Semenov criterion

In Section 2.5.2, the Semenov diagram was used to show the critical cooling medium temperature. In the same way it allows discrimination of a stable operation conditions from a runaway situation. A stable operation is achieved for a limit value of the Semenov criterion / (also called Semenov number) ... 

A more comprehensive approach consists of studying the variation of the Semenov criterion as a function of the reaction energy. Such an approach is presented in [12], where the reciprocal Semenov criterion is studied as a function of the dimensionless adiabatic temperature rise. This leads to a stability diagram similar to those presented in Figure 5.2 [11, 13]. The lines separating the area of parametric sensitivity, where runaway may occur, from the area of stability is not a sharp border line it depends on the models used by the different authors. For safe behavior, the ratio of cooling rate over heat release rate must be higher than the potential of the reaction, evaluated as the dimensionless adiabatic temperature rise. 

Figure 5.2 Stability diagram presenting the variation of the reciprocal Semenov criterion as a function of the dimensionless adiabatic temperature rise.

The last criterion Da/St says that this ratio must be significantly smaller than 1. This may be interpreted as smaller than 0.1. This limit is reached for a cooling medium temperature of approximately 30 °C at maximum. The limits corresponding to the other criteria may be directly read from the intercept of the representative curves. A similar interpretation of the Villermaux criterion shows a maximum temperature of approximately 20 °C and finally the Semenov criterion a temperature of 10 °C. 

The Semenov criterion means that for a cooling medium temperature above 10 °C, the initial heat release rate of the reaction cannot be removed by the cooling system. This delivers a broad enough margin for performing the reaction with a cooling system temperature below this level. This is a static criterion. 

Figure 5.4 Dynamic stability criteria as a function of the cooling system temperature. Squares represent the Villermaux criterion, triangles the Semenov criterion, and stars the ratio Da St.

Thus, the equations describing the thermal stability of batch reactors are written, and the relevant dimensionless groups are singled out. These equations have been used in different forms to discuss different stability criteria proposed in the literature for adiabatic and isoperibolic reactors. The Semenov criterion is valid for zero-order kinetics, i.e., under the simplifying assumption that the explosion occurs with a negligible consumption of reactants. Other classical approaches remove this simplifying assumption and are based on some geometric features of the temperature-time or temperature-concentration curves, such as the existence of points of inflection and/or of maximum, or on the parametric sensitivity of these curves. 

Tr(C) reported in Fig. 4.8, and corresponding to safe operative conditions according to the Adler and Enig criterion, are obtained with the Semenov number Se = 0.47, which is well above the maximum critical value provided by the Semenov criterion, Sec = 0.377, as given by (4.28). This difference mainly arises from the inclusion into the mathematical model of the terms accounting for consumption of reactant A. 

In the specific case of chemical drums with a height equal to three times the radius, the Frank-Kamenetskii criterion is 8cri, = 2.37 [1]. A cube with a side length 2ro, can be converted to its thermally equivalent sphere. The Semenov number then becomes... 

As a fifth attempt, an increase of the heat transfer at the wall in the Thomas model is not practicable and would not be efficient, since the major part of the resistance to heat transfer is the conductivity in the product itself, as shown by the high value of the Biot criterion, 300, which is closer to Frank-Kamenetskii conditions than to Semenov conditions. 

It is well known that Semenov theory is a good approximation for a highly exothermic reaction systems, i.e., Bd 00. Zheng and Keith have shown that Eq. (12) is too conservative when reactant consumption on ignition criterion needs to be considered. 

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