Drainage in a model stratified porous medium

TL;DR

This study investigates how non-wetting fluids drain stratified porous media, revealing a threshold capillary number that determines whether flow occurs only in coarse layers or also in finer ones, with implications for geological processes.

Contribution

It provides a quantitative model explaining the transition in flow behavior based on capillary number in stratified porous media.

Findings

Flow occurs only in coarse strata at low Ca.

Above a threshold Ca, flow invades finer strata.

The extent of invasion increases with Ca.

Abstract

We show that when a non-wetting fluid drains a stratified porous medium at sufficiently small capillary numbers Ca, it flows only through the coarsest stratum of the medium; by contrast, above a threshold Ca, the non-wetting fluid is also forced laterally, into part of the adjacent, finer strata. The spatial extent of this partial invasion increases with Ca. We quantitatively understand this behavior by balancing the stratum-scale viscous pressure driving the flow with the capillary pressure required to invade individual pores. Because geological formations are frequently stratified, we anticipate that our results will be relevant to a number of important applications, including understanding oil migration, preventing groundwater contamination, and sub-surface CO$_{2}$ storage.