Static Liquid Hold-Up

According to the model by Gelbe [22], the static hquid hold-up hst is dependent on the physical properties and the specific hquid load ul. If the hquid load ul tends to zero, the static hold-up reaches its maximum value - adhesion hold-up hn- The following apphes  

As the hquid load ul increases, the static hquid hold-up decreases and finally reaches zero at the so-called critical UL,crit value, i.e.  

This means that the total liquid hold-up hL can be equated with the dynamic liquid holdup hj). According to Mersmann and Deixler [44], the static hquid hold-up hL,st prevails in the case of very low, dimensionless liquid load Bl, acc. to Eq. (4-16)  

the static liquid hold-up reaches the value of the adhesion hold-up hn- The adhesion hold-up hn is dependent on the following number [44], see Fig. 4-2, 

The adhesion hold-up values of the packing elements with diameters of d 0.025—0.090 m and systems analysed in this book are expected to be very low, i.e. approx. 1% and below, as the dimensionless ratio Wep/ErL is in the range of approx. 70-1300. 

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The static liquid hold-up can be determined from the difference with the weight of the TBR after a minimum time of draining with the same TBR dry packing. 

Figure 5.2-24. Experimental static liquid hold-up as a function of the Eotvos number (after Wammes et al. [34]).

Van Swaaij [52] and Charpentier et al. [53] proposed a relationship between the static liquid hold-up, I3stat, and the dimensionless Eotvos number, Eo. At high Eotvos numbers the static hold-up is inversely proportional to Eo, whereas at low Eotvos numbers, the static holdup reaches a maximum value. 

Wammes et al. [34], by employing three different liquids (water - ethanol and 40 % ethyleneglycol aqueous solution) with 3 mm glass spheres, obtained experimentally determined static hold-up data. Figure 5.2-24 shows the values of the static holdup as a function of the Eotvos number together with data of other authors. Wammes et al. [34] concluded that the static liquid hold-up is not affected by the total reactor pressure. 

Ortiz-Arroyo, A. Larachi, F. Iliuta, I. Method for inferring contact angle and for correlating static liquid hold-up in packed beds. Chem. Eng. Sci. 2003, 58 (13), 2835-2855. 

Total liquid hold-up in packed bed, h[ = static hold-up, hg, plus operating hold-up, ho [64, 66]. 

A well-substantiated correlation for air-water systems taken from the trickle bed literature (Morsi and Charpentier, 1981) was used for the volumetric mass transfer coefficients in the / , and (Rewap)i terms in the model. The hi term was taken from a correlation of Kirillov et al. (1983), while the liquid hold-up term a, in Eqs. (70), (71), (74), (77), and (79) were estimated from a hold-up model of Specchia and Baldi (1977). All of these correlations require the pressure drop per unit bed length. The correlation of Rao and Drinkenburg (1985) was employed for this purpose. Liquid static hold-up was assumed invariate and a literature value was used. Gas hold-up was obtained by difference using the bed porosity. 

The total external liquid hold-up is equal to the sum of the static-and dynamic-hold-ups. 

Pulsed columns, depicted in Fig. 6.3-2, are frequently used in solvent extraction. The design of pulsed packed colunms is identical with the design of static packed columns. Just the two-phase liquid hold-up is periodically vertically moved with the frequency /. Typically, the pulsation height is about 0.8-1.2 cm. Very common is a pulsation intensity of a / 1-2.5 cm/s. The pulsation effects a decrease of droplet size and, in turn, an increase of interfacial mass transfer rates. 

The static hold-up is independent of liquid and gas rates, since it represents the liquid held in the packing after a period of drainage time, usually until constant weight of material is received. This requires approximately 1 hour for a 10-in. dia. x 36-in. packed height tower. Table 9-34 adequately summarizes the data. 

In order to use the data in systems handling liquids other than water correction equations and charts are used [66]. The charts are more convenient to use and are presented in Figures 9-46 A, B, C, D. First, determine the total or static hold-ups for water at 20°C second, determine separately the correction for viscosity, density, and surface tension third, multiply the water hold-up by each... 

Static hold-up for water, ft- /ft packing volume Water hold-up, ft liquid/ft tower volume Enthalpy of air saturated at bulk water temperature, Btu/lb dry air... 

As shown in Fig. 8.6, several typical flow patterns can be found in the monolith channels, depending on gas-liquid ratio, flow rates, viscosity, surface tension, and channel diameter. All of these flow patterns show a very low static hold-up, but only two are regular and allow stable operation the so-called Taylor-flow and the film-flow regime. 

Constants and k2 are dependent on packing size and shape and can be obtained by measuring 6q for wetted packing (with static hold up) but without liquid flow. The equation is not valid for high intraction regimes. 

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