Emergence of non-Fickian transport in truncated pluri-Gaussian permeability fields

TL;DR

This study uses numerical simulations to investigate how high-contrast, discontinuous permeability fields generated by truncated pluri-Gaussian models cause a transition from Fickian to non-Fickian scalar transport, influenced mainly by permeability contrast and connected channels.

Contribution

It introduces a novel unified finite-volume framework for simulating advective-diffusive transport in complex, high-contrast porous media generated by pluri-Gaussian models, highlighting the factors triggering non-Fickian behavior.

Findings

High permeability contrasts induce non-Fickian transport.

Connected high-permeability channels enhance non-Fickian effects.

Transport remains Fickian for contrasts up to one order of magnitude.

Abstract

We present a numerical simulation study of advective-diffusive scalar transport in three-dimensional high-contrast discontinuous permeability fields, generated with a truncated pluri-Gaussian geostatistical approach. A range of permeability contrasts, correlation lengths, and P\'eclet numbers are studied to characterise the transition to non-Fickian transport behaviour. This is triggered by high permeability contrasts between different zones and is enhanced by the presence of connected higher permeability channels, which are characterised by high advective flow velocities. In this case, the overall transport behaviour deviate from the macroscopic advection-dispersion model based on a Fickian analogy. The numerical experiments are run with an Eulerian approach using a novel unified numerical framework based on the finite-volume library \of, for i) generating random pluri-Gaussian porous media, ii) solving the steady state Darcy-scale flow, iii) solving the advection diffusion equation, iv) computing post-processing quantities such as first order statistics, spatial probability density functions and breakthrough curves. We identify a hierarchy of non-Fickian transport triggering factors, the strength of permebility contrast being the pivotal driver. The P\'eclet number and the characteristic length at which facies transitions are observed as secondary factors. Transport remains Fickian when the facies conductivities differ by up to one order of magnitude. Greater permeability contrasts act strengthen the emergence of fast flow channels leading to non-Fickian transport.