Nonideal Flow Patterns

TABLE 17.3. Some Isothermal Rate Equations and Their Integrals 

The reaction VgA + VbB VrR + VsS between ideal gases at constant Tand P 

Equations readily solvable by Laplace transforms. For example  

Inversion of the transforms can be made to find the concentrations A, B, and C as functions of the time f. Many such examples are solved by Rodiguin and Rodiguina, 1964). 

In many instances the heat transfer aspect of a reactor is paramount. Many different modes have been and are being employed, a few of which are illustrated in Section 17.6. The design of such equipment is based on material and energy balances that incorporate rates and heats of reaction together with heat transfer coefficients. Solution of these balances relates the time, composition, temperature, and rate of heat transfer. Such balances are presented in Tables 17.4—17.7 for four processes  

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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).]... 

Figure 11.1 Nonideal flow patterns which may exist in process equipment.

All patterns of flow other than plug and backmix flow may be called nonideal flow patterns because for these the design methods are not nearly as straightforward as those for the two ideal flow patterns. The methods of treating nonideal patterns either have only recently been developed or are yet to be developed. 

In real vessels flow is usually approximated by plug or backmix flow however, for proper design, the departure of actual flow from these idealizations should be accounted for. Here we intend to consider these nonideal flow patterns to characterize them, to measure them and to use this information in design. 

The treatment of these nonideal flow patterns divides naturally into two parts. 

At some point in most processes, a detailed model of performance is needed to evaluate the effects of changing feedstocks, added capacity needs, changing costs of materials and operations, etc. For this, we need to solve the complete equations with detailed chemistry and reactor flow patterns. This is a problem of solving the R simultaneous equations for S chemical species, as we have discussed. However, the real process is seldom isothermal, and the flow pattern involves partial mixing. Therefore, in formulating a complete simulation, we need to add many additional complexities to the ideas developed thus far. We will consider each of these complexities in successive chapters temperature variations in Chapters 5 and 6, catalytic processes in Chapter 7, and nonideal flow patterns in Chapter 8. In Chapter 8 we will return to the issue of detailed modeling of chemical reactors, which include all these effects. 

Fig. 2. Some typical examples of nonideal flow patterns that can occur in process equipment. (From Levenspiel, O., Chemical Reaction Engineering. John Wiley Sons, New York, 1962. Reprinted by permission of John Wiley Sons, Inc.)...

A well-known traditional approach adopted in chemical engineering to circumvent the intrinsic difficulties in obtaining the complete velocity distribution map is the characterization of nonideal flow patterns by means of residence time distribution (RTD) experiments where typically the response of apiece of process equipment is measured due to a disturbance of the inlet concentration of a tracer. From the measured response of the system (i.e., the concentration of the tracer measured in the outlet stream of the relevant piece of process equipment) the differential residence time distribution E(t) can be obtained where E(t)dt represents... 

For a continuous reactor with a nonideal flow pattern, characterized by the differential residence time distribution E t), the following expression holds for the conversion nonideai. which is attained in case complete segregation of all fluid elements passing through the reactor can be assumed ... 

Nonideal Flow Patterns 556 Residence Time Distribution 556 Conversion in Segregated and Maximum Mixed... 

We will pursue the analysis, however, in the sense that it is more important to fit the initial portion of the breakthrough curve than the end (certainly so in design applications). One should also recognize that end-of-breakthrough data can be less reliable because they are more susceptible to influences of extraneous factors such as nonideal flow patterns, the sensitivity of the chemical analysis, and instrumental uncertainty. Continuing then... 

When a physical mass transfer experiment is carried out in the same equipment k[ A is obtained, so that both and A are known. For this purpose it is often preferable to exclusively use experiments involving mass transfer and reaction. This eliminates the problems associated with coming close to gas-liquid equilibrium and with nonideal flow patterns. k[ A can be obtained by using an instantaneous reaction in the liquid so that, according to the film theory. 

NONIDEAL FLOW PATTERNS AND POPULATION BALANCE MODELS... 

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