Flow displacement in eroded regions inside annular ducts

This work presents a numerical study of the displacement of two fluids through vertical annular ducts with an enlargement in the cross section. This flow is found in cementation operations in the oil industry. A successful cementing operation is obtained when the cement slurry is able to effectively displace the drilling fluid from the annular space between the wellbore and the casing. The process is very complex, since both fluids can have non-Newtonian behaviour, and the flow is time-dependent. In addition, in many situations the wells have some eroded regions, where the cross-sectional area is larger than the regular well annular cross section. The optimization of the displacement efficiency is important not only because of the cost of the process, but also due to security problems, since a unsuccessful operation may result in the collapse of the oil well. The displacement efficiency is a function of the fluids rheology, the density ratio, the flow rate, and the geometry. This work presents an analysis of the influence of rheology, flow rate and geometry on the displacement process inside annular ducts with an eroded region. The governing conservation equations are solved for an axisymmetric flow using the finite volume method. The multiphase problem is dealt using the volume of fluid method. Flow pattern along the eroded region and the displacement efficiency are presented and discussed for different pairs of fluids. The results show that the displacement through the eroded region is better for larger aspect ratios (or longer eroded regions). It is also observed that inertia tends to shift the interface towards the exit wall of the eroded region, leading to lower displacement efficiencies.