Intermittent two-phase flow in porous media: insights from pore-scale direct numerical simulation

Abstract: Recent X-ray imaging experiments have revealed that multiphase flow through porous media involves transient fluctuations in local occupancy, even under fixed macroscopic steady-state conditions where capillary forces dominate at the pore scale. To examine how intermittency manifests at the pore scale we perform direct numerical finite volume simulations (DNS) of immiscible two-phase flow through a micro-CT-derived Bentheimer sandstone geometry at capillary numbers in the Darcy and intermittent flow regimes. We show that intermittent disconnection and reconnection are accompanied by strongly coupled local pressure redistribution and non-wetting phase flow. This behaviour contrasts with the Darcy flow regime, in which the phases remain predominantly in fixed pathways. Macroscopically the computed pressure-gradient-capillary-number relationship ($\nabla P$-Ca) recovers both the linear Darcy and the sub-linear intermittent scaling regimes consistent with previous experimental measurements. We show how an increase in intermittency leads to the transition from the linear to the sub-linear regime. Using topology-aware snap-off detection, we show that the spatial extent of intermittency increases with capillary number. Spectral, local-geometry, and network-connectivity analyses provide further evidence that the intermittent elements organise into connected conduits embedded within a stable backbone of fixed flow pathways: intermittency is a network-coupled rather than purely local process. This work characterises the pore-scale manifestation of intermittency as a periodic sequence of drainage and imbibition displacements triggered by local pressure fluctuations whose macroscopic consequence is to improve the overall mobility of the fluid phases.