Non‐Gaussian Particle Tracking: Application to scaling of transport processes in heterogeneous porous media

Observation of scale-dependent dispersion and non-Gaussian concentration distributions under field-scale transport in heterogeneous media motivates investigation of alternatives to the classical Fickian diffusion model. A numerical model of non-Gaussian transport, employing a particle-tracking approach, is examined here. Non-Gaussian behavior is represented through modeling of the correlation between components of the random dispersive vector applied at each time step in the random walk particle-tracking algorithm. This model is applied to a number of highly detailed, synthetic hydraulic conductivity fields. By simultaneously modeling particle movement at two different scales, the impact of the small-scale heterogeneity on the correlation structure of the dispersive vectors at the larger scale can be observed directly. It is shown that accounting for the correlation structure of the dispersive vectors greatly improves prediction of arrival distributions (breakthrough curves) over the standard Fickian model. This improvement is especially evident when the model scale is not much larger than the correlation length of hydraulic conductivity but persists at relatively large transport distances. In particular, the non-Gaussian model is better able to represent the late arrival tail, which has important implications for the design and implementation of aquifer remediation methods. It is also shown that the apparent scale dependence of field dispersivity results at least in part from neglecting the correlation structure of local velocity perturbations.