Effective Rheology of Immiscible Two-Phase Flow in Porous Media

TL;DR

This paper shows that immiscible two-phase flow in porous media can be modeled as a Bingham viscoplastic fluid, with flow behavior transitioning from quadratic to Newtonian depending on flow rate, based on simulations and mean field calculations.

Contribution

It introduces a generalized Darcy law incorporating Bingham viscoplastic behavior for two-phase flow in porous media, supported by numerical and theoretical analysis.

Findings

Flow behaves as a Bingham viscoplastic fluid at certain rates.

Flow rate depends quadratically on excess pressure difference.

Flow becomes Newtonian at higher rates.

Abstract

We demonstrate through numerical simulations and a mean field calculation that immiscible two-phase flow in a porous medium behaves effectively as a Bingham viscoplastic fluid. This leads to a generalized Darcy equation where the volumetric flow rate depends quadratically on an excess pressure difference in the range of flow rates where the capillary forces compete with the viscous forces. At higher rates, the flow is Newtonian.