Kinetic model discrimination

Kinetic Model Discrimination. To discriminate between the kinetic models, semibatch reactors were set up for the measurement of reaction rates. The semi-batch terminology is used because hydrogen is fed to a batch reactor to maintain a constant hydrogen pressme. This kind of semi-batch reactor can be treated as a bateh reactor with a constant hydrogen pressme. The governing equations for a bateh reactor, using the product formation rate for three possible scenarios, were derived, as described in reference (12) with the following results ... 

Another advantage of forced periodic feed experiments, which has not been fully exploited so far, is that the technique could be used for kinetic model discrimination, a technique in which large deviations could be induced into calculated reponses between rival models under consideration. Hawkins has carried out experiments on oxidation of CO for discriminating between several Hougen and Watson rival models. Cutlip et al have compared experimental forced periodic feed CO oxidation experimental transients with simulations using an elementary step model and compared theory with experiment in studies of the variation of the conversion as a function of time period of the forced oscillation. 

Keywords methane combustion, perovskite, kinetics, model discrimination, MVK mechanism... 

Kinetic Model Discrimination and Parameter Fitting 95 Three possible rate expressions were considered tl = fejCisoCMA... 

Duggleby, R. G., Morrison, J. F. (1978). Progress curve analysis in enzyme kinetics model discrimination and parameter estimation. Biochim. Biophys. Acta 526, 398 09. 

The positive values obtained in practically all cases indicate that all these models may be plausible representations of the data and indeed, the correlation coefBcients, R, are greater than 0.9. Thus, statistical compliance is not a sufficient basis for model discrimination. Specifically, the thermodynamic consistency of the estimates, as proposed by Boudart et al. [3], is appropriate further scrutinizing criterion during kinetic modelling and has been gainfully employed in other reactions [4-6]. 

There are several methods for discrimination between rival models. Froment and Hosten (1981), Bischoff and Froment (1991), and Kittrell (1970) summarized them and discussed applications for kinetic models. Here only approximate methods will be presented. 

The results of the kinetic study and model discrimination show that insertion of SM is rate-controlling. Two reasons may explain why this step is ratecontrolling. First, the protection group in om SM is very bulky, making the reaction slow, which is consistent with literature data (8) showing the size effect on reactivity. Second, a free aniline group in the SM could bond with Rh and reduce the catalyst reactivity. 

As a third example let us consider the growth kinetics in a chemostat used by Kalogerakis (1984) to evaluate sequential design procedures for model discrimination in dynamic systems. We consider the following four kinetic models for biomass growth and substrate utilization in the continuous baker s yeast fermentation. 

To examine the fitness of the kinetic model CAER used for study of the water effect, we conducted model discrimination using the kinetic data of 15% Co/Si02 by comparing values of the standard function of mean absolute relative residual (MARR), which is simply defined as... 

The magnitudes of concentrations of intermediates and of step velocities appearing in these mechanisms are the parameters in kinetic models that form the next step for further discrimination. A detailed treatment of model building for this purpose is beyond the scope of this article. The subject is briefly discussed here in the context of the methods presented. 

This example demonstrates how reaction calorimetry in combination with IR-ATR spectroscopy can be used to discriminate between different postulated reaction models, and to determine the kinetic and thermodynamic parameters for the selected model. In practical applications, when different (semi-) empirical models can be postulated, model discrimination is crucial. 

One frequently experiences difficulty in discriminating between rival kinetic models derived from the Hougen-Watson procedure, because of the comparable degree of fitting to steady state kinetic data [l -6]. 

Figure 2. Test for the discrimination of rival kinetic models by the transient response method. Key --------, Model 1 in Table 1 — Model 2 in Table l and...

The text reviews the methodology of kinetic analysis for simple as well as complex reactions. Attention is focused on the differential and integral methods of kinetic modelling. The statistical testing of the model and the parameter estimates required by the stochastic character of experimental data is described in detail and illustrated by several practical examples. Sequential experimental design procedures for discrimination between rival models and for obtaining parameter estimates with the greatest attainable precision are developed and applied to real cases. 

A kinetic expression that is selected should satisfy certain statistical tests and physicochemical constraints, before it can be indicated as an adequate model. These tests often cannot be applied together, due to lack of information, but should be considered as far as possible in the evaluation and selection of the best rate expression. When still a set of competitive expressions are left some model discrimination techniques may be applied or additional experiments should be conducted, based on a careful, efficient planning. 

The development of unsteady-state kinetic models requires application of dynamic relaxation methods (Section A.5.2.6). More reliable models can be achieved by coupling these transient techniques with a direct determination of intermediate products on the surface of the catalyst [2, 3]. There is no unified or standard method suitable for discrimination of the unsteady-state kinetics models for either of the catalytic processes. 

Figure 3.4 represents the pressure dependencies of tq for these three cases. It is evident that this initial dependency of rate on pressure gives a quick insight into which kinetic model best describes the experimental results of the reaction under consideration. It is ideal for model discrimination purposes where one tries to select the best kinetic description for a process. In applying this, two important aspects must be realised ... 

The practical value of the quantitative theory of radical copolymerization depends to a great extent on the adequacy of the applied kinetic model to the real systems. Hence, in Sect. 6 we shall discuss the issues of model discrimination and also the problems of reliability and validity of the calculations of the model parameters with an account of the potentialities of the modern experimental techniques. 

Discrimination of the Kinetic Models and Estimation of their Parameters... 

Initial reaction rates obtained with a pure feed in which only reactants are present can be used for the discrimination between rival kinetic models, i.e. to identify whether adsorption, desorption, or surface reactions are the rate-determining steps. When pure A is fed to an integral reactor, for example, initial rates are observed at the inlet, where the product concentration is still zero. Comparing possible rate equations, which are often simpler in case of absence of products, with experimental data obtained at different concentrations of A, helps to reveal the appropriate [33,35]. 

Heterogeneously catalyzed reactions are usually studied under steady-state conditions. There are some disadvantages to this method. Kinetic equations found in steady-state experiments may be inappropriate for a quantitative description of the dynamic reactor behavior with a characteristic time of the order of or lower than the chemical response time (l/kA for a first-order reaction). For rapid transient processes the relationship between the concentrations in the fluid and solid phases is different from those in the steady-state, due to the finite rate of the adsorption-desorption processes. A second disadvantage is that these experiments do not provide information on adsorption-desorption processes and on the formation of intermediates on the surface, which is needed for the validation of kinetic models. For complex reaction systems, where a large number of rival reaction models and potential model candidates exist, this give rise to difficulties in model discrimination. 

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