In this study, the green element method is used to model petroleum problems such as oil production due to expansion mechanism, one and two dimensional spontaneous imbibition and water flooding. Despite of boundary element method that its applications in reservoir engineering are limited to simulation of single phase fluid flow in homogenous media, green element method can solve multi-phase flow in heterogamous media. In this thesis, by this method the governing partial differential equation for these processes are modeled and then solved. In one dimensional medium, green element method can successfully simulate the oil production from heterogamous reservoir due to expansion mechanism. The...