Page 84 - Elements of Chemical Reaction Engineering Ebook

Sec. 2.4 Reactors in Series 55

I Schelvne FA0 x,
CSTR: V, = ~ = 0.867(0.5)(303) = 131.4 dm3
-rAI
Who’s on first? V, = FAo 1
0.8
Who is. PFR: = 0.867(151) = 130.9 dm3
05 -rA
V,,,,, = 262 dm3 (liters)
Scheme B will give the smaller total reactor volume for an intermediate conversion
of 50%. This result is shown in Figure E2-7.1. However, as is seen in Problem P2-3,
the relative sizes of the reactors depend on the intermediate conversion. Comlpare
your results in Example 2-7 with those in Problem P2-3.

The previous examples show that if we know the molar flow rate to the
reactor and the reaction rate as a function of conversion, then we can calculate
the reactor volume necessary to achieve a specified conversion. The reaction
rate does not depend on conversion alone, however. It is also affected by the
initial concentrations of the reactants, the temperature, and the pressure. Con-
sequen~ ly, the experimental data obtained in the laboratory and presented in
Table %-I as -rA for given values of X are useful only in the design of
full-scale reactors that are to be operated at the same conditions as the labora-
tory experiments (temperature, pressure, initial reactant concentrations). This
conditional relationship is generally true; Le., to use laboratory data directly
for sizing reactors, the laboratory and full-scale operating conditions musit be
identical. Usuall:y, such circumstances are seldom encountered and we must
revert to the metlhods described in Chapter 3 to obtain -r, as a function of X.
We need only However, ir is important for the reader to realize that if the rate of reac-
-14 = t(x) and tion is civailable dely as a function of conversion, -r, = f(X), or ifit can be
FA,, to me reactors
generared by some interniediate calculation, one can design a variety of reac-
tors or cornhiriation of reactors.
Rnally, let’s consider approximating a PFR with a number of small,
equal-volume CSTRs of V, in series (Figure 2-8). We want to compare the total

Figure 2-8 Modeling a PFR with CSTRli in series.