An important problem that occurs during drilling, completion and gravel packing operations is the contamination among fluids. The drilling fluids and cement pastes present a non Newtonian (viscoplastic) behavior, while the spacer fluids, used as an attempt to avoid contamination, are Newtonian. The analysis of the flow displacement and of the interface configuration between these fluids helps to determine contamination and the displacement efficiency, and is an important tool for the process optimization. In this work we performed a numerical study to analyze the displacement of one fluid by another through a non-rectilinear, horizontal annular channel, using Fluent Software (Ansys Inc.). The solution of the conservation equations of mass and momentum is obtained via the finite volume technique, and using the volume of fluid method to handle the multi-fluid situation. The effects of rheological parameters on the interface shape and displacement efficiency are investigated. When the viscoplastic liquid pushes the Newtonian one, the displacement efficiency decreases as we increase the velocity and the viscosity of the displaced fluid. Moreover, the fingering undesired phenomenon is observed for higher velocities. On the opposite situation, when the Newtonian fluid pushes the viscoplastic one, the displacement efficiency increases with the velocity and viscosity of the displacer fluid, and the fingering is observed at lower flow rates. The effect of viscosity ratio was also investigated, but it is shown that it does not affect the displacement efficiency.