Reactor Design for Autocatalytic Reactions

There are many reactions in which the products formed can themselves act as catalysts for the reaction. Thus, there will be a range of compositions for which the reaction rate accelerates as the reaction proceeds. This phenomenon is known as autocatalysis, and reactions of this type pose 

An antocatalytic reaction is one in which the reaction rate is proportional to a prodnct concentration raised to a positive exponent. Some of the first articles in the literature of chemical kinetics deal with reactions of this type. For example, in 1857, Baeyer (12) reported that the reaction of bromine with lactose was autocatalytic. The hydrolyses of several esters also fit into the autocatalytic category, because the acids formed by reaction give rise to hydrogen ions that serve as catalysts for subsequent reaction. Among the most significant autocatalytic reactions are fermentation reactions, which involve the action of a microorganism on an organic feedstock. 

When heated above 200 C, pure 5-methyl-2-oxazolidinone decomposes into two products, CO2 gas and A-(2-hydroxy-propyl)imidazolidinone. The stoichiomelry is 

While we have taken some hberties with the numerical values that we will subsequently employ, the following set of mechanistic equations has been proposed in an effort to explain the observed autocatalytic kinetic behavior (13)  

If the following values (in m /(kmol-Msec)) are assumed for the reaction rate constants = 1.02, 

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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. 

In this case, no specific problem in quantitative terms has been posed and solved. For the first step, which is a solid-solid reaction, experimental details have been given because it is a unique solid-solid reaction, perhaps the only known autocatalytic one. Having clearly established this fact, general procedures are described for the two reactors involved, since no experimental data are available for attempting a specific design. The thrust here is the description of a procedure for calculating the outlet solid size distribution given the inlet size distribution. This is an important factor in solid-phase reactions. 

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