A Consecutive Reaction Sequence

The first consideration in any design and optimization problem is to decide the boundaries of the system. A reactor can rarely be optimized without considering the upstream and downstream processes connected to it. Chapter 6 attempts to integrate the reactor design concepts of Chapters 1-5 with process economics. The goal is an optimized process design that includes the costs of product recovery, in-process recycling, and by-product disposition. The reactions are 

Note that the production of C is not stoichiometrically determined but that the relative amounts of B and C can be changed by varying the reaction conditions. Had C been stoichiometrically determined, as in the production of byproduct HCl when hydrocarbons are directly chlorinated, there is nothing that can be done short of very fundamental changes to the chemistry, e.g., using CIO2 rather than CI2. Philosophically, at least, this is a problem for a chemist rather than a chemical engineer. In the present example, component C is a secondary or side product such as a dichlorinated compound when 

CHEMICAL REACTOR DESIGN, OPTIMIZATION, AND SCALEUP Pure A 

FIGURE 6.1 Simplified process flow diagram for consecutive reaction process. 

Few reactions are completely clean in the sense of giving only the desired product. There are some cases where the side products have commensurate value with the main products, but these cases are becoming increasingly rare, even in the traditional chemical industry, and are essentially nonexistent in fields like pharmaceuticals. Sometimes, C is a hazardous waste and has a large, negative value. 

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For a consecutive reaction sequence A=>B=>C when the rate equations are of first order and diffusional limitations can be neglected... 

The simplest example of a consecutive reaction is that described by a sequence... 

A similar reaction sequence (consecutive loss of OH, NO and H) has been established for the molecular ions of dinitrophenylhydrazones of a, /3-unsaturated aldehydes34,74. ... 

We now proceed to the main topic of this chapter and examine the situation for an electrochemical reaction that involves multiple consecutive electron-transfer steps of the kind referred to in a general way in the introduction. A hypothetical reaction sequence involving n consecutive electron-transfer reduction steps is given in Scheme 1. The A,s are stable species that can be reactants or products and the ks are reaction intermediates of lower stability. The ZjS indicate the number of electrons trans-... 

Many electrode reactions are consecutive in nature and if one has a consecutive reaction—and it contains only a few steps—it is indeed a common experience that one of the successive reactions has a much greater influence on the rate than the others. In extreme cases, the one reaction in a sequence of, say, four, has a 99% control over the rates of the other reactions in the series. 

Other recent work in the field of optimization of catalytic reactors experiencing catalyst decay includes the work of Romero e/ n/. (1981 a) who carried out an analysis of the temperature-time sequence for deactivating isothermal catalyst bed. Sandana (1982) investigated the optimum temperature policy for a deactivating catalytic packed bed reactor which is operated isothermally. Promanik and Kunzru (1984) obtained the optimal policy for a consecutive reaction in a CSTR with concentration dependent catalyst deactivation. Ferraris ei al. (1984) suggested an approximate method to obtain the optimal control policy for tubular catalytic reactors with catalyst decay. 

Eind the optimal temperature profile T t) that maximizes the concentration of component B in the consecutive reaction sequence of Equation 6.6 for a PER subject to the constraint that f= 0.8 h. 

In both of these limits, it is the rate of the slowest reaction that determines the rate of formation of the product. This is a general feature of consecutive reactions. If one reaction step in a consecutive reaction is considerably slower than the other steps, then the rate constant of the slowest reaction will govern the rate of product formation. This slowest reaction is referred to as the rate-determining step in a reaction sequence. 

Confronted with the need to develop a sustainable chemistry, we have witnessed an amazing increase in the efficiency and selectivity of synthetic methods in the last fifty years. In order to solve the problems associated with the traditional step-by-step procedures, such as the cumbersome, time-consuming, and expensive isolation of intermediates, several new criteria have been introduced atom, redox, step and pot economy or protecting-group-free synthesis. It is obvious that all variants of one-pot domino and cascade reactions or multicomponent consecutive reactions sequences may allow fulfilling these criteria. 

The sequence of events after catcium activation of aequorin The following is an example of a consecutive reaction in which a rapid rise in signal is followed by a slow decay and yet, 2 is smaller than Hastings... 

Figure 2.4 gives an example, taken from the work of Creighton and coworkers (1984), of a consecutive reaction between an adsorbed hydrocarbon fragment, called ethylidyne (Ptn=C-CH3, where Pt denotes the surface of a platinum crystal), and deuterium. The reaction sequence is... 

The most commonly postulated mechanism for the desmolase reaction has been the suggestion of the enzymatic consecutive reaction sequence cholesterol 20a-hydroxycholesterol — (22R)-20a,22-dihydroxycholesterol pregnenolone (Shimizu et al., 1961, 1962 Constantopoulos and Tchen, 1961). This hypothetical scheme was actually advanced on the basis of three suppositions (1) cholesterol is cleaved between C-20 and C-22, as was discussed in a previous section, (2) 20a-hydroxycholesterol was formed from cholesterol-4- C by a cow adrenocortical homogenate in the presence of 20a-hy-droxycholesterol as a trapping agent (Solomon et al., 1956), and (3) both 20a-hydroxycholesterol and (22R)-20a,22-dihydroxycholesterol are much more efficiently transformed to pregnenolone than is cho-... 

This chapter has refined the definition of a tandem process and its three variants cascade, consecutive, and sequential. Unlike a more intuitive definition of a tandem process, which is essentially synonymous to a multistep reaction sequence, this definition of a tandem process focuses on the presence of a special connection between its components. As a consequence, this definition is not concerned whether or not an intermediate can be isolated. Moreover, one or even several additional reactions may take place between the components of a tandem process (e.g.. Scheme 16.6). 

The EROS (Elaboration of Reactions for Organic Synthesis) system [26] is a knowledge-based system which was created for the simulation of organic reactions. Given a certain set of starting materials, EROS investigates the potential reaction pathways. It produces sequences of simultaneous and consecutive reactions and attempts to predict the products that will be obtained in those reactions. 

It is immediately clear that in these cases of thermodynamic control of the composition of the reaction mixture one sometimes may find, with parallel reactions, the curves whose forms are typical for consecutive reactions and vice versa. In other cases, consecutive reaction with the sequence A —> B — C may simulate the sequence A —> C —> B (Figs. 4b and 4c). 

Consecutive reactions. In the sequence of Eq. (4-1), prove that the half-time for the disappearance of A occurs at fmax for I when k = a 2. What is the numerical value of a ... 

Radioactive decay provides splendid examples of first-order sequences of this type. The naturally occurring sequence beginning with and ending with ° Pb has 14 consecutive reactions that generate a or /I particles as by-products. The half-lives in Table 2.1—and the corresponding first-order rate constants, see Equation (1.27)—differ by 21 orders of magnitude. 

The next phase of the problem is to find those values for T and V that will give the lowest product cost. This is a problem in optimization rather than root-finding. Numerical methods for optimization are described in Appendix 6. The present example of consecutive, mildly endothermic reactions provides exercises for these optimization methods, but the example reaction sequence is... 

All other things being equal, as they are in this contrived example, the competitive reaction sequence of Equation (6.6) is superior for the manufacture of B than the consecutive sequence of Equation (6.1). The CSTR remains a doubtful choice, but the isothermal PER is now better than the adiabatic PER. The reason for this can be understood by repeating Example 6.5 for the competitive reaction sequence. 

Consecutive Reactions. The prototypical reaction is A B C, although reactions like Equation (6.2) can be treated in the same fashion. It may be that the first reaction is independent of the second. This is the normal case when the first reaction is irreversible and homogeneous (so that component B does not occupy an active site). A kinetic study can then measure the starting and final concentrations of component A (or of A and A2 as per Equation (6.2)), and these data can be used to fit the rate expression. The kinetics of the second reaction can be measured independently by reacting pure B. Thus, it may be possible to perform completely separate kinetic studies of the reactions in a consecutive sequence. The data are fit using two separate versions of Equation (7.8), one for each reaction. The data will be the experimental values of for one sum-of-squares and b ut for another. 

Beneficial micro reactor properties mainly refer to improving heat management as a key for obtaining a partial reaction in a consecutive sequence, when large heats are released by reaction steps other than the partial one (see also Section 3.3.1). 

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