Axial dispersion combined effect with mass transfer resistance

The curves calculated in this way at constant for different combinations of Pe and S [i.e., for different combinations of axial dispersion and mass transfer resistance but the same linear combination 1/Pe + 5(1 + 5/0/15] show close agreement with each other and with the curve calculated from the simple linearized rate model using an overall lumped coefficient to account for the combined effects of axial dispersion, diffusion, and external mass transfer resistance. 

Axial Dispersion Effects In adsorption bed calculations, axial dispersion effects are typically accounted for by the axial diffusionhke term in the bed conservation equations [Eqs. (16-51) and (16-52)]. For nearly linear isotherms (0.5 < R < 1.5), the combined effects of axial dispersion and mass-transfer resistances on the adsorption behavior of packed beds can be expressed approximately in terms of an apparent rate coefficient for use with a fluid-phase driving force (column 1, Table 16-12) ... 

This coefficient combines the broadening effects of axial dispersion and the mass transfer resistances. The former effects decrease with increasing mobile phase velocity while the latter increase, hence there is an optimum velocity for which H is minimum. The solution of the general rate model shows that H is related to the column parameters through the equation... 

Axial dispersion, D When a band migrates along a column packed with non-porous particles, it spreads axially because of the combination effects of axial diffusion and the inhomogeneity of the pattern of flow velocity in a packed bed. This combination of effects is accounted for by a single term, proportional to the axial dispersion coefficient. It is independent of the mass transfer resistance and of the other contributions of kinetic origin to band broadening. 

Figure 9.7 Combined effects of axial dispersion and mass-transfer resistance for a Langmuir system with (5 — 0.33. The curves are normalized to the point T(mid), (C/C ) = 0.5 6 is the parameter. [After D.M. Ruthven, Principles of Adsorption and Adsorption Processes, reprinted with permission of John Wiley and Sons, New York, (NY), (1984).]...

FIGURE 8,22. Combined effects of axial dispersion and mass transfer resistance for a favorable Langmuir equilibrium system ( ==0.33). a) Constant pattern breakthrough curves for various values of (fluid film resistances + axial dispersion), (h) The same curves plotted on a modified time scale with 7 = t/(1 + B). [Reprinted with permission from Chem. Eng. Sci 30. Garg and Ruthvcn (ref. 54). Copyright 1975, Pcrgamon Press, Ltd.)... 

FIGURE 8.23, Theoretical constant-pattern breakthrough curves for irreversible adsorption showing combined effects of axial dispersion and (external) mass transfer resistance. <1.0 corresponds essentially to plug flow with external film resistance while oo corresponds to axial dispersion with negligible mass transfer resistance. Curves are calculated from expression given by Acrivos. ... 

An equivalent analysis of the combined effects of axial dispersion and mass transfer resistance has been presented by Rhee and Amundson, based on shock layer theory. From the mass balance over the shock layer it may be shown that the propagation velocity [Eq. (8.13)] is not affected by mass transfer resistance or axial dispersion. For an equilibrium system with axial dispersion the differential mass balance [Eq. (8.1)] becomes, under constant pattern conditions. 

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