Dynamic Stability of Reactors

Accidents happening in polymerization reactors are practically always due to a lack of control of the course of reaction caused by a disturbance of the heat balance, which results in a temperature increase leading to loss of control of the reactor and a runaway reaction. In this section a systematic procedure based on a failure scenario with six key questions, allowing assessment of the criticality of a process, is presented. Since the heat balance is at the center of our concerns in matters of thermal control of reactors, the different terms of the heat balance will be examined. Finally, aspects of the dynamic stability of reactors and of the thermal stability of reaction masses are analyzed. 

In order to assess the dynamic stability of the example reaction in the reactor described above, we can apply different criteria as described in Section 5.2. The following criteria are used Semenov Equation 5.7, Villermaux Equation 5.12, and the ratio Da/St Equation 5.18. The reaction number B is also represented. Since they are a function of the cooling system temperature, they were calculated as a function of this temperature. The results are represented in Figure 5.4. 

The dynamic stability of the reactor can be studied by using the temperature-conversion trajectory, as represented in Figure 6.9. During the adiabatic period, the trajectory is linear with a slope equal to the adiabatic temperature rise. If no cooling is applied, the maximum temperature Tlnax would be reached for a conversion %A,max ... 

In many processes the slurry reactor is be selected because it has the highest volume capacity, and the best heat transfer characteristics. This can be particularly important when the dynamic stability of the process is critical (section 8.3.2). 

In continuous polymerizations, the main problem is the dynamic stability of the reactor. The stability problems have various different aspects the thermal stability as introduced above (see Section 11.2.4), the concentration stability, the particle number stability, and the viscosity stability. Even under isothermal conditions these problems may lead to multiplicity or oscillatory behavior. It is worth emphasizing the fact that stability and safety are in no case synonymous a reactor may be unsafe even if working at a stable working point, or conversely it may be run safely at an instable working point. But knowledge of stability limits of the reactor is essential for the design of a safe process. 

This analysis is limited, since it is based on a steady-state criterion. The linearisation approach, outlined above, also fails in that its analysis is restricted to variations, which are very close to the steady state. While this provides excellent information on the dynamic stability, it cannot predict the actual trajectory of the reaction, once this departs from the near steady state. A full dynamic analysis is, therefore, best considered in terms of the full dynamic model equations and this is easily effected, using digital simulation. The above case of the single CSTR, with a single exothermic reaction, is covered by the simulation examples, THERMPLOT and THERM. Other simulation examples, covering aspects of stirred-tank reactor stability are COOL, OSCIL, REFRIG and STABIL. 

AUTOREFRIGERATED REACTOR OF LUYBEN DYNAMIC STABILITY ANALYSIS... 

Chemical Kinetics, Tank and Tubular Reactor Fundamentals, Residence Time Distributions, Multiphase Reaction Systems, Basic Reactor Types, Batch Reactor Dynamics, Semi-batch Reactors, Control and Stability of Nonisotheimal Reactors. Complex Reactions with Feeding Strategies, Liquid Phase Tubular Reactors, Gas Phase Tubular Reactors, Axial Dispersion, Unsteady State Tubular Reactor Models... 

In the operation of BWRs, especially when operating near the threshold of instability, the stability margin of the stable system and the amplitude of the limit cycle under unstable condition become of importance. A number of nonlinear dynamic studies of BWRs have been reported, notably in an International Workshop on Boiling Water Reactor Stability (1990). The following references are mentioned for further study. 

Program REFRIG2 simulates the dynamic behaviour of the reactor and generates a phase-plane stability plot for a range of reactor concentrations and temperatures. 

N. Kunimatsu. Stabilization of nonlinear tubular reactor dynamics with recycle. In 1st Int. Conference on Control of Oscillations and Chaos, volume 2, pages 291-295, 1997. 

F. Teymour and W.H. Ray. The dynamic behavior of continuous solution polymerization reactors-IV. Dynamic stability and bifurcation analysis of an experimental reactor. Chem. Eng. Sci., 44(9) 1967-1982, 1989. 

Capping. Capped silica-alumina was prepared by vapor phase transfer of hexamethyldisilazane (> 99.5%, Aldrich) onto calcined silica-alumina until there was no further uptake, as indicated by stabilization of the pressure. The reactor was evacuated and the material heated to 350°C under dynamic vacuum for 4 h to remove ammonia produced during the capping reaction. 

During normal operation, it is essential to ensure sufficient cooling in order to control the temperature of the reactor, hence to control the reaction course. This typical question should be addressed during process development. To ensure the thermal control of the reaction, the power of the cooling system must be sufficient to remove the heat released in the reactor. Special attention must be devoted to possible changes in the viscosity of the reaction mass as for polymerizations, and to possible fouling at the reactor wall (see Chapter 9). An additional condition, which must be fulfilled, is that the reactor is operated in the dynamic stability region, as described in Chapter 5. 

The Villermaux criterion and the Da/Si criterion are dynamic stability criteria, meaning that with a cooling medium temperature above the limit level, 20 resp. 30 °C, the reactor will be operated in the instable region and present the phenomenon of parametric sensitivity. If instead of B12, B is used, both criteria lead to the same result. This should not be surprising since they derive from the same heat balance considerations, that is, the heat release rate of the reaction increases faster with temperature than the heat removal does. 

However, the circumferential wall heat transfer area increases as the aspect ratio increases. So, from a heat transfer, dynamic stability perspective, a large aspect ratio is desirable. Figure 2.8 shows the effect of aspect ratio on the various design and operating parameters for a design conversion of 80%. Increasing L/D increases heat transfer area, which decreases the required AT driving force and raises jacket temperature. The reactor stability index improves substantially. 

Of course, there is no guarantee that the steady-state economic optimum set of reactor compositions is the best set in terms of reactor stability. This is one of the many classical examples of the inherent engineering tradeoff between steady-state economics and dynamic controllability that occurs in many processes. 

This is consistent with the fact that these constraints correspond to the limit as the purge flow rate and the inflow of the impurity become zero. In this limit, the number of moles of the impurity leaving the reactor is identical to that leaving the condenser, hence the redundant constraint. Note also that, in the fast time scale, only the flow rates F, R, and L affect the dynamics and can be used for addressing control objectives such as stabilization of holdups, production rate, and product quality. The purge flow rate has, of course, no effect on the dynamics in this fast time scale. 

It is worth mentioning that only those stationary solutions of a set of algebraic Eqs. (8.1) can be realized in practice, which are stable. Therefore, we have the problem of determining the stability of the stationary solution by using a relevant set of dynamic equations. For the continuous reactors, in contrast to the batch reactors, such a set is principally more complex since it depends on kinetic parameters of the initiation and termination reactions. 

We show the reactor and jacket temperatures (T and T ) along with CA, the concentration of component A in the reactor. Initially, when the simulation started, the heat transfer area was sufficiently large to maintain open-loop static and dynamic stability. However, a few minutes into the simulation, we reduced UA by 20 percent. This creates dynamic instability with complex eigenvalues as in Eq. (4.25). The reactor temperature and composition start oscillating with a growing amplitude. However, the amplitude growth stops roughly 5 hours after the onset of instability and the reaction enters into a limit cycle of constant period and amplitude. 

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