Page 162 - Adsorption Technology & Design, Elsevier (1998)

150 Design procedures

complex model should be sufficiently general to provide a good description
in most systems.

Isothermal, equilibrium controlled systems
The simplest packed bed design arises with a single dilute adsorbate in a
carrier fluid when it can be assumed that the process is isothermal, that there
is plug flow, and that there are no mass transfer resistances. In such a
situation, instantaneous equilibrium exists at all points in the system.
Without the axial dispersion term and taking the velocity outside the partial
differential term for the convective flow, equation (6.19) is simplified to:

ac Of (~)Oq
- 0 (6.22)
U ~ + + pp
Oz Ot Ot
The full derivation of this equation is provided elsewhere (Ruthven 1984,
Coulson et al. 1991). In general terms the equilibrium isotherm may be
described as follows:
q* =f(c) (6.23)

As shown by Coulson et al. (1991) the velocity with which a point of given
fluid concentration propagates through the bed is given as follows:

(6.24)
(O )c u
(1_~) dq*
1 + pp dc

For a given point on the isotherm the speed of that point in the MTZ is seen
to be constant and to be dependent on the bulk fluid velocity, the bed
voidage and the slope of the isotherm at the concentration in question. With
an unfavourable isotherm the gradient dq*/dc increases as the fluid
concentration c increases. Hence, using equation (6.24) it can be seen that a
point of high concentration in the MTZ will move at a slower rate than a
point of low concentration. Thus the MTZ will broaden out as it progresses
through the bed. On the other hand, for a favourable isotherm (such as a
Type I isotherm described in Section 3.2), a point of high concentration, i.e.
one near the trailing edge of the MTZ, will travel faster through the column
and catch up with points of lower concentration at the leading edge of the
MTZ. In theory it would seem from equation (6.24) that points of high
concentration could overtake points of low concentration in the MTZ. In
practice however, the effects of axial dispersion (omitted from equation