Numerical simulation of transport in porous media: some problems from micro to macro scale

TL;DR

This paper explores the multiscale simulation of flow and transport in porous media, highlighting pore-scale velocity structures, permeability estimation, and advanced numerical methods to improve modeling accuracy.

Contribution

It introduces a method for estimating large-scale permeability from point measurements and demonstrates high-order finite element methods to improve transport simulations.

Findings

Velocity PDFs are skewed with negative velocities, affecting dispersion.

A successful adjoint-based method estimates permeability fields from velocity data.

High-order finite element methods reduce non-physical oscillations in convection-dominated transport simulations.

Abstract

This paper deals with simulation of flow and transport in porous media such as transport of groundwater contaminants. We first discuss how macro scale equations are derived and which terms have to be closed by models. The transport of tracers is strongly influenced by pore scale velocity structure and large scale inhomogeneities in the permeability field. The velocity structure on the pore scale is investigated by direct numerical simulations of the 3D velocity field in a random sphere pack. The velocity probability density functions are strongly skewed, including some negative velocities. The large probability for very small velocities might be the reason for non-Fickian dispersion in the initial phase of contaminant transport. We present a method to determine large scale distributions of the permeability field from point-wise velocity measurements. The adjoint-based optimisation algorithm delivers fully satisfying agreement between input and estimated permeability fields. Finally numerical methods for convection dominated tracer transports are investigated from a theoretical point of view. It is shown that high order Finite Element Methods can reduce or even eliminate non-physical oscillations in the solution without introducing additional numerical diffusivity.