Forced Imbibition in Stratified Porous Media: Fluid Dynamics and Breakthrough Saturation

TL;DR

This study develops an analytical and numerical model to understand how stratification in porous media affects imbibition dynamics and breakthrough saturation, revealing optimal conditions for minimal residual nonwetting fluid.

Contribution

It introduces a combined analytical and pore network model to analyze imbibition in stratified media, highlighting the impact of permeability stratification and capillary number tuning.

Findings

Breakthrough saturation minimized at specific capillary number Ca*

Fluid dynamics significantly influenced by stratification and viscosity ratio

Provides quantitative guidelines for flow control in stratified porous systems

Abstract

Imbibition, the displacement of a nonwetting fluid by a wetting fluid, plays a central role in diverse energy, environmental, and industrial processes. While this process is typically studied in homogeneous porous media with uniform permeabilities, in many cases, the media have multiple parallel strata of different permeabilities. How such stratification impacts the fluid dynamics of imbibition, as well as the fluid saturation after the wetting fluid breaks through to the end of a given medium, is poorly understood. We address this gap in knowledge by developing an analytical model of imbibition in a porous medium with two parallel strata, combined with a pore network model that explicitly describes fluid crossflow between the strata. By numerically solving these models, we examine the fluid dynamics and fluid saturation left after breakthrough. We find that the breakthrough saturation of nonwetting fluid is minimized when the imposed capillary number Ca is tuned to a value Ca$^*$ that depends on both the structure of the medium and the viscosity ratio between the two fluids. Our results thus provide quantitative guidelines for predicting and controlling flow in stratified porous media, with implications for water remediation, oil/gas recovery, and applications requiring moisture management in diverse materials.