Page 149 - Materials Chemistry, Second Edition

132 Practical Design Calculations for Groundwater and Soil Remediation

Second-order reactions: The design equations for the second-order reactions
are similar in format for PFRs and CFSTRs. The only difference is that
the C in the denominator on the right-hand side of Equation (4.22)
out
(see Table 4.2) is replaced by C in Equation (4.26) (see Table 4.3). Since
in
C > C , the ratio of C /C of a PFR will be smaller than that of a
in
out
in
out
CFSTR for the same C , k, and τ. The smaller C /C ratio means that
in
in
out
the effluent concentration from a PFR would be lower than that from a
CFSTR for the same C , k, and τ.
in
Example 4.13: A Soil Slurry Reactor with First-Order Kinetics (PFR)
A soil slurry reactor is used to treat soil that contains 1,200 mg/kg of TPH.
The required final soil TPH concentration is 50 mg/kg. From a bench-scale
study, the rate equation was found to be
γ = −0.25C in mg / kg / min

Assume that the reactor behaves as a PFR. Determine the required residence
time.

Strategy:
It is a first-order reaction, and the reaction-rate constant is equal to
0.25/min.
Solution:
Insert the known values into Equation (4.24) to find out the value of τ:

50
C out − (0.25)τ
= = e
C in 1200
τ = 12.7 min

Discussion:
1. For the same inlet concentration and reaction-rate constant, the
required residence time to achieve a specified final concentra-
tion is 12.7 min for a PFR, which is much shorter than that for a
CFSTR, 92 min (Example 4.11).
2. For the first-order kinetics, the reaction rate is proportional to the
concentration inside the reactor (i.e., γ = kC reactor ). The higher the
reactor concentration, the faster is the reaction rate. For CFSTRs,
by definition, the reactor concentration is equal to the effluent
concentration (i.e., 50 mg/kg in this case). For PFRs, by definition,
the reactor concentration decreases from C (1,200 mg/kg) at the
in
inlet to C (50 mg/kg) at the outlet. The average concentration
out