Ind.Eng. Chem. Res. 1993,32, 1717-1722
1717
Measurement of Effective Diffusivities of Toluene in Activated Carbon in the Presence of Supercritical Carbon Dioxide Ching-Chih Lai and Chung-Sung Tan' Department of Chemical Engineering, National Tsing Hua University, Hsinchu, Taiwan 30043, Republic of China
The effective diffusivities of toluene in supercritical carbon dioxide in activated carbon pellets were measured from the sorption curves of toluene in a spinning basket reactor a t temperatures 308,318, and 328 K and pressures up to 163bar. It was observed that the effective diffusivities at supercritical conditions were strongly dependent on carbon dioxide density but weakly dependent on temperature and the amount of toluene adsorbed. The equilibrium amount of toluene adsorbed on activated carbon was also obtained from the sorption rate experiment which could be correlated by the Toth isotherm expression.
Introduction
8
Because supercritical carbon dioxide has a high masstransfer rate and a good extractive power for organic compounds, it has been proven as an effective solvent for regenerating activated carbon loaded with organic compounds (Modell et al., 1979; DeFilippi et al., 1980; Kander and Paulaitis, 1983; Tan and Liou, 1988,1989). From the design point of view, the information on the adsorption isotherm,intraparticle diffusion, interphase mass transfer, and axial dispersion are essentialfor a regenerationprocess. The experimental data as well as the theory for adsorption equilibrium at supercritical conditions were reported recently (Tan and Liou, 1990; Wu et al., 19911, but the information on kinetic data, especially intraparticle diffusion, is still limited. To interpret the experimental data for the desorption of ethyl acetate from activated carbon with supercritical carbon dioxide, Recasens et al. (1989) observed that the intraparticle diffusion played an important role. In their study, however, the effective diffusivities were evaluated by regressing the desorption data with the assumptions of a model which assumes a linear adsorption isotherm and linear driving force model. Erkey and Akgerman (1990) used the chromatography technique to evalute the effective diffusivities of naphthalene in alumina in the presence of supercritical carbon dioxide. However, in their approach, the effective diffusivity is not the sole transport property determined. The experimental techniques for measuring effective diffusivity in gas and liquid phases at ambient conditions have been studied extensivelyin the past decades. Haynes (1988) provides an excellent review on this subject. The earliest and simplest method is the steady-state measurement (Scheidegger,1960). The steady-state methods in general cannot observe the dead-end pore diffusion; as a result of this deficiency the dynamic methods, such as time-lag measurement (Barrer, 1951),sorption rate measurement (Ma and Lee, 1976), and chromatography measurement (Hsu and Haynes, 1981), were then developed. While the dynamic methods can cover the deadend pore diffusion,more analytical efforts involvingmodel discrimination, system nonlinearity, apparatus dead volume, and nonideal input need to be considered. This is especially true for chromatographymeasurement, because the effective diffusivity can only be measured accurately when the interphase mass transfer and axial dispersion
* To whom correspondence should be addressed.
15
12
1. Heater 2. CCQ Cylinder 3. Pressure Reguiator 4. Filter 5. Boaster 6. Surge Tank 7. Pretreating Column
u u 8. Valve 9. Ball Valve 10. Basket 11. Heat Exchanger 12. Circulation Pump 13. Sampling Valve 14. Vacuum Pump
15. Autoclave P. Pressure Gauge PC. Micro-Computer R. Magnetic Stirror UV. UV Detector TC. Thermal Controller
Figure 1. Experimental apparatus used for effective diffusivity measurement.
effectsare identified. Although the dynamic methods have their disadvantages, it is believed that they provide more reliable data than the steady-state methods. In this study, the effective diffusivities of toluene in supercritical COz in activatedcarbon pellets were measured from the sorption rate experiment in a spinning basket reactor at temperatures 308,318, and 328 K and pressures up to 163 bar. This technique was chosen because the interphase mass transfer resistance was observed to be negligible at high spinning speeds. The numerical values of effective diffusivity could be obtained by fitting the entire sorption curve with the solutions of the mass balance equations. When the concentration of toluene eventually reached a constant value, the equilibrium amount adsorbed could also be determined from this experimental technique.
Experimental Section The experimental apparatus used for the effective diffusivity measurement at supercritical conditions is illustrated in Figure 1. The main parts of the apparatus contained a spinning basket reactor (AutoclaveEngineers Inc.) and a circulation loop with UV (ISCO) monitoring. The internal volume of the reactor was 529.1 cm9,and the total volume of the circulation loop includingpump tubing, filter,and UV cell was about 4.2 cm3. The reactor consisted of four Carberry type baskets, a magnetic stirrer, and a thermal controller. Each basket is 1.5 cm long, 1.9 cm
0888-5885/93/2632-1717$04.00/0 1993 American Chemical Society
1718 Ind. Eng. Chem. Res., Vol. 32, No. 8, 1993 Table I. Physical Properties of the Activated Carbon Pellets surface area (BET area) 13do m2/g porosity 0.445 pore volume 30-102 A 0.15 cm3/g 102-103 A 0.15 cm3/g 109-104 A 0.12 cmYg 104-106 A 0.08 cmS/g >l@ A 0.05 cm3/g solid density 1.385 g/cm3
wide, and 3.3 cm tall. About 13 g of activated carbon was loaded in these baskets. The spinning speed of the magnetic stirrer could be as high as 3000rpm. The thermal controller could maintain the desired temperature up to 673 K with a deviation of 0.5 K. A pressure gauge with a range up to 280 bar was located upon the reactor to indicate the system pressure. In the circulation loop, a minipump (LDC/MiltonRoy) was used to recycle the fluid at a flow rate of 10 cm3/min. In order to ensure the pumping efficiency, the incoming fluid was liquidized by a heat exchanger at 270 K. To keep the UV detector at constant temperature, the tubes connected with the detector were wrapped with a heating tape whose temperature was controlled at 300 K. The UV wavelength was 261 nm, at which the maximum absorbenceof toluene in carbon dioxide was observed. The sorption rate experiment was operated batchwise at constant temperature and constant volume. Since the reactor mainly contained carbon dioxide, the pressure was also observed as constant. To perform the experiment, one first turned on the heater to heat and maintain the carbon dioxide cylinder at around 320 K. Under this situation the carbon dioxide could be easily pressurized and was then sent to a surge tank by a booster (Autoclave EngineersInc.). Both carbon dioxide and toluene (Merck, LC grade) of 99.7% purity were used as received. The activated carbon (Degussa, WSIV) used in this study was first screened to obtain a 5-6 mesh fraction (the average particle size is 0.368 cm). It was then boiled in distilled water and dried in an oven at 390 K. The physical properties of the activated carbon pellets are listed in Table I. Before the experiment, activated carbon pellets were weighed and loaded in the baskets. After a 30-minvacuum treatment by the vacuum pump to remove the residual air in the reactor, the high-pressure C02 was allowed to flow into the reactor. When the pressure and temperature of thereactor reached the desired values, toluene was injected into the reactor by a six-port samplingvalve located in the circulation loop. The loop volume of the sampling valve was 0.5 cm3. After injection, the toluene dissolved into the supercritical carbon dioxide immediately, and then diffused into and adsorbed onto the activated carbon pellets. The change of the toluene concentration with time was monitored by an on-line UV detector and was recorded in a microcomputer. In order to assure that the dissolution rate is rapid, several blank runs without activated carbon loaded in the reactor were performed. It was observed that the time required to change the toluene concentration from zero to the steady-state value was within 20 s, which was short compared with the time required to complete the sorption rate experiment. The calibration curves between the UV absorbance and the toluene concentration were established by the same procedures as for the experimentsobserving the dissolution rate. Since the volume of the reactor and the amount of toluene injected were known, the toluene concentration was easily determined. From the UV absorbances corresponding to different amounts of toluene injected, the
calibration curves at various temperatures and pressures were then obtained. In each sorption rate experiment, the toluene concentration would eventually reach an equilibrium value. The equilibrium amount of toluene adsorbed onto activated carbon could then be calculated by subtracting the equilibrium concentration from the initial concentration. Thus the sorption rate experiment provided not only the sorption response curve but also the adsorption equilibrium. After the equilibrium concentration was attained, a known amount of toluene was injected to begin the experiment at another toluene concentration. For each temperature and pressure, 12 runs, Le., 12 injections, were made. Since the supercriticalcarbon dioxide is an excellent solvent for regenerating activated carbon loaded with organic compounds (DeFilippi et al., 1980; Tan and Liou, 1989), the activated carbon, after finishing the last run, was regenerated by supercritical carbon dioxide at 328 K and 170 bar until no toluene was detected in the effluent carbon dioxide stream, and then was under a vacuum treatment at 393 K for 12 h. After these two treatments, the regenerated activated carbon was used for subsequent runs at another temperature and pressure.
Results and Discussion In order to determine effective diffusivity from the sorption rate experiment, a mathematical model based on the following assumptions was developed: 1. The interphase mass transfer resistance was negligible at high spinning speeds. 2. The activated carbon pellets were spherical particles with uniform size. 3. The intraparticle diffusion behavior could be described by an effective diffusivity which was a constant in the concentration range of each run. 4. The adsorption rate on the interior surface of the pellets was much faster than the diffusion rate; thus the local equilibrium assumption was applied. The mass-transfer equation in the bulk fluid can then be written as
3
V-acb = -aD, at Where Vis the bulk fluid volume, Cb is the concentration of toluene in the bulk fluid, a is the total external surface area of the activated carbon pellets, D, is the effective diffusivity, and c is the concentration of toluene in the particle. The mass-transfer equation within the particle is written by
where q is the amount of toluene adsorbed on activated carbon. The concentration c and the loading q might be combined as Q, which is expressed by
8 = P#-
+ ePc
(3)
Upon substitution of eq 3 into 2, we have (4)
By the local equilibrium assumption, Q could be related to c by the chain rule as follows: (5)
The initial and boundary conditions for eqs 1 and 5 are
Ind. Eng. Chem. Res., Vol. 32, No. 8, 1993 1719 0.30 I
I
Experimental Data 0.25
0.8
Numerical Solutions
Y
k %!
0.20
8
0.15
e
-0
0.6
u"
d
0.4
c)
c
d
O.1° 0.05
0
0.32
0
0.45 0.69
A
0.00
4
0.000
I
I
I
0.002
0.2
n n V."
0
0.006
0.004
100
200
t
0.25
3
0.20
a 2
$i 0.15
4
4
0.10
isotherms measured in this study are obviously nonlinear. Several well-known relations were tested, however, only the Toth isotherm relation
0.05
4
0.00 0.000
I
I
I
0.002
0.006
0.004
9'
Toluene Concentration, g/cma
0.25
Y
2 %!
0.20
4
0.15
'
600
Table 11. Estimated Values of the Parameters in the Toth Isotherm Expression T,K pC, g/cms q0 b m 308 0.32 1.282 0.1061 0.219 0.0865 0.321 0.829 308 0.45 0.475 0.0535 0.420 308 0.69 0.849 0.0663 0.296 318 0.32 0.800 0.0880 0.323 318 0.45 0.0859 0.353 318 0.69 0.629 0.0709 0.287 0.886 328 0.32 0.691 0.0748 0.350 328 0.45 0.556 0.0760 0.384 328 0.69
I
u
0.30
500
Figure 3. Typical sorption curves.
0.30
I
400
Time, s
Toluene Concentration, g/cma
a
300
t / 32s K
pa. g/cma 0.32
0
0.05
0.45 0.69
4
0.00 J
0.000
I
I
0.002
0.004
(b
+ c"')'/"'
provided the best fit. The average deviation at various operating temperatures and pressures was found to be less than 1.0%. The fitted parameters q o , b, and m are listed in Table 11. Because the analytical solution is not available for the Toth isotherm expression, the numerical solution was applied for evaluation of effective diffusivity. The orthogonal collocationmethod (Villadsen and Michelsen, 1978) applied in the r-direction incorporated with the IMSL integration subroutine DGEAR was used for obtaining the concentration change in the real time domain for a specified value of De. Eleven interior collocation points in the r-direction were found to be enough to control the error of numerical solutions within 0.15%. Some typical sorption curves obtained experimentally are shown in Figure 3 in which c b is the dimensionless concentration defined by
I
0.10
qoc
I 0.006
Toluene Concentration, g/cma
Figure 2. Adsorption isotherm of toluene on.activated carbon at (a) 308,(b) 318,and (c) 328 K.
t
