Density unstable fluid displacement in vertical annuli

We study displacement flows involving pairs of Newtonian and shear-thinning fluids in vertical annular geometries using experimental and computational methods. This investigation is motivated by the primary cementing of casing strings, which is part of the well construction operation. In displacement scenarios that involve density-unstable fluid pairs, it is well-known that buoyancy can increase the inter-mixing between fluids and hence contaminate cementing fluids due to gravity-driven instabilities. Our study seeks to investigate how the imposed flow rate, the degree of inner pipe centralization, and the viscosity of the fluids affect the displacement efficiency in such cases. The study complements our recent paper [R. Zhang et al., “Vertical cementing displacement flows of shear-thinning fluids,” Phys. Fluids 35, 113110 (2023)], which focused on density-stable configurations, and here we consider the more challenging, density-unstable displacement flows. Our experiments and three-dimensional computational results are in general agreement. The results show that displacements improve for viscosity-stable conditions, i.e., when the displacing fluid is the more viscous fluid. Characteristic fingering patterns occur in the interface region of the fluids for viscosity-unstable conditions. The eccentricity of the inner pipe is seen to promote the channeling of fluids, and viscosity-unstable conditions can exacerbate this effect further. A degree of stabilization of density unstable displacements can be achieved by increasing the imposed flow rate and the viscosity of the fluids while maintaining a stable viscosity ratio.