Macromixing models

Baldyga and Bourne (1999) present a comprehensive overview and comparison of macromixing models available in the literature for use in chemical reaction engineering. 

The TIS and DPF models, introduced in Chapter 19 to describe the residence time distribution (RTD) for nonideal flow, can be adapted as reactor models, once the single parameters of the models, N and Pe, (or DL), respectively, are known. As such, these are macromixing models and are unable to account for nonideal mixing behavior at the microscopic level. For example, the TIS model is based on the assumption that complete backmixing occurs within each tank. If this is not the case, as, perhaps, in a polymerization reaction that produces a viscous product, the model is incomplete. 

In the following sections, we first develop the two macromixing models, TIS and DPF, and then the two micromixing models, SFM and MMM. 

The tank-in-series (TIS) and the dispersion plug flow (DPF) models can be adopted as reactor models once their parameters (e.g., N, Del and NPe) are known. However, these are macromixing models, which are unable to account for non-ideal mixing behavior at the microscopic level. This chapter reviews two micromixing models for evaluating the performance of a reactor— the segregrated flow model and the maximum mixedness model—and considers the effect of micromixing on conversion. 

Experimental RTD data from real commercial reactors is needed. This type of data would be very useful in examining the applicability of macromixing models discussed here to large-scale systems. Furthermore, with the help of such data, one could evaluate the usefulness of various models for scaleup purposes, and their applicability to systems other than air and water. 

The applicability of the proposed macromixing models have been generally restricted to the bubble- and trickle-flow conditions. Their usefulness in correlating RTD in pulsating- and spray-flow regimes needs to be investigated. 

So far, only the axial dispersion model has been used for scaleup purposes. Very little knowledge on the effects of reactor configuration and flow conditions on the parameters of more complex macromixing models (e.g., the two-parameters model, etc.) is available. Since these complex models are more realistic, more information on the relation between their parameters and the system conditions, such as packing size, fluid properties, and flow rates, needs to be obtained. At present, complex models are not very useful for scaleup purposes. 

It appears, at present, that although crossflow and other macromixing models described earlier give a more correct description of the trickle flow process, the dispersion model predicts the conversion data satisfactorily, at least for simple reactions. 

Thus, the segregated flow model is based on the fundamental assumption that the fluid elements are independent or do not mix (macromixing model). Until now, we considered a perfect mixture in the mass balance and concentration uniform, no interaction between the fluid elements (micromixing), called unsegregated model. 

Now let us consider the macromixing model (segregated) for a system at constant volume from the rate expression ... 

Macromixing models play an essential role in modeling and scale-up of chemical reactors. Besides, the areas where micromixing is a controlling factor, are now clearly identified selectivity in complex reactions involving at least a fast step between unmixed reactants, crystallization and precipitation reactions, oxygen supply in fermentors. .. this list is not exhaustive. 

Figure 3.3 Micro-macromixer model [22] - a schematic representation of the discrete simulation procedure.

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