Problem Statement: Cells capable of degrading polychlorinated biphenol (PCB) are entrapped in spherical gel beads 0.5 cm in diameter. The beads are packed into a column 30 cm in diameter and fill 85% of the column volume (i.e., void fraction=0.15). The column is fed with 1000ppm of PCB at 0.1 L/min. Biodegradation follows the following rate expression.
r(s)=rm*s/(K+s+Ki*s2)
where rm= 0.01 g/L-h
K=0.001 g/L Ki=0.001 L/g
Solution:
(This is an artificially made-up problem to facilitate easy
calculation.) As an engineer, you should make sure that the units
are compatible. 1000 ppm is the same as 1g/L. Units are
extremely important in numerical answers, unless the answer
happens to be dimensionless.
Note that the substrate concentration ranges
between 0.01g/L to 1g/L. Both the K and the
Kis2 terms are small compared to
s. Thus, the biodegradation rate is zero order (i.e.,
constant) with r=rm=0.01 g/L-h.
To degrade from 1g/L to 0.01g/L requires a residence time of
sin-sout 1g/L-0.01g/L
t = ------- = ------------- = 99h
rm 0.01g/L-h
The length traveled in 99h is:
60min 0.1L 1000cm3 4
(99h)(-----)(----)(-------)(-----------) = 840cm = 8.4m
h min L p*30cm*30cm
Solution:
PCB biodegradation is a slow process, and conversion is normally
reaction limited. Besides, the reaction rate is constant; thus,
even in the presence of mass transfer limitation there is no
difference in the reaction rate. The effectiveness factor, which
is the ratio of the observed rate conversion with mass transfer
resistance to the ideal case without mass transfer resistance, is
1. The height of the actual column needed is increased by a
factor of the void volume.
height = 8.4m/0.85 = 9.9m
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