Flow regime holdups

Nonintrusive Instrumentation. Essential to quantitatively enlarging fundamental descriptions of flow patterns and flow regimes are localized nonintmsive measurements. Early investigators used time-averaged pressure traverses for holdups, and pilot tubes for velocity measurements. In the 1990s investigators use laser-Doppler and hot film anemometers, conductivity probes, and optical fibers to capture time-averaged turbulent fluctuations (39). 

The evaluation of the parameters for this flow regime requires the calculation of the Reynolds number and hydraulic diameter for each continuous phase. The hydraulic diameter can be determined only if the holdup of each phase is known. This again illustrates the importance of understanding the fluid mechanics of two phase systems. Once the hydraulic diameter is known, the Reynolds number can be evaluated with the knowledge of the in situ phase velocity, and the parameters of the model equations can be evaluated. 

For batch liquid, usG f = usG. The subscript w in symbols denotes water property. SI units are used in this equation. For the derivation of this correlation, air velocities up to 0.305 m/s and liquid velocities up to 0.09 m/s were used. The Hughmark correlation has been derived for the heterogeneous flow regime. In Figure 3.31, the effect of liquid flow on gas holdup for the air-water system is presented. 

As long as the flow regime is trickling, the gas phase is incompressible, which means that neither the velocities nor the holdups depend on the axial position (no axial gradients of these variables). 

In the same way, Larachi et al. [48] evaluated with an important trickle-flow-regime database (4,000 experiments) different phenomenological models for liquid holdup and two-phase pressure drop in TBR. Table 5.2-5 summarizes the respective scatters (mean relative error and deviation) between the experimental values of pressure drop, AP/Z, and liquid holdup, fit, and their predictions by the different models. 

Figure 2. Relative liquid holdup versus S/u, in the pulsing flow regime. System is cur-water. Key 9,2.5 X 2.5 and X> 4 X 4 Raschig rings.

It is shown, that the performance of a pulsing packed column can be split up into its two component parts, the pulses and the zones in between pulses. The pulses can be described as parts of the bed already in the dispersed bubble flow regime the zones-in between the pulses as parts of the bed still in the gas-continuous regime. The pulse frequency is linearly dependent upon the real liquid velocity. The properties of the pulse, like holdup, velocity and height are quite independent upon all the parameters except gas flow rate. 

The following developments will be restricted to laminar liquid flow with weak gas-liquid interactions. However, this is not a limitation of the proposed methodology which could be easily applied to any other flow regime. Applications will be presented for the modelling of the irrigation rate, the dynamic liquid holdup and the apparent reaction rate in the absence of external mass transfer limitations and in the case of non volatile liquid reactants (i.e. approximatively the operating conditions of petroleum hydrotreatment). 

The existing data for dynamic saturation (dynamic holdup divided by bed porosity) in the trickle-flow regime (18, 20, 21, 24, 25) can be correlated by the following equation ... 

Dynamic tracer tests can be used to determine dynamic holdup and catalyst contacting which in trickle-flow regime can be correlated with Reynolds and Gallileo number. A simple reactor model for gas limiting reactant when matched to experimental results for one solvent and one catalyst activity predicts reactor performance well for different catalyst activities and in other solvents over a wide range of liquid velocities. 

The effect of liquid and vapor rates on the operating holdup is shown in Fig. 8.21. In the preloading regime holdup is essentially independent of vapor flow (100,101), but is a strong function of liquid flow rate and packing size. Smaller-size packings and high liquid rates tend to have more holdup. 

Previous hydrodynamic studies of trickle-beds are primarily experimental work involving pilot scale columns, for instance, constructing flow regime maps, and correlating pressure drop and liquid holdup data (1-5). Although these contributions have provided much insight, there is a lot of uncertainty in applying these data for industrial applications. 

In this paper correlations presented by Sato et al. for liquid holdup and pressure drop in trickle bed reactors were used to examine the characteristics of large-scale columns. The trickling-pulsing transition relationship given by Ng was also employed to determine the flow regime present. Some interesting phenomena were observed, specifically ... 

Two forms of Eq. (6-21) have been proposed. For low values of the Reynolds number of liquid flow, liquid holdup in a packed column can be predicted by consideration of laminar liquid flow down inclined surfaces against a pressure gradient In this viscous flow regime,... 

Specchia and Baldi90 presented separate correlations for the dynamic liquid holdup in the poor interaction regime (i.e., gas-coirtinuous-flow regime) and the high-in teraction regime (i.e., pulsed and spray flow).In the poor-interaction regime, they presented a relation... 

This correlation was in reasonable agreement with the low gas flow (Gg < 0.01 g cm-2 s1) data of Sato et al.74 for a benzoic acid-water system with 5.5- and 12.2-mmparticle diameter. Hirose et al.38 made extensive measurements in trickle-flow, pulsed-flowrand bubble-flow regimes and correlated the enhancement factor in Ks due to parallel gas flow with the liquid velocity. They found that this enhancement factor (ratio of Ks in the presence of gas flow to Ks in the absence of gas flow) was inversely proportional to the total liquid holdup and to a first approximation has the value 2. Their data for Ks as a function of liquid velocity... 

The experimental data were largely obtained in bubble-flow and pulsed-flow regimes. A typical radial variation in the liquid holdup obtained under pulsed-flow regime is shown in Fig. 7-11. Runs nos. 1 and 2 in this figure are duplicate runs. Although the manner in which the column was packed may have had some effect on the holdup profile, it is clear from this figure that the liquid holdup profile was relatively flat in the center of the tube and was very sharp near the wall. It should be noted that the liquid holdup in this study was defined in terms of fraction of open reactor volume occupied by the liquid. 

Recommendations The gas holdup in the bubble-flow regime can be estimated using either Cq. (7-13) or F.q. (7-14). For the estimation of liquid holdup in the bubble-flow regime, use of Eq. (7-9) is recommended. In the pulsed-flow regime, the data of PERC and Eq. (7-15) would be useful. More experimental work with the hydrocarbon systems is needed. 

Chen8,9 studied the gas holdup of a 7-cm i.d. 244-cm long column randomly packed with open-end screen cylinders of various sizes (1.27 cm x 1.27 cm and 1.9 cm x 1.9 cm) and screen meshes (8-14 mesh). The results with an air-water system were obtained in the bubble-flow regime. The screen cylinders were found to reduce the gas holdup. The results showed that for t/0g < 4 cm s, the gas holdup was a linear function of gas velocity, a result similar to the one obtained in an unpacked bubble-column bul not in a column packed with Raschig rings or other conventional packings. He also showed that for low gas velocity, l/0G < 3.64 cm s 1 the parameter (hG - 1ig)//ig was a unique linear function of liquid velocity (independent of gas velocity). Here, /iG is the gas holdup at zero liquid velocity. He also obtained a relationship between the gas holdup and the slip velocity between gas and liquid. All the data were graphically illustrated, however, no analytical correlation was presented. 

Significant literature on the axiaj dispersion in gas and liquid phases for countercurrent-flow packed-bed columns have been reported. Trickle- and bubble-flow regimes have been considered. Unlike the holdup, there is quite a discrepancy in the results of various investigators. Almost all the RTD data are correlated by a single-parameter axial dispersion model. A summary of the reported axial dispersion studies in countercurrent flow through a packed bed is given in Table 8-1. 

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