Pore-scale Numerical Modelling of Gravity-driven Drainage in Porous Media with Disordered Microstructure

Abstract

Multiphase flow through a porous medium involves complex interactions between capillarity, viscosity, wettability and gravity during gravity-driven drainage process. In contrast to these factors, the effect of pore distribution on liquid retention is less understood. The interplay of these factors results in sophisticated fluid displacement behaviours that are difficult to systematically and quantitatively assess. To investigate the hydro-mechanical and morphological features during drainage in porous media, we employ an open-source platform of computational fluid dynamics, which adopts direct numerical simulation by solving Navier-Stokes equations and employing volume of fluid method to track the liquid-liquid interface. Our work can be divided into three components and the main results include: (1) Before introducing the disordered microstructure, we performed simulations for drainage processes in granular media with combinations of surface tension, wettability, and viscosity. It is found that the residual volume of wetting phase presents three clear different regimes from strong hydrophilic to strong hydrophobic conditions. Compared with viscosity ratio between the wetting and non-wetting fluids, the formation of liquid patch is more strongly influenced by capillarity. (2) For better understanding multiphase flow mechanism in porous media with random pore configuration, we defined an advanced index for assessing the disorder degree of the microstructure. This disorder index quantitatively evaluates the fluctuation of local porosity, based on Voronoi tessellations, compared with global porosity in computational domain. The validity of this index is proved by characterising the disorder-induced reinforcement of liquid-holding capacity after gravity-driven drainage. (3) Using the disorder index, we focus on the residual volume and morphological characteristics of saturated patches and compare the effect of disorder under different wettability (i.e., the contact angle), gravity and capillarity (characterised by a modified Bond number) conditions. Pore-scale simulations reveal that the highly-disordered porous media are favourable to enhance liquid retention and provide various morphologies of entrapped saturated zones, which is also confirmed by the lognormal distribution of liquid patches. In addition, the disorder index is positively correlated with the characteristic curve index (n) in van Genuchten equation. In this work, a series of numerical simulations are presented and corresponding empirical equations are established to predict liquid retention mechanism in disordered porous media. In particular, we provide a new perspective to investigate the influences of pore topology on the drainage efficiency and distribution characteristics of wetted zones. It is expected that the findings will benefit a wide range of industrial applications involving drainage processes in porous media, e.g., drying, carbon sequestration, and underground water remediation.