Oil recovery by water injection is a common method in petroleum industry. Although the macroscopic point of view monitoring the sweep efficiency is the usual approach, several phenomena could studied more effectively at the microscale. Capillary and viscous forces, together with geometry arrange of the medium, are responsible by the mobilization and trapping the oil. With the goal of studying the dynamic of the microscopic process and the influence of discretization algorithms, boundary condition, and time step, in this work it is used the software Ansys Fluent, with volume of fluid technique, to simulate the two-phase, transient, Newtonian and laminar flow. The 2D Cartesian domain is a system with circular constrictions representing a simplified porous media initially fully filled with oil where the periodic boundary condition is applied. At the microscale, oil films are retained around the grains walls and recirculation acts trapping the oil. This volume is slowly removed result of the continuous water injection. Two stages are well identified in this process. One with linear decrease whit time, which is in according with our analytical prediction until the water breakthrough, followed by the stabilization where the continue water injection has no effect in the oil displacement. Consequently, the oil recovery is not complete, a fraction of it will remains in the porous medium. In addition, it is possible to identify the numerical algorithms for this microscale immiscible liquid/liquid displacement problem, which presents the more coherent physical results.