Modelling of reactors

A survey of the mathematical models for typical chemical reactors and reactions shows that several hydrodynamic and transfer coefficients (model parameters) must be known to simulate reactor behaviour. These model parameters are listed in Table 5.4-6 (see also Table 5.4-1 in Section 5.4.1). Regions of interfacial surface area for various gas-liquid reactors are shown in Fig. 5.4-15. Many correlations for transfer coefficients have been published in the literature (see the list of books and review papers at the beginning of this section). The coefficients can be evaluated from those correlations within an average accuracy of about 25%. This is usually sufficient for modelling of chemical reactors. Mathematical models of reactors arc often more sensitive to kinetic parameters. Experimental methods and procedures for parameters estimation are discussed in the subsequent section. 

Different reactor networks can give rise to the same residence time distribution function. For example, a CSTR characterized by a space time Tj followed by a PFR characterized by a space time t2 has an F(t) curve that is identical to that of these two reactors operated in the reverse order. Consequently, the F(t) curve alone is not sufficient, in general, to permit one to determine the conversion in a nonideal reactor. As a result, several mathematical models of reactor performance have been developed to provide estimates of the conversion levels in nonideal reactors. These models vary in their degree of complexity and range of applicability. In this textbook we will confine the discussion to models in which a single parameter is used to characterize the nonideal flow pattern. Multiparameter models have been developed for handling more complex situations (e.g., that which prevails in a fluidized bed reactor), but these are beyond the scope of this textbook. [See Levenspiel (2) and Himmelblau and Bischoff (4).]... 

These two types of deviations occur simultaneously in actual reactors, but the mathematical models we will develop 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... 

The variance approach may also be used to determine n. From Illustration 11.2 the variance of the response data based on dimensionless time is 30609/(374.4)2, or 0.218. From equation 11.1.76 it is evident that n is 4.59. Thus the results of the two approaches are consistent. However, a comparison of the F(t) curves for n = 4 and n = 5 with the experimental data indicates that these approaches do not provide very good representations of the data. For the reactor network in question it is difficult to model the residence time distribution function in terms of a single parameter. This is one of the potential difficulties inherent in using such simple models of reactor behavior. For more advanced methods of modeling residence time effects, consult the review article by Levenspiel and Bischoff (3) and textbooks written by these authors (2, 4). 

In Section 11.1.3.2 we considered a model of reactor performance in which the actual reactor is simulated by a cascade of equal-sized continuous stirred tank reactors operating in series. We indicated how the residence time distribution function can be used to determine the number of tanks that best model the tracer measurement data. Once this parameter has been determined, the techniques discussed in Section 8.3.2 can be used to determine the effluent conversion level. 

The dispersion and stirred tank models of reactor behavior are in essence single parameter models. The literature contains an abundance of more complex multiparameter models. For an introduction to such models, consult the review article by Levenspiel and Bischoff (3) and the texts by these individuals (2, 4). The texts also contain discussions of the means by which residence time distribution curves may be used to diagnose the presence of flow maldistribution and stagnant region effects in operating equipment. 

The design q>roblem can be approached at various levels of sophistication using different mathematical models of the packed bed. In cases of industrial interest, it is not possible to obtain closed form analytical solutions for any but the simplest of models under isothermal operating conditions. However, numerical procedures can be employed to predict effluent compositions on the basis of the various models. In the subsections that follow, we shall consider first the fundamental equations that must be obeyed by all packed bed reactors under various energy transfer constraints, and then discuss some of the simplest models of reactor behavior. These discussions are limited to pseudo steady-state operating conditions (i.e., the catalyst activity is presumed to be essentially constant for times that are long compared to the fluid residence time in the reactor). 

We turn now from a discussion of general principles to specific models of reactor behavior. 

In this work we attempt to measure kinetics data in a time short compared with the response time of the catalyst stoichiometry. An alternative is to measure kinetics in a true steady state, i.e., to increase the line-out time at each reactor condition until hysteresis is eliminated. The resulting apparent reaction orders and activation energies would be appropriate for an industrial mathematical model of reactor behavior. 

Other factors that must be considered in the modeling of reactors, factors that influence the number of equations and their degree of nonlinearity but not their form, are... 

Dynamic Tracer Tests, Reaction Studies, and Modeling of Reactor Performance... 

In this section, an attempt is made to define the mathematical models of reactors encountered both in the laboratory and in industrial practice. Theoretical and practical considerations about reactors can be found in books on chemical kinetics [1—13], chemical reaction engineering [20— 31], or specialized books (see, for example, refs. 35—37 for pyrolysis reactors). 

At the other extreme, it may be argued that the traditional low-dimensional models of reactors (such as the CSTR, PFR, etc.) should be abandoned in favor of the detailed models of these systems and numerical solution of the full convection-diffusion reaction (CDR) equations using computational fluid dynamics (CFD). While this approach is certainly feasible (at least for singlephase systems) due to the recent availability of computational power and tools, it may be computationally prohibitive, especially for multi-phase systems with complex chemistry. It is also not practical when design, control and optimization of the reactor or the process is of main interest. The two main drawbacks/criticisms of this approach are (i) It leads to discrete models of very high dimension that are difficult to incorporate into design and control schemes. 

First, select a reactor arrangement and catalyst configuration. The next step is to select a reactor model for calculating the reaction volume. An exact model of reactor performance must include mass transfer of reactants from the fluid to the catalyst sites within the pellet, chemical reaction, and then mass transfer of products back into the fluid. Table 7.13 lists the steps, and Figure 7.5 illustrates the processes involved. Here, only simple models are of interest to estimate the reaction volvune for a preliminary design. The reaction volume is that volume occupied by the catalyst pellets and the space between them. We must provide additional volume for internals to promote uniform flow and for entrance and exit sections. The total volume is called the reactor volume. After calculating the reactor volume, the next step is to determine the reactor length and diameter. 

Figure 23.2 depicts four models of reactor shape changes in order to study and evaluate the chemical and physical peculiarities of volume- and shape-change modulated kinetics as well as thermod3mamics of bio-related... 

A. The cost of building rigorous models of reactor kinetics and hydraulics that give accurate prediction of byproduct yields is usually not justified. The amount of time available for the project is usually insufficient for such models to be built. 

This model of reactor behavior is illustrated in Example 6-7 by predicting the conversion from Eq. (4-11) for the same conditions as used in Examples 6-5 and 6-6. 

Such goals call not only for a reliable modelling of reactors and an improvement of separation techniques, but also for a fundamental understan ng of the underlying chemical processes. 

The overall description (model) of a reactor is obtained through process synthesis by combining models of reactor hydrodynamics, mass transfer and heat exchange with an appropriate cell (subcellular) or population model ( 1).Description of a population should take into consideration possible dispersed or aggregated (the distinct morphological appearances of a culture pellets, mycelium, flocks, growth on reactor wall in the form of microbial film) forms of population. Biomass support particles are gaining appreciable importance in aerobic (40) as well as in anaerobic processes. 

Model of Reactor Performance for the Production of Semi-Synthetic -Lactam Antibiotics... 

Mathematical models of reactor kinetics are used to describe the concentration distributions of various reactants, intermediates and products within the reactor during the course of the reaction. In order to validate these models, concentration distributions must be measured. However, as these chemical reactions, under real process conditions, generally occur within metal reactors enclosed by a heating or pressure mantle, it is not... 

The most important feature of a CSTR is its mixing characteristics. The idealized model of reactor performance presumes that the reactor contents are perfectly mixed so that the properties of the reacting fluid are uniform throughout. The composition and temperature of the effluent are thus identical with those of the reactor contents. This feature greatly simplifies the analysis of stirred-tank reactors vis-h-vis tubular reactors for both isothermal and nonisothermal... 

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