Buoyancy effects on micro-annulus formation: Density unstable Newtonian-Bingham fluid displacements in vertical channels

Buoyant miscible displacement flow of a Bingham fluid by a Newtonian fluid along a vertical plane-channel is studied, in the high Péclet number regime. The displacing fluid is lighter than the displaced fluid and the flow direction is upwards, hence density-unstable. The flow is effectively governed by 4 dimensionless parameters: the Newtonian Bingham number (BN), the viscosity ratio (m), the Reynolds number (Re), and modified Froude number (Fr). This is a simple model for micro-annulus formation in the primary cementing of oil and gas wells. The micro-annulus layers correspond to residual drilling mud that remains on the walls after displacement. Here we show that in density unstable situations static residual wall layers can exist for yield stresses below the minimum for density stable regimes. The layers are partially static and may also be thicker than the fully static layers encountered in density stable flows. Adverse buoyancy gradients (represented here by large χ=2ReFr2), also seems to promote instability of the flow. These instabilities are various, ranging from Rayleigh-Taylor type frontal instabilities, through to Kelvin-Helmholz type inertial waves, and more viscous-controlled inverse bamboo and mushroom morphologies. We present an overview of flow regimes within our parameter space and approximate onset criteria. It is unclear whether or not the instabilities observed result in improved fluid displacement efficiency.