Water Resources Research | 2019
Mechanisms, Upscaling, and Prediction of Anomalous Dispersion in Heterogeneous Porous Media
Abstract
5 We study the upscaling and prediction of large scale solute dispersion in heterogeneous 6 porous media with focus on preasymptotic or anomalous features such as tailing in break7 through curves and spatial concentration profiles as well as non-linear evolution of the 8 spatial variance of the concentration distribution. Spatial heterogeneity in the hydraulic 9 medium properties is represented in a stochastic modeling approach. Direct numerical 10 Monte Carlo simulations of flow and advective particle motion combined with a Markov 11 model for streamwise particle velocities give insight in the mechanisms of preasymptotic 12 and asymptotic solute transport in terms of the statistical signatures of the medium and 13 flow heterogeneity. Based on the representation of equidistantly sampled particle veloc14 ities as a Markov process, we derive an upscaled continuous time random walk approach 15 that can be conditioned on the flow velocities and thus hydraulic conductivity in the in16 jection region. In this modeling framework, we identify the Eulerian velocity distribu17 tion, advective tortuosity and the correlation length of particle velocities as the key quan18 tities for large scale transport prediction. Thus, the upscaled model predicts the spatial 19 concentration profiles, their first and second centered moments as well as the breakthrough 20 curves obtained from direct numerical Monte Carlo simulations in spatially heterogeneous 21 conductivity fields. The presented approach allows to relate the medium and flow prop22 erties to large scale preasymptotic and asymptotic solute dispersion. 23