Page 112 - The engineering of chemical reactions

96 Single Reactions in Continuous Isothermal Reactors

From the previous equation we have
CAo
_I1
:,u t= $$=i(&-$--)=&(A-;)=9min
-,
s
CA
so that
V = 4 x 9 = 36 liters

Comparison with batch reactor

We could proceed as before to write out the expressions for the irreversible reaction
A + products, r=kC;
for different values of n, but in fact we have already worked these problems in the previous
chapter.
In a PFTR the time t that a molecule has spent in the reactor is z/u, and the time for
the molecule to leave the reactor is L/u, which is the total time that a molecule has spent
in the reactor,

TPFTR = lb&h
Therefore, to find the behavior of a PFTR for kinetics that we have solved in a batch reactor,
all we have to do is make the transformation tt,&, -z+ rPi7rn. The solution for the rtth-order
irreversible reaction from Chapter 2 is

1CA = C&l + (n - l)kC;,‘t]l’(‘-n) 1

(except for 12 = l), where all we did was replace t for the batch reactor by r for the PFTR.
We can write for the residence time in a constant-density, constant-cross-section PFTR

tpflR = v/v = L/u
because, for constant reactor cross section At, we have V = AtL and v = uAt.
The PFTR was in fact assumed to be in a steady state in which no parameters vary
with time (but they obviously vary with position), whereas the batch reactor is assumed
to be spatially uniform and vary only with time. In the argument we switched to a moving
coordinate system in which we traveled down the reactor with the fluid velocity u, and in
that case we follow the change in reactant molecules undergoing reaction as they move
down the tube. This is identical to the situation in a batch reactor!
We can show this more formally by writing dt -+ dz/u,
dCA dCA
- -+ u - = -r(C,)
dt dz
which shows that the performance of batch reactor and PFTR are identical, with the reaction
time t in a batch reactor corresponding to the residence time r in a PFTR. Again, we note
that a PFTR “acts like” a batch reactor, while a CSTR “looks like” a batch reactor.