Page 322 - Modeling of Chemical Kinetics and Reactor Design

292 Modeling of Chemical Kinetics and Reactor Design

− ( r ) =− dC C = kC C − k C C (5-94)
C net 2 A C 1 A B
dt
+ ( r D )= dC D = kC C C (5-95)
A
2
dt
Rearranging Equations 5-92, 5-93, and 5-94 gives

dC
A kC C + k C C )
=−( 1 A B 2 A C (5-96)
dt
dC B =− kC C
dt 1 A B (5-97)

dC C = kC C − k C C
dt 1 A B 2 A C (5-98)

Equations 5-95, 5-96, 5-97, and 5-98 are first order differential
equations and the Runge-Kutta fourth order method is used to simulate
the concentrations, with time, of components A, B, C, and D at varying
ratios of k /k of 0.5, 1.0, and 2.0 for a time increment ∆t = 0.5 min.
1
2
At the start of the batch process, the initial concentrations at time t =
3
3
0, are C AO = C BO = 1.0 mol/m , C CO = C DO = 0.0 mol/m . The
computer program BATCH55 simulates the concentrations of A, B, C,
and D for a period of 5 minutes. Figures 5-12, 5-13, and 5-14,
respectively, show the profiles of the concentrations with time, and
the effect of k /k on the concentrations of species of A, B, C, and
1
2
D. The maximum conversion of component C depends on the ratio
of k /k .
2
1
COMPLEX REACTIONS IN A BATCH SYSTEM
Industrial chemical reactions are often more complex than the earlier
types of reaction kinetics. Complex reactions can be a combination
of consecutive and parallel reactions, sometimes with individual steps
being reversible. An example is the chlorination of a mixture of
benzene and toluene. An example of consecutive reactions is the
chlorination of methane to methyl chloride and subsequent chlorination
to yield carbon tetrachloride. A further example involves the chlorina-
tion of benzene to monochlorobenzene, and subsequent chlorination