Finite volume solution for two-phase flow in a straight capillary

TL;DR

This paper introduces a finite volume numerical model for two-phase flow in straight capillaries that accounts for inertial effects, improving predictions of interfacial dynamics relevant to porous media flow.

Contribution

The study develops a novel finite volume model based on averaged Navier-Stokes equations that captures complex interfacial dynamics including inertia in polygonal capillaries.

Findings

Successfully predicts capillary rise and corner imbibition dynamics

Incorporates inertial effects often neglected in network models

Provides a foundation for more realistic pore-scale flow simulations

Abstract

The problem of two-phase flow in straight capillaries of polygonal cross section displays many of the dynamic characteristics of rapid interfacial motions associated with pore-scale displacements in porous media. Fluid inertia is known to be important in these displacements but is usually ignored in network models commonly used to predict macroscopic flow properties. This study presents a numerical model for two-phase flow which describes the spatial and temporal evolution of the interface between the fluids. The model is based on an averaged Navier-Stokes equation and is shown to be successful in predicting the complex dynamics of both capillary rise in round capillaries and imbibition along the corners of polygonal capillaries. The model can form the basis for more realistic network models which capture the effect of capillary, viscous and inertial forces on pore-scale interfacial dynamics and consequent macroscopic flow properties.