Page 160 - Adsorption Technology & Design, Elsevier (1998)

148 Designprocedures

(e.g. Coulson et al. 1991, Ruthven 1984) and is not repeated again here. If
the flow pattern can be represented as axially dispersed plug flow then the
differential fluid phase mass balance for a single adsorbate is given by:
t32c cO (uc) c3c (1 -el t3q = 0
(6.19)
-D L ~ + Oz + ~ pP ~ e ] cot
The equation is written in terms of concentration and therefore is suitable
for a liquid feedstock. By use of an appropriate equation of state, equation
6.19 is readily adapted for a gas feed. The loading on the adsorbent q is
expressed in units of mass/mass. The first term represents axial dispersion
within the bed; the axial dispersion coefficient is DL. The second term
represents convective flow within the bed; the interstitial velocity is u (and is
equal to the superficial velocity divided by the bed voidage). The third term
represents the accumulation of adsorbate in the fluid phase while the fourth
term represents the rate of adsorption which may be a function of both the
fluid phase concentration and the loading on the adsorbent. In general:

a__.qq = f(q, c) (6.20)
c~t
The dynamic response of the bed is given by the simultaneous solution of
equations (6.19) and (6.20), subject to the imposed initial and boundary
conditions. If the fluid comprises more than one adsorbate then the
conservation equation (6.19) and the rate equation (6.20) must be written
for each component. In addition, the continuity equation must be satisfied.
For example, for a system which contains two adsorbable components,
rather than one adsorbate in a non-adsorbing carrier fluid, equations (6.19)
and (6.20), which must be written for both components, are not independent
and there is only one MTZ. The continuity equation must be satisfied:
(Cl + c2) = c (6.21)

The situation is quite different for a system which comprises two adsorbates
in a non-adsorbing carrier fluid. In this case two distinct mass transfer zones
will be formed.
The shape of the MTZ which is generated by a particular design model is
determined by a number of factors, the most important of which are the
shape of the equilibrium isotherm, the concentration of the adsorbable
components, the choice of flow model, and the choice of kinetic model.
The shape of the isotherm has an important role to play in determining
whether the MTZ will sharpen, disperse or remain of fixed shape. When the
isotherm is linear the MTZ will exhibit dispersive behaviour unless the
adsorption is equilibrium controlled. Analytical solutions to the conserva-