Parameters 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).]... 

Use of Software Packages to Determine the Model Parameters 988 Other Models of Nonideal Reactors Using CSTRs and PFRs 990... 

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. 

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. 

Figure 5.14 (d) Selectivity and yield variations with Type III kinetic parameters in a nonideal reactor (10 CSTR units in series). 

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. 

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. 

By and large we can describe the results of the analysis of distributed parameter systems (i.e., flow reactors other than CSTRs) in terms of the gradients or profiles of concentration and temperature they generate. To a large extent, the analysis we shall pursue for the rest of this chapter is based on the one-dimensional axial dispersion model as used to describe both concentration and temperature fields within the nonideal reactor. The mass and energy conservation equations are coupled to each other through their mutual concern about the rate of reaction and, in fact, we can use this to simplify the mathematical formulation somewhat. Consider the adiabatic axial dispersion model in the steady state. 

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. 

In formulating and using nonideal reactor models one should keep in mind our overall objective which is to build and operate an ideal reactor. Only ideal reactors are scaleable and their performance predictable. The nonideal flow models and experimental RTD curves are needed to assess deviations from ideality. When these deviations are small, a successful one-or-two parameter model can be constructed to interpret them. When deviations are large, one should concentrate on finding ways to diminish them rather than to interpret them. Multiparameter models are difficult to use and have very little value in scaleup. The exceptions are situations when the variations of some model parameters can be predicted independently based on first principles or based on accumulated experimental evidence. 

The Dispersion model can be used to predict the performance of a nonideal reactor in the absence of a measured RTD. However, the geometric parameters and the flow conditions of the nonideal reactor must fall within the range of existing correlations for the intensity of dispersion. ... 

A mathematical model for nonideal flow in a vessel provides a characterization of the mixing and flow behavior. Although it may appear to be an independent alternative to the experimental measurement of RTD, the latter may be required to determine the parameters) of the model. The ultimate importance of such a model for our purpose is that it may be used to assess the performance of the vessel as a reactor (Chapter 20). 

The TIS and DPF models, introduced in Chapter 19 to describe the residence time distribution (RTD) for nonideal flow, can be adapted as reactor models, once the single parameters of the models, N and Pe, (or DL), respectively, are known. As such, these are macromixing models and are unable to account for nonideal mixing behavior at the microscopic level. For example, the TIS model is based on the assumption that complete backmixing occurs within each tank. If this is not the case, as, perhaps, in a polymerization reaction that produces a viscous product, the model is incomplete. 

In previous chapters treating ideal reactors, a parameter frequently used was the space-time or average residence time x, which was defined as being equal to V/v. It will be shown that no matter what RTD exists for a particular reactor, ideal or nonideal, this nominal holding time, x, is equal to the mean residence time.,r . 

Here we use a single parameter to account for the nonideality of our reactor. This parameter is most always evaluated by analyzing the RTD determined from a tracer test. Examples of one-parameter models for a nonideal CSTR include the reactor dead volume V, where no reaction takes place, or the fraction / of fluid bypassing the reactor, thereby exiting unreacted. Examples of one-parameter models for tubular reactors include the tanks-in-series model and the dispersion model. For the tanks-in-series model, the parameter is the number of tanks, n, and for the dispersion model, it is the dispersion coefficient D,. Knowing the parameter values, we then proceed to determine the conversion and/or effluent concentrations for the reactor. 

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... 

These results highlight a) Photodegradation reaction rates should be defined on the basis of phenomenologically meaningful parameters, case of W rr, b) Reaction rate evaluation is a task that should be developed carefully, accounting for possible nonidealities in the photocatalytic reactor such as particle wall fouling. 

Figure 24.9 shows the conversions of the models discussed previously in function of the parameter 1//3. It explains the behavior of ideal reactors (mixing perfect or piston) and nonideal, taking into consideration the real residence time of the set of molecules in the reactor. 

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