Nonisothermal Multiple Chemical Reactions

Most reacting systems involve more than one reaction and do not operate iso-thermally. This section is one of the most important sections of the book. It ties together ail the previous chapters to analyze multiple reactions that do not take place isothermally. 

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Discussed the design of nonisothermal operations with multiple chemical reactions. 

Multiple steady-state behavior is a classic chemical engineering phenomenon in the analysis of nonisothermal continuous-stirred tank reactors. Inlet temperatures and flow rates of the reactive and cooling fluids represent key design parameters that determine the number of operating points allowed when coupled heat and mass transfer are addressed, and the chemical reaction is exothermic. One steady-state operating point is most common in CSTRs, and two steady states occur most infrequently. Three stationary states are also possible, and their analysis is most interesting because two of them are stable whereas the other operating point is unstable. 

In the general case of nonisothermal shrinking-core systems controlled both by chemical reaction and diffusion, the thermal effect of the reaction may bring about multiple steady states and instability due to sudden transition of rate-controlling steps during the reaction. The problem of thermal instability in noncatalytic gas-solid reactions was first pointed out by Cannon and Denbigh [37] and has been discussed by Shen and Smith [23] and Wen and coworkers [38, 39]. 

In the transition region between regimes I and JJ where the chemical reaction and diffusion present a comparable resistance to the overall progress of reaction, multiple solutions may occur and the possibility of instability arises when the reaction is exothermic [15]. The criteria for the existence of multiple steady state for chemical reactions in porous catalyst pellets have been studied extensively [17-21]. The effect of net gas generation or consumption on nonisothermal reaction in a porous solid was analyzed by Weekman [22]. 

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. 

The locus classicus of this important principle for chemical engineers is the nonisothermal stirred tank in which a single reaction takes place (for multiple reactions, see pp. 16-17). Consider the reaction... 

There are various improvements that can be made to the presented model, some improvements could be accomphshed. Foremost among these possible future-work directions is the inclusion of nonisothermal effects. Such effects as ohmic heating could be very important, especially with resistive membranes or under low-humidity conditions. Also, as mentioned, a consensus needs to be reached as to how to model in detail Schroder s paradox and the mode transition region experiments are currently underway to examine this effect. Further detail is also required for understanding the membrane in relation to its properties and role in the catalyst layers. This includes water transport into and out of the membrane, as well as water production and electrochemical reaction. The membrane model can also be adapted to multiple dimensions for use in full 2-D and 3-D models. Finally, the membrane model can be altered to allow for the study of membrane degradation, such as pinhole formation and related failure mechanisms due to membrane mechanical effects, as well as chemical attack due to peroxide formation and gas crossover. 

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. 

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