Fogler, Reactores Quimicos

Fogler_ECRE_CDROM.book Page 945 Wednesday, September 17, 2008 5:01 PM

Models for Nonideal Reactors

14

Success is a journey, not a destination. Ben Sweetland

Use the RTD to evaluate parameters

Overview Not all tank reactors are perfectly mixed nor do all tubular reactors exhibit plug-flow behavior. In these situations, some means must be used to allow for deviations from idealbehavior. Chapter 13 showed how the RTD was sufficient if the reaction was first order or if the fluid was either in a state of complete segregation or maximum mixedness. We use the segregation and maximum mixedness models to bound the conversion when no adjustable parameters are used. For non-first-order reactions in a fluid with good micromixing, more than just the RTD is needed. These situations compose agreat majority of reactor analysis problems and cannot be ignored. For example, we may have an existing reactor and want to carry out a new reaction in that reactor. To predict conversions and product distributions for such systems, a model of reactor flow patterns is necessary. To model these patterns, we use combinations and/or modifications of ideal reactors to represent real reactors. With thistechnique, we classify a model as being either a one-parameter model (e.g., tanks-in-series model or dispersion model) or a two-parameter model (e.g., reactor with bypassing and dead volume). The RTD is then used to evaluate the parameter(s) in the model. After completing this chapter, the reader will be able to apply the tanks-in-series model and the dispersion model to tubular reactors. Inaddition, the reader will be able to suggest combinations of ideal reactors to model a real reactor.

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Fogler_ECRE_CDROM.book Page 946 Wednesday, September 17, 2008 5:01 PM

946

Models for Nonideal Reactors

Chap. 14

14.1 Some Guidelines
The overall goal is to use the following equation RTD Data + Kinetics + Model = Prediction
Conflicting goals

A Model Must • Fit the data • Beable to extrapolate theory and experiment • Have realistic parameters

The choice of the particular model to be used depends largely on the engineering judgment of the person carrying out the analysis. It is this person’s job to choose the model that best combines the conflicting goals of mathematical simplicity and physical realism. There is a certain amount of art in the development of a modelfor a particular reactor, and the examples presented here can only point toward a direction that an engineer’s thinking might follow. For a given real reactor, it is not uncommon to use all the models discussed previously to predict conversion and then make a comparison. Usually, the real conversion will be bounded by the model calculations. The following guidelines are suggested when developingmodels for nonideal reactors: 1. The model must be mathematically tractable. The equations used to describe a chemical reactor should be able to be solved without an inordinate expenditure of human or computer time. 2. The model must realistically describe the characteristics of the nonideal reactor. The phenomena occurring in the nonideal reactor must be reasonably described physically, chemically,and mathematically. 3. The model must not have more than two adjustable parameters. This constraint is used because an expression with more than two adjustable parameters can be fitted to a great variety of experimental data, and the modeling process in this circumstance is nothing more than an exercise in curve fitting. The statement “Give me four adjustable parameters and I can fit an elephant;give me five and I can include his tail!” is one that I have heard from many colleagues. Unless one is into modern art, a substantially larger number of adjustable parameters is necessary to draw a reasonable-looking elephant.1 A one-parameter model is, of course, superior to a two-parameter model if the one-parameter model is sufficiently realistic. To be fair, however, in complex systems (e.g.,...