Reactor nonisothermal

One important reason to consider the nonisothermal reactor is because it is the major cause of accidents in chemical plants. Thermal runaway and consequent pressure buildup and release of chemicals is an ever-present danger in any chemical reactor. Engineers must 

Chemical reactors may look similar to other units of chemical processing and sometimes they behave similarly, but the nonisothermal chemical reactor has nonhnearities that never occur in nonreacting systems. 

The assumed isothermal operating mode of the ideal reactors is practically unrealizable for highly exothermic reactions in technical reactors, so that in practice, in addition to the mass balance (Equation 2.2-44), an energy balance (Equation 2.2-45) must be considered  

The two equations are coupled through the temperature dependence of the reaction rate ry(T). Since this dependence is usually expressed by an Arrhenius term, this system of differential equations must be solved numerically, since the Arrhenius term can not be completely integrated. In the following, descriptions of the most important models are given with consideration of a nonisothermal mode of operation. 

Chemistry Oxidation of an aqueous glucose solution with pure oxygen under supercritical conditions [Franck 1999], that is, homogeneous fluid phase. 

Kinetics pseudo-first order reaction with respect to glucose (A) 

Continuous ideal tubular reactor with adiabatic reaction control 

In practice the heat effects associated with chemical reactions result in nonisothermal conditions. In the case of a batch reactor the temperature changes as a function of time, whereas an axial temperature profile is established in a plug flow reactor. The application of the law of conservation of energy, in a similar 

For a batch reactor, the accumulation of enthalpy results from the production of enthalpy and the transfer of heat from the surroundings  

For a steady-state perfectly mixed flow reactor the energy balance can be made over the complete reactor  

If more than one reaction occurs, the enthalpy production terms in Eqns. 7.41, 7.42 and 7.44 have to be obtained from a summation. 

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Omoleye, J. A., Adesina, A. A., and Udegbunam, E. O., Optimal design of nonisothermal reactors Derivation of equations for the rate-temperature conversion profile and the optimum temperature progression for a general class of reversible reactions, Chem. Eng. Comm., Vol. 79, pp. 95-107, 1989. 

Chapter 1 treated single, elementary reactions in ideal reactors. Chapter 2 broadens the kinetics to include multiple and nonelementary reactions. Attention is restricted to batch reactors, but the method for formulating the kinetics of complex reactions will also be used for the flow reactors of Chapters 3 and 4 and for the nonisothermal reactors of Chapter 5. 

The axial dispersion model is readily extended to nonisothermal reactors. The turbulent mixing that leads to flat concentration profiles will also give flat temperature profiles. An expression for the axial dispersion of heat can be written in direct analogy to Equation (9.14) ... 

Previous chapters have discussed how isothermal or adiabatic reactors can be scaled up. Nonisothermal reactors are more difficult. They can be scaled by maintaining the same tube diameter or by the modeling approach. The challenge is to increase tube diameter upon scaleup. This is rarely possible and when it is possible, scaleup must be based on the modeling approach. If the predictions are satisfactory, and if you have confidence in the model, proceed with scaleup. 

The steady-state design equations (i.e., Equations (14.1)-(14.3) with the accumulation terms zero) can be solved to find one or more steady states. However, the solution provides no direct information about stability. On the other hand, if a transient solution reaches a steady state, then that steady state is stable and physically achievable from the initial composition used in the calculations. If the same steady state is found for all possible initial compositions, then that steady state is unique and globally stable. This is the usual case for isothermal reactions in a CSTR. Example 14.2 and Problem 14.6 show that isothermal systems can have multiple steady states or may never achieve a steady state, but the chemistry of these examples is contrived. Multiple steady states are more common in nonisothermal reactors, although at least one steady state is usually stable. Systems with stable steady states may oscillate or be chaotic for some initial conditions. Example 14.9 gives an experimentally verified example. 

Nonisothermal reactors. Nonisothermal operation brings additional complexity to the superstructure approach1112. In the first instance, the optimum temperature... 

Nonisothermal reactors with adiabatic beds. Optimization of the temperature profile described above assumes that heat can be added or removed wherever required and at whatever rate required so that the optimal temperature profile can be achieved. A superstructure can be set up to examine design options involving adiabatic reaction sections. Figure 7.12 shows a superstructure for a reactor with adiabatic sections912 that allows heat to be transferred indirectly or directly through intermediate feed injection. 

As with isothermal reactor design, the optimization of superstructures for nonisothermal reactors can be carried out reliably, using simulated annealing. 

Figure 7.12 Superstructure for a Nonisothermal reactor with adiabatic sections.

For nonisothermal reactors the key questions that the reactor designer must answer are (1) How can one relate the temperature of the reacting system to the degree of conversion that has been accomplished and (2) How does this temperature influence the subsequent performance of the system In responding to these questions the chemical engineer must use two basic tools—the material balance and the energy balance. The bulk of this chapter deals with these topics. Some stability and selectivity considerations are also treated. 

Balakrishna, S. and L. T. Biegler. Targeting Strategies for the Synthesis and Energy Integration of Nonisothermal Reactor Networks. Ind Eng Chem Res 31 2152-2164 (1992). 

For detailed versions of Fig. 18.8 which show ( versus Mj and cl versus plus discussion and problems dealing with nonisothermal reactors, see Chapter 22 in Levenspiel (1996). 

Cleland and Wilhelm (C18) used a finite-difference technique which could be used for nonlinear reactions, but they limited their study to a first-order reaction. Experiments were also performed to test the results of the theory. In a small reaction tube, the two checked quite well. In a large tube there were differences which were explained by consideration of natural convection effects which were due to the fact that completely isothermal conditions were not maintained. This seems to be the only experimental data in the literature to date, and shows another area in which more work is needed. The preceding discussion considered only isothermal conditions except for Chambre (C12) who presented a general method for nonisothermal reactors. 

Throughout this book the reaction we will focus on for many examples will be variations of the preceding reaction A B, r zz kCA, ao 2 moles/liter, k = 0.5 min". Do = 4 liter/min. We wiU compare it for several reactors in this chapter, and in Chapters 5 and 6 we win examine it for nonisothermal reactors. Watch for it. 

The question of choosing a PFTR or a CSTR will occur throughout this book. From the preceding arguments it is clear that the PFTR usuaUy requires a smaller reactor volume for a given conversion, but even here the CSTR may be preferred because it may have lower material cost (pipe is more expensive than a pot). We will later see other situations where a CSTR is clearly preferred, for example, in some situations to maximize reaction selectivity, in most nonisothermal reactors, and in polymerization processes where plugging a tube with overpolymerized solid polymer could be disastrous. 

There are many interesting problems in which complex chemistry in nonisothermal reactors interact to produce complex and important behavior. As examples, the autocatalytic reaction, A — B, r = kC/ Cg, in a nonisothermal reactor can lead to some quite complicated properties, and polymerization and combustion processes in nonisothermal reactors must be considered very carefully in designing these reactors. These are the subjects of Chapters 10 and 11. 

For the nonisothermal reactors we need to solve the mass- and energy-balance equations... 

Let us return to the graphical construction we developed in earlier chapters for isothermal reactors, because for nonisothermal reactors T is stiU the area under curves of plots of 1/r versus Cao — CA. For the first-order irreversible reaction in an adiabatic reactor 1/fad is given by... 

Thus we see that for nonisothermal reactors this 1/r versus Cao Ca curve is not always an increasing function of conversion as it was for isothermal reactors even with positive-order kinetics. Since the 1/r curve can have a rninimum for the nonisothermal reactor, we confirm the possibility that the CSTR requires a smaller volume than the PFTR for positive-order kinetics. This is hue even before the multiple steady-state possibilities are accounted for, which we will discuss in the next chapter. This is evident from our 1 /r plot for the PFTR and CSTR and will occur whenever r has a sufficiently large maximum that the area under the rectangle is less than the area under the curve of 1/r versus Cao Ca-... 

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