Page 318 - Modeling of Chemical Kinetics and Reactor Design

288 Modeling of Chemical Kinetics and Reactor Design

− ( r ) =− dC A = kC − k C (5-79)
A net 1 A 2 B
dt

− ( r ) =− dC B = kC + k C − k C (5-80)
B net 2 B 3 B 1 A
dt

+ ( r ) = dC C = kC (5-81)
C 3 B
dt
Rearranging Equations 5-79 and 5-80 gives

dC A = kC − k C
dt 2 B 1 A (5-82)

dC
B = k + ) (5-83)
k C
1
A
dt kC −( 2 3 B
Equations 5-81, 5-82 and 5-83 are first order differential equations
that can be solved simultaneously using the Runge-Kutta fourth order
method. Consider two cases:

• Case I: At time t = 0, C AO = 1.0, C = C = 0, and k = k =
1
BO
2
CO
1, k = 10
3
• Case II: At time t = 0, C AO = 1.0, C BO = C CO = 0, and k = 1,
1
k = k = 10
2
3
The developed batch program BATCH53 simulates the concentra-
tions of A, B, and C with time step ∆t = 0.05 hr for 1 hour. Figures 5-9
and 5-10 show plots of the concentrations versus time for both cases.
CONSECUTIVE REVERSIBLE REACTIONS

Consider the chemical reversible reactions

A←→ B← → C (5-84)


k 1
k 3
k 2 k 4
in a constant volume batch reactor under isothermal condition. For first
order reaction kinetics, the rate equations are: