Mixing in autocatalytic reactions

As a canonical model representing the reaction A + B — 2B (see Sect. 3.1.3) we consider the Fisher equation (4.16) with advection (Neufeld et ah, 2002b) 

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The vast majority of chemical reactions are sufficiently slow not to observe a dramatic influence of mixing on yields and selectivities. Exceptions are polymerizations, interfacial polycondensations, precipitations, and some fast reactions - usually performed in semibatch mode - such as autocatalytic reactions, neutralizations, nitrations, diazo couplings, brominations, iodinations, and alkaline hydrolysis, which are often encountered in the manufacture of fine chemicals. 

Illustration 9.5 indicates that one may have parallel paths leading from reactants to products and that in the case of an autocatalytic reaction, one path may be preferred over a second until the product level builds up to a point where the second becomes appreciable. In this example, the magnitudes of the rate constants are such that the vast majority of the reaction occurs by the autocatalytic path. In cases such as these it is desirable to use a CSTR or recycle reactor to enhance the reaction rate by virtue of the back-mixing of product species. 

For autocatalytic reactions all sorts of reactor arrangements are to be considered if product recycle or product separation with recycle is allowable. In general, for a rate-concentration curve as shown in Fig. 6.21 one should always try to reach point M in one step (using mixed flow in a single reactor), then follow with plug flow or as close to plug flow as possible. This procedure is shown as the shaded area in Fig. 6.21a. 

Consider the autocatalytic reaction A R, with = 0.001 C Cr mol/ liter-s. We wish to process 1.5 liters/s of a C o = 10 mol/liter feed to the highest conversion possible in the reactor system consisting of four 100-liter mixed flow reactors connected as you wish and any feed arrangement. Sketch your recommended design and feed arrangement and determine Af from this system. 

When the rate equation is complex, the values predicted by the two models are not necessarily limiting. Complexities can arise from multiple reactions, variation of density or pressure or temperature, incomplete mixing of feed streams, minimax rate behavior as in autocatalytic processes, and possibly other behaviors. Sensitivity of the reaction to the mixing pattern can be established in such cases, but the nature of the conversion limits will not be ascertained. Some other, possibly more realistic models will have to be devised to represent the reaction behavior. The literature has many examples of models but not really any correlations (Naumann and Buffham, 1983 Wen and Fan Westerterp et al., 1984). 

Physically, this means that mixing with the reaction products is a very effective means of overcoming the delay of an autocatalytic or exothermic reaction related to accumulation in the system of the active product or to heating. As may also be easily shown, in the case of exothermic reaction the maximum rate corresponds to very significant dilution by the reaction products—up to 70-80%. 

In a recycle reactor, part of the exit stream is recycled back to the inlet of the reactor. For a stirred-tank reactor, recycle has no effect on conversion, since we are essentially just mixing a mixed reactor. For a plug flow reactor, the effect of recycle is to approach the performance of a CSTR. This is advantageous for certain applications such as autocatalytic reactions and multiple reaction situations where we have a PFR but really require a CSTR. 

It can be confirmed that it is the polyisoprenyllithium formed in the initiation step which provides the autocatalytic mechanism [51], If isoprene and sec.-butyllithium are mixed in presence of polyisoprenyllithium the latter having been formed earlier in a separate reaction), then the initial rate of reaction of the sec.-butyllithium and isoprene is much faster than normal and no induction period occurs. The actual rate is then roughly that expected had the polyisoprenyllithium been formed normally as part of the initiation step (Fig. 8). These results also imply rapid mixing of sec.-BuLi and polyisoprenyllithium aggregates because if exchange was not rapid, the added polymer species could have little effect on the initiation process. 

The behavior of a bistable chemical reaction system under mixing in many respects is quite similar to the autocatalytic case. A standard example is the model studied by Neufeld et al. (2002b), Menon and Gottwald (2005), or Cox and Gottwald (2006), given by... 

As already mentioned, mixing can also have a significant effect on competing autocatalytic reactions as observed in the distribution of chirality of crystals in the experiments of Kondepudi et al. (1990). This was reproduced in a numerical model by Metcalfe and Ottino (1994) in a system of two competing autocatalytic reactions, of the... 

Thus, the reactor size for plug flow is given by the area under a curve (l/r,<) versus Xa — area 1 in Fig. 10.2.b-3a. For perfectly mixed flow, on the other hand, the size is given by the area of the rectangle with ordinate jrA xAt) (i.e., evaluated at the exit conversion), which is the sum of areas 1 + 2. Clearly, for this case where the rate monotonically increases with concentration, the plug flow reactor will always have the smaller area, and thus a smaller size. However, Fig. 10.2.b-3h is a plot for another type of rate form, which could result from an autocatalytic reaction, a dual site catalytic mechanism, negative order, or any other form where the rate has a maximum in the concentration range. Here, we can see that... 

Lintz, H. G. and W. Weber. The Study of Mixing in a Continuous Stirred Tank Reactor Using an Autocatalytic Reaction. Chem. Eng. Science 35 (1980) 203. 

Quite complex kinetic behavior has been identified on some surfaces. For instance, on Ir(100), the TPD data from NO-saturated surfaces display two N2 desorption peaks, one at 346 K from the decomposition of bridge-bonded NO, and a second at 475 K from the decomposition of atop-bonded NO molecules [13], Interestingly, the first feature is quite narrow, indicating an autocatalytic process for which the parallel formation of N20 appears to be the crucial step. An additional complication arises from the fact that this Ir(100) surface undergoes a (1x5) reconstruction, and that NO adsorbed on the metastable unreconstructed (lxl) phase leads to N2 desorption at lower temperatures. In another example, on the reconstructed hexagonal Pt(100) surface, when a mixed NO + CO adsorbed layer is heated, a so-called surface explosion is observed where the reaction products (N2, C02 and N20) desorb simultaneously in the form of sharp peaks with half-widths of only 7 to 20 K. The shape of the TPD spectra suggests again an autocatalytic mechanism [14],... 

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