Page 41 - Packed bed columns for absorption, desorption, rectification and direct heat transfer

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On the second question the similarity theory gives the possibility to
obtain equations for geometrically similar objects. Often in case, for example,
of random packings the factors important for the process are not just the form of
the packing elements but values like specific surface area and free volume. The
experience shows that by using these values instead of some geometrical
parameters or together with some of them, it is possible to obtain criterion
equations describing well a group of packings with elements which are not
geometrically similar. Of course, this must be always experimentally proved.
It is also a case of importance when the packings are with the same kind
of form but, because of different free volumes or height to hydraulic diameter
ratios, they are not similar. Theoretically, in this case the similarity theory is not
valid. But by the same considerations as for the example above, it follows that
the only difference in the equations for all such not similar packings is the
difference in their experimental constants. It means that if they are replaced by
relations of the dimensionless geometrical parameters of the packings,
theoretically, the obtained equation describes the processes not only in
geometrically similar, but also in geometrically not similar systems of the same
kind. Of course, to obtain simple equations for the constants, the difference in
the packing form should not be too great. Otherwise, this approach is not
possible or leads to errors, not always very great. For example there are
equations for calculating the mass transfer coefficient of Raschig rings, Berl
saddles and Intalox saddles although their forms are not of the same kind.

1.4, Equilibrium in gas (vapour) - liquid systems

At condition of equilibrium the concentration in each of the phases is a
function of the concentration in the other one:

(112)

where C G and C L are the equilibrium concentrations of the transferred
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component in the gas, respectively in the liquid phase, for example, in kg/m .
The function is always monotonously increasing and can be obtained
experimentally. The equilibrium problems are very complicated and are subject
of special books which can be found in internet, as for example [13-15].
Hereafter only some basic equations, used in case of absorption (desorption)
and rectification, are given. In case of absorption in ideal solutions, Eq. (112) in
a useful form can be obtained easily from the equation of Henry: