Understanding fluid flow in porous media is of tremendous importance for many industrial and environmental applications at various spatial and temporal scales. The present study consequently focuses on CFD 2D modeling of single-phase flow in steady mode, and unsteady mode oil-water flows by the Volume-of-Fluid method (VOF) in oil reservoir using ANSYS Fluent while meshing has been done on Gambit. The effects of temperature and permeability on water flow in porous medium, which was considered as a reservoir have been studied in this work, velocity and pressure distributions, also have been presented. In oil-water flow simulation, total pressure and oil volume fraction distributions have been visualized. Besides, the study of pressure gradient and permeability effects on the breakthrough time and on the recoverable oil has been carried out.