Mixing segregated flow

If the deviations are small then they can be described by the dispersion model (additional dispersive flow is is superimposed on the plug flow) or cell model (cascade of ideal stirred tanks). For larger deviations the calculation of nonideal reactors is generally difficult. A more simply treated special case occurs when the volume elements flowing through the reactor are macroscopically but not microscopically mixed (segregated flow). This case can be solved by the Hofmann-Schoenemann method (see below). 

Semi - mixed - segregated flow of a dispo rion and free phase. Bubbly interface. Dispersion volume less than half of the total pipe volume. 

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. 

FIG. 23-13 The two limiting flow patterns with the same RTD. a) Segregated flow, in which all molecules of any exit stream have the same residence time, (h) Maximum mixed flow, in which all molecules of an external stream with a certain life expectation are mixed with all molecules of the internal stream that have the same life expectation. 

FIG. 23 14 Comp arison of maximiim mixed, segregated, and ping flows, (a) Relative volumes as functions of variance or n, for several reaction orders, (h) Second-order reaction with n = 2 or 3. (c) Second-order, n = 2. (d) Second-order, n = 5. 

In the segregated flow model the contents of the volume elements of the fluid do not mix with one another as they move through the reactor. Each element may be considered as a small closed system that moves through the reactor. The different systems spend varying amounts of time in the reactor, giving rise to the measured residence time distribution func-... 

To illustrate the nature of the limits that the segregated flow and mixing models place on the expected conversion level, it is useful to examine what happens to two elements of fluid that have the same volume V, but that contain different reactant concentrations C1 and C2. We may imagine two extreme limits on the amount of mixing that may occur. 

The basic premise of the segregated flow model is that the various fluid elements move through the reactor at different speeds without mixing with one another. Consequently, each little fluid element will behave as if it were a batch reactor operating at constant pressure. The conversions attained within the various fluid elements will be equal to those in batch reactors with holding times equal to the residence times of the different fluid elements. The average conversion level in the effluent is then given by... 

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. 

A reactor has a residence time distribution like that of that of two equal completely mixed tanks in series. The rate equation is -dC/dt = 0.5C1-5. Inlet concentration is C0 = 1.2 lbmol/cuft and the feed rate is 10 Ibmol reactant/min. Conversion required is 95%. Find the reactor volume needed (a) assuming segregated flow (b) in a two stage CSTR. 

Data of tracer concentration in effluent of impulse input to a reactor are given in the first two columns (Fogler, 1992). A second order reaction with C0 = 8 and several values of specific rate is to be carried out here. Find conversion under max mixed and segregated flow conditions. 

A second order reaction is to be checked under plug flow, max mixed and segregated flow conditions when E(tr) of the reactor is Erlang with n = 3.(a) When conversion in a PFR is 90%, what are the other conversions (b) Find the relative reactor volumes when all three conversions are 90%. 

However, the solution for the CSTR obtained by the RTD equation is correct only for first-order kinetics. For other rate expressions the conversion predicted by the RTD is incorrect for a mixed reactor because molecules do not simply react for time t, after which they leave the reactor. Rather, the fluid is continuously mixed so that the history of the fluid is not describable in these terms. This expression for conversion in the CSTR is applicable for segregated flow, in which drops of fluid enter the reactor, swirl in the reactor, and exit after time t because then each drop behaves as a batch reactor with the RTD describing the probability distribution of the drops in the CSTR. 

This situation describes an emulsion reactor in which reacting drops (such as oil drops in water or water drops in oil) flow through the CSTR with stirring to make the residence time of each drop obey the CSTR equation. A spray tower (liquid drops in vapor) or bubble column or sparger (vapor bubbles in a continuous liquid phase) are also segregated-flow situations, but these are not always mixed. We wiU consider these and other multiphase reactors in Chapter 12. 

Figure 17.2. Relative volumes of maximum-mixed and segregated flow reactors with the same RTDs identified by n = 1 /< , as a function of conversion for second- and half-order reactions. For first-order reactions the ratio is unity throughout.

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