Measurement and analysis of non-Fickian dispersion in heterogeneous porous media

Abstract

Contaminant breakthrough behavior in a variety of heterogeneous porous media was measured in laboratory experiments, and evaluated in terms of both the classical advection–dispersion equation (ADE) and the continuous time random walk (CTRW) framework. Heterogeneity can give rise to non-Fickian transport patterns, which are distinguished by “anomalous” early arrival and late time tails in breakthrough curves. Experiments were conducted in two mid-scale laboratory flow cells packed with clean, sieved sand of specified grain sizes. Three sets of experiments were performed, using a “homogeneous” packing, a randomly heterogeneous packing using sand of two grain sizes, and an exponentially correlated structure using sand of three grain sizes. Concentrations of sodium chloride tracer were monitored at the inflow reservoir and measured at the outflow reservoir. Breakthrough curves were then analyzed by comparison to fitted solutions from the ADE and CTRW formulations. In all three systems, including the “homogeneous” one, subtle yet measurable differences between Fickian and non-Fickian transport were observed. Quantitative analysis demonstrated that the CTRW theory characterized the full shape of the breakthrough curves far more effectively than the ADE.