Fluid Behavior in Mixing Vessels

One of the simplest models for convective mass transfer is the stirred tank model, also called the continuously stirred tank reactor (CSTR) or the mixing tank. The model is shown schematically in Figure 2. As shown in the figure, a fluid stream enters a filled vessel that is stirred with an impeller, then exits the vessel through an outlet port. The stirred tank represents an idealization of mixing behavior in convective systems, in which incoming fluid streams are instantly and completely mixed with the system contents. To illustrate this, consider the case in which the inlet stream contains a water-miscible blue dye and the tank is initially filled with pure water. At time zero, the inlet valve is opened, allowing the dye to enter the... 

Backmix flow (BMF) is the flow model for a CSTR, and is described in Section 2.3.1. BMF implies perfect mixing and, hence, uniform fluid properties throughout the vessel. It also implies a continuous distribution of residence times. The stepwise or discontinuous change in properties across the point of entry, and the continuity of property behavior across the exit are illustrated in Figure 2.3. 

Ideal flow models contain inherent assumptions about mixing behavior. In BMF, it is assumed that all fluid elements interact and mix completely at both the macroscopic and microscopic levels. In PF, microscopic interactions occur completely in any plane perpendicular to the direction of flow, but not at all in the axial direction. Fluid elements at different axial positions retain their identities as they progress through the vessel, such that a fluid element at one axial position never interacts with a fluid element at another position. 

The over-all behavior of a gas-liquid agitated system will depend on basic phenomena of mass transfer, bubble dynamics, and the fluid-dynamic regime in the mixing vessel. A general discussion of mass transfer is beyond the scope of this review, and the book by Sherwood and Pigford (S5) is recommended as a guide to that subject. 

To compare the hydrodynamic behavior of supercritical CO2 and water, laser-Doppler velocimetry (LDV) measurements have been performed in a specially designed high-pressure mixing vessel provided with glass windows. For the same geometry. Computational Fluid Dynamics (CFD) calculations have been made for both media. 

It should be noted that high polymer concentration normally results in the occurrence of autoacceleration, which makes the reaction fluid hard to mix. If the effective glass ffansition temperature of the system is reached by this increase in polymer concenffation, then the autoacceleration behavior causes the fluid to viffify in the reaction vessel. If there is no dispersant used when this happens, then a mixing catastrophe occurs, and the reaction vessel would just have to be dismantled for a messy cleaning job. A rule-of-thumb that we use to avoid the gel effect in undispersed reactor fluid systems is that we do not run the reaction beyond 20-25 wt% polymer composition, either by addition of a solvent (at least 75% by weight of total reactor fluid) or by allowing only 20 wt% of the monomer to react to form the polymer. 

When the vessel outlet stream of the marked fluid elements are monitored, several possibilities can be observed in between the extreme behaviors of plug flow and complete mixing. With plug flow, no marked fluid is observed until a time elapsed equal to the mean residence time of the vessel, at which point all the marked fluid elements leave the vessel. With complete mixing, the shape obtained reflects the instantaneous mixing of the tracer at time... 

The axial dispersion and tanks-in-series models are the two most common of models that have been developed as general semi-empirical correlations of mixing behavior, presumably bearing some relation to the actual flow pattern in the vessel. The model parameters have to be determined from experimental data and are then correlated as functions of fluid and flow properties and reactor configurations for use in design calculations. 

Despite their popularity, these methods normally have an inherent limitation—the fluid dynamics information they generate is usually described in global parametric form. Such information conceals local turbulence and mixing behavior that can significantly affect vessel performance. And because the parameters of these models are necessarily obtained and fine-tuned from a given set of experimental data, the validity of the models tends to extend over only the range studied in that experimental program. 

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