Mechanisms, Upscaling, and Prediction of Anomalous Dispersion in Heterogeneous Porous Media

We study the upscaling and prediction of large-scale solute dispersion in heterogeneous porous media with focus on preasymptotic or anomalous features such as tailing in breakthrough curves and spatial concentration profiles as well as nonlinear evolution of the spatial variance of the concentration distribution. Spatial heterogeneity in the hydraulic medium properties is represented in a stochastic modeling approach. Direct numerical Monte Carlo simulations of flow and advective particle motion combined with a Markov model for streamwise particle velocities give insight in the mechanisms of preasymptotic and asymptotic solute transport in terms of the statistical signatures of the medium and flow heterogeneity. Based on the representation of equidistantly sampled particle velocities as a Markov process, we derive an upscaled continuous time random walk approach that can be conditioned on the flow velocities and thus hydraulic conductivity in the injection region. In this modeling framework, we identify the Eulerian velocity distribution, advective tortuosity, and the correlation length of particle velocities as the key quantities for large-scale transport prediction. Thus, the upscaled model predicts the spatial concentration profiles, their first and second centered moments, and the breakthrough curves obtained from direct numerical Monte Carlo simulations in spatially heterogeneous conductivity fields. The presented approach allows to relate the medium and flow properties to large-scale preasymptotic and asymptotic solute dispersion.SCOPUS: ar.j