The Study Of Numerical Method In Miscibility Displacement Degraded Problem

We first introduce a new technology (Preformed Particle Gel flooding tech-nology) to enhance oil recovery. Since the permeability vanishes when the hole is plugged by PPG, we use the porous medium incompressible immiscible dis-placement degradation model or the two-phase multi-component degradation model in reservoir numerical simulation.The miscible displacement model is described as follows: where Ω is a bounded domain in R2,J=(O,T],T is bounded, K(c)→0.Equation (0.1) is pressure equation,equation (0.2) is concentration equa-tion, K(c)→0. the variable unknown in the model is Darcy velocityu,pressurep, concentrationc. In this paper, we use mixed finite element method when solving pressure equation to get higher precision than the ordinary method which u is calculated by the pressure gradient.We use characteristic finite element method when solving concentration equation to get better simu-lation of physical phenomenon and improve the accuracy of the concentration solution c.Since pressure equation is a degradation problem, we definite a new norm space to analyze the existence and uniqueness of the solution and the interpo-lation theory,also we get the priori error estimates for immiscible displacement degradation problem. Since the coupled miscibility displacement degradation problem is hard to solve at the same time.we decoupled it, first we use R-T mixed finite element for the pressure equation, then we use characteristic fi-nite element method for concentration equation with the decoupled parameters solved by explicit method (low computation, simple format).Since the concen-tration equation is convection-diffusion problem, if we use the finite difference or finite element method to solve this problem, it will bring a series of prob-lems(numerical oscillation), but when we use characteristic method, physical phenomena which the equations describes will be simulated effectively,also it can reduce the physical shocks and time step restriction.The two-phase multi-component degradation model describes as follows: Where equation (0.3) is pressure equation,(0.4) is concentration Equation,β→0. We use central finite difference method, the pressure equations is solved by implicit finite difference, the concentration equation is solved by explicit finite difference, the variables unknown is Pl, Sl, Ckl, C.The chemical flooding numerical simulation software will simulate more and more nodes with the expanded scale of chemical flooding reservoir, so we use the parallel technology in reservoir numerical simulation software to meet the actual production needs.The article is divided into three chapters:Chapter1,we introduce the background of reservoir numerical simulation degradation problem briefly.Chapter2,we introduce the numerical method and mathematical model of miscibility displacement degradation problem.Chapter3,we introduce the parallel research of the finite difference method in Two-phase Multi-component Model.