Page 156 - Materials Chemistry, Second Edition

Mass-Balance Concept and Reactor Design 139

(d) The residence time of the first reactor = 3 m /(0.04 m /min)
3
3
= 75 min
The residence time of the second reactor
= 1 m /(0.04 m /min) = 25 min
3
3

Q, C 0 Q, C 1 Q, C 2
3 m 3 1 m 3

Use Equation (4.28) to find the final effluent concentration:

C 2  C 2   C 2   C 1   1   1 
×
=   =     =    
+
+
C 0  1,800  C 1   C 0   1(0.1)(75)   1(0.1)(25) 
C = 60.5 mg/kg (It is below the cleanup level.)
out

Discussion:
1. The total volume of the reactor(s) for each of the four configura-
tions is 4 m .
3
2. The effluent concentration from the first setup (one large reac-
tor) is the highest. Actually, having a series of smaller CFSTRs in
series will always be more efficient in conversion than having a
single large CFSTR. A PFR can be viewed as an infinite series of
small CFSTRs, and a PFR is always more efficient than a CFSTR
of equal size.
3. For the configurations having two small reactors in series, the
setup with two equal-size reactors yields the lowest effluent
concentration.
4. For two reactors of different sizes, the sequence of the reactors
does not affect the final effluent concentration, provided that
the rate constants in the reactors are the same.

Example 4.19: PFRs in Series

Subsurface soil at a site is impacted by diesel fuel at a concentration of 1,800
mg/kg. Aboveground remediation, using slurry bioreactors, is proposed.
3
The treatment system is required to handle a slurry flow rate of 0.04 m /min.
The required final diesel concentration in the soil is 100 mg/kg. The reaction
is first-order with a rate constant 0.1/min, as determined from a bench-scale
study.