Perfect mixer

Equations 8-148 and 8-149 give the fraction unreacted C /C o for a first order reaction in a closed axial dispersion system. The solution contains the two dimensionless parameters, Np and kf. The Peclet number controls the level of mixing in the system. If Np —> 0 (either small u or large [), diffusion becomes so important that the system acts as a perfect mixer. Therefore,... 

Kramers et al. (K21) measured gas residence-time distribution in a mechanically agitated gas-liquid contactor of 0.6-m diameter for various gas velocities and agitator speeds. In the region where agitation has an effect on the gas-liquid interfacial area (cf. the study by Westerterp et al. (W5), Section V,D,1), the residence-time distribution was found to resemble closely that of a perfect mixer. 

Gas holdup may be of the same magnitude in the various operations, although for bubble-columns, the presence of electrolytes or surface-active agents appears to be a condition for high gas holdup. The gas residence-time distribution resembles that of a perfect mixer in the stirred-slurry operation, and comes close to piston flow in the others. 

In summary, we have considered three characteristic times associated with a CSTR /mix, ri/2, and t. Treating the CSTR as a perfect mixer is reasonable provided that /mix is substantially shorter than the other characteristic times. 

Solution The exit concentration from the perfect mixer is... 

Example 4.9 Find the conversion for a first-order reaction in a composite system that consists of a perfect mixer and a piston flow reactor in parallel. 

Unsteady behavior in an isothermal perfect mixer is governed by a maximum of -I- 1 ordinary differential equations. Except for highly complicated reactions such as polymerizations (where N is theoretically infinite), solutions are usually straightforward. Numerical methods for unsteady CSTRs are similar to those used for steady-state PFRs, and analytical solutions are usually possible when the reaction is first order. 

Suppose the following reactions are occurring in an isothermal perfect mixer ... 

Danckwerts (D8) discussed the case of a perfect mixer. For the completely segregated case, all molecules within a point have the same age, a, and so... 

In practical cases, a rule-of-thumb is needed to know whether dispersion must be taken into account. One can use the equivalence between the mixing caused by a number of perfect mixers in series, and the degree of axial dispersion that produces the same degree of dispersion. We can use the following equation ... 

The shape of the residence time or cumulative residence time distributions are used when optimizing the mixing ability of a system. Often, this shape is compared to the residence time in an ideal or perfect mixer. Such a mixer is a well stirred tank, as depicted in Fig. 6.51(a). Here, two components, a primary and secondary component, are fed to the tank at a total flow rate Q. The output can be regarded as a flow rate Q with a concentration (1 — Co) of... 

Figure 6.52 compares the cumulative residence time distributions of a perfect mixer to Poiseuille flow. Disregarding the fact that the stirring tank s output starts at t = 0, we can see that the overall shape of the curve with the prefect mixer is much broader, pointing to a more homogeneous output, or simply, a better mixer. 

The fraction of the material within the system for times between t and t + dt is equal to I(t)dt, where t is the age or length of time a fluid element has been in the vessel. I(t) has properties similar to E(t) for a perfect mixer. 

The RTD in a system is a measure of the degree to which fluid elements mix. In an ideal plug flow reactor, there is no mixing, while in a perfect mixer, the elements of different ages are uniformly mixed. A real process fluid is neither a macrofluid nor a microfluid, but tends toward one or the other of these extremes. Fluid mixing in a vessel, as reviewed in Chapter 7, is a complex process and can be analyzed on both macroscopic and microscopic scales. In a non-ideal system, there are irregularities that account for the fluid mixing of different... 

For example, at r = 1 min, C = 0.223 x 10 kg/m ) Verify graphically that the tank is functioning as a perfect mixer—that is. that the expression of part (b) fits the data—and determine the effective volume P(m ) from the slope of your plot. 

This expression derived by Lin (1979) appears to be correct and needs to be tested with experimental data. There are a number of models for non-ideal flows, that is, flows that fall between the ideal conditions of a perfect mixer and plug flow. Some of the models for non-ideal flow were discussed in Levenspiel (1972) and Rao and Loncin (1974a). 

Although approximate, equation 10 is used in this study for determining the number of perfect mixers to be used in the cell model below. 

In the present study, all the experiments were carried out with two layers of particles. As mentioned abiove, we can assume that the value of Pe,a for SCF is approximately equal to 2.0 when Re is greater than 1.0. Then, the number of perfect mixers in a packed bed can be determined by equation 10. With two layers of particles, the number of cells is three that is, n = 3 in equation 11. If a different model is used the mass transfer coefficients will change slightly. 

The following scheme is a three loop model consisting of six perfectly mixer reactors which simulates a mixer [75]. 

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