Much research has been focused on mass transfer phenomena in packed beds. For Peclet numbers above 200, empirical relations have been derived that predict the value of the mass transfer coefficient as a function of the Reynolds number and the Schmidt number. These relations are more or less similar to the well-known relation that Rant and Marshall derived for mass transfer around a single sphere in an infinite medium Sh = alpha + beta (ReScdelta)-Sc-gamma. For packed beds of spherical particles an alpha-value of 3.89 can be calculated on basis of fundamental considerations. However, Sherwood numbers much lower than this minimum value have been observed at Peclet numbers below 100. Several explanations have been proposed for this apparent discrepancy, such as misinterpretation of the experimental results due to unjustified neglection of axial dispersion or wall channeling. III this work, a model that predicts the combined effects of axial dispersion and wall channeling has been developed. With this model, it is possible to explain the results obtained with undiluted beds in which all particles are active in the process of mass transfer. However, such an explanation is not possible for the results obtained with diluted beds in which not all particles are active. Therefore, in the case of diluted beds other reasons for the apparent drop in mass transfer rate must exist. In the present investigation, it is demonstrated that the drop again originates from misinterpretation of the experimental results. It is shown, both experimentally and theoretically, that low Sherwood numbers can be obtained when large differences exist between the local concentration, experienced by an active particle and the mixed cup concentration of the whole bed cross-section.