Reaction yield, micromixing effect

In order to implement the PDF equations into a LES context, a filtered version of the PDF equation is required, usually denoted as filtered density function (FDF). Although the LES filtering operation implies that SGS modeling has to be taken into account in order to capture micromixing effects, the reaction term remains closed in the FDF formulation. Van Vliet et al. (2001) showed that the sensitivity to the Damkohler number of the yield of competitive parallel reactions in isotropic homogeneous turbulence is qualitatively well predicted by FDF/LES. They applied the method for calculating the selectivity for a set of competing reactions in a tubular reactor at Re = 4,000. 

The effect of coalescence and break-up of droplets on the yield of chemical reactions was studied by Villermaux (33). Micromixing effects may occur even in batch reactors if there is a drop size distribution and mass-transfer control. Although practical rules for the design and scale-up of liquid-liquid reactors are available as Oldshue showed in the case of alkylation (152), many problems remain unsolved (.5) mass transfer effects, high hold-up fractions (> 20 %), large density differences, high viscosities, influence of surfactants. 

The Friedel-Crafts alkylation of aromatic and heteroaromatic compounds often suffers from a polyalkylation problem owing to competitive, consecutive alkylation reactions. Owing to the large exothermicity of the reaction, the product distribution has proved difficult to control on the macroscale, resulting in synthesis of a large proportion of dialkylated products (the monoalkylated dialkylated ratio may be 1 1). Yoshida et al. carried out an alkylation reaction in a microchannel at —78 °C as per Fig. 5 [3]. Yoshida et al. also demonstrated the effect of mixing on alkylation yields and selectivity by using an efficient multilamination micromixer (supplied by IMM channel width = 25 xm) and a T-mixer (500 xm). 

Figure 13-32 Yield of R in the reaction A- -B R R- -B S from experimental data of Middleton et al. (1986) and from their simulations, which assume no local mixing rate effect. Simulations using paired-interaction closure agree with the Middleton et al. simulations, showing that the controlling mixing rate is not micromixing.

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