Page 67 - Introduction to chemical reaction engineering and kinetics

3.4 Experimental Strategies for Determining Rate Parameters 49

first on approaches to determine concentration-related parameters in the rate law, and
then on temperature-related parameters. The objective of experiments is to obtain a set
of point rates (Section 1.4.1) at various conditions so that best values of the parameters
may be determined.
Methods of analyzing experimental data depend on the type of reactor used, and, in
some types, on the way in which it is used. For a BR or a PFR, the methods can be di-
vided into “differential” or “integral.” In a differential method, a point rate is measured
while a small or “differential” amount of reaction occurs, during which the relevant re-
action parameters (ci, T, etc.) change very little, and can be considered constant. In an
integral method, measurements are made while a large or “integral” amount of reac-
v
tion occurs. Extraction of rate-law parameters (order, A, E,J from such integral data
“OF
0 involves comparison with predictions from an assumed rate law. This can be done with
simple techniques described in this and the next chapter, or with more sophisticated
computer-based optimization routines (e.g., E-Z Solve). A CSTR generates point rates
directly for parameter estimation in an assumed form of rate law, whether the amount
of reaction taking place is small or large.

3.4.1 Concentration-Related Parameters: Order of Reaction

3.4.1.1 Use of Constant-Volume BR
For simplicity, we consider the use of a constant-volume BR to determine the kinetics
of a system represented by reaction (A) in Section 3.1.2 with one reactant (A), or two
reactants (A and B), or more (A, B, C, . . .). In every case, we use the rate with respect
to species A, which is then given by

(-rA) = -dc,ldt (constant density) (2.2-10)

We further assume that the rate law is of the form (--I~) = k,cgcgc& and that the
experiments are conducted at fixed T so that kA is constant. An experimental proce-
dure is used to generate values of cA as a function of t, as shown in Figure 2.2. The
values so generated may then be treated by a differential method or by an integral
method.

3.4.1.1.1 Differential methods
Differentiation of concentration-time data. Suppose there is only one reactant A, and
the rate law is

(-r/J = k,ci (3.4-1)

From equation 2.2-10 and differentiation of the c*(t) data (numerically or graphically),
values of (-Y*) can be generated as a function of cA. Then, on taking logarithms in
equation 3.4-1, we have

ln(-IA) = InkA + nlnc, (3.4-2)

0 from which linear relation (ln( -rA) versus In cA), values of the order n, and the rate
constant kA can be obtained, by linear regression. Alternatively, kA and n can be ob-
v
tained directly from equation 3.4-1 by nonlinear regression using E-Z Solve.
7O.F