Two main statements of oil-to-water displacements are considered - with and without surface tension on the free interface. Both theoretical and numerical results are presented and discussed. Some interior contradictions of the classical Muscat and Buckley-Leverett models are revealed and explained. The main attention is paid to the microscale numerical solution on the base of Direct Numerical Solver approach for both statements. The numerical results prove the very different behavior of a free interface with and without surface tension. When there is no surface tension nothing limits the stretch of the water tongue within the oil. On the contrary, the presence of surface tension results in the formation and detachment of a series of droplet from the free interface. Subsequently, these droplets propagate along the capillary. 1D upscaling of these processes is done and compared with 1D Muscat and Buckley-Leverett models.