Nonideal reactors, conversion

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).]... 

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

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. 

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... 

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... 

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. 

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... 

Figure 5.15 (a) Conversion in a nonideal reactor for a Type II reaction system. 

A comparison of conversion and yield for the Type II reaction in terms of the kinetic parameters using a nonideal reactor model (n= 10) is shown in Figure 5.15c. Here as the value of (ki/kj) decreases, yield and conversion in the nonideal reactor approach the ideal value in this case this is a limiting value owing to the equality of the selectivity in the two reactor models. 

Figure 5.15 (c) Conversion and yield, Type II, in a nonideal reactor. 

In a large incinerator operating at high Reynolds number, about 1 % of the gas flows in the laminar boundary layer near the wall, where the average velocity and temperature are mueh lower than the midstream values. The conversion in the boundary layer is decreased, because the temperature effect is more important than the increase in residenee time. The predicted effect of boundary-layer flow on toluene destruction in a large incinerator is shown in Figure 6.9 [26]. There is little effect at 99% conversion, but for X > 0.999, the nonideal reactor requires more than twice the residence time of an ideal plug-flow reactor. 

ILLUSTRATION 11.6 Use of the Dispersion Model to Determine the Conversion Level obtained in a Nonideal Reactor... 

The reactors with recycle are continuous and may be tanks or tubes. Their main feature is increasing productivity by returning part of unconverted reactants to the entrance of the reactor. For this reason, the reactant conversion increases successively and also the productivity with respect to the desired products. The recycle may also be applied in reactors in series or representing models of nonideal reactors, in which the recycle parameter indicates the deviation from ideal behavior. As limiting cases, we have ideal tank and tubular reactors representing perfect mixture when the recycle is too large, or plug flow reactor(PFR) when there is no recycle. 

Therefore, depending on the recycle ratio, one obtains solutions that may indicate an increase in the final conversion or productivity and may represent behavior of nonideal reactor. The recycle ratio would be a parameter that indicates the deviation from ideal behavior. It is equivalent to the average residence time, which also indicates the extent of deviation from the ideal behavior of a reactor. 

The influence of different process and geometrical parameters on conversion was estimated in case of an irreversible first-order catalytic reaction. The influence of temperature nonuniformity (when temperature varies between the channels) had the largest impact on conversion in a nonideal reactor as compared to non-uniform flow distribution and nonequal catalyst amount in the channels. Obtained correlations were used to estimate the influence of a variable channel diameter on the conversion in a microreactor for a heterogeneous first-order reaction. It was found that the conversion in 95% of the microchannels varied between 59 and 99% at = 0.1 and Damkohler number of 2. Figure 9.1a shows conversion as a function of Damkohler number for an ideal microreactor and a microreactor with variations in the channel diameter (aj = 0.1). It can be seen that although the conversion in individual channels can vary considerably, the effect of nonuniformity in channel diameter on the overall reactor conversion is smaller. The lower conversion in channels with a higher flow rate is partly compensated by a higher conversion in channels with a lower flow rate. Due to the nonlinear relation between the channel diameter and the flow rate, the effects do not cancel completely and a decrease in reactor conversion is observed. 

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

One engineering design area, i.e., impacted by nonideal reactor behavior and the accompanying fluid residence time distribution(s) is scaleup. Suppose that a reactor study is conducted at the pilot scale level and that the conversion (or the equivalent) associated with volume flow rate Qs are judged to be acceptable. The classical scaleup problem is to then design a larger process with flow rate qs which results in the same conversion. The scaleup factor SF is. 

Tracer techniques have long been employed in an attempt to describe nonideal reactor behavior by quantifying residence time information and data. As noted in an earlier section, some of the elements of a fluid remain in a reactor longer than other elements, with the result that the conversion may vary from element to element depending on its residence time. 

The teachings of this simple example can be extended to any number of vessels in series. In general, E t)fora series of independent vessels will not depend on the order of the vessels. However, in Chapter 4, we learned that the final conversion from two different reactors in series may depend on the order of the two reactors. Although knowledge of the exit-age distribution is necessary to calculate the performance of a nonideal reactor, E(f) alone is not always sufficient for this purpose. 

The conversion of A in the nonideal reactor is lower than in the ideal PFR, as expected. However, the difference is not large. The mixing associated with the broadened residence time distribution shown in Figure 10-6 is not sufficient to cause a significant conversion difference between the nonideal reactor and the ideal PFR. 

Since the total reactor volume is 10001 and the volumetric flow rate is 1001/min, each reactor will have a volume of 5001 and a space time r of 5 min. LetXA,i be the fractional conversion of A in the stream leaving the first reactor and let XAa be the conversion of A in the stream leaving the second reactor, and the final conversion from the whole nonideal reactor. 

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