Page 150 - Materials Chemistry, Second Edition

Mass-Balance Concept and Reactor Design 133

in the PFR (625 mg/kg as the arithmetic average or 245 mg/kg
as the geometric average) is much higher than 50 mg/kg, which
makes the reaction rate much higher. Consequently, the required
residence time would be much shorter.

Example 4.14: A Low-Temperature Thermal Desorption
Reactor with Second-Order Kinetics (PFR)
A low-temperature thermal desorption reactor is used to treat soil that con-
tains 2,500 mg/kg of TPH. The required final soil TPH concentration is 100
mg/kg. From a bench-scale study, the rate equation was found to be

γ = – 0.12 C in mg/kg/hr
2
The soil is carried through the reactor on a conveyor belt. Assume that the
reactor behaves as a PFR. Determine the required residence time.

Strategy:
It is a second-order reaction, and the reaction-rate constant is equal to
0.12/(mg/kg/h).

Solution:
Insert the known values into Equation (4.26) (see Table 4.3) to find out
the value of τ:
100 1
= =
C out
τ
+
C in 1,200 1 0.12 (1,200)
τ = 0.08 h = 4.8 min
Discussion:
Again, for the same initial concentration and reaction-rate constant, the
required residence time to achieve the specified final concentration
is 4.8 min for a PFR, which is much shorter than that for a CFSTR, 55
min (as shown in Example 4.12).

4.5 Sizing the Reactors

Once the reactor type is selected and the required residence time to achieve
the desired removal is determined, sizing a reactor is straightforward.
The longer the compound needs to stay in a reactor to achieve the desired
removal, the larger the reactor would be for a given flow rate.