Multiple reactions

Multiple reactions, in series, in parallel, or both, introduce no new concepts. Nature minimizes Gibbs energy, regardless of how many reactions are occurring. As the number or reactions increases, the mathematics and the number of variables to be accounted for increase. 

We consider next systems where more than one reactions take place, which is often the case in gas-phase reactions. The thermodynamic analysis of such systems is straightforward for, as we saw in Section 12.6, each reaction is in equilibrium. Thus for a system involving r reactions, there are r progress of the reaction variables with equilibrium values of ei,C2,. . through which all compositions are expressed. 

Determination thus of the equilibrium conversion requires the calculation of the r values of e, by solving a system of r equations with r unknowns. And this is where the problem lies. The equations are very nonlinear and solution of the resulting system becomes difficult. For r = 2, a trial-and-error or a graphical solution can be easily determined. For r = 3, a graphical solution is possible, but somewhat tedious. If repeated 

We will demonstrate the graphical method for systems involving two and three reactions in the following three Examples. These cover the majority of industrial applications, since systems involving more than three reactions are relatively rare. For the approach that uses Lagrange multipliers, see among others Smith and Van Ness Daubert or Oliver et al (1962). 

One of the most important industrial reactions is the catalytic production of the synthesis gas  

An additional reaction takes place to a significant extent  

In most industrially relevant reacting systems, one main reaction typically makes the desired products and several side reactions make byproducts. The specific rate of production or consumption of a particular component in such a reaction set depends upon the stoichiometry and the rates. For example, assume that the main reaction for making vinyl acetate, Eq. (4.4.1, proceeds with a rate r (mol/L s) and that the side reaction, Eq. (4.8), proceeds with rate r2 (mol/L s). Then the net consumption of ethylene is (-l)r1 - (-1 )r2 (mol/L s). Similarly, the net consumption of oxygen is (-0.5)fi + (— 3)r2, and the net production of water is (l)r-, + (2)ra. For a given chemistry (stoichiometry), our ability to control the production or consumption of any one component in the reactor is thus limited to how well we can influence the various rates. This boils down to manipulating the reactor temperature and/ or the concentrations of the dominant components. Occasionally, the reaction volume for liquid-phase reactions or the pressure for gas-phase reactions can also be manipulated for overall production control. These are the fundamentals of reactor control. 

It is most unusual for only a single desired reaction to occur in a chemical reactor. Nature is typically not that generous and exacts a penalty that takes the form of side reactions generating undesired impurity components. The side reactions can involve other transformations of the reactant species (in parallel with the desired reaction) or further 

They also have a major impact on the design of the entire process. To suppress undesirable side reactions, it is often necessary to operate the reactor with a low concentration of one of the reactants and an excess of other reactants. These must be recovered in a separation section and recycled back to the reaction section. 

In the following, we will discuss the analytical solution of some multiple chemical reaction systems in detail. The terms multiple reactions or composite reactions are usually used in this context. Multiple, simultaneous reactions occur in many industrial processes such as oil refining, polymer production, and, especially, organic synthesis of fine chemicals. It is thus of utmost importance to be able to optimize the reaction conditions, so that the yield of the desired product is maximized and the amounts of by-products are minimized. 

We will observe three main categories of composite reactions and, in addition, try and provide an overview of the treatment of complex reaction systems in general. The temperature and density of the reaction mixture are assumed to remain constant, which implies that the volume and volumetric flow rate should remain at a constant level. The three principal categories of composite reactions are parallel, consecutive, and consecutive-competitive reactions. The following reaction schemes illustrate it better  

Overview. Seldom is the reaction of interest the only one that occurs in a chemical reactor. Typically, multiple reactions will occur, some desired and some undesired. One of the key factors in the economic success of a chem-ical plant is the minimization of undesited side reactions that occur along with the desired reaction. 

In this chapter, we discuss reactor selection and general mole balances for multiple reactions. First, we describe the four baste types of multiple reactions series, parallel, independent, and complex. Next, we define the selectivity parameter and discuss how it can be used to minimize unwanted side reactions by proper choice of operating conditions and reactor selection. We then develop the algorithm that can be used to solve reaction engineering problems when multiple reactions are involved. Finally, a number of examples are given that show how the algorithm is applied to a number of real reactions. 

Reaction mixtures encountered in industrial practice often show complex behavior and the overall reaction rate comprises several individual reactions, forming a multiple reaction scheme. There are two basic reaction schemes allowing the construction of more complex ones [5]. The consecutive reactions are also called reaction in series  

The second basic reaction scheme is competitive reactions, also called reaction in parallel  

In Equations 2.13 and 2.14, the reactions are supposed to be first-order in each compound, but different reaction orders may be encountered. With multiple 

So far we have considered reactor systems where only one reaction is occurring. However, this is seldom the case. Take as an example the partial oxidation reaction over a selective catalyst. Often this reaction is 

We are going to consider two basic types of multiple reactions 

Obviously the reactant concentration decreases with time, exponentially if the reactions are first order, as in the example used in the plot. The concentration of intermediate B will increase in the beginning, as a lot of B is formed from reactant A, whose concentration is still high, but only a little is consumed to C as there is still little B to power this second reaction. As more and more B is formed however, while at the same time less and less A is left, the reaction rate of the second reaction will become greater than that of the first reaction, resulting in a maximum of the intermediate concentration. 

The relative position of the maximum, as well as its value, depends on the ratio of the kinetic constants, i.e. which of the two reactions is faster and by how much. 

In a parallel reaction network of first-order reactions, the selectivity does not depend upon reaction time or residence time, since both products are formed by the same reactant and with the same concentration. The concentration of one of the two products will be higher, but their ratio will be the same during reaction in a batch reactor or at any position in a PFR. The most important parameters for a parallel reaction system are the reaction conditions, such as concentrations and temperature, as well as reactor type. An example is given in the following section. 

If more than one reaction takes place, the rate of each reaction must be known in order to calculate the total rate of formation or consumption of a species. Thus, 

Total rate of formation of i when multiple reactions take place 

Because Czn — cznch and ca— 4c c 2, we can write Equation (E9.15) in terms of the mean activity coefBcient as follows  

When multiple reactions are considered, each reaction has its own corresponding extent of reaction, Thus, we must keep track of the stoichiometry of each species i for each of the k separate chemical reactions. Reaction (9.5) can be written for each separate reaction (1, 2,.. . k. . . R) thus, we must now sum over all of the i species for each of the k reactions. Mathematically, we accomplish this task by using a double sum, as follows  

Similarly, Equation (9.7) must be written for each of the k extents of reaction. Again, the mathematics requires a sum over all R reactions  

Summing over all i species, in, for example, the vapor phase  

Each equilibrium constant can be found by using appropriate thermochemical data, as discussed in Section 9.4. Once values for Ki and K2 are obtained. Equations (E9.16C) and (E9.16D) can be solved for the two unknowns, and 2- It is then straightforward to find the number of moles and mole fractions of the species present 

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Single reactions. Most reaction systems involve multiple reactions. In practice, the secondary reactions can sometimes be neglected, leaving a single primary reaction to consider. Single reactions are of the type... 

Multiple reactions in parallel producing byproducts. Rather than a single reaction, a system may involve secondary reactions producing (additional) byproducts in parallel with the primary reaction. Multiple reactions in parallel are of the tj ie... 

Multiple reactions in series producing byproducts. Rather than... 

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

Multiple reactions also can occur with impurities that enter with the feed and undergo reaction. Again, such reactions should be minimized, but the most efiective means of dealing with byproduct reactions caused by feed impurities is not to alter reactor conditions but to introduce feed purification. 

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 2.2 summarizes these arguments to choose a reactor for systems of multiple reactions in parallel. 

In the preceding section, the choice of reactor type was made on the basis of which gave the most appropriate concentration profile as the reaction progressed in order to minimize volume for single reactions or maximize selectivity for multiple reactions for a given conversion. However, after making the decision to choose one type of reactor or another, there are still important concentration effects to be considered. 

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) ... 

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. 

The choice of reactor temperature depends on many factors. Generally, the higher the rate of reaction, the smaller the reactor volume. Practical upper limits are set by safety considerations, materials-of-construction limitations, or maximum operating temperature for the catalyst. Whether the reaction system involves single or multiple reactions, and whether the reactions are reversible, also affects the choice of reactor temperature, as we shall now discuss. 

The selection of reactor pressure for vapor-phase reversible reactions depends on whether there is a decrease or increase in the number of moles and whether there is a system of single or multiple reactions. 

Multiple reactions producing byproducts. The arguments presented for the effect of pressure on single vapor-phase reactions can be used for the primary reaction when dealing with multiple reactions. Again, selectivity is likely to be more important than reactor volume for a given conversion. 

Most processes are catalyzed where catalysts for the reaction are known. The choice of catalyst is crucially important. Catalysts increase the rate of reaction but are unchanged in quantity and chemical composition at the end of the reaction. If the catalyst is used to accelerate a reversible reaction, it does not by itself alter the position of the equilibrium. When systems of multiple reactions are involved, the catalyst may have different effects on the rates of the different reactions. This allows catalysts to be developed which increase the rate of the desired reactions relative to the undesired reactions. Hence the choice of catalyst can have a major influence on selectivity. 

Because the characteristic of tubular reactors approximates plug-flow, they are used if careful control of residence time is important, as in the case where there are multiple reactions in series. High surface area to volume ratios are possible, which is an advantage if high rates of heat transfer are required. It is sometimes possible to approach isothermal conditions or a predetermined temperature profile by careful design of the heat transfer arrangements. 

Figure 2.10 Choosing the reactor to maximize selectivity for multiple reactions producing byproducts.

Multiple reactions. For multiple reactions in which the byproduct is formed in parallel, the selectivity may increase or decrease as conversion increases. If the byproduct reaction is a higher order than the primary reaction, selectivity increases for increasing reactor conversion. In this case, the same initial setting as single reactions should be used. If the byproduct reaction of the parallel system is a... 

For multiple reactions in which the byproduct is formed in series, the selectivity decreases as conversion increases. In this case, lower conversion than that for single reactions is expected to be appropriate. Again, the best guess at this stage is to set the conversion to 50 percent for irreversible reactions or to 50 percent of the equilibrium conversion for reversible reactions. 

It should be emphasized that these recommendations for the initial settings of the reactor conversion will almost certainly change at a later stage, since reactor conversion is an extremely important optimization variable. When dealing with multiple reactions, selectivity is maximized for the chosen conversion. Thus a reactor type, temperature, pressure, and catalyst are chosen to this end. Figure 2.10 summarizes the basic decisions which must be made to maximize selectivity. ... 

Reactor conversion. In Chap. 2 an initial choice was made of reactor type, operating conditions, and conversion. Only in extreme cases would the reactor be operated close to complete conversion. The initial setting for the conversion varies according to whether there are single reactions or multiple reactions producing byproducts and whether reactions are reversible. 

Recycling byproducts for improved selectivity. In systems of multiple reactions, byproducts are sometimes formed in secondary reactions which are reversible, such as... 

Consider the example of a process that involves the following multiple reactions ... 

Reducing waste from multiple reactions producing waste byproducts. In addition to the losses described above for single reactions, multiple reaction systems lead to further waste through the formation of waste byproducts in secondary reactions. Let us briefly review from Chap. 2 what can be done to minimize byproduct formation. 

The reactivity of size-selected transition-metal cluster ions has been studied witli various types of mass spectrometric teclmiques [1 ]. Fourier-transfonn ion cyclotron resonance (FT-ICR) is a particularly powerful teclmique in which a cluster ion can be stored and cooled before experimentation. Thus, multiple reaction steps can be followed in FT-ICR, in addition to its high sensitivity and mass resolution. Many chemical reaction studies of transition-metal clusters witli simple reactants and hydrocarbons have been carried out using FT-ICR [49, 58]. 

An alternative approach to peptide sequencing uses a dry method in which the whole sequence is obtained from a mass spectrum, thereby obviating the need for multiple reactions. Mass spec-trometrically, a chain of amino acids breaks down predominantly through cleavage of the amide bonds, similar to the result of chemical hydrolysis. From the mass spectrum, identification of the molecular ion, which gives the total molecular mass, followed by examination of the spectrum for characteristic fragment ions representing successive amino acid residues allows the sequence to be read off in the most favorable cases. 

The genome, through its constituent DNAs, provides all of the codes needed for building a wide range of peptides, proteins, and enzymes, which in turn utilize raw materials (food) to form an animate body and keep it going. These multiple reactions work together as a unit within a water-filled cell. 

However, this reaction does not take place in a single step, and multiple reactions must be used. One such route involves using sulfuric acid to decompose the H2SiFg ... 

Generalization of this result to multiple reactions produces... 

Multiple Reactions When a substance participates in several reactions at the same time, its net rate of decomposition is the algebraic sum of its rates in the individual reactions. Identify the rates of the individual steps with subscripts, dC/dt)i, dC/di)9,. Take this case of three reactions,... 

For a single equation, Eqs. (7-36) and (7-37) relate the amounts of the several participants. For multiple reactions, the procedure for finding the concentrations of all participants starts by assuming that the reactions proceed consecutively. Key components are identified. Intermediate concentrations are identified by subscripts. The resulting concentration from a particular reaction is the starting concentration for the next reaction in the series. The final value carries no subscript. After the intermediate concentrations are ehminated algebraically, the compositions of the excess components will be expressible in terms of the key components. 

For multiple reactions, material balances are required for each stoichiometry. 

Sampling of a two-fluid phase system containing powdered catalyst can be problematic and should be considered in the reactor design. In the case of complex reacting systems with multiple reaction paths, it is important that isothermal data are obtained. Also, different activation energies for the various reaction paths will make it difficult to evaluate the rate constants from non-isothermal data. 

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