Reactor cascade conversion

The use of the reactor cascade model to estimate the conversion level attained in a first-order reaction is discussed in Illustration 11.7. 

Another interesting case is the one-pot four-enzyme cascade conversion of glycerol into a heptose sugar on gram scale [11], in which a pH switch method is applied to temporarily turn off one of the enzymes involved (Fig. 13.6). The four consecutive enzymatic conversion steps in one and the same reactor, without separation of intermediates, consist of ... 

Apart from new catalytic methods, cascade conversions require new process technologies, such as in situ product recovery, reactor design, and compartmental-ization. In the long term, part of the present-day stoichiometric chemistry as well as bio- and chemocatalytic conversions in multi-step syntheses will gradually be replaced by cascade catalysis in concert, and full fermentations by cell factory design, or combinations thereof (Fig. 13.17). 

Feeding the monomers in different composition in the course of reaction may compensate the change of monomer composition with conversion ratio. In a reactor cascade, a part of the mixture can be fed back into the forgoing reactors, in order to keep the ratio of monomers constant (6). 

For a 100 times slower reaction, the heat exchange becomes fully uncritical, but the conversion of 99% can only be reached with a volume of 90 m3, which is unrealistic. The situation improves with a higher reactor temperature or with a different combination of reactors cascade of CSTRs or CSTR followed by a tubular reactor. 

In the pre-polymerization vessels, the rubber solution is polymerized to a conversion of 20-30 %. This phase is where the particle structure, the RPS and the RPSD are fixed. In industry, the pre-polymerization is carried out in continuous-flow stirred tank reactors (Shell, Monsanto, Mitsui Toatsu), tower reactors (Dow Chemical), stirred reactor cascades (BASF) or loop reactors with static mixers (Dainippon Ink and Chemicals). 

Whereas the pre-polymerization is carried out at temperatures of from 100 to 150 °C, the main polymerization is carried out at up to 180 °C. Its only aim is to increase the conversion and, thus, improve the economic efficiency of the processes. Target conversions are above 90 %. In order to be able to dissipate the heat of reaction from the solutions of exponentially increasing viscosity in a controlled manner, a number of reactors are generally connected in series. The designs vary considerably. For example, conical reactors with helical ribbon stirrers, horizontal tank reactors with paddle stirrers, reactor cascades and tower cascades have been proposed. 

The liquid-phase oxidation of o-xylene was of little comparable technical significance following the introduction of gas-phase oxidation, and was used only in rare cases. In the early 1970 s, Rhone Poulenc (Chauny/France) started a plant with a capacity of 19,000 tpa. In a process developed by Rhone Poulenc/Progil, o-xylene was fed into a three-stage cascade reactor together with acetic acid and the solution of the catalyst (Co-salts). In the first reactor a conversion of between 50 and 60% was achieved, in the second between 35 and 40% and in the third between 8 and 10%. The reaction was carried out under a pressure of 6 bar and at temperatures ranging from 150 to 165 °C. 

For ideal isothermal reactors, the conversion of a reactant A can be calculated by one parameter, the Damkoehler number. (For a cascade of CSTRs we also need the number of CSTRs.) For a reaction order n and a rate constant k, Da equals for a batch reactor (t = reaction time) and r (r = resi-... 

Continuous polymerization in a staged series of reactors is a variation of this process (82). In one example, a mixture of chloroprene, 2,3-dichloro-l,3-butadiene, dodecyl mercaptan, and phenothiazine (15 ppm) is fed to the first of a cascade of 7 reactors together with a water solution containing disproportionated potassium abietate, potassium hydroxide, and formamidine sulfinic acid catalyst. Residence time in each reactor is 25 min at 45°C for a total conversion of 66%. Potassium ion is used in place of sodium to minimize coagulum formation. In other examples, it was judged best to feed catalyst to each reactor in the cascade (83). 

As a rule, sulfonation takes place continually in a cascade or a falling film reactor (Table 14) at about 50-70°C. The S03 is steadily diluted to a concentration of 5-10 vol % with air or an inert gas. The LAB conversion reaches a value between 92% and 98% [156,157]. Mixing of the already formed alkyl-benzenes with fresh S03 leads to undesired highly sulfonated byproducts. In order to prevent these side reactions, all processes operate concurrently. 

A modern sulfochlorination is run continuously (Fig. 7). To limit the formation of di- and polysulfochlorides (Fig. 8) up to eight reactors are connected in a cascade. For a 25% alkane conversion, a residence time of 4-5 h is necessary if the circulating and cooling systems are appropriately designed. Since a lower gas flow rate promotes the formation of di- and polysulfochlorides, it makes no sense to run a sulfochlorination plant much below name-plate capacity. 

Consecutive reactions, isothermal reactor cmi < cw2, otai = asi = 0. The course of reaction is shown in Fig. 5.4-71. Regardless the mode of operation, the final product after infinite time is always the undesired product S. Maximum yields of the desired product exist for non-complete conversion. A batch reactor or a plug-flow reactor performs better than a CSTR Ysbr.wux = 0.63, Ycstriiuix = 0.445 for kt/ki = 4). If continuous operation and intense mixing are needed (e.g. because a large inteifacial surface area or a high rate of heat transfer are required) a cascade of CSTRs is recommended. 

As Levenspiel points out, the optimum size ratio is generally dependent on the form of the reaction rate expression and on the conversion task specified. For first-order kinetics (either irreversible or reversible with first-order kinetics in both directions) equal-sized reactors should be used. For orders above unity the smaller reactor should precede the larger for orders between zero and unity the larger reactor should precede the smaller. Szepe and Levenspiel (14) have presented charts showing the optimum size ratio for a cascade of two reactors as a function of the conversion level for various reaction orders. Their results indicate that the minimum in the total volume requirement is an extremely shallow one. For example, for a simple... 

Determine the reactor size requirements for cascades composed of one, two, and three identical CSTR s. Use an algebraic approach and assume isothermal operation at 25 °C where the reaction rate constant is equal to 9.92 m3/ kmole-ksec. Reactant concentrations in the feed are equal to 0.08 kmole/m3. The liquid feed rate is equal to 0.278 m3/ksec. The desired degree of conversion is equal to 87.5%. 

Obviously this approach is not easily extended to cascades containing more than three reactors and, in those cases, an alternative trial and error procedure is preferable. One chooses a reactor volume and then determines the overall fraction conversion that would be obtained in a cascade of N reactors. When one s choice of individual reactor size meets the specified overall degree of conversion, the choice may be regarded as the desired solution. This latter approach is readily amenable to iterative programming techniques using a digital computer. 

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. 

For a CSTR equal in volume to the tubular reactor, one moves along a line of constant kCB0T in Figure 8.16 in order to determine the conversions accomplished in cascades composed of different numbers of reactors but with the same overall space time. The intersection of the line/cCg0T = 19.6 and the curve for N = 1 gives fB = 0.80. 

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 ... 

We can characterize the mixed systems most easily in terms of the longitudinal dispersion model or in terms of the cascade of stirred tank reactors model. The maximum amount of mixing occurs for the cases where Q)L = oo or n = 1. In general, for reaction orders greater than unity, these models place a lower limit on the conversion that will be obtained in an actual reactor. The applications of these models are treated in Sections 11.2.2 and 11.2.3. 

Determination of Conversion Levels Based on the Cascade of Stirred Tank Reactors Model... 

In Section 11.1.3.2 we considered a model of reactor performance in which the actual reactor is simulated by a cascade of equal-sized continuous stirred tank reactors operating in series. We indicated how the residence time distribution function can be used to determine the number of tanks that best model the tracer measurement data. Once this parameter has been determined, the techniques discussed in Section 8.3.2 can be used to determine the effluent conversion level. 

Use the model based on a cascade of stirred tank reactors to predict the conversion that will be attained in the reactor of Illustration 11.1. Assume that the value of the first-order rate constant is 3.33 x 10 3sec-1. 

The safety aspects of the cascade reactor are the same as for the CSTR, whereas the focus should be on the first stage, where usually the greatest conversion increase takes place, that is, the heat release is also greatest. Moreover, at this stage the conversion is lowest, implying the highest degree of accumulation. 

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... 

This technique gives a high yield of triisobutylaluminum the degree of aluminum conversion can reach up to 90% in case of a cascade of four reactors equal in volume. 

A potential choice of manipulated inputs to address the control objectives in the slow time scale is [ 3 Mrsp]t, i.e., the product flow rate from the column reboiler, and the setpoint for the reactor holdup used in the proportional feedback controller of Equation (3.35). This cascade control configuration is physically meaningful as well intuitively, the regulation of the product purity 23 is associated with the conversion and selectivity achieved by the reactor, which in turn are affected by the reactor residence time. 

---