Flow-Area Relations in Immiscible Two-Phase Flow in Porous Media

TL;DR

This paper develops a theoretical framework linking local fluid velocities to average seepage velocities in immiscible two-phase flow within porous media, supported by numerical simulations that validate the model.

Contribution

It introduces a novel distribution-based formalism connecting local velocities to seepage velocities and their moments, advancing understanding of two-phase flow in porous media.

Findings

The formalism re-establishes known relationships between seepage velocities.

It derives new relations involving higher moments of velocity distributions.

Numerical simulations confirm the theoretical predictions.

Abstract

We present a theoretical framework for immiscible incompressible two-phase flow in homogeneous porous media that connects the distribution of local fluid velocities to the average seepage velocities. By dividing the pore area along a cross-section transversal to the average flow direction up into differential areas associated with the local flow velocities, we construct a distribution function that allows us not only to re-establish existing relationships between the seepage velocities of the immiscible fluids, but also to find new relations between their higher moments. We support and demonstrate the formalism through numerical simulations using a dynamic pore-network model for immiscible two-phase flow with two- and three-dimensional pore networks. Our numerical results are in agreement with the theoretical considerations.