Page 38 - Elements of Chemical Reaction Engineering Ebook

Sec. 1.3 Batch Reactors 9

A B
Il--Be Movable

Figure 1-3 Batch reactors for gas-phase reactions.

Example 1-2 Constant Volume or Constant Pressure:
Does It Make a Difference?

Write the mole balance for dimethyl ether in terms of the reactor volume, concen-
tration, and rate of formation of dimethyl ether for both a constant-pressure and a
constant-volume batch reactor.

Solution
To reduce the number of subscripts, we write the reaction symbolically as

A --+ M+H+C
where A is dimethyl ether, M is methane, H is hydrogen, and C is carbon monoxide.
For both batch reactors, the mole balance on A is
--- (1-5)
1 dNA -
V dt “
In writing the mole balance for dimethyl ether for a batch reactor, the only assump-
tion made is that there are no spatial variations in r,.
Constant-volume batch reactor. The reactor is perfectly mixed so that the
concentration of the reacting species is spatially uniform. Because the volume is
constant we can take V inside the differential and write the mole balance in terms of
the concentration of A:

1 dNA - d(N.4’V) - dCA - (El-2.1)
V dt dt dt ‘ A
Constant-pressure batch reactor. To write the mole balance for this reactor
in terms of concentration, we again use the fact that

N, = CAV

(El-2.2)

(El-2.3)