Ideal Reactors and Reactor Combinations

The ideal flow reactors are the CSTR and the PFR. (This chapter later introduces a third kind of ideal reactor, the segregated CSTR, but it has the same distribution 

The washont fnnction for a CSTR is found from its response to a negative step change in tracer concentration, Equation 15.1  

A CSTR has an exponential distribution of residence times. The corresponding differential distribution can be found from Equation 15.7  

Example 15.1 shows how it can be determined in the time domain as the response to a delta function input. 

Apply a delta function input to a CSTR to determine fit). 

The ideal flow reactors are the CSTR and the PFR. (This chapter later introduces a third kind of ideal reactor, the segregated CSTR, but it has the same distribution of residence times as the regular, perfectly mixed CSTR.) Real reactors sometimes resemble these ideal types or they can be assembled from combinations of the ideal types. 

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Understanding Reactor Flow Patterns As discussed above, a RTD obtained using a nonreactive tracer may not uniquely represent the flow behavior within a reactor. For diagnostic and simulation purposes, however, tracer results may be explained by combining the expected tracer responses of ideal reactors combined in series, in parallel, or both, to provide an RTD that matches the observed reactor response. The most commonly used ideal models for matching an actual RTD are PRF and CSTR models. Figure 19-9 illustrates the responses of CSTRs and PFRs to impulse or step inputs of tracers. 

Computer simulation of the reactor kinetic hydrodynamic and transport characteristics reduces dependence on phenomenological representations and idealized models and provides visual representations of reactor performance. Modem quantitative representations of laminar and turbulent flows are combined with finite difference algorithms and other advanced mathematical methods to solve coupled nonlinear differential equations. The speed and reduced cost of computation, and the increased cost of laboratory experimentation, make the former increasingly usehil. 

Reactor models consisting of series and parallel combinations of ideal reactors... 

This section indicates a few useful generalizations that are pertinent in considerations of isothermal series and parallel combinations of ideal plug flow and stirred tank reactors. 

This expression may be combined with equations 10.1.4 and 10.1.8 in order to analyze the different situations that may arise in operating the various types of ideal reactors. These analyses are the subject of Sections 10.2 to 10.4. 

These levels are illustrated in Figure 1.1. Levels (1) and (2) are domains of kinetics in the sense that attention is focused on reaction (rate, mechanism, etc.), perhaps in conjunction with other rate processes, subject to stoichiometric and equilibrium constraints. At the other extreme, level (3) is the domain of CRE, because, in general, it is at this level that sufficient information about overall behavior is required to make decisions about reactors for, say, commercial production. Notwithstanding these comments, it is possible under certain ideal conditions at level (3) to make the required decisions based on information available only at level (1), or at levels (1) and (2) combined. The concepts relating to these ideal conditions are introduced in Chapter 2, and are used in subsequent chapters dealing with CRE. 

Chapter 17 Comparisons and Combinations of Ideal Reactors This results in ... 

In this chapter, we develop some guidelines regarding choice of reactor and operating conditions for reaction networks of the types introduced in Chapter 5. These involve features of reversible, parallel, and series reactions. We first consider these features separately in turn, and then in some combinations. The necessary aspects of reaction kinetics for these systems are developed in Chapter 5, together with stoichiometric analysis and variables, such as yield and fractional yield or selectivity, describing product distribution. We continue to consider only ideal reactor models and homogeneous or pseudohomogeneous systems. 

Our treatment of Chemical Reaction Engineering begins in Chapters 1 and 2 and continues in Chapters 11-24. After an introduction (Chapter 11) surveying the field, the next five Chapters (12-16) are devoted to performance and design characteristics of four ideal reactor models (batch, CSTR, plug-flow, and laminar-flow), and to the characteristics of various types of ideal flow involved in continuous-flow reactors. Chapter 17 deals with comparisons and combinations of ideal reactors. Chapter 18 deals with ideal reactors for complex (multireaction) systems. Chapters 19 and 20 treat nonideal flow and reactor considerations taking this into account. Chapters 21-24 provide an introduction to reactors for multiphase systems, including fixed-bed catalytic reactors, fluidized-bed reactors, and reactors for gas-solid and gas-liquid reactions. 

RTD functions for combinations of ideal reactors can be constructed (Wen and Fan 1975) based on (1.6) and (1.7). For non-ideal reactors, the RTD function (see example in Fig. 1.4) can be measured experimentally using passive tracers (Levenspiel 1998 Fogler 1999), or extracted numerically from CFD simulations of time-dependent passive scalar mixing. 

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. 

The notions of different combinations of ideal reactors and residence time distributions are essential in analyzing these problems and in suggesting appropriate solutions. We summarize the many applications of chemical reaction engineering in Figure 8-18, which indicates the types of molecules, reactors, and reactors we can handle. 

When a conversion and an RTD are known, a value of k may be estimated by trial and error so the segregated integral is equal to the known value. If a series of conversions are known at several residence times, the order of the reaction that matches the data may be estimated by trial and error. One has to realize, however, that the RTD may change with residence time. Alternatively, for known intrinsic kinetics, a combination of ideal reactors that reasonably match both RTD and performance may be considered. 

Ideal reactors work under very simple limiting conditions, mainly concerning the residence time distribution. The operation of an ideal reactor is essentially controlled by chemical kinetics and thus the kinetic analysis of a chemical reaction is facilitated by the use of such a reactor. Furthermore, most laboratory and industrial reactors operate under conditions very near to ideality or may be modelled by simple combinations of ideal reactors. There are three main types of ideal reactors ... 

The state of mixing in a given reactor can be evaluated by RTD experiments by means of inert tracers, by temperature measurements, by flow visualization and, finally, by studying in the reactor under consideration the kinetics of an otherwise well-known reaction (because its mechanism has been carefully elucidated from experiments carried out in an ideal reactor, the batch reactor being generally chosen as a reference for this purpose). From these experimental results, a reactor model may be deduced. Very often, in the laboratory but also even in industrial practice, the real reactor is not far from ideal or can be modelled successfully by simple combinations of ideal reactors this last approach is of frequent use in chemical reaction engineering. But... 

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 ... 

In addition to the one-parameter models of tanks-in-series and dispersion, many other one-parameter models exist when a combination of ideal reactors is to model the real reactor. For example, if the real reactor were modeled as a PFR and CSTR in series, the parameter would be the fi action,/, of the total reactor volume that behaves as a CSTR Another one-parameter model would be the fi action of fluid that bypasses the ideal reactor. We can dream up many other situations which would alter the behavior of ideal reactors in a way that adequately describes a real reactor. However, it m be that one parameter is not sufficient to yield an adequate comparison between theoiy... 

It can be shown how a real reactor might be modeled by one of two different combinations of ideal reactors. These are but two of an almost unlimited number of combinations that could be made. However, if we limit the number of adjustable parameters to two (e.g., volume of the exchange reactor and exchange flow rate), the situation becomes much more tractable. Once a model has been chosen, what remains is to check to see whether it is a reasonable model and to determine the values of the model s parameters. Usually, the simplest means of obtaining the necessary data is some form of tracer test. These tests have been described in Chapter 13, together with their uses in determining the RTD cf a reactor system. Tracer tests can be used to determine the RTD, which can then be used in a similar manner to determine the suitability of the model and the value of its parameters. 

In the previous model we have attempted to model a real reactor with combinations of ideal reactors. The model had two parameters, a and p. If these parameters are known, we can readily predict the conversion. In the following section we shall see how we can use tracer experiments and RTD data to evaluate the model parameters. 

Figure 14-14 Combinations of ideal reactors used to model real PFRs. (a) two PFRs in parallel (b) PFR and CSTR in parallel.

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