Page 159 - Elements of Chemical Reaction Engineering 3rd Edition

Sec. 4.2 Scale-up of Liquid-Phase Batch Reactor Data to the Design of a CSTR 131

This time is the time t needed to reduce the reactant concentration in a batch
reactor from an iinitial value C,, to some specified value CAS
The total cycle time in any batch operation is considerably longer than
the reaction time, tR, as one must account for the time necessary to fill (9) and
empty (t,) the reactor together with the time necessary to clean the reactor
between batches, t,. In sbme cases the reaction time calculated from Equation
(4-5) may be only a small fraction of the total cycle time, ti.
t, = ff + t, + fc 4- tR

Typical cycle times for a batch polymerization process are shown in Table 4- 1.
Batch polymerization reaction times may vary between 5 and 60 h. Clearly,
decreasing the reaction time with a 604 reaction is a critical problem. As the
reaction time is reduced, it becomes important to use large lines and pumps to
achieve rapid transfers and to utilize efficient sequencing to minimize the cycle
time.

TABLE 4-1. TYPICAL CYCLE TIMES FOR A BATCH
POLYMERIZATION PROCESS
-
Activity Time (h)
1. Charge feed to the reactor and agitate, 1.5-3.0
Batch operation
times 2. Heat to reaction temperature, f, 1.c2.0
3 Carry out reaction, rR (varies)
4. Empty and clean reactor, r, 0 5-1.0
Total time excluding reaction 3.0-6 0
-
It is important to have a grasp of the order of magnitude of batch reaction
times, tR, in Table 4-1 to achieve a given conversion, say 90%, for the different
values of the specific reaction rate, k. We can obtain these estimates by constd-
ering the irreversjble reaction
A--+B
carried out in a constant-volume batch reactor for a first- and a second-order
reaction. We start with a mole balance and then follow our algorithm as shown
in Table 4-2.

TABLE 4-2. ALGORITHM TO ESTIMATE REACTION TIMES
-
Mole balance

Rate law Firs t-order Second-order
-rA = kCA -rA = kCi
Stoichiometry (V = Yo) c, = 5 = c,, (1 - X)
VO
Combine = k(1 - X) dX
-& = kC*,(1 -
dt
Integrate t=j;ln- 1 X
1
t=
1-x kCAd1 - X)