Upscaled dynamic capillary pressure for two-phase flow in porous media

Abstract

A closed expression for the average pressure difference (often called the macroscopic dynamic capillary pressure in the literature) is proposed for two-phase, Newtonian, incompressible, isothermal and creeping flow in homogeneous porous media. This upscaled equation complements the average equations for mass and momentum transport derived in a previous article. Consistently with this work, the expression is derived employing a simplified version of the volume-averaging method that makes use of elements of the adjoint method and Green's formula. The resulting equation for the average pressure difference is novel, as it shows that this quantity is controlled by the pressure gradient (and body forces) in each phase, as well as interfacial effects, and is applicable to situations in which the fluid–fluid interface is not necessarily at its steady position. The effective-medium quantities associated with the sources are all obtained from the solution of a single adjoint (or closure) problem to be solved on a (periodic) unit cell representative of the process. The average pressure difference predicted by the derived expression is validated through excellent comparisons with direct numerical simulations performed in a model porous structure.

The Dynamics of Per- and Polyfluoroalkyl Substances (PFAS) at Interfaces in Porous Media: A Computational Roadmap from Nanoscale Molecular Dynamics Simulation to Macroscale Modeling

“…40 A closed expression for the average pressure difference (referred to as the capillary pressure at a macroscale) has been proposed. 41 However, the complex behavior of PFAS challenges such upscaling approaches. The quantitative constitutive relationships are purely based on empirical studies (and disconnected from theoretical upscaling) and have limited applicability.…”

“…The mass and momentum upscaled equations were obtained, and generalized Darcy-like dominant and viscous coupling terms were presented . A closed expression for the average pressure difference (referred to as the capillary pressure at a macroscale) has been proposed …”

“… 40 A closed expression for the average pressure difference (referred to as the capillary pressure at a macroscale) has been proposed. 41 …”