Rates of diffusion of helium, nitrogen, and carbon dioxide through alumina pellets were measured a t atmospheric pressure and room temperature. The cylindrical pellets, 3/4 in. diameter and % in. in length, were prepared from a-alumina particles with a mean pore radius of 65 A.Surface area and pore volume data indicated that the corresponding mean pore radius of the micro and macropores in the whole pellet was 96 A.The results showed that Knudsen type of diffusion was the controlling transport process despite the large fraction of void volume in the macropores. Carbon dioxide diffused more rapidly than expected, suggesting the possibility of migration of physically adsorbed molecules along the pore walls.The diffusion rates were about 16% higher than predicted, with a mean pore radius (Wheeler model) based upon the void volume of both micro and macropores used. However there is no logical basis for using this mean pore radius for o pellet having widely separated, micro and macropore size distributions.
Analogous correlations were developed for the heat transfer coefficients and for pressure drop, the dimensionless groups in the above being the same as for open tubes. The two relationships are applicable for the range in DT/DP ratio from 14 to 3 and in NR. from 40,000 to 300. The first is satisfactory within +15% for heating of liquids in the above packed tube, the second within flO% for most of the data of packed tubes reported so far. CRITERIA OF FLOW IN PACKED BEDSThe packed beds containing small packings have received much attention; the flow and transfer processes in them have been studied with different methods of approach, for example empirical correlations, analysis based on differential equations, and analysis by means of statistical concepts for turbulent diffusion. As shown in the following brief discussion, the availablc information provides the basis for a conclusion that is important for the present study; this is that the packed columns may be conveniently divided into two classes: the packed beds with DT/Dp ratios greater than 10 or 12 and the packed tubes with smaller DT/Dp ratios. In the former, ana1og;y among the three transfer processes is found by the use of the modified Reynolds number [ N ' R , ; ( D~W , ,~) /~] as the criterion of flow. In the latter it appears that the Reynolds number based on tube diameter ( D T w~) / p ] can be used advantageously for satisfactory empirical correlations. In the above as well as in the following account the term packed bed is used to specify the packed systems containing (nonconducting) smooth, spherical, randomly packed packings of uniform size with DT/Dp ratios greater than 12. The term packed tube is used for the packed systems of same properties with smaller DT/D, ratios.Data and different empirical correlations for heat transfer coefficients at the tube wall of packed columns have been reported by Colburn (18) and 20). These correlations are based on the dimensionless groups N,, and N R . and a complex function of the Dp/DT ratio. Schumacher (10) used the above data to show a single comprehensive correlation represented in a plot of log NNu vs. log N R s . The significant part of this Page 246correlation, given as is applicable when N R , is greater than 9,500 and also pertains mostly to the data of packed tubes with small D J D p ratios. The suitability of this simple relationship, without any need for a complex correction factor based on Dp/DT ratio, indicated that the tube-diameter-based Reynolds number is to be preferred for the correlation of the heat transfer data of the present investigation in packed tubes.It is remarkable that none of the available correlations for pressure drop [including that of Leva and co-workers ( 1 5 , 1 6 ) ] is satisfactory for the case of packed tubes, as is evident from a recent report (13). On the other hand, for (spherical) packed beds the two apparently different correlations of Chilton and Colburn (14) and Ergun (8) Recently Baron ( I ) and Wilhelm and co-workers (2,3) used the approaches based on differenti...
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