Laminar annular displacement flows with rotating inner cylinder in large annuli

We present computational results from simulations of displacement flows in inclined and horizontal eccentric annuli, both with and without a rotating inner cylinder. The study is aimed at understanding flows in the industrial process of primary cementing of oil and gas wells. Following from Sotoudeh and Frigaard [“Computational study of Newtonian laminar annular horizontal displacement flows with rotating inner cylinder,” Phys. Fluids 36, 083113 (2024)], we explore larger-scale annuli and flows that are more inertial. These compare favorably with results from a series of displacement flows in a large laboratory experiment. This establishes the utility of the three-dimensional simulations as a tool for in depth understanding of the effects of inner cylinder (casing) rotation. We find that rotation affects the displacement effectiveness directly by adding an azimuthal Couette component to the flow. This moves (advects) the fluids around the annulus, particularly near the inner cylinder wall. For adverse viscosity ratios m, sufficient rotation appears to increase the displacement efficiency, but for large viscosity ratios it is found to sometimes reduce an already effective displacement. These results are all focused at lab-scale experimental annuli. Over the full length of a typical oil or gas well, the casing will rotate many more times during than in an experiment. Thus, our conclusions based on a single annular volume pumped may need modification.