Conversion in Nonideal Reactors

Equation (B) may be integrated for successive stages in an n-stage system. For the first stage Cj j = Cq, so that 

When there is just one stage n =1) this becomes the familiar result for a single tank. In general Eq. (C) gives the response in the effluent from the first stage of an n-stage system. 

Continuing to the second stage, we note that and that this is given by Eq. (C). Hence Eq. (B) becomes 

Integrating gives the response for the effluent from the second stage of an n-stage unit, 

For the third stage (/ = 3) Cj j in Eq. (B) becomes Ca, as given by Eq. (E). Proceeding as before, we find that the response in the effluent from the third stage is 

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Ways we use (he RTD data to predict conversion in nonideal reactors... 

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).]... 

Conversion in a reactor with nonideal flow can be determined either directly from tracer information or by use of flow models. Let us consider each of these two approaches, both for reactions with rate linear in concentration (the most important example of this case being the first-order reaction) and then for other types of reactions where information in addition to age distributions is needed. 

Perhaps more important than conversion deficits in nonideal reactors are the associated changes in selectivity and yield in more complex reactions. Let us look at a Type III system (A —> B C) to illustrate this. For selectivity in a PFR, Type III reaction, we had previously derived... 

Overall the analysis here should convey the message that generalizations concerning selectivity or yield performance in nonideal reactors with reference to an ideal model are slippery conversion, however, is perhaps somewhat more predictable. We may normally expect modest taxes on conversion as the result of nonideal exit-age distributions if the reaction system involves selectivity/yield functions these will also be influenced by the exit-age distribution, but the direction is not certain. Normally nonideality is reflected in a decrease in yield and selectivity, but there are possible interactions between the reactor exit-age distribution and the reaction kinetic parameters that can force the deviation in the opposite direction. Keep in mind that the comparisons being offered here are not analogous to those for PFR-CSTR Type III selectivities given in Chapter 4, which were based on the premise of equal conversion in the two reactor types. 

To complete this discussion of conversion, selectivity, and yields in nonideal reactors, let us consider a similar set of illustrations for a Type II system. Recall that... 

Calculate the effect of recycle on the conversion in tubular reactors with plug flow. NONIDEAL FLOW PATTERNS AND POPULATION BALANCE MODELS 655... 

Program to calculate conversion of first order reaction in nonideal % reactor using various models... 

In this section, we apply the axial dispersion flow model (or DPF model) of Section 19.4.2 to design or assess the performance of a reactor with nonideal flow. We consider, for example, the effect of axial dispersion on the concentration profile of a species, or its fractional conversion at the reactor outlet. For simplicity, we assume steady-state, isothermal operation for a simple system of constant density reacting according to A - products. 

The conversion in a real, hence, nonideal, stirred tank reactor can be calculated for the model proposed by Cholette and Cloutier (see Section IV,D). The exit stream consists of reacted fluid from the active backmix region combined with unreacted bypassing fluid. By material balance, then,... 

In this section we discuss the use of the tanks-in-series model to describe nonideal reactors and calculate conversion. We will analyze the RTD to determine tlie number of ideal tanks in series that will give approximately the same RTD as the nonideal reactor. Next we will apply the reaction engineering analysis developed in Chapters 1 through 4 to calculate conversion. We are first going to develop the RTD equation for three tanks in series (Figure 14.1) and then generalize to n reactors in series to derive an equation that gives the number of tanks in series that best fits the RTD data. 

This chapter has discussed how to predict conversions in a nonideal reactor. Almost always, we would need to measme or estimate a reactor s RTD. If the reaction is first-order, the conversion can be predicted knowing only the RTD, as shown in Chapter 13. More extensive knowledge of flow pattern characteristics is not required for predicting conversions for first-order reactions. 

In Pan 2 we will learn how to use the residence time data and functions to make predictions of conversion and exit concentrations. Because the residence time distribution is not unique for a given reaction system, we must use new models if we want to predict the conversion in our nonideal reactor. We present the five most common models to predict conversion and then close the chapter by applying two of these models, the segregation model and the maximum mixedness model, to single and to multiple reactions. 

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. 

One of these approaches is to use the exit-age distribution directly. For ideal reactors this will allow determination of limits between which the actual conversion must lie. These two limits are, of course, those of complete segregation and maximum mixedness as described in Chapter 4. For nonideal reactors one follows the same procedure employing the experimentally determined exit-age distribution. 

A second approach is to use various combinations of the ideal reactor models in simulation of nonideal behavior. This may seem a bit contradictory at first, but hopefully our later discussion will be sufficient to illuminate the reasoning behind this method. A hint of this approach is given by the discussion in Chapter 4 on the comparisons between the conversions in PFR and CSTR sequences of the same total... 

When experimental data on F t) or E t) are available, one can model the effects of nonideal behavior by fitting the response using n as an adjustable parameter. Then integral expressions conforming to equation (5-1) may be set up in terms of E t) from equation (5-16) for computing conversions in the nonideal reactor. Derive the appropriate equations for a second-order reaction using this approach. 

It is shown that these deviations do not become large until n approaches, say, 2 to 4. From Figure 5.3 it is clear that for = 20 there are significant differences already between the residence-time and exit-age distributions of the nonideal reactor and the plug-flow case, yet the deficit in conversion is only 1.5%. The reason for this is a... 

This is not a particularly desirable result for the nonideal reactor, since it indicates that the individual elfects on conversion and selectivity are multiplied together in determination of the net loss in yield. For 5, (III) > 1, unfortunately, the decrease in yield due to nonideality is then greater than individual losses in either conversion or selectivity a given loss in conversion may show up as two or three times that amount in the yield of a desired product. On the other hand, trends in conversion and selectivity tend to compensate each other for 5, (III) < 1 this in shown in Figure 5.14c for the same reaction parameters used in Figures 5.14a and b. Plotted are the product of conversion and selectivity for the two reaction systems (intrinsic selectivity > and < 1) as a function of n. It is clear that for 5, -(III) > 1, the -value decrease for yield is larger in each case than the corresponding decreases for conversion or selectivity. 

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