Page 344 - Elements of Chemical Reaction Engineering Ebook

Sec. 6.4 Sorting It All Out 31 5

6.4 Sorting It All Out
In Example 6-8 we were given the rate !aws and asked to calculate the product dis-
tributiom. The inverse of the problem described in Example 643 must frequently be
solved. Specifically, the rate laws often must be determined from the variation in
the product distribution generated by changing the feed concentrations. In some
instances this determination may not be possible without carrying out indepen-
dent experiments on some of the reactions in the sequence. The best strategy to
use to sort out all of the rate law parameters will vary from reaction sequence to
reaction sequence. Consequently, the strategy developed for one system may not
be the best approach for other multiple-reaction systems. One general rule is to
start an analysis by looking for species produced in only one reaction; next, study
the species involved in only two reactions, then three. and so on.
When the intermediate products (e.g., species G) are free radicals, it may
not be ]possible to perform independent experiments to determine the rate law
Nonlinear parameters. Consequently, we must deduce the rate law parameters from
lcast-squares changes in the distribution of reaction products with feed conditions. Urtder
these circumstances, the analysis turns into an optimization problem to estimate
the best values of the parameters that will minimize the sums of the squiues
between the calculated variables and measured variables. This process is basi-
cally the same as that described in Section 5.4.2, but more complex, owing to
the larger number of parameters to be determined. We begin by estimating the
12 parameter values using some of the methods just discussed. Next, we use our
estimates to use nonlinear regression techniques to determine the best estim<ates
of our parameter values from the data for all of the experiment^.^ Software pack-
ages such as SimuSolvlo are becoming available for an analysis such as this one.

6.5 The Fun Part
I'm not talking about fun you can have at an amusement park, but CRE fun.
Now that we have an understanding on how to solve for the exit concentrations
of multiple reactions in a CSTR and how to plot the species concentralion
down the length of a PFR or PBR, we can address one of the most important
and fun areas of chemical reaction engineering. This area, discussed in Secl.ion
6.1, is learning how to maximize the desired product and minimize the undes-
ired product. It is this area that can make or break a chemical process finan-
cially. It is also an area that requires creativity in designing the reactor
schemes and feed conditions that will maximize profits. Here you can mix and
match reactors, feed streams, and side streams as well as vary the ratios of feed
concenlration in order to maximize or minimze the selectivity of a particular
species Problems of this type are what I call digital-age problem" because

See, for example, Y. Bard, Nonlinear Parameter Estimation, (Academic Press, San
Diego, Calif.: 1974).
lo The SimuSolv Computer Program is a proprietary product of The Dow Chemical
Company that is leased with restricted rights according to license terms and condi-
tions. SimuSolv is a trademark of The Dow Chemical Company.
H. Scott Fogler, Teaching Critical Thinking, Creative Thinking, and Problem Solving
in the Digital Age, Phillips Lecture (Stillwater, Okla.: OSU Press, 1997).