Biphasic flow: structure and upscaling, consequences on macroscopic transport properties

TL;DR

This paper reviews how biphasic flow in porous media forms fractal patterns influenced by forces and boundary conditions, affecting stability, structure, and macroscopic transport properties, with insights from experiments and upscaling models.

Contribution

It provides a comprehensive review of biphasic flow patterns, fractal geometries, and upscaling methods in porous media, highlighting the influence of microscopic structures on macroscopic properties.

Findings

Flow patterns depend on capillary, gravitational, and viscous forces.

Fractal dimensions vary with flow velocity and conditions.

Upscaling relates microscopic structures to macroscopic transport properties.

Abstract

In disordered porous media, two-phase flow of immiscible fluids (biphasic flow) is organized in patterns that sometimes exhibit fractal geometries over a range of length scales, depending on the capillary, gravitational and viscous forces at play. These forces, as well as the boundary conditions, also determine whether the flow leads to the appearance of fingering pathways, i.e., unstable flow, or not. We present here a short review of these aspects, focusing on drainage and summarizing when these flows are expected to be stable or not, what fractal dimensions can be expected, and in which range of scales. We base our review on experimental studies performed in two-dimensional Hele-Shaw cells, or addressing three dimensional porous media by use of several imaging techniques. We first present configurations in which solely capillary forces and gravity play a role. Next, we review configurations in which capillarity and viscosity are the main forces at play. Eventually, we examine how the microscopic geometry of the fluid clusters affects the macroscopic transport properties. An example of such an upscaling is illustrated in detail: For air invasion in a mono-layer glass-bead cell, the fractal dimension of the flow structures and the associated scale-ranges, are shown to depend on the displacement velocity. This controls the relationship between saturation and the pressure difference between the two phases at the macroscopic scale. We provide in this case expressions for dynamic capillary pressure and residual fluid phase saturations.