Backward Particle Tracking of Anomalous Transport in Multi‐Dimensional Aquifers

Abstract

AbstractBackward particle tracking (BPT) remains a subject of research and applications in hydrology for decades, and most BPT models and software suits assume Fickian diffusion even though pollutant transport in natural aquifers is usually non‐Fickian. To fill this knowledge gap, BPT models were presented in this study for pollutants undergoing sub/super‐diffusion in multi‐dimensional geological media. The resultant BPT governing equations were adjoint models derived for four equally possible, vector fractional diffusion equations. BPT solvers followed a two‐step backward Lagrangian scheme, which differed from its forward Lagrangian scheme in super‐dispersive jumps and boundary conditions. BPT parameter estimability depended on the type of parameters and aquifers according to Monte Carlo analyses: (a) most parameters could be estimated using medium properties or tracer snapshots, while the mean velocity and the space‐dependent dispersion coefficient had poor estimability, and (b) fractured aquifers had a lower estimability for BPT parameters than alluvial aquifers. Mathematical evaluation and field applications showed that the adjoint of the vector fractional‐divergence advection‐dispersion equation (FD‐ADE) identified the source location of pollutants undergoing multiscaling super‐diffusion better than the other BPT models. The adjoint of the vector FD‐ADE and its Lagrangian solver, therefore, were recommended to backtrack pollutants undergoing anomalous transport in aquifers with various degrees of heterogeneity and any dimension and boundary conditions.