First-order reactions exothermic multiple

Fig. 15. Temperature vs heat generation or removal in estabHshing stationary states. The heavy line (—) shows the effect of reaction temperature on heat-generation rates for an exothermic first-order reaction. Curve A represents a high rate of heat removal resulting in the reactor operating at a low temperature with low conversion, ie, stationary state at a B represents a low rate of heat removal and consequently both a high temperature and high conversion at its stationary state, b and at intermediate heat removal rates, ie, C, multiple stationary states are attainable, c and The stationary state at c ...

Safe Design of Cooled Tubular Reactors for Exothermic Multiple First Order Reactions... 

Table I. Criteria for the safe design of cooled tubular reactors with multiple exothermic first order reactions...

Another interesting phenomenon can emerge under non-isothermal conditions for strongly exothermic reactions there will be multiple solutions to the coupled system of energy and mass balances even for the simplest first-order reaction. Such steady-state multiplicity results in the existance of several possible solutions for the steady state overall effectiveness factor, usually up to three with the middle point usually unstable. One should, however, note that the phenomenon is, in practice, rather rarely encountered, as can be understood from a comparison of real parameter values (Table 9.2). 

M. Shacham, N. Bauner, and M. B. Cuflip [Chem. Eng. Edu., 28,30-35 (1994)] discussed the existence of multiple steady states for exothermic reactions being carried out in a single CSTR. In particular, these authors considered an irreversible first-order reaction of the form... 

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. 

A cascade of three continuous stirred-tank reactors arranged in series, is used to carry out an exothermic, first-order chemical reaction. The reactors are jacketed for cooling water, and the flow of water through the cooling jackets is countercurrent to that of the reaction. A variety of control schemes can be employed and are of great importance, since the reactor scheme shows a multiplicity of possible stable operating points. This example is taken from the paper of Mukesh and Rao (1977). 

Salnikov specifically reported multiple singular points and a limit cycle establishing the existence of oscillations in chemical reactions. Bilous and Amundson (1955) referred to Salnikov s (1948) paper as the first work where periodic phenomenon in reaction systems was discussed. They also indicated that a reaction A -> B in CSTR is irreversible, exothermic, and kinetically first order. Considering mass balance and heat balance equations it is known that at the steady states, the heat consumption... 

An exothermic first-order reactive system in a sequence of jacketed CSTRs is considered. Several alternative process designs are constructed and studied with respect to their static and dynamic controllability properties to multiple and simultaneous process disturbances. The same system has been studied by numerous researchers (Ref 14, 15, 44) and served as an illustrative example of process design and control interactions. The reaction is carried out in either a single reactor or two reactors in series (Fig. 1). The dynamic model (see Ref 14, 15) contains four state variables per reactor namely the reactor s volume, concentration and temperature and the jacket temperature. Model parameters for the system are shown in Table... 

The specific models we will analyse in this section are an isothermal autocatalytic scheme due to Hudson and Rossler (1984), a non-isothermal CSTR in which two exothermic reactions are taking place, and, briefly, an extension of the model of chapter 2, in which autocatalysis and temperature effects contribute together. In the first of these, chaotic behaviour has been designed in much the same way that oscillations were obtained from multiplicity with the heterogeneous catalysis model of 12.5.2. In the second, the analysis is firmly based on the critical Floquet multiplier as described above, and complex periodic and aperiodic responses are observed about a unique (and unstable) stationary state. The third scheme has coexisting multiple stationary states and higher-order periodicities. 

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