Page 146 - Materials Chemistry, Second Edition

Mass-Balance Concept and Reactor Design 129

TABLE 4.2
Design Equations for CFSTRs
Order of Reaction Design Equation Equation No.
0 C out = C in − kτ (4.21)
1
C out
1 = same as Equation (4.20)
k
C in 1 +τ
1
C out
2 = (4.22)
+τ
C in 1( k C) out
4.4.2 CFSTRs
Let us now consider a steady-state CFSTR with a first-order reaction. As
mentioned previously, by definition, the concentration in the effluent from
a CFSTR is the same as that in the reactor; and the concentration in the reac-
tor is uniform and constant. Under steady-state conditions, the flow rate is
constant, and Q = Q . By inserting Equation (4.10) into Equation (4.5), the
out
in
mass-balance equation can be expressed as follows:
0 = QC in − QC out + ( V)(− kC reactor )
(4.19)
= QC in − QC out + ()(− )
V
kC out

With a simple mathematical manipulation, Equation (4.19) can be rearranged as:

C out 1 1
= = (4.20)
k
C in 1+ k VQ( /) 1+τ
Table 4.2 tabulates the design equations for CFSTRs in which zeroth-, first-,
and second-order reactions take place.

Example 4.11: A Soil Slurry Reactor with First-Order Kinetics (CFSTR)
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

The content in the reactor is fully mixed. Assume that the reactor behaves as
a CFSTR. Determine the required residence time.