Page 218 - Elements of Chemical Reaction Engineering Ebook

Sec. 4.7 Unsteady-State Operation o‘f Reactors 189

4.7.1 Startup of a CSTR

An expanded The startup of a fixed volume CSTR under isothermal conditions is rare,
ver’”on O* rhr\ but it does occur occasionally. Here we want to determine the time necessary
section an be
found on the to reach steady-state operation. We begin with the general mole balance equa-
CD-ROM tion applied to Figure 4- 13a:

dNA
FA, - FA + rAV = - (4-43)
dt
Conversion does not have any meaning in startup because one cannot separate
the moles reacted from the moles accumulated in the CSTR. Consequently, we
must use concentration rather than conversion as our variable in the balance
equation. For liquid-phase (u = u,) reactions with constant overflow (V = V0),
using t = V,/u,, we can transform Equation (4-43) to

CA,-C, + rAt = z dC.4 - (4-44)
dt
For a first-order reaction ( - YA = kCA) Equation (4-44) then becomes

(4-45)

which solves to

(4-46)

Letting t, be the time necessary to reach 99% of the steady-state concentra-
tion, CA5:

CAI3
= 1 + zk (4-47)
Rearranging Equation (4-46) for CA = 0.99CA, yields

(4-4.8)

For slow reactions:

(U-49)
For rapid reactions:
Time to reach
steady state in 4.6
an isothermal t, = F, (4-50)
CSTR n
For most first-order systems, steady state is achieved in three to four space
times.