where the subindexes L, G, and S indicate liquid, gas, and solid, and i indicates the region in which the holdup is considered, that is, gas separator (s) the riser (r), the down-comer (d), or the total reactor (T).

The importance of the holdup is twofold: (1) the value of the holdup gives an indication of the potential for mass transfer, since for a given system a larger gas holdup indicates a larger gas-liquid interfacial area; and (2) the difference in holdup between the riser and the downcomer generates the driving force for liquid circulation. It should be stressed, however, that when referring to gas holdup as the driving force for liquid circulation, only the total volume of the gas is relevant. This is not the case for masstransfer phenomena, in this case, the interfacial area is of paramount importance, and therefore some information on bubble size distribution is required for a complete understanding of the process.

Because gas holdup values vary within a reactor, average values, referring to the whole volume of the reactor, are usually reported. Values referring to a particular section, such as the riser or the downcomer, are much more valuable, since they provide a basis for determining liquid velocity and mixing. However, such values are less frequently reported.

The geometric design of the ALR has a significant influence on the gas holdup. Changes in the ratio Ad/Ar, the cross-sectional areas of the downcomer and the riser, respectively, will change the liquid and gas residence time in each part of the reactor and hence their contributions to the overall holdup. Gas holdup increases with decreasing Ad/Ar (44-47).

Gas Holdup in Internal Airlift Reactors. Correlations presented for internal-loop ALRs are shown in Table 1. These take into account liquid properties and geometric differences within a particular design. Most of the correlations take the form:

where vr is the gas holdup in the riser, JG is the superficial gas velocity (gas volumetric flow rate per unit of cross-sectional area), iap is the effective viscosity of the liquid, and a, b, C, and a are constants that depend on the geometry of the reactor and the properties of the liquid. The correlation can be used to predict the holdup in a system that is being designed or simulated as a function of the operating variables, the geometry of the system, or the liquid properties. Such correlations are effective for fitting data for the same type of reactor (e.g., a split-vessel reactor) with different area ratios or even different liquid viscosities, but they are mostly reactor-type specific.

The cyclic flow in the ALR complicates the analysis of the system. The riser gas holdup depends strongly on the geometric configuration of the gas-liquid separator and the water level in the gas separator. This has been shown experimentally in a split-vessel rectangular ALR (60), but the premise can essentially be extended to any internal-loop ALR. Analysis of the system revealed that these factors influence the gas disengagement and hence the gas recirculation in the downcomer. When this influence is taken into account and the holdup is plotted against the true gas superficial velocity, JG,true, which is defined as the sum of the gas superficial velocity due to the freshly injected gas, Qin, and to the recirculated gas, Qd, that is,

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