Adsorption - Principles of Chemical Separations with Environmental Applications - page 210

1

0

1500 1700 1900 2100 2300 2500 2700 2900

−

1

− y = − 0.0082 x + 18.8

−

− 5

Volume of water treated (L)

Figure 7.13 Breakthrough curve data applied to the estimation of the rate
constant k 1 , Example 7.2.

which is a straight line on a plot of effluent solute concentration vs volume of fluid
treated, and the pilot column breakthrough data can be used to determine k 1 , q 0 , and other
parameters of the design column.

Example 7.2: fixed-bed column design by the kinetic approach

Problem:
Redo the previous example using the kinetic approach. Given the data in Table 7.6,
determine the following values:
(a) k 1 (reaction constant); (b) q 0 ; and (c) mass of carbon required in the design column
Solution:
The points which pertain to the breakthrough portion of the data are plotted in the
appropriate form in Figure 7.13. Note that it is a straight line.
(a) Remember from the previous Equation (7.17) that:

= −

k 1 C 0
Q

Slope , (7.19)

or

0082 L − 1 (15 L 10 − 4 L k 1 = 0 . / hr) (L / 200 mg) = 6 . 15 × / hr · mg .

(b) Remember also that

k 1 q 0 M
Q

Intercept = , (7.20)

or

10 − 4 L)(1 q 0 = (18 . 8)(15 L / hr)(hr · mg / 6 . 15 × / 4 . 13 kg)

10 5

= 1 . 11 × mg TOC / kg GAC .

(c) Substituting the design volume into Equation (7.18) and solving for M :

hr)(3.75 m 3 ) m 3 10 3

Q = (2( BV ) / × 1000 L / = 7.5 × L / hr