Page 77 - Packed bed columns for absorption, desorption, rectification and direct heat transfer

72

It is easy to see that the Bodenstein numbers can be obtained by
multiplying the corresponding Peclet numbers by H/d p.
In fact the piston flow model, as well as the diffusion model, gives too
ideal picture of the structure of the flows. They take into account neither the
diffusion boundary layer nor the real movement of the phases. These models are
especially far from the real situation in the apparatus in respect to the liquid
phase which moves not like a piston flow but in the form of film, drops and jets
which are not only separate in space but have also different and continuously
changing velocities. Nevertheless, not only the diffusion model but in some
cases also its simpler variant, the piston flow model, gives often very good
description of the mass transfer processes in industrial apparatuses. This can be
explained with the comparatively weak influence of the real structure of the
flows on the mass transfer. On the other side using in the model such
experimentally obtained values as mass transfer coefficient, effective surface,
and Peclet number, it is possible to take into account the important for the mass
transfer rate characteristics of the flows structures. In Chapter 8 the cases when
it is possible to use the simpler piston flow model, and when it is necessary to
use the diffusion model are considered and specified.
Theoretically it is possible to write the differential equations for the
mass transfer in case of a nonuniform distribution of the phases over the column
cross-section. As boundary conditions in this case also the initial distribution
over the column cross-section for both of the phases and the conditions on the
column wall should be given. Of course, the equations for calculating the
Bodenstein or Peclet numbers in radial direction have to be also known. The
determination of the necessary additional conditions in comparison to the
simpler model, Eqs. (250) to (257), is very complicated and together with the
difficulties to solve the system make the whole model unusable. Nevertheless,
in literature there are some investigations on calculating the Peclet number in
radial direction.

1.6. Principle types of equations for calculation of the performance
characteristics of the packing

The similarity theory and the dimensional analysis give the possibility
to obtain equations for calculation of the performance characteristics of the
packings in dimensionless form. Each equation has two important
characteristics, the type of the function and the experimental constants. The
complete equations, with their experimental constants are presented in Chapter
3 together with the description of the respective packings.
Besides the dimensionless equations valid for different dimensions and
often for different types of packings, there are a lot of equations with
experimental constants valid not only for one packing type but also only for one