Page 85 - Packed bed columns for absorption, desorption, rectification and direct heat transfer

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1.6.5. Peclet numbers

As a geometrical characteristic in Bodenstein numbers, used by the
diffusion model (Eqs.(250) to (255)), the height of the packing is employed.
Because the axial mixing is a hydrodynamic process, the axial mixing
coefficients are functions of the geometrical parameters of the packing,
important for the hydrodynamics, like its specific surface area, but not its
height. That is why for the dimensionless equations taking into account the axial
mixing coefficients, the Bodenstein number is not proper. Instead of it, similar
number called Peclet number is used. It can be obtained for the gas and for the
liquid phases as follows:

= ^ r , (270)
Pe r =Bo r
aH e(l-H d).a.D c

Pe T =Bo, = r • (271)
L
aH H d.a.D L

The dimensional analysis gives the following types of equations for
determination of the Peclet numbers:

for the gas phase

2
Pe r =f(Re,,Re r,Ga r,——,—,£,l,..L), (272)

for the liquid phase

f . (273)

The equation for the gas phase is especially complicated because it
should reflect the influence not only of the gas hydrodynamics, but also of the
liquid phase.
Because of the small effect of the axial mixing in the gas phase on the
mass transfer in the packing and the great experimentel difficulties in this area,
the number of investigations in Ms field is insufficient. The problem is
discussed in details in Chapter 3.