Irreversible Series-Parallel Reactions

The following example illustrates a combination of semibatch and semicontinuous operation for an irreversible reaction, with one reactant added intermittently and the other flowing (bubbling) continuously, that is, a combination of Figures 12.3(a) and 12.4(a). Chen (1983, pp. 168-211, 456-460) gives several examples of other situations, including reversible, series-reversible, and series-parallel reactions, and nonisothermal and autothermal operation. 

Irreversible series-parallel reactions can be analyzed in terms of their constituent series reactions and parallel reactions in that optimum contacting for favorable product distribution is the same as for the constituent reactions. 

Figure 8.9 shows that the concentration of intermediate in reversible series reactions need not pass through a maximum, while Fig. 8.10 shows that a product may pass through a maximum concentration typical of an intermediate in the irreversible series reaction however, the reactions may be of a different kind. A comparison of these figures shows that many of the curves are similar in shape, making it difficult to select a mechanism of reaction by experiment, especially if the kinetic data are somewhat scattered. Probably the best clue to distinguishing between parallel and series reactions is to examine initial rate data—data obtained for very small conversion of reactant. For series reactions the time-concentration curve for S has a zero initial slope, whereas for parallel reactions this is not so. 

At the same time, as a chemist I was disappointed at the lack of serious chemistry and kinetics in reaction engineering texts. AU beat A B o death without much mention that irreversible isomerization reactions are very uncommon and never very interesting. Levenspiel and its progeny do not handle the series reactions A B C or parallel reactions A B, A —y C sufficiently to show students that these are really the prototypes of aU multiple reaction systems. It is typical to introduce rates and kinetics in a reaction engineering course with a section on analysis of data in which log-log and Anlienius plots are emphasized with the only purpose being the determination of rate expressions for single reactions from batch reactor data. It is typically assumed that ary chemistry and most kinetics come from previous physical chemistry courses. 

Consider the following reactions, namely the second order irreversible reaction aA + bB — rR + sS, the series reaction A — B — C, and the parallel reaction A BA->C... 

The irreversible and reversible complex or multiple reactions have a different behavior and as such cannot be solved by simple integral methods. In most cases, numerical methods are employed. These reactions can occnr in series, parallel, or a combination of both. The goal is to determine the rate constants for reactions of any order. Although the order of these reactions is not integer, we can assnme that it is entire in the different steps. In such cases, an analytical solution can be obtained. The most complex solutions of generic order will not be studied in this chapter. Consider the three cases as follows. 

Chapter 2 covers the basic principles of chemical kinetics and catalysis and gives a brief introduction on classification and types of chemical reactors. Differential and integral methods of analysis of rate equations for different types of reactions—irreversible and reversible reactions, autocatalytic reactions, elementary and non-elementary reactions, and series and parallel reactions are discussed in detail. Development of rate equations for solid catalysed reactions and enzyme catalysed biochemical reactions are presented. Methods for estimation of kinetic parameters from batch reactor data are explained with a number of illustrative examples and solved problems. 

The simplest sets of reactions involve series or parallel first-order irreversible reactions. We will first consider these cases because they have simple analytical solutions and are useful prototypes of more complicated reaction sets. These can be considered in the energy diagrams similar to those we discussed in the previous chapter for single reactions. 

If a resistor is added in series with the parallel RC circuit, the overall circuit becomes the well-known Randles cell, as shown in Figure 4.11a. This is a model representing a polarizable electrode (or an irreversible electrode process), based on the assumptions that a diffusion limitation does not exist, and that a simple single-step electrochemical reaction takes place on the electrode surface. Thus, the Faradaic impedance can be simplified to a resistance, called the charge-transfer resistance. The single-step electrochemical reaction is described as... 

Most poisons are type (1), i.e., independent compounds present tn the feed, perhaps in minute quantities, that deactivate the site with a mechanism different from the main reaction. Examples are also found of types (2) and (3), where either parallel or series reactions generate side products that poison the sites. These mechanisms may also be classified as examples of kinetic inhibition but are considered poisoning if adsorption on the site is irreversible. In situations where multiple sites are involved (for example, dual-functional catalytic reforming), poisoning patterns become more complex. 

It should be noted that appreciable amounts of isomers are produced at every stage—i.e., the process, strictly speaking, consists of a series of parallel-consecutive reactions, with differing production rates for each isomer. In determining the total rate of isomer production, we regard the process of decachloropentane production as consisting of six irreversible consecutive reactions. 

The net rate of the first reversible reaction can be given as rmt i = kl Ca Cb — k2 Cd Ce. The second reaction is in series with the first and we find it has kinetics that are given by r = k3 Cd Ce. It is irreversible. The third reaction, A to G, is parallel to that of the first reaction and it too is reversible. This reaction is second order in the forward direction and first order in the reverse direction. 

The second model provides an additional reaction by splitting the initial process of the two-box model into an equilibrium reaction and a parallel reversible reaction. Both these reactions tend towards the same Freundlich equilibrium. This model can be conceptualised as dividing a single set of Freundlich sorption sites into a portion which is rapidly accessible and a portion which is kinetically controlled. The Freundlich processes are followed in series by a third, irreversible process. In addition to the four independent parameters of the first model, the three-box model includes/, the fraction of the Freundlich sorption sites reaching equilibrium instantaneously. 

Lu, Y.P., Dixon, A.G., Moser, W.R. and Ma, Y.H., 1997c. Analysis and Optimization of Cross-Flow Reactors with Staged Feed Policies - Isothermal Operation with Parallel Series, Irreversible Reaction Systems. Chemical Engineering Science, 52(8) 1349-1363. 

The multiple reactions involve parallel, series, and mixed reactions. They consist of complex reactions in which the specific rates of each reaction should be determined. They often occur in industrial processes. These reactions can be simple, elementary, irreversible and reversible, or even nonelementary. Some cases are ... 

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