Dynamic holdup

The sohd can be contacted with the solvent in a number of different ways but traditionally that part of the solvent retained by the sohd is referred to as the underflow or holdup, whereas the sohd-free solute-laden solvent separated from the sohd after extraction is called the overflow. The holdup of bound hquor plays a vital role in the estimation of separation performance. In practice both static and dynamic holdup are measured in a process study, other parameters of importance being the relationship of holdup to drainage time and percolation rate. The results of such studies permit conclusions to be drawn about the feasibihty of extraction by percolation, the holdup of different bed heights of material prepared for extraction, and the relationship between solute content of the hquor and holdup. If the percolation rate is very low (in the case of oilseeds a minimum percolation rate of 3 x 10 m/s is normally required), extraction by immersion may be more effective. Percolation rate measurements and the methods of utilizing the data have been reported (8,9) these indicate that the effect of solute concentration on holdup plays an important part in determining the solute concentration in the hquor leaving the extractor. 

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. 

For different particle sizes, the dynamic holdup can be calculated as follows. According to the related holdup equations, the dynamic liquid holdup based on the void (available) bed volume is proportional to dp 0Mi 0/ 6, dp particle sizes, which is true for low df/D values (see the following subsection). Thus, the following analogy can be used ... 

A typical value for m is between 0.54 and 0.72. For dynamic holdup, the value of 0.72 can be used for irregular-shaped particles similar to activated carbon and zeolites. 

The first method for determining the dynamic liquid hold-up uses weighing experiments. After the TBR has reached its desired operating point, the gas-aid liquid inlets are closed simultaneously. The amount of liquid trickling out of the column is called the dynamic holdup. 

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 ... 

Relations of the rate of mass transfer between gas and liquid and the influence of the stagnant and dynamic holdup were not researched intensively, until the present work, although papers on the general subject have been presented (3-6). Lately an interesting paper about mass transfer from liquid to solid in pulsing flow was presented by Luss and co-workers (7 ). 

Mass transfer between stagnant and dynamic holdup... 

Residence time distribution measurements, together with a theoretical model, provide a method to calculate the rate of mass transfer between the liquid flowing through the column, the dynamic holdup, and the stagnant pockets of liquid in between the particles. We have chosen the cross flow model (10). It has to be noted that the model starts from the assumption that the flow pattern has a steady-state character, which is in conflict with reality. Nevertheless, average values of the number of mass transfer units can be calculated as well as the part of the liquid being in the stagnant situation. 

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 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. 

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. 

Here, PeL = LJLdp/EZL, Reu = dppLUL/pLi GaL = dlgpl/pl, UL is the interstitial liquid velocity, and EZL is the liquid-phase axial dispersion coefficient. Furzer and Michell28 correlated the Peclet number to the dynamic holdup by a relation... 

Here. U0L is the superficial liquid velocity and UG the gas pore velocity. The dynamic holdups were approximately 90 percent of the values anticipated from the Otake-Okada38 correlation. The data were compared with those obtained by Dunn et al.16 and Sater and Levenspiel.43... 

For different particle sizes, the dynamic holdup can be calculated as follows. According to the related holdup equations, the dynamic liquid holdup based on the void (available)... 

The liquid-phase holdup is expressed as a fraction of bed volume, i.e., volume of liquid present per volume of empty reactor. This is then subdivided into external holdup, liquid contained in the void fraction of the bed outside of the catalyst particles, and internal holdup, liquid within the pore volume of the catalyst. There is an even further subdivision of the external holdup into a static holdup —the amount of liquid in the bed that remains after the bed has been allowed to drain freely—and dynamic holdup which depends on a number of factors but is most simply defined as the difference between total holdup and static holdup. ... 

Liquid holdup, which is expressed as the volume of liquid per unit volume of bed, affects the pressure drop, the catalyst wetting efficiency, and the transition from trickle flow to pulsing flow. It can also have a major effect on the reaction rate and selectivity, as will be explained later. The total holdup, h, consists of static holdup, h, liquid that remains in the bed after flow is stopped, and dynamic holdup, h, which is liquid flowing in thin films over part of the surface. The static holdup includes liquid in the pores of the catalyst and stagnant packets of liquid held in crevices between adjacent particles. With most catalysts, the pores are full of liquid because of capillary action, and the internal holdup is the particle porosity times the volume fraction particles in the bed. Thus the internal holdup is typically (0.3 — 0.5)(0.6), or about 0.2-0.3. The external static holdup is about... 

The dynamic holdup depends mainly on the particle size and the flow rate and physical properties of the liquid. For laminar flow, the average film thickness is predicted to vary with, as in flow down a wetted-wall column or an inclined plane. In experiments with water in a string-of-spheres column, where the entire surface was wetted, the holdup did agree with theory [28]. For randomly packed beds, the dynamic holdup usually varies with a fractional power of the flow rate, but the reported exponents range from 0.3 to 0.8, and occasionally agreement with the 1/3 power predicted by theory may be fortuitous. 

Dynamic holdup data from a few sources are shown in Figure 8.12. The lowest two lines are for water in beds of glass beads 0.48 cm in diameter... 

Similar results were found by Henry and Gilbert [33], who studied sulfur removal, nitrogen removal, and hydrocracking in small reactors. Most of the first-order plots were curved upward when LHSV was used, but straight lines were obtained with LHSV. The explanation proposed was that the reaction rate was directly proportional to the dynamic holdup, which was predicted to increase with following... 

According to Otake and Okada [26] for nonporous spherical packing c = 1.295, a = 0.676, p = —0.44, and y = 1.0, whereas Satterfield et al. [27] arrived at c = 1.0, a = 0.333, p — —0.33, and y = 0. Note that the dynamic holdup is independent of the gas flow rate, but varies with the liquid flow rate. Goto and Smith [28] observed agreement between their experimental data and Otake and Okada s correlation for large-particle diameters only and between their data and Satterfield et al. s correlation for small-particle diameters only. The following external or total holdup equation is proposed by Midoux [71] ... 

Little is known on the effect of the gas flow rate on kobs- The effect should be small if the liquid is saturated with the gas. According to Charpentier et al. [36], an increase in G decreases s, but favors the exchange between dynamic holdup... 

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