Page 351 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

12.1 Introduction 353

deteriorate on longer storage due to oxidation, polymerisation and other chemical changes. The
operation is usually performed at the highest convenient temperature to reduce viscosity and increase
rate of diffusion and ease the motion of adsorbent particles through the liquid. The faster approach to
equilibrium more than compensates the decrease in equilibrium concentration at the higher temper-
ature. The highest permissible temperature can be close to the boiling point of the liquid provided the
solid can withstand that temperature. Nevertheless, where the adsorption isotherm is strongly affected
by temperature, the operation is best handled at room temperature.
Temperature rise due to adsorption can be ignored when (i) the quantity of solution treated is much
larger compared to the amount adsorbed, (ii) solute is adsorbed much more strongly compared to other
constituents of solution and (iii) adsorbent is insoluble in solution.
The component mass/mole balance can be expressed on solute free concentration basis, i.e., in
terms of Y moles (mass) adsorbed /moles (mass) solute free solvent, and X moles adsorbed/mole solute
free adsorbent.
For single-stage operation, this yields a linear operating curve of slope ð A s =L s Þ on the X Y
plane, similar to the operating line for absorption.
L s ðY i Y o Þ¼ A s ðX o X i Þ (12.1)
In the above equation, L s and A s are the mass (moles) of solute free solvent and solute free
adsorbent, respectively, and subscripts i and o represent the respective inlet and the outlet
concentration.
For an ideal stage, the adsorbate loading on the adsorbent is in equilibrium with the concentration
of adsorbate in solution at the process temperature. Quite often equilibrium is given by Freundlich
1=K c 1=K c
equation q ¼ K F ðpÞ or q ¼ K F ðcÞ , where p and c represent adsorbate partial pressure (in
case of gas adsorption) and adsorbate concentration (in liquid adsorption) at exit. In this case, the
amount of (fresh) adsorbent required to effect the change in feed concentration in a single ideal stage
(equilibrium contacting) is given by

A s ðY 0 Y 1 Þ
¼ (12.2)
L s 1=K c
ðY 1 =K F Þ
For N stages in crosscurrent flow, the total amount of adsorbent required is
" #
A s 1=K c ðY 0 Y 1 Þ ðY 1 Y 2 Þ ðY N 1 Y N Þ
¼ K þ þ :::: þ (12.3)
F
L s ðY 1 Þ 1=K c ðY 2 Þ 1=K c ðY N Þ 1=K c
While for countercurrent operation with fresh adsorbent, the solute balance for N stages gives
L s ðY 0 Y N Þ¼ A s ðX 1 Þ (12.4)
and the adsorbent requirement in the N th stage is
A s ðY N 1 Y N Þ
¼ (12.5)
L s ðY N =K F Þ 1=K c