In the petroleum industry, Reservoir Simulation plays an important role to forecast production behaviour. In this field it is essential to know the reservoir production performance under different types of exploitation. This is a key in choosing the accurate production process for a reservoir. To aim this, the main tool used for a reservoir engineer is reservoir simulation. Nowadays reservoir simulations still have some gaps such as the simulation at different scales. Commercial simulators cannot reproduce precisely the reservoir behaviour and the physics at the microscopic scale. If a reservoir simulator could be able to replicate pore scale events, they could have a more realistic representation of the reservoir physics. This thesis tries to emulate drainage in three different 2-D heterogeneous porous media patterns with a porous plate at the production end, which restricts oil flow, but it conducts water; water being the wetting fluid and oil the non-wetting fluid. The porous medium was inserted in an open source software for computational fluid dynamics (CFD) called OpenFOAM capable of making simulations on a micro scale and capable of reproducing pore events such as snap-off, Haines-jumps, disconnected ganglia of oil and the simultaneous filling of neighboring pores. In this thesis, graphs of the variation in fluid saturations versus time are presented in order to compare drainage process in different porous media.