Combinations of ideal reactors

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

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

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. 

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. 

The main features of this behavior may be captured by a simple modeling approach based on a proper combination of ideal reactors. The simplest example is... 

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 ... 

Insofar as reactions are carried out in real reactors, it is very important to be able to ascertain that the reactor may be modelled by a single ideal reactor, by a combination of ideal reactors, or by some other model. 

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... 

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... 

Two-Parameter Models—Modeling Real Reactors with Combinations of Ideal Reactors... 

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.

Figure 14-15 Combinations of ideal reactors to model a real CSTR Two CSTTRs with interchange (a) exit from the top CSTR (b) exit firm the bottom CSTR...

If a real reactor is modeled as a combination of ideal reactors, the model should have at most two parameters. 

P14-15p Choose one or more cf the reaction schemes in Figure 14-14and/or Examples 14-2 and 14-3. Use the reactions in one of the examples in Chapter 6 to apply to the these combinations of ideal reactors. Start with ot = 0.5 and p = 0.5 and then vary a and p. 

Modeling real reactors with a combination of ideal reactors is discussed together with axial dispersion in... 

Link types are defined to relate certain entity types of one document to entity types of another. Arbitrary many-to-many relationships are supported. For instance, it can be expressed that a combination of ideal reactor models (CSTR, PFR) and interconnecting streams as well as the aggregated connectors within a SimulationSpec document correspond to a single reactor and its ports represented in a PFD document. Link types are used for two purposes First, they provide a formal notation for a part of the organizational knowledge. Second, they constrain link templates that are defined in the next model. 

As discussed in Section 13.1, the RTD can be used to diagnose problems in existing reactors. As we will see in funher detail in Chapter 14, the RTD functions (/) and (r) can be used to model the real reactor as combinations of ideal reactors,... 

The premise for the two-parameter model is that we can u.se a combination of ideal reactors to model the real reactor. For example, consider a packed bed reactor with channeling. Here the response to a pulse tracer input would show two dispersed pulses in the output as shown in Figure 13-10 and Figure 14-1. 

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