Stable and unstable capillary fingering in porous media with a gradient in grains size

TL;DR

This paper combines theoretical, experimental, and simulation approaches to understand how gradients in grain size and external forces influence the stability of drainage patterns in porous media, revealing a unifying framework for dual fluid flow.

Contribution

It introduces a unified theory linking structural gradients and external forces to drainage pattern stability, supported by novel experiments and simulations.

Findings

Structural gradients and external forces similarly stabilize invasion fronts.

The width of stable fronts scales with the gradient of pore invasion thresholds.

Scaling exponent of -0.57 derived from percolation theory for 2D systems.

Abstract

We present a theoretical and experimental investigation of slow drainage in porous media with a gradient in the grains size (and hence in the typical pores' throats), in an external gravitational field. We mathematically show that such structural gradient and external force have a similar effect on the obtained drainage patterns, when they stabilise the invasion front. With the help of a newly introduced experimental set-up, based on the 3D-print of transparent porous matrices, we illustrate this equivalence, and extend it to the case where the front is unstable. We also present some invasion-percolation simulations of the same phenomena, which are inline with our theoretical and experimental results. In particular, we show that the width of stable drainage fronts mainly scales with the spatial gradient of the average pore invasion threshold and with the local distribution of this (disordered) threshold. The scaling exponent results from percolation theory and is -0.57 for 2D systems. Overall, we propose a unifying theory for the up-scaling of dual fluid flows in most classical scenarii.