Other Models for Nonideal Reactors

OTHER MODELS FOR NONIDEAL REACTORS 10.5.1 Moments of Residence Time Distributions... 

Other Models for Nonideal Reactors 433 The material balance on tracer in the bottom zone is... 

Use of the CSTR sequence as a model for nonideal reactors has been criticized on the basis that it lacks certain aspects of physical reality, such as the absence of backward communication between the individual mixing cell units. Such may be the case nonetheless the mathematical simplicity of the approach makes it very attractive, particularly for systems with complex kinetics, nonisothermal effects, or other complicating factors. 

In the quantitative development in Section 24.4 below, we assume the flow to be ideal, but more elaborate models are available for nonideal flow (Chapter 19 see also Kastanek et al., 1993, Chapter 5). Examples of types of tower reactors are illustrated schematically in Figure 24.1, and are discussed more fully below. An important consideration for the efficiency of gas-liquid contact is whether one phase (gas or liquid) is dispersed in the other as a continuous phase, or whether both phases are continuous. This is related to, and may be determined by, features of the overall reaction kinetics, such as rate-determining characteristics of mass transfer and intrinsic reaction. 

By and large we can describe the results of the analysis of distributed parameter systems (i.e., flow reactors other than CSTRs) in terms of the gradients or profiles of concentration and temperature they generate. To a large extent, the analysis we shall pursue for the rest of this chapter is based on the one-dimensional axial dispersion model as used to describe both concentration and temperature fields within the nonideal reactor. The mass and energy conservation equations are coupled to each other through their mutual concern about the rate of reaction and, in fact, we can use this to simplify the mathematical formulation somewhat. Consider the adiabatic axial dispersion model in the steady state. 

The results of the simulation allow us to evaluate the extent of the nonidealities of the simulated operando FTIR reaction cell. A comparison of the simulation results obtained with the CAT-PP and with the ideal PFR model is provided in Figure 3.12, in which the experimental data, the results of the simulation with the ideal reactor mode, and the results of CAT-PP are compared (Corbetta et al, 2014). It is clear that the ideal PFR and the CAT-PP simulations are in good agreement with each other. This proves that the adopted FTIR cell may be described as an ideal reactor or not, thus proving an ex-postvalidation of the hypothesis done by Visconti et al. (2013) to develop a spectrokinetic model for the NOx storage over a representative LNT catalyst on the basis of a set of transient surface and gas-phase experimental data collected in such a cell. 

For further interpretation of stagnancy or bypassing we need a flow model. At that point, however, all information generated loses its generality and becomes model dependent. We will consider nonideal reactor models later after we review some other model independent features of the RTDs. 

In a bubble-column reactor for a gas-liquid reaction, Figure 24.1(e), gas enters the bottom of the vessel, is dispersed as bubbles, and flows upward, countercurrent to the flow of liquid. We assume the gas bubbles are in PF and the liquid is in BMF, although nonideal flow models (Chapter 19) may be used as required. The fluids are not mechanically agitated. The design of the reactor for a specified performance requires, among other things, determination of the height and diameter. 

Conversion in a reactor with nonideal flow can be determined either directly from tracer information or by use of flow models. Let us consider each of these two approaches, both for reactions with rate linear in concentration (the most important example of this case being the first-order reaction) and then for other types of reactions where information in addition to age distributions is needed. 

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... 

These two types of deviations occur simultaneously in actual reactors, but the mathematical models we discuss assume that the residence-time distribution function may be attributed to one or the other of these flow situations. The first class of nonideal flow conditions leads to the segregated flow model of reactor performance. This model may be used with the residence-time distribution function to predict conversion levels accurately for first-order reactions that occur isothermally (see Section 11.2.1). The second... 

The chief weakness of RTD analysis is that from the diagnostic perspective, an RTD study can identify whether the mixing is ideal or nonideal, bnt it is not able to uniquely determine the namre of the nonideality. Many different nonideal flow models can lead to exactly the same tracer response or RTD. The sequence in which a reacting fluid interacts with the nonideal zones in a reactor affects the conversion and yield for all reactions with other than first-order kinetics. This is one limitation of RTD analysis. Another limitation is that RTD analysis is based on the injection of a single tracer feed, whereas real reactors often employ the injection of multiple feed streams. In real reactors the mixing of separate feed streams can have a profound influence on the reaction. A third limitation is that RTD analysis is incapable of providing insight into the nature... 

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