Liquid holdup averaging

Farooqi, S. 1. and Richardson, J. F. Trans. Inst. Chem. Eng. 60 (1982) 292-305. Horizontal flow of air and liquid (Newtonian and non-Newtonian) in a smooth pipe Part 1 Correlation for average liquid holdup. 

Fig. 9 illustrates the effect of superficial gas and liquid velocities on the cross-sectionally averaged liquid saturation at the middle of the column (2.5D axial position). It is obvious that the effect of gas velocity on the liquid saturation is not significant within the range of flows studied. This could be due to the fact that solid and liquid holdups are very small, leaving enough space for the gas to flow upwards without significant interactions with the liquid phase flowing downward. 

The measured cross-sectionally averaged liquid holdup (i.e. measured liquid saturation times the bed voidage) are consistent with previously reported results [4], For a similar packing structure, Illiuta and Larachi [4] found liquid holdups, as calculated by their mechanistic model and compared with the reported experimental results, slightly lower than the values obtained in this study. However, there are some differences between the two studies this work was performed in a smaller diameter column ( 30 cm versus... 

Liquid residence time in the packed rotor varies as a function of packing depth, packing type, rotor speed, and liquid properties (26). Two basic approaches have been applied to the measurement of liquid in the rotor. The first measure is the average residence time of the liquid within the rotor, and the second is the liquid holdup on the packing. Due to the flow patterns described previously, not all of the rotor packing is wetted and not all of the liquid resides on the packing surface. As a result, average residence time and liquid holdup are distinct measures of liquid flow, contrary to the experience with packed towers. 

Step 3. The Reynolds number Re is calculated in this step. Dukler developed experimental data determining liquid holdup in two-phase flow systems. Re values above 200,000 are free of liquid slugs and holdup. If Re is greater than 200,000, then the flow is in the froth zone, or it is simply homogeneous flow as a mixture. For homogeneous flow, the average density of the two-phase flow fluid mixture is ... 

The averaging of the dynamic liquid holdup is achieved in a similar way by introducing Eq.2 and 9 into Eq.7. 

Downcomer aeration factor prediction. The fractional liquid holdup varies from about 0.3 in the froth zone to close to unity in the clear liquid zone (Fig. 6.12a). The height of each zone is a complex function of system properties, operating conditions, and downcomer geometry. This makes it practically impossible to theoretically predict the average downcomer aeration factor <(>. . Correlations in the literature (e.g., 46) are based on limited data obtained in atmospheric pressure simulator work with small downcomers. It is therefore difficult to recommend them for commercial-size applications. Zuiderweg (17) presented a plot of downcomer aeration factors derived theoretically from commercial-scale high-pressure flood data. However, the plot is based on a handful of data and is therefore difficult to recommend for general aeration factor prediction. 

It should be noted that the liquid holdup is a time averaged value. In practice, for flows in the pulsing regime at a given column depth, the holdup will vary with time due to the alternating passage of liquid and gas rich slugs. 

The average total liquid holdup in a trickle bed reactor decreases with increasing bed depth in a low pressure laboratory or pilot scale column. However, for commercial use where there is a moderate to high pressure input, the holdup is essentially constant (Figure 5). 

Various methods for estimating KLs are described by Satterfield.150 The most conservative estimate of KLS is obtained as KI S = D/<5,, where D is the molecular diffusivity of the reactant in the liquid phase and <5L the average thickness of liquid film surrounding the particles. This estimation assumes no turbulence in the liquid film. The average thickness of the liquid film can be obtained from a knowledge of the dynamic liquid holdup and the outside area of catalyst particles per unit volume of the reactor, os. For example, if the dynamic liquid holdup is 50 percent of the void volume e, then <5L = e/2as. Various methods for estimating fcL and Ks under trickle-flow conditions are described in Chap. 6. 

Figure 7-12 Dynamic and total liquid holdup as a function of average gas interparticle pore velocity in a 10.2-cm-i.d. column packed with 1.9-cm x 1.9-cm ceramic cylinders.22...

The influence of liquid holdup is shown in Table XVB. For any given operating condition, the average volumetric rate of absorption of oxygen... 

The values of fractional liquid holdup, e, at the inlet and exit are found to be 0.37 and 0.43, respectively. For this case, can be assumed to be constant and equal to the average value of 0.4. 

The predictions from equation (4.6) will be compared first with the experimental values of average liquid holdup for cocmrent two-phase flow of a gas and shear-thinning liquids. For a liquid of given rheology (m and n), the pressure gradient (—Api/L) may be calciflated using the methods presented in Chapter 3 but oifly the power-law model will be used here. 

Figure 4.5 shows representative experimental results for average values of liquid holdup a, as a function of the parameter x, together with the predictions of equation (4.6). The cmwes refer to a series of aqueous china clay suspensions... 

Figure 4.5 Average liquid holdup data for kaolin suspensions in 65% aqueous glycerol solution in streamline flow (D = 42 mm)...

Figure 4.6 Effect of superficial liquid velocity an average liquid holdup...

Figure 4.7 Average liquid holdup as a function of modified parameter Xmod...

In Figure 4.7, the experimentally determined values of average liquid holdup, ai, are plotted against the modified parameter Xmod for suspensions of kaolin in aqueous glycerol (same data as shown in Figure 4.5) and it will be seen that they are now well correlated by equation (4.9). 

Thus, in summary, average liquid holdup can be estimated using equation (4.6) for Newtonian liquids imder all flow conditions, and for non-Newtonian liquids in transitional and turbulent regimes (Re /f > 2000). 

---