Page 86 - Packed bed columns for absorption, desorption, rectification and direct heat transfer

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To obtain equations for calculating of industrial apparatuses using the
similarity theory and the dimensional analysis theory we should have reliable
experimental data for any given value. The methods for investigation of the
packings to obtain the necessary data are considered in Chapter 2.

1.7. About the possibility of purely theoretical calculation of the
performance characteristics of a packed column

The development of the computational methods and the computers put
the question whether the time of a calculation without any experiment of the
performance characteristics of the packed bed column is already coming, or
whether it is possible to come. Some circumstances in this area are discussed
below.
The first step of any model of this type is to make a mathematical
model of the packing form. For random packings this problem can be solved
only as a statistical task. It is impossible to know for sure whether this statistical
description of the form of the packing reflects the real hydrodynamic and mass
transfer situation in the column, especially having in mind the great capital
investments for an industrial column. In case of some types of structured
packings, especially these with smooth walls, the mathematical description of
the packing form is easier. But in all cases the industrial packings operate at gas
velocity for which the gas flow is turbulent. To be more precise, they operate in
an area where the influence of Reo is not to be neglected, and it cannot be
described theoretically without any experimentally obtained constants.
The prediction of the hydrodynamics of the liquid phase is some easier
when the wetted area of the packing is known, i.e. again in case of smooth
packings with vertical walls.
The determination of the surface of the drops and jets, trickling in the
packing, without any experiment is also a problem with no solution, at least
until now.
At the same time the similarity theory and the dimensional analysis, as
already mentioned, give the possibility, by using experimental data, to obtain
dimensionless equations which are solutions of the differential equations of the
corresponding processes.
Nevertheless, in the literature there are purely theoretical solutions [51]
of the problems. In all eases the obtained results should be validated by
comparison with independent experimental data.

Nomenclature

Latin
A- dimensionless number in Eq (259) related to the liquid holdup;