Lagrangian characterization of contaminant transport through multidimensional heterogeneous media with limited heterogeneity information

Solute transport through regional-scale fractured rocks and heterogeneous porous media typically exhibits several “anomalous” features including 1) different growth rates along different directions, due to an anisotropic depositional or structural geologic environment; and 2) channeling along preferential flow paths. Simulating such plume characteristics can be computationally intensive using a traditional advection-dispersion equation because anomalous features of transport generally depend on local-scale subsurface properties. Here we (1) extend the fractional-order advection-dispersion equations (fADEs) to the case of spatially dependent coefficients, and (2) develop an alternative simulation approach that solves multidimensional fADEs in a Lagrangian framework using novel random walk methods. These methods allow us to simulate many of the characteristics of anomalous dispersion, as well as directiondependent spreading rates and channeling, without the need to explicitly define local-scale heterogeneity in a numerical model. We apply the new techniques to simulate results from the MADE site tracer tests.