then all the data for the different gas separators may be represented by a single relationship, such as equation 3. In other words, if the actual gas flow is known, the influence of gas recirculation (which depends on Ad/Ar and the design of the gas separator) has been already taken into account and does not need to be considered again. Nevertheless, this simple approach has a drawback in that the true gas superficial velocity is difficult to measure because the gas recirculation rate is usually not known. A method for evaluation of the extent of the maximum gas recirculation has recently been developed and will be discussed later in this article.

Thus, correlations that take into account all the variables, which may be easily measured, remain the option of choice. Table 1 shows most of the correlations of this type that have been proposed for the riser holdup in internal-loop ALRs. Comparison of a number of these correlations shows that there is reasonable agreement between the predictions of the different sources (Fig. 7).

Figure 7 can be used as an example of the actual state-of-the-art in ALR design. A number of correlations have been proposed, and three variables (Ad/Ar, iap, and JG) have been tested by most researchers. The ranges in which these variables were studied varies from source to source. In addition, some other variables (such as bottom clearance, top clearance or gas separator design, and surface tension) have been used by some authors but ignored by others. One example is the disengagement ratio defined by Siegel and Merchuk (64), which represents the mean horizontal path of a recirculating bubble relative to the external diameter and is equivalent to the parameter obtained by dimensional analysis (1) as:

Ds 4D

where D is the diameter of column and Ds the diameter of

326 BIOREACTORS, AIR-LIFT REACTORS Table 1. Gas Hold-Up in Internal-Loop ALR

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