Three-dimensional simulations of high-density and high-viscosity laminar and turbulent displacements in canonical and complex geometries

The displacement of one fluid by another in a pipeline occurs in a wide variety of industrial applications, and has important financial and environmental consequences. The effects of fluid properties, including the density and viscosity ratios, as well as flow regime, whether laminar or turbulent, are studied numerically for horizontal pipe geometries; both miscible and immiscible displacements are considered. The simulations are first validated against analytical solutions available for both the laminar and turbulent regimes. The temporal evolution of the volume fraction of the fluid initially resident in the pipe is tracked as a measure of the effectiveness of the displacement process. The thickness of the film of resident fluid left behind following the initial stages of the flow is also measured and its dependence on system parameters presented. It is also shown that for large viscosity ratios (of order $10^7$), gravitational effects play an important role in the dynamics. Finally, we extend the range of simulations to cover complex geometrical configurations including U-bends, and static mixers, which are of industrial relevance.