Investigation of Taylor bubble dynamics in annular conduits with counter-current flow

This study numerically investigates counter-current slug flow by considering the motion of a Taylor bubble in annular conduits with downward-flowing liquids using the Volume-of-Fluid method implemented in the commercial computational fluid dynamics software ANSYS Fluent (Release 19.2). The translational velocity of a counter-current ascending or co-current descending Taylor bubble in vertical concentric annuli and the corresponding distribution parameter (C-0) are analyzed. The latter is correlated in terms of Eotvos number (Eo) and inverse viscosity number (Nf) within the range of Eo between 40 and 400 and Nf between 40 and 320. The proposed correlation provides an accurate fit to the numerical data with an average error of 2.64%, and is successfully compared with published numerical findings. In general, the smooth and stable shape of the bubble is disrupted as the counter-current flow velocity (Fr-l) increases above a critical value, leading to the formation of surface waves and the displacement of the bubble tip away from the annular gap center and towards the outer pipe. C-0 increases with Eo and Nf, plateauing at high values of Eo. The effects of annulus inclination (theta) and eccentricity (epsilon) on bubble rise velocity are examined within the common range of theta and epsilon encountered during the drilling of oil, gas, or geothermal wells, i.e. 0 degrees <= theta <= 60 degrees and 0 <= epsilon <= 0.7, and their impact on the C-0. The increasing Fr-l and theta lead to a streamlined bubble with pointed nose and thus a reduction in the wrap angle (theta(wrap)), ultimately leading to reduced drag compared to the vertical annulus case and a decrease in C-0. As the epsilon increases, which is accompanied by an increase in the degree of bubble eccentricity, the corresponding C-0 decreases. For a constant Eo = 100 and Nf = 160 with inclination angle of theta = 40 degrees and eccentricity of epsilon = 0.5, the C-0 < 1 is observed.