Multiscale Representative Elementary Volume Determination in Complex Porous Media: An Integrated Hydrodynamic and Thermodynamic Modelling Approach

Abstract

Understanding fluid transport in microporous media remains a complex challenge due to the intricate interplay of heterogeneity and scale-dependent behaviours. This study introduces a novel multiscale discretisation framework, specifically tailored for dual-porosity systems, and integrates it with an enhanced multiphase solver to determine representative elementary volumes (REVs) across contrasting pore structures. The proposed numerical approach incorporates a hybrid formulation combining two-phase Darcy flow for macro-scale domains with Navier–Stokes and volume-of-fluid (VOF) interface tracking for micro-scale regions. This enables simulation of complex immiscible flows with explicit resolution of both macro- and microporous pathways. A dedicated mesh refinement strategy ensures computational efficiency while preserving geometric fidelity across porosity scales. We apply this framework to two carbonate samples: the Savonnieres carbonate and the Mount Gambier limestone. In the Savonnieres sample, REV convergence could not be achieved even at the largest available micro-CT volume (1000³ voxels, ~ 3.8 mm³) due to pronounced microstructural clustering. In contrast, the Mount Gambier limestone exhibited stable hydrodynamic and thermodynamic REV behaviour above 1200³ voxels (~ 3.21 mm³), closely matching experimental core-scale estimates. These findings reinforce the robustness of the proposed methodology and underscore its potential for broader application to microporous media with diverse heterogeneity profiles.