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Mechanisms, upscaling, and prediction of anomalous dispersion in heterogeneous porous media

Abstract : We study the upscaling and prediction of large‐scale solute dispersion in heterogeneous porousmedia with focus on preasymptotic or anomalous features such as tailing in breakthrough curves andspatial concentration profiles as well as nonlinear evolution of the spatial variance of the concentrationdistribution. Spatial heterogeneity in the hydraulic medium properties is represented in a stochastic modelingapproach. Direct numerical Monte Carlo simulations offlow and advective particle motion combined with aMarkov model for streamwise particle velocities give insight in the mechanisms of preasymptotic andasymptotic solute transport in terms of the statistical signatures of the medium andflow heterogeneity. Basedon the representation of equidistantly sampled particle velocities as a Markov process, we derive an upscaledcontinuous time random walk approach that can be conditioned on theflow velocities and thus hydraulicconductivity in the injection region. In this modeling framework, we identify the Eulerian velocitydistribution, advective tortuosity, and the correlation length of particle velocities as the key quantities forlarge‐scale transport prediction. Thus, the upscaled model predicts the spatial concentration profiles, theirfirst and second centered moments, and the breakthrough curves obtained from direct numerical MonteCarlo simulations in spatially heterogeneous conductivityfields. The presented approach allows to relate themedium andflow properties to large‐scale preasymptotic and asymptotic solute dispersion.
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Alessandro Comolli, Vivien Hakoun, Marco Dentz. Mechanisms, upscaling, and prediction of anomalous dispersion in heterogeneous porous media. Water Resources Research, American Geophysical Union, 2019, 55 (10), pp.8197-8222. ⟨10.1029/2019WR024919⟩. ⟨hal-02384240⟩

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