Upscaling of Anomalous Pore-Scale Dispersion

We study the upscaling of advective pore-scale dispersion in terms of the Eulerian velocity distribution and advective tortuosity, both flow attributes, and of the average pore length, a medium attribute. The stochastic particle motion is modeled as a time-domain random walk, in which particles move along streamlines in equidistant spatial steps with random velocities and thus random transition times. Particle velocities describe stationary spatial Markov processes, which evolve along streamlines on the mean pore length. The streamwise motion is projected onto the mean flow direction using tortuosity. This upscaled stochastic particle model predicts accurately the (non-Fickian) transport dynamics obtained from direct numerical simulations of particle transport in a three-dimensional digitized Berea sandstone sample. It captures all aspects of transport and sheds light on the dependence of the upscaled transport behavior on the flow heterogeneity and the initial particle distribution, which are critical for the accurate modeling of dispersion from the pre-asymptotic to asymptotic regimes.