Reaction kinetics adiabatic

A semi-batch reactor is used to convert reactant, A, to product, B, by the reaction A —> 2B. The reaction is carried out adiabatically. The reaction kinetics are as before... 

It is possible, by making certain -assumptions about the reaction kinetics, to correct adiabatic data measured in equipment with high thermal inertia. Methods are discussed in.A2.7.2. These assumptions introduce uncertainty. Extreme caution must be applied if data are extrapolated to temperatures higher than those measured in the test. In particular, the possibility of side reactions or secondary... 

If the curing reaction occurs at adiabatic or isothermal conditions above the glass transition temperature of the ultimately cured polymer, the reaction kinetics is adequately described by the adopted mechanism 5> 16,l7 69 7i However, at temperatures substantially below the final glass transition temperature, the reaction rate at a certain... 

The reaction can be truly adiabatic for a wide range of experimental conditions. It initiates in the kinetic region and reaches a limit of 94-96 % conversion, which corresponds to the topological limit for these systems 5>14, l617-5169). The reaction kinetics is well described by the adopted mechanism 51,69 and the resulting experimental kinetic and thermodynamic reaction parameters are similar to those obtained in isothermal experiments. 

To reduce the number of parameters in the kinetic equations that are to be determined from experimental data, we used the following considerations. The values klt k2, and k4 that enter into the definition of the constant L, (236), are of analogous nature they indicate the fraction of the number of impacts of gas molecules upon a surface site resulting in the reaction. So the corresponding preexponential factors should be approximately the same (if these elementary reactions are adiabatic). Then, since k1, k2, and k4 are of the same order of magnitude, their activation energies should be almost identical. It follows that L can be considered temperature independent. 

To obtain a more realistic estimation of the behavior of an autocatalytic reaction under adiabatic conditions, it is possible to identify the kinetic parameters of the Benito-Perez model from a set of isothermal DSC measurements. In the example shown in Figure 12.11, the effect of neglecting the induction time assumes a zero-order reaction leading to a factor of over 15 during the time to explosion. Since this factor strongly depends on the initial conversion or concentration of catalyst initially present in the reaction mass, this method must be applied with extreme care. The sample must be truly representative of the substance used at industrial scale. For this reason, the method should be only be applied by specialists. 

Those simplified models are often used together with simplified overall reaction rate expressions, in order to obtain analytical solutions for concentrations of reactants and products. However, it is possible to include more complex reaction kinetics if numerical solutions are allowed for. At the same time, it is possible to assume that the temperature is controlled by means of a properly designed device thus, not only adiabatic but isothermal or nonisothermal operations as well can be assumed and analyzed. 

Statistical methods represent a background for, e.g., the theory of the activated complex (239), the RRKM theory of unimolecular decay (240), the quasi-equilibrium theory of mass spectra (241), and the phase space theory of reaction kinetics (242). These theories yield results in terms of the total reaction cross-sections or detailed macroscopic rate constants. The RRKM and the phase space theory can be obtained as special cases of the single adiabatic channel model (SACM) developed by Quack and Troe (243). The SACM of unimolecular decay provides information on the distribution of the relative kinetic energy of the products released as well as on their angular distributions. 

The Arrhenius equation and the energy balance equation were used to obtain a modified version of the equation for the second order adiabatic reaction kinetics. 

The second order adiabatic reaction kinetic equation was obtained by combining Equations 1 and 2 ... 

At high pressures the heat evolved is sufficient for adiabatic operation of reactors. Since the normal operating temperatures of industrial converters lie between 800 and 1100°C and pressures between 1 and 10 atm, homogeneous gas-phase reactions may contribute to the observed product distribution. The initiation temperatures for homogeneous oxidation are of course a function of pressure, so that in the laboratory the catalytic reaction may be isolated by working at low pressures under molecular beam conditions. In this way the reaction kinetics can be observed over very wide temperature ranges (usually up to 1200 °C). Studies of ammonia oxidation carried out in this way range from 0.1 to 10 Torr total pressure. ... 

Industrial reactors used in the petrochemical industry for exothermic reactions, with a few exceptions, are either fixed-beds (adiabatic or non-adiabatic) or fluidized-beds when the heat developed is too high to be removed in a fixed-bed reactor. In the last few decades, interest has been mainly directed towards the control of these reactors, which is strictly related to an understanding of the complex phenomena that occur at the interface between the different phases present in the reaction environment, and of the heat and mass transfer influence on the reaction kinetics. 

This increase of temperature has substantial implications for reaction kinetics during HP treatment cycles. Additionally, in real (non-adiabatic) situations, thermal equilibrium with the environment occurs, which produces a time and spatially varied temperature field. However, for hexane, a temperature increase of 40 times or more (in comparison with... 

A conservative criterion for stability is that 9 be less than 1.0. The actual stability limit depends on the reaction kinetics and on a, the ratio of the adiabatic temperature rise to AT),... 

It provides a direct measure of the hazard potential related to the process. It combines thermodynamics and reaction kinetics by being directly proportional to the temperature dependence of the reaction rate represented by the activation temperature E/R and the adiabatic temperature increase. Reactions with a small to moderate hazard potential are characterized by thermal reaction number values around 2, and processes with an extremely high potential have values up to 50 and more. To illustrate the meaning especially of this number, which, if applied correctly, has a similar significance to the adiabatic temperature increase for chemical hazard assessment, the relationship between activation temperature, adiabatic temperature increase and the thermal reaction number B is presented in Fig. 4-4. As a typical process temperature 25°C is assumed. 

Finally a fourth boundary condition shall be valid to support the worst case character of the procedure. The reaction order necessary for the formal kinetic description of a process has a severe influence on the pressure/time and respectively the tempera-ture/time-profiles to be expected. Industrial experience has shown that approximately 90% of all processes conducted in either batch or semibatch reactors can be described with a second order formal kinetic rate law. But it remains uncertain whether this statement, which is related to isothermal or isoperibolic operation with a rather limited overheating, remains valid if the reaction proceeds adiabatically and if side reactions contribute to the gross reaction rate at a much higher degree. In consequence, it shall be assumed for a credible worst case evaluation that the disturbed process follows a first order kinetics. Any reactions occurring in reality will almost certainly proceed at a much lower rate. 

Sample outputs for epoxy + AEP are shown in Figures 2 and 3. Figure 2 illustrates the typical fit that is possible using data from a single experiment. Kinetic constants obtained from one trial do not satisfactorily predict other experiments at different starting temperatures, however. Therefore, it is advantageous to correlate several files of data simultaneously, as in Figure 3. The equation obtained when this is done represents the adiabatic reaction kinetics ... 

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