Packings axial mixing

The axial dispersion coefficient [cf. Eq. (16-51)] lumps together all mechanisms leading to axial mixing in packed beds. Thus, the axial dispersion coefficient must account not only for moleciilar diffusion and convec tive mixing but also for nonuniformities in the fluid velocity across the packed bed. As such, the axial dispersion coefficient is best determined experimentally for each specific contac tor. 

Kramers and Alberda (K20) have reported some data in graphical form for the residence-time distribution of water with countercurrent air flow in a column of 15-cm diameter and 66-cm height packed with 10-mm Raschig rings. It was concluded that axial mixing increased with increasing gas flow rate and decreasing liquid flow rate, and that the results were not adequately represented by the diffusion model. 

Carberiy (C7) and Epstein (E6) discussed the magnitudes of the corrections necessary for dispersion in packed beds. It was found that for many practical cases of interest, the axial mixing effect was very small. 

Of the various methods of weighted residuals, the collocation method and, in particular, the orthogonal collocation technique have proved to be quite effective in the solution of complex, nonlinear problems of the type typically encountered in chemical reactors. The basic procedure was used by Stewart and Villadsen (1969) for the prediction of multiple steady states in catalyst particles, by Ferguson and Finlayson (1970) for the study of the transient heat and mass transfer in a catalyst pellet, and by McGowin and Perlmutter (1971) for local stability analysis of a nonadiabatic tubular reactor with axial mixing. Finlayson (1971, 1972, 1974) showed the importance of the orthogonal collocation technique for packed bed reactors. 

Figure 19.7. Sketch of a foam fractionating column. Surfactants or other foaming agents may be introduced with the feed or separately at a lower feed point. Packing may be employed to minimize axial mixing.

The experimental studies have shown that, in gas-liquid trickle-bed reactors, significant axial mixing occurs in both gas and liquid phases. When the RTD data are correlated by the single-parameter axial dispersion model, the axial dispersion coefficient (or Peclet number) for the gas phase is dependent upon both the liquid and gas flow rates and the size and nature of the packings. The axial dispersion coefficient for the liquid phase is dependent upon the liquid flow rate, liquid properties, and the nature and size of the packings, but it is essentially independent of the gas flow rate. 

Schmaltzer and Hoelscher [4.32] had suggested this model for the description of the axial mixing and the mass transfer in a packed column. Another particularization can be made in the case when the types of trajectory are chains corresponding to the completely random displacement (for example in the steps k = 1, which represent a displacement ahead, it is possible to have a small step towards the right or the left. In a k-type chain, the probability to realize a step towards the right is noted pk whereas represents the probability for the particle to realize a step towards the left (then, the probability p (a) is expressed according to relation (4.63)). 

In Eq. (15-135), is the specific wall surface (cmVcm ) and flp is the specific packing surface (cmvcm ). This term is dropped for a spray column (Cl = 0). The model coefficients are summarized in Table 15-19. Most of the axial mixing data available in the literature are for the continuous phase dispersed-phase axial mixing data are rare. Becker recommends assuming HDU = HDU, when dispersed-phase data are not available. Becker presents a parity plot (Fig. 15-33) based on small- and large-scale data for packed and spray columns. 

FIG. 15-33 Parity plot comparing spray and packed column results incorporating axial mixing model. [Reprinted from Becker, Chemie Ing. Technik, 74(1-2), pp. 59-66 (2002). Copyright 2002 Wiley-VCH.]... 

Figure 15-37 and Table 15-21 provide only general guidelines. To estimate mass-transfer rates in packed towers, the calculation procedure outlined by Seibert, Reeves, and Fair [Ind. Eng. Chem. Res., 29(9), pp. 1901-1907 (1990)] and corrected for axial mixing [as in Eqs. (15-127) to (15-136)] is recommended. The overall mass-transfer coefficient is obtained by using Eq. (15-126). The predictive method of Handles and Baron [AIChE3(1), pp. 127-136 (1957)] allows calculation of the dipersed-phase coefficient ... 

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