Quantifying the impact of the velocity field organization on the solute transport properties
Résumé
We propose a framework to quantify the velocity field organization in heterogeneous media for modelling solute transport. The Lagrangian velocity correlation properties are analyzed from numerical simulation of transport in heterogeneous permeability fields. The two-point Lagrangian correlation function is shown to be insufficient in general to quantify the velocity field spatial organization. An alternative method is proposed based on the Lagrangian velocity correlation properties conditioned on the solute particle initial velocity. It allows capturing the effect of the different spatial organization of high and low velocity zones. For the permeability fields studied, we find that low velocity zones are associated with larger Lagrangian correlation times than high velocity zones. We define a random walk model that can simulate solute transport with velocity dependent correlation and discuss its properties and applicability.