Page 311 - Modeling of Chemical Kinetics and Reactor Design

Introduction to Reactor Design Fundamentals for Ideal Systems 281

+ ( r C )= dC C = kC B (5-64)
2
dt
Rearranging Equations 5-62 and 5-63 gives

dC
A =− kC (5-65)
dt 1 A

dC
B = kC − k C (5-66)
dt 1 A 2 B

Equations 5-64, 5-65, and 5-66 are first order differential equations,
which require initial or boundary conditions. For the batch reactor,
these are the initial concentrations of A, B, and C. In addition to the
initial concentrations, the rate constants k and k are also required
2
1
to simulate their concentrations. The concentration profiles depend on
the values of k and k (i.e, k = k , k > k , k > k ). Assume that at the
2
2
1
1
2
1
1
2
3
beginning of the batch process, at time t = 0, C AO = 1.0 mol/m , and
C BO = C CO = 0. For known values of k and k , simulate the concen-
1
2
trations of A, B, and C for 10 minutes at a time interval of t = 0.5
min. A computer program has been developed using the Runge-Kutta
fourth order method to determine the concentrations of A, B, and
C. The differential Equations 5-64, 5-65, and 5-66 are expressed,
respectively, in the form of X-arrays and functions in the computer
program as
dC
C = X(1), A = F( ) 1 (5-67)
A
dt
dC
C = X(2), B = F( ) 2 (5-68)
B
dt
dC
C = X(3), C = F( ) 3 (5-69)
C
dt
where
F 1 ( )=− K1 * X 1 ( ) (5-70)

F 2 ( )= K1* X 1 ( )− K2* X 2 ( ) (5-71)