  Multiphase flow through a porous medium involves complex interactions between
gravity, wettability and capillarity during drainage process. In contrast to
these factors, the effect of pore distribution on liquid retention is less
understood. In particular, the quantitative correlation between the fluid
displacement and level of disorder has not yet been established. In this work,
we employ direct numerical simulation by solving the Navier-Stokes equations
and using volume of fluid method to track the liquid-liquid interface during
drainage in disordered porous media. The disorder of pore configuration is
characterized by an improved index to capture small microstructural
perturbation, which is pivotal for fluid displacement in porous media. Then, we
focus on the residual volume and morphological characteristics of saturated
zones after drainage and compare the effect of disorder under different
wettability (i.e., the contact angle) and gravity (characterized by a modified
Bond number) conditions. Pore-scale simulations reveal that the
highly-disordered porous medium is favourable to improve liquid retention and
provide various morphologies of entrapped saturated zones. Furthermore, the
disorder index has a positive correlation to the characteristic curve index (n)
in van Genuchten equation, controlling the shape of the retention
characteristic curves. It is expected that the findings will benefit to a broad
range of industrial applications involving drainage processes in porous media,
e.g., drying, carbon sequestration, and underground water remediation.
