We investigate the simulation of one-phase and two-phase flow through heterogeneous porous media.The derived matrix, resulting from reservoir simulation of groundwater flow problems, can result in a large and ill-conditioned system, i.e. the matrix has a high condition number, and the modelling takes large computation time. In this thesis report, the Two-Level Preconditioned Conjugate Gradient method with deflation techniques will be considered. Recently, new Two-Level preconditioners are constructed using the AMG approach. In this research we compare this approach with the standard Two-Level preconditioners. We found that the performance of these methods can be improved by using a special starting vector and previous time-step as initial condition. From the results we see that the performance and the memory storage of the methods are similar. However, the cheapest methods per iteration resulted DEF1, DEF2, R-BNN2, and ROM.