Reactor models, classification

Table 12.1 Pseudo-homogeneous and heterogeneous reactor model classification...

Before discussing in more detail what reaction models (Sect. 2) and reactor models (Sect. 3) are, some general considerations about the classification of models appear convenient. 

Wave motion similar to that examined in the previous section occurs in other applications of fixed-bed technology. Important among these are processes involving ion exchange or selective adsorption. While these are for the most part separation processes and may or may not include chemical reactions, the analysis is too closely related to what we have been discussing to allow it to pass by now. The nature of the equilibrium between fiuid and solid phases plays a more direct and obvious role than in pseudo-homogeneous reactor models, and provides a convenient means for classification. 

In the following section, a classification of fixed bed reactor models is proposed and a brief description of each model type is reported. 

Even though the model in Table 3.1 results from several assumptions (detailed in Section 3.2.1), it can be considered as quite comprehensive. In fact, what is commonly found in the fitera-ture is a simplified version of this model The well-known classification of fixed-bed reactor models by Froment [51] and Froment and Bischoff [62] clearly exemplifies how a more general model unfolds into a hierarchy of several others with decreasing complexity. The dimensionafity of the model (usually one- or two-dimensional) and the presence of interphase and intraparticular resistances to mass/heat transfer are the main basis for distinguishing between different categories. 

Models for a continuous reactor without recycle will be identical with those developed for the batch reactor. We will therefore confine ourselves to a continuous reactor with recycle. Although the low conversion per pass make the hydrodynamic classification of the reactor of little significance, it will still be convenient to develop the continuous reactor model on the basis of a plug-flow reactor. 

In this chapter we discuss chemical reactor types and show how, despite the variety of reactions and the almost unlimited variety and possibilities for reactor design, only a few equations are needed to describe the reaction progress. Reactor modeling is, therefore, in many cases comparatively straightforward, and is facilitated by the classification into ideal reactors and real reactors. 

A classification of dispersion models for fixed-bed tubular reactors, for example, is given by Froment and Hofmann [2]. For more complex flow patterns more elaborated and complete models are required where the flow fields are described via the solution of the Navier-Stokes equations. The understanding of the complex flow phenomena involved as well as the solution of these vector equations make the problem much more difficult to analyze spending reasonable costs and efforts. The advanced reactor models are discussed in the subsequent chapters, only a brief introduction to the idealized reactor models are presented in this chapter as these models are principal tools for chemical reaction engineers. In particular, the idealized models are easy to calculate, and they give the extreme values of the conversions between which those realized in a real reactor will occur provided there is no bypassing of reactants in the reactor. 

Chapter 7 serves as an introduction for the main issues that need to be considered for modeling hydroprocessing reactors. It provides a comprehensive review of the most important features of the various reactors used for upgrading of heavy feeds, such as characteristics and classification, process variables, and fundamentals. Reactor modeling is exemplified with the hydrotreating of a heavy oil-derived gas oil. 

The second classification is the physical model. Examples are the rigorous modiiles found in chemical-process simulators. In sequential modular simulators, distillation and kinetic reactors are two important examples. Compared to relational models, physical models purport to represent the ac tual material, energy, equilibrium, and rate processes present in the unit. They rarely, however, include any equipment constraints as part of the model. Despite their complexity, adjustable parameters oearing some relation to theoiy (e.g., tray efficiency) are required such that the output is properly related to the input and specifications. These modds provide more accurate predictions of output based on input and specifications. However, the interactions between the model parameters and database parameters compromise the relationships between input and output. The nonlinearities of equipment performance are not included and, consequently, significant extrapolations result in large errors. Despite their greater complexity, they should be considered to be approximate as well. 

Ideal reactors can be classified in various ways, but for our purposes the most convenient method uses the mathematical description of the reactor, as listed in Table 14.1. Each of the reactor types in Table 14.1 can be expressed in terms of integral equations, differential equations, or difference equations. Not all real reactors can fit neatly into the classification in Table 14.1, however. The accuracy and precision of the mathematical description rest not only on the character of the mixing and the heat and mass transfer coefficients in the reactor, but also on the validity and analysis of the experimental data used to model the chemical reactions involved. 

Coal combustion processes can be classified based on process type (see Table 9.1), even though classification based on the particle size, the flame type, the reactor flow type, or the mathematical model complexity is also possible [7]. 

Fluidized reactors are the fifth type of primary reactor configuration. There is some debate as to whether or not the fluidized bed deserves distinction into this classification since operation of the bed can be approximated with combined models of the CSTR and the PFR. However, most models developed for fluidized beds have parameters that do not appear in any of the other primary reactor expressions. 

A theoretical and experimental study of multiplicity and transient axial profiles in adiabatic and non-adiabatic fixed bed tubular reactors has been performed. A classification of possible adiabatic operation is presented and is extended to the nonadiabatic case. The catalytic oxidation of CO occurring on a Pt/alumina catalyst has been used as a model reaction. Unlike the adiabatic operation the speed of the propagating temperature wave in a nonadiabatic bed depends on its axial position. For certain inlet CO concentration multiplicity of temperature fronts have been observed. For a downstream moving wave large fluctuation of the wave velocity, hot spot temperature and exit conversion have been measured. For certain operating conditions erratic behavior of temperature profiles in the reactor has been observed. 

Jensen and Ray (50) have recently tabulated some 25 experimental studies which have demonstrated steady state multiplicity and instabilities in fixed-bed reactors many of these (cf., 29, 51, 52) have noted the importance of using a heterogeneous model in matching experimental results with theoretical predictions. Using a pseudohomogeneous model, Jensen and Ray (50) also present a detailed classification of steady state and dynamic behavior (including bifurcation to periodic solutions) that is possible in tubular reactors. 

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