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4.2 Design of Adsorption and Ion-Exchange Processes 299

where La can be calculated by using eq. (4.8):

1
La 0.1873
1 KC o

Then, a trial-and-error procedure is needed for estimating the equilibrium liquid-phase
, dimensionless concentration. In this w we get ay X = 0.1 and thus

C
X e C e C X o 9.975 mg/L
C o

The parameter w is calculated by using eq. (4.33):

C C
w o e 0.9
C o

Then, the roots of eq. (4.58) are a = –3.477 and b = 0.777. To use the model, we need to
transform the solid loading q into U ( t ):
t

C
C t ()
Ut () o
C o C e
where the liquid concentration C ( t ) can be calculated from the follo wing relationship:

C C t ()
q o V
t
m
In Table 4.22, t and the corresponding v alues of U ( t ) are gi en. v

Table 4.22
U ( t ) v ersus t
t (min) U(t)

15 0.22
30 0.27
60 0.36
120 0.47
180 0.56