Non-Fickian Transport: Quantifying Tracer Transport Measurements

A broad range of non-Fickian transport behaviors in laboratory- and field-scale geological media has been effectively quantified within the continuous time random walk (CTRW) framework, in both descriptive and predictive capacities. We consider several such example applications of CTRW theory, accounting also for transitions from non-Fickian to Fickian behavior. The CTRW framework is based on a picture of transport as a sequence of particle transition rates (e.g., between pore spaces, fracture intersections) and the incorporation of the full spectrum of these rates into the transport equations. In disordered systems, the statistically rare, slow transition rates can strongly limit the overall transport. Even in small-scale, "homogeneous" porous media, subtle and residual pore-scale disorder effects can lead to non-Fickian transport. But situations arise where two apparently distinct transport regimes may be present, as in the cases of fractured porous rocks and heterogeneous media with long-range layers of high permeability. We extend the CTRW transport equations to deal explicitly with these cases. Our focus is on the coupling of the spectrum of particle transition rates with multiple rate mass transfer into less mobile states (e.g., regions with adsorption/desorption or diffusion), in which the spectrum of transfer rates may be significantly different. In this context, experimental data are analyzed from two different transport scenarios. We examine conservative tracer transport in a fractured porous medium, and sorbing species being transported through a heterogeneous porous domain; in both cases, the enhanced CTRW framework effectively reproduces the experimental data.