Applications to Nonideal Reactors

U overall heat transfer coefficient [J m-2 K 1 s 1] v characteristic velocity [ms 1] 

Caccavale et at., Control and Monitoring of Chemical Batch Reactors, Advances in Industrial Control, 

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Interpretation of tracer data by means of residence time theory, in the extremes of complete and minimum segregation, has been reviewed and extended to treat transient response under reacting conditions. While residence time theory was initially developed for industrial application to nonideal steady state reactors, its transient extension seems especially well suited for describing segments of natural flows which are too complex to interpret using simpler models, such as dispersion. 

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).]... 

V. Application of Nonideal Patterns of Flow to Chemical Reactors. 171... 

In Chaps. 5 and 6 model-based control and early diagnosis of faults for ideal batch reactors have been considered. A detailed kinetic network and a correspondingly complex rate of heat production have been included in the mathematical model, in order to simulate a realistic application however, the reactor was described by simple ideal mathematical models, as developed in Chap. 2. In fact, real chemical reactors differ from ideal ones because of two main causes of nonideal behavior, namely the nonideal mixing of the reactor contents and the presence of multiphase systems. 

DPMs can also be used to understand the influence of particle properties on fluidization behavior. It has been demonstrated that ideal particles with restitution coefficient of unity and zero coefficient of friction, lead to entirely different fluidization behavior than that observed with non-ideal particles. Simulation results of gas-solid flow in a riser reactor reported by Hoomans (2000) for ideal and nonideal particles are shown in Fig. 12.8. The well-known core-annulus flow structure can be observed only in the simulation with non-ideal particles. These comments are also applicable to simulations of bubbling beds. With ideal collision parameters, bubbling was not observed, contrary to the experimental evidence. Simulations with soft-sphere models with ideal particles also indicate that no bubbling is observed for fluidization of ideal particles (Hoomans, 2000). Apart from the particle characteristics, particle size distribution may also affect simulation results. For example, results of bubble formation simulations of Hoomans (2000) indicate that accounting... 

The similarity of the behavior of the sequence of a large number of CSTRs to that of a PFR has important applications in the modeling of nonideal reactors, since from the illustration above it is apparent that for 1 < < oo we have obtained a conversion result corresponding to something intermediate between the ideal Umits of the single CSTR and the PFR. However, since the example we have given is a very specific one and since this type of modeling is sufficiently important to be the topic of a subsequent section, we will not pursue the matter further at this point. 

The log-normal distribution has been employed as an appropriate model in a wide variety of situations from nonideal reactor studies to environmental management to biology to economics. Additional applications include the distributions of personal incomes, inheritances, bank deposits, and also the distribution of organism growth subject to many small concentrations of impurities. Perhaps the primary application of the log-normal distribution has been to represent the distribution for particle sizes in gaseous emissions from many industrial processes. ... 

We deliberately separate the treatment of characterization of ideal flow (Chapter 13) and of nonideal flow (Chapter 19) from the treatment of reactors involving such flow. This is because (1) the characterization can be applied to situations other than those involving chemical reactors and (2) it is useful to have the characterization complete in the two locations so that it can be drawn on for whatever reactor application ensues in Chapters 14-18 and 20-24. We also incorporate nonisothermal behavior in the discussion of each reactor type as it is introduced, rather than treat this behavior separately for various reactor types. 

First, different typologies of nonideal batch reactors are considered. In particular gas-liquid reactors are discussed, which may be used for different industrial applications (e.g., reactions of oxidation) and are often encountered in the case of gassy reactions (i.e., liquid-phase reactions which do not produce significant thermal effects but in which the production of gaseous products may lead to explosions). 

Obviously, many such combinations can be assembled and the intelligent application of a given combined model to interpretation of nonideal flows in a particular reactor must rely on additional information concerning geometric properties such as stirrer placement, feed inlet and product withdrawal placement, corners or internal structural elements leading to dead volumes, and so on. A certain amount of intuition is also a useful commodity in each modeling. ... 

The reader may very well wonder what happened to the chemical reaction, since we have mostly discussed mixing models in this chapter without reference to reaction. In review of the various approaches to modeling nonideal flow effects on reactor performance, however, we find that in fact a number of these have already been treated, although perhaps with different applications in mind. The classes of reactor models we have treated are... 

The problem of nonideal flow is directly related to scale-up. For example, there is no reason to pilot-plant if the reactor operates in an ideal mode. However, the magnitude or degree of (he nonideality of flow can significantly impact design and performance equations. This effect should not be ignored by the practicing engineer in some applications it is discussed in mote detail in a later section. 

At present, computational fluid dynamics methods are finding many new and diverse applications in bioengineering and biomimetics. For example, CFD techniques can be used to predict (1) velocity and stress distribution maps in complex reactor performance studies as well as in vascular and bronchial models (2) strength of adhesion and dynamics of detachment for mammalian cells (3) transport properties for nonhomogeneous materials and nonideal interfaces (4) multicomponent diffusion rates using the Maxwell-Stefan transport model, as opposed to the limited traditional Fickian approach. 

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