Page 160 - Elements of Chemical Reaction Engineering 3rd Edition

132 Isothermal Reactor Design Chap. 4
For first-order reactions the reaction time to reach 90% conversion (Le.,
X = 0.9) in a constant-volume batch reactor scales as

If k = 10-4 S-1,

tR = 2'3 = 23,000 s = 6.4 h
10-4 S-1
The time necessary to achieve 90% conversion in a batch reactor for an irre-
versible first-order reaction in which the specific reaction rate is s-l is 6.4 h.
For second-order reactions, we have

tR = =9OOOs = 2.5h
10-3 S-1
Table 4-3 gives the order of magnitude of time to achieve 90% conversion for
first- and second-order irreversible batch reactions.

TABLE 4-3. BATCH REACTION TIMES
First-Order Second-Order Reaction 7ime
k (s-l) kC,o (s-') tR

Estimating Reaction 10-4 10-3 Hours
Times 10-2 10-1 Minutes
1 10 Seconds
loo0 10,Ooo Milliseconds

I Example 4-1 Determining k from Batch Data
It is desired to design a CSTR to produce 200 million pounds of e,.ylene glycol per
year by hydrolyzing ethylene oxide. However, before the design can be carried out,
it is necessary to perform and analyze a batch reactor experiment to determine the
specific reaction rate constant. Since the reaction will' be carried out isothermally,
the specific reaction rate will need to be determined only at the reaction temperature
of the CSTR. At high temperatures there is a significant by-product formation, while
at temperatures below 40°C the reaction does not proceed at a significant rate; con-
sequently, a temperature of 55°C has been chosen. Since the water is usually present
in excess, its concentration may be considered constant during the course of the
reaction. The reaction is first-order in ethylene oxide.
CH2-OH
/"\ I
CH,-CH, + H20 H2s04 > CH,-OH
A +B catalyst C