Gas Emission Control - Mathematics and Statistics for the Environment - page 473

where
C B = Breakthrough capacity.
C s = Saturation capacity.
MTZ = Mass transfer zone length.
D = Adsorption bed depth.

Equation 16.15 is used mainly as a check to ensure that the proposed bed depth is longer than the
MTZ. Actual bed depths are usually many times longer than the length of the MTZ.
The total amount of adsorbent required is usually determined from the adsorption isotherm, as
illustrated in Example 16.8. Once this has been set, the bed depth can then be estimated by know-
ing the tower diameter and density of the adsorbent. Example 16.8 illustrates how this is done.
Generally, the adsorbent bed is sized to the maximum length allowed by the pressure drop across
the bed.

■ EXAMPLE 16.8
Problem: Assume the same conditions as stated earlier in Example 16.7. Estimate the amount of
carbon that would be required if the adsorber were to operate on a 4-hour cycle. The molecular
weight of CCl 4 is 154 lb/lb-mole (USEPA, 1981, p. 5-18).
Solution: From Example 16.7, we know that the carbon used will remove 30 lb of vapor for every
100 lb of carbon at saturation conditions. First compute the flow rate ( Q ) of CCl 4 :

Q = 15,000 scfm × 0.00068 = 10.2 scfm CCl 4

Convert to pounds per hour:

3

ft
min

lb-mol
359 ft

154 lb 60 min

hr

×

× × = 262 .

10 . lb/hr

3

lb-mol

The amount of carbon (at saturation) required (assuming that the working charge is twice the satura-
tion capacity). (Note that this gives only a rough estimate of the amount of carbon needed.)

2 × 3500 = 7000 lb × 3182 kg carbon per 4-hour cycle per adsorber

■ EXAMPLE 16.9
The following example is based on a number of adsorber design maximum and minimum rules of
thumb. It is intended as a guide to illustrate how to “red flag” any parameters that may be greatly
exceeded.

Problem : A solvent degreaser is designed to recover toluene from a 3.78 m 3 is (8000 acfm) air stream
at 25°C (77°F) and atmosphere pressure. The company is planning to use a two-bed carbon adsorp-
tion system with a cycle time of 4 hours. The maximum concentration of toluene is kept below 50%
of the lower explosive limit (LEL) for safety purposes. Using Figure 16.16, the adsorption isotherm
for toluene, and the additional operational data, estimate (USEPA, 1981, p. 5-36):

1. The amount of carbon required for a 4-hour cycle

2. Square feet of surface area required based on a 0.58 m/s (100 fpm) maximum velocity

3. Depth of the carbon bed