Subordinated advection-dispersion equation for contaminant transport

A mathematical method called subordination broadens the applicability of the classical advection-dispersion equation for contaminant transport. In this method the time variable is randomized to represent the operational time experienced by different particles. In a highly heterogeneous aquifer the operational time captures the fractal properties of the medium. This leads to a simple, parsimonious model of contaminant transport that exhibits many of the features (heavy tails, skewness, and non-Fickian growth rate) typically seen in real aquifers, We employ a stable subordinator that derives from physical models of anomalous diffusion involving fractional derivatives. Applied to a one-dimensional approximation of the MADE-2 data set, the model shows excellent agreement.