Nonisothermal data

Table 16.10 Catalytic reduction of NO Estimated Model Parameters by Nonlinear Least Squares Using Nonisothermal Data...

Catalytic Hydrogenation of 3-Hydroxypropanal (HPA) to 1,3-Propanediol (PD) - Nonisothermal Data... 

The chapter ends with a case study. Four different reduced kinetic models are derived from the detailed kinetic model of the phenol-formaldehyde reaction presented in the previous chapter, by lumping the components and the reactions. The best estimates of the relevant kinetic parameters (preexponential factors, activation energies, and heats of reaction) are computed by comparing those models with a wide set of simulated isothermal experimental data, obtained via the detailed model. Finally, the reduced models are validated and compared by using a different set of simulated nonisothermal data. 

In this chapter we are concerned only with the rate equation for the i hemical step (no physical resistances). Also, it will be supposed that /"the temperature is constant, both during the course of the reaction and in all parts of the reactor volume. These ideal conditions are often met in the stirred-tank reactor (see-Se c." l-6). Data are invariably obtained with this objective, because it is extremely hazardous to try to establish a rate equation from nonisothermal data or data obtained in inadequately mixed systems. Under these restrictions the integration and differential methods can be used with Eqs. l-X and (2-5) or, if the density is constant, with Eq. (2-6). Even with these restrictions, evaluating a rate equation from data may be an involved problem. Reactions may be simple or complex, or reversible or irreversible, or the density may change even at constant temperatur (for example, if there is a change in number of moles in a gaseous reaction). These several types of reactions are analyzed in Secs. 2-7 to 2-11 under the categories of simple and complex systems. 

Such a situation can be dealt with in two ways. The first way is to analyze the data as such. The temperature dependence of the rate parameters is then directly included into the continuity equation and the resulting equation is numerically integrated along the tube with estimates for the parameters. If the gas temperature profile itself is not available or insufiBciently defined, the energy equation has to be coupled to the continuity equation. To determine both the form of the rate equation and the temperature dependence of the parameters directly from nonisothermal data would require excessive computations. 

The equivalent reactor volume concept, introduced by Hougen and Watson [1] allows for a second way of dealing with nonisothermal data it first reduces the data to isothermality and determines the temperature dependence of the rate parameters in the second stage only. The equivalent reactor volume has been defined as that volume, which, at the reference temperature T, and the reference total pressure p,i, would give the same conversion as the actual reactor, with its temperature and pressure profiles. It follows that... 

Example 9J2-1 Derivation of a Rate Equation for the Thermal Crackii of Acetone from Nonisothermal Data... 

We have so far considered only procedures for obtaining rate equations from isothermal data. It is also possible to obtain such data from nonisothermal experiments, especially those carried out adiabatically. Since, as will be shown later in Chapter 10, there is a unique relationship between conversion and temperature in an adiabatic reactor, a single equation can be used to obtain concentration and temperature profiles in such a reactor (in fact, one can do away with concentrations altogether). Then, by considering several constant temperature zones (which can be as narrow as possible) of the reactor, equations can be written for each section in which the rate constant is expressed in terms of an Arrhenius equation. This equation can then be solved to obtain the kinetic parameters k and E from nonisothermal data. 

It is clear from the preceding that the kinetic analysis of a process based upon nonisothermal data may be a demanding problem from the computational point of view. The reverse problem — designing or simulating a reactor when the... 

Derivation of a rate equation for the thermal cracking of acetone from nonisothermal data ... 

In order to model realistic adhesive processing, usually with a broad temperature range, nonisothermal tests usually need to be undertaken. The comprehensive isothermal chemoviscosity model, based on Eq. 23.130, can then be extended to nonisothermal temperature cure cycle through nonlinear regression analysis of nonisothermal data. 

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