Dispersion, axial in packed beds

When a fluid flows through a packed bed there is a tendency for axial mixing to occur. Any such mixing is undesirable since it reduces the efficiency of separation. The minimization of axial dispersion is therefore a major design objective, particularly when the separation factor is small. 

Flow through a packed bed may generally be adequately represented by the axial dispersed plug flow model  

In this model the effects of all mechanisms which contribute to axial mixing are lumped together into a single effective axial dispersion coefficient. More detailed models which include, for example, radial dispersion are generally not necessary and in many cases it is in fact possible to neglect axial dispersion altogether and assume ideal plug flow. 

Considering the bed as an assemblage of randomly oriented cylindrical pores isuggests Y, 1/V 2, which is dose to the experimental values derived from dispersion measurements for gases at low Reynolds number. More detailed investigation reveals that the bed tortuosity (1/Yi) is related to the voidage. Wicke has suggested  

FIGURE 73. Variation of Peclet number with Reynolds number for flqw of gases through packed beds, (a) Data of Hsu and Haynes (column 1, 0.36 mm column 2, R, 0.17 

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Fig. 8. Axial dispersion in packed beds, dispersed plug flow model (L13).

Cao is the inlet molar density of reactant A at z = 0, a. interpeiiet is the interpellet diffusion coefficient of species A which accounts for axial dispersion in packed beds, the dimensionless rate of the 7 th reaction is... 

If there is only one chemical reaction on the internal catalytic surface, then vai = — 1 and subscript j is not required for all quantities that are specific to the yth chemical reaction. When the mass transfer Peclet number which accounts for interpellet axial dispersion in packed beds is large, residence-time distribution effects are insignificant and axial diffusion can be neglected in the plug-flow mass balance given by equation (22-11). Under these conditions, reactor performance can be predicted from a simplified one-dimensional model. The differential design equation is... 

Axial dispersion in packed beds, and Taylor dispersion of a tracer in a capillary tube, are described by the same form of the mass transfer equation. The Taylor dispersion problem, which was formulated in the early 1950s, corresponds to unsteady-state one-dimensional convection and two-dimensional diffusion of a tracer in a straight tube with circular cross section in the laminar flow regime. The microscopic form of the generalized mass transfer equation without chemical reaction is... 

Analysis of experimental data for interpellet axial dispersion in packed beds has generated the following empirical correlation, as described by equation (22-84) and Table 22-6 ... 

Tsotsas, E. and Schlunder, E.U., 1988a. On Axial-Dispersion in Packed-Beds with Fluid-Flow. Chemical Engineering and Processing, 24(1) 15-31. 

J. Carberry, First order rate processes and axial dispersion in packed bed reactors, Can. J. Chem. Eng. 36 (1958) 207. 

Ahn, B.-J., Zoulalian, A., and Smith, J.M. (1986) Axial dispersion in packed beds with large wall effect. AIChEJ., 32, 170-174. 

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