One-dimensional solute transport modelling in aggregated porous media Part 2. Effects of aggregate size distribution

Abstract

The influence of various aggregate size distributions on solute transport is analysed from a quantitative and qualitative point of view. Uniform, normal, log-normal and discrete aggregate size distributions are considered. The model described in Part 1 is used to calculate the breakthrough curves. The second-order moments and the sum of squared differences are used to compare the responses calculated with the distributions and with the mean radius. The influence of a distribution depends on the velocity, and consequently on the proportion of aggregates in situations of local equilibrium or physical non-equilibrium. Breakthrough curves calculated from normal distributions, whatever their spread, do not differ significantly from those calculated using the mean radii, while slightly skewed narrow distributions generate significant differences. Thus, the skewness and not only the spreading of the distribution seem to modify the spreading of solute. The problem of using a unique ‘mean radius’ instead of a distribution is also considered. It is shown that the problem does not have a simple answer. For a given distribution, the existence of an acceptable mean radius depends strongly on the contrast between the mobile phase residence time and the distribution of characteristic diffusion times. Also, intuitively, acceptable mean radii are more easily found for narrow distributions. In most cases, it appears that a mean radius cannot be used instead of the distribution. The analysis of the way the distributions modify the breakthrough curves suggests that simple bimodal distributions presenting fast- and slow-reacting sites could be used in lieu of complete distributions.