Reaction parallel

Parallel reactions have to be distinguished from the consecutive ones. Parallel reactions of the simplest type are those in which the same reactant A can react in two or more independent ways to form the same or different reaction products 

Denoting the rate constants of parallel reactions by kj and kg, the kinetic equations for uni- and bimolecular reactions are 

Consider elementary reactions A— B and A——— C. The rate equations for these reactions for a constant volume batch system (i.e., constant density) are 

Rearranging and integrating Equation 3-95 between the limits with the boundary conditions at time t = 0, CA = CAO, CB = CBO, Cc = Cco, gives  

If -In CA/CAO or -In (1 - XA) is plotted against time t, the slope of the line is (kx + k. Also, dividing Equation 3-96 by Equation 3-97 gives 

An example of parallel reactions involves the two modes of decomposition of an alcohol  

Generally, these occur simultaneously. The relative amount of ethylene and acetaldehyde obtained therefore depends on the relative speed of the two reactions competing with each other for the available alcohol. These speeds, in turn, are determined by the choice of catalyst and temperature. 

In the real world, several reactions usually occur at the same time. In this case, we must write the various reactions as separate, independent reactions. So, for example, in the case of combustion, carbon monoxide can be produced through incomplete combustion of a fuel. In order to describe the production of both CO and CO, we write each reaction separately  

By controlling the rate of formation of the desired product relative to the rate of formation of the undesired product, we control the selectivity of the reaction and the amount of waste produced. 

Consider the following reaction between nitrogen dioxide and fluorine  

In the first 10.0 seconds of the reaction, the concentration of fluorine dropped from O.IOM to 0.082M. 

The amount of NO can now be obtained by a second application of this equation, except now where the extent of reaction is known and the change in NO concentration is the unknown  

The preceding chapter on single reactions showed that the performance (size) of a reactor was influenced by the pattern of flow within the vessel. In this and the next chapter, we extend the discussion to multiple reactions and show that for these, both the size requirement and the distribution of reaction products are affected by the pattern of flow within the vessel. We may recall at this point that the distinction between a single reaction and multiple reactions is that the single reaction requires only one rate expression to describe its kinetic behavior whereas multiple reactions require more than one rate expression. 

Since multiple reactions are so varied in type and seem to have so little in common, we may despair of finding general guiding principles for design. Fortunately, this is not so because many multiple reactions can be considered to be combinations of two primary types parallel reactions and series reactions. 

In this chapter we treat parallel reactions. In the next chapter we treat series reactions as well as all sorts of series-parallel combinations. 

Let us consider the general approach and nomenclature. First of all, we find it more convenient to deal with concentrations rather than conversions. Second, in examining product distribution the procedure is to eliminate the time variable by dividing one rate equation by another. We end up then with equations relating the rates of change of certain components with respect to other components of the systems. Such relationships are relatively easy to treat. Thus, we use two distinct analyses, one for determination of reactor size and the other for the study of product distribution. 

The two requirements, small reactor size and maximization of desired product, may run counter to each other. In such a situation an economic analysis will yield the best compromise. In general, however, product distribution controls consequently, this chapter concerns primarily optimization with respect to product distribution, a factor which plays no role in single reactions. 

A species may participate in a number of reactions simultaneously. In the simplest case, we may have 

If the kinetic orders of these reactions are b and c, respectively, then 

If b — c, the relative production rates for B and C will depend on the rate coefficients only. Improvements in the relative yield of B can now be achieved only by changing the reaction temperature or by using a catalyst. The reactor flow pattern will not affect the product distribution but it wiU affect the conversion of A. In a constant-volume batch reactor, if 

When more than one reactant is involved, the relative yields of reaction products will depend on a greater number of variables. Then it is not usually possible to deduce the best operating strategy by simple inspection of the reaction scheme. Under these circumstances, it is worthwhile developing a formalised procedure for choosing the best reactor and operating conditions. Reaction selectivity is discussed in more detail below. 

In many reaction processes, the desired product, B, may participate in subsequent reactions. For example 

Readers might have noticed that the two chain reactions, (i) Reactions 2-121 and 2-122 and (ii) Reactions 2-116 and 2-117, are similar, but were treated differently. Reactions 2-116 and 2-117 were treated using the quasi-equilibrium assumption, but may also be treated using the steady-state concept. The result is a more complicated expression, which would reduce to the experimental reaction rate law if ii6b- Readers can work this problem out as an exercise. Therefore, the 

Some net (overall) reactions may be accomplished by several paths, with each path leading to the same end result. Such reactions are called parallel reactions. In a parallel reaction, the overall reaction rate is the sum of all paths  

In treating parallel reaction, two concepts are often used (i) the concept of rate-determining path, in which the fastest path is the rate-determining path, and (ii) the concept of steady state, also called the concept of quasi-stationary states of trace-level intermediates. 

One example of parallel reactions is the electron transfer between Fe + and Fe + in an aqueous solution. One path is through Reaction 2-31  

The forward reaction rate constant is k3if=k3ib = 0.87 M s (Table 1-la) for the above reaction, and the backward reaction rate constant is about the same (isotopic fractionation between Fe + and Fe + is very small). 

A reaction network for a set of reactions occurring in parallel with respect to species A may be represented by 

The product distribution is governed by the relative rates at which these steps occur. For example, if the rale laws for the first two steps aie given by 

The product distribution depends on the factors (cA,. . . , T) that govern this ratio, and the design and operation of a reactor is influenced by the requirement for a favorable distribution. 

From the point of view of kinetics, we illustrate here how values of the rate constants may be experimentally determined, and then used to calculate such quantities as fractional conversion and yields. 

In other words, if we follow reaction with respect to A, we can obtain the sum of the rate constants, but not their individual values. 

In this example, three reactions, originating from a common reactant. A, are taking place. Any number of reactions may occur in parallel. Moreover, it is not necessary that there be only one reactant. For example. 

The top reaction, between carbon monoxide and hydrogen to form methanol, is the basis for all conunercial methanol synthesis plants, and is desirable. This reaction is carried out using a heterogeneous catalyst containing copper and zinc oxide, and is quite reversible at conunercial reaction conditions. The bottom, undesirable reaction is referred to as methanation. It is relatively slow with today s methanol synthesis processes and catalysts. However, methanation can be important if die catalyst becomes contaminated with elements such as nickel and iron, which catalyze the methanation reaction. 

Anoth important example of parallel reactions is die selective catalytic oxidation of CO in the presence of H2  

The top reaction is desirable since the objective of this process is to oxidize a relatively low concentration of CO in the presence of a high concentration of H2, with little or no consumption of Hz. Therefore, the bottom reaction is undesirable.  

Designing a catalyst for the selective oxidation of CO in the presence of high concentrations of Hz is a major scientific challenge. Nevratheless, the selective catalytic oxidation of CO has been used to increase the production rate of existing ammonia synthesis plants. This reaction network also is a critical element in the developing technology for Hz-powered fuel cells. In this context, the process is referred to as PROX (preferential oxidation). 

The rate equations for simultaneous coupled reactions are constructed by combining terms of the type (1.2.1-1). For simple first order parallel reactions 

With coupled reactions it is of interest to express how selective A has been converted into one of the products, e.g., Q. This is done by means of the selectivity, preferably defined in moles of Q produced per mole of A converted. The differential, point or instantaneous selectivity at a given time, q, can be written  

The overall or global selectivity over the time span 0-f during which the reacting species were in contact is obtained after integration. It is generally different from the instantaneous value, but in the particular case of parallel reactions with the same order the two are identical  

In terms of conversions the selectivity should be phrased as the fraction of A converted into Q — not the conversion of  

With complex processes like thermal cracking of a mixture of hydrocarbons to produce ethylene, use is often made of the yield of a component Q. This is usually defined in terms of weight kg of Q produced per 100 kg of A fed (not converted ). 

If reagent participates in several elementary stages simultaneously, then such reaction is called parallel. Parallel reactions are probably the most common in practice, especially in organic synthesis. Kinetic scheme of parallel reaction with two elementary stages of first order and two final products  

Substitution this ration into second and third equations of the set allows to obtain integrated forms of kinetic correlations for reaction s products (Fig. 1.16)  

for example, substance 5 is a target product, then we can define its yield without awaiting for the end of the process. 

This conclusion, however, should not be extended on the parallel reactions, in which products are already present in reactionary mixture at zero time, which corresponds to the set of entry conditions Ca 0) = Ca, C g(0)=Cg , Cc(0) = Cco- In this case a technique of excluding time as an independent variable could be properly applied to find integrated forms of kinetic equations. 

we can express current concentration of product B through current concentration of substance C  

An important application arising from a knowledge of reversible electrode potentials is the assessment of possible parallel side reactions. In typical 

EXAMPLE 2.10. Parallel Reactions of Metal Deposition and Hydrogen Evolution 

THE PROBLEM Determine appropriate conditions of pH and concentration of cobalt which favor its deposition from an aqueous solution of cobalt sulfate. 

Although cobalt deposition proceeds via a complex reaction path involving deposition and discharge of hydroxide species, for this example we shall assume two reactions occurring at the cathode, namely  

The standard equilibrium potential for cobalt deposition Eqo can be taken as —0.277 V. 

The first reaction type is when the reactants form, not just the desired products, but also other undesired products in parallel with the main reaction. We want to show here the implications of parallel reactions, so we consider a simple batch isothermal reactor at constant volume  

Assuming first-order kinetics, we can express the change with time in the concentrations of reactant A (CA) and products B (Cb) and C (Cq)  

The kinetic rate constants are kg and kc. We can analytically solve these differential equations, assuming that we start at time zero with only reactant A (CA0)  

One aspect of optimizing the operation of a batch reactor is establishing the temperature such that the selectivity is as high as possible. If the activation energies of the two reactions are different, changing temperature shifts the ratio of the rates. 

If the chemistry involves two reactants, selectivity is affected by the concentrations of the reactants. For example, supposed that there are two parallel reactions in which C is the desired product and D is the undesired product  

Parallel reaetions often have meehanisms of different reaetion order. An example is the solvolysis reaetions in the presenee of added nueleophiles  

The major factors determining the rate of the anodic partial reaction are pH and additives. Since OH- ions are reactants in the charge-transfer step, for example, Eq. (59), the effect of pH is direct and significant (e.g. see Ref. 55). Additives may have an inhibiting or an accelerating effect. 

The transport equations for the five chemical species have the form 

Note that the rank of the reaction coefficient matrix in this case is again two. 

The usual initial and inlet conditions for binary mixing with parallel reactions are 

the relative amounts of the products R and S produced by the system will depend on the relative magnitudes of k, k2, and the rate of micromixing between the two inlet streams. 

The parallel reaction system can be written in terms of two reaction-progress variables (Ti, Y2) and the mixture fraction f. A linear relationship between c and (co, Y, f) can be derived starting from (5.162) with y1 = A0B0/(A0 + Bo) and y2 = A0Cq/(Ao + Co)  

In this section, we discuss various means of minimizing the undesired product. U. through the selection of reactor type and conditions. We also discuss the development of efficient reactor schemes. 

The rate of disappearance of A for this reaction. sequence is the sum of the rates of formation of U and D  

In this section, we examine ways to maximize the instantaneous selectivity. Son , for different reaction orders of the desired and undesired product..  

Case 1 a, For the case where the reaction order of the desired product is greater than the reaction order of the undesired product, let a be a positive number that is the difference between these reaction orders (o 0)  

upon substitution into Equation (6-10). we obtain 

The rank of the matrix v is equal to the number of the degrees of advancement in the following mechanisms. Therefore one would expect that the conditions of equal number of r and rank of the matrix stated at the beginning of Section 2.1.4 is sufficient for the optimal reduced matrix. 

One realises that in both the reactions the same dependence on the concentrations exists. If the concentrations a and b are chosen to be independent, eq. (2.6) will become explicitly 

By this means one obtains the non-trivial balance-equations Ab - Aa and Ac = -Aa - Ad. 

Both the degrees of advancement show a linear dependence for kineti-cal reasons. A comparison of the rates in the last column of the scheme makes it evident that 

Taking into account that the degrees of advancement are zero at t = 0 (a general rule in kinetics), integration of the above equation gives 

Consider that Pi and Pi are the final products and that the constants ki, ki are unknown. 

By making dimensionless, dividing and integrating Equations 6.56 and 6.57, we obtain  

To determine k, we can use Equation 6.59 from the product concentrations 2 substituting when the time t — oo, and therefore, cpA = 0. 

We can then determine the concentration of B2, substituting Equation 6.60 into Equation 6.59 and into Equation 6.56. After integration, we have  

With this relation, we can express the above equation as a function of ppi. Considering 9 = k t and knowing the concentration of the prodncts Pi and P2, we can determine ki. The constant k can be determined by Equation 6.61. 

Rale laws tor formaliun of desired and undcsired products 

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An example of a parallel reaction system occurs in the production of ethylene oxide ... 

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

Consider the system of parallel reactions from Eq. (2.4) with the corresponding rate equations. " ... 

Multiple reactions in parallel producing byproducts. Consider again the system of parallel reactions from Eqs. (2.16) and (2.17). A batch or plug-flow reactor maintains higher average concentrations of feed (Cfeed) than a continuous well-mixed reactor, in which the incoming feed is instantly diluted by the PRODUCT and... 

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 parallel producing byproducts. Once the reactor type is chosen to maximize selectivity, we are in a position to alter selectivity further in parallel reaction systems. Consider the parallel reaction system from Eq. (2.20). To maximize selectivity for this system, we minimize the ratio given by Eq. (2.21) ... 

An example of such recychng in a parallel reaction system is in the Oxo process for the production of C4 alcohols. Propylene and synthesis gas (a mixture of carbon monoxide and hydrogen) are first reacted to ra- and isobutyraldehydes using a cobalt-based catalyst. Two parallel reactions occur ... 

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. 

Figure 3-2. Two reaction equations showing two completely different uses for the (+) symbol a) giving a fully balanced single reaction, b) combining two parallel reactions into a single equation that is not stoichiometrically balanced.

Acetaldehyde oxidation generates peroxyacetic acid which then reacts with more acetaldehyde to yield acetaldehyde monoperoxyacetate [7416-48-0], the Loesch ester (26). Subsequently, parallel reactions lead to formation of acetic acid and anhydride plus water. 

Step 4 of the thermal treatment process (see Fig. 2) involves desorption, pyrolysis, and char formation. Much Hterature exists on the pyrolysis of coal (qv) and on different pyrolysis models for coal. These models are useful starting points for describing pyrolysis in kilns. For example, the devolatilization of coal is frequently modeled as competing chemical reactions (24). Another approach for modeling devolatilization uses a set of independent, first-order parallel reactions represented by a Gaussian distribution of activation energies (25). 

The abihty of a four-parameter, two-parallel reaction model to correlate pilot-scale rotary kiln, toluene-desorption results (26) is shown in Figure 6. The model assumes that the adsorbed toluene consists of two fractions, T and F, which are tightly and loosely bound, respectively. 

Sulfites. The Hterature concerning dialkyl sulfites is extensive, although less than for sulfates. Reactions involving alkylation are similar to those of sulfates. Sulfites also undergo elimination, transesterification, and isomerization. The last two parallel reactions of phosphites. 

The exploration of the chemistry of azirines has led to the discovery of several pyrrole syntheses. From a mechanistic viewpoint the simplest is based upon their ability to behave as a-amino ketone equivalents in reactions analogous to the Knorr pyrrole synthesis cf. Section 3.03.3.2.2), as illustrated in Schemes 91a and 91b for reactions with carbanions. Parallel reactions with enamines or a-keto phosphorus ylides can be effected with electron-deficient 2//-azirines (Scheme 91c). Conversely, electron-rich azirines react with electron deficient alkynes (Scheme 91d). 

In the case of parallel reactions, the fastest reaction will set or control the overall change. In all rate determining cases, the relative speed of the reactions will change with the temperature. This is caused by different energies of activation among the steps in the sequence. This is just one more reason for limiting rate predictions from measurements within the studied domain to avoid extrapolation. 

The reaction mechanism depends on the chemistry of the active oxidant and chemical contaminants. Multiple sequential and parallel reaction steps occur frequently. Partial oxidation produces noxious byproducts. 

A semi-batch reactor has the same disadvantages as the batch reactor. However, it has the advantages of good temperature control and the capability of minimizing unwanted side reactions by maintaining a low concentration of one of the reactants. Semi-batch reactors are also of value when parallel reactions of different orders occur, where it may be more profitable to use semi-batch rather than batch operations. In many applications semi-batch reactors involve a substantial increase in the volume of reaction mixture during a processing cycle (i.e., emulsion polymerization). 

The following details mathematical expressions for instantaneous (point or local) or overall (integral) selectivity in series and parallel reactions at constant density and isotliermal conditions. An instantaneous selectivity is defined as the ratio of the rate of formation of one product relative to the rate of formation of another product at any point in the system. The overall selectivity is the ratio of the amount of one product formed to the amount of some other product formed in the same period of time. 

Similarly, for a parallel reaction, in which all the steps are of the same order... 

Tipnis, S. K., Penny, W. R., and Fasano, J. B., An experimental investigation to determine a scale-up method for fast competitive parallel reactions in agitated vessels, AIChE Annual Meeting, St. Louis, November 1993. 

Bourne, J.R. and Yu, S., 1994. Investigation of micromixing in stirred tank reactors using parallel reactions. Industrial and Engineering Chemistry Research, 33, 41-55. 

When potassium fluoride is combined with a variety of quaternary ammonium salts its reaction rate is accelerated and the overall yields of a vanety of halogen displacements are improved [57, p 112ff. Variables like catalyst type and moisture content of the alkali metal fluoride need to be optimized. In addition, the maximum yield is a function of two parallel reactions direct fluorination and catalyst decomposition due to its low thermal stability in the presence of fluoride ion [5,8, 59, 60] One example is trimethylsilyl fluoride, which can be prepared from the chloride by using either 18-crown-6 (Procedure 3, p 192) or Aliquot 336 in wet chlorobenzene, as illustrated in equation 35 [61],... 

Parallel reactions of the Schemes VI and VII type have attracted much interest because of their analytical utility. If a mixture of two or three reactants can be arranged to undergo parallel reactions, with appropriate rate constant ratios, it may be possible to determine the composition of the initial mixture. Brown and Fletcher introduced the extrapolation technique discussed above for this purpose, and many modifications of the approach have since been made. ... 

Change of reaction conditions to minimize kinetic complications. For example, if two parallel reactions have substantially different activation energies, their relative rates will depend upon the temperature. The reaction solvent, pH, and concentrations are other experimental variables that may be manipulated for this purpose. 

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