One of the most complex and critical stages during the construction ofoil wells is the primary cementing process, defined as the process of installingcement in the annulus between the casing and the exposed formation to thewell [1]. Primary cementing provides permanent zonal isolation to preventcontamination or migration of unwanted fluids in the annulus, protects thecasing from corrosion, and provides hydraulic and mechanical stability forthe casing throughout the productive life of the oil well. In this process,during the drilling stage, irregularities in the cross-section (washouts) can begenerated because of various partial collapses of the open wellbore section dueto the presence of poorly consolidated rocks in the formation. A successfulprimary cementing operation will depend on whether the spacer fluid systemand cement slurry adequately and completely displace the drilling fluid fromthe annulus and washouts.Motivated by this industrial problem, the present dissertation uses aDirect Numerical Simulation (DNS) numerical simulator to systematically analyze the hydrodynamic behavior and calculate the displacement efficiency between two miscible newtonian fluids through an annulus containing an expansion followed by an abrupt contraction. We investigate how different viscositiesand densities of the injected and displaced fluids, their miscibility, injectionrate, and the dimension of the rectangular washout affect the two-phase flow.We consider an axisymmetric geometry during vertical displacement processes,and the governing equations are solved in cylindrical coordinates, allowing theinvestigation of different annular clearances. Due to the miscibility betweenthe fluids, our results predict very high displacement efficiencies, close to 100Non-newtonian fluids are commonly used during the industrial processof primary cementing of oil wells. However, the high displacement efficienciesfound in our results motivate further studies on the influence of miscibilityin displacements of complex fluids. These results also encourage the use ofspacer fluids attempting to control the interfacial properties. Therefore, the useof systems that approximate the rheological and hydrodynamic conditions ofdisplacement between miscible newtonian fluids may contribute to an increasein displacement efficiency and, consequently, optimize the displacement processof fluid systems, aiming at improvements in the integrity of well cementing.