Multiple reaction exotherms

This set of first-order ODEs is easier to solve than the algebraic equations where all the time derivatives are zero. The initial conditions are that a ut = no, bout = bo,... at t = 0. The long-time solution to these ODEs will satisfy Equations (4.1) provided that a steady-state solution exists and is accessible from the assumed initial conditions. There may be no steady state. Recall the chemical oscillators of Chapter 2. Stirred tank reactors can also exhibit oscillations or more complex behavior known as chaos. It is also possible that the reactor has multiple steady states, some of which are unstable. Multiple steady states are fairly common in stirred tank reactors when the reaction exotherm is large. The method of false transients will go to a steady state that is stable but may not be desirable. Stirred tank reactors sometimes have one steady state where there is no reaction and another steady state where the reaction runs away. Think of the reaction A B —> C. The stable steady states may give all A or all C, and a control system is needed to stabilize operation at a middle steady state that gives reasonable amounts of B. This situation arises mainly in nonisothermal systems and is discussed in Chapter 5. 

By thermodynamic convention, l Hp < 0 for exothermic reactions, so that a negative sign is attached to the heat-generation term. When there are multiple reactions, the heat-generation term refers to the net effect of all reactions. Thus, the term is an implicit summation over all M reactions that... 

Schutz, J. Chem. Eng. Sci. 43 (8) (1988) 1975. Agitated thin film reactors and tubular reactors with static mixers for rapid exothermic multiple reactions. 

We have chosen to concentrate on a specific system throughout the chapter, the methanation reaction system. Thus, although our development is intended to be generally applicable to packed bed reactor modeling, all numerical results will be obtained for the methanation system. As a result, some approximations that we will find to apply in the methanation system may not in other reaction systems, and, where possible, we will point this out. The methanation system was chosen in part due to its industrial importance, to the existence of multiple reactions, and to its high exothermicity. 

In practice the epoxide-amine cure is often accelerated by the addition of catalysts such as boron trifluoride complexes, and the boron trifluoride-ethylamine adduct (BFE) is widely used for this purpose. In addition to catalysing the epoxide-amine reactions, BFE can initiate homopolymerisation of epoxide. The accelerating effect of BFE is illustrated by DSC scans for the TGDDM/DDS/BFE system in Figure 12. The multiple-peaked exotherm associated with the BFE-catalysed TGDDM/DDS cure indicates that the kinetics of this system are more complex than those for the cure with amine alone. For this system the overall heat of reaction was found to decrease with increasing BFE concentration 89). For DDS alone Q0 was about 110 kJ per mole epoxide while the value for BFE alone was 75 kJ/mole, and the DDS/BFE values were between these limits. It appears that the proportion of epoxide homo-polymerisation relative to amine or hydroxyl addition increases with increasing BFE concentration. 

The advantages of a semi-batch reaction, that is, a better selectivity in the case of multiple reactions or a better control of the reaction course in the case of exothermal reactions, are obtained if the reaction rate is controlled by the progressive addition of one or more reactants. Indeed, this objective can only be achieved if the added reactant is immediately converted and does not accumulate in the reactor [3]. Often a reaction is said to be feed controlled only because a reactant is fed. This is not always the case, since the feed rate must be adapted to the reaction rate, and the concentration of the added compound (B) is maintained at a low level during the reaction. 

Application of the Thermal Theory to Multiple Reactions. For a flame driven by a single exothermic reaction (of the type nA B + C. ..), the laminar burning velocity SL according to the classical thermal theory of Zeldovich, Frank-Kamentskii and Semenov (ZFKS) is given by (4)... 

Westerterp K.R. and Ptasinsky K.J. "Safe design of cooled tubular reactors for exothermic, multiple reactions. Parallel reactions. Development of criteria". Chem. Eng. Sci. in print. 

One of the major goals at the undergraduate level is to bring students to the point where they can solve complex reaction problems, such as multiple reactions with heat effects, and then ask What if..." questions and look for optimum operating conditions. One problem whose solution exemplifies this goal is the Manufacture of Styrene. Problem P8-26, This problem is particularly interesting because two reactions are endothermic and one is exothermic. 

Numerical exploration of the equations (8.73-74) shows that the curves Qc-T have a S-shape for irreversible reactions, and a maximum for reversible reactions (non-represented). The shape is more complex in the case of multiple reactions, because simultaneously exothermic or endothermic reactions in the individual steps. 

Westerlink, E.J., and K.R. Westerterp, Safe Design of Cooled Tubular Reactors for Exothermic Multiple Reactions Multiple Reaction Na-works, Chem. Eng. Sci., 43(5), 1051 (1988). 

Figure 5.1 Heat balance multiplicity during exothermic reaction in a CSTR (from [6]).

The shape of the exotherm contains important information. A symmetric exotherm, such as those in Figs. 2.69,2.70, and 2.77, suggests a relatively simple reaction without the complexity of multiple reactions. In Figs. 2.69 and 2.70, for example, the reaction of epoxy with primary amine is indistinguishable from its reaction with secondary amine, resulting in the symmetric peak. If the... 

The exciting issue of steady-state multiplicity has attracted the attention of many researchers. First the focus was on exothermic reactions in continuous stirred tanks, and later on catalyst pellets and dispersed flow reactors as well as on multiplicity originating from complex isothermal kinetics. Nonisothermal catalyst pellets can exhibit steady-state multiplicity for exothermic reactions, as was demonstrated by P.B. Weitz and J.S. Hicks in a classical paper in the Chemical Engineering Science in 1962. The topic of multiplicity and oscillations has been put forward by many researchers such as D. Luss, V. Balakotaiah, V. Hlavacek, M. Marek, M. Kubicek, and R. Schmitz. Bifurcation theory has proved to be very useful in the search for parametric domains where multiple steady states might appear. Moreover, steady-state multiplicity has been confirmed experimentally, one of the classical papers being that of A. Vejtassa and R.A. Schmitz in the AIChE Journal in 1970, where the multiple steady states of a CSTR with an exothermic reaction were elegantly illustrated. 

FIGURE 17.2 Heat balance multiplicity during exothermic reaction. With permission from Reference 17, HiU CG. Chemical Engineering Kinetics and Reactor Design. New York Wiley 1977. 

Example 13-7 Agitated Thin-Film Reactors and Tubular Reactors with Static Mixers for a Rapid Exothermic Multiple Reaction (Schutz, 1988)... 

Schutz, J. (1988). Agitated thin-fihn reactors and tubular reactors with stator mixers for a rapid exothermic multiple reaction, Chem. Eng. ScL, 43, 1975-1980. 

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