Heterogeneous regime, bubble columns

For the heterogeneous flow regime, the Akita-Yoshida correlation derived for bubble column reactors is proposed (Akita and Yoshida, 1973 Ramachandran and Chaudhari, 1984 Behkish, 2004 Koide, 1996) ... 

The addition of solids has been found to increase or even decrease the gas holdup, depending on the experimental conditions. When the solids addition promotes bubble break up, the average bubble size is smaller, the bubble rising velocity is reduced, and the gas holdup increases (DOE, 1985). The following correlation of Koide et al. (1963) is used in slurry bubble columns and for the heterogeneous and transition regimes (Koide et al., 1984 Koide, 1996) ... 

Suppose that the reaction takes place in a slurry bubble column and that it is desirable to work in the heterogeneous flow regime. Moreover, assume that the liquid is batch and well mixed and the flow of the gas approximates the ideal plug flow. 

The transition from homogeneous to heterogeneous regime in case of bubble columns was qualitatively described in the introduction. At a certain critical superficial gas velocity, a small disturbance in the hold-up profile sets in liquid circulation, which in turn magnifies the hold-up disturbance. In this way, the disturbance grows, and finally an approximately parabolic gas hold-up profile and intense liquid circulation develop, which are the characteristics of the heterogeneous regime. 

This admits periodic solutions for each value of A, and in general A = m. This indicates multiple cells in the horizontal direction. We restrict ourselves to just one horizontal cell, i.e., n = 1. The value of n = 1 corresponds to one horizontal cell, and all the values of n that are greater than 1 correspond to multiple cells in the horizontal direction. In bubble column transitions, the multiple cells in horizontal direction have been observed only in shallow bubble columns in which the height-to-diameter ratio is less than 1. In the present case, we have considered HID > 1. Therefore, the transition to the heterogeneous regime is characterized by one cell in the horizontal direction. Thus, the first transition appears to correspond to a single cell in the horizontal direction ... 

In bubble columns, gas is dispersed in a continuous liquid phase. Uniform bubble size and bubble concentration characterize the homogeneous regime, particularly in the traverse direction indicating the absence of bulk liquid circulation. In contrast, the heterogeneous regime is characterized by a nonuniform bubble concentration, especially in the traverse direction, because of liquid circulation. 

FIGURE 11.17 (a) Schematic representation of the homogeneous regime uniform concentration and size distributions of bubbles in the transverse direction, (b) Schematic representation of the heterogeneous regime nonuniform concentration and bubble size distributions in the transverse direction. (From Bhole, M. R. and Joshi, J. B. Stability analysis of bubble columns Predictions for regime transition. Chem. Engr. Set, 4493-4507 (2005).)... 

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