Page 173 - Adsorption Technology & Design, Elsevier (1998)

Design procedures 161

calculate pressure drops in which case the variation of fluid physical
properties with composition and temperature should be included
when using these equations which represent an approximate
momentum balance. For rapid PSA processes attention needs to be
paid to the fact that the pressurization step is unlikely to be
completely divorced from adsorption. Equally, desorption is likely
to occur simultaneously with depressurization. The interest in
improving the efficiency of PSA processes by reducing the cycle
time has led to strong research activity in the dynamics of the
pressure changing steps (Crittenden et al. 1994 and 1995).
(5) Mass transfer through the external fluid film, and macropore,
micropore and surface diffusion may all need to be accounted for
within the particles in order to represent the mechanisms by which
components arrive at and leave adsorption sites. In many cases
identification of the rate controlling mechanism(s) allows for
simplification of the model. To complicate matters, however, the
external film coefficient and the intraparticle diffusivities may each
depend on composition, temperature and pressure. In addition the
external film coefficient is dependent on the local fluid velocity
which may change with position and time in the adsorption bed.
(6) The adsorption isotherms relate the local fluid phase composition
within the particles to the amount adsorbed on the surface. The
amount of any one species that is adsorbed depends on the local
temperature and on the partial pressure or concentration of that
component, and because of co-adsorption effects, on the partial
pressures or concentrations of all the other components.

No general analytical solution exists and the computational effort precludes
numerical solution of the full set of equations. Simplifying assumptions
therefore are usually made. The principal differences between models lie in
the ways in which the mass and heat transfer processes are handled.
If the process can be assumed to be isothermal then there are several
significant gains to be made in reducing the complexity of the design
equations. This is perhaps the most important simplification. First, the heat
balance equations (6.39) and (6.40) can be omitted. Second, the depen-
dencies of physical properties, fluid velocities, adsorption equilibria and
other parameters on temperature are no longer required and can be omit-
ted. Guidance on when it is likely to be safe to assume isothermal operation
has been provided earlier in this chapter.
The second most important simplification is the assumption of instantane-
ous local equilibrium, i.e. there are no mass transfer resistances and the
adsorbates are uniformly distributed throughout the particles. The benefits