It might be pointed out that the dispersion equation used byClift et 81. (1974) is valid for analyzing the stability of a gas bubble in liquid-solid fluidized beds (the so-called three-phase fluidized beds), but then the “intermediate” and “complete” equations must be suitably modified before attempting any comparisons.
Literature Cited Bellman, R., Pennington. R. H., Quart. ~ p p l~. a t h .12, , 151 (1954). Clifi, R.9 Grace, J. R.,Weber, M. E., lnd. EnQ. Chem. Fundam., 13,45 (1974). Wilson, A. J., Proc. Camb. Phil. SOC.,81, 595 (1965).
Instituttet f o r Kemiteknik Danmarks tekniske H$jskole 2800 Lyngby, Denmark
Vinay K. Bhatia
Stability of Bubbles in Fluidized Beds Sir: We are grateful to Dr. Bhatia for pointing out a possible refinement of our analysis of the stability of bubbles in fluidized beds, to account for the density but not the viscosity of the fluidizing fluid. We agree entirely that our “simplified” dispersion equation is not strictly applicable to liquid fluidized beds, and our original paper states explicitly that it is to be used only for gas fluidized systems where the density of the fluidizing fluid is very much smaller than that of the particulate phase. For liquid fluidized beds, Dr. Bhatia’s dispersion equation appears to represent a useful method for calculating the growth rate of infinitesimal disturbances. The essential difference between his result and our “intermediate” and “complete” equations is that whereas he treats the bubble and dense phases as distinct, our model allows for percolation of the fluidizing fluid through the roof of a bubble. The close agreement between the two sets of numerical predictions further confirms our conclusion that the velocity of the interstitial fluid has negligible effect on bubble stability, which is determined primarily by the effective kinematic viscosity of the dense phase. I t may be noted that this conclusion could not have been reached without the analysis presented in our paper. Dr. Bhatia’s suggestion that our simplified dispersion equation can be used for analysis of the stability of a gas bubble in a three-phase fluidized bed must be viewed with
caution. The experiments of Henriksen and Ostergaard (1974) suggest that surface tension a t the gas-liquid interface determines a minimum disturbance wavelength below which a perturbation will not grow. This is predicted by the Bellman and Pennington analysis, but was specifically excluded from our treatment since there is nothing equivalent to surface tension in the fluid-particle systems we were concerned with. In addition, Dr. Bhatia does not mention what values he would use for the effective kinematic viscosity of the liquid-solid “dense phase” in a three-phase fluidized bed. We are mystified by the suggestion that our “intermediate” and “complete” equations must be “suitably modified” in order to be applied to a three-phase bed. These equations specifically account for percolation of the fluidizing fluid through the bubble interface. Since this does not occur in a three-phase bed, we find it difficult to conceive of any modification which could make these equations applicable. Literature Cited Henriksen, H. K., Ostergaard, K.,Chem. Eng. Sci.. 29, 626 (1974).
Department of Chemical Engineering McGill University Montreal, Quebec, Canada H3C 3G1
R. Clift J. R. Grace* M. E. Weber
A Second Mode of Operating Packed Columns and Wetted Wall Columns Sir: In their recent article on this topic, Leung et al. (1975) assert “For a fixed set of gas and liquid rates below the flooding flow rates in a . . . packed column, two modes of operation are possible, viz., normal and incipient flooding. The latter has not been reported previously.” These are surprising claims. Two modes of operation of packed towers, the bubbling mode and the ordinary trickling mode, have been thoroughly investigated by earlier workers. Presumably Leung et al. are proposing, in “incipient flooding,” a third and novel mode. This claim I dispute. Perhaps the clearest exposition of the two well-known modes is to be found in the work of Musil et al. (1968).
These workers report complete curves of holdup and pressure gradient against gas rate for a range of fixed liquid rates. Except for the flow control system employed by Leung et al., both the apparatus and the flow ranges used by the two groups were similar; the results may be almost directly compared. Typical curves from the work of Musil et al. are shown in Figure 1. They show clearly that for a fixed liquid rate there is a maximum possible countercurrent gas flow. This we know as the flooding rate. For gas flows less than flooding, both liquid holdup and gas phase pressure gradient are double valued. When the bottom chamber of the column and the packing are initially filled with liquid and kept Ind. Eng. Chem., Fundam., Vol. 15, No.
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Superficial gas velocitj (m/5)
Figure 1. Modes of operation of a packed column. Curves are taken from Musil et al. (1968). Air rate as shown; superficial water velocity 0.0035 m/sec; glass Raschig rings size 10.3 mm in a glass column of diameter 100 mm, packed height 1.75 m.
that way, a column operates in the bubbling or flooded mode (colonne noy6e), with high holdup and pressure drop. When the bottom chamber contains mainly gas, and liquid drains away freely, operation is in the ordinary trickling mode (colonne arros6e) with lower holdup and pressure drop. No instability was reported in either mode. These observations may be used to explain the results reported by Leung et al. They used a packing support grid with voidage less than that of the packing-a grid that would flood at flow rates less than the flooding rates for the packing. Then, after the gas rate was set, using the pressure-actuated flow controller, liquid was added at a rate greater than the grid flooding rate until, with backup of liquid in the packing, the preset pressure drop was reached. The flow was then brought back to a steady value by the controller. At this point the tower would be operating in the two modes a t the same time, trickling in the upper part, bubbling below. The surface of separation would necessarily be somewhere between the differential pressure sensing points. The restricting grid was essential to the operation if the tower were to operate without the bottom chamber flooded. Without this restriction, more flexible operation could have
been achieved with less trouble and expense by the use of an adjustable liquid seal. In an earlier report of this work, Brooks et al. (1974) implicitly propose this kind of explanation, when they write of “flooding flowrates” and “flooded operation.” But now they specifically reject it. Part of the problem arises from an ambiguous use of the words “flooding” and Wooded.” At one point they are used to describe bubbling operation, at another to describe operation at limiting flows. But that is not the whole story. In the later article they assert, “In the incipient flooding mode both liquid and gaseous phases are continuous. For a given column, higher flow rates can be achieved in the ‘incipient flooding mode’ than in the ‘emulsification operating mode.’ ” But neither in their article nor in the thesis on which it is based (Hutton 1974) do they adduce the slightest experimental evidence for these claims. They have not shown how they established whether the gas phase was continuous. They have not reported any contrasting behavior of the column in the simple bubbling mode. They have not furnished any photographs or even given a verbal description of the appearance of the column by which the reader might judge. I t is a commonplace of the scientific method that assertations made without evidence may be rejected without apology. And again, that new explanations can be ignored if the conventional ones are sufficient. That is my position. I believe that the results can be satisfactorily explained in terms of the well-known operating modes. No evidence has been presented to support the claim of novel phenomena. Nomenclature g = local gravitational acceleration, m/sec2 h = total holdup, dimensionless p = pressure, N/m2 z = column height, m e = dry voidage, dimensionless p~ = liquid density, kg/m3 Literature Cited Brooks, P. C., Hutton, B. E. T., Leung, L. S., Nicklin, D. J., Ch8m. Eng., 81, (4) 152 (1974). Hutton, B. E. T., Ph.D. Thesis, University of Queensland, 1974. Leung, L. S., Hutton, B. E. T., Nicklin, D. J., Ind. Eng. Chem. Fundam., 14, 63 (1975). Musil, L.. Prost, C., Le Goff, P., Chim. Ind., Gen. Chim., 100, 674 (1968)
Department of Chemical Engineering Uniuersity of New South Wales Kensington, New South Wales 2033 Australia
John E.Buchanan
A Second Mode of Operating Packed Columns and Wetted Wall Columns Sir: In his letter Buchanan asserted that our “incipient flooding” mode of operation is the same as the “bubbling column” operation. Operation of a bubbling column is of course well known, and we apologize for not mentioning such operation in our paper. In a bubbling column, the gas travels up the bed in the form of bubbles; i.e., the gas phase is discontinuous. In the incipient flooding mode described in our paper, we claim that the gas phase is continuous and 88
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is therefore different from the bubbling mode. The three different modes of countercurrent operation are summarized in Figure 1.Figure l a shows the normal mode of operation, Figure l b the bubbling mode, and Figure ICthe “incipient flooding” mode of operation. The existence of the incipient flooding mode was first demonstrated in a wetted wall column where we can observe readily that both phases are continuous. The experi-
