Dispersion in a packed bed

To identify the pertinent HETP equation that describes dispersion in a packed bed, the following logical procedure will require to be carried out. 

Horvath and Lin [10,11] showed how the different contributions to peak dispersion in a packed bed could be defined in an expression for H, which was applied [12] to CEC by Dittman et al. it was demonstrated that the major contribution of eddy diffusion to H in HPLC was considerably reduced in CEC. Minimal reduced plate heights h = (H/dp), generally found to be near 2 in HPLC, should be reduced to near 1 or less, giving rise to plate numbers over 10s for a 40-cm-long CEC column with 3-pm particles. Horvath and Lin showed [11] how their expression for H could be simplified to... 

The bulk diffusion coefficient of lipase was estimated [55]. The dispersion coefficient is used to characterize the axial dispersion in a packed bed. This parameter accounts for the dispersion due to molecular diffusion as well as eddy diffusion due to velocity differences around the particles. A correlation used to estimate the dispersion coefficient Dm in fixed beds was developed by Chung and Wen [56]. 

Gupta R, Bansal A. Effect of bed configuration on dispersion in a packed-bed reactor. Industrial and Engineering Chemistry Research 2010 49 9525-9528. 

FIG. 16-9 General scheme of adsorbent particles in a packed bed showing the locations of mass transfer and dispersive mechanisms. Numerals correspond to mimhered paragraphs in the text 1, pore diffusion 2, solid diffusion 3, reaction kinetics at phase boundary 4, external mass transfer 5, fluid mixing. 

The Peclet numbers decrease when the dispersion coefficients increase. In the Reynolds number range of 10-200, in a packed bed of pellets, Peii = 2 and PeH = 0.5 (119, 120). The dispersions in the transverse... 

Radial dispersion coefficient for heat in a packed-bed 9.3 Axial dispersion coefficient for temperature in PDE Sec. 9.1 model... 

Neglecting radial effects, the dispersion equation for dispersed tracer with bulk flow in a packed bed is ... 

In most adsorption processes the adsorbent is contacted with fluid in a packed bed. An understanding of the dynamic behavior of such systems is therefore needed for rational process design and optimization. What is required is a mathematical model which allows the effluent concentration to be predicted for any defined change in the feed concentration or flow rate to the bed. The flow pattern can generally be represented adequately by the axial dispersed plug-flow model, according to which a mass balance for an element of the column yields, for the basic differential equation governing llie dynamic behavior,... 

This is the standard dispersion model for P, and the aim of investigating more complex situations has often been to reduce them to this form with D = De, an effective dispersion coefficient that wraps up the complexities of the underlying situation in a single quantity. Whether this is wise is another matter. For example, in a packed bed the flow is obviously very complex, but both theory [4] and experiment can be invoked to justify an effective Peclet number, URIDe, of about 2. The question that hangs over the use of Eq. (33) is that it is a parabolic equation, with infinite signal speed and controversial boundary conditions. 

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

So far, the separation efficiencies reported with the submicron packed beds have not offered a significant improvement over those obtained with particle diameters in the 1 pm range [66,119-121]. Fig. 4.17 depicts the separation of a test mixture obtained in a packed bed with particles of about 0.5 pm in diameter. As reported by Luedtke, et al. [121], plate heights of about three times the particle diameter (H = 3dp) are achieved. This has been attributed to band dispersion due to temperature effects and instrumental limitations, such as the maximum electric field that can be applied with existing units and detection systems [121], Plots of plate height versus linear... 

In the chromatographic method a pulse or step change in sor-bate concentration is introduced into the carrier stream at the inlet of a packed adsorption column and the diffusional time constant is determined from the dispersion of the response signal at the column outlet. Since heat transfer in a packed bed is much faster than in a closed system the chromatographic method may, in principle, be used to follow somewhat faster sorption processes. 

In a packed-bed reactor, the backward flux of energy is limited to the relatively small effect of conduction through the packing. The principal dispersion mechanism is variation in flow rate from point to point, coupled with lateral mixing. 

Models with varying degrees of complexity have been employed to analyze the experimental results by a variety of techniques. The most comprehensive models include terms to account for axial dispersion in the packed bed, external mass transfer, intraparticle diffusion in both macropore and micropore regions of the pellet and a finite rate of adsorption. Of the several methods of analysis, the most popular ones are based on the moments of the response curve. The first moment of the chromatogram is defined by Equation 5.25 in which the concentration now is taken at the outlet of the column. The second central moment is calculated from equation... 

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