Measurement and Analysis of Non-Fickian Dispersion in Heterogeneous Porous Media

Field and laboratory analyses of transport in heterogeneous porous media often demonstrate non-Fickian patterns, as distinguished by ``anomalous" early arrival and late time tails in breakthrough curves. As such, the classical advection-dispersion equation (ADE), which describes dispersion as a Fickian diffusive process, does not describe such transport adequately. Recently, a continuous time random walk (CTRW) framework has been shown to be a potentially valuable tool in the assessment of dispersive processes in heterogeneous media. Here, particle motion is approximated as a series of discrete steps, each having a different velocity. A particle's position is determined at the points of transition between these steps. A continuous time random walk (CTRW) is then introduced to account for the cumulative effects of a sequence of transitions. The ADE can be derived from the CTRW theory under specific, limiting conditions. In this study, heterogeneity structures that give rise to non-Fickian transport were examined using laboratory experiments. Contaminant breakthrough behaviour in a variety of heterogeneous porous media was measured experimentally, and evaluated both in terms of the ADE and the CTRW frameworks. Experiments were conducted in two flow cells (dimensions: 2.0 x 0.7 x 0.1 m and 1.0 x 0.5 x 0.1 m) packed with clean sieved sand of specified grain sizes. Three sets of experiments were performed, using: an ``homogeneous" packing, a random packing using sand of two grain sizes, and an exponentially correlated structure using sand of three grain sizes. Concentrations of chloride were monitored at the inflow reservoir and measured at the outflow reservoir. Breakthrough curves were then plotted and analyzed by comparison to fitted solutions from the ADE and CTRW formulations. In all three packings, including the ``homogeneous" one, distinct non-Fickian migration behaviour was observed. Quantitative analysis demonstrated that the CTRW theory characterized the full shape of the breakthrough curves far more effectively than the ADE.