Computer simulation of two-phase immiscible fluid motion in unsaturated complex fractures using a volume of fluid method

[1] Complex fluid behavior in unsaturated fracture and fracture networks, such as film flow, the migration, fragmentation, and coalescence of droplets, and rivulet flow with or without meandering or pulsation, has been widely observed in laboratory experiments. In this study, a modified two-dimensional volume of fluid (VOF) method was used to simulate liquid motion in partially saturated fracture apertures under a variety of flow conditions. This modeling approach systematically incorporates the effects of inertial forces, viscosity, gravity acting on the fluid densities, fracture wall wetting, and the pressure drop across curved fluid-fluid interfaces due to surface tension. This allows us to obtain a better understanding of the fundamental physics governing unsaturated fluid flow in fracture apertures. The VOF method is able to handle the complex dynamics of fluid-fluid interfaces and free surfaces in unsaturated fractures by using a fixed Eulerian grid. Fragmentation and coalescence of the fluids are automatically handled without resorting to complex adaptive mesh refinement or interface repairing algorithms. The wetting of fracture walls was modeled by imposing contact angles near the contact lines ( contact points in two-dimensional simulations), and different contact angles were automatically chosen depending on whether the liquid interface is advancing, receding, or essentially stationary. The qualitative agreements between the numerical simulations and complex multiphase fluid dynamics reported in laboratory experiments clearly demonstrate the potential value of the VOF method for the mechanistically based modeling of immiscible liquid motion in unsaturated fracture networks.