Dynamics of displacement flows of viscoplastic fluids in obstructed eccentric annuli at moderate Reynolds numbers

Abstract

As a sequel to Mitishita et al. [“Turbulent displacement flows of viscoplastic fluids in obstructed eccentric annuli: Experiments,” Phys. Fluids 34, 053114 (2022)], we present an experimental study of laminar displacement flows in obstructed eccentric annuli. Xanthan gum (XG) solutions (0.35%, 0.50%, or 0.75%) are used to displace a 0.15% viscoplastic Carbopol solution. The eccentricity of the annulus section is set to near 0.5. We study the effect of a solid obstruction in the narrow side of the annulus, similar to that provided by a consolidated residual cuttings bed, and compare the results to unobstructed displacement flows. While we predicted that all displacements would be in the laminar regime, we actually observe mixed regimes where the initial displacement of Carbopol can be transitional or turbulent. With the obstruction on the narrow side of the annulus, we observe the formation of cavities in the Carbopol layer, both upstream and downstream of the obstruction. We believe that the cavities are formed because the obstruction behaves like an abrupt contraction/expansion. This geometric irregularity affects the velocity profiles of the displacing fluid near the obstruction. Once the cavities reach the bottom of the pipe, we observe that the remaining Carbopol layer is more easily eroded. The dynamics of the Carbopol removal also share similarities to cleaning of soil layers in pipes, as described by Palabiyik et al. [“Flow regimes in the emptying of pipes filled with a Herschel–Bulkley fluid,” Chem. Eng. Res. Des. 92, 2201–2212 (2014)].