Page 304 - Modeling of Chemical Kinetics and Reactor Design

274 Modeling of Chemical Kinetics and Reactor Design

I =− 1 ( [ ln 1 − X )] X A + 1 θ B ( [ ln −2 X )] X A
A
A
B (θ − ) 2 2 0 B (θ − ) 2 2 0

+ 1   1   X A (5-43)
(2 −θ B) (θ B −2 X )

A  0
or

 θ − 2X )  2X ( θ − 2) 
1 ln  B (  A  − A B  = kC 2 t
B(
B (
−
2
θ − 2)    θ ( 1 X )  θθ − 2X )  AO holding time (5-44)
A 
A 

B
B
The holding time t holding time is given by the expression
 B (  θ −2 X )  2 X (θ − ) 2 
1
1
t holding time = 2 ln  A  − A B  (5-45)
B(
A 
kC 2 AO (θ B − )  θ B(1 − X ) θθ B − 2 X ) 
A 


2
Given the initial concentrations of A and B, the fractional conver-
sion X , and the rate constant k as the following: C = 0.001 gmol/1,
A
AO
2
2
5
C BO = 0.003 gmol/1, X = 0.9, k = 10 [(liter) /(gmol • min)], and θ B
A
= C BO /C AO = 3, gives
 (  32 0 9) 0 9 3 2) 
(
1 −× .  − 2 × . −  = 5 2
0 001) t
2  ln
(
(
( 32)   31 0 9)  33 2 0 9)   10 ×( . holdingtime
−

− .

−× .
. [
−
1 1 386 − 0 5] = 10 t holding time
1
.
or t holding = 8.86 min. In other words, it would take approximately 9
minutes to convert 90% of reactant A charged to the 1-liter reactor.
The Microsoft Excel spreadsheet (EXAMPLE5-1.xls) was used to
calculate the holding time.
Example 5-2
Determine the conversion for an isothermal batch reactor using the
stoichiometry of Example 5-1 and the same values of initial con-
centrations of A, B, C, and D in a reactor volume of 1 liter operating
2
5
2
for 4 minutes. The rate constant is k = 10 [(liter) /(gmol • min)].