Page 142 - Materials Chemistry, Second Edition

Mass-Balance Concept and Reactor Design 125

Example 4.7: Batch Reactor (Determine the Required Residence
Time with a Known Rate Constant)
A batch reactor is to be designed to treat soil containing 200 mg/kg of poly-
chlorinated biphenyls (PCBs). The required removal, conversion, or reduc-
tion of PCBs is 90%. The rate constant is 0.5 h . What is the required residence
-1
time for this batch reactor? What is the required residence time if the desired
final concentration is 10 mg/kg?

Strategy:
Although the order of the reaction is not mentioned in the problem
statement, it is a first-order reaction because the units of k are
1/time.

Solution:
(a) For a 90% reduction (η = 90%)

C = C (1 − η)
f
i
= 200 (1 − 90%) = 20 mg/kg
Insert the known values into Equation (4.16)

20 = 0.1 = e − (0.5)τ
200

τ = 4.6 h
(b) To achieve a final concentration of 10 mg/kg:

10 = 0.05 = e − (0.5)τ
200

τ = 6.0 h

Example 4.8: Batch Reactor (Determine the Required Residence
Time with an Unknown Rate Constant)

A batch reactor was installed to remediate soil impacted by PCBs. A test
run was conducted with an initial PCB concentration of 250 mg/kg. After
10 hours of batchwise operation, the concentration dropped to 50 mg/kg.
However, it is required to reduce the concentration down to 10 mg/kg.
Determine the required residence time to achieve the final concentration of
10 mg/kg.