Page 56 - Packed bed columns for absorption, desorption, rectification and direct heat transfer

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The main difference between the model of Lewis and Whitman and the
models of Higbie, Danekwerts and Kishinevski is that the first model is based
on the first Fiek's low and the rest of the models — on the second Fiek's low.
This leads to different exponents at the diffusivity predicted by them. So as
already mentioned, the model of Lewis and Whitman leads to an exponent equal
to 1 both for gas and liquid phase. The other three models predict an exponent
value of 0.5 for the liquid phase. The model of Levich gives an exponent equal
to 0.5 for liquid side controlled processes and equal to 2/3 for gas side
controlled ones.
In details the problems of the mass transfer models are discussed in the
appendix written by Rosen A.M., B.A Kaderov and B.C. Krilov at the end of
the Russian edition of Astarita's book [20].

1.5.3. Other dimensions of the partial and overall mass transfer coefficients and
the driving force

From all of the theoretical models it follows that the dimension of title
mass transfer coefficients, both partial and overall, is equal to the dimension of
the velocity, m/s.
As already mentioned the dimension of the driving force, both for gas
3
and liquid phase, is equal to unit of mass per unit of volume, i.e. kg/m or
3
kmol/m .
In this book the above mentioned dimension is always used. Besides
them, other units of measure are also used in literature for the driving force and
the corresponding mass transfer coefficients.
In some cases the driving force is given in bar, or even in mm HG.
2
Then the dimension of the mass transfer coefficient is kmol/(m .h.bar) or
2
kmol/(m .h.mm HG). As a unit of measure for time here h instead of s is used.
In case of dimensionless driving force, for example kg/kg, kmol/kmol,
kg/kg of the inert component or kmol/kmol of the inert component, the
2
2
dimension of the mass transfer coefficient is kg/(m s) or kmol/(m s).
3
Theoretically in all kinds of driving forces except this given as kg/m or
3
kmol/m , the mass transfer coefficient is a function of the concentration. That is
why it is to be recommended to calculate the mass transfer rate using this
dimension. Nevertheless, in some cases the mass transfer coefficient depends on
the concentration. The reason can be as follows:
1. Influence of the concentration on the parameters which the mass
transfer coefficient depends on, such as diffusivity, viscosity and density;
2. Instead of the real driving force with chemical potential using that
with concentration.
Both influences can be token into account when calculating industrial
columns: