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4.2 Design of Adsorption and Ion-Exchange Processes 301

For propellers, N P = 0.32 (see Table 3.4) and thus (eq. (3.107))

P N N D 3 5
P P a 0.16 W/m 3
s
V V
Assuming that D f = 10 –9 m 2 /s and using the Leurn correlation (3.118), the vins–Glastonb
value of the mass transfer coeficient is found to be f k 1.3 10 5 m/s. The dif ference
f
between this value and the value gien by Meshk v o et al . is due to the approximate v alue
of D f used in this e xample.
The Biot number is (eq. (4.104))
kd C fp o
Bi 82.41
Dq 2 sma x

which is much higher that the value of 30. So, it is reasonable to assume that intraparticle
resistance dominates, as Meshk o et al . (2001) found e. xperimentally
By means of the Zwietering equation (3.114), with S = 6.5 for propellers (see able 3.6), T
we find that the minimum rotational speed for complete suspension is 40.58 rps, much
higher than the operating value of 3.33 rps (200 rpm). This means that the solid particles
are not fully suspended in the liquid phase.
Finally, using the Calderbank correlation (3.271), the minimum rotational speed for sur-
face aeration is found to be 55.16 rps, which is fairly higher than the operation agitation
speed, and thus surface aeration is a oided. v

Some comments on d y es : Dyes can be a threat to both human health and environment.
Focusing on the effect of dyes on human health, it should be pointed out that on e xpo-
sure to an environment containing vapors of dyes, one would experience headaches and
dizziness. After inhaling large portions of these v limbs could get paralyzed and apors,
damage of the inner organs may take place. Nowadays, the risks associated with the use
v
of such dyes hae been widely recognized and many countries hae posted man v y
restrictions to their use. In Europe, the launch of a new standard called ISO 14000 has
banned the import of all materials dyed with poisonous dyes.

Example 3
A volume of 100 L of a solution containing 1000 ppm Pb 2 and minor amounts of other ions
has to be treated. The desired fThe a ailable adsorbent is a inal concentration is 100 ppm. v
zeolite with a particle size of 1.3 mm, density of 2 g/cm 3 , and the REC is Q M = 176 mg/g.
Suppose that we hae eficient agitation and solid dif f v fusion is the controlling mechanism.
Solid diffusion is about 6.4 10 –10 cm 2 /s. Furthermore, the system obeys a f v orable a
Langmuir isotherm with La = 0.03 and the maximum exchange level is q max = 106 mg/g.
Estimate the time needed in an agitated batch reactor for lowering the solution concen-
tration to the value of 100 ppm for different masses of zeolite. Furthermore, propose a
. design for the reactor