Residence-time distribution maximum mixedness

Maximum mixedness Exists when any molecule that enters a vessel immediately becomes associated with those molecules with which it will eventually leave the vessel. This occurs with those molecules that have the same life expectation. A state of maximum mixedness is associated with every residence time distribution (RTD). 

When the residence time distribution is known, the uncertainty about reactor performance is greatly reduced. A real system must lie somewhere along a vertical line in Figure 15.14. The upper point on this line corresponds to maximum mixedness and usually provides one bound limit on reactor performance. Whether it is an upper or lower bound depends on the reaction mechanism. The lower point on the line corresponds to complete segregation and provides the opposite bound on reactor performance. The complete segregation limit can be calculated from Equation (15.48). The maximum mixedness limit is found by solving Zwietering s differential equation. ... 

The limits for part (b) are at the endpoints of a vertical line in Figure 15.14 that corresponds to the residence time distribution for two tanks in series. The maximum mixedness point on this line is 0.287 as calculated in Example 15.14. The complete segregation limit is 0.233 as calculated from Equation (15.48) using/(/) for the tanks-in-series model with N=2 ... 

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. 

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. 

A reaction of order 1.5 is conducted under such flow conditions that its residence time distribution is like that of a three stage CSTR. Under maximum mixedness conditions the rate equation is... 

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

In the case of a maximum mixedness reactor, one works best with the life expectancy b. The life expectancy distribution in the feed stream,/(f>), is exactly the same as the residence time distribution in the product stream,/(/). One can generalize the Zwietering (1959) equation for a maximum mixedness reactor to the case of continuous mixtures (Astarita and Ocone, 1990) to obtain the following functional differential equation for cix,b) ... 

After studying this chapter the reader will be able to describe the cumulative F(t), external age E(t), and internal age I(t) residence-time distribution functions and to recognize these functions for PFR, CSTR, and laminar flow reactions. The reader will also be able to apply these functions to calculate the conversion and concentrations exiting a reactor using the segregation model and the maximum mixedness model for both single and multiple reactions. 

In a reactor with a segregated fluid, mixing between particles of fluid does not occur until the fluid leaves the reactor. The reactor exit is, of course, the latest possible point that mixing can occur, and any effect of mixing is postponed until after all reaction has taken place. We can also think of completely segregated flow as being in a state of minimiun mixedness. We now want to consider the other extreme, that of maximum mixedness consistent with a given residence-time distribution. 

In Pan 2 we will learn how to use the residence time data and functions to make predictions of conversion and exit concentrations. Because the residence time distribution is not unique for a given reaction system, we must use new models if we want to predict the conversion in our nonideal reactor. We present the five most common models to predict conversion and then close the chapter by applying two of these models, the segregation model and the maximum mixedness model, to single and to multiple reactions. 

For blends of SEES with graphite powder, CORI produced better mixedness. Volume resistivity is higher for the final composites Similar maximum pressure for both configurations. Narrower residence time distribution Erol and Kalyon 2005... 

The residence time distribution measures features of ideal or nonideal flows associated with the bulk flow patterns or macromixing in a reactor or other process vessel. The term micromixing, as used in this chapter, applies to spatial mixing at the molecular scale that is bounded but not determined uniquely by the residence time distribution. The bounds are extreme conditions known as complete segregation and maximum mixedness. They represent, respectively, the least and most molecular-level mixing that is possible for a given residence time distribution. 

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