Dynamics of immiscible two-phase flow in porous media

The interplay among capillary, viscous, and buoyancy forces has been extensively studied in small-scale 2D micromodels, revealing a rich variety of displacement patterns (Lenormand et al., JFM, 1988; Primkulov et al., JFM, 2021). However, their combined effect on long-term flow dynamics in realistic, large-scale porous media remains poorly understood. Here, we present a dynamic pore-network model that bridges this gap by simulating immiscible two-phase displacement across large domains.

By treating each pore body as a computational cell, this method draws inspiration from the classical two-phase Darcy’s framework where the motion of each phase is governed by a transport equation (Joekar-Niasar et al., JFM, 2010; Chen et al., WRR, 2020). To close the system, we construct theoretical capillarity models that prescribe the pore-scale fluid interface shape. Our model captures a wide range of displacement patterns—including viscous fingering, invasion percolation, percolation with trapping, compact displacement, and precursor film flow—highlighting its capability as a predictive tool. Moreover, by analyzing ensemble-averaged statistics in the fingering regime, we derive hyperbolic upscaled equations suitable for field-scale simulation of hydrogen storage in saline aquifers.