Stretching, Dispersion and Mixing in 2D Darcy scale heterogeneous porous media

Mixing in porous media is the process from which the homogenization of an initially segregated system is done. It is a key process for a vast type of applications, from ground remediation methods to numerous engineering applications where the facilitation of chemical reactions is needed. This process is the result of the interaction of spatial velocity fluctuations and diffusion or local-scale dispersion. The velocity fluctuations are induced by spatial medium heterogeneities at the pore, Darcy or regional scales which will enhance mixing by stretching the fluid elements of the groundwater. Stretching of fluid elements augments the ratio of surface to volume of the solute, making thus place for diffusion to destroy the concentration gradients on pore-scale. The main objective of this work is to unravel and quantify the mechanisms and laws that explain the impact of structure on stretching and dispersion dynamics in heterogeneous porous media, constituting two fundamental mechanisms for the understanding of mixing. The objectives are thus to quantify and understand the impact structure and media on stretching and dispersion on 2D Darcy scale heterogeneous porous media. Upscaling models for the previous mechanisms are also derived to predict large scale transport behaviors and understand the key parameters governing these mechanisms.
The methodology consists of numerical and theoretical derivations. The heterogeneity of the media is modeled by a stochastic model to systematically study the impact of spatial variability. Transport is analyzed through a Lagrangian framework by particle tracking. Deterministic and stochastic models for breakthrough curves, dispersion coefficients and stretching rates are proposed, demonstrating strong agreement.