Liquid holdup static

Ln(weir) is zero for the condition Mn< Mns. M is the mass of liquid on plate n, and Mns is the mass of liquid on the plate corresponding to the weir height or static liquid holdup on the plate. The rate of loss of liquid from the plate by weepage, however, will depend on the total mass of liquid on the plate... 

Packed fractional distillation columns run in the batch mode are often used for low-pressure drop vacuum separation. With a trayed column, the liquid holdup on the trays contributes directly to the hydraulic head required to pass through the column, and with twenty theoretical stages that static pressure drop is very high, e.g., as much as 100-200 mm Hg. 

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. 

In this equation, %hvt corresponds to the % portion of the void (available) bed volume, which is occupied by the liquid, where us is in cin/s. The constant part in the liquid holdup correlation (21%) is the static liquid holdup. This correlation is derived in beds with no liquid distributors and for particle sizes in the range 1.18-1.4 mm. 

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). 

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 ... 

FIG. 19-42 The static liquid holdup for porous and nonporous solids. (Fig. 7.7 in Ramachandran and Chaudhari, Three-Phase Catalytic Reactors, Gordon and Breach, 1983.)... 

In practice, the thickness of liquid films in trickle beds has been estimated to vary between 0.01 and 0.2 mm (0.004 and 0.008 in). The dynamic liquid holdup fraction is 0.03 to 0.25, and the static fraction is 0.01 to 0.05. The high end of the static fraction includes the liquid that partially fills the pores of the catalyst. The effective gas-liquid interface is 20 to 50 percent of the geometric surface of the particles, but it can approach 100 percent at high liquid loading. This results in an increase of reaction rate as the amount of wetted surface increases (i.e., when the gas-solid reaction rate is negligible). 

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. 

Several points about this model should be noted. First, it takes into account both macromixing as well as micromixing (in the rippled films at the junctions) iir the trickle-bed reactor to correlate the RTD and, second, it assumes that the mixing at the static junctions is achieved by hydrodynamic effects, rather than by diffusion effects, as is often postulated.13-29 The model is not tested against the data from porous packing, where a significant portion of the static liquid holdup is due to the liquid in the pores of the packings. 

When the reaction occurs only in the liquid phase, only dynamic or operating holdup is important for kinetic data evaluation. However, when the reaction occurs both in the liquid and gas phases, both static and dynamic liquid holdups affect the reaction rates. 

The liquid holdup is largely measured by a tracer technique. In this technique the total liquid holdup (dynamic -4- static) is obtained by multiplying the liquid flow rate by the mean residence time. There are a large number of holdup correlations reported in the literature. Since some correlations are for the total liquid holdup and some for the dynamic holdup, proper precautions should be taken in using these correlations. The liquid holdup has been defined in terms of either void volume or the total volume of the column. 

The static liquid holdup is often correlated by the Eotvos number, Eo (= pi.0dp/ffL> where dp is the nominal particle diameter and g the gravitational acceleration). Such a correlation103 is illustrated in Fig. 6-5. The correlation indicates that smaller particle diameter and fluid density and larger surface tension give larger static liquid holdup. The correlation also indicates that a porous material gives a larger static liquid holdup than a nonporous material. 

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... 

Figure 6-11 Axial dispersion as a function of the ratio of dynamic to static liquid holdup.101...

Liquid holdup is a function of liquid flow rate and column pressure drop. Two types of holdup have been defined. Static holdup is the volume of liquid per volume of packing that remains after gas and liquid flows are stopped and bed has drained. Static holdup depends on packing surface characteristics. The second type is operating holdup that is the volume of liquid per volume of packing that drains out of the bed after gas and liquid flows have been stopped. The gas flow rate has little effect on holdup below loading. 

A further advantage of absorption plus reaction is the increase in the mass-transfer coefficient. Some of this increase comes from a greater effective interfacial area, since absorption can now take place in the nearly stagnant regions (static holdup) as well as in the dynamic liquid holdup. For NHj absorption in H2SO4 solutions, K a was 1.5 to 2 times the value for absorption in water.Since the gas-film resistance is controlling, this effect must be due mainly to an increase in effective area. The values of K a for NH3 absorption in acid solutions were about the same as those for vaporization of water, where all the interfacial area is also expected to be effective. The factors and... 

If the catalyst particles are not completely wetted by the liquid phase and the pores consequently not completely filled with liquid phase (static holdup gives some indication of whether this is the case or not), the situation is considerably more complex. In addition to being a function of the Thiele modulus, the catalytic effectiveness will now depend on the fraction of external wetting, rjcs, and the fraction of pore volume filled with liquid, rji. Dudokovic [M.P. Dudokovic, Amer. Inst. Chem. Eng. Jl., 23, 940 (1977)] proposed a reasonable approach that accounts for all three factors. If the reaction proceeds only on the catalyst surface effectively wetted by the liquid phase and components of the reaction mixture are nonvolatile, then one can in principle modify the definition of the Thiele modulus to... 

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