Comparison of ideal reactors

FIGURE 3.20 A consecutive reaction A R — (left) and in BR and PFRs, respectively (right). 

9 NUMERICAL SOLUTION OF MASS BALANCES FOR VARIOUS COUPLED REACTIONS 

Reaction scheme (6) is typical in the oxidation of hydrocarbons (A, R, and S) in the presence of a large amount of oxygen. Therefore, the reactions become pseudo-first-order from the viewpoint of hydrocarbons, and the practically constant oxygen partial pressure can be included in the rate constants. The intermediate product, R, represents a partial oxidation product (such as phthalic anhydride in the oxidation of o-xylene or maleic anhydride in the oxidation of benzene), whereas S represents the undesirable byproducts (CO2, H2O). The triangle system (7) represents monomolecular reactions such as isomerizations A, for instance, can be 1-butene, which is subject to an isomerization to ds-2-butene and trflns-2-butene. 

FIGURE 3.21 Selected isothermal model reactions (a) examples of numerical solutions to the model reaction (5) (b). 

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TABLE 6.3 Comparison of Ideal Reactors for Consecutive, Endothermic Reactions... 

Chapter 17 Comparisons and Combinations of Ideal Reactors This results in ... 

Our treatment of Chemical Reaction Engineering begins in Chapters 1 and 2 and continues in Chapters 11-24. After an introduction (Chapter 11) surveying the field, the next five Chapters (12-16) are devoted to performance and design characteristics of four ideal reactor models (batch, CSTR, plug-flow, and laminar-flow), and to the characteristics of various types of ideal flow involved in continuous-flow reactors. Chapter 17 deals with comparisons and combinations of ideal reactors. Chapter 18 deals with ideal reactors for complex (multireaction) systems. Chapters 19 and 20 treat nonideal flow and reactor considerations taking this into account. Chapters 21-24 provide an introduction to reactors for multiphase systems, including fixed-bed catalytic reactors, fluidized-bed reactors, and reactors for gas-solid and gas-liquid reactions. 

In addition to the one-parameter models of tanks-in-series and dispersion, many other one-parameter models exist when a combination of ideal reactors is to model the real reactor. For example, if the real reactor were modeled as a PFR and CSTR in series, the parameter would be the fi action,/, of the total reactor volume that behaves as a CSTR Another one-parameter model would be the fi action of fluid that bypasses the ideal reactor. We can dream up many other situations which would alter the behavior of ideal reactors in a way that adequately describes a real reactor. However, it m be that one parameter is not sufficient to yield an adequate comparison between theoiy... 

A useful classification of lands of reaclors is in terms of their concentration distributions. The concentration profiles of certain limiting cases are illustrated in Fig. 7-3 namely, of batch reactors, continuously stirred tanks, and tubular flow reactors. Basic types of flow reactors are illustrated in Fig. 7-4. Many others, employing granular catalysts and for multiphase reactions, are illustratea throughout Sec. 23. The present material deals with the sizes, performances and heat effects of these ideal types. They afford standards of comparison. 

Adiabatic Reaction Temperature (T ). The concept of adiabatic or theoretical reaction temperature (T j) plays an important role in the design of chemical reactors, gas furnaces, and other process equipment to handle highly exothermic reactions such as combustion. T is defined as the final temperature attained by the reaction mixture at the completion of a chemical reaction carried out under adiabatic conditions in a closed system at constant pressure. Theoretically, this is the maximum temperature achieved by the products when stoichiometric quantities of reactants are completely converted into products in an adiabatic reactor. In general, T is a function of the initial temperature (T) of the reactants and their relative amounts as well as the presence of any nonreactive (inert) materials. T is also dependent on the extent of completion of the reaction. In actual experiments, it is very unlikely that the theoretical maximum values of T can be realized, but the calculated results do provide an idealized basis for comparison of the thermal effects resulting from exothermic reactions. Lower feed temperatures (T), presence of inerts and excess reactants, and incomplete conversion tend to reduce the value of T. The term theoretical or adiabatic flame temperature (T,, ) is preferred over T in dealing exclusively with the combustion of fuels. 

The above computation is quite fast. Results for the three ideal reactor t5T)es are shown in Table 6.3. The CSTR is clearly out of the running, but the difference between the isothermal and adiabatic PFR is quite small. Any reasonable shell-and-tube design would work. A few large-diameter tubes in parallel would be fine, and the limiting case of one tube would be the best. The results show that a close approach to adiabatic operation would reduce cost. The cost reduction is probably real since the comparison is nearly apples-to-apples. ... 

Figure 5.18 Comparison of space-time yields of direct fluorination of toluene for the falling film micro reactor (FFMR), micro bubble column (MBC) and laboratory bubble column (LBC) referred to the reaction volume (a) and referred to an idealized reactor geometry (b) [38],...

Size Comparisons Between Cascades of Ideal Continuous Stirred Tank Reactors and Plug Flow Reactors. In this section the size requirements for CSTR cascades containing different numbers of identical reactors are compared with that for a plug flow reactor used to effect the same change in composition. 

The F(t) curve for a laminar flow tubular reactor with no diffusion is shown in Figure 11.6. Curves for the two other types of idealized flow patterns are shown for comparison. 

Equation 13.5-2 is the segregated-flow model (SFM) with a continuous RTD, E(t). To what extent does it give valid results for the performance of a reactor To answer this question, we apply it first to ideal-reactor models (Chapters 14 to 16), for which we have derived the exact form of E(t), and for which exact performance results can be compared with those obtained independently by material balances. The utility of the SFM lies eventually in its potential use in situations involving nonideal flow, wheic results cannot be predicted a priori, in conjunction with an experimentally measured RTD (Chapters 19 and 20) in this case, confirmation must be done by comparison with experimental results. 

In this chapter we deal with single reactions. These are reactions whose progress can be described and followed adequately by using one and only one rate expression coupled with the necessary stoichiometric and equilibrium expressions. For such reactions product distribution is fixed hence, the important factor in comparing designs is the reactor size. We consider in turn the size comparison of various single and multiple ideal reactor systems. Then we introduce the recycle reactor and develop its performance equations. Finally, we treat a rather unique type of reaction, the autocatalytic reaction, and show how to apply our findings to it. 

A comparison of the various types of reactor concepts, in a general sense, is actually only possible between the batch, the CSTR and the PFR. The cascade of CSTRs, depending on the number of vessels n in the series, more or less behaves as an ideal mixer for n->l or an ideal plug flow for n- - . The fed-batch reactor is more difficult to situate. Although the concentration of compounds important for the rate of reaction can be controlled optimally during the whole fed period, the reactor volume is only partially utilized, especially in the beginning. Nevertheless, this reactor concept certainly has decisive advantages in many cases, as shown by the fact that it is one of the most widely used. 

Table 8.2 Comparison of safety characteristics of different ideal reactors.

I have chosen to make the comparison using a zero-order reaction only. Tables I and II indicate that this is conservative for the two ideal reactor types, and it seems plausible to assume that it is also so for real reactors. The degree of conservatism is little more than a few percent in reactor volume. This restriction is thus a useful way to keep the ultimate results in a simple form without compromising their utility. 

Figure 11.10. Comparison of conversions in a dense Pd membrane reactor with five different ideal flow pauems [Itoh et al., 1990]...

Comparison of Eqs. (4-2) and (4-5) shows that the form of the design equations for ideal batch and tubular-flow reactors are identical if the realtime variable in the batch reactor is considered as the residence time in the flow case. The important point is that the integral c/C/r is the same in both reactors. If this integral is evaluated for a given rate equation for an ideal batch reactor, the result is applicable for an ideal tubular-flow reactor this... 

J d) is plotted against d/d in Fig. 6-7 also shown are the curves for the two ideal reactors, taken from Fig. 6-5. The comparison brings out pertinent points about reactor behavior. Although the plug-flow reactor might be expected to be a better representation of the laminar case than the stirred-tank reactor, the RTD for the latter more closely follows the laminar-reactor curve for 6/6 from about 0.6 to 1.5. However, there is no possibility for 6 to be less than 0.5 in the laminar-flow case. Hence the stirred-tank form is not applicable at all in the low 6 region. At high 6 the three curves approach coincidence. Conversions for these reactors are compared in Sec. 6-7. 

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