Mixing maximum mixedness

Early versus Late Mixing—Maximum Mixedness. 19-18... 

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. 

Maximum mixedness model The fluid in a flow reactor that behaves as a micro fluid. Mixing of molecules of different ages occurs as early as possible. 

Part (c) in Example 15.15 illustrates an interesting point. It may not be possible to achieve maximum mixedness in a particular physical system. Two tanks in series—even though they are perfectly mixed individually—cannot achieve the maximum mixedness limit that is possible with the residence time distribution of two tanks in series. There exists a reactor (albeit semi-hypothetical) that has the same residence time distribution but that gives lower conversion for a second-order reaction than two perfectly mixed CSTRs in series. The next section describes such a reactor. When the physical configuration is known, as in part (c) above, it may provide a closer bound on conversion than provided by the maximum mixed reactor described in the next section. 

Equation (15.48) governs the performance of the completely segregated reactor, and Equation (15.49) governs the maximum mixedness reactor. These reactors represent extremes in the kind of mixing that can occur between molecules that have different ages. Do they also represent extremes of performance as measured by conversion or selectivity The bounding theorem provides a partial answer ... 

Suppose is a function of a alone and that neither dSt Ajda nor d Alda change sign over the range of concentrations encountered in the reactor. Then, for a system having a fixed residence time distribution. Equations (15.48) and (15.49) provide absolute bounds on the conversion of component A, the conversion in a real system necessarily falling within the bounds. If d S A/dc > 0, conversion is maximized by maximum mixedness and minimized by complete segregation. If d 0i A/da < 0, the converse is true. If cf- A/da = 0, micro-mixing has no effect on conversion. 

The difference between complete segregation and maximum mixedness is largest when the reactor is a stirred tank and is zero when the reactor is a PFR. Even for the stirred tank case, it has been difficult to find experimental evidence of segregation for single-phase reactions. Real CSTRs approximate perfect mixing when observed on the time and distance scales appropriate to industrial reactions, provided that the feed is premixed. Even with unmixed... 

The segregated-flow reactor model (SFM) represents the micromixing condition of complete segregation (no mixing) of fluid elements. As noted in Section 19.2, this is one extreme model of micromixing, the maximum-mixedness model being the other. 

The maximum-mixedness model (MMM) for a reactor represents the micromixing condition of complete dispersion, where fluid elements mix completely at the molecular level. The model is represented as a PFR with fluid (feed) entering continuously incrementally along the length of the reactor, as illustrated in Figure 20.1 (after Zwieter-ing, 1959). The introduction of feed incrementally in a PFR implies complete mixing... 

Maximum mixedness exists when any molecule that enters a vessel immediately becomes associated with those molecules with which it will eventually leave the vessel, that is, with those molecules that have the same life expectation. All molecules with the same life expectation are completely mixed regardless of their internal ages. A state of MM is associated with every RTD. MM Is not the same as ideal mixing the latter is associated with an exponential RTD. 

FIGURE 15.15 Extreme mixing models for an arbitrary residence time distribution (a) complete segregation (b) maximum mixedness. 

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. 

ASME CFSTR CFD CFM DIERS exp IR HA/AN HAZOP MM MMM American Society of Mechanical Engineers Continuous flow stirred tank reactor Computational fluid dynamics Computational fluid mixing Design Institute for Emergency Relief Systems exponential Infrared (spectroscopy) Hazard analysis Hazard and operability studies Michaelis-Menten Maximum-mixedness model... 

Conversely, if the particles on a same vertical line are really mixed, then maximum mixedness is achieved. In addition, if the fluid is well micromixed, then, Zwieteringfs equation applies ... 

In maximum mixedness (or earliest possible mixing), the feed is intimately mixed with elements of fluid of different ages, for instance, using multiple side inlets at various points along a plug flow reactor. The... 

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