Reactors for Multiple Reactions

COMPARISON OF BATCH, TUBULAR AND STIRRED-TANK REACTORS FOR MULTIPLE REACTIONS. REACTOR YIELD... 

General Expression for a Semibatch Reactor for Multiple Reactions with Inflow of Liquid and Outflow of Liquid and Vapor Scheme 4... 

Reactors for multiple reactions (series or parallel reactions) are designed to achieve maximum yield or selectivity of desired products (Section 2.1.8). Consider a series reaction... 

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. 

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... 

A batch or plug-flow reactor should be used for multiple reactions in series. 

The key to optimum design for multiple reactions is proper contacting and proper flow pattern of fluids within the reactor. These requirements are determined by the stoichiometry and observed kinetics. Usually qualitative reasoning alone can already determine the correct contacting scheme. This is discussed further in Chapter 10. However, to determine the actual equipment size requires quantitative considerations. 

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 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. 

For a batch reactor with multiple reactions the mass-balance equation on species j is... 

For multiple reactions we are not only interested in the conversion but also the selectivity to form a desired product and the yield of that product. In fact, selectivity is fiequently much more important than conversion because we can always increase the conversion by using a larger reactor, a lower flow rate, or a higher temperature, but poor selectivity necessarily requires consumption (loss) of more reactant for a given amount of desired product, and separation of reactants and products and disposal costs increase markedly as the amount of undesired product increases. 

It is evident that for multiple reactions with variable density, we rapidly arrive at rather complex expressions that require considerable manipulation even to formulate the expressions, which can be used to calculate numerical values of the reactor volume required for a given conversion and selectivity to a desired product. 

It is worthwhile to compare the conversion obtained in an isothermal plug flow reactor with that obtained in a CSTR for given reaction kinetics. A fair comparison is given in Fig. 7.3 for irreversible first-order kinetics by showing the conversion obtained in both reactors as a function of To- The conversion of A obtained in a plug flow reactor is higher than that obtained in a CSTR. This holds for every positive partial reaction order with respect to A. For multiple reactions selectivities and yield enter into the picture. 

The mathematical model for the plug flow reactor with multiple reactions... 

The behaviour of the trajectories - the relation between the reactor temperature and the conversion XA of the reactant - has been analysed extensively by us [16,17,18,19] for multiple reactions. 

There are a number of instances when it is much more convenient to work in terms of the number of moles (iV, N-g) or molar flow rates (Fj, Fg, etc.) rather than conversion. Membrane reactors and multiple reactions taking place in the gas phase are two such cases where molar flow rates rather than conversion are preferred. In Section 3.4 we de.scribed how we can express concentrations in terms of the molar flow rates of the reacting species rather than conversion, We will develop our algorithm using concentrations (liquids) and molar flow rates (gas) as our dependent variables. The main difference is that when conversion is used as our variable to relate one species concentration to that of another species concentration, we needed to write a mole balance on only one species, our basis of calculation. When molar flow rates and concentrations are used as our variables, we must write a mole balance on each species and then relate the mole balances to one another through the relative rates of reaction for... 

In this chapter we discuss reactor selection and general mole balances for multiple reactions. There are three basic types of multiple reactions series, parallel, and independent. In parallel reactions (also called competing reactions) the reactant is consumed by two different reaction pathways to form different products ... 

Selectivity, reactor schemes, and staging for multiple reactions, together with evaluation of the corresponding design equations, are presented in... 

Use this form for multiple reactions and manbrane reactors... 

For multiple reactions occurring in either a semibatch or batch reactor, Equation (9-18) can be generalized in the same manner as the steady-state energy balance, to give... 

Tanks-in-Series Model Versus Dispersion Model. We have seen that we can apply both of these one-parameter models to tubular reactors using the variance of the RTD. For first-order reactions the two models can be applied with equal ease. However, the tanks-in-series model is mathematically easier to use to obtain the effluent concentration and conversion for reaction orders other than one and for multiple reactions. However, we need to ask what would be the accuracy of using the tanks-in-series model over the dispersion model. These two models are equivalent when the Peclet-Bodenstein number is related to the number of tanks in series, n, by the equation ... 

The continuity equation for each ideal model reactor yields for multiple reactions (60, 61)... 

The results of Sections VI,B and C for multiple reactions still hold for flow reactors. The selectivity function [Eqs. (67), (69), or (71)] apply exactly to an ideal MER, within the reactor and at its exit. For an ideal CER, the same equations give the local selectivity along the reactor (60-62). The choice of suitable electrochemical reactors for parallel steps depends then on the reaction order of the desirable path with respect to the reactant. Although the surface and volume requirements of a MER are larger than those of a CER, the former would favor a low-order path. An economic trade-off exists, therefore, between reactor costs, subsequent separations of unwanted products, and waste of raw reactants. 

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. 

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