Batch Reactor - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 172

product concentration is high in the reaction mixture, the reaction is slowed significantly due
to the feedback regulation. The intermediate product B formed is very low when the final
product concentration is high in the reactor.

4.5. SUMMARY

Batch reactor is widely used in industry and is the preferred reactor in laboratories and in
pharmaceutical industries. The performance of a batch reactor can be analyzed via mole
balance. For each species in the reactor, there is one mole balance equation that yields a differ-
ential equation:

d n j

d

t ¼ r j V

(4.23)

with initial conditions set in the reactor as t C j 0 . If the reactor is not oper-

ated isothermally, an energy balance equation is needed as well,

¼ 0, n j ¼ n j 0 ,orC j ¼

N S N R

d d d ðpVÞ

d

¼ Q W s V C Pj n j

t

r i DH Ri (4.24)

t

j¼1 i¼1

with t T 0 .

The reaction rates are needed before the batch reactor problems can be solved. The concen-
tration and number of moles are related by definition:
C j ¼ n j
V

¼ 0, T ¼

(4.28)

For liquid phase reactions,

V ¼ r 0

r V 0

(4.29)

And for gas phase reactions, the ideal gas law may be used to approximate the volume
change:

N S

V ¼ RT
P

n j (4.30)

j¼1

The solutions to the differential equations can be obtained either analytically (for simple
kinetics) or numerically with an automatic integrator.
The reactor preparation time (loading, unloading, etc.) affects the overall batch reactor
operation performance. The reactor volume can be obtained from Eqn (4.22)
V ¼ t B Q ¼ t P þ t f þ t U Q (4.22)

where t B is the batch time or the total time required for one batch operation that includes the
time for pre-reactor starting time t P , the reaction time t f and the reactor unloading and clean-
ing time t U, and Q is the volumetric rate that is treated with the batch reactor.