Integral method of kinetic analysis

The rate expressions Rj — Rj(T,ck,6m x) typically contain functional dependencies on reaction conditions (temperature, gas-phase and surface concentrations of reactants and products) as well as on adaptive parameters x (i.e., selected pre-exponential factors k0j, activation energies Ej, inhibition constants K, effective storage capacities i//ec and adsorption capacities T03 1 and Q). Such rate parameters are estimated by multiresponse non-linear regression according to the integral method of kinetic analysis based on classical least-squares principles (Froment and Bischoff, 1979). The objective function to be minimized in the weighted least squares method is... 

The data given below are provided by J. H. Raley, F. E. Rust, and W. E. Vaughn J.A.ChS., 70,98 (1948)]. They were obtained at 154.6°C under a 4.2-mmHg partial pressure of nitrogen, which was used to feed the peroxide to the reactor. Determine t he rate coefficient by means of the differential and integral method of kinetic analysis. 

Figure 2.3.a-2 Relation between differential and integral methods of kinetic analysis and differential and integral reactors. 

C The integral Method of Kinetic Analysis The integration of the rate equation leads to... 

Discrimination Using the Integral Method of Kinetic Analysis... 

Example 23,d.2-I Sequential Design of Experiments for Optimal Parameter Estimation in n-pentane Isomerization. Integral Method of Kinetic Analysis... 

The integral method of kinetic analysis can be conveniently used when the expression for can be analytically integrated. When the differential method is applied, N, i4 is obtained as the slope of a curve giving (px)hi (Pa)i>m a function of p, VIF, arrived at by measuring the amount of A abmrbed at different gas flow rates. 

Determine a suitable kinetic model by means of both the differential and integral method of kinetic analysis. 

Integral Method of Kinetic Analysis Substituting the rate equation in Eq. 9.1-2 leads to ... 

L2.4.1 The Differential Method of Kinetic Analysis L2.4.2 The Integral Method of Kinetic Analysis Coupled Reactions... 

When the integral method of kinetic analysis is applied, numerical integration of the continuity equations containing the rate equations is generally necessary for the comparison of the predicted and experimental responses for each experiment in each iteration cycle of the parameter estimation. Examples can be found in the work of De Pauw and Froment [1975] on n-pentane reforming in the presence of coke formation, in the work of Emig, Hofmann, and Friedrich [1972] on methanol oxidation, and in Example 2.6.4.A on benzothiophene hydrogenolysis. 

ETHANOL DEHYDROGENATION SEQUENTIAL DISCRIMINATION USING THE INTEGRAL METHOD OF KINETIC ANALYSIS... 

The data can also be obtained in an integral fixed reactor, of course. Information on the coke content profile in a tubular reactor may yield valuable information as to the mechanism of coking—parallel or consecutive—and, therefore, as to the form of Pq, as will be shown in the next section. If the integral method of kinetic analysis is applied to the data, as was done by De Pauw and Froment [1975], the conversion 4 replaces the rate Pa in the objective function, requiring integration of the rate equation. 

Apply the differential and integral methods of kinetic analysis (see Chapter 2) to determine the rate coefficients and order at the different temperatures. To work out the integral method of kinetic analysis, it is necessary to express pA as a function of x. A rigorous expression would only be possible if all reactions taking place were exactly known. Therefore, undertake an empirical fit of this function. 

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