Page 57 - Packed bed columns for absorption, desorption, rectification and direct heat transfer

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First, the influence of the concentration on the diffusivity, viscosity and
density is considered in the mathematical models.
Second, a proper equation for calculating of equilibrium concentration
is used, taking into account the difference between concentration and chemical
potential.

1.5.4. Basic mathematical models of the mass transfer processes in industrial
packed bed columns

1.5.4.1. Generally about the models
The first step for describing of the mass transfer processes in industrial
apparatuses, as already mentioned, is to describe the elementary act of transfer
trough the interface. The second one is, using the knowledge for this elementary
act and the hydrodynamic situation in the apparatus, to describe the total mass
transfer in it. There are a lot of models for describing of the mass transfer in the
industrial apparatuses in chemical and related branches of industry. The more
important of them are presented in the monograph by Levenspiel [53].
Generally the models could be divided into two groups. Models, which accept a
homogenous structure of the flows in the apparatus as a whole, and other by
which the apparatus is considered as divided into parts with different flow
structures. The construction of the packed bed column usually corresponds to
the first group of models. The main representatives of this group are the piston
flow model and the diffusion model.
According to the first of them, the velocity of any elementary part of
gas or liquid flow in the column in a given cross-section is constant and has one
and the same direction for a phase, Fig. 8(a). In the diffusion model an
additional movement of micro volumes comprising the main piston flow of each
phase is considered, Fig. 8 (b).

i

(a) (b)

Fig. 8. Scheme of the structure of the flows: (a), piston flow model; (b) diffusion model.

The direction and the velocity of the micro volumes is continuously
changing being different for each micro volume of the flow. This leads to axial