Holdup studies in three-phase fluidized beds and related systems

Previous research in three-phase fluidization has provided some experimental data on individual phase holdups, but no unified bed model for predicting these holdups under a variety of circumstances. A step in this direction is made here with the development of a "generalized wake model", which builds upon the earlier analyses of 0stergaard, of Efremov and Vakhrushev, and of Rigby and Capes. The present analysis takes into account 1. the effect of size and particle content of the bubble wakes, 2. the circulation of solids initiated by particle entrainment in the bubble wakes, and 3. the relative motion between the continuous phase and the dispersed phases. It does not take into account any surface effects, especially the solids wettability. The expression used for estimating the wake volume fraction was necessarily arbitrary, due to the paucity of relevant information on bubble wakes, especially in the presence of solids. Comparison of the generalized wake model with previous analyses indicates that the earlier models are special cases of the generalized Wake model. Where the wake volume fraction can be neglected, the generalized model reduces to the "gas-free model," which follows from the mechanism proposed by Volk. This simplified model gives good prediction of solids holdup for previous experimental data oh three-phase fluidization of heavy and/or large particles, in which the paradoxical bed contraction on introduction of gas is no longer observed. Experiments to test the generalized wake model were carried out over a particle diameter range of 1/4 - 3 mm and a particle density range of 2.5 - 11.1 gm/cm³, using water (1 c.p.), aqueous glycerol (2.1 c.p.) and aqueous polyethylene glycol (63 c.p.), covering the particle Reynolds number range of 0.36 - 1800. The experiments were performed in 20 mm and 2 inch diameter transparent columns. The liquid superficial velocity was varied from 0.4 to 39 cm/sec and the gas (air) superficial velocity from 0.2 to 21.0 cm/sec. Holdups in the three-phase fluidized bed, as well as in the gas-liquid regions above and below the bed, were measured by the pressure drop gradient method and by the valve shut-off technique. Attempts were made to analyze, as well as to modify, the methods used for measuring holdups. Thus, whereas the expanded bed height in the 20 mm glass column was obtained from somewhat arbitrary visual observations, the expanded bed height in the 2 inch perspex column was obtained by the intersection of two straight lines, one of positive (three-phase region) and one of negative (two-phase region) slope, resulting from a plot of the pressure drop profile in the axial direction. Similarly, attempts to improve upon the gas holdup measurement techniques produced an electro-resistivity probe with a slight variation in design from that employed by Nassos and Bankoff, well suited for measurements in air-water flow. The subsequent use of the probe for measuring gas holdups in three-phase fluidized beds was not as successful. For the beds of small light particles/ the knowledge of wake characteristics—the size as well as the particle content of the bubble wakes—was shown to be of critical importance for solids holdup predictions and of little consequence for gas holdup predictions. On the other hand, for the large or heavy particles, the gas-free model again sufficed for predictions of solids holdup, thereby suggesting the insignificant role of bubble wakes in these systems. The operation of the three-phase fluidized beds in the Stokes regime, though subject to particle elutriation, similarly showed no apparent effect of bubble wakes. The generalized wake model was thus vindicated by the experiments, as was a proposed correlation for bubble rise velocity in the absence or presence of solids, which was incorporated into the model.

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