The cementation process is an important step in the construction of oil and gas wells. It provides zonal isolation and support for the well bore. During the cementation, it is necessary to displace the drilling mud by the cement slurry. To avoid mixing of these liquids, spacer fluids are usually used. Therefore, it is common to have three or more liquids flowing through the eccentric annular space. A complete analysis of the flow in the annular space that occurs during cementation is extreme complex, because of the presence of different liquids, that often present non-Newtonian characteristic and the flow is three dimensional and transient. Thus, a complete model has a prohibitive high computational cost. Simplified models are available in the literature and are used by the oil industry in commercial simulation software for cementation. However, the strong simplifying assumptions limit the range of parameters at which these models are accurate. In this work, a 2D model for this 3D flow was developed using the lubrication theory. The developed model considered the variation of the inclination and eccentricity along the well and the non-Newtonian behavior of the flowing liquids. The results show how the liquid properties and well geometry affect the efficiency of the displacement process.