Adsorption - Principles of Chemical Separations with Environmental Applications - page 198

C f

Fluid
solute
concentration

C d

Inlet L e L s L d Outlet

Distance from inlet ( L )

Figure 7.5 Fluid solute concentration vs position in the adsorption column.

From the column inlet to L e , the sorbent is loaded to capacity and the solute concentra-
tion in the fluid phase is C f . From L e to L d , the MTZ exists where adsorption is occurring.
From L d to the column exit, the fluid solute concentration is C d . Refer back to the parking
lot analogy with discussion in this section (compare Figure 7.3(a) and (b) with Figures 7.4
and 7.5, respectively).
The various transport processes described in Section 7.7 affect the length of the MTZ.
As the fluid dispersion and/or the diffusional mass transfer resistances increase, the length
of the MTZ will increase. We will see how the adsorption isotherm affects the MTZ in
Section 7.9.1. Also, in Section 7.10, we will see how the breakthrough curves (Figure 7.4)
can be used for column design and scale-up. It is important to note that if the flow conditions
are changed (particle size, sorbent, etc.) then the mass transfer characteristics of the column
will change and, consequently, the resulting breakthrough curve will also change (i.e., be
very careful when using these methods).
If the fluid solute concentration in the column propagates as a stoichiometric front
(plug-flow), the position of the front would be L s in Figure 7.5. This corresponds to the
portion of the column from L s to L d as being unused. When L d corresponds to the column
length L c , the length of the unused bed ( LUB ) can be defined as

1 L c .

L s
L c

LUB = − (7.5)

Defining t s as the time that the stoichiometric front would arrive at the column exit, an
analogous expression using the plot in Figure 7.4 is

1

L c .

t d
t s

= −

LUB (7.6)