Research On Numerical Simulation Of Reservoir Based On Discontinuous Galerkin Finite Element Method

Reservoir seepage process is multiphase and multicomponent,and even includes mass transfer,heat transfer among components,and complex physical and chemical interactions between fluid and reservoir rock.The equations of these complex behaviors often reflect the nature of the transport equation.In this context,discontinuous finite element method has received extensive attention in recent years as a high-precision,high-resolution numerical method suitable for solving transport equations.It can improve the accuracy of the solution by increasing the polynomial order of the solution function.The discontinuous finite element method has both the ability of the classical finite element method to deal with various complex problems flexibly and the characteristic of the finite volume method that the physical meaning is clear and locally conserved.Compared with other commonly used numerical methods,it has certain advantages.In view of the certain advantages of discontinuous finite element method and the study of reservoir seepage problems are relatively few.In this paper,the use of discontinuous finite element method to calculate the seepage problem of the reservoir is carried out,and the calculation performance of the discontinuous finite element method to the seepage problem is verified by numerical experiments.Firstly,based on the basic equation of elastic single-phase seepage,the discrete process of discontinuous finite element method is introduced,and the matrix equation and iterative solution method of single-phase seepage problem are deduced.In view of the high-precision characteristics of discontinuous finite element method,this paper uses the Chebyshev-guasslobatto node to generate Lagrange polynomial node basis functions.Numerical computations are performed using higher-order basis approximate solution functions.Then,for the oil-water two-phase seepage problem,this paper uses the equation system defined by the global pressure as the solution object.The diffusion term is handled using the locally discontinuous finite element method using the sequential implicit solution method.The pressure gradient can be calculated directly.The convection term under tensor permeability is processed by introducing an upwind style using pressure gradients.Finally,based on the principles and methods introduced above,this paper uses MATLAB to compile a calculation program,and uses high-order approximation to solve the problems of homogeneous single-phase seepage and oil-water two-phase seepage,anisotropic single-phase seepage and oil-water two-phase seepage under tensor permeability Perform numerical calculations.Give the corresponding pressure distribution map,saturation distribution map...