Page 151 - Materials Chemistry, Second Edition

134 Practical Design Calculations for Groundwater and Soil Remediation

For flow reactors such as CFSTRs and PFRs, the residence time, or the
hydraulic detention time, τ, can be defined as:
V
τ= (4.27)
Q
where V is the volume of the reactor and Q is the flow rate. For a PFR, by
definition, each fluid particle should spend exactly the same amount of time
flowing through the reactor. On the other hand, for a CFSTR, most fluid parti-
cles would flow through the reactor in a shorter or longer time than the aver-
age residence time. Therefore, the value of τ in Equation (4.27) is the average
hydraulic detention time, which is used in determining the size of the reactor.
For a batch reactor, the residence time calculated from Equations (4.16),
(4.17), and (4.18) (see Table 4.1) is the actual time needed for reaction to be
accomplished. For system operation and design, an engineer needs to take
the time needed for load, unload, and idle into consideration.

Example 4.15: Sizing a Batch Reactor
A soil slurry batch reactor is used to treat soils that contain 1,200 mg/kg of
TPH. It is required to treat the slurry at 30 gal/min. The required final soil
TPH concentration is 50 mg/kg. From a bench-scale study, the rate equation
was found to be

γ = −0.05C in mg / kg / min

The time required for loading and unloading of the slurry for each batch is 2
h. Size the batch reactor for this project.

Strategy:
It is a first-order reaction, and the reaction-rate constant is equal to 0.05/
min.

Solution:
(a) Insert the known values into Equation (4.16) to find out the value
of τ:

50
C out − (0.05)τ
= = e
C in 1200

τ = 64 min (needed for reaction)
(b) The total time needed for each batch
= reaction time + time for loading and unloading
= 64 + 120 = 184 min