Petroleum and gas industry is doing enormous research to investigate new process and methods for the extraction of oil and gas from natural reservoirs after primary and secondary recovery, these processes are named as Enhanced Oil Recovery (EOR). A lot of simulation techniques have been adopted to study the behaviour and predict the physical mechanisms of oil recovery. Different characteristic functions including capillary pressures, relative permeabilities and fluid saturations are helpful in predicting the effects of wettability alteration, viscosity, and surface tension on oil recovery. In this work, simulations have been carried out by using finite element method (FEM), for two-phase fluid flow in porous media. A 3-dimensional cylindrical shaped porous media was designed, same as the laboratory-scale setup for EOR. Brooks-Corey model and Ban Genuchten models were used for the calculation of capillary pressure with changing the saturation of water and oil. The proposed model is capable to predict capillary pressure, relative permeability and speed of fluid at different positions in porous media with random wettability conditions. © Published under licence by IOP Publishing Ltd.