Page 42 - Elements of Chemical Reaction Engineering Ebook

Sec. 1.4 Continuous-Flow Reactors 13

[t is usually most convenient to have the reactor volume V rather than the
reactor length y as the independent variable. Accordingly, we shall change
variables using the relation dV = A dy to obtain one form of the design equa-
tion for a tubular reactor:

dF.
-J = (].-lo)
dV 'J
We also note that for a reactor in which the cross-sectional area A varies along
the length of the reactor, the design equation remains unchanged. This equa-
tion can be generalized for the reactor shown in Figure 1-6, in a manner simi-

Figure 1-6

lar to that preseinted above, by utilizing the volume coordinate V rather than a
linear coordinate y. After passing through volume V species j enters subvoliume
AV at volume I7 at a molar flow rate Fj(V). Species j leaves subvolume A'V at
volume (V + AV), at a molar flow rate FJ(V + AV). As before, AV is chosen
small enough so that there is no spatial variation of reaction rate within the
subvoliume :

AV
ri dV = rj AV (1-11)

After accounting for steady-state operation in Equation (1-4), it is combined
with Equation (1 - 1 1) to yield
Fj(V) - Fj(V+ AV) -k r, AV = 0

Rearranging gives

Fj(V+ AV) - Fj(V) -
- rj
AV
and taking the liinit as AV+O, we again obtain Equation (1-10):
-qTk

(1-10)
Tubular
reoctor
Consequently, we see that Equation (1-10) applies equally well to our model
of tubuiar reactors of variable and constant cross-sectional area, although it is