Page 160 - Materials Chemistry, Second Edition

Mass-Balance Concept and Reactor Design 143

flow rate of 50 L/min, an off-the-shelf reactor would provide a hydrau-
lic retention of 5 min and reduce TCE concentration from 200 to 16 ppb.
However, the discharge limit for TCE is 3.2 ppb. Assuming the reactors are
of ideal plug flow type and the reaction is first-order, how many reactors
would you recommend? What would be the TCE concentration in the final
effluent?

Solution:
(a) Use Equation (4.24) to find out the reaction-rate constant:

16
C out − k ()(5)
= = e
C in 200

k = 0.505/min
(b) Use Equation (4.29) to find out the final effluent concentration
from two PFRs in series:

C 2  C 2   C 2   C 1  − (0.505)(5) − (0.505)(5) − 5.05
=   =     = e ( )( e ) = e
C 0  200   C 1   C o 

C = 1.28 ppb (It is less than 3.2 ppb.)
out
Two PFRs, each with 5-min residence time, would be needed.

Discussion:
We can also determine the total residence time needed to reduce the
final concentration to 3.2 ppb first, and then determine the number
of PFRs needed.
Use Equation (4.24) to find out the required residence time

3.2
= = e
C out − (0.505)( )τ
C in 200

τ = 8.2 min (Two PFRs are needed.)

4.6.2 Reactors in Parallel

For reactors in parallel, the reactors share the same influent (the influent is
split and fed to the reactors). The flow rate to each reactor in parallel can be