%0 Journal Article
%T The Effects of Mixing, Reaction Rates, and Stoichiometry on Yield for Mixing Sensitive Reactions¡ªPart I: Model Development
%A Syed Imran A. Shah
%A Larry W. Kostiuk
%A Suzanne M. Kresta
%J International Journal of Chemical Engineering
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/750162
%X There are two classes of mixing sensitive reactions: competitive-consecutive and competitive-parallel. The yield of desired product from these coupled reactions depends on how fast the reactants are brought together. Recent experimental results have suggested that the mixing effect may depend strongly on the stoichiometry of the reactions. To investigate this, a 1D, dimensionless, reaction-diffusion model at the micromixing scale was developed. Assuming constant mass concentration and mass diffusivities, systems of PDE's were derived on a mass fraction basis for both types of reactions. Two dimensionless reaction rate ratios and a single general Damk£¿hler number emerged from the analysis. The resulting dimensionless equations were used to investigate the effects of mixing, reaction rate ratio, and reaction stoichiometry. As expected, decreasing either the striation thickness or the dimensionless rate ratio maximizes yield, the reaction stoichiometry has a considerable effect on yield, and all three variables interact strongly. 1. Introduction Mixing and apparent reaction rate are intrinsically related: reactions involving multiple reactants cannot occur without the reactants being contacted intimately at a molecular level. In a reactor, reactants are added at the macro- or meso-scale. For the reaction to occur, the pure reactants need to be homogenized at the molecular scale so that molecules can collide. If the mixing is fast enough, the intrinsic chemical kinetics governs the rate of production of new species. This requires a reduction of scale and of differences in concentration, which is the very definition of mixing as it pertains to chemical reactions. In two known classes of reaction, the progress of the reaction depends heavily on how quickly the reactants are brought together. These reactions consist of two or more competitive reactions either occurring in parallel, where two or more reactions involving the same reactants take place at the same time, or in a consecutive sequence, where the desired product of one of the reactions participates in a second undesired reaction with the original reactants. Both types of reaction schemes can involve considerable production of unwanted by-product despite the desired reaction being as much as a million times faster than the undesired reaction. Typical representations of these reaction schemes are given in Table 1. For both cases, , is the desired product, and is the undesired by-product. Therefore, for a perfectly homogeneous mixture of reactants present in a stoichiometric ratio of one ( ), the yield
%U http://www.hindawi.com/journals/ijce/2012/750162/