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4.2 Design of Adsorption and Ion-Exchange Processes 323

anion exchange resin (Lewatit MP 64) of 0.59-mm particle diameter was used, with 0.654
g/cm 3 bulk density. The influent stream contained 1.273 mmol/L of HCrO 4 – and the super-
ficial velocity was 0.134 cm/s. Furthermore, the isotherm of the HCrO 4 –resin system at
24 °C was found to be of Freundlich type with Fr 0.194 and K F 1.815
(mmol/g)(l/mmol) 0.194 . Finally, the solid-phase diffusion coeficient was found to be 1.43 f
10 –8 cm 2 /s. The approximate value of 1.19 10 9 m 2 /s could be used for the HCrO 4 –
liquid-phase diffusion coefficient. Finally, assume the value of 0.41 for bed porosity .
Using the Miura–Hashimoto model, calculate the time needed to reach a breakpoint
concentration of 0.636 mmol/L HCrO 4 – (50% of inlet concentration). According to the
ero v experimental results gien by Ri v et al . (2004), the specified breakpoint concentration
is reached after 1000 BV (bed v olumes).

Solution
The Reynolds and Schmidt numbers are

du ps
Re p 0.79

Sc 842
D f

Using the correlation of illiamson (eq. (3.346)), W

Sh 2.4 0.66 Re Sc p 0.34 0.33 11.35

then

kd fp
Sh k 0.00229 cm/s
f
D f

The solid-side mass transfer coeficient is (eq. (4.174)) f

15 D 3
sb
ka su 2 0.000161 g/scm
r
o
where (eq. (4.177))

3 1
)
60 cm
a u (1
r o