Page 149 - Adsorption Technology & Design, Elsevier (1998)

138 Design procedures

regenerated to a residual loading of q0 then it would be necessary to replace
the right-hand side of equation (6.2) by M (q-qo). After contacting, the
equilibrium is given by:
q = Kcf (6.3)

Simultaneous solution of equations (6.2) and (6.3) gives the mass of
adsorbent required to effect the purification:

M = ~ -- 1 (6.4)

This equation shows that the mass of adsorbent required can be reduced if an
adsorbent with a higher equilibrium constant can be found. Equation (6.2)
can be rearranged to give a linear relationship between q and cf:

V
q - --~ (co- cf) (6.5/

If the adsorbent were not initially free from the impurity at the start of the
adsorption process then the linear relationship would be:
V
q = -7: (co- cf) + qo (6.6)
M

The simultaneous solution to equations (6.3) and either (6.5) or (6.6) can
be found graphically, as shown in Figure 6.2 (a) and (b), respectively.
Whether or not an analytical solution can be found in the case of a non-
linear isotherm depends on the shape of the isotherm. If an analytical
solution is not possible then the solution may be found graphically as
shown in Figure 6.2 (c).
Powdered or granular adsorbents are usually added to a process in slurry
form in such a way as to allow adequate dispersion and mixing. The
adsorbent can be removed as a settled sludge. When large quantities of
adsorbent are required consideration should be given to using a multiple
batch or cross-flow system. For example, one way of reducing the amount of
adsorbent required is to carry out the batch processing in two steps, as shown
in Figure 6.3. Here the total amount of adsorbent is split arbitrarily into two
parts M1 and M2. The feed is first contacted with a fresh batch of adsorbent
and the impurity concentration is reduced to Cl. After separation of the fluid
from the adsorbent in the first stage the fluid is contacted with a further fresh
batch of adsorbent. In multibatch systems each subsequent batch of
adsorbent removes less and less impurity as the impurity concentration
decreases.