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.

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