Page 77 - Elements of Chemical Reaction Engineering 3rd Edition

Sec. 2.4 Reactors in Series 49

The corresponding rate of reaction -?-A2 is evaluated at the conversion
X,. Substituting for FA1 and FA2 yields

Reactor 2 (2-19)

The volume folr the third reactor, V,, is found by integrating Equafion (2-15)
between the limits X2 and X3:

Reactor 3

To demonstrate these ideas, let us consider three different schemes of reactors
in series: two CSTRs, two PFRs, and a PFR connected to a CSTR. To size
these reactors we shall use laboratory data that give the reaction rate at differ-
ent conversions. The reactors will operate at the same temperature and pressure
as were used in obtaining the laboratory data.
We will now use FA0 calculated in Example 2-1 together
with Figure 2-1 to size eactors for the three reactor schemes,. The
first scheme to be cons wo CSTRs in series shown in Figure 2-3.
For the first reactor in which the rate of disappearance of A is -rAl at conver-
sion XI, the volume necessary to achieve the conversion X, is

Xi 0.4

FAo% I

Figure 2-3 Two CSTRs in series.

In the second rpactor, the rate of disappearance of A, -rA2, is evaluated
and the conversion is that of the exit stream of reactor 2, X2. The volume nec-
essary to increase the conversion in reactor 2 from XI to X, was derived previ-
ously and is given by Equation (2-19):

FAO (x2 - xl>
v2 = (12- 19)
-rA2