Parallel and Consecutive Reactions

K for this simple reaction as the quotient of the concentration of the products and the reactants  

With this definition and the relationships between the concentrations of A and B, it can be shown from equation 20.33 that as t oo  

The last equation is especially noteworthy for its simplicity (and its potential usefulness), although all three equations above are applicable to first-order or pseudo first-order reactions. These three expressions (and the concepts used to derive them) represent one connection between kinetics and thermodynamics. Other expressions can be derived for higher-order reactions, but they all mimic similar ideas in mass conservation and the mathematics of differential equations. 

The previous section used a simple reaction, A — B, to introduce a connection that does exist between kinetics and thermodynamics. Many chemical equations are not this simple. For some reactions, more than one product is possible these are parallel reactions. And commonly, in other cases, the product of the first reaction is the reactant of a second reaction, which may in turn be the reactant of another reaction, and so on. These are examples of consecutive reactions. 

Consider a system in which the rate laws of both reactions are first-order with respect to A. If we start such a reaction with only A present, the initial rate of disappearance of A can be written as 

The rate equations of simple reactions for which the concentrations of reactants, intermediates, and products depend on time can be solved analytically. Steady-state conditions appear as a special case in the kinetics of irreversible consecutive reactions. 

Expression (2.81) is readily integrated by using the boundary condition that [7 ] = [/ o] at = 0 

The case of a series of irreversible consecutive reactions is a bit more complicated. 

Let us reconsider the sequence of two reaction steps from reactant R to intermediate / to product P. We will now simplify the system and assume that the reaction proceeds in one direction only  

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Selectivity of parallel and consecutive reactions and of reac tions in a porous catalyst... 

As an example of the system in which parallel and consecutive reactions occur simultaneously, we have chosen the hydrogenation of crotonaldehyde, which may lead through two two-stage paths (via butyraldehyde and via crotyl alcohol) to the same final product, butanol... 

Not only the desired reaction leading to the organic sulfonic acid takes place. Parallel and consecutive reactions occur resulting in undesired byproducts and color bodies. 

Table I gives the compositions of alkylates produced with various acidic catalysts. The product distribution is similar for a variety of acidic catalysts, both solid and liquid, and over a wide range of process conditions. Typically, alkylate is a mixture of methyl-branched alkanes with a high content of isooctanes. Almost all the compounds have tertiary carbon atoms only very few have quaternary carbon atoms or are non-branched. Alkylate contains not only the primary products, trimethylpentanes, but also dimethylhexanes, sometimes methylheptanes, and a considerable amount of isopentane, isohexanes, isoheptanes and hydrocarbons with nine or more carbon atoms. The complexity of the product illustrates that no simple and straightforward single-step mechanism is operative rather, the reaction involves a set of parallel and consecutive reaction steps, with the importance of the individual steps differing markedly from one catalyst to another. To arrive at this complex product distribution from two simple molecules such as isobutane and butene, reaction steps such as isomerization, oligomerization, (3-scission, and hydride transfer have to be involved.

Vayenas, C. G. and S. Pavlou. 1987b. Optimal catalyst distribution for selectivity maximization in pellets parallel and consecutive reactions. Chem. Eng. Sci. 42(7) 1655-1666. 

Even though the governing phenomena of coupled reaction and mass transfer in porous media are principally known since the days of Thiele (1) and Frank-Kamenetskii (2), they are still not frequently used in the modeling of complex organic systems, involving sequences of parallel and consecutive reactions. Simple ad hoc methods, such as evaluation of Thiele modulus and Biot number for first-order reactions are not sufficient for such a network comprising slow and rapid steps with non-linear reaction kinetics. 

The hydrogenation of acetopnenone wnich has an aromatic unsaturated ring and a caroonyl functional group involves a sequence of several competitive parallel and consecutive reactions. 

These parallel and consecutive reactions for n-butylbenzene are shown in Fig. 5. 

An under-stoichiometric mixture of methane and oxygen (2 1) was diluted with 70% nitrogen, preheated and distributed within the distribution module and continuously delivered to the single wells. For the catalytic combustion of methane, a number of parallel and consecutive reactions occur [57]. During the tests mostly carbon dioxide was obtained according to the formula ... 

The reactor set-up was applied to the catalytic combustion of methane at low temperatures [56], For the catalytic combustion of methane, a number of parallel and consecutive reactions are known to occur [85], Cullis et al. [86] also found that under low-temperature conditions the conversion of methane is nearly completely due to the formation of these total oxidation products, a result which was confirmed in the experiments. 

Note that the interference of chemical reactions may alter the effective rate constant of the secondary reaction and break the independence principle of elementary chemical reactions. Moreover, under these conditions non-spontaneous reactions may proceed, which are eliminated in parallel and consecutive reactions. 

Equation (19-22) indicates that, for a nominal 90 percent conversion, an ideal CSTR will need nearly 4 times the residence time (or volume) of a PFR. This result is also worth bearing in mind when batch reactor experiments are converted to a battery of ideal CSTRs in series in the field. The performance of a completely mixed batch reactor and a steady-state PFR having the same residence time is the same [Eqs. (19-5) and (19-19)]. At a given residence time, if a batch reactor provides a nominal 90 percent conversion for a first-order reaction, a single ideal CSTR will only provide a conversion of 70 percent. The above discussion addresses conversion. Product selectivity in complex reaction networks may be profoundly affected by dispersion. This aspect has been addressed from the standpoint of parallel and consecutive reaction networks in Sec. 7. 

The design of the optimal ratio of the reactor diameter (2R) to the inert particle diameter is also important for both the consecutive-parallel and consecutive reactions. This ratio can be varied by changing either particle or reactor diameter. Obviously, larger packing particles will lead to lower pressure... 

It was reported that the degradation of cefixime in an alkaline solution follows parallel and consecutive reactions as ... 

Acrolein is hydrogenated by a network of parallel and consecutive reactions. The main frame of the reaction is ... 

From equations 21 and 22 the striking difference between parallel and consecutive reactions immediately becomes clear whereas the selectivity for the first type is only a function of the temperature, it is for consecutive reactions also a function of the conversion of A and P. Moreover, for consecutive reactions the selectivity always decreases with increasing conversion For consecutive reactions two different situations may be considered ... 

The influence of electrostatic effects on the rate of hydrolysis of peptides is demonstrated vividly by the studies of Long and co-workers (1963) who made quantitative kinetic studies of the parallel and consecutive reactions which occur on hydrolysis of tripeptides. These workers employed an... 

Perhaps the most successful application since FCC is the Sohio process. The reasons for the success are explained as follows. First, the process achieved high conversion and selectivity in FCB, even in a reaction system involving several parallel and consecutive reactions. Second, the process was industrialized directly by the use of fluid beds, rather than by passing through the stage of fixed beds. Callahan a/. (Cl) have reported on development of the initial catalyst, bismuth molybdate, for the Sohio process. 

Parallel-consecutive reactions belong to the mixed type which have the characteristics of both parallel and consecutive reactions. The following example comprises two parallel chains, each composed of three simple reactions ... 

Currently only competing parallel and consecutive reactions are used for determining micro-mixing. 

In many catalytic systems multiple reactions occur, so that selectivity becomes important. In Sec. 2-10 point and overall selectivities were evaluated for homogeneous well-mixed systems of parallel and consecutive reactions. In Sec. 10-5 we saw that external diffusion and heat-transfer resistances affect the selectivity. Here we shall examiineHEieHnfiuence of intrapellet res ahces on selectivity. Systems with first-order kinetics at isothermal conditions are analyzed analytically in Sec. 11-12 for parallel and consecutive reactions. Results for other kinetics, or for nonisothermal conditions, can be developed in a similar way but require numerical solution. ... 

Complex Reaction Systems The Existence of Parallel and Consecutive Reactions... 

The ratio Qpn of the relative amounts of the products p-(62) and n-(62) depends strongly on the reaction conditions.69 Qpn can range from Qpn 1 to Qpn 1. A mathematical model for the mechanism of the Ugi reaction, a complex system of parallel and consecutive reactions, was established by a computer-assisted analysis of Qpn as a function of the concentration of the reactants in methanol at 0 C.2o,m.69 jn a solution of (58M60), or (58) and (61), we have an equilibrium of the species (63M66). The formulas (63M66) describe primarily the stoichiometric composition of the species. The formula (64) represents, for instance, the equilibrium system (64a)-(64c), where (64a) is a tight ion pair, (64b) is a pair of diastereomers and (64c) is a hydrogen-bonded adduct. 

Figure 1 shows the scheme of the metabolic pathway for obtaining the acrylic acid. Several parallel and consecutive reactions take place and are necessary to find out operating conditions, which allow the desired product to be obtained. 

Direct oxidation or hydroxylation of aromatics and particularly alkylbenzenes, is a complex reaction consisting of a variety of parallel and consecutive reactions. Low temperature procedures involving hydrogen peroxide as the oxidant have been reported. They include hydroxylation over Ti-silicalites TS-1 d TS-2. Perego et al. [1] reported that toluene and phenol could be oxidized at 80 C into a mixture of cresols and dihydroxybenzenes respectively. More recently, Hari Prasad Rao et al. observed that phenol [2] and toluene [3] could also be oxidized over VS-2, the vanadium substituted silicalite-2. 

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