MOMENT ANALYSIS FOR ANOMALOUS TRANSPORT WITH SPATIOTEMPORAL FRACTIONAL DISPERSION

The evolution of the first five spatial moments are investigated systematically for spatiotemporal fractional dispersion. Three fractional-order transport equations, including the time fractional advection-dispersion equation, the fractal mobile-immobile equation, and the fully fractional advection-dispersion equation, are considered. Analytical solutions verify numerical results and reveal the anomalous evolution of the moments. Following Adams and Gelhar's work on the classical ADE, we find that a simultaneous analysis of all moments is critical in discriminating between different non-local models. The evolution of dispersion among the sub- to super-diffusive rates is further explored numerically by a non-Markovian random walk particle tracking method that can be used for any heterogeneous boundary or initial value problem in 3D. Further simulations of the bromide snapshots measured at the MADE experiment, using all three models with parameters fitted by the observed moments, indicate clearly the importance of all moments in model selection.