Ind. Eng. Chem. Process Des. Dev. 1084, 23,337-341
(column 8) is to be expected at conversion levels higher than 97% only for the fastest reactions measured. During the reaction the decrease of the hydrogen diffusion coefficient DHand saturation concentration cHiwith changing liquid composition does not affect the extent of mass transfer effects on global kinetics significantly. From mass transfer calculations it may be concluded that most of the experiments were'not influenced by mass transfer effects. Only the runs at higher temperatures and low pressures may be affected to some extent by absorption limitations. However, the apparent activation energies at different pressure levels do not show a tendency to decrease with decreasing pressure. Nomenclature
ci = concentration of component i, mol/L cHi = saturation concentration of hydrogen, mol/L Di = diffusivity of component i, m2/s d = particle diameter, m $ = activation energy, kJ/mol H = Henry's constant, (L bar)/mol Ki = adsorption constant of component i, L/mol k = rate constant, mol/(L s w/w o/w) kHLa = volumetric absorption coefficient, s-l m K = amount of catlayst used, w/w k mKO= amount of catalyst poisoned, w/w L p H = hydrogen pressure, bar Q = KB/KA = relative adsorptivity R = gas constant, J/(mol K) -PA = reaction rate, mol/(L s)
XA
337
= conversion of component A
vie = external effectiveness factor for component i vii
= internal effectiveness factor for component i
Subscripts A = 2,4-dimethylnitrobenzene B = 2,4-dimethylaniline H = hydrogen K = catalyst L = liquid phase Registry No. 2,4-Dimethylnitrobenzene, 89-87-2; 2,4-dimethylaniline, 95-68-1;Pd, 7440-05-3. Literature Cited Acres, G. J. K.; Cooper, B. J. J . Appl. Chem. Biotechnol. 1972, 22, 769. Andersson, B. AIChE J . 1982, 2 8 , 333. Buehlmann, Th. PhD. Thesis No. 7115, ETH Zurich, 1982. Buehlmann, Th.; Gut, G.; Kut. 0. M. Chlmle 1982, 36, 469. Carberry, J. J. "Chemical and Catalytic Reaction Engineering";McGraw-HIII: New York, 1976; p 386. Gut, G.; Meier, R. U., Zwicky, J. J.; Kut. 0. M. Chimle 1975, 2 9 , 295. Gut, G.; Buehlmann, Th. Chlmle 1981, 35, 64. Gut, G. Swiss Chem. 1982, 4 / 3 a , 17. Jana, D.; Malti, M. M.; Avasthl, 8. N.; Pallt, S . K. "Proceedings, 4th National Symposium on Catalysis, 1970", 1980; p 140. Just, G. 2.Phys. Chem. 1901, 37, 342. Kalantrl, P. B.; Chandalla, S. B. Ind. Eng. Chem. Process Des. Dev. 1982, 2 1 , 108. Satterfield, C. N. "Mass Transfer In Heterogeneous Catalysis"; Cambridge University Press: Cambridge, MA, 1970. Sokol'skaya. A. M. Russ. J . Phys. Chem. 1975, 49, 246. Sokol'skii, d. v.; Omarkulov, T. 0.; Dzharikbaev, T. K. Dokl. Akad. Nauk SSSR 1977, 232, 1359. Yao, H. C.; Emmett, P. H. J . Am. Chem. SOC. 1959, 81, 4125. Zwlcky, J. J.; Gut, 0. Chem. Eng. Sci. 1978, 33, 1363.
Receiued for reuiew December 27, 1982 Accepted June 10, 1983
T = temperature, K, "C t = time s, min
Lateral Mixing of Solids in Batch Gas-Solids Fluidized Beds Yan-fu Shlt and L. T. Fan' Department of Chemical Engineering, Kansas State University, Manhattan, Kansas 66506
The lateral dispersion coefficients of particles, D,, were measured in a rectangular gas-solids fluidized bed and
the effects of various factors on D, were studied. Based on the results, an expression has been derived to correlate D, as a function of the particle characteristics, properties of the fluidizing medium, and operating conditions.
Table I. Properties of Solid Particles
Introduction
Lateral mixing of solids in gas-solids fluidized beds influences the performance of physical and chemical processes carried out in them, e.g., thermal decomposition and drying of particulate matter and combustion of coal (see, e.g., Fan et al., 1979; Fan and Chang, 1981; Chang et al., 1982). According to Grace (1981), knowledge of such lateral or radial mixing can be more important than that of axial mixing in assessing the performance of a gas-solids fluidized-bed processing unit. Thus, the subject of lateral mixing of solids in fluidized beds has attracted the interest of a substantial number of researchers (Brotz, 1956 Gabor, 1964; Mori and Nakamura, 1965; Highley and Merrick, 'On leave from Chengdu University of Science and Technology,
Chengdu, China.
material silica gel sand
d,
mm 1.125 0.491
Umf I
PS,
g/cm3 2.61 2.62
Emf
0.387 0.446
cmls 61.71 20
1971; Hirama et al., 19751, and some experimentally measured lateral dispersion coefficients have been reported; however, the available data are far from sufficient. On the basis of the so-called bubble model, Kunii and Levenspiel (1969) have proposed an equation for predicting the lateral dispersion coefficient, D,,, but it appears that the equation has not been thoroughly validated experimentally (Hirama et al., 1975). The purposes of this work were to determine experimentally the lateral dispersion coefficientsof particles, D,,, in a batch gas-solids fluidized bed, to interpret the data
0196-4305/84/1 l23-0337$Q1.50/0 0 1984 American Chemical Society
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Ind. Eng. Chem. Process.Des. Dev., Vol. 23, No. 2, 1984 Partition
Table 11. Summary of the Experimental Conditions and Results
Pocked bed distributer I
+L
6
0
0
-
i
T
Figure 1. Schematic of experimental apparatus; dimension in mm.
obtained in the light of the plausible mechanisms of lateral mixing of solids, and eventually to develop a fairly general correlation for eatimating D, as a function of the properties of fluidized particles and fluidizing medium and of the operating conditions. Experimental Methods Material. Silica gel and sand particles were fluidized by air under room conditions (1 atm and 25 f 5 "C); characteristics of these particles are shown in Table I. Particles dyed by red food color were used as tracer. Apparatus. The fluidized bed employed is illustrated in Figure 1. I t was constructed of transparent plastic (Plexiglas) plates. Its dimensions were 600 mm length, 50 mm width and 350 mm height. The fluidizing air was supplied to the bed through a packed bed between two 60-mesh screens. This packed bed served as the distributor. Procedure. The experimental procedure was the same as that employed by Brotz (1956). A partition was inserted in the center of the bed where particles were filled to a static bed height between 1.97 and 5.23 cm. One half of the bed was charged with dyed particles and the other with undyed particles. The particles were fluidized at a constant superficial air velocity. When the stable state of fluidization was established, the partition was quickly removed. After a specified time interval the air feed was terminated. The run time varied from about 0.5 to 2.5 min depending on the air velocity and fluidized particles, and the samples of the mixed particles were taken from different lateral positions of the bed. A weighed sample was washed with a known volume of water. A spectrophotometer was used to measure the concentration of dye dissolved into the wash water from which the concentration of tracer particles in the sample was recovered. Results and Discussion The experimental conditions and results are summarized in Table 11. A typical set of concentration profile data is illustrated in Figure 2 (run 1). Totally, 15 runs were carried out. Treatment of Data. The one-dimensional diffusion model was used to characterize lateral mixing of solids in a gas-solids fluidized bed. The governing differential equation of the model is
ac at
a2c ax2
- = DB,-
The appropriate initial and boundary conditions are t=O,O
