Adsorption Isotherm

For a particular single gas-solid combination, one of five types of adsorption isotherm is found (see Figure 5.20.10). In separation processes, the favorable isotherms, types 1 and 2 are most frequently encountered.

From considering kinetics for a single gas impacting a uniform solid surface and adsorbing without chemical change, Langmuir (1921) deduced that the fraction of a surface covered by a monolayer varies with the partial pressure of the adsorbate Pa. The following equation gives the mass of adsorbate adsorbed per unit mass of adsorbent kjPa a k2Pa + 1

where k1 and k2 are constants. Equation 5.20(11) is known as the Langmuir isotherm, and the shapes are types 1 and 2 in Figure 5.20.10.

Assuming that the number of sites of energy Q (Nq) is related to a base value for Q, Q0, as follows:

then Equation 5.21(11) reduces to the following approximation:

Key: 1 = High loading (highly favorable)

2 = Favorable

3 = Linear

4 = Low loading (unfavorable)

5 = Irreversible c, ppm

Key: 1 = High loading (highly favorable)

2 = Favorable

3 = Linear

4 = Low loading (unfavorable)

5 = Irreversible

FIG. 5.20.10 Adsorption loading profiles.

When expressed as the volume of adsorbate adsorbed per unit mass of adsorbent v, as follows:

or expressed in terms of concentration in the gas phase c and at the absorbent surface w, as follows:

the expression is known as the Freundich isotherm. For a binary, or higher, mixture in which the components compete for surface sites, the expression is more complex (Yang 1987). Table 5.20.4 gives the values for parameters k and n in the Freundich isotherm for selected adsorbates.

Ideally, an adsorbent adsorbs the bulk of a pollutant from air even when that material is in low concentration. The adsorption profile for such behavior is called favorable and is shown as curves 1 and 2 in Figure 5.20.10. If high concentrations must be present before significant quantities are adsorbed (curve 4), the profile is called unfavorable adsorption.

As a pollutant is adsorbed onto the adsorbent, the concentration in the air stream falls. The adsorbent continues to absorb the pollutant from the air stream until it is close to saturation. Thus, as the air stream passes through a bed of adsorbate, the pollutant concentration varies along the bed length. This adsorption wave progresses through the bed with time (see Figure 5.20.11). At time t1, the bed is fresh, and essentially all pollutant is adsorbed close to the entrance of the bed. At time t2, the early part of the bed is saturated, but the pollutant is still effectively adsorbed. At time t3, a small concentration of pollutant remains in the air stream at the exit. When the pollutant concentration at the exit meets or exceeds the limiting value, the bed is spent and must be replaced or regenerated. For some pollutants, the breakthrough of detectable amounts of pollutants is unacceptable. To avoid exceeding acceptable or regulated limits for pollutant concentrations in exit gases, replacing or regenerating adsorbent beds well before the end of the bed's lifetime is essential.

The profiles shown in Figure 5.20.11 are for a single pollutant in an air stream. An adsorber normally operates in a vertical arrangement to avoid bypassing gases. For multiple pollutants, the process is more complex as each pollutant can exhibit different behavior or competition can occur between pollutants for adsorption sites (Yang 1987; Kast 1981). The bed design must be able to adsorb and retain each pollutant.

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