Series reaction

Finally, let s return to the series of two reactions that we considered in Chapter 7. 

Suppose that both reactions are irreversible and first order, with the rate constants shown above. 

If there are no gradients in the catalyst particle, the ratio of the rate of formation of R to the rate of disappearance of A for the whole particle is given by 

IMs ratio of reaction rates is the selectivity to R based on A, as defined in Chapter 7. The symbol for the instantaneous or point selectivity is used here because the selectivity for the particle as a whole corresponds to the selectivity at a point in the reactor. 

When an internal transport resistance is present, the concentrations of A, R, and S vary with position inside the catalyst particle. Therefore, the selectivity will also vary with position. Nevertheless, the symbol s(R/A) wUl be used to represent the selectivity of a whole particle. However, when an internal transport resistance is present, the equations that describe reaction and transport inside the catalyst particle must be solved to obtain s(R/A). 

A kinetics scheme for a set of (irreversible) reactions occurring in series with respect to species A, B, and C may be represented by 

We derive the kinetics consequences for this scheme for reaction in a constant-volume batch reactor, the results also being applicable to a PFR for a constant-density system. The results for a CSTR differ from this, and are explored in Example 18-4. 

Consider the following simplified version of scheme 5.5-1, with each of the two steps being first-order  

For reaction in a constant-volume BR, with only A present initially, the concentrations of A, B and C as functions of time t are governed by the following material-balance equations for A, B and C, respectively, incorporating the two independent rate 

This result may be used to eliminate cA in equation 5.5-3, to give a differential equation from which cB(f) may be obtained  

The second reaction type involves reactants forming products, but then the products undergo further reaction in series with the main reaction. We want to show here the implications of series reactions, so we consider a simple batch isothermal reactor at constant volume  

Assuming first-order kinetics, we can write the change with time in the concentrations of reactant A (Ca) and products B (CB) and C (Cc)  

The kinetic rate constants are feB and fec. We can solve these differential equations analytically, assuming that we start at time zero with only reactant A (Cao)- 

If series reactions are conducted in a CSTR, the concentrations in the reactor can be adjusted to influence selectivity and conversion. Because the production of the undesirable product C depends on the concentration of the desired product B, this concentration should be kept small. The reactor can be operated with low conversion (small concentration of B). 

Of course, this means that the concentration of A is large, so recovery and recycle of unreacted A is required to make the process economical. 

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An example of a series reaction system is the production of formaldehyde from methanol ... 

Mixed parallel and series reactions producing byproducts. In more complex reaction systems, both parallel and series reactions can occur together. Mixed parallel and series reactions are of the type... 

An example of mixed parallel and series reactions is the production of ethanolamines by reaction between ethylene oxide and ammonia ... 

Here the ethylene oxide undergoes parallel reactions, whereas the monoethanolamine undergoes a series reaction to diethanolamine and triethanolamine. 

Multiple reactions in series producing byproducts. Consider the system of series reactions from Eq. (2.7) ... 

Selectivity for series reactions of the types given in Eqs. (2.7) to (2.9) is increased by low concentrations of reactants involved in the secondary reactions. In the preceding example, this means reactor operation with a low concentration of PRODUCT—in other words, with low conversion. For series reactions, a significant reduction in selectivity is likely as the conversion increases. 

But what is the correct choice a byproduct reaction calls for a continuous well-mixed reactor. On the other hand, the byproduct series reaction calls for a plug-flow reactor. It would seem that, given this situation, some level of mixing between a plug-flow and a continuous well-mixed reactor will give the best... 

Figure 2.3 Choice of reactor type for mixed parallel and series reactions when the parallel reaction has a higher order than the primary reaction.

Multiple reactions in series producing byproducts. For the series reaction system in Eq. (2.18), the series reaction is inhibited by low concentrations of PRODUCT. It has been noted already that this can be achieved by operating with a low conversion. 

If the reaction involves more than one feed, it is not necessary to operate with the same low conversion on all the feeds. Using an excess of one of the feeds enables operation with a relatively high conversion of other feed material, and still inhibits series reactions. Consider again the series reaction system from Example 2.3 ... 

An example of where recycling can be effective in improving selectivity is in the production of benzene from toluene. The series reaction is reversible. Hence recycling diphenyl to the reactor can be used to suppress its formation at the source. 

Mixed parallel and series reactions producing byproducts. As with parallel and series reactions, use of an excess of one of the feeds can be effective in improving selectivity with mixed reactions. As an... 

Solution We wish to avoid as much as possible the production of di- and triethanolamine, which are formed by series reactions with respect to monoethanolamine. In a continuous well-mixed reactor, part of the monoethanolamine formed in the primary reaction could stay for extended periods, thus increasing its chances of being converted to di- and triethanolamine. The ideal batch or plug-flow arrangement is preferred, to carefully control the residence time in the reactor. 

Series reactions occur in which the tert-butyl hydrogen sulfate reacts to unwanted tert-butyl alcohol ... 

Other series reactions form unwanted polymeric material. 

In fact, it is often possible with stirred-tank reactors to come close to the idealized well-stirred model in practice, providing the fluid phase is not too viscous. Such reactors should be avoided for some types of parallel reaction systems (see Fig. 2.2) and for all systems in which byproduct formation is via series reactions. 

Intraparticle mass transport resistance can lead to disguises in selectivity. If a series reaction A — B — C takes place in a porous catalyst particle with a small effectiveness factor, the observed conversion to the intermediate B is less than what would be observed in the absence of a significant mass transport influence. This happens because as the resistance to transport of B in the pores increases, B is more likely to be converted to C rather than to be transported from the catalyst interior to the external surface. This result has important consequences in processes such as selective oxidations, in which the desired product is an intermediate and not the total oxidation product CO2. 

In the benzazole series, reactions of the type discussed for monocyclic derivatives in Section 4.02.3.1.9 are generalized by Scheme 45 and examples are given in Table 9. 

An industrial example of series reactions is the substitution process involving methane and chlorine ... 

Figure 5-7. Concentrations versus time of A, B, and C in a series reaction...

Consecutive reactions are those in which the product of one reaction is the reactant in the next reaction. These are also called series reactions. Reversible (opposing) reactions, autocatalytic reactions, and chain reactions can be viewed as special types of consecutive reactions. 

Exploitation of analytical selectivity. We have seen, in our discussion of the A —> B C series reaction (Scheme IX), that access to the concentration of A as a function of time is valuable because it permits to be easily evaluated. Modern analytical methods, particularly chromatography, constitute a powerful adjunct to kinetic investigations, and they render nearly obsolete some very difficult kinetic problems. For example, the freedom to make use of the pseudoorder technique is largely dependent upon the high sensitivity of analytical methods, which allows us to set one reactant concentration much lower than another. An interesting example of analytical control in the study of the Scheme IX system is the spectrophotometric observation of the reaction solution at an isosbestic point of species B and C, thus permitting the A to B step to be observed. 

Consider the series reaction A—>B—>C. If the first step is very much slower than the second step, the rate of formation of C is controlled by the rate of the first step, which is called the rate-determining step (rds), or rate-limiting step, of the reaction. Similarly, if the second step is the slower one, the rate of production of C is controlled by the second step. The slower of these two steps is the bottleneck in the overall reaction. This flow analogy, in which the rate constants of the separate steps are analogous to the diameters of necks in a series of funnels, is widely used in illustration of the concept of the rds. 

Alfuzosin (91) is a prazosin-like hypotensive adrenergic a-1 receptor blocker with the special structural feature that two carbons have been excised conceptually from the piperazine ring normally present in this series. Following the usual sequence for this series, reaction of 4-amino-2-chloro-7-dimethoxyquinazoline (89) with the tetrahydro-2-furyl amide of 3-methylaminopropyla-mine (90) gives alfuzosin (91) [25], Alfuzosin is claimed to cause less orthostatic hypotention (dizziness or fainting upon sudden rising) than prazosin. 

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