In drilling operation of wells it is necessary to use a drilling fluid that has many functions. Flow in the annular space between the drill pipe and the well occurs during the return to the surface. The correction prediction of this flow is important and the complete study is very complex: the fluid has non-Newtonian behavior, the drill pipe is rotating and a varying eccentricity of the drill pipe is possible. Previous analyses in the literature study effects of the rotation and the rheological behavior of the fluid, but consider a constant eccentricity along the axial coordinate. In this work, the equations of momentum and mass conservation that govern the flow is simplified by the lubrication approximation and a twodimensional problem that has simple solution and lower computational cost is obtained. Similar models available neglect the curvature and are only accurate for radius ratio close to one. The formulation developed in this work considers all terms, leading to a lubrication approximation in cylindrical coordinates. The consequence of this approximation is a differential equation for the pressure field. The rheological behavior of the fluid will be evaluated using the method of Equivalent Newtonian Viscosity. With pressure field is possible to determinate the velocity that varies along axial coordinate. The accuracy of the model was analyzed using solutions available in literature (constant eccentricity case). The results show the effects of the variation of the eccentricity on the friction factor and the existence of azimuthal flow even without rotation of the drill pipe.