Abstract
We perform pore-scale resolved direct numerical simulations of immiscible two-phase flow in porous media to study the evolution of fluid interfaces. Using a Smoothed-Particle Hydrodynamics approach, we simulate saturation-controlled primary drainage in heterogeneous, partially wettable 2D porous microstructures. While imaging the evolution of fluid interfaces near capillary equilibrium becomes more feasible as fast X-ray tomography techniques mature, imaging methods with suitable temporal resolution for viscous-dominated flow have only recently emerged. In this work, we study viscous fingering and stable displacement processes. During viscous fingering, pore-scale flow fields are reminiscent of Bretherton annular flow, that is, the less viscous phase percolates through the core of a pore-throat forming a hydrodynamic wetting film. Even in simple microstructures wetting films have major impact on the evolution of fluid interfacial area and are observed to give rise to nonnegligible interfacial viscous coupling. Although macroscopically appearing flat, saturation fronts during stable displacement extend over the length of the capillary dispersion zone. While far from the dispersion zone fluid permeation obeys Darcy’s law, the interplay of viscous and capillary forces is found to render fluid flow within complex. Here we show that the characteristic length scale of the capillary dispersion zone increases with the heterogeneity of the microstructure.
Highlights
Assessing the stability and evolution of saturation fronts, or, from a pore-scale point of view, interfaces between immiscible bulk fluid phases, is key with respect to understanding a multitude of subsurface processes
While invasion percolation is considered a suitable stochastic model for capillary fingering, viscous fingering is stochastically reminiscent of diffusion-limited aggregation (DLA) [61,62,63]
Nearly onesixth of total resistance is due to viscous coupling and this trend is expected to be even more pronounced for finer microstructures, larger domain sizes, and higher saturations. These results suggest that viscous coupling terms should be accounted for in macroscopic models for viscous fingering in porous media since otherwise lubrication effects are lumped into relative permeability functions, which, by definition, are related to momentum exchange between solid and fluid phases only
Summary
Assessing the stability and evolution of saturation fronts, or, from a pore-scale point of view, interfaces between immiscible bulk fluid phases, is key with respect to understanding a multitude of subsurface processes. Depending on the governing capillary number (Ca), viscosity ratio (M), properties of the porous microstructure, and boundary conditions, primary drainage results in flow regimes as diverse as viscous fingering, stable displacement, or capillary finger branching [1]. In traditional macroscopic continuum models, a phenomenological extension of Darcy’s law is assumed to be applicable with relative permeability and capillary pressure functions representing constitutive model inputs [2]. Calibration of these constitutive relations in light of a particular flow regime typically renders them nonlinear and hysteretic [3,4,5]. In an attempt to face the latter, contemporary models acknowledge the role of interfacial areas in hysteresis [6,7,8,9,10] or explicitly account for mass-exchange between hydraulically reservoir-connected and reservoirdisconnected subphases [11, 12]
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