Ideal Flow Reactors - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 240

or

C je

Z

d C j
r j

V
Q ¼

(5.107)

C j0

for constant density reactions. To make use of the batch concentration data as shown
in Fig. 5.22 , we need to know how the reaction rate is related to the concentration change.
In a batch reactor, mole balance leads to Eqn (4.2), or

d n j
d t

r j V Batch ¼ (5.108)

Again for constant density reactions ( r ¼ constant 0 V batch ¼ constant), Eqn (5.108) is

reduced to

d C j
d t

r j ¼ (5.109)

Thus, the integration of Eqn (5.107) may be taken on the batch concentration data via
Eqn (5.109) .

C je C je t @ C je

Z Z Z

V
Q ¼

d C j
r j ¼

d C j
d C j = d t ¼

d t ¼ t e t 0 (5.110)

C j0 C j0 t @ C j0

Therefore, the integration rates can be read off directly from the batch concentration profile
(data). Referring to Fig. 5.22 and Eqn (5.110) , if the conversion is known (or specified), we can

C A0

C A

Slope of the tangent =

r Ae

C Ae

0

0

t

FIGURE 5.22 Finding the rate of reaction from the batch concentration data.