The Differential Method for Kinetic Analysis

A classical example of this method is the study of the hydrogenation of isooctenes of Hougen and Watson [27]. By considering all possible mechanisms and rate determining steps they set up 18 possible rate equations. Each equation was confronted with the experimental data and the criterion for acceptance of the model was that the parameters ki, K, . had to be positive. In this way 16 of the 18 possible models could be rejected. The choice between the seventeenth 

b-l lends itself particularly well for determining a, b, c, and d, which are combinations of the parameters of Eq. Z2-19, by linear regression. This method has been criticized it is not sufficient to estimate the parameters but it also has to be shown that they are statistically significant. Furthermore, before rejecting a model because one or more parameters are negative it has to be shown that they are significantly negative. This leads to statistical calculations (e.g., of the confidence intervals). 

Yang and Hougen [33] proposed to discriminate on the basis of the total pressure dependence of the initial rate. Initial rates are measured, for example, with a feed consisting of only A when no products have yet been formed (i.e., when = 0). Nowadays this method is only one of the so-called 

Clearly these relations reveal by mere inspection which one is the rate-determining step (see Fig. 2.3.b-l). A more complete set of curves encountered when r o s plotted versus the total pressure or versus the feed composition can be found in Yang and Hougen [39]. 

These methods are illustrated in what follows on the basis of the data of Franckaerts and Froment [40]. They studied the dehydrogenation of ethanol into acetaldehyde in an integral type flow reactor over a Cu-Co on asbestos catalyst. 

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