Page 183 - Introduction to chemical reaction engineering and kinetics

7.3 Polymerization Reactions 165

rco* = k&,foccH; = chKd2{[1 + f3~&&I,J(k&p - l} (7.2-2)
4k2

Furthermore, the rate of disappearance of CH4 is

(-~cIL,) = 2rczHs + rco, = klcMocCH, (7.2-3)

which is also the limiting rate for either product, if the competing reaction is completely
suppressed.

7.2.2 Computer Modeling of Complex Reaction Kinetics

In the examples in Sections 7.1 and 7.2.1, explicit analytical expressions for rate laws are
obtained from proposed mechanisms (except branched-chain mechanisms), with the
aid of the SSH applied to reactive intermediates. In a particular case, a rate law obtained
in this way can be used, if the Arrhenius parameters are known, to simulate or model
the reaction in a specified reactor context. For example, it can be used to determine
v
the concentration-(residence) time profiles for the various species in a BR or PFR, and
7O.v
0 hence the product distribution. It may be necessary to use a computer-implemented nu-
merical procedure for integration of the resulting differential equations. The software
package E-Z Solve can be used for this purpose.
It may not be possible to obtain an explicit rate law from a mechanism even with the
aid of the SSH. This is particularly evident for complex systems with many elementary
steps and reactive intermediates. In such cases, the numerical computer modeling pro-
cedure is applied to the full set of differential equations, including those for the reactive
intermediates; that is, it is not necessary to use the SSH, as it is in gaining the advantage
of an analytical expression in an approximate solution. Computer modeling of a react-
ing system in this way can provide insight into its behavior; for example, the effect of
changing conditions (feed composition, T, etc.) can be studied. In modeling the effect
of man-made chemicals on atmospheric chemistry, where reaction-coupling is impor-
tant to the net effect, hundreds of reactions can be involved. In modeling the kinetics
v
of ethane dehydrogenation to produce ethylene, the relatively simple mechanism given
in Section 6.1.2 needs to be expanded considerably to account for the formation of a
“OF
0 number of coproducts; even small amounts of these have significant economic conse-
quences because of the large scale of the process. The simulation of systems such as
these can be carried out with E-Z Solve or more specific-purpose software. For an ex-
ample of the use of CHEMKIN, an important type of the latter, see Mims et al. (1994).
The inverse problem to simulation from a reaction mechanism is the determination
of the reaction mechanism from observed kinetics. The process of building a mecha-
nism is an interactive one, with successive changes followed by experimental testing
of the model predictions. The purpose is to be able to explain why a reacting system
behaves the way it does in order to control it better or to improve it (e.g., in reactor
performance).

7.3 POLYMERIZATION REACTIONS

Because of the ubiquitous nature of polymers and plastics (synthetic rubbers, nylon,
polyesters, polyethylene, etc.) in everyday life, we should consider the kinetics of their
formation (the focus here is on kinetics; the significance of some features of kinetics in
relation to polymer characteristics for reactor selection is treated in Chapter 18).
Polymerization, the reaction of monomer to produce polymer, may be self-polymeri-
zation (e.g., ethylene monomer to produce polyethylene), or copolymerization (e.g.,