RATES OF ADSORPTION IN T H E BENZENE-HEXANE SYSTEM JOHN SHEN AND J. M. S M I T H University of California, Davis, Calif.
Breakthrough curves were measured for mixture and single-component adsorption of benzene and n-hexane at the same conditions as previously reported for equilibrium data. The single-component results showed that for the largest particle size and a t the highest temperature, 130" C., the rate was controlled by intraparticle diffusion. At these conditions surface diffusion was estimated to account for more than 90% of the intraparticle transport. For smaller particle sizes axial diffusion affected the breakthrough curves, and at lower temperatures surface adsorption was probably a significant resistance. In the linear isotherm range ( 1 30" C.) the rate of adsorption of benzene from mixtures was the same as in single-component adsorption. At other conditions interaction effects were involved and the mixture results could not b e predicted from the single-component measurements.
VER-ALL
rates of adsorption of hydrocarbons are suffi-
0 ciently low that breakthrough curves and design condi-
tions for separation processes depend upon rate data as well as equilibrium information. Since the over-all rates are influenced significantly by internal diffusion resistances (Masemune and Smith, 1964, 1965a; Rimpel, 1965), rates become particularly low and breakthrough curves flat as the particle size of the adsorbent increases. When the adsorption isotherm is linear, the differential equations describing the process can be integrated and the breakthrough curve predicted as a function of parameters describing the relative resistances. Masamune and Smith (1 96513) summarized the results when the adsorption was governed by combinations of external diffusion, intraparticle diffusion, and local adsorption resistances. Lapidus and Amundson (1956) and van Deempter et al. (1956) included the effect of axial diffusion. When the equilibrium isotherms are not linear, only numerical solutions for each specific situation are available. Two cases have been reported: that of Tien and Thodos (1959) which took into account external and intraparticle diffusion resistances and supposed that the local adsorption rate was proportional to the 0.5 power of the concentration in the gas, and that of Hall et ~ l (1966) . which considered that intraparticle diffusion was controlling and that the local rate was given by the Langmuir equation. These analytical papers were concerned with single-component adsorption. With mixtures the interaction effects further complicate the problem and no theories have been developed which include the effects of the important resistances. If the equilibrium isotherms are linear, and hence unaffected by other adsorbing components, the theory for linear isotherms can be equally well applied to mixtures, but this is rarely the case. The only theory which has been proposed for mixture adsorption is that of DeVault (1943) and Klein, Tondeur, and Vermeulen (1965) which neglects diffusion and local surface adsorption resistancesthat is, equilibrium is assumed a t any point in the bed at all times. This procedure does take into account in a n approximate way the interaction effects in mixture adsorption. Experimental data for rates of adsorption of mixtures are also limited. The closest reference to the present work is that of Needham et d. (1966) on the adsorption of binary hydrocarbon gases on silica gel. There results showed strong 106
l&EC FUNDAMENTALS
interaction effects which make it impossible to analyze the data. The objective of the present work was to measure breakthrough curves for benzene and n-hexane, alone and in mixtures. For small regions of this system the foregoing paper showed that the isotherms were linear, and quantitative analysis is possible to ascertain the resistances which control the rate. For other conditions strong interaction effects exist and the purpose was to determine the nature of these interactions when one component, benzene, was preferentially adsorbed.
Apparatus and Procedure
The equipment described by Shen and Smith (1968) was used for measuring breakthrough curves. After pretreatment or regeneration of the bed, adsorption was initiated by closing the bypass valve, thus sending a gas of given composition and flow rate through the bed. The time measurements were corrected for the holdup between the inlet of the adsorber vessel and the entrance to the bed, and the holdup between the bed exit and the detector. The run was terminated when the exit concentration became equal to the inlet concentration. A potential error is dispersion in the tubing between the exit of the bed and the detector. This problem was investigated experimentally by Masamune and Smith (1964, 1965a). At the velocities (in the exit line) used in this work, which were 2.87, 5.75, and 11.5 cm. per second, the concentration change due to dispersion was insignificant. The chief variables in the rate measurefients were particle size of gel and temperature, although some runs were made at 110" C. for different gas velocities. The partial pressure of hydrocarbons in the feed gas was constant and equal to 0.01 atm. Three beds, each with a different average particle size, were studied. The properties of the beds and the operating temperatures are given in Table I. The breakthrough curves for mixture adsorption were made in a manner similar to that described earlier for the equilibrium measurements. However, a continuous analysis was not possible because the gas composition leaving the bed changed
Table 1.
Operating Variables for Rate Measurements
(Single component adsorption) Btd I
Mesh number Average particle radius, cm. Net weight of silica gel, E. Bed length, cm. Interparticle void fraction Bulk density of bed, g./cc. Adsorption temperatures,
-
O
c.
. I
Bed 2
40-48
120-1 40
0.054 0.7076 2 .o 0.291
0.0169 0.7126 2.0
0,00575 0,6404 2.0
0.286
0.357
0,807
0,725
0.801
70, 90, 110, 70, 90, 110, 70 and 90 and 130 and 130 1 1 1
Total pressure, atm. Flow rate of gas (27' C., 1 atm.), cc./min. 61.5a Pressure drop across bed Negligible Inlet hydrocarbon gas partial pressure, atm. 0.01 0
Bed 3
14-1 6
61.5a Negligible
61 . 5
0.01
0.01
1) as it competes unsuccessfully for sites with the more slowly adsorbed benzene. This indicates that the adsorption zone (defined as the region of the bed where most of the adsorption occursfor example, the length of the bed where 0.1 < C/Co > 0.9) of hexane travels down the bed a t a higher velocity than that for benzene, and also that hexane is simultaneously adsorbed and desorbed until its adsorption zone moves out the end of the bed. This concurrent adsorption and desorption along with
1,o
-P= -
0.8
V
0.6
&-
az &-
0.4
Bu
a 0 0163 cm 0474 FROM F I G 6
k x
w
- PURE-BENZENE
0.2
0.0 0.5
0.7
0.9
1.i DIMENSIONLESS TIME.
1.55
1.3
eb
Figure 10. Converted breakthrough curves for benzene in mixture adsorption at 130' C. VOL 7
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111
1.0
0.8
n
-
..
n
0
U
0
0.6
U
u \
-z
I
U
z
0
4
P c u Iz
I* cz
W
I-
U z U 0
z W U z
0 .L) M I X T U R E OATA ( BENZENE )
E
A 0 0 V SEPARATE RUNS FOR
W x
c
a =0.00515 cm - PURE-BENZENE DATA FROM
W x
fIG 7
0.8 DIMENSIONLESS TIME. eb
Figure 1 1 . Converted breakthrough curves for benzene in mixture adsorption at 70" C.
nonlinear isotherms represent a complex problem. Some information can be extracted from qualitative study of the breakthrough curves, and a very approximate prediction method can be developed by assuming equilibrium at all points in the bed. Analysis of the breakthrough curves shows that two extremes exist. I n the first the adsorption zone overlaps that for hexane. I n this circumstance benzene begins to appear in the stream leaving the bed while hexane is still being adsorbed. This is illustrated in Figure 1 where, between 80 and 140 seconds, the exit concentrations of both components are increasing with time. The other extreme is when the adsorption zone for benzene is confined to the region where hexane is being desorbed. This is illustrated in Figure 2, where the breakthrough curve for benzene lies in the time interval when n-hexane concentration decreases. I n this case the adsorption zone for benzene is separated from that for hexane. The steepness of the breakthrough curves-that is, the over-all rate-determines how close to either extreme a particular set of conditions will be. In Figure 1 the rate is low because of the large intraparticle diffusion resistance associated with the largest particle size. In contrast, in Figure 2, for 70" C. and the smallest particle size, the rate is very high. The importance of surface diffusion is evident in this figure. The intraparticle diffusion resistance is low, not only because of the small particle size, but also because the surface migration increases as temperature decreases. Breakthrough Curves from Equilibrium Theory. The equilibrium theory, originally developed by DeVault (1943) for ion exchange columns, requires for our study that for both hexane and benzene equilibrium be reached at all points in the bed. Axial dispersion is neglected. Breakthrough curves will then be vertical lines. As such they will not represent the actual behavior such as shown in Figure 1. Comparison with experimental results will be better for conditions where 112
ILEC FUNDAMENTALS
0.95
1.15
1.05
DIMENSIONLESSTIME.
1.20
e,
Figure 12. Converted breakthrough curves for benzene in mixture adsorption at 70" C.
the rate is very high, as in Figure 2. The method predicts a desorption region for hexane, but only in terms of a rectangular shape. The data required are equilibrium isotherms for the components alone and in the mixture. At a time before hexane appears in the exit gas, the equilibrium theory allows the bed to be considered as three zones (Figure 13) : I n zone I the gas contains no hydrocarbon, all the benzene and hexane having been adsorbed in prior zones; in zone I1 only hexane is present in the gas, benzene having been adsorbed in zone 111; and in zone 111 both hydrocarbons are present. Hexane is displaced in zone I11 by the adsorption of benzene and carried forward by the gas stream to zone 11. Hence the concentration profile for hexane will be a-b-c-d.e. The mixture equilibrium data showed that the adsorption of benzene is not influenced greatly by the presence of hexane. Approximately, the adsorption of benzene in zone 111 may be considered as single-component adsorption. Curve a-b-f will then represent the concentration profile for benzene in the bed. T o evaluate the concentration level along c-d, (Cmax/Co)h, consider a time interval At during which the adsorption zone of benzene (zone 111) travels a distance AZ. The mass balance equation for benzene across the moving boundary between zones I11 and I1 is:
is the equilibrium adsorption of benzene from a gas where mixture of concentration (Co)b, Similarly, a mass balance for hexane is
Here is the equilibrium adsorption of hexane in zone I11 from a gas mixture of concentration (Co)h, and ( N m a x o ) h is the equilibrium adsorption of hexane from a gas containing
c
uo
0.8
-z \
U
0
A O D V SEPARATE RUNS FOR
c p: c
U
a = 0 . 0 5 4 cm.
A*
z
W
y 0.4 8
V SEPARATE RUNS FOR
---
a:0.0169 cm. CALC. FROM EPUlllBRlUM
t W x
2 0
Figure 13. Concentration profile in bed according to equilibrium theory
;-ri
-
0
uo U \
----- - .
1.0
Figure 15. Converted breakthrough curves for n-hexane in mixture adsorption at 130" C.
1.3
*
-e---
? -i
1.0
c
0
U
A
Ip:
U
E
W
0.6
SEPARATE RUNS CALC FROM E L l U l t I B R I U M
c
z
U z 0 U
U
z U 0 x W
0 0
---
P
c U c =
c
1
6
L)
DIMENSIONLESS TIME. 8 h
c
U
2
0
t
w x
0.0
0
tll
tb
0.2
'
CORRECTED TIME, t
I
I I
BREAKTHROUGH CURVE
HYDROCARBDN
Othdcba
n.HEXANE
Othtbba
BENZENE
Figure 14. Breakthrough curves according to equilibrium theory
I
0
0
2
6
L(
DIMENSIONLESS TIME, Oh
Figure 16. Converted breakthrough curve for n-hexane in mixture adsorption at 70" C.
only hexane (zone 11) at a concentration (Crnsx)h. Dividing Equations 9 and 10 gives
Equation 1, or data such as shown in Figures 2 and 3 of Shen and Smith (1968), give a second (equilibrium) relationship between (Nrns.o)h and (Cm& Simultaneous solution of Equation 11 with this second relationship establishes (Cm&. Mixture adsorption equilibrium data are needed to determine ( f l 0 ) h and (No)*. The other quantities necessary to establish the breakthrough curves in Figure 13 are the times required for the adsorption zone of hexane (d-e of Figure 13) and benzene (6-f) to reach the exit of the bed. These times are noted as th and tb in Figure 14, which depicts the breakthrough curves corresponding to Figure 13. These times are obtained from the following mass balances for benzene and hexane :
I n Figures 15 and 1G are shown, as dashed lines, examples of breakthrough curves predicted from Equations 11 to 13. Experimental results are indicated by the points and solid curves. Results a t other temperatures are similar. The equilibrium theory cannot predict effects of particle size or velocity, since individual resistances are not considered. Clearly, better theoretical methods are needed for treating adsorption from gas mixtures. Conclusions
For this system breakthrough curves in mixture adsorption were the same as the single-component curves for the preferentially adsorbed component (benzene) in the linear isotherm region. When the isotherm is nonlinear, the single-component and mixture data for benzene cannot be quantitatively related using theory now available. For hexane, the preferential adsorption of benzene causes the breakthrough curve in mixtures to have a desorption region. Hence mixture results were not simply related to singlecomponent breakthrough curves, even in the linear isotherm region. Methods need to be developed for predicting over-all VOL 7
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113
rates of adsorption in mixtures when there is competition for adsorption sites. A retarding factor in this development is likely to be the uncertainty about surface diffusion rates in mixture adsorption. Analysis of the single-component data indicated that more than 90% of the intraparticle diffusion was due to surface migration. At present it is not possible to predict surface diffusion rates for single components and no data have been found for binary or multicomponent systems. Since intraparticle diffusion is usually an important resistance, and sometimes a controlling one, the design of adsorption separation processes rests heavily upon a better understanding of surface diffusion in both single- and multicomponent adsorption. For the largest particle sizes and a t the highest temperature, linear isotherms permitted a quantitative analysis of the singlecomponent breakthrough curves. Intraparticle diffusion was found to control the rate of adsorption for both benzene and hexane a t these conditions. For smaller particle sizes, or lower temperatures, axial diffusion and/or surface adsorption resistance were important. External (film) diffusion resistance was not significant a t the conditions studied. Semiquantitative prediction of breakthrough curves for mixture adsorption can be made by assuming local equilibrium and using single-component and mixture equilibrium isotherms. Acknowledgment
T h e financial support for this work was provided by the American Chemical Society, Petroleum Research Fund, through Grant 1633. Nomenclature a
A, C CO
(C),, D12
D, (DJ0
DK
2
114
= average pore radius, cm. = cross-sectional area of bed, sq. cm. = concentration of adsorbable component in gas phase
= feed composition, g. moles/cc. maximum concentration of hexane in gas for mixture adsorption,. g. moles/cc. = molecular diffusivity in binary system of components 1 and 2, sq. cm./sec. = effective intraparticle diffusivity, sq. cm./sec. = gas phase (in pores) contribution to effective intraparticle diffusivity, sq. cm./sec. = Knudsen diffusivity, sq. cm./sec. = external mass transfer coefficient, cm./sec. = total length of bed, cm. =
IhEC FUNDAMENTALS
Y1
Ya
z
= amount of hexane adsorbed on silica gel in equilibrium with a gas mixture of hexane concentration (CJh,g. moles/(g. silica gel) = amount of hexane adsorbed in equilibrium with a single component gas of hexane concentration (C,Jh,g. moles/(g. silica gel) = modified Reynolds number, (2a)up/p = Schmidt number, p / p 0 1 2 = time, sec. = breakthrough time at infinite rate, defined by Equation 2 or 3, sec. = OK. = superficial velocity, cm./sec. = dimensionless parameter defined by Equation 4 = dimensionless parameter defined by Equation 6 = bed length, cm.
GREEKSYMBOLS CB
9 P
= void fraction in bed = dimensionless time defined by Equation 1 = gas density, g./cc.
PB
= density of bed, g./cc.
?
= particle density, g./cc. = tortuosity factor
literature Cited
Babcock, R. E., Green, D. W., Perry, R. H., A.Z.Ch.E. J . 12, 922 (1966). Deempter, J. J. van, Zuiderweg, F. J., Klinkenberg, A,, Chem. Eng. Sci. 5 , 271 (1956). DeVault. D.. J . Am. Chem. Soc. 65.532 (1943). Hall, K.’ R.; Eagleton, L. C., Acrivos, A,,‘ Vermeulen, T., IND. ENG.CHEM. FUNDAMENTALS 5,212 (1966). Klein, G., Tondeur, D., Vermeulen, T., University of California Sea Water Conversion Laboratory. Rept. 65-3 (June 1965). Lapidus, L., Amundson, N. R., J . Phys. Chem. 56,984 (1956): Masamune, S., Smith, J. M., A.Z.Ch.E. J . 10, 246 (1964); 11, 41 (1965a). Masamune, S., Smith, J. M., A.1.Ch.E. J . 11, 34 (1965b). Needham, R. B., Campbell, J. M., McLeod, H. O . , Znd. Eng. Chem. Process Design Develop. 5, 122 (1966). Rimpel, A. E., Ph.D. dissertation, Carnegie Institute of Technology, Pittsburgh, Pa., 1965. Schneider, P., Smith, J. M., “Adsorption Rate Parameters from Chromatography,” to be published, A.I.Ch.E. J . (1968a). Schneider, P., Smith, J. M., “Chromatographic Study of Surface Diffusion,” to be published, A.I.Ch.E. J . (1968b). Shen, John, Smith, J. M., IND.END.CHEM.FUNDAMENTALS 7,100 (1968). Tien, C.,Thodos, G., A.1.Ch.E. J . 5 , 373 (1959). Wakao, N., et al., Kagakn Kogaku 22,780 (1598). RECEIVED for review March 3, 1967 ACCEPTED October 18, 1967
