Isoperibolic Reactor

For reactions characterized by high values of Q, the onset of a thermal explosion can be controlled by adjusting the batch time, tt, the explosion occurs if t, and does not in the opposite case. Hence, the reactor performance shows a typical on-off behavior, being characterized by either complete or negligible reactant conversion. It follows that reactions of interest must be carried out under explosion conditions, provided that the reactor vessel withstands the final internal pressure and the thermal shock caused by the sudden temperature increase. A similar map can be drawn with reference to undesired secondary reactions and, in this respect, operative parameters must be adjusted in order to avoid the ignition stage within the batch length. 

The assumption of constant wall temperature is often more realistic for chemical reactors than the adiabatic case. In this respect, starting from the pioneering theory of thermal explosions developed by Semenov at the beginning of the last century [8], significant advances have been made by the related scientific literature with approaches that can be roughly classified as geometric and sensitivity-based, as described in detail in the following. 

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In real systems, the increase of temperature is accompanied by a corresponding increase of pressure, which may lead to an explosion (i.e., to an uncontrolled increase of pressure). Nevertheless, the analysis of temperature patterns with simple kinetics is enough to study the problem for adiabatic reactors and for constant wall temperature (isoperibolic) reactors, whereas the more complex case of controlled wall temperature requires the adoption of more advanced methods. 

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. 

The RC1 reactor system temperature control can be operated in three different modes isothermal (temperature of the reactor contents is constant), isoperibolic (temperature of the jacket is constant), or adiabatic (reactor contents temperature equals the jacket temperature). Critical operational parameters can then be evaluated under conditions comparable to those used in practice on a large scale, and relationships can be made relative to enthalpies of reaction, reaction rate constants, product purity, and physical properties. Such information is meaningful provided effective heat transfer exists. The heat generation rate, qr, resulting from the chemical reactions and/or physical characteristic changes of the reactor contents, is obtained from the transferred and accumulated heats as represented by Equation (3-17) ... 

Figure 6.8 Substitution reaction in the isoperibolic batch reactor for different switching temperatures for the cooling system. Upper plot reactor temperature as a function of time. Lower plot yield (NP/NA0) as a function of time. The parameter is the temperature at which the cooling system is switched on.

The term isoperibolic is derived from calorimetry where it designates experiments performed with a constant surrounding temperature. For a reactor, it means that... 

Figure 6.10 Example substitution reaction in the Isoperibolic batch reactor starting from 25°C with a constant cooling system temperature (Tc) at 25 °C. Reactor temperature (T,°C) and conversion as a function of time (h).

The polytropic mode this is a combination of different types of control. As an example, the polytropic mode can be used to reduce the initial heat release rate by starting the feed and the reaction, at a lower temperature. The heat of reaction can then be used to heat up the reactor to the desired temperature. During the heating period, different strategies of temperature control can be applied adiabatic heating until a certain temperature level is reached, constant cooling medium temperature (isoperibolic control), or ramped to the desired reaction temperature in the reactor temperature controlled mode. Almost after the... 

This is the simplest system for temperature control of a reactor only the jacket temperature is controlled and maintained constant, leaving the reaction medium following its temperature course as a result of the heat balance between the heat flow across the wall and the heat release rate due to the reaction (Figure 9.9). This simplicity has a price in terms of reaction control, as analysed in Sections 6.7 and 7.6. Isoperibolic temperature control can be achieved with a single heat carrier circuit, as well as with the more sophisticated secondary circulation loop. 

Bosch, J., Strozzi, F., Zbilut, J.P. and Zaldivar, J.M. (2004) On-line runaway detection in isoperibolic batch and semibatch reactors using the divergence criterion. Computers and Chemical Engineering, 28 (4), 527-44. 

In this chapter, the reactor dynamics under adiabatic and isoperibolic conditions is analyzed, while the temperature-controlled case is addressed in Chap. 5. It must be pointed out that these conditions can be easily realized in laboratory investigations, e.g., in reaction calorimetry, but represent mere ideality at the industrial scale. Nevertheless, this classification is useful to recognize the main paths leading to runaway without the burden of a more complex mathematical approach. 

For a safe operation, the runaway boundaries of the phenol-formaldehyde reaction must be determined. This is done here with reference to an isoperibolic batch reactor (while the temperature-controlled case is addressed in Sect. 5.8). As shown in Sect. 2.4, the complex kinetics of this system is described by 89 reactions involving 13 different chemical species. The model of the system consists of the already introduced mass (2.27) and energy (2.30) balances in the reactor. Given the system complexity, dimensionless variables are not introduced. 

The safety technical assessment of cooled batch reactors is based among other things on a recognition which is best understood by a schematic comparison of today s most common modes of operation. These are, as presented in Figure 4-38, isothermal, isoperibolic and partially controlled operation. 

In a first step the isoperibolic and the partially controlled mode of operation shall be investigated more closely because they are common in industrial practice and they have an analogy to a mode of operation for homogeneous cooled tube reactors (c.f. introduction to Section 4.3.1.2). For these two modes the analysis of the heat balance leads to an equation with two unknowns the maximum reaction temperature and the corresponding value for the conversion. 

Having completed the safety assessment for the isoperibolic batch processes, isothermal batch reactors now shall be considered. The most critical point in the course of process, which is the point of occurrence of the maximum driving temperature difference, is mathematically characterized in this case ... 

At this point the remark made in Section 4.1.3.1 about an optimized start-up strategy for the cooled CSTR shall be explained. The safety technical assessment procedure for the cooled isoperibolic SBR has demonstrated that in the case of correct design a prediction of the maximum reaction temperature is easily possible. This can be utilized for the optimization of the start up of the CSTR. The later steady state operating temperature of the CSTR is defined as the set value for the maximum SBR process temperature. In a next step one of the two reactants of the CSTR process is charged initially. Then the reactor is started as a semibatch process by feeding the second reactant. When the maximum temperature is reached, the feed of the initially charged reactant is started, and the feed streams are adjusted in such a way that the Stanton number of the CSTR is established. This way the initial oscillations are elegantly avoided. 

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. 

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