Study Of Symmetric Mixed Covolume Method And Numerical Simulation Of Heterogeneous Reservoir

In the first part of the article,the symmetric mixed covolume methods on rectangular grids is introduced to solve nonlinear parabolic equations. We use the lowest order Raviart-Thomas mixed element space on rectangulars to prove the first order optimal rate of convergence for approximate pressure as well as for approximate velocity. The numerical experiment shows that the convergence rates are all in agreement with the theoretical analysis.In the second part we consider the technology of numerical Simulation of heterogeneous reservoir. Black oil model is a basic model in reservoir simula-tion, and also the most widely used model. Although great progress has been made in the discretization and numerical solution of this model,there still exist some problems to be studied. In this article, we study the large-scale sparse linear equations derived from the fully implicit formulation in reservoir simu-lation, and apply the Constrained Pressure Residual technology to the linear equations.In this article, we apply the Constrained Pressure Residual technology to the numerical simulation of actual fractured-vuggy reservoirs, select a better method of extracting pressure equation and a solution of the pressure equation, and finally develop a fast and efficient method for solving linear equations. The Constrained Pressure Residual technology is faster and more efficient than BILUO+KRYLOV subspace method which is the most popular method at present under the condition of the same precision and greatly reduces running time of the reservoir simulator.