Pore-scale Mixing and the Evolution of Hydrodynamic Dispersion in Porous Media

TL;DR

This paper investigates how pore-scale mixing mechanisms influence large-scale hydrodynamic dispersion in porous media, providing a theoretical framework to predict dispersion behavior based on pore characteristics and flow conditions.

Contribution

It introduces a new theory linking pore-scale mixing mechanisms to the evolution of hydrodynamic dispersion, accounting for both anomalous and normal regimes.

Findings

Identifies three key pore-scale mixing mechanisms affecting dispersion.

Derives a predictive theory based on pore length, velocity distribution, and Péclet number.

Explains transition between anomalous and normal dispersion regimes.

Abstract

We study the interplay of pore-scale mixing and network-scale advection through heterogeneous porous media, and its role for the evolution and asymptotic behavior of hydrodynamic dispersion. In a Lagrangian framework, we identify three fundamental mechanisms of pore-scale mixing that determine large scale particle motion, namely, the smoothing of intra-pore velocity contrasts, the increase of the tortuosity of particle paths, and the setting of a maximum time for particle transitions. Based on these mechanisms, we derive a theory that predicts anomalous and normal hydrodynamic dispersion based on the characteristic pore length, Eulerian velocity distribution and P\'eclet number.