Page 164 - Adsorption Technology & Design, Elsevier (1998)

152 Design procedures

Thus, the time for the leading edge of the MTZ to pass through a bed of
length L is given by:

t = -- 1 + pp bqm (6.30)
u

For most adsorption systems of industrial significance, the isotherm is
favourable towards adsorption over the range of concentration of interest.
Whilst this might be good for the adsorption step, the isotherm is of course
unfavourable for the desorption step. Therefore in desorption the MTZ is
usually expected to be dispersive, thereby leading to a continuously
spreading concentration profile. Ruthven (1984) provides further informa-
tion for isotherms which have more complicated shapes, including those
which have a point of inflection.
This simple analysis for an isothermal and equilibrium controlled process can
be extended to concentrated systems in which u must remain within the
differential of the second term in equation (6.19). The analysis can also be
extended to systems which include more than a single adsorbable component.
Consider the case of a feed stream which contains only two adsorbable
components, i.e. a system which does not include a non-adsorbing carrier fluid.
In this case both components can be expected to be concentrated in the fluid
and hence the variation in fluid velocity over the MTZ must be taken into
account. Two differential fluid phase mass balance equations must be written,
one for each component. Equation (6.31) is shown for component 1. The axial
dispersion term is retained to create a general equation.
_DL02Cl 0cl Olgt~Cl (~)Oqx
.... + U ~ + C l ~ + + pp = 0 (6.31)
Oz Ot dt
OZ 2 OZ
A similar equation can be written for component 2. In addition the
continuity equation (6.21) must be written and so the two conservation
equations are not independent. If it can be assumed that the total
concentration in the fluid phase c remains constant, which is likely to be true
for gaseous systems in which the pressure drop is small, and approximately
true for liquid mixtures when the components have similar molar volumes,
then the mass conservation equations can be combined. If it is possible to
neglect axial dispersion, then the propagation velocity of points of given
concentration in the MTZ is given by:
(6.32)

+
-----
1 + pp (1 a)dq*l y~
_
dc, -~c2 ]