Currently in the oil industry, the numerical simulation is often used to eval-uate different processes through powerful software tools that help to prevent an experimental research in a real well, which can be an expensive and sometimes impractical task. The purpose of this study is to present a numerical investigation to find a better efficiency in the cementation process in eroded wells. In this pro-cess, one fluid displaces another through a tube with variable cross sectional area. Both fluids may have non-Newtonian behavior. The analysis is done by the nu-merical solution of the governing equations, using the finite volume method. Pre-vious studies showed that the displacement process through vertical wells are ruled primarily by the viscosity and density ratios of the fluids, the eccentricity of the annulus, and the Reynolds number. In addition, other variables such as the casing rotation and well geometry can influence the displacement efficiency. Then, the analysis of the influence of these parameters in the flow pattern through the well and removal efficiency in eroded wells will be performed, and will help to optimize the cleaning and removal processes.