An Improved IMPES Algorithm For The Simulation Of Incompressible Multiphase Flow In Porous Media

This thesis focuses on the improvement of IMplicit-Pressure and Explicit-Saturation(IMPES)algorithm for simulation of incompressible and immiscible multi-phase flows in porous media.We mainly consider the numerical algorithms and their applications of two-phase flow and three-phase flow models in reservoirs.The mathematical model of the incompressible and immiscible multi-phase flows in porous media mainly includes the partial differential equations composed of elliptic flow equations and hyperbolic conservation equations.These coupled equations contain very complex nonlinear characteristics,and the analytical solutions can not be obtained.The IMPES method is widely used in reservoir simulation.The traditional IMPES method is to add the conservation equation of saturation and obtain an elliptic equation only containing one pressure by combining Darcy's laws and saturation constraint conditions.Then the cell-centered finite difference method is used for spatial discretization,so as to implicitly solve the pressure distribution.Furthermore,the saturation equation is discretized by explicit scheme in time and combining with cell-centered difference for spatial discretization,so that the saturation distribution of each phase is solved in next time step.In the solution process of the traditional IMPES algorithm,a corresponding reference phase needs to be selected,and the mass of non-reference phase cannot be conserved.In view of the above problems existed in the traditional IMPES algorithm,an improved IMPES algorithm is proposed.The improved IMPES algorithm is to obtain a linear algebraic equations of pressure by summing the fully discrete mass conservation equations and combining the Darcy laws with saturation constraint conditions of each phase,so as to solve pressure distribution.Further we can solve the Darcy velocity of each phase.Then the Darcy velocity is brought into the corresponding mass conservation equation,and the saturation of each phase is calculated in next time step.Among them,the cell-centered difference method with the upwind scheme is used for spatial discretization.Compared with the traditional IMPES algorithm,the improved IMPES algorithm has local and global mass conservation for all phases of multi-phase flow.In addition,it is unbiased for all phases and does not need to select the phases.Finally,this article also applies several typical examples of two-phase flow and three-phase flow problems to verify the effectiveness,stability and reliability of the proposed algorithm by Matlab programming.