Page 152 - Adsorption Technology & Design, Elsevier (1998)

140 Design procedures

Vm 3 Vm 3 2 ~ Vm 3
Co kg/m 3 c~ kg/m 3
cf kg/m 3

~r M, kg
I ql kg/kg
1' q2 kg/kg
Figure 6.3 Stagewise contacting of a batch of fluid with three batches of adsorbent.

Simultaneous solution of the impurity mass balance with the equilibrium
relationship for the first batch vessel yields M1"

)
M1 = ~ -- 1 (6.7)

The loading ql is in equilibrium with the intermediate concentration cl.
Simultaneous solution of the impurity mass balance with the equilibrium
relationship for the second batch vessel yields M2:

/142-~ -- 1 (6.8)

For the total mass of adsorbent to be a minimum, the differential of (M1 +
M2) with respect to the intermediate concentration cl needs to be zero.
Hence, it can be shown that:
cl = (c0.cf) ~ (6.9)

Substitution of cl from equation (6.9) into equations (6.7) and (6.8) shows
that the minimum amount of adsorbent for this purification is given when:

[V(c~176 -- 1 (6.1 O)
M1 = M2 = [K~ cf ]