Shorter Communications REFERENCES H. M., Regelungstechnik. Modern theorien und ihne Verwendbarkeit, Symp. on Control held at Heidelberg, Sept. 1956). 121 GILBILARO L. G. and LEES F. L., Chem. Engng Sci. 1969 24 85. JI 1968 14 805. PI BUFFHAM B. A. and GIBILARO L. G.,A.I.Ch.E. K., Chem. Engng Sci. 1970 25 583. [41 MICHELSEN M. L. and 0STERGAARD
Engineerinp Science, 1972. Vol. 27, pp. 447-448.
Void distributions (First received
p. 243. R. Oldenbourg 1957. (Proc. of
Printed in Great Britain
in a bubbly fluidized bed I97 1; accepted
1. INTRODUCTION MOST STUDIES of the local properties of bubbly fluidized beds have been conducted with two-dimensional cells. In these, being essentially Hele-Shaw cells, the wall effects are certainly important, if not dominant, and time-average variations along any horizontal line parallel to the walls may justifiably be neglected. Indeed, nearly all current models for fluidized-bed behavior assume uniform time-average properties throughout the bed. The closest previous work to that reported here is that of Bakker and Heertjes[ 11, who determined time-average void fraction patterns in a fluidized bed 4 in. in dia., using a capacitance probe. They concluded that the radial variation in porosity was in general less than 10 per cent, which would appear certainly to justify the assumption of a gradientless bed. We find, however, in this work, using a resistivity probe, radial variations of the order of 30 per cent in a 11.25 in. dia. bed, which would indicate that commercial units probably have very significant radial variations in porosity. 2. EXPERIMENTAL Coke particles in the range of 18 to 40 lnesh were fluidized by air in a lucite column 5 ft high and 11.25 in. id. The rest height of the bed was 28 in., a& the porosity, measured by mercury displacement, was 0.49. The air flow rates ranged from 1400 to 4000ft3/hr at a supply pressure of 2Opsi. entering through a Qin. thick microporous stainless-steel plate. The resistivity probe and the circuit is similar to that introduced by Neal and Bankoff for the measurement of time-average void fraction in a mercury-nitrogen concurrent flow. The principle depends upon the fact that the leakage path to ground is virtually an open circuit when a bubble contacts the bare probe tip. Goldschmidt and LeGoff adapted the probe to a fluidized coke bed and studied bubble size distributions, while Osberg et a1. made an extensive statistical study of a bubbly coke bed, using a two-point resistivity probe. In the present case the probes consisted of 0.04-in. dia. tungsten rods, insulated except for a single bare spot, and placed horizontally along a diameter at elevations of 6, 12, 18, 24, 30 and 36in. from the distribution plate. A radial traverse could thus be made by pulling the rod in and out. To ensure minimum resistance to ground, two 6 in. wide copper sheets were embedded along the full height of the wall. The simple electrical circuit consisted of a 30-V d.c. source, a series resistance of 1 M, an integrator and a recorder. The average value of the bed resistance to ground was about 0, I M
24 May 197 I)
at the maximum flow range, and decreased for smaller flows. Values of 0.5-2.0 M for the series resistance, R,, produced only a 5 per cent variation in the time-average signal a, where a is a dimensionless voltage such that (Y= 0 corresponds to the packed bed, and (Y= I corresponds to an empty bubble at the probe bare spot. The time-average local excess bed porosity may thus be identified with 8. 3. RESULTS Radial traverses were made over the flow range of l4004022 ft3/hr at six elevations, with results as shown in Figs. l-4. Additional data can be found elsewhere T51. These rather interesting results can be notddf (1) There is, at every level and at every flowrate, a monotonic decrease in void-fraction from the center radially outwards. At 4022 ftYhr, corresponding to a suuerficial velocitv of 1.6 ftlsec, measured at up&reamEonditions, the fractional increase in void fraction from the wall to the center was in the range of 0.2-0.45. Qualitatively similar results were reported by Bakker and Heertjes in a bed 4 in. in dia., but with a radial variation of less than 10 per cent. One might expect, based on these results, even larger radial variations in commercial units. This radial void fraction pattern is consistent with a preferential channeling of gas flow near the center, and a downflow of solids along the walls. Very similar behavior is observed in liquid-gas bubbly systems.
4 24in 5 30in 6 361”
Fig. 1. Flow rate: 1400 ft*/hr.
Fig. 2. Flow rate: 2325 ft3/hr.
Fig. 4. Flow rate: 4022 ft3/hr. porous wall in which solid particles are kept away distributor by the entering gas velocity. The fact minimum of the isopore curves are located some above the distributor was also noted by Bakker and
from the that the distance Heertjes
[Il. (3) Some experiments were conducted to determine the effect of inlet maldistribution on the void fraction pattern. In this series of experiments, the porous plate was blocked over diameters of 2, 4, 8, 10.75 in. respectively, the last one leaving free a small annulus of tin. width. Rather surprisingly, even when the flow was blocked from a 10.75 in. dia. central portion of the distributor, no effect on the radial void fraction distribution could be observed 6 in. above the distributor. This implies that wakes behind obstructions are indeed short, and calls into question the system of baffles and grids commonly used in commercial units to redistribute the flow. Acknowledgement-This work was supported by the National Science Foundation under Grant G K- 1744. Fig. 3. Flow rate: 3041 ft3/hr. (2) The void fraction decreases with distance above the distributor, and then begins to increase monotonically. The minimum point depends upon the flow rate and radial position. There is clearly, therefore, an effect due to the horizontal
Department of Chemical Engineering Northwestern University Evanston, Illinois, U.S.A.
tNow serving with the French Army.
REFERENCES 111 BAKKER P. J. and HEERTJES P. M., Chem. Engng Sci. 1960 12 260. [21 NEAL G. L. and BANKOFF S. G.,A.I.Ch.E.JI 1963 9490.  GOLDSCHMIDT D. and LeGOFF P., Trans. Inst. them. Engrs. 196745T 196.  PARK W. H., KANG W. K., CAPES C. E. and OSBERG G. L., Chem. Engng Sci. 1969 24 85 1 [S] LARROUX G. J., M. S. Thesis, Northwestern University 1970.
G. J. LARROUXt Y. G. KIM S. G. BANKOFF