Page 148 - Materials Chemistry, Second Edition

Mass-Balance Concept and Reactor Design 131

PFR. The concentration in the reactor (C reactor ) decreases from C at the inlet
in
to C at the exit. Under the steady-state condition, the flow rate is constant,
out
and Q = Q . By inserting Equation (4.10) into Equation (4.5), the mass-bal-
out
in
ance equation can be expressed as follows:
0 = QC in − QC out + ( V)(− ) (4.23)
kC reactor
C reactor is a variable. The equation can be solved by considering an infinitesi-
mal section of the reactor and integrating the equation. The solution can be
expressed as follows:

C out − kV Q(/ ) − kτ
= e = e (4.24)
C in
Table 4.3 tabulates the design equations for PFRs in which zeroth-, first-,
and second-order reactions take place.
When comparing the design equations for PFRs in Table 4.3 and those for
CFSTRs in Table 4.2, the following remarks can be derived:

Zeroth-order reactions: The design equations are identical for both reac-
tor types. This means that the conversion rate is independent of the
reactor types, provided all the other conditions are the same.
First-order reactions: The ratio of the effluent and influent concentra-
tions is linearly proportional to the inverse of the residence time for
CFSTRs, while this ratio is exponentially proportional to the inverse
of the residence time for PFRs. In other words, the effluent concen-
tration from PFRs decreases more sharply with the increase of the
residence time than that from CFSTRs provided all the other condi-
tions are the same. We can also say that for a given residence time (or
reactor size), the effluent concentration from a PFR would be lower
than that from a CFSTR. (More discussion and examples will be
given later in this section.)

TABLE 4.3
Design Equations for PFRs
Order of Reaction Design Equation Equation No.
0 C out = C in − kτ (4.25)

1 C out = C e( −τ k ) same as Equation (4.24)
in
2 C out = C in (4.26)
kC)
1(+τ in