Dispersion number

Swaroop et al. [Powder Technology, 28, 253-260 (Mar.-Apr. 1981)] found that the material holdup is higher and the vessel dispersion number Dl/L (see subsection on Continuous Mill Simulation) is lower in the rod mill than in the ball mill under identical dimensionless conditions. This indicates that the known narrow-product-size distribution from rod mills is partly due to less mixing in the rod mill, in addition to different breakage kinetics. 

A one-dimensional seareh optimization teehnique, sueh as the Fibonaeei seareh, is employed to miniiTtize Equation 8-113. A eomputer program (PROG81) was developed to estimate the equivalent number of ideal tanks N for the given effluent traeer response versus time data. Additionally, the program ealeulates the mean residenee time, varianee, dimensionless varianee, dispersion number, and the Peelet number. 

Flow patterns in the reaetor ean vary greatly. To eharaeterize baekmixing, of the longitudinal dispersion number, D/uL, is often used,... 

In a paeked bed or flow in pipes, the dispersion number is also defined as D/ud, where d is the partiele size in paeked beds or the tube diameter in empty pipes. 

The dimensionless group Dg/uL is known as the dispersion number and is the parameter that measures the extent of axial dispersion. The degree to whieh axial dispersion influenees tlie performanee of a ehemieal reaetor is determined by tlie value of the Peelet number (Np ). A high value of Npg eoiTesponds to a slightly dispersed reaetor. That is,... 

Using the experimental residenee time distribution data of Levenspiel and Smith in Example 8-2, determine the number of ideal tanks N, the varianee, dispersion number, and Peelet number. 

Computer program PROGS 1 determines the number of tanks, the varianee, dispersion number, and the Peelet number from Hull and von Rosenberg data. The results of the simulation suggest that about three stirred tanks in series are equivalent to the RTD response eurve. Figure 8-44 shows the shows E(6), Fe p(6), and Fjy[gjgi(6) versus 6. 

Naturally, there are two more Peclet numbers defined for the transverse direction dispersions. In these ranges of Reynolds number, the Peclet number for transverse mass transfer is 11, but the Peclet number for transverse heat transfer is not well agreed upon (121, 122). None of these dispersions numbers is known in the metal screen bed. A special problem is created in the monolith where transverse dispersion of mass must be zero, and the parallel dispersion of mass can be estimated by the Taylor axial dispersion theory (123). The dispersion of heat would depend principally on the properties of the monolith substrate. Often, these Peclet numbers for individual pellets are replaced by the Bodenstein numbers for the entire bed... 

A dimensionless dispersion number, based on the probable number of passes through the shear zone for an ingredient to be dispersed, was developed for scale-up of mixing of short fiber... 

Figure 4.16. Concentration profiles in the tubular reactor for extreme and intermediate values of the dispersion number. 

The term Lu / D is known as the Peclet number, Pe, and its inverse as the dispersion number. The magnitude of the Peclet number defines the degree of axial mixing in the reactor. 

The influence of dispersion on the yield of an intermediate produced in a series reaction has also been studied. When 3 JuL is less than 0.05, Tichacek s results (22) indicate that the fractional decrease in the maximum amount of intermediate formed relative to plug flow conditions is approximated by l/uL itself. Results obtained at higher dispersion numbers are given in the original article. 

Explain carefully the dispersed plug-flow model for representing departure from ideal plug flow. What are the requirements and limitations of the tracer response technique for determining Dispersion Number from measurements of tracer concentration at only one location in the system Discuss the advantages of using two locations for tracer concentration measurements. 

Calculate (a) the mean residence time of tracer in the vessel and (b) the dispersion number. If the reaction vessel is 0.8 m in diameter and 12 m long, calculate also the volume flowrate through the vessel and the dispersion coefficient. 

Parameter for molecular diffusion model In a moving zone, equivalent to the reciprocal of Peclet number, dispersion number Reynolds number, Re Prandtle number, Pr Schmidt number Sc... 

A more precise appreciation of conditions in the reactor can be gained from the reactor dispersion number (see Sect. 3.3 of this chapter and Sect. 5.4 of Chap. 6). 

Using the chart given by Levenspiel [2], a value of Re = 4 x 10 corresponds to D ud 0.3 and thus the reactor dispersion number... 

With this value of the reactor dispersion number, the departure from true plug flow in the reactor will be very small. 

With the same aspect ratio as before, this corresponds to a Reynolds number of about lO" and flow will again be turbulent. The reactor dispersion number is 0.002, which again implies that the performance of the actual reactor will be very close to that calculated on the basis of the plug-flow assumption. 

For a particular reactor, the dispersion number can be determined by analysis of the response at the reactor outlet to the injection of a tracer at the inlet. The procedure is fully described in Chap. 6. Alternatively, use may be made of published correlations [2], which give the reactor dispersion number as a function of either the Reynolds number or the product of the Reynolds and Schmidt numbers. Once a value of the reactor dispersion number is available, it can be used in one of the following ways to determine reactor performance for particular cases. 

The only two parameters appearing in eqn. (65) are the dispersion number, DjiiL, or inverse Peclet number, and the Damkohler number, or dimensionless rate group, t/jCa," - Solutions to eqn. (65) are therefore functions only of these two groups. If term (4) in eqn. (65) is absent, then... 

It may be that the extent of dispersion is to be determined from correlations rather than by direct experimental means. Suitable correlations based on large quantities of data exist for common reactor geometries, i.e. tubular reactors, both empty and packed, fluidised beds or bubble columns. Some of these are expressed in graphical form in, for instance, refs. 17, 21 and 26. Most forms of correlation give the intensity of dispersion D/ud as a function of Reynolds and/or Schmidt numbers if this intensity is multiplied by an aspect ratio, i.e. djL for a tubular reactor, then the dispersion number is obtained. 

Much of Fig. 18 refers to conditions under which the dispersion model should only be used with caution. Levenspiel [26] suggests that, if DluL is greater than unity, then other models may be more appropriate and Dudukovic and Felder [59] comment that the dispersion model should only be used with confidence when the dispersion number is less than 0.05. As is clear from both Figs. 16 and 18, these conditions represent relatively minor deviations from the plug flow ideal. 

On the assumption that the closed vessel of Example 11.1, Chapter 11, is well represented by the dispersion model, calculate the vessel dispersion number D/uL. The C versus t tracer response of this vessel is... 

Find the vessel dispersion number of this system. 

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