Page 81 - Elements of Chemical Reaction Engineering Ebook

52 Conversion and Reactor Sizing Chap. 2

Example 2-6 Sizing Plug-Flow Reactors in Series

Using either the data in Table.2-2 or Figure 2-5, calculate the reactor volumes V,
and V2 for the plug-flow sequence shown in Figure 2-4 when the intermediate con-
version is 40% and the final conversion is 80%. The entering molar flow rate is the
same as in the previous examples, 0.867 mol/s.

Solution
In addition to graphical integration we could have used numerical methods to sue
the plug-flow reactors. In this example, we shall use Simpson’s rule (see Appendix
A.4) to evaluate the integrals.

The overall
conversion of two
PRFs in series is the
same as one PRF For the first reactor, Xo = 0, X, = 0.2, X2 = 0.4, and AX = 0.2,
with the same total
volume.

r:)
Selecting the appropriate values from Table 2-2, we have

VI = (0.867 mol/s) - [189+4(200)+250] L.s/rnol

= 71.6 L = 71.6 dm3

For the second reactor,

=FAoT[-+4-+- 1 1 1
AX
-rA(0.4) -rA(O.6) -rA(O.8) (E2-6.2)

[250+4(400) + 8001 L.s/mol

= 153 L = 153 dm3
The total volume is then

V = VI f V, = 225 L = 225 dm3

The final sequence we shall consider is a CSTR and plug-flow reactor in
series. There are two ways in which this sequence can be arranged (Figure