Ideal reactor types

For idealized reactor types there are two opposing factors that influence the overall molecular weight distribution. 

Ridelhoover and Seagrave [57] studied the behaviour of these same reactions in a semi-batch reactor. Here, feed is pumped into the reactor while chemical reaction is occurring. After the reactor is filled, the reaction mixture is assumed to remain at constant volume for a period of time the reactor is then emptied to a specified level and the cycle of operation is repeated. In some respects, this can be regarded as providing mixing effects similcir to those obtained with a recycle reactor. Circumstances could be chosen so that the operational procedure could be characterised by two independent parameters the rate coefficients were specified separately. It was found that, with certain combinations of operational variables, it was possible to obtain yields of B higher than those expected from the ideal reactor types. It was necessary to use numerical procedures to solve the equations derived from material balances. 

Chapter 1 reviews the concepts necessary for treating the problems associated with the design of industrial reactions. These include the essentials of kinetics, thermodynamics, and basic mass, heat and momentum transfer. Ideal reactor types are treated in Chapter 2 and the most important of these are the batch reactor, the tubular reactor and the continuous stirred tank. Reactor stability is considered. Chapter 3 describes the effect of complex homogeneous kinetics on reactor performance. The special case of gas—solid reactions is discussed in Chapter 4 and Chapter 5 deals with other heterogeneous systems namely those involving gas—liquid, liquid—solid and liquid—liquid interfaces. Finally, Chapter 6 considers how real reactors may differ from the ideal reactors considered in earlier chapters. 

The CRE method which leads to Eq. 6 or Eq. 8 fits the measured versus T data from any of the three ideal reactor types, is direct, is less prone to fiddling, and is more reliable. 

The above computation is quite fast. Results for the three ideal reactor types are shown in Table 6.3. The CSTR is clearly out of the running, but the difference between the isothermal and adiabatic PFR is quite small. Any reasonable shell-and-tube design would work. A few large-diameter tubes in parallel would be fine, and the limiting case of one tube would be the best. The results show that a close approach to adiabatic operation would reduce cost. The cost reduction is probably real since the comparison is nearly apples-to-apples. ... 

The rate constants are given by Equation (6.3), and both reactions are endothermic as per Equation (6.4). The flow diagram is identical to that in Figure 6.1, and all cost factors are the same as for the consecutive reaction examples. Table 6.1 also applies, and there is an interior optimum for any of the ideal reactor types. 

The semibatch reactor is a cross between an ordinary batch reactor and a continuous-stirred tank reactor. The reactor has continuous input of reactant through the course of the batch run with no output stream. Another possibility for semibatch operation is continuous withdrawal of product with no addition of reactant. Due to the crossover between the other ideal reactor types, the semibatch uses all of the terms in the general energy and material balances. This results in more complex mathematical expressions. Since the single continuous stream may be either an input or an output, the form of the equations depends upon the particular mode of operation. 

The semibatch reactor is one of the primary ideal reactor types since it can not be accurately described as either a continuous or a batch reactor. A semibatch reactor is usually classified as a type of transient reactor. 

Three ideal reactor types are relevant from reactor theory [15], the two continuous flow types, the plug flow reactor (PFR) and continuous flow stirred tank reactor (CSTR), and the well-stirred batch reactor. The... 

In spite of the differences in construction all reactors suited for kinetic studies can be classified into the three ideal reactor types mentioned above. It is stressed here that kinetic data should be acquired in laboratory reactors that are suited for kinetic studies and should not be a small-scale replica of the reactor intended to be used in practice. 

The classification in Figure 5 serves the description of the reactors used. Here, two ideal contacting types are used, the plug flow mode and the ideally mixed mode, both for the fluid and the solid phase. By appi-cation of the design equations of these ideal reactor types the experimental results are interpreted in a straightforward manner. For two phases, two contacting types and two operation modes (batch and flow) eight combinations arise ... 

P 0 corresponds to the well-mixed reactor, P to plug flow. Solutions of Equation (12) for a selected set of positive finite values of P fills in the region between the two idealized reactor types. Hlavacek and Hoffman performed the necessary numerical calculations for a few selected values of the parameters and presented their results in a set of plots. Since their plots were intended for illustration rather than for quantatative use in design, I have repeated the calculations for a selected set of parameters. 

I have chosen to make the comparison using a zero-order reaction only. Tables I and II indicate that this is conservative for the two ideal reactor types, and it seems plausible to assume that it is also so for real reactors. The degree of conservatism is little more than a few percent in reactor volume. This restriction is thus a useful way to keep the ultimate results in a simple form without compromising their utility. 

The present chapter is not meant to be exhaustive. Rather, an attempt has been made to introduce the reader to the major concepts and tools used by catalytic reaction engineers. In order to give the reader a feel of the applicability of these concepts and tools. Section 8.2 gives an overview of the most important industrial reactors. Section 8.3 is a review of ideal reactor types. Emphasis is placed on the way mathematical model equations are constructed for each reactor category. Basically, this boils down to the application of the conservation laws of mass, energy and possibly momentum. Section 8.4 presents an analysis of the effect of the finite rate at which reaction species and/or heat are supplied to or removed from the locus of reaction, i.e. the catalytic site. Finally, the material developed in Sections 8.3 and 8.4 is applied to the design of laboratory reactors and the analysis of rate data in Section 8.5. 

This article first describes the ideal reactor types, namely batch, plug flow, and completely mixed reactors. Then, the petroleum reactors are discussed based on whether the reaction occurs in the vapor, liquid, or mixed vapor-liquid phase. More specifically, the naphtha-processing reactors are examined first, then gradually moving to heavier hydrocarbons, like kerosene and distillate, that react partially in the liquid and gas phases, and finally ending with a discussion on reactors processing heavy hydrocarbons like petroleum residuum, which reacts completely in the liquid phase. 

The computation is quite fast. Results for the three ideal reactor types are shown in Table... 

Well-defined limits of macro- and micromixing can be obtained in a number of instances, and these serve to define corresponding ideal reactor types. Deviations of mixing from these limits are sometimes termed nonideal flows. Since it is difficult to define a measure for quantities such as the degree of micromixing or, indeed, to make measurements on the hydrodynamic state of the internals of a reactor system, extensive use has been made of models that describe the observable behavior in terms of external measurements. As in any other kind of modeling, these models may not be... 

Consider the series flow combination of a PFR and two CSTRs shown in Figure 8.18a. In terms of the fundamental design equations for these idealized reactor types [(8.2.7) and (8.3.4)], it can be said that... 

The three ideal reactor types and the more complex systems are all to be met in electrochemical technology. There are, however, some additional factors which are only relevant to electrolytic processes and these will be reviewed in the next section, prior to the discussion of cell design. 

Most chemical reactors used in practice can be classified according to some common criteria and assigned to the so-called basic or ideal reactor types. On the basis of the characteristics of ideal reactors, the complex interactions of chemical reaction kinetics, mass, heat, and impulse transport can be discussed in a general way. The behaviors of many actually used reactors approach the ideal types so that their fundamental relationships can be applied at least for a first reactor design. In other cases, the reactor behavior of real systems must be described with the help of models often containing the ideal reactors as individual elements (see Chapter 3). 

In Oiapter 3 the importance of mixing in chemical reactors was indicated with the defmition of two ideal reactor types the plug flow reactor, in which no mixing takes place at all, and the perfectly mixed continuous reactor, with infinite mixing rates. The concept of mixing itself, however, was not analysed. 

The molar balances of the three ideal reactor types, tube reactor, BR, and CSTR, Equations 3.8,3.18, and 3.25, can be written in the following form—provided that only the molar balances of the key components are taken into account ... 

In this section, we will discuss the calculation principles for consecutive reactions, that is, situations in which two or more reactions are coupled in a series. An especially interesting question in this connection is how the reactor should be operated in order to obtain the best possible yield of a reactive intermediate product. The ideal reactor types are compared in this context. As before, the temperature, density, volume, and volumetric flow rate of the reaction mixture are assumed to remain constant. 

The simulation results from the combined reaction scheme (5), in Figure 3.21, illustrate clearly the differences between the ideal reactor types, as well as the effect of the concentration of the composite (parallel) reactant, B, on product distribution. If the amount of B is maintained at a low level (Figure 3.21), a great deal of the intermediate product. 

How can tracer methods help us in solving these two problems We know that reactor performance, as measured by conversion of the limiting reactant or by product selectivity, is a function of kinetics, flow pattern and mixing pattern in the reactor. The flow and mixing phenomena in various reactor geometries are complex, and we are currently unable to characterize them completely (at an economical cost). The only reactors that we know how to design, predict their performance and scale up with confidence, are those that behave as the two ideal reactor types, i.e. the plug flow (PFR) and the continuous flow stirred tank reactor (CSTR). 

It has been shown that various small scale models consisting of idealized reactor types can be used to simulate large scale fermentation processes, with respect to dissolved oxygen inhomogeneities. The reaction kinetic expressions, material balances on substrates, and products have to be formulated and solved in the context of the combined model network. The choice of the model configuration depends on (1) the system that has to be simulated, (2) knowledge of the hydrodynamics of the system, and (3) the equipment available and financial resources. 

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