Effect of radial velocity profiles on axial dispersion in packed beds: Transient formulation

Abstract

For a single-phase flow in a packed bed, systematic radial velocity profiles promote the axial dispersion of a solute identified as trans-column dispersion and quantified by the corresponding dispersion coefficient. In a recent contribution, we evaluated the magnitude of such a dispersive effect for a long enough bed, i.e., the asymptotic behavior. However, in many practical cases, this last condition is not accomplished, and the dispersion coefficient will be lower than the asymptotic value. The development of the trans-column dispersion is addressed based on a two-dimensional two-zone model and the application of the Taylor–Aris method of moments. The results show satisfactory agreement compared with available literature data. The effect of the vessel-to-particle diameter ratio on the development of the trans-column dispersion coefficient is also explored. As the initial growth rate of the dispersion coefficient is lower, the higher the diameter ratio, and the opposite trend holds for the asymptotic value, the net effect of the diameter ratio weakens up to distances of some tens of particle diameter. This result can be identified as one of the reasons for the controversy that still prevails in assessing the contribution of the trans-column dispersion to the total axial dispersion. Further aspects discussed concern suitable approximations to evaluate the development of the trans-column dispersion coefficient and the comparison between the results from the Taylor–Aris method of moments and from the residence time distribution approach.