Page 159 - Adsorption Technology & Design, Elsevier (1998)

Design procedures 147

the flowing fluid compared with the speed at which the MTZ can travel is
critical since it is in the MTZ that the heat is being generated by adsorption.
The cross-over ratio R is defined as:

cf (qtf -- qres)
R = (6.18)
c~ (co- c*o~)

where cf is the fluid specific heat
cs is the solid specific heat
q0* is the adsorbate loading in equilibrium with the feed concentration
Co
c*es is the fluid concentration in equilibrium with the residual loading
on the adsorbent after a regeneration step, qres.
When R = 1 the thermal wave progresses through the bed more or less at
the same speed as the mass transfer zone. Hence, virtually all the heat
released on adsorption can be expected to be retained in the MTZ and the
isothermal assumption should not be made unless either the heat of
adsorption is low and/or the concentration of the adsorbable component is
low. When R is very much less than unity the thermal wave lags behind the
MTZ and hence the heat of adsorption can be retained in the equilibrium
portion of the bed (that is, from the entrance up to L~ shown in Figure 5.6
(b)). Retention of the heat of adsorption in this way is beneficial to the
subsequent desorption step (Garg and Ausikaitis 1983). When R is very
much greater than unity the heat is easily removed from the MTZ and it is
safe to invoke the isothermal assumption. Further discussion on the cross-
over ratio is given in Section 7.5.3.
Energy balances may need to be retained in the rigorous model if the heat
of adsorption is significant and is retained in, or lags behind, the MTZ. Real
packed bed adsorption systems are likely to encompass the entire spectrum
from near-isothermal to near-adiabatic operation. Since the behaviour of
each extreme is quite different it is important to know whether either of the
extreme cases can be regarded as a reasonable representation or whether a
more general model is required.

6.5.2 Isothermal operation
If it is possible to assume isothermal conditions exist within a packed bed
then the energy balance may be omitted from the analysis and only the mass
conservation equation is required. Derivation of the bed mass conservation
equation is provided in most texts describing the principles of adsorption