Page 190 - Adsorption Technology & Design, Elsevier (1998)

176 Designprocedures

laminar, i.e. Re < 10. The pressure gradient is directly proportional to the
superficial velocity u (or mass velocity G):
AP peu
= (6.69)
L B

where p is the fluid viscosity, and B is the permeability coefficient, which
must be determined experimentally.
Channelling at the wall may become significant if the ratio of the adsorber
bed diameter to particle diameter is less than 30. Consider for example the
situation in which the void fraction near the walls of a packed bed is 0.5 while
the void fraction in the central region is 0.35. The Ergun equation could be
used to calculate that the ratio of the velocities in the two regions would be
between 2 and 5 for a given pressure drop across the bed. This disparity in
velocity will be the greatest when the velocity is relatively low. This is
because the pressure gradient at low velocities is controlled by viscous

1.0

0.9
Viscous range

0.8
Wall effect
factor
Turbulent range
0.7 --
(Re> 10)

0.6

O.5 I I J ....... I ......
0 0.05 0.1 0.15 0.2 0.25
Particle diameter / Tube diameter

Figure 6.11 Dependence of wall factor on particle diameter to bed diameter ratio
(adapted from Furnas 1929).