Page 64 - Elements of Chemical Reaction Engineering 3rd Edition

36 Conversion and Reactor Sizing Chap. 2

Constant-volume batch reactors are found very frequently in industq. In par-
ticular, the laboratory bomb reactor for gas-phase reactions is widely used for
obtaining reaction rate information on a small scale. Liquid-phase reactions in
which the volume change during reaction is insignificant are frequently carried
out in batch reactors when small-scale production is desired or operating diffi-
culties rule out the use of continuous systems. For a constant-volume batch
reactor, Equation (2-5) can be arranged into the form

For batch-reactor systems in which the volume varies while the reaction is pro-
ceeding, the volume may usually be expressed either as a function of time
alone or of conversion alone, for either adiabatic or isothermal reactors. Con-
sequently, the variables of the differential equation (2-6) can be separated in
one of the following ways:

dX
V dt = NAo -
- rA
or

These equations are integrated with the limits that the reaction begins at
time zero (ie., t = 0, X = 0). When the volume is varied by some external
source in a specific manner (such as a car cylinder piston compressing the
reacting gas according to the equation V = VI + V, sin of), the equation
relating time and conversion that one would use is

dX
loi Vdt = NAo

However, for the more common batch reactors in which volume is not a
predetermined function of time, the time t necessary to achieve a conversion X
is

L I
Design
Equation Equation (2-6) is the differential form of the design equation, and Equations
(2-8) and (2-9) are the integral forms for a batch reactor. The differential form
is generally med in the interpretation of laboratory rate data.