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Intensity of dispersion

The inverse of the Bodenstein number is eD i/u dp, sometimes referred to as the intensity of dispersion. Himmelblau and Bischoff [5], Levenspiel [3], and Wen and Fan [6] have derived correlations of the Peclet number versus Reynolds number. Wen and Fan [6] have summarized the correlations for straight pipes, fixed and fluidized beds, and bubble towers. The correlations involve the following dimensionless groups ... [Pg.732]

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. [Pg.265]

A 12-m length of pipe is packed with 1 m of 2-mm material, 9 m of 1-cm material, and 2 m of 4-mm material. Estimate the variance in the output C curve for a pulse input into this packed bed if the fluid takes 2 min to flow through the bed. Assume a constant bed voidage and a constant intensity of dispersion given by IMudp = 2. [Pg.320]

If a pulse of tracer is injected into a flowing stream, this discontinuity spreads out as it moves with the fluid past a downstream measurement point. For a fixed distance between the injection point and measurement point, the amount of spreading depends on the intensity of dispersion in the system, and this spread can be used to characterize quantitatively the dispersion phenomenon. Levenspiel and Smith (L16) first showed that the variance, or second moment, of the tracer curve conveniently relates this spread to the dispersion coefficient. [Pg.110]

Knowing the viscosity and density of the reaction mixture, the flow channel diameter, void fraction of the bed, and the superficial fluid velocity, it is possible to determine the Reynolds number, estimate the intensity of dispersion from the appropriate correlation, and use the resulting value to determine the effective dispersion coefficient Del or I). Figures 8-32 and 8-33 illustrate the correlations for flow of fluids in empty tubes and through pipes in the laminar flow region, respectively. The dimensionless group De l/udt = De l/2uR depends on the Reynolds number (NRe) and on the molecular diffusivity as measured by the Schmidt number (NSc). For laminar flow region, DeJ is expressed by ... [Pg.733]

This dispersion number, (D/uL), for fluid flow in a cylinder can be obtained from a chemical engineering correlation by Levenspiel [9] noting that the intensity of dispersion D/udf, (where df is the diameter of the cylinder) is plotted as a function of Reynolds s number Re = up JlXg, pg is the gas density and p.g is the gas viscosity. (Please note that the Reynolds s number of the flow is altered by the presence of particles. Particles increase the gas density and reduce the effective kinematic viscosity. The net result is to accentuate turbulence and... [Pg.282]

The degree of polymer crystallinity, which characterizes the share of regularly packed molecules is estimated by the intensity of dispersion in maximum 1 m. Some differences connected with introduction of a dye are observed, namely intensity of dispersion is a bit lower both along the equator and meridian. This speaks about the fact that introduction of the additive leads to the decrease of a number of reflective planes (decrease of reflection centres), which, in its turn, is connected either with deterioration of polymer crystalline stmcture or with rotation of reflective planes. [Pg.26]

Assuming a unique dispersion process and the applicability of the theory of kinematic dispersion, the intensity of dispersion I q) is given by... [Pg.394]

According to the Equation 19.2, the intensity of dispersion for an ideal structure will be the Fourier transform of the autoconvolution of the difference between the local and the average electronic densities, that is. [Pg.397]

Porod predicted that, for an ideal lamellar system of two phases (Fig. 19.5) in which neither fluctuations of density within phases nor interfacial thickness of finite wide are present, the intensity of dispersion diminishes proportionally to the reciprocal of the fourth power of q, which is mathematically expressed as... [Pg.397]

I (q) is the intensity of dispersion for a structure with finite thickness, and pf iq) is the Fourier transform of h (r) in the reciprocal space. Because the width of the function h(r) should be small compared to the average regions of constant density (for a two-phase system), the width of the function H(q) will be considerably larger than that of the intensity. In this way, the intensity of dispersion is affected essentially only at large q values, that is, in the Porod s region. As a consequence, and using Equation 19.13, the result is... [Pg.397]

A theoretical analysis of solid mixing is rather complicated. Statistical units are used based on the variance of concentration in different zones of the compound, leading to a parameter, termed the intensity of dispersion. Other parameters based on the dimension of length are coimected to the real location of the dispersed particle. [Pg.110]

What boundary conditions are satisfied in practice and how to obtain the RTD experimentally is less clear. The uses of two-place measurements and the extension of impulse response theory to open systems are discussed in (4). For small intensity of dispersion (large Pe ) the boundary conditions effect diminishes and approximate expressions can be used for the E-curve (see Table 1). [Pg.140]

The above formulas are provided as theoretical guidance for the use of the dispersion model. For evaluation of actual coefficients the reader can consult the numerous experimental studies and correlations for tubes, packed and fluidized beds presented by Wen and Fan (58). One should remember that theory only justifies the use of the axial dispersion model at large Peclet nuu ers (Pe >> 1) and at small intensities of dispersion, i.e. D /uL < 0.15. Therefore, attempts in the literature to apply the dispersion model to small deviations from stirred tank behavior, i.e. for large intensities of dispersion, D /uL > 1, such as in describing liquid backmixing in bubble columns, should be considered with caution. Better physical models of the flow patterns are necessary for such situations and the dispersion model should be avoided. [Pg.142]

The dispersion model is at best only an approximate representation of physical reality, often in contradiction with selected physical evidence. For example, the dispersion model predicts the appearance of tracer upstream of the injection point, yet, all the experimental evidence in packed beds points to downstream spreading of the dye only. The boundary conditions of the dispersion model are often difficult to meet in practice. Considering the above discrepancies between the model and physical reality it seems hardly justified to do the elaborate boundary value problem calculations. This is especially true since for RTDs close to PFR micromixing effects cannot be pronounced. It seems more appropriate to relate the intensity of dispersion as given by eq. (37) to an equivalent number of tanks in series. [Pg.143]

Figure 10-7 Intensity of dispersion for liquids and gases flowing through packed beds. Figure 10-7 Intensity of dispersion for liquids and gases flowing through packed beds.
The parameter Dsi/ulc that is plotted on they-axis is known as the intensity of dispersion or the local Dispersion number. For the situation shown in Figure 10-7, the intensity of dispersion depends on the particle Reynolds number. Re (= IcUp/fi). For gases, Dsi/ulc also depends on the Schmidt number, p/pDf. ... [Pg.418]

The intensity of dispersion depends on local conditions, e.g., particle size and superficial velocity. However, the geometric factor is inversely proportional to the reactor length L. Therefore, for fixed local conditions, the Dispersion munber decreases as the reactor becomes longer. [Pg.418]

In many previous correlations, the intensity of dispersion was expressed in terms of the equivalent diameter of a spherical particle. In fact, spherical particles were used in many of the studies on which Figure 10-7 is based. In this chapter, for consistency, the correlations have been converted to the same characteristic dimension that was used in Chapter 9. [Pg.418]

A correlation for turbulent flow in empty pipes is shown in Figure 10-8. The structure of this correlation is the same as that shown previously, i.e., an intensity of dispersion is... [Pg.418]

Figure 10-8 Intensity of dispersion for fluids flowing through empty pipes in turbulent flow. Figure 10-8 Intensity of dispersion for fluids flowing through empty pipes in turbulent flow.
The Dispersion model can be used to predict the performance of a nonideal reactor in the absence of a measured RTD. However, the geometric parameters and the flow conditions of the nonideal reactor must fall within the range of existing correlations for the intensity of dispersion. ... [Pg.435]

Can the Dispersion model be used for the analysis or design of a radial-flow, fixed-bed reactor, based on the existing intensity of dispersion correlations ... [Pg.435]


See other pages where Intensity of dispersion is mentioned: [Pg.733]    [Pg.684]    [Pg.101]    [Pg.102]    [Pg.70]    [Pg.283]    [Pg.2254]    [Pg.2237]    [Pg.12]    [Pg.547]    [Pg.74]    [Pg.57]    [Pg.931]    [Pg.140]    [Pg.143]    [Pg.143]    [Pg.145]    [Pg.418]   
See also in sourсe #XX -- [ Pg.110 ]




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