1300
Ind. Eng. Chem. Process Des. Dev. 1985, 2 4 , 1300-1302
Satterfield, C. N.; Stenger, H. G., Jr. Ind. Eng. Chem. Process D e s . Dev. 1985. 2 4 . 407. Sebastkn, H. M.; Simnick, J. J.; Lin, H.-M.; Chao, K.4. Can. J. Chem. Eng. 1978, 56, 743. Sebastian, H . M.: Simnick. J. J.: Lin. H.-M.; Chao. K.G. J. Chem. Ena. Date 1978, 2 3 , 305. Sebastian, H. M.; Simnick. J. J.; Lin, H.-M.; Chao, K.-C. J. Chem. f n g . Data 1979, 24, 343. Sebastian, H. M.; Simnick, J. J.: Lin, H A . ; Chao, K . 4 . J. Chem. f n g . Data 1980, 25, 68. Simnick, J. J.; Lawson, C. C.; Lin, H.-M.; Chao, K.-C. AIChf J. 1977, 23, 469. Simnick, J. J.; Liu, K. D.; Lin, H.-M.; Chao, K.-C. Ind. f n g . Chem. Process Des. Dev. 1978, 17. 204.
Stenger, H. G., Jr.; SatterfkM, C. N. Ind. Eng. Chem. Process Des. Dev . 1985, 24, 411.
Department of Chemical David K. Matsumoto Engineering Charles N. Satterfield* Massachusetts Znstitute of Technology Cambridge, Massachusetts 02139 Receiued for review June Accepted December
28, 1984 14, 1984
On the Adsorptlon of Ethane by 4A Zeolite Pellets
The differential adsorbent bed (DAB) technique has been applied to the study of isothermal adsorption of ethane at a pressure of 90 torr by 4A zeolite pellets. Experimentaldata were fwnd to be well represented by an isothermal, constant Fickian diffusivity model consistent with previous data at lower ethane pressures.
The sorption of ethane by Type 4A zeolite has been studied previously by Kondis and Dranoff (1971a, 1971b), Eagan and Anderson (1975), and Yucel and Ruthven (1980). Kondis and Dranoff first investigated the isothermal sorption of ethane from dilute mixtures with helium by Linde 4A zeolite crystals, pelletized crystals, and Linde 4A molecular sieve pellets (with clay binder) using a gravimetric apparatus. For gas mixtures containing up to 8 vol 7% ethane (60 torr) a t 1 atm of total pressure in the temperature range of 25-117 "C, they found that (1) intracrystalline diffusion was rate-controlling, (2) macropore diffusion was rapid for both types of pellets, and (3) the uptake was well represented by the usual Fick's law diffusion model with constant diffusivity. For spherical particles, response to a step change in gas-phase concentration for this model is
where Qt is the average ethane concentration in the zeolite crystal a t time t , R is the average crystal radius, and D is the diffusivity. Over the concentration range investigated, Kondis and Dranoff found that the diffusivity was independent of ethane concentration and reported diffusivities for crystals and crystal pellets of 4-46 X lo-'' cm2/s over the 25-117 OC temperature range. The diffusivities for the molecular sieve pellets were about of those of the zeolite crystals; however, the diffusional activation energies for these materials were about the same (5.66 kcal/mol for zeolite crystals; 5.23 kcal/mol for molecular sieve pellets). Eagan and Anderson used a volumetric apparatus to determine diffusivities in Linde 4A crystals for ethane pressures up to 300 torr in the temperature range of 0-20 "C. A t 10 "C, they reported diffusivities ranging from 3 X cm2/s a t 50 torr to 9.4 X cm2/s a t 300 torr, suggesting that diffusivity is a function of adsorbed ethane concentration. While this conclusion contradicts the results of Kondis and Dranoff, the differences can be reconciled by considering the concentration ranges investigated. Most of Kondis and Dranoff a experiments fell within the linear portion of the equilibrium isotherm while those of Eagan and Anderson were largely outside this
range. Indeed, in other experiments with ethane pressures approaching 1atm, Kondis and Dranoff (1971~) also found that diffusivity was dependent on the adsorbed concentration. Eagan and Anderson reported an activation energy of from 7 to 9 kcal/mol after correcting the diffusivity for the nonlinear isotherm. Yucel and Ruthven used a gravimetric apparatus to determine diffusivities in laboratory synthesized 4A crystals for ethane pressures up to 250 torr in the temperature range of 50-150 "C. The average crystal diameter of the zeolite samples ranged from 7.3 to 40 pm, which is larger than commercially manufactured crystals (1-4 pm). They found the diffusivities to be independent of crystal size and the magnitude to be up to 3 times those reported by Kondis and Dranoff. Yucel and Ruthven also studied a zeolite sample supplied by Eagan and Anderson and reported that their data confirm exactly the extrapolation of Eagan and Anderson's data. For comparison, Yucel and Ruthven tested a Linde 4A crystal sample and found diffusivities 2 orders of magnitude lower than those determined for their own crystals. They reported activation energies of 8.2 kcal/moI for their own crystals and 6.3 kcal/mol for the Linde crystals. Yucel and Ruthven also reported an activation energy of 5.6 kcal/mol from a volumetric counterdiffusion study performed by Taylor utilizing l/s-in. Linde pellets in the temperature range of 31-79 "C (see also Ruthven, 1980). The goal of the investigation reported here was to test the extension of the constant diffusivity model of Kondis and Dranoff to higher ethane concentrations for Linde 4A molecular sieve pellets. Adsorption data were obtained a t ethane gas-phase pressures of 90 torr over the temperature range of 25-81 "C; a t 25 "C, this concentration is outside the linear range of the equilibrium isotherm. A second objective of this work was to evaluate the differential adsorbent bed (DAB) technique for studying adsorption rates. Historically, measurements of sorption rates have been made by using a gravimetric technique in which the weight change of the adsorbent is monitored during the adsorption process. While the gravimetric technique is quite efficient for the measurement of single-component adsorption kinetics, it cannot readily be extended to measure the uptake of individual components
0196-4305/85/1124-1300$01.50/00 1985 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 24,
from multiadsorbate streams. However, the DAB technique described in this communication can be easily adapted to multicomponent studies; such a study is currently being pursued in this laboratory. The results reported here served to demonstrate the validity of the DAB technique in addition to providing new data concerning ethane sorption. Experimental Section Measurements were made by using the (DAB) technique in which the ethanelhelium gas mixture was passed through a short (differential) packed bed of adsorbent for a predetermined length of time. The adsorbent was contained within a lI2-in.(1.27 cm) copper tube and supported by a glass wool plug and copper screen. Bed depth was approximately 1.3 cm. A l/gin. (0.32 cm) thermowell was located along the tube axis and within the packed bed. The gas mixture flow rate was very rapid compared to the rate of adsorption so that there was negligible change in the ethane gas-phase concentration through the bed. The large gas flow also allowed for rapid dissipation of any heat generated by adsorption; consequently, operation was isothermal. This was confirmed by a thermocouple located within the thermowell. At the end of the selected time period, inlet and outlet valves were closed simultaneously, thereby isolating the DAB from the feed. The DAB was then connected to an evacuated sample bomb of known volume and heated to 250 "C to thermally desorb the accumulated ethane. After a wait of about 50 min for desorption to occur, the DAB was swept with a small amount of helium to drive the remaining desorbed ethane into the sample bomb. The temperature and pressure of the sample bomb were measured, and the ethane content was determined by using a gas chromatograph. This information allowed the calculation of the amount of ethane recovered and hence, after correcting for the ethane trapped in the DAB void spaces, the amount of ethane sorbed. By varying the time period over which the adsorbent was exposed to the gas mixture, an adsorption rate curve (loading vs. time) could be developed. Equilibrium adsorption data could also be obtained in this manner by use of sufficiently long adsorption times. Ethane adsorption experiments were conducted a t 25, 49, and 81 "C with a gas-phase concentration step change from 0% to 12% ethane (90-torr ethane pressure) at 1atm of total pressure. All the data reported here were obtained with a single loading of 1.17 g of 4A molecular sieve pellets, these were 1/16 in. diameter extrudates manufactured by Linde-Union Carbide (lot No. 940881080303). Results and Discussion Limited adsorption equilibrium data were obtained during the course of this study. Data obtained a t 25 "C were in excellent agreement with the equilibrium isotherm at 25.2 "C reported by Kondis and Dranoff (1971b) while data obtained a t 49 "C were in excellent agreement with the equilibrium isotherm at 50 "C reported by Yucel and Ruthven (1980). The data a t 81 " C were not readily comparable with previous investigations. Figure 1 shows a typical adsorption rate curve obtained a t 49 "C; similar curves were obtained a t 25 and 81 "C. Values of the diffusional time constant ( D / R 2 )were determined by graphically matching the adsorption rate curves to a plot of eq 1 (fraction of equilibrium loading sorbed vs. In (Dt/R2)0.5).Generally good fits were obtained. The resultant diffusional time constants were found to be s-l a t 49 "C, and 1.88 4.13 X s-l a t 25 "C, 7.56 X X s-l at 81 "C. These results obtained from 12% ethane in helium are very close to those reported by Kondis and Dranoff for 4A molecular sieves. They had determined
O/R2 = 7.56 x
No. 4, 1985 1301
sec-'
119% Lot t940881080303
2 0.50
-.-a W
' 0 i
0.25
.-
i
V
2
LL
0.0
10
4
40
100
t 4 (sec4)
Figure 1. Adsorption rate curve. 3.0
-
1 .o
r
0.6 u
*
z
N
0.3
a \ a
0.1
2.5
3.0
I/T x 103
3.5
(OK-')
Figure 2. Arrhenius relationship for D / R 2 .
D / R 2to be 4.5-5.0 X s-l at 25 OC for up to 8% ethane in helium. From the trend shown in Eagan and Anderson's results, one might expect that the Fickian diffusivity would increase with ethane concentrations above 8% and consequently that D / R 2 would be larger than the values reported by Kondis and Dranoff. However, this parameter also depends on the average zeolite crystal radius and is sensitive to small variations in R. Since there is no assurance that the particles used previously had exactly the same crystal size distribution as in the present study, some variation in diffusional time constants is not unexpected. The data suggest that the corresponding Fickian diffusivity is at best a very weak function of loading over the range studied in this work. Since diffusion into the zeolite crystal is an activated process, an Arrhenius plot (Figure 2) can yield a corresponding activation energy. The activation energy calculated from a least-squares fit is 5.58 kcal/mol. This is comparable to Kondis and Dranoff's 5.23-5.66 kcal/mol and Taylor's 5.6 kcal/mol. The present results indicate that the isothermal, constant diffusivity Fickian model adequately represents the kinetics of ethane adsorption on a Linde 4A molecular sieve for ethane pressures up to 90 torr in the 25-81 "C range. The consistency with previous results confirm the validity of the DAB technique employed. and supports its future use in measuring the individual component kinetics in a multiadsorbate system.
Ind. Eng. Chem. Process Des. Dev. 1985, 2 4 , 1302-1305
1302
Registry No. Ethane, 74-84-0.
Yucel, H.; Ruthven, D. M. J. Chem. Soc., Faraday Trans. 1 1980, 76, 60-70.
Literature Cited Eagan, J. D.; Anderson, R. B. J. Colloid Interface Sci. 1975. 50, 419-433. Kondis, E. F.; Dranoff, J. S. Adv. Chem. Ser. 1971a, No. 102, 171-179. Kondls, E. F.: Dranoff, J. S . Ind. Eng. Chem. Process D e s . D e v . 1971b. 70, 108-1 14. Kondis, E. F.: Dranoff, J. S. AIChE Symp. Ser. 1971c,No. 67(117), 25-34. Ruthven, D. M. I n "The Propertles and Appllcations of Zeolites"; Townsend, R.. Ed.; The Chemical Society: London, 1980; pp 43-57.
Chemical Engineering Department Northwestern University Evanston, [ilinois 60201
Norman W. Carlson Joshua S. Dranoff*
Received for review May 29, 1984 Revised manuscript received January 11, 1985 Accepted February 6, 1985
Optimal Fixed-Bed Reactor Operation via Ordered Partlcie-Size Profile Many industrial reactors are of the fixed-bed type and the catalytic reactions for which they are employed are often exothermic. I t is well-known that for such reactions, the nonisothermal effectiveness factors exceed unity and go through their respective maxima before settling down to asymptotic values for exclusively pore diffusion regime. Higher rates and therefore h w r conversions can be obtained if at every cross section of the reactor the system could be characterized and governed by values close to these maxima being appropriate to the existing temperatures and conversion. A convenient way of achieving this is to operate the reactor with a particle-size profiie along the axial direction, since the Thiele parameter for a given fluid-solid system is directly related to particle size in addition to concentration and temperature. As an example, a first-order exothermic reaction and plug flow model are chosen. Relative performances under adiabatic and nonisothermal conditions with and without particle size profiles are compared. I n addition, multistage operation with interstage cooling has been analyzed. It has been shown conclusively that an ordered particle-size profile indeed, very significantly, improves the reactor performance.
The catalyst effectiveness factor (a) for various rate models has been considered by Aris (1975), Petersen (1965), Carberry (1976), and Froment (1979). The nonisothermal situation represented by the exothermicity factor (0) and Arrhenius factor (v) has gained more attention due to the presence of multiplicity and a maxima in 7 values (Weisz and Hicks, 1962). Tinkler and Metzner (1961) have analyzed the nonisothermal effectiveness factor for a first-order reaction in a spherical pellet. This work presents a strategy that allows the operation of packed bed reactors at a values close to extremal values by varying the particle size along the reactor length. The analysis considers a first-order, irreversible, exothermic heterogenous reaction on spherical catalyst pellets. The effect of temperature on diffusivity (D)is neglected.
Adiabatic Reactor with Particle-Size Profile Based on plug flow model, the steady-state mass and energy balances for an adiabatic reactor are written as
and
the Arrhenius form for k as k = Ae-E/RT,eq 4 is written as
where eB = A ( l - c)ppSg. The dimensionless form of the adiabatic equation of path is (Y
= A [ l - ( l / j ) ( A - l)]
The adiabatic temperature rise (p), 6, and the conversion ( x ) are given by
From the results of Tinkler and Metzner (1961),it may be seen that at 4 = 2.0, the effectiveness factor at various 6 values is very close to the respective maxima. Therefore, the rate will be maximum if this value of 4 is chosen. This justifies the choice of = 2.0. If the Thiele-parameter is fixed a t a value of 2, for an effective diffusivity of 0.01, the particle size can be related to 2, as a =
The adiabatic path equation is obtained by combining eq 1 and 2 as
P=
-R T2 (-AH/pCp)
[ T,
RTo
Po
+
+
(-AH/pC,)
1.
(3)
Equation 3 decouples eq 1 and 2 resulting in (4)
The initial condition is given by A(o) = 1.0. Substituting
(6)
0.2[e(y,/2A)-(B/2)]
(8)
From the results of Tinkler and Metzner (1961),it can be inferred that at 4 = 2.0, the 1 values at different a ( = P y ) values follow '7 = 100.167'2b0.1625 (9) With this equation of 7, the temperature profile and hence the concentration and the particle-size profiles are obtained. Equations 5-9 are solved by the Runge-Kutta Gill scheme with double-precision floating point arithmetic on a DEC 1090 system. Typical results are shown in Figure 1. For the purpose of comparison the following packedbed reactors are also considered: (1)an adiabatic reactor with particles of the same size; (2) adiabatic reactors in series with interstage cooling and appropriate particle size
0196-4305/85/1124-1302$01.50/00 1985 American Chemical Society
