Static holdup

Static holdup is the amount of liquid remaining on packing that has been fully wetted and then drained. Total holdup is the amount of liquid on the packing under dynamic conditions. Operating holdup is the amount of liquid attributed to operation and is measured experimentally as the difference between total and static holdup. Thus,... 

Static holdup depends upon the balance between surface-tension forces tending to hold hquiciin the bed and gravity or other forces that tend to displace the liquid out of the bed. Estimates of static holdup (for gravity drainage) may be made from the following relationship of Shulman et al. [Am. Jn.st. Chem. Eng. J., 1, 259 (1955)] ... 

For other packings and for the case in which static holdup is changed by gas flowing through the bed, the method of Dombrowsld and Brownell [Jnd. Eng. Chem., 46, 1207 (1954)], which correlates static holdup with a dimensionless capillary number, should be used. 

Operating holdup contributes effectively to mass-transfer rate, since it provides residence time for phase contact and surface regeneration via agglomeration and dispersion. Static holdup is hmited in its contribution to mass-transfer rates, as indicated by Thoenes and Kramers [Chem. Eng. ScL, 8, 271 (1958)]. In laminar regions holdup in general has a negative effecl on the efficiency of separation. 

In conclusion, one can state that the available information on holdup is in general agreement, although some difference exists with respect to the influence of gas flow rate and to the magnitude of static holdup. 

The success of periodic flow interruption is due to the liquid static holdup within the porous catalyst pellets and the interstices of the catalyst bed. 

Liquid holdup is critical in the downflow operation of fixed beds, in contrast to the upflow operation where the liquid occupies practically the whole external free void volume of the bed. Total liquid holdup ht consists of two parts static h, and dynamic holdup liA. Static holdup is related to the volume of liquid that is adherent to the particles surface, whereas dynamic holdup is related to the flowing pari of the liquid. 

Static holdup is a function of the Eotvos number Eo (Van Swaaij el al., 1969) ... 

However, the most rigorous analysis on static holdup is found in the work of Saez el al. (1991), where the maximum value of static holdup based on the total volume of the bed... 

Here, the dynamic liquid holdup (in m3/m3) refers to the portion of the void (available) bed volume that has been occupied by the liquid. There are also correlations for the static holdup, that is, when the flow rate is zero after wetting. Dynamic liquid holdup is normally between 0.03 and 0.25, whereas the static liquid holdup is between 0.01 and 0.05, and for nonporous catalysts, usually he s < 0.05 (see Section 3.6.3 Perry and Green, 1999). 

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. 

This correlation gives, for perfectly wettable solids, fairly good estimates of the static holdup for different particle-geometries and sizes. Saez and Carbonnel [26] used the hydraulic diameter, instead of the nominal particle diameter, as the characteristic length in the Eotvos number, to include the influence of the particle geometry on the static hold-up. However, no improvement could be obtained in correlating the data with this new representation. 

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. 

The bed void volume available for flow and for gas and liquid holdup is determined by the particle size distribution and shape, the particle porosity, and the packing effectiveness. The total voidage and the total liquid holdup can be divided into external and internal terms corresponding to interparticle (bed) and intraparticle (porosity) voidage. The external liquid holdup is further subdivided into static holdup eLs (holdup remaining after bed draining due to surface tension forces) and dynamic holdup eLrf. Additional expressions for the liquid holdup are the pore fillup Ft and the liquid saturation SL ... 

The static holdup can be correlated with the Eotvos number NBo as it results from a balance of surface tension and gravity forces on the liquid held up in the pores in absence of flow ... 

For instance Fig. 19-42 illustrates the dependence of the static holdup on the Eotvos number for porous and nonporous packings. 

Figure 8. Static holdup versus total holdup jar various pulse frequencies. Raschig rings 4 mm. Key 0,0 Hz , 2 Hz +, 1 Hz X, 3 Hz A, 4 Hz A> 5 Hz and...

Static holdup is liquid remaining on the packing after it has been fully wetted and drained for a long time. The contribution of static holdup to mass transfer rates is limited (99). Static holdup can be estimated using the relationship of Shulman et al. (100), as recommended (14). Shulman 8 correlation was derived during the first generation of random packing, but the author is not aware of any updated alternatives. 

EXTERNAL STATIC HOLDUP LIQUID-SOLID CONTACTING CORRELATION CONSTANTS 0.0204 ... 

The holdup of a phase is usually defined as the volume of the phase per unit reactor volume. However, for a fixed-bed reactor, the gas and liquid holdups are often defined on the basis of void volume of the reactor. In a fixed-bed reactor, the liquid and sometimes gas holdups are divided into two parts dynamic holdup, which depends largely on the gas and liquid flow rates and the properties of the fluids and the packing material, and static holdup, which depends to a major extent on the nature of the packing (e.g., porosity of the packing) and the fluids properties. The relationships between the holdups of various phases and the system variables for a variety of three-phase reactors are discussed in Chaps. 6 through 9. 

As shown in Fig. 3-9, flow over the packing surface between junctions is assumed to be laminar. At each junction a fraction, q, of the flow enters the perfectly mixed regions, corresponding to the static holdup region, while the remainder of the flow bypasses the mixing. The probability of an element of fluid being mixed at each junction is taken as q. Michell and Furzer66 derived the expression for the mean residence time for the liquid as... 

In deriving the above equation, it is assumed the laminar film portions of the flow were vertical streamline films of length dp. Lp is the total packed-bed height, packing size, and p, the liquid density. /i5L is the static holdup of... 

The parameter P can be found from the value of the Peclet number for high values of hd /hSL, where hai. and hiL are the dynamic and static holdups (fractions of void volume). At other values of hn./hsL, P is assumed to remain constant. If... 

Schiesser and Lapidus82 showed that the jiorosity of the packings could significantly affect the residence-time distribution and, hence, the axial dispersion coefficient. This indicates the effect of static holdup on the axial dispersion. Van Swaaij et al.103 showed that the liquid-phase axial dispersion depends upon the ratio of dynamic to static liquid holdup (i.e., /ijl/ILl) as long as this ratio is approximately below 8. If > 8, the Peclet number becomes essentially... 

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