Table
5 shows the true kinetic coefficients used by Domagalski et al. for
generating simulated data. These parameter values were used in the
current study to compute true kinetic and equilibrium coefficients via
Arrhenius expressions:
\(k_{i}(T)=k_{i,ref}\exp\left(-\frac{E_{a,i}}{R}\left(\frac{1}{T}-\frac{1}{T_{\text{ref}}}\right)\right)\)(17)
\(K_{\text{eq}}(T)=K_{eq,ref}\exp\left(-\frac{\Delta H_{1}}{R}\left(\frac{1}{T}-\frac{1}{T_{\text{ref}}}\right)\right)\)(18)
where \(k_{i}\) is the \(i\)th kinetic coefficient, \(R\) is the
universal gas constant, \(T\) is the temperature in \(K\), and\(T_{\text{ref}}\ \)= 313.15 K = 40 °C is a reference temperature. In
equation (18), \(K_{\text{eq}}\ \)is the equilibrium coefficient for
reaction (1), and \(\Delta H_{1}\) is the reaction enthalpy. Table 6
provides measurement noise variances used in this study for generating
simulated data.21 Figure 2 shows one set of simulated
old data generated using the values in
Table 5 and Table 6. As shown in the simulated true response in
Figure 2, consumption of catalyst D is initially very fast and then the
catalyst gets released via reaction (2) as the product is formed.
Table
5. True values of the kinetic coefficients and equilibrium constant6