Nonlinear Orthostatic Scheme Of Polymer Flooding Model Based On Porous Media Flow

Polymer flooding technology is used to solve the problem of remaining oil displacement in the early production area.Its mathematical model is based on the mathematical physics knowledge of porous media flow and the accurate simulation of the complex subsurface conditions of the reservoir with corner grid.Because the traditional method does not satisfy the discrete extreme value principle,the experimental results will appear obvious oscillation during the numerical experiment of reservoir simulation.In this thesis,we use the extreme value principle to prove the positive of each equation in the polymer flooding model.By constructing the nonlinear correctness scheme of the polymer flooding model to eliminate the shock,we prove the positive of the construction scheme by continuous extreme value principle.In this thesis,a modified method of nonlinear formalization of the diffusion equation is used to construct the formalization of the pressure equation.The formalization of the pressure equation is constructed on the general star polygon grid.The flow rate is constructed with the unknowns and auxiliary variables in the center of the block by using geometric relations,and the auxiliary variables are eliminated by interpolation,get the formalism of pressure equation and proved its positive.For the saturation equation,an implicit upstream scheme is constructed and its positive property is proved.For the component concentration equation,a positive scheme is constructed and its positive property is proved by referring to the construction ideas of the above two equations.By applying the orthographic scheme to the program,numerical experiments are conducted to verify that the positive scheme can get better simulation results than the original one.