In CSTR cascade

In order to reduce the disparities in volume or space time requirements between an individual CSTR and a plug flow reactor, batteries or cascades of stirred tank reactors ard employed. These reactor networks consist of a number of stirred tank reactors confiected in series with the effluent from one reactor serving as the input to the next. Although the concentration is uniform within any one reactor, there is a progressive decrease in reactant concentration as ohe moves from the initial tank to the final tank in the cascade. In effect one has stepwise variations in composition as he moves from onfe CSTR to another. Figure 8.9 illustrates the stepwise variations typical of reactor cascades for different numbers of CSTR s in series. In the general nonisothermal case one will also en-... 

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. 

These relations support our earlier assertion that for the same overall conversion the total volume of a cascade of CSTR s should approach the plug flow volume as the number of reactors in the cascade is increased. 

CSTR cascade and a PFR reactor. Note how rapidly PFR behavior is approached as N increases. Levenspiel has also included lines of constant kx on this figure, and these lines may be useful in solving certain types of design problems, as we will see in Illustration 8.10. 

Analysis of CSTR Cascades under Nonsteady-State Conditions. In Section 8.3.1.4 the equations relevant to the analysis of the transient behavior of an individual CSTR were developed and discussed. It is relatively simple to extend the most general of these relations to the case of multiple CSTR s in series. For example, equations 8.3.15 to 8.3.21 may all be applied to any individual reactor in the cascade of stirred tank reactors, and these relations may be used to analyze the cascade in stepwise fashion. The difference in the analysis for the cascade, however, arises from the fact that more of the terms in the basic relations are likely to be time variant when applied to reactors beyond the first. For example, even though the feed to the first reactor may be time invariant during a period of nonsteady-state behavior in the cascade, the feed to the second reactor will vary with time as the first reactor strives to reach its steady-state condition. Similar considerations apply further downstream. However, since there is no effect of variations downstream on the performance of upstream CSTR s, one may start at the reactor where the disturbance is introduced and work downstream from that point. In our generalized notation, equation 8.3.20 becomes... 

An exothermic reaction with the stoichiometry A 2B takes place in organic solution. It is to be carried out in a cascade of two CSTR s in series. In order to equalize the heat load on each of the reactors it will be necessary to operate them at different temperatures. The reaction rates in each reactor will be the same, however. In order to minimize solvent losses by evaporation it will be necessary to operate the second reactor at 120 °C where the reaction rate constant is equal to 1.5 m3/kmole-ksec. If the effluent from the second reactor corresponds to 90% conversion and if the molal feed rate to the cascade is equal to 28 moles/ksec when the feed concentration is equal to 1.0 kmole/m3, how large must the reactors be If the activation energy for the reaction is 84 kJ/mole, at what temperature should the first reactor be operated ... 

This equation is the CSTR cascade analog of equation 9.1.11 for a PFR. It indicates that the overall yield is a summation over the instantaneous yields weighted by the fraction of the concentration change that takes place in each tank. 

A V - W where V is the desired product. These liquid phase reactions are to be carried out in a cascade of two equal volume CSTR s in series. If the reactors are to be sized so as to maximize the concentration of species V in the effluent from the second reactor, determine the reactor volumes necessary to process 500 gal/hr of feed containing 6 moles/gal of species A. No V or W is present in the feed. What fraction of the A ends up as V The rate constants kx and k2 are both equal to 0.5 hr - L... 

The reactor temperature controller (loop 2) is the primary controller, whereas the jacket temperature controller (loop 3) is the secondary controller. The advantage of the cascade control is that the reactor temperature control quickly reacts by the cascade system to disturbances in cooling fluid inlet conditions. The d3mamics of the transfer function G32 is faster than that of G 22-In the CSTR cascade control there are two control loops using two different measurements temperatures T and Tj, but only one manipulated variable Fj. The transfer function of the primary controller is the following ... 

Pibouleau et al. (1988) provided a more flexible representation for the synthesis problem by replacing the single reactor unit by a cascade of CSTRs. They also introduced parameters for defining the recovery rates of intermediate components into the distillate, the split fractions of top and bottom components that are recycled toward the reactor sequence, as well as parameters for the split fractions of the reactor outlet streams. A benzene chlorination process was studied as an example problem for this synthesis approach. In this example, the number of CSTRs in the cascade was treated as a parameter that ranged from one up to a maximum of four reactors. By repeatedly solving the synthesis problem, an optimum number of CSTRs was determined. 

Sulfonation of p-nitrotoluene (PNT) is performed in a cascade of Continuous Stirred Tank Reactors (CSTR). The process is started by placing a quantity of converted mass in the first stage of the cascade, a 400-liter reactor, and heating to 85 °C with jacket steam (150°C). PNT melt and Oleum are then dosed in simultaneously (exothermal reaction). When 110°C is reached, cooling is switched on automatically. On the day of the accident, a rapid increase in pressure took place at 102 °C. The lid of the reactor burst open and the reaction mass, which was decomposing, flowed out like lava, causing considerable damage. 

Around the same time, Glasser et al. (17) retrieved and extended the insightful methods of Horn (18) and presented graphical procedures known as the attainable region (AR) method. Their approach requires the graphical construction of the convex hull of the problem and helps to exemplify the need for a systematic and general methodology. In principle, the reactor network with maximum performance in terms of yield, selectivity, or conversion can be located on the boundary of the AR in the form of DSR and CSTR cascades with... 

Poehlein and Degraff [336] extended the derivation of Gershberg and Long-field [330] to the calculation of both molecular weight and particle size distribution in the continuous emulsion polymerization of St in a CSTR. On the other hand, Nomura et al. [163] carried out the continuous emulsion polymerization of St in a cascade of two CSTRs and developed a novel model for the system by incorporating their batch model [ 14], which introduced the concept that the radical capture efficiency of a micelle relative to a polymer particle was much lower than that predicted by the diffusion entry model (pocd -°). The assumptions employed were almost the same as those of Smith and Ewart (Sect. 3.3), except that the model did not assume a constant value of p. The elementary reactions and their rate expressions employed in the first stage are as follows ... 

Gerrens and Kuchner [337] investigated the continuous emulsion polymerization kinetics in a cascade of three CSTRs, and with St and MA as monomers with different solubilities in water. They showed that the experimental results obtained with St agreed with the predictions from the Gershberg and Longfield... 

The high-temperature solution process is state-of-the-art for the production of ethylene homopolymers as well as ethylene/1-olefin copolymers with a wide range of average molecular mass and copolymer composition [15]. This process is performed in a CSTR or in a cascade of two reactors, like the low-temperature process. Only the downstream equipment is different. The diluent is an aliphatic hydrocarbon such as cyclohexane, n-hexane, or a Cg-Cio alkane fraction. Homogeneous catalyst and co-catalyst are fed into the polymerization reactor mixed with solvent. Ethylene, hydrogen to regulate average molecular mass, and the comonomer are injected either as a gas or as a liquid. Temperature can be con-... 

The CSTR is used extensively in situations where intense agitation is required, such as the addition of a gaseous reactant to a liquid by transfer between the bubbles and the continuous liquid, and the suspension of a solid or second liquid within a continuous liquid phase. Polymerization reactions are sometimes conducted in CSTRs. It is common to employ a cascade or series of CSTRs in which the effluent from the first reactor is used as feed to the second and so forth down the cascade (Figure 1.4). The cascade permits one to realize high conversion of reactant, while minimizing total reactor volume. 

Equations (8.3.26) and (8.3.27) are generally applicable to all types of CSTR cascades. If one recognizes that the use of such cascades is almost invariably restricted to liquid systems and that in such systems density changes caused by reaction or thermal effects are usually quite small, then additional relations or simplifications can be developed from these starting equations. In particular, this situation implies that at steady state the volumetric flow rate between stages is substantially constant. It also implies that for each reactor, 7, = t,, and that the following relation between concentration and fraction conversion is appropriate ... 

Figure 8.13 Maximization of rectangles applied to find the optimum intermediate conversion and optimum sizes of two CSTRs in a cascade configuration. (Adapted from O. Levenspiel, Chemical Reaction Engineering, 2nd ed. Copyright 1972. Reprinted by permission of John WUey Sons, Inc.)...

Figure 8.14 is in essence a plot of this ratio versus the fraction conversion for various values of N, the number of identical CSTRs employed. The larger the value of N, the smaller the discrepancy in reactor volume requirements between the CSTR cascade and a PFR reactor. Note... 

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