1246
Ind. Eng. Chem. Res. 1989,28, 1246-1250
Axial Dispersion of Supercritical Carbon Dioxide in Packed Beds Chung-Sung Tan* and Din-Chung Liou Department of Chemical Engineering, National Tsing Hua University, Hsinchu, Taiwan 30043, Republic of China
The axial dispersion coefficients under supercritical operation in a packed bed were measured by injection of a pulse of methane into supercritical carbon dioxide. The experimental data showed that the axial dispersion coefficient increased with the interstitial velocity and the packed particle diameter. When the operation pressure increased and the operation temperature decreased, the axial dispersion coefficient increased. This trend may be due to the increase of the density and viscosity of the supercritical carbon dioxide. The bed length offered a negligible effect when it exceeded a certain value, while the ratio of bed diameter to particle diameter was larger than 10. Axial dispersion of a gas or a liquid has been extensively studied in the past (McHenry and Wilhelm, 1957; Ebach and White, 1958; Liles and Geankoplis, 1960; Miller and King, 1966; Edwards and Richardson, 1970; Wakao et al., 1974; Scott et al., 1974; Kubo et al., 1978; Han et al., 1985; Gunn, 1987), but for a supercritical fluid, no information, that we know of, is available in the literature. Supercritical fluid technology has received widespread attention in chemical, petrochemical, food, and pharmaceutical industries. In many applications such as the purification of organic chemicals, the removal of caffeine from coffee beans and tea leafs, the regeneration of activated carbon and catalyst particles, and the extraction of oils from oil shales, this technology has been recognized to be more effective and efficient than the conventional separation technologies (Paulaitis et al., 1983; Rizvi et al., 1986, Tan and Liou, 1988; Triday and Smith, 1988). Under supercritical operations, it is believed that the transport mechanisms would be similar to those under gaseous and liquid operations; therefore, the axial dispersion may play an important role in a packed bed. Though the behavior of a supercritical fluid lies between those of a gas and a liquid, the interpolation of axial dispersion coefficients of gases and liquids to supercritical states still remains questionable. Hence, the main objective of the present study is to experimentally measure the axial dispersion under supercritical operation. For gases and liquids, factors influencing axial dispersion in a packed bed have been discussed in the literature. Scott et al. (1974) observed that the effect of the bed length on axial dispersion could be neglected when the ratio of bed length to particle diameter was larger than 50. Han et al. (1985) proposed a criterion,
which, if satisfied, indicated that the axial dispersion would not vary with the bed length. Several investigators also found that the axial dispersion would increase with the flow rate and particle size (Liles and Geankoplis, 1960; Schneider and Smith, 1968; Fu et al., 1986). To examine whether the above mentioned factors offer similar effects on axial dispersion of a supercritical fluid is the other objective of this study. Experimental Section To study axial dispersion in a packed bed experimentally, it is common to measure the outlet response resulting from an inlet disturbance. The disturbance may be a step or pulse function or a sine-wave function. In this study,
the pulse function was used, and carbon dioxide was employed as the carrier and methane as the tracer. Figure 1shows the schematic setup of the apparatus in which all lines were made of 0.63-cm-0.d. Carbon dioxide of 99.7% purity was compressed to a surge tank by a diaphragm compressor (Superpressure Inc.). The range of operation pressure varied from 60 to 140 atm. The pressure in the fixed bed was read by a pressure indicator (Robertshaw Co.) and was maintained within 1.0% deviation from the desired value. A preheating coil of 110-cm length was immersed in a constant-temperature bath whose accuracy was within 0.5 K. This length was found long enough to make the temperature of the carbon dioxide equal to that of the bath through the use of a thermocouple inserted in the packed bed in the preliminary runs. The temperature range varied from 308 to 328 K. The methane with the same pressure as the carbon dioxide flowed through a six-port sampling valve (Rheodyne Inc.), which was also immersed in the constant-temperature bath. When the measurement started, this six-port sampling valve was switched to let the carbon dioxide pass through the sampling loop containing 20 pL of methane and to carry the pulse toward the packed bed. The inside diameter of the bed was 2.12 cm, which was packed with glass beads. Three diameters of the glass beads, 0.05,0.10, and 0.20 cm, were used in this study, which corresponded to D l d , of 42, 21, and 10, respectively. When this ratio is larger than 10, it is believed that a uniform distribution of the fluid can be achieved in the bed if the length is large enough (Tan and Wu, 1988). The outlet concentration of the methane was detected by a FID gas chromatograph (Varian 3700). This was done by first expanding the outlet fluid by a metering valve and then passing the fluid through the GC which was equipped with a sampling valve. The samples were taken every 5 s until no methane was detected. The flow rate of the carbon dioxide in the packed bed was determined by dividing the total volume of the carbon dioxide measured by a wet test meter by the operation period. The accuracy for the volume measurement was within 1.0%. Model Equations The mass balance of the methane in the packed bed may be written by
For a pulse function, the solution at the outlet is available (Hill, 1979) and can be written by
C=
* To whom
correspondence should be addressed. 0888-5885/89/2628-1246$01.50/0
ML V(4aEt)'I2
0 1989 American Chemical Society
-
( L - Ut)2 4Et
]
(3)
Ind. Eng. Chem. Res., Vol. 28, No. 8, 1989 1247
0 CO2 Cylinder 0 Regulator
@ Preheating Coil
0
@ Filter
Pressure Indlcotor @ Six-Port Sampling valve
@ Compressor Q Surge Tank
8 0
@ Heating Tape @ Gas Chromatograph @ wet ~~~t et^^
I n t e r s t i t io1 Velocity
@ CHI, Cylinder
Packed Column Metering Valve
8 Constant Temperature Bath
Figure 1. Schematic diagram of the apparatus used for measurement of axial dispersion.
,
cm/sec
Figure 3. Effect of pressure on axial dispersion a t 308 K and d, = 0.05 cm. I
//
n
l L O a t m , 3 2 8 K . dp=O.lOcm ,L:295cm, u.0.02 c m l s e c A 0
-
_____
o.ooo11 0
Figure 2. Comparison of the response data with the model and illustration of the reproducibility tests.
Levenspiel and Smith (1957) also reported the moment expressions as JmCt dt
U
CY2
=
L
(2)
0.002
1
0.005
I
0.01
I
0.02
1
0.05
I
010
I n t e r s t i t i a l V e l o c i t y , cm /sec
T i m e , sec
P1 =
0001
(4)
Lacdt
L m C t 2d t 2
- P1
(5)
f m Cdt
JO
The axial dispersion coefficient E thus can be estimated either by fitting the experimental data with eq 3 (real-time method) or by using eq 4-6 (moment method).
Experimental Results and Discussion In this study, the following operation variables were varied to observe their effects on the axial dispersion: flow rate, pressure, temperature, particle size, and bed length. Several runs at different combinations of the operation variables indicated that the measured axial dispersion coefficients by the real-time method and the moment method were quite consistent with a maximum deviation of less than 5.0%. This illustrates that either of the methods can be used to estimate the axial dispersion coefficient under supercritical operations. A typical example of the comparison of the response data and the
Figure 4. Effect of pressure on axial dispersion a t 308 K and d, = 0.1 cm.
model prediction using the real-time method is shown in Figure 2 from which it can also be observed that no significant tailing occurred in the experiment. The mass of the methane flowing out of the bed was checked against the injection amount by integrating the response curve at the outlet with respect to time. The agreement was found to be excellent, with a maximum deviation of less than 1.5%. The reproducibility tests were also performed in this study, which showed that the exit concentrations could be reproduced within 7.0% and the calculated axial dispersion coefficients within 3.0%. One of these tests is illustrated in Figure 2. If the Peclet number is defined as d,u/E, the literature has reported that it is usually less than 1.0 for liquids and larger than 2.0 for gases (Ebach and White, 1958; Fu et al., 1986; Gunn, 1987; Hill, 1979). The present measurements showed that the Peclet number lies between 0.60 and 2.7 for all combinations of operation variables. Since it has been realized that the behavior of a supercritical fluid lies between those of a gas and a liquid, the measured values in the present study seem reasonable. The effect of pressure on axial dispersion is illustrated in Figures 3-6. When the pressure was varied from 60 to 140 atm, the axial dispersion coefficient increased with pressure. Since at 60 atm the operation phase belongs to the gas phase, it may be concluded that the dispersion coefficients in the supercritical phase are larger than those in the gaseous phase. The axial dispersion in a packed bed may be a combination of the effects of molecular diffusion and convection, if we assumes that the molecular diffusion decreases with increasing the pressure, as predicted by the Wilke-Chang equation. The measured results suggest that
I
1248 Ind. Eng. Chem. Res., Vol. 28, No. 8, 1989
: 0.0100
0.001
0.002
I
I
I
I
I
0.005
0.01
a02
0.05
010
Interstitial
~
A
308K
Velocity, c m /sec
I n t e r s t i t i a l Velocity, c m /sec
Figure 5. Effect of pressure on axial dispersion at 308 K and d, = 0.2 cm.
I
100otm. dp:O.lcm, Lz29.5cm
Figure 8. Effect of temperature on axial dispersion at 100 atm.
~~
328K, d p = 0 2 0 c m , L: 2 9 5 c m
0.001
0002
I
I
0.005
0,Ol
I 0.05
I
Interstitial
0.02
I
I ai0
0,00OlL/ 0.001
1
0.002
I
0.005
1
0.01
lnterstitlol
Velocity, c m / s e c
I
I
0.05
0.02
I
010
I
Velocity, cm/sec
Figure 9. Effect of temperature on axial dispersion at 120 atm.
Figure 6. Effect of pressure on axial dispersion at 328 K and d, = 0.2 cm.
l L 0 a t m . dp ZOlOcm. L:29.5cm 318K
A
308K
/
O
O
n
;I f
a
Q3
0.0005
8 3 A
00001 O
0001
D
B
o
0002
A
m
0005
001
2
002
005
W
010
Interstitial Velocity cm/sec
0.001
I
I
I
1
I
0.002
0.005
0.01
0.02
0.05
I 010
I n t e r s t i t i a l Velocity, c m / s e c
Figure 7. Effect of temperature on axial dispersion at 60 atm.
Figure 10. Effect of temperature on axial dispersion at 140 atm.
the contribution by the convection is more important under supercritical operation. Figure 7 shows that, when the operation was in the gas phase, the dependence of the axial dispersion coefficient on temperature was not as distinguished. But when the pressure was raised to the supercritical phase, the dependence became more pronounced over the temperature range 308-328 K, and the axial dispersion coefficient decreased as the temperature increased, which is illustrated in Figures 8-10. This dependence is again opposite to that of the molecular diffusion. Hence, the molecular diffusion might not play an important role for the axial dispersion as compared with the convection. From Figures 3-10 it can also be seen that the axial dispersion coefficient varied linearly with the interstitial velocity in the logarithmic scale. The slope for all com-
binations of operation variables was shown to be a constant of 1.0 (fO.l). For gases and liquids, the increase of axial dispersion with flow rate was also observed (Ebach and White, 1958; Liles and Geankoplis, 1960; Fu et al., 1986). Figures 11-13 show that the axial dispersion coefficient increased with the particle diameter when the latter varied from 0.05 to 0.20 cm. This trend is similar to those for gases and liquids, as mentioned before. The effect of the bed length on the axial dispersion coefficient is shown in Figure 14. It can be seen that, when the bed length was larger than 13.0 cm, the axial dispersion was no longer dependent on the bed length. This observation illustrates that the criterion suggested by Han et al. (1985), i.e., eq 1, can be also applied to the supercritical carbon dioxide. It should also be noted that the ratio of the bed diameter to the particle diameter employed in this
Ind. Eng. Chem. Res., Vol. 28, No. 8, 1989 1249 308K, 100otm, dp.OIOcm 10.2cm
0.0050
:
0,001
0,002
I
I
I
I
I
Q005
0.01
0.02
0.05
OJO
s
1
*
19.5Cm 29.5cm
- 4%A-
I
I n t e r s t i t i o I Vel oc It y , c m / sec
i n t e r s t i t io1 Velocity. c m /sec
Figure 11. Effect of particle size on axial dispersion at 120 atm and
318 K.
Figure 14. Axial dispersion at various bed lengths.
3.0
1
0
t
0.5 0.3L 0.3
0
0
I
I 3.0
1
I
1.o
0.5
2.0
I
1
50
10.0
I
20.0
1
30.0
Reynolds Number, dpUP/P I n t e r s t i t i a l Velocity, c m /sec
Figure 12. Effect of particle size on axial dispersion at 140 atm and
318 K.
Figure 15. Plot of Pe versus Re. Table I. Density and Viscosity of Carbon Dioxide at Different Temperatures and Pressures
308 K
P, atm 60 80 100 120 140 g/cms.
0.0001
0,001
I 0.002
I
o.005
I
0.01
I
a02
I
0.05
om1
I
I n t e r s t i t i a l Velocity, c m / s e c
Figure 13. Effect of particle size on axial dispersion at 140 atm and
308 K.
study was at least 10, since below this value it is difficult to achieve a uniform distribution of a supercritical fluid in a packed bed according to the observation by Tan and Wu (1988). Table I lists the density and viscosity of carbon dioxide at different operation temperatures and pressures. Since the mole fraction of methane in carbon dioxide was quite small, the density and viscosity of the carbon dioxide and methane mixture could be regarded to be the same as those of the pure carbon dioxide. From Table I and Figures 3-10, it can be seen that the axial dispersion coefficient increases with the density and viscosity. Through this observation, the effects of pressure and temperature on axial dispersion under supercritical operations may be
318 K
328 K -
pa
pb
pa
pb
pa
pb
0.31 0.44 0.71 0.75 0.80
1.82 2.98 5.54 6.45 6.84
0.19 0.26 0.50 0.60 0.70
1.82 2.21 3.70 5.21 5.91
0.16 0.21 0.35 0.48 0.60
1.84 2.08 2.67 3.83 4.79
g/(s.cm) x io4.
illustrated in terms of density and viscosity. In order to see their effects on axial dispersion as well as the particle size and interstitial velocity, we tried to use the dimensionless groups first. But from Figure 15 it can be seen that a simple correlation in terms of the Peclet and Reynolds numbers was hard to obtain. Several other forms of the correlation in terms of the Peclet, Reynolds, Schmidt, and E p / p dimensionless groups, such as suggested by Edwards and Richardson (1970) and Gunn (1987), were also tested, but the regression analyses indicated that the average deviation was larger than 20% for all these forms. Two of these correlations are given as follows: Pe = 1.634Re0.265S~-O~919 E p / p = 1.304Re0.772
(7) (8)
The average deviations for eq 7 and 8 are 21 % and 31% , respectively. It appears that much work needs to be done to obtain a suitable equation to correlate these dimensionless groups. Nevertheless, an equation that does not contain those dimensionlessgroups was found to correlate the data quite well in this study, which is written as
1250 Ind. Eng. Chem. Res., Vol. 28, No. 8, 1989
E = 0.085U0.914dp0.388Pr 0.725PI0.676
(9)
This equation generates the average deviation -8.5% over the entire ranges of the present operations. Conclusions In this study, the axial dispersion under supercritical operation was measured by using the pulse technique. The value of the Peclet number was found to be in the range 0.6-2.7, which exists between those for liquids and gases. The numerical values of the axial dispersion coefficient were observed to depend on the density and viscosity of the fluid. When they increased, the axial dispersion coefficient also increased. It was also found that the axial dispersion coefficient increased with the particle diameter, while the ratio of the bed diameter to the particle diameter satisfied the criterion for a uniform distribution in the bed. When eq 1was satisfied, the bed length offered a negligible effect on the axial dispersion. The measured axial dispersion coefficient was found to vary linearly with the interstitial velocity in the logarithmic scale. The slope was observed to be about 1.0 for all combinations of operation variables. The dependence of the axial dispersion upon the Reynolds and Schmidt numbers and the physical properties and operation variables was correlated, through which it was found that the correlations in terms of the Peclet, Reynolds, and Schmidt dimensionless groups did not offer satisfactory prediction. This suggests that much work needs to be done to obtain a correlation applicable for supercritical fluids. Acknowledgment Financial support from the National Science Council of ROC is gratefully acknowledged. Nomenclature C = concentration of methane, mol/cm3 D = molecular diffusivity, cmz/s d, = particle diameter, cm E = axial dispersion coefficient, cm2/s L = bed length, cm M = injection amount, mol P = pressure, atm Pe = Peclet number, d , u / E Re = Reynolds number, d p u p / y S c = Schmidt number, y / ( p D ) t = time, s u = interstitial velocity V = void volume in packed bed Greek Symbols = defined in eq 5
CY
tb
= void fraction in the bed
y
= viscosity of COP,g/(cm.s)
y,
= defined in eq 4
viscosity of COPat the critical point, g/(cm.s) reduced viscosity of CO2, p l y c p = density of C 0 2 , g/cm3 pc = density of C02 at the critical point, g/cm3 pr = reduced density of COz, p / p c pc = pI =
Registry No. C02, 124-38-9.
Literature Cited Ebach, E. A.; White, R. R. Mixing of Fluids Flowing Through Beds of Packed Solids. AIChE J. 1958,4, 161-169. Edwards, M. F.; Richardson, J. F. The Correlation of Axial Dispersion Data. Can. J. Chem. Eng. 1970, 48, 466-467. Fu, C. C.; Ramesh, M. S. P.; Haynes, H. W. Analysis of Gas Chromatography Pulse Dispersion Data for the System n-Butanel Zeolite Nay. A E h E J. 1986, 32, 1848-1857. Gunn, D. J. Axial and Radial Dispersion in Fixed Beds. Chem. Eng SC~. 1987, 42, 363-373. Han, N. W.; Bhakta, J.; Carbonell, R. G. Longitudinal and Lateral Dispersion in Packed Beds: Effect of Column Length and Particle Size Distribution. AIChE J. 1985, 31, 277-288. Hill, C. G. Chemical Engineering Kinetics & Reactor Design; Wiley & Sons: New York, 1979. Kubo, K.; Aratani, T.; Mishima, A.; Yano, T. Identification of Axial Liquid Mixing Models for Packed Beds. J.Chem. Eng. Jpn. 1978, 1 1 , 234-236. Levenspiel, 0.;Smith, W. K. Notes on the Diffusion-Type Model for the Longitudinal Mixing of Fluids in Flow. Chem. Eng. Sci. 1957, 6 , 227-233. Liles, A. W.; Geankoplis, C. J. Axial Diffusion of Liquids in Packed Beds and End Effects. AIChE J. 1960,6, 591-595. McHenry, K. W.; Wilhelm, R. H. Axial Mixing of Binary Gas Mixtures Flowing in a Random Bed of Spheres. AIChE J. 1957, 3, 83-91. Miller, S. F.; King, C. J. Axial Dispersion in Liquid Flow Through Packed Beds. AIChE J . 1966, 12, 767-773. Paulaitis, M. E.; Krukonis, V. J.; Kurnik, R. T.; Reid, R. C. Supercritical Fluid Extraction. Rev. Chem. Eng. 1983, 1, 179-250. Rizvi, S. S. H.; Benado, A. L.; tollweg, J. A,; Daniels J. A. Supercritical Fluid Extraction: Fundamental Principles and Modeling Methods. Food Technol. 1986, June, 55-65. Schneider, P.; Smith, J. M. Adsorption Rate Constants from Chromatography. AIChE J . 1968, 14, 762-771. Scott, D. S.; Lee, W.; Papa, J. The Measurement of Transport Coefficients in Gas-Solid Heterogeneous Reactions. Chem. Eng. S C ~1974, . 29, 2155-2167. Tan, C. S.; Liou, D. C. Desorption of Ethyl Acetate from Activated Carbon by Supercritical Carbon Dioxide. Ind. Eng. Chem. Res. 1988, 27, 988-991. Tan, C. S.; Wu, Y. C. Supercritical Fluid Distribution in a Packed Column. Chem. Eng. Commun. 1988,68, 119-131. Triday, J.; Smith, J. M. Dynamic Behavior of Supercritical Extraction of Kerogen from Shale. AIChE J. 1988, 34, 658-668. Wakao, N.; Iida, Y.; Tanisho, S. Determination of Fluid Dispersion Coefficients in Packed Beds. J. Chem. Eng. Jpn. 1974, 7, 438-440.
Received for review September 9, 1988 Revised manuscript received March 20, 1989 Accepted April 18, 1989
