Validation of the Reduced Models

The quality of the reduced kinetic models, as compared to the detailed model, has been evaluated in simulation by comparing their ability in tracking a few assigned temperature profiles. For the sake of simplicity, only the results obtained for the temperature profile shown in Fig. 3.2 are presented. The test profile considered consists of three steps heating of reactants up to a set-point temperature, reaction phase at constant temperature, and cooling down to ambient conditions. 

The models are compared in Table 3.3, in terms of the root mean squared errors for the concentrations 

Detailed First order Second order First order Second order 

In Table 3.4, the comparison is performed in terms of phenol conversion and of the asymptotic values of phenol (Ca,0o) and trimethylolphenol (Cp co) concentrations. Thus, whereas the data in Table 3.3 account for the accuracy in reconstructing the concentrations and the specific thermal power, the data in Table 3.4 are related to the accuracy in predicting the final values of concentration, which are of more practical interest. 

Moreover, the results are graphically shown in Figs. 3.3—3.6. In detail, Fig. 3.3 shows the results obtained with the kinetic model (3.57) with first-order kinetics. The fitting of concentrations (left) is rather poor in particular, the asymptotic values at the largest reaction times are not correctly estimated. This reduced model underestimates the Anal product concentration and overestimates the final conversion of phenol by more than 7 percent, which corresponds to an error of more than 43 percent on the phenol concentration and of about 13 percent on product concentration (Table 3.4). A better fitting is obtained for the specific thermal power (Fig. 3.3, right). 

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