Figure 7. Some correlations proposed for prediction of gas holdup in the riser of internal-loop ALRs (Table 1). Gas holdup (tpr) is presented as a function of superficial gas velocity (JG). Other parameters related to geometry and physicochemical properties that were used in the calculations are shown on the figure.

ticular type of reactor with the same physicochemical properties of the system. If this option is not available, then correlation 9 in Table 1 (55) is recommended for prediction of the gas holdup in the riser.

Gas holdup in the downcomer is lower than that in the riser. The extent of this difference depends mainly on the design of the gas separator (67). The downcomer gas holdup is linearly dependent on the riser holdup, as a consequence of the continuity of liquid flow in the reactor. Many expressions of this type have been published (68). At low gas flow rates, ud is usually negligible, since most of the bubbles have enough time to disengage from the liquid in the gas separator. This usually happens at the low gas flow rates frequently used for animal cell cultures.

The gas holdup in the separator is very close to the mean gas holdup in the whole reactor (1) as long as the top clearance Ct is relatively small (one or two diameters). For larger top clearances, the behavior of the gas separator begins to resemble that of a bubble column, and the overall performance of the reactor is influenced by this change.

External-Loop Airlift Reactors. From the point of view of fluid dynamics, neither the external configuration (shape and architecture) nor the fact that both riser and down-comer are easily accessible is the most important difference between external- and internal-loop reactors. The most important point is that the gas separator of the external-loop ALR is built in such way that gas disengagement is usually much more effective in this type of reactor. This can be easily seen in Figure 2. In concentric tubes or split vessels, the shortest path that a bubble has to cover from the riser to the downcomer is a straight line across the baffle that separates the two sections. In the case of external-loop ALRs, there is usually a minimum horizontal distance to be covered, which increases the chances of disengagement of the bubbles. In this case, it is worth pointing out that if gas does appear in the downcomer, then most of it will be fresh air entrained in the reactor because of interfacial turbulence or vortices that appear in the gas separator above the entrance to the downcomer. In many of the studies reported in the literature on holdup in external-loop ALRs, total disengagement is attained. No such data are available for the concentric tubes of split-vessel ALRs, since total disengagement is possible only at very low gas flow rates.

Several authors (37,69-73) have presented their results of gas holdup as the gas velocity versus the superficial mixture velocity, based on the drift flux model of Zuber and Findlay (74). These authors derived general expressions for prediction of the gas holdup and for interpretation of experimental data applicable to nonuniform radial distributions of liquid velocity and gas fraction. The drift velocity is defined as the difference between the velocity of the particular phase (U) and the volumetric flux density of the mixture (J where:

The drift velocities of the gas and liquid phases may thus be expressed as:

Zuber and Findlay (74) derived the relationship [8], which has been shown to be more than adequate to provide a correlation of gas holdup measurements in tower reactors with high liquid velocities, such as ALRs (71):

Jg t

where A is cross-sectional area, C0 is distribution parameter, J is superficial velocity, JG is superficial gas velocity, UG linear gas velocity, and u is gas holdup.

Equation 7 describes the relationship between the gas velocity in a two-phase flow and the volumetric flow density of the mixture, J.

As stressed by Zuber and Findlay (74), J has the advantage of being independent on space coordinates for both one-dimensional flow and multidimensional irrotational flows. The distribution parameter C0 is given by (75):

1 f

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