Modeling anomalous dispersion in heterogeneous porous media using spatial Markov models for Lagrangian velocities.
A cargo de: Vivien Hakoun
Understanding and predicting solute transport in porous media is important for environmental applications such as the remediation of contaminated aquifers and for the purpose of risk assessment. Porous aquifers often have heterogeneous hydraulic properties which impact the groundwater flow field, resulting in complex solute transport behaviors. In this context, performing accurate transport predictions is a challenge: advection-dispersion models based on effective transport parameters cannot be applied; perturbation theories are limited to hydraulic conductivity fields with log-variance smaller than 1; these models do not account for (non-Fickian) solute behaviors such as early and late breakthrough times and the non linear growth of solute dispersion. Here, we study direct numerical simulations of solute transport at Darcy-scale in correlated heterogeneous hydraulic conductivity fields with broad point distributions. We characterize the stochastic dynamics of Lagrangian velocities that are sampled along streamlines in an isochrone and equidistant fashion. We propose a Markov-chain continuous time random walk (CTRW) approach to quantify the evolution of the statistics of Lagrangian velocities under different injection conditions. Comparing two models to reproduce velocity transitions, we find that Lagrangian statistics are best reproduced using a mean-reverting Ornstein-Uhlenbeck model which parameter can be estimated from geostatistical properties of the hydraulic conductivity field. On the basis of this CTRW approach, we discuss a stochastic model based on flow and medium properties only. We apply this model to predict non-Fickian transport behaviors obtained by direct numerical simulations of transport in synthetic heterogeneous hydraulic conductivity fields. Our predictions are in close agreement with the direct numerical simulations.