Packed beds mass-transfer coefficients

In packed beds, mass transfer coefficients are often correlated by means of a Chilton—Colburn factor, Ju, analogous to their Jh heat transfer (Sect. 4.4.4)... 

Second, the packed bed Mass transfer coefficients can be estimated from Eq. 2.36 in the form ... 

To determine the mass-transfer rate, one needs the interfacial area in addition to the mass-transfer coefficient. For the simpler geometries, determining the interfacial area is straightforward. For packed beds of particles a, the interfacial area per volume can be estimated as shown in Table 5-27-A. For packed beds in distillation, absorption, and so on in Table 5-28, the interfacial area per volume is included with the mass-transfer coefficient in the correlations for HTU. For agitated liquid-liquid systems, the interfacial area can be estimated... 

FIG. 16"10 Sherwood mimher correlations for external mass-transfer coefficients in packed beds for e = 0.4 (adapted from Siiziild, gen. refs.). 

Parameters a and b are related to the diffusion coefficient of solutes in the mobile phase, bed porosity, and mass transfer coefficients. They can be determined from the knowledge of two chromatograms obtained at different velocities. If H is unknown, b can be estimated as 3 to 5 times of the mean particle size, where a is highly dependent on the packing and solutes. Then, the parameters can be derived from a single analytical chromatogram. 

Speed-up of mixing is known not only for mixing of miscible liquids, but also for multi-phase systems the mass-transfer efficiency can be improved. As an example, for a gas/liquid micro reactor, a mini packed-bed, values of the mass-transfer coefficient K a were determined to be 5-15 s [2]. This is two orders of magnitude larger than for typical conventional reactors having K a of 0.01-0.08 s . Using the same reactor filled with 50 pm catalyst particles for gas/Hquid/solid reactions, a 100-fold increase in the surface-to-volume ratio compared with the dimensions of laboratory trickle-bed catalyst particles (4-8 mm) is foimd. 

In this cell, mechanical vibration is applied to the cell housing to enhance the transfer in the parallel plate tank cell [248]. The vibrations are transfered to the electrolyte resulting in an increase of the mass-transfer coefficient. The cell is extensively used in industry for the pretreatment of higher and high metal concentrations which is finally purified by a packed bed electrolysor if the required conversion is not too high [247],... 

Wakao, N. and Funazkri, T. Chem. Eng. Sci. 33 (1978) 1375. Effect of fluid dispersion coefficients on particle-fluid mass transfer coefficients in packed beds. 

The point of view based on a physical model started with the 1935 paper of Higbie [30], While the main problem treated by Higbie was that of the mass transfer from a bubble to a liquid, it appears that he had recognized the utility of his representation for both packed beds and turbulent motion. The basic idea is that an element of liquid remains in contact with the other phase for a time A and during this time, absorption takes place in that element as in the unsteady diffusion in a semiinfinite solid. The mass transfer coefficient k should therefore depend on the diffusion coefficient D and on the time A. Dimensional analysis leads in this case to the expression... 

In general, the material balances and the corresponding solutions for trickle and bubble bed reactors are the same, under the assumption that the plug-flow condition holds for both phases. Of course, the appropriate correlations should be used for the estimation of mass transfer coefficients. However, in packed bubble bed reactors, the liquid-phase is frequently found in a complete mixed state, and thus some adjustments have to be made to the aforementioned models. Two special cases will be presented here. 

Note that the mass transfer coefficients are higher in the packed bubble bed reactor compared to those in the trickle-bed reactor under the same conditions, as expected. 

Note that in the packed bubble bed reactor, the conversion achieved is higher by 14.02% due to the higher mass transfer coefficients compared to the trickle bed, especially the gas-liquid one, which is 3.61 times higher in the packed bubble bed reactor. 

Finally, in Fig. 3.4-12 [24], a comparison is given for the overall, gas-based, mass transfer coefficient for several liquid-to-gas and solid-to-gas packed beds and column systems. In Fig. 3.4-12, for a given data point, the vertical distance up to the Tan et al. [27] correlation (which is for a solid-to-fluid boundary layer) would provide a measure of the liquid-side mass-transfer resistance associated with the liquid. This is so because amount of the large gas... 

Fig. 3.4-12. Comparison of the overall, gas-based, mass-transfer coefficient for several liquid-to-gas and solid-to-gas packed beds and column systems [24] with permission of Pergamon Press...

Numerous investigations have been conducted of mass transfer coefficients in vessels with a variety of kinds of packings. Many of the mote acceptable results are cited in recent books on mass transfer, for instance, those of Sherwood et al. (Mass Transfer, McGraw-Hill, New York, 1975), Cussler (Diffusion, Cambridge, 1984), and Hines and Maddox (1985). A convenient correlation of mass transfer coefficients in granular beds covering both liquid and vapor films is that of Dwivedi and Upadhyay [Ind. Eng. Chem. Process Des. Dev. 16, 157 (1977)], namely,... 

Real experiments for the determination of external mass transfer coefficients are used as an example for virtual experiments with CFD. Here experimental studies (Williamson et al., 1963 Wilson and Geankopolis, 1966) on the flow of two liquids, namely water and a propylene glycol-water mixture, through a packed bed of spherical particles made from solid benzoic acid are... 

The mass-transfer coefficients are taken from [14], assuming that they are the same order of magnitude in a packed bed and spray tower ... 

Both criteria for extraparticle gradients contain observables and can be calculated based on experimental observations of reaction rates. For heat and mass transfer coefficients in packed beds various correlations exist in terms of dimensionless numbers. In Table 1 the most appropriate ones for laboratory reactors are given [5, 7, 30, 31]. Values of k( and h for gases in laboratory systems range between O.l-lOms-1 and 100-1000JK-1s-1 m-2, respectively. In the case of monoliths, other correlations should be used because of the different geometry [32-34],... 

The extraction of toluene and 1,2 dichlorobenzene from shallow packed beds of porous particles was studied both experimentally and theoretically at various operating conditions. Mathematical extraction models, based on the shrinking core concept, were developed for three different particle geometries. These models contain three adjustable parameters an effective diffusivity, a volumetric fluid-to-particle mass transfer coefficient, and an equilibrium solubility or partition coefficient. K as well as Kq were first determined from initial extraction rates. Then, by fitting experimental extraction data, values of the effective diffusivity were obtained. Model predictions compare well with experimental data and the respective value of the tortuosity factor around 2.5 is in excellent agreement with related literature data. 

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