Investigating Darcy-scale assumptions by means of a multiphysics algorithm

Abstract

Multiphysics (or hybrid) algorithms, which couple Darcy and pore-scale descriptions of flow through porous media in a single numerical framework, are usually employed to decrease the computational cost of full porescale simulations or to increase the accuracy of pure Darcy-scale simulations when a simple macroscopic description breaks down. Despite the massive increase in available computational power, the application of these techniques remains limited to core-size problems and upscaling remains crucial for practical large-scale applications. In this context, the Hybrid Multiscale Finite Volume (HMsFV) method, which constructs the macroscopic (Darcy-scale) problem directly by numerical averaging of pore-scale flow, offers not only a flexible framework to efficiently deal with multiphysics problems, but also a tool to investigate the assumptions used to derive macroscopic models and to better understand the relationship between pore-scale quantities and the corresponding macroscale variables. Indeed, by direct comparison of the multiphysics solution with a reference pore-scale simulation, we can assess the validity of the closure assumptions inherent to the multiphysics algorithm and infer the consequences for macroscopic models at the Darcy scale. We show that the definition of the scale ratio based on the geometric properties of the porous medium is well justified only for single-phase flow, whereas in case of unstable multiphase flow the nonlinear interplay between different forces creates complex fluid patterns characterized by new spatial scales, which emerge dynamically and weaken the scale-separation assumption. In general, the multiphysics solution proves very robust even when the characteristic size of the fluid-distribution patterns is comparable with the observation length, provided that all relevant physical processes affecting the fluid distribution are considered. This suggests that macroscopic constitutive relationships (e.g., the relative permeability) should account for the fact that they depend not only on the saturation but also on the actual characteristics of the fluid distribution.

Local instabilities during capillary-dominated immiscible displacement in porous media

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Modeling Pore-Scale Two-Phase Flow: How to Avoid Gas-Channeling Phenomena in Micropacked-Bed Reactors via Catalyst Wettability Modification

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