Page 165 - Adsorption Technology & Design, Elsevier (1998)

Design procedures 153

where yt is the mole fraction of component 1 in the fluid phase. The
propagation velocity of points of given concentration in the MTZ therefore
depend on the equilibria of both components. Setting yt = 0 in equation
(6.32) yields equation (6.24) for a trace component. If yl is finite then even
when the carrier fluid is non-adsorbing, i.e. dqS/dc2 = 0, the propagation
velocity varies with composition according to equation (6.33).

u
= (6.33)
1 + pp (~-~-~) (1 - yl) ddqc~

Isothermal, rate controlled systems

In most practical adsorption systems finite resistances to mass transfer of
adsorbing molecules must be expected. Even for processes which are
commonly assumed to be equilibrium controlled, such as the production of
oxygen-enriched air using a zeolite, mass transfer resistances are likely to
have an impact on performance, and hence must be included in its design,
especially when cycle times are very short (Sircar and Hanley 1995). Some
analytical solutions to the general mass conservation equation (6.19) are
available but in order to be able to use them a number of simplifying
assumptions and approximations must be valid. Typical of these are
assumptions of a linear isotherm, a rectangular isotherm (irreversible
equilibrium), a non-linear (Langmuir) isotherm with a pseudo second-order
reaction kinetic rate law, and plug flow.
Consider a dilute system containing a single adsorbable component. The
fluid phase mass balance is given by equation (6.19), in which the adsorbate
loading over the whole adsorbent pellet is given by

q
(6.34)

For an adsorbent bed which is initially free from the adsorbate (that is, it has
been perfectly regenerated), and for a step change in adsorbate concentra-
tion at the bed entrance at time zero, the initial and boundary conditions are
given by

q (R,O,z) = c(O,z) = 0 for t < 0
(6.35)
c (t,0) = co for t > 0 (6.36)