ON THE CHARACTERIZATION OF ANOMALOUS DISPERSION: A RANDOM WALK PARTICLE TRACKING METHOD

Anomalous dispersion, characterized by 1) super-Fickian plume growth rates, 2) power-law early and/or the late tail of the solute breakthrough curve, or 3) power-law leading edge of the plume profile, has been observed in many laboratory- and field-scale tests. Anomalous dispersion has been parsimoniously described by the nonlocal, space and/or time fractional advection-dispersion equation, in which the characteristic coefficients were usually treated as constants. The constants were estimated by the site-wide characteristics of the hydraulic conductivity field, and allowed analytical solutions for simple boundary value problems. For more accuracy in a non-homogeneous system where the potential non-stationary heterogeneity tends to cause local variations of solute transport, the nonlocal governing equation may contain space- (or time-) dependent transport parameters that capture the local variation of the strength of the nonlocal spreading. Since analytical solutions are not available in this case, we developed a Lagrangian framework based on random walk particle tracking to approximate the fractional dispersion in space and time. This novel numerical algorithm is superior to the traditional methods by allowing 1) variable parameters including the velocity, dispersion magnitude and directionality (through the mixing measure), and the index of the time-fractional derivative, 2) a coupled or decoupled jump size and waiting time for solute particles, and 3) different scaling rates and strength of dispersion in different directions (which may correspond to flowlines). Thus it captures the main features of a typical anomalous dispersion, such as multi-scaling spreading rates and arbitrary plume fringes, which cannot be characterized by the traditional 2nd-order advection-dispersion equation unless tremendous information about the fine-scale velocity field is available. Examples are given, including tritium transport at the MADE site, to demonstrate the applicability, flexibility and efficiency of this Lagrangian framework.