The Mass-Conservative Characteristic Finite Difference Method For Miscible Displacement Problem

The miscible displacement problem attracts great attentions in industrial oil recovery around the world.Recently,dozens of countries and regions around the world have discovered the miscible displacement problem.After injecting water into the oil layer,the water will displacement oil of the oil layer,this is the so-called miscible displacement problem.Therefore,this problem has been widely concerned by the international community.Many countries are actively carrying out research miscible displacement problem.The mathematical model of miscible displacement problem is composed of the pressure equation and the concentration equation.In this paper,we study a new mass-conservative characteristic finite difference method for miscible displacement problem.First,we introduce common finite difference scheme and the mass-conservative characteristic finite difference method.Then,the method is used to deal with the Sobolev equations,and structuring a characteristic finite difference scheme,testing the mass conservation of the format,and giving examples.After that,this method is further extended to the miscible displacement problem in the porous media,the characteristic finite difference schemes of incompressible miscible displacement problem and compressible miscible displacement problem are constructed respectively.The mass conservation of the format is also verified,and a one-dimensional two-dimensional model example is given to verify the correctness of the theory.In this paper,a new mass-conservation characteristics finite difference method is applied to the miscible displacement problem.Through the intensive study of the numerical solution of miscible displacement problem,we strive to break through the instability and the computational complexity of the traditional methods in the study of the problems,and make some important progress in both theoretical analysis and practical calculation.The new method combines the characteristic technique with mass-preserving interpolation,not only keep mass balance but also maintain the time second order accuracy and the space second order accuracy.Through model analysis,format construction,theoretical proof,we provide a more efficient numerical algorithm for the numerical simulation of miscible displacement problem,which can help the actual production activities.