Page 158 - Adsorption Technology & Design, Elsevier (1998)

146 Design procedures

6.5 RIGOROUS METHODS

Many events occur in the MTZ during adsorption which render the analysis
complex. First, one or more adsorbates transfer from the fluid bulk by
convection or diffusion across the fluid film which is external to the solid
surface. Secondly, these adsorbates penetrate the particle by Maxwell,
Knudsen and surface diffusion mechanisms (see Chapter 4), and adsorb
onto the internal surface where the heat of adsorption is released. Heat may
then be transferred to the adsorbent, to the flowing process fluid, and, via
the vessel wall, to the surrounding environment. Heat and mass transfer
may occur in the MTZ by bulk and diffusive flows in both the radial and axial
directions. An additional complexity is that the flow through a packed bed
may not be uniform across its entire cross-sectional area. This may be
because of channelling of fluid at the wall or because of temperature
gradients created when the heat of adsorption is released.
An additional complication arises in cyclic fixed bed processes. A number
of cycles will be required from start-up of the equipment up to the point at
which each successive cycle is identical, this situation being that which is
desired for normal operation. The fundamental governing equations do not
change during this start-up phase. However, the boundary conditions vary
with the cycle number and are dependent on the previous cycle. This start-
up phase is normally of short duration compared with the period of steady
operation, and thus is perhaps of more academic than practical interest.
Analyses of start-up events can be found in Ruthven (1984), Yang (1987),
Ruthven et al. (1994) and Tien (1994).
Situations which particularly complicate the design process include non-
ideal gas behaviour (with high pressures), multicomponent separations
(requiring the relevant thermodynamic and kinetic information), high heats
of adsorption (e.g. with water on zeolites) which cause significant variations
in temperature, axial and radial dispersions of mass and heat, and high
concentrations of adsorbates in the feedstock (e.g. separation of air into
oxygen and nitrogen).

6.5.1 Thermal effects
For the sake of simplicity many fixed bed designs incorporate the isothermal
assumption which is normally valid when the adsorbable component
concentration is low, or the heat of adsorption is low, or the thermal wave
and the mass transfer zone are well separated at the end of the bed. A
relatively simple method is available to test whether the last criterion is valid
(Ruthven 1984).
The rate at which the heat can be carried out of the mass transfer zone by