Adsorption Behavior in Packed Beds

Adsorption is performed most commonly in fixed vertical beds of porous granular adsorbents. Flow of adsorbing fluid usually is down through the bed, that of regenerant usually is upward. Moving and fluidized beds have only a limited application in the field. 

The rate of mass transfer from fluid to solid in a bed of porous granular adsorbent is made up of several factors in series  

in terms of a time parameter r, at a number of values of a parameter Z, which involves the bed length Z. In Example 15.2, this chart is used to find the concentration profile of the effluent, the break and exhaustion times, and the % utilization of the adsorbent bed. In this case, the model affords a fair comparison with experimental data. 

Many investigations have been conducted of the mass transfer coefficient at the external surfaces of particles and of other diffusional mechanisms. Some of the correlations are discussed in Chapters 13 and 17. A model developed by Rosen [Ind. Eng. Chem. 46, 1590 (1954)] takes into account both external film and pore diffusional resistance to mass transfer together with a linear isotherm. A numerical example is worked out by Hines and Maddox (1985, p. 485). 

In the model developed by Thomas [J. Am. Chem. Soc. 66, 1664 (1944)], the controlling mechanism is the surface kinetics represented by the Langmuir isotherm. Extensions of this work by Vermeulen et al. (1984) incorporate external surface and pore diffusional resistances. 

No comprehensive comparisons of the several models with each other and with experimental data appear to have been published. 

---

In either equation, /c is given by Eq. (16-84) for parallel pore and surface diffusion or by Eq. (16-85) for a bidispersed particle. For nearly linear isotherms (0.7 < R < 1.5), the same linear addition of resistance can be used as a good approximation to predict the adsorption behavior of packed beds, since solutions for all mechanisms are nearly identical. With a highly favorable isotherm (R 0), however, the rate at each point is controlled by the resistance that is locally greater, and the principle of additivity of resistances breaks down. For approximate calculations with intermediate values of R, an overall transport parameter for use with the LDF approximation can be calculated from the following relationship for sohd diffusion and film resistance in series... 

Axial Dispersion Effects In adsorption bed calculations, axial dispersion effects are typically accounted for by the axial diffusionhke term in the bed conservation equations [Eqs. (16-51) and (16-52)]. For nearly linear isotherms (0.5 < R < 1.5), the combined effects of axial dispersion and mass-transfer resistances on the adsorption behavior of packed beds can be expressed approximately in terms of an apparent rate coefficient for use with a fluid-phase driving force (column 1, Table 16-12) ... 

In most adsorption processes the adsorbent is contacted with fluid in a packed bed. An understanding of the dynamic behavior of such systems is therefore needed for rational process design and optimization. What is required is a mathematical model which allows the effluent concentration to be predicted for any defined change in the feed concentration or flow rate to the bed. The flow pattern can generally be represented adequately by the axial dispersed plug-flow model, according to which a mass balance for an element of the column yields, for the basic differential equation governing llie dynamic behavior,... 

Fortunately, the effects of most mobile-phase characteristics such as the nature and concentration of organic solvent or ionic additives the temperature, the pH, or the bioactivity and the relative retentiveness of a particular polypeptide or protein can be ascertained very readily from very small-scale batch test tube pilot experiments. Similarly, the influence of some sorbent variables, such as the effect of ligand composition, particle sizes, or pore diameter distribution can be ascertained from small-scale batch experiments. However, it is clear that the isothermal binding behavior of many polypeptides or proteins in static batch systems can vary significantly from what is observed in dynamic systems as usually practiced in a packed or expanded bed in column chromatographic systems. This behavior is not only related to issues of different accessibility of the polypeptides or proteins to the stationary phase surface area and hence different loading capacities, but also involves the complex relationships between diffusion kinetics and adsorption kinetics in the overall mass transport phenomenon. Thus, the more subtle effects associated with the influence of feedstock loading concentration on the... 

However, by examining the adsorption behavior of polypeptides and proteins with comparable porous and nonporous particles in finite baths, packed columns and expanded or fluidized beds, an iterative simulation approach based on the heuristic principles described earlier and along the lines of the flow diagram shown in Fig. 32 can be developed, leading ultimately to the implementation of useful scale-up criteria. Along the way, computer simulations, generated from the analysis of the concentration-time... 

---