The arbitrary Lagrange-Euler (ALE) finite element technique is used to simulate 3-D displacement of two immiscible Newtonian fluids in vertical annular welts. For equally viscous fluids the effect of distinct fluid densities is investigated in the region of low to intermediate Reynolds numbers. Comparison with a simple theory for drainage of thin films is performed. It is found that recirculations deform the fluid-fluid interface significantly in situations dominated by buoyancy forces. Also, a deviation from the concentric annular geometry is shown to induce azimuthal transport of fluid. Finally, the efficiency of the displacement is analysed for Various flow situation.