Role of pore-size distribution on effective rheology of two-phase flow in porous media

TL;DR

This paper investigates how pore-size distribution influences the rheological behavior of two-phase flow in porous media, revealing a transition from non-linear to linear flow regimes affected by pore structure and saturation.

Contribution

It introduces analytical and numerical approaches to study the impact of pore-size distribution on flow rheology and identifies conditions causing a crossover in flow behavior.

Findings

Pore-size distribution affects the power-law exponent in flow rheology.

A crossover from non-linear to linear flow occurs with increasing flow rate.

Flow behavior varies with fluid saturation levels.

Abstract

The flow of immiscible fluids inside a porous medium shows non-linearity in the form of a power law in the rheological properties of the fluids under steady state flow conditions. However, different experimental and numerical studies have reported different values for the exponent related to this power law. Here we explore how the rheological properties of the two-phase flow in porous media depends on the distribution of the pore sizes and how it affects the power-law exponent. The pore-size distribution controls fluctuation in the pore radii and their density in a porous material. We present two approaches, analytical calculations using a capillary bundle model and numerical simulations using dynamic pore-network modeling. We observe crossover from a non-linear to linear rheology when increasing the flow rate where the non-linear part is highly affected by the pore-size distribution. We have also carried out the study for different saturations of the two fluids.