Multiple-Reaction Systems

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. 

Multiple Reactions—Choosing a reactor type to obtain the best selectivity can often be made by inspection of generalized cases in reaction engineering books. A quantitative treatment of selectivity as a function of kinetics and reactor type (batch and CSTR) for various multiple reaction systems (consecutive and parallel) is presented in [168]. 

We next need to describe the rates of transformations of chemical species among each other. For this we use the symbol r for a single reaction and r,- for the ith reaction in a multiple reaction system Reaction rates are basically empirical expressions that describe the dependence of the rate of transformation on the parameters in the system. 

These rates are the rates of production of species A, B, and C (rj = Vjr) so these rates are written as negative quantities for reactants and positive quantities for products. This notation quickly becomes cumbersome for complex reaction stoichiometry, and the notation is not directly usable for multiple reaction systems. 

We also need to describe the rates of multiple-reaction systems. We do this in the same way as for single reactions with each of the i reactions in the set of R reactions being described by a rate r,-, rate coefficient ki, order of the forward reaction with respect to species j, etc. 

For a multiple-reaction system with reversible reactions, we can describe each of the R reactions through a reaction rate r,-,... 

To summarize, we can always find a single concentration variable that describes the change in aU species for a single reaction, and for R simultaneous reactions there must be R independent variables to describe concentration changes. For a single reaction, this problem is simple (use either or X), but for a multiple-reaction system one must set up the notation quite carefully in terms of a suitably chosen set of R concentrations or Xi S-... 

Semibatch reactors are especially important for bioreactions, where one wants to add an enzyme continuously, and for multiple-reaction systems, where one wants to maximize the selectivity to a specific product. For these processes we may want to place one reactant (say, A) in the reactor initially and add another reactant (say, B) continuously. This makes Ca large at all times but keeps Cg small. We will see the value of these concentrations on selectivity and yield in multiple-reaction systems in the next chapter. 

In a variable-density reactor the residence time depends on the conversion (and on the selectivity in a multiple-reaction system). Also, in ary reactor involving gases, the density is also a function of reactor pressure and temperature, even if there is no change in number of moles in the reaction. Therefore, we frequently base reactor performance on the number of moles or mass of reactants processed per unit time, based on the molar or mass flow rates of the feed into the reactor. These feed variables can be kept constant as reactor parameters such as conversion, T, and P are varied. 

In this chapter we consider the performance of isothermal batch and continuous reactors with multiple reactions. Recall that for a single reaction the single differential equation describing the mass balance for batch or PETR was always separable and the algebraic equation for the CSTR was a simple polynomial. In contrast to single-reaction systems, the mathematics of solving for performance rapidly becomes so complex that analytical solutions are not possible. We will first consider simple multiple-reaction systems where analytical solutions are possible. Then we will discuss more complex systems where we can only obtain numerical solutions. 

Before we develop the equations for dealing with multiple-reaction systems, we consider a very important reaction system that is the largest and most important petrochemical process outside the petroleum refinery, the olefins industry. 

In this chapter we consider how we should design chemical reactors when we want to produce a specific product while converting most of the reactant and rninitnizing the production of undesired byproducts. It is clear that in order to design any chemical process, we need to be able to formulate and solve the species mass-balance equations in multiple-reaction systems to determine how we can convert reactants into valuable products efficiently and economically. 

As developed in Chapter 2, for any multiple-reaction system we write the reactions... 

Note that for multiple-reaction systems we can simply substitute 52 v,jr/ for vjr in the mass-balance expressions for a single-reaction mass-balance equation. The difference with multiple reactions is that now we must solve R simultaneous mass-balance equations rather than the single equation we had with a single reaction. 

We have considered several simple examples of multiple reaction systems. While the simplest of these systems have analytical solutions, we rapidly come to situations where only numerical solutions are possible. 

APPROXIMATE RATE EXPRESSIONS FOR MULTIPLE-REACTION SYSTEMS... 

This reaction is actually a multiple-reaction system that involves the major steps... 

Thus our unimolecular isomerization reaction actually occurs by a sequence of steps and is therefore a multiple-reaction system We need a simplified expression for the overall rate of this rate in terms of Ca alone because zl is an intermediate whose concentration is always very small just as for the free-radical intermediates and dimers in the previous examples. 

Most multiple-reaction systems are more comphcated series-parallel sequences with multiple reactants, some species being both reactant and product in different reactions. These simple rules obviously will not work in those situations, and one must usually solve the mass-balance equations to determine the best reactor configuration. 

These considerations are only valid for isothermal reactors, and we shall see in the next two chapters that the possibility of temperature variations in the reactor can lead to much more interesting behavior. We will also see in Chapter 7 that with catalytic reactors the situation becomes even more complicated. However, these simple ideas are useful guides in the choice of a chemical reactor type to carry out multiple-reaction systems. We will stiU use these principles as the chemical reactors become more complicated and additional factors need to be included. 

For conversions with multiple reactions we encounter a problem we have escaped previously. In a multiple-reaction system we need a symbol for the conversion of each reaction and also a symbol for the conversion of each reactant. In Chapter 4 we defined the conversion of a species as Za for reactant A and as Xj for thejth reactant. If we are talking about the conversion of each reaction, we need a symbol such as X for the ith reaction. We should therefore not use Xs for both of these quantities. However, rather than introducing a new variable, we will simply use Xj to specify the conversion of a species and X to indicate the conversion of a reaction. We will not use these quantities enough to make this ambiguity too confusing. 

Multiple reaction systems further complicate our fives. Recall that selectivity issues can dominate reactor performance, and rninirnally we have to solve one equation for each... 

Students may have seen the acetaldehyde decomposition reaction system described as an example of the application of the pseudo steady state (PSS), which is usually covered in courses in chemical kinetics. We dealt with this assumption in Chapter 4 (along with the equilibrium step assumption) in the section on approximate methods for handling multiple reaction systems. In this approximation one tries to approximate a set of reactions by a simpler single reaction by invoking the pseudo steady state on suitable intermediate species. 

In polymerization we play the standard game we use for any multiple-reaction system by writing the mass balance for each species using our standard mass-balance equation for a multiple-reaction system. 

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. 

The recycle reactor is used to control the reaction kinetics of multiple reaction systems. By controlling the concentration present in the reactor, one can shift selectivity toward a more desired product for nonlinear reaction kinetics. 

This tutorial paper begins with a short introduction to multicomponent mass transport in porous media. A theoretical development for application to single and multiple reaction systems is presented. Two example problems are solved. The first example is an effectiveness factor calculation for the water-gas shift reaction over a chromia-promoted iron oxide catalyst. The methods applicable to multiple reaction problems are illustrated by solving a steam reformer problem. The need to develop asymptotic methods for application to multiple reaction problems is apparent in this example. 

For multiple-reaction systems the maximum selectivity for a given product will require operation at a different temperature for each location in the reactor. However, it is rarely of value to find this optimum temperature-vs-position relationship because of the practical difficulty in achieving a specified temperature profile. It is important to be able to predict the general t)q)e of profile that will give the optimum yield, for it may be possible to design the reactor to conform to this general trend. These comments apply equally to batch reactors, w here the temperature-time relationship rather than the temperature-position profile is pertinent. 

A stirred tank may give better or worse selectivities than a tubular-flow unit in multiple-reaction systems. As usual, the key point is the relative values of the activation energies for the reactions. In particular, for a set of parallel reactions, where the desired product is formed by the reaction with the higher activation energy, the stirred tank is advantageous. The production of allyl chloride considered in Example 5-2 is a case in point. The performance of a stirred-tank reactor for this system is discussed next, and the results are compared with the performance of the tubular-flow reactor. 

In Example 5-3 the temperature and conversion leaving the reactor were obtained by simultaneous solution of the mass and energy balances. The results for each temperature in Table 5-7 represented such a solution and corresponded to a diiferent reactor, i.e., a different reactor volume. However, the numerical trial-and-error solution required for this multiple-reaction system hid important features of reactor behavior. Let us therefore reconsider the performance of a stirred-tank reactor for a simple single-reaction system. 

---