Figure 9 for the 10.16-cm tray spacing and for the various sytems tested. These data
2090 Ind. Eng. Chem. Res., Vol. 26, No. 10, 1987 1 .oo
1 Tray Spacing
O”O 0.60
1
E
7
15.24 cm
/
I
a 0.50
iC
5
0.40
0.30
0.40
0
0.20 0.10
0
- +
Uc Uc
0.00
= =
0.034 cmis 0.048 cmis
I
0.20
I
I
I
0.40
0.60
0.80
0.00
0.00
0.20
1.oo
0.00
0.20
0.40
0.60
0.80
1.oo
Experimental Efficiency
Figure 13. Parity plot for overall efficiency in the sieve tray column. (*) Data for 10.2-em column, by Rocha et al. (1986).
Dirporred Phase Velocity (emir)
Figure 11. Effect of continuous phase flow rate on overall stage efficiency in the sieve tray column. SC/I/W system a t 40 OC and 102.0 atm; tray spacing = 15.24 em. 100
, 0 +
0
Spray Sieve Tray Reschig Rings (Rathkamp, 1986)
-&-AAI
I
I
I
Dispersed Phase Velocity (cmis)
Figure 12. Efficiency of different column internals: S C / I / W system at 40 “ C and 102.0 atm.
were reduced to overall column efficiency data and are presented in Figure 10. There appears to be a slight increase in the overall efficiency as the velocity of the dispersed phase increases. The effect on efficiency of the velocity of the continuous phase is minimal, as shown in Figure 11. This can be explained by the apparent significant resistance to mass transfer residing in the dispersed phase. Values of overall efficiencies obtained were in the range of 40-60% at the tray spacings used and are higher than those typically found in liquid/liquid extraction. Values ranging from 6% to 16% were obtained in the same column for a conventional extraction system (toluene/acetone/ water) under similar flow conditions. Also, comparisons showed no difference in efficiency between liquid (near-critical)and supercritical COPfor both spray and tray columns. In Figure 12, the performances of the spray and tray columns are compared; this figure also includes some of the data obtained by Rathkamp (1986) for the same column but packed with 6.2-cm Raschig rings. The volumetric mass-transfer efficiency of the spray column appears to be nearly equal to that of the tray column. This behavior can be explained by noting that the small column diameter appeared to minimize backmixing effects; also, since most of the mass transfer occurs during drop rise,
the contribution of several drop formation steps offered by the trays is slight. In a larger column, one would not expect this behavior. The effect of backmixing would lower the efficiency of the spray column much more than it would for the tray column. The efficiency of the packed column is greater than that of the tray or spray column because of increased residence times for the dispersed phase as well as a higher interfacial area for mass transfer. However, the flows used in the packed column experiments were lower than those for the spray and tray columns as dictated by the limited throughput capacity of the packed column.
Modeling of Experimental Results One of the purposes of this work was to establish the applicability of mathematical models for mass transfer efficiency, developed for conventional liquid-liquid extraction, to supercritical extraction operations. The appropriate models should apply if the effects of physical properties are correctly accounted for, since the fluid dynamics of a process extracting a solute using a dense supercritical fluid are inherently the same as those encountered in extraction with an immiscible liquid. The model selected for evaluation represents a slight modification of the one published by Rocha (1984) and Rocha et al. (1986). It is composed of individual modules for predicting hydraulic parameters, mass-transfer coefficients, and Murphree and overall efficiencies. These modules have been developed for liquid-liquid extraction in spray and sieve-tray contactors. All the different mass-transfer sections or regimes that occur between the drop formation on a tray and the coalescence under the tray immediately above are accounted for in the model. Table I11 shows the equations used in the present work; variations from the Rocha model appear in eq 9,13, and 14 and are due to the work of Seibert (1986). For the systems studied, the model generally underpredicted overall efficiencies but provided a reasonably good fit to the data as shown in Figure 13. No correlation factors were used to modify the model. Some data for liquid-liquid extraction systems obtained by Rocha et al. for several interfacial tensions are included in Figure 13 for comparison purposes. Some of the data for a tray spacing of 15.24 cm fall outside the range of confidence of the model. The reason for this has not been determined; it is possible that it is caused by some experimental error in the data. Nevertheless, the applicability of the model appears to be clear, especially since the general trend of efficiency underprediction in a small column such as the one used in this
Ind. Eng. Chem. Res., Vol. 26, No. 10, 1987 2091 Table 111. Mass-Transfer Model Relationships overall efficiency (Lewis, 1936)
Eo =
Murphree efficiency Emd
-
1))
In h 1.1KfdAf K,dA, = Qdpd + 0.5K,dA, + 0.1KfdAf
overall coeff, drop formation Kfd
In [ I +
=
'c ]
[
-1
individ. coeff for drop kf, = 1.3p,[D,/(tm)l05 formation, continuous phase (Higbie, 1935; Popovich et al., 1964) individ. coeff for drop k f d = 1.3pd[Dd/(tf*)lo5 formation, dispersed phase (Higbie, 1935; Popovich et al., 1964) time of drop formation tf = N0Vp/($ interfacial area for drop Af = Nard, formation overall coeff, dispersed phase -1
transfer coefficients. This is caused by low distribution coefficients. Overall column efficiencies in supercritical extraction tend to be higher than those found in liquid-liquid extraction. This is caused by significantly higher values of the mass-transfer coefficients, particularly for the supercritical or near-critical phase. Mass transfer during drop rise appears to contribute the most to the total mass transfer when using sieve trays, not unlike in conventional liquid-liquid extraction; in the absence of backmixing, the volumetric efficiency of a spray column is therefore very close to that of a tray column. Finally, it seems that efficiency models developed for liquid-liquid extraction are applicable to supercritical or high-pressure extraction as long as they have a mechanistic base. Work is now under way to assess the effect of column diameter as well as to determine the effect of other internals such as packings.
Acknowledgment individ. coeff for drop rise, k,, = 0.698p,(D,/dp)[p(,/ (pJI,)]O continuous phase (Seibert, [p,U,d,/~,]~~(l - @) 1986) individ. coeff for drop rise, 0.0O375pdUs dispersed phase (Handlos h d = 1 + (Pd/Pc) and Baron, 1957) when bd/(PdDd)lo5 < 6,1 (/ld/l*c) individ. coeff for drop rise, O.O23pdU, dispersed phase (Laddha k r d = and Degaleesan, 1978) bd/(PdDd)lo5 when interfacial area, drop rise
[kd/bdDdIo5
+
X
,
6,1
b d / d
A, = (64/dp)(Ac01 - Adorv)(Ht - h,)
Hydraulic Relationships for Model drop diameter (Seibert, d, = 1.15MF[~/(Apg)]~~' 1986) where MF = 1.0 for transfer, continuous to dispersed MF = 1.0-1.8 for transfer, dispersed to continuous operational holdup (Seibert, q4 = u d / (Ue,,e-('9203) 1986) where
slip velocity (Thornton, 1956)
4Apdg
u w = ( 3cDPc -)
u = -u d+ - uc
O5
9 1-9 height of coalesced layer Pdu2 (Major and Hertzog, 1955; h, = 0.501Pilhofer and Goedl, 1977) APg
Reynolds number
(
-
Re = douoPd/Pd
work can be beneficial as to the use of the model for larger columns where the actual efficiencies will be lower.
Conclusions Experimental studies were conducted to establish and quantify the parameters that affect mass-transfer efficiency in countercurrent column contadors of the spray and sieve tray types. Even though the studies were done in a small-scale column, some of the results should be applicable to larger size extractors; the matter of effective scale-up is yet to be addressed fully. Significant resistance to mass transfer in the highpressure extraction of 2-propanol and ethanol from water with COz resides in the COz phase in spite of high mass-
This work was funded by The Separations Research Program at the University of Texas at Austin. J. L. Bravo and Dr. J. L. Humphrey provided valuable advice and counsel during several stages of the work.
Nomenclature a = effective interfacial area, cm2/cm3 A = interfacial area, cm2 Acol = cross-sectional area of column, cm2 Adow = cross-sectional area of downcomer, cm2 CD = drag coefficient, dimensionless do = hole diameter, cm d = drop diameter, cm If = diffusion coefficient, cm2/s E m d = Murphree stage efficiency, dimensionless Eo = overall tray efficiency, dimensionless g = acceleration due to gravity, 980 cm/s2 h, = height of the coalesced layer, cm Ht = plate spacing, cm HTUd = height of an overall mass-transfer unit, dispersed phase basis, cm HETS = height equivalent to a theoretical stage, cm k = individual phase mass-transfer coefficient, cm/s K = overall mass-transfer coefficient, g/(s.cm*) Kd = overall mass-transfer coefficient based on the dispersed phase, cm/s m = distribution coefficient, or slope of the equilibrium curve, (weight fraction of solute in dispersed phase)/ (weight fraction of solute in continuous phase) MF = correction factor for direction of solute transfer, dimensionless MW = molecular weight No = number of perforations per plate P = pressure, atm Q = volumetric flow, cm3/s Re = Reynolds number (dOUOPd//ld), dimensionless RF = recovery fraction (1 - X,/Xf), dimensionless T = temperature, OC tf = time for drop formation, s U = superficial velocity of phase, cm/s U,,, = velocity through downcomer, cm/s U, = velocity through sieve hole, cm/s Us = slip velocity, cm/s U,, = slip velocity without drop interactions, cm/s V = drop volume, cm3 $ = mass fraction solute in feed X , = mass fraction solute in raffinate Greek Symbols Ap =
phase density difference, g/cm3
X = extraction factor [ (mQdpd/(Q,p,)]
I n d . Eng. Chem. Res. 1987,26, 2092-2098
2092 I.(
= viscosity, CP (0.01 g/(cms))
constant, 3.1416 p = density, g/cm3 CJ = interfacial tension, dyn/cm 4 = operational holdup, dimensionless r =
Subscripts
c = continuous phase
d = dispersed phase f = formation r = rise (or fall) s = superficial cross-section basis S y s t e m Identification A = acetone
E = ethanol I = 2-propanol LC = carbon dioxide, near-critical or liquid SC = carbon dioxide, supercritical T = toluene W = water Registry
No. COz, 124-38-9; H,CCH,OH,
64-17-5; H 3 C C H -
(OH)CH,, 67-63-0.
Literature Cited Brunner, G., Presented at San Francisco AIChE Meeting, Nov 1984. Brunner, G.; Kreim, M. K. Ger. Chem. Eng. 1986, 9, 246. Eisenbach, W. 0. Proc. Am. Chem. SOC.1985, 30(3), 206. Gilbert, M. I,. M.S. Thesis, The University of Delaware, Newark, 1985. Handlos, A. E.; Baron, T. AICHE J . 1957, 3, 127. Higbie, R. Trans. AZChE t935, 31, 365. Hough, E. W.; Heuer, G. J.; Walker, J. W. Pet. Trans. AZME 1959, 216, 469. Johnston, K. P. In Encyclopedia of Chem. Tech., 3rd Ed.; Wiley: New York, 1984; Vol. 3, p 872. Kander, R. G. Ph.D. Dissertation, The University of Delaware, Newark, 1986.
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Received for review February 9, 1987 Revised manuscript received June 30, 1987 Accepted July 23, 1987
Use of Bifurcation Map for Kinetic Parameter Estimation. 1. Ethane Oxidation Michael P. Harold* and Dan Luss University of Houston, Department of Chemical Engineering, Houston, Texas 77004
Kinetic and transport parameters may be estimated from a set of experimental ignition and extinction points, i.e., a bifurcation map. Initial estimates of some of the parameters can be obtained from a preliminary analysis of temperature rise on the extinguished branch. The technique was used to fit the bifurcation points for ethane oxidation on a single Pt/A1,0, pellet. T h e dependence of the gas density on ambient temperature was found to have an important impact on the multiplicity features. T h e fit of data removed from the ignition or extinction points was not as good as that of the singular points. A method is presented for overcoming this limitation. It is well-known that steady-state multiplicity may occur in chemically reacting systems. The qualitative features of the multiplicity patterns may be used to infer the functional forms of the rate expression (Harold et al., 1987a,b). Moreover, the ignition and extinction points are sensitive functions of the kinetic parameters and can be used for kinetic model identification and fit. Hiam et al. (1968),Schwartz et al. (1971),and &der and Weller (1974) determined the activation energy of several reactions from measurements of the ignition points. Jiracek et al. (1971)
* Present address: Department of Chemical Engineering, University of Massachusetts, Amherst, MA 01003. 0888-5885/87/2626-20!32$01.50/0
used bifurcation diagrams, exhibiting multiplicity, to check the validity of a rate expression for hydrogen oxidation. Beskov et al. (1976) used ignition and extinction conditions to fit kinetic parameters for ammonia oxidation. Recently, Herskowitz and Kenney (1983) and Dauchot and Dath (1984) used ignition points to fit a kinetic expression. Lyberatos et al. (1984) suggested the use of bifurcation caused by periodic forcing for kinetic parameter fitting. Conrad and Treguer-Seguda(1984) used bifurcation points for parameter estimation of immobilized enzyme systems. The purpose of this study is to examine the advantages and disadvantages of estimating kinetic parameters from a set of experimental ignition and extinction points. 1987 American Chemical Society
