Page 309 - Modeling of Chemical Kinetics and Reactor Design

Introduction to Reactor Design Fundamentals for Ideal Systems 279

Equation 5-58 gives an expression for the reaction time and frac-
tional conversion for an isothermal constant pressure batch reactor.
Considering an nth order irreversible reaction represented by A → bB
n
with (–r ) = kC , the design equation is
A
A
n
− ( r A )=− 1 dN A = kC A
V dt
or in terms of the fractional conversion X ,
A
dX A = kC (1 − X ) {1 +( b − ) } 1 − n
n
n−1
X
1
dt AO A A (5-59)
or

X A
t = 1 n− ∫ dX A − (5-60)
n
kC AO 1 0 (1 − X ) {1 +( b − ) } 1 n
X
1
A
A
Equation 5-60 is the generalized equation, which can be used to
determine the reaction time of an nth order reaction with b, the
stoichiometric coefficient of the product component B.
NUMERICAL METHODS FOR REACTOR
SYSTEMS DESIGN

In Chapter 3, the analytical method of solving kinetic schemes in
a batch system was considered. Generally, industrial realistic schemes
are complex and obtaining analytical solutions can be very difficult.
Because this is often the case for such systems as isothermal, constant
volume batch reactors and semibatch systems, the designer must
review an alternative to the analytical technique, namely a numerical
method, to obtain a solution. For systems such as the batch, semi-
batch, and plug flow reactors, sets of simultaneous, first order ordinary
differential equations are often necessary to obtain the required solu-
tions. Transient situations often arise in the case of continuous flow
stirred tank reactors, and the use of numerical techniques is the most
convenient and appropriate method.
Various types of numerical techniques have been developed
based on the degree of accuracy and efficiency. One of the popular