Page 37 - Elements of Chemical Reaction Engineering Ebook

8 Mole Balances Chap. 1

From this equation we see that rl will be an indirect function of position, since
the properties of the reacting materials (e.g., concentration, temperature) can
have different values at different locations in the .reactor.
We now replace GJ in Equation (1-3),

by its integral form to yield a form of the general mole balance equation for
any chemical species j that is entering, leaving, reacting, andor accumulating
within any system volume V

This is ;? basic
equation for
chemical reaction dt
engineering
From this general mole balance equation we can develop the design equations
for the various types of industrial reactors: batch, semibatch, and continu-
ous-flow. Upon evaluation of these equations we can determine the time (batch)
or reactor volume (continuous-flow) necessary to convert a specified amount of
the reactants to products.

1.3 I Batch Reactors

A batch reactor has neither inflow nor outflow of reactants or products while
the reaction is being carried out; F,, = F, = 0. The resulting general mole bal-
ance on species j is

dN. V
2 1 rjdV
=
dt
If the reaction mixture is perfectly mixed so that there is no variation in the
rate of reaction throughout the reactor volume, we can take rJ out of the inte-
gral and write the mole balance in the form

NAL
Figure 1-3 shows two different types of batch reactors used for gas-phase
reactions. Reactor A is a constant-volume (variable-pressure) reactor and Reac-
tor B is a constant-pressure (variable-volume) reactor. At,time t = 0, the reac-
tants we injected into the reactor and the reaction is initiated. To see clearly
t
the different forms the mole balance will take for each type of reactor, consider
the following examples, in which the gas-phase, decomposition of dimethyl
ether is taking place to form methanb, hydroglen, and carbon monoxide:

(CH3)ZO CH,+f€z +CO