Mixing and segregation in chemical reactors

BATSEG, SEMISEG, COMPSEG - Mixing and Segregation in Chemical Reactors... 

Baldyga, J. (2000) Mixing and segregation in chemical reactors, in Chemical Engineering Dynamics (eds J. Ingham,... 

Chemical reactions will take place only when the reactant molecules are in intimate contact. In some cases, especially with very fast reactions or viscous liquids, segregation of the reactants can exist, which make the reaction rates and selectivities dependent on the mixing intensity. In chemical reactor engineering, the assumption is usually made that only mean concentrations need be considered. In reality, concentration values fluctuate about a mean, and in some cases these fluctuations must be considered in detail. This field is very complex and is still the subject of much research. This example serves only to introduce these concepts and to show how simulations can be made for certain simple situations. 

The statistical description of multiphase flow is developed based on the Boltzmann theory of gases [37, 121, 93, 11, 94, 58, 61]. The fundamental variable is the particle distribution function with an appropriate choice of internal coordinates relevant for the particular problem in question. Most of the multiphase flow modeling work performed so far has focused on isothermal, non-reactive mono-disperse mixtures. However, in chemical reactor engineering the industrial interest lies in multiphase systems that include multiple particle t3q)es and reactive flow mixtures, with their associated effects of mixing, segregation and heat transfer. 

Figure 7.3. The conversion of chemical reactions of various orders (0.5, 1 and 2) in continuous reactors with perfect macro-mixing perfectly micro-mixed (full lines) and completely segregated (dotted lines), as a function of the Damkbhler number see defenition next page. For order 1 both lines coincide.

In contrast to segregated flow, in which the mixing occurs only after each sidestream leaves the vessel, under maximum mixedness mixing of all molecules having a certain period remaining in the vessel (the life expectation) occurs at the time of introduction of fresh material. These two mixing extremes—as late as possible and as soon as possible, both consistent with the same RTD—correspond to performance extremes of the vessel as a chemical reactor. 

At the same symposium, Danckwerts (D2) drew attention to the effect of incomplete mixing on homogeneous reactions. He introduced the concept of segregation, which indicates that in the same vessel there are clumps of fluid which have different concentrations, caused by incomplete mixing. The effect on the conversion of chemical reactors is again an increase in conversion for reactions of an order greater than 1 and a decrease in conversion when the order is less than 1. 

The IAD I(a,t) in a chemical reactor is specially interesting and it does not seem that sufficient attention has been paid to the possibilities offered by this function. For instance, let us consider a semi-batch reactor, and let Q(t) be the feed flowrate of an incompressible fluid. The instantaneous fluid volume is V = /q Q(tf)dtf, from which the IAD is written I(a,t) = Q(t-a)/V. I(a,t) can be used to calculate the chemical conversion in different segregation states. Consider a species of concentration C produced with the rate t. If the mixture is assumed to be well mixed at the molecular scale, one obtains the familiar mass balance equation... 

A number of fine reviews have appeared recently which address in part the problems mentioned and the models employed. Rietema (R12) discusses segregation in liquid-liquid dispersion and its effect on chemical reactions. Resnick and Gal-Or (RIO) considered mass transfer and reactions in gas-liquid dispersions. Shah t al. (S16) reviewed droplet mixing phenomena as they applied to growth processes in two liquid-phase fermentations. Patterson (P5) presents a review of simulating turbulent field mixers and reactors in which homogeneous reactions are occurring. In Sections VI, D-F the use of these models to predict conversion and selectivity for reactions which occur in dispersions is discussed. 

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