This paper describes a set of numerical simulations of the displacement flow of three non-Newtonian fluids through annular eccentric wells. The main application of this work is the studying of drilling and completion processes of oil wells where a cement slurry pushes the drilling mud, used in the drilling process to lubricate the drill and to remove the produced drilling cuts. To avoid contamination, a spacer fluid is usually inserted between them. Both drilling mud and cement slurry behave as non-Newtonian fluids, and the spacer fluid can be Newtonian or non-Newtonian. The analysis of flow and interface configuration between these fluids helps to determine contamination, and is an important tool for the process optimization. The numerical solution of the governing conservation equations of mass and momentum is obtained with the Fluent software, using the finite volume technique and the volume of fluid method. The effects of rheological parameters, density ratios and pumped volume of the spacer fluid are investigated. The results obtained show that the displacement is better when a more viscous spacer fluid is used. The results also show that using lower amounts of the spacer fluid can lead to contamination, which is worse in the smaller gap region of the annular space, in the case of non-rectilinear well. It was also observed that the density ratios play a major role in the cementing operation. (author)