A Positive-preserve Scheme Of Two-phase Flow Model In Porous Media

Reservoir numerical simulation is to use the computer to solve the reservoir related mathematical model,simulate the underground oil and water flow,give the oil and water distribution at a certain moment,to predict the reservoir dynamics.Porous media flow model is widely used in reservoir numerical simulation,groundwater pollution and control,coalbed methane production and other fields.It is a coupling system composed of fluid mass conservation equation and component concentration equation.Common porous media flows include two-phase flow model,black oil model and component model,among which two-phase flow model is the most basic percolation model,which is a physical image and mathematical equation describing the characteristics of two-phase flow,including the mass conservation equation of water phase and oil phase.In traditional reservoir numerical simulation,two point flux approximation and multiple point flux approximation are commonly used,but in general,due to the influence of permeability in the form of corner grid and tensor,the scheme is not guaranteed,and there will be obvious oscillation in the actual numerical experiment.To avoid such oscillations,we propose an orthostatic scheme based on the two-phase flow model of porous media flows.This thesis is based on the two-phase flow model of porous media flow.The correctness of the analytical solution is proved by the extremum principle.There should be no oscillation in the numerical simulation.Combining with the nonlinear orthogonality of the diffusion equation,a orthogonality scheme based on the two-phase flow model is proposed,and the orthogonality of the pressure equation and saturation equation of the two-phase flow model is constructed.Finally,a practical example is given to verify the correctness of the scheme,and it is proved that the scheme can avoid non-physical shock.