Numerical Simulation Of Anisotropic Reservoirs Based On Hybrid Finite Element Method

Permeability anisotropy is a common phenomenon in oil reservoirs, and fluid flow in anisotropic reservoirs is very complex. However, the existing reservoir numerical simulation software cannot accurately simulate the flow in permeability anisotropic reservoirs. In order to solve this difficult problem, the mixed finite element method is used, as well as the following work:(1) For characterization of permeability tensor field in anisotropic reservoirs, coordinate transformation and Darcy's law are combined to derive the directional permeability formula. Using the ellipsoidal curved surface fitting method to fit permeability in all directions, the permeability tensor is acquired. Based on matrix algebra algorithm and interpolation of the permeability tensor, the whole area of tensor field is obtained. After comparison, geometric average is utilized to upscale permeability tensor field.(2) Introducing mixed finite element method and using the variational principle, the Darcy flow equation and mass conservation equation of the equivalent integral weak form are derived. According to discretization idea, with the interpolation function, the weak integral form can be converted into equivalent form of matrix. Using topological ideas and depicting the topological relations between grid elements, the problem of the coefficient matrix combination is solved.(3) For single-phase and oil-water two-phase flow problems, the mixed finite element method is used to build block center grid node system and grid system. Consequently the matrix form of the steady or unsteady state of single-phase flow and the matrix form of compressible or incompressible oil-water two phase flow are derived. Preconditioning conjugate gradient method and Newton iteration method are utilized to solve the linear or nonlinear equations in discretization system.(4) On the platform of MATLAB, a new simulator is compiled, which enables to simulate fluid flow in a vertical fracture well, a horizontal well and an injection-production well system the pressure field, velocity field and the streamline in the reservoirs are plotted. Finally the effect of permeability anisotropy on fluid flow is analyzed.Based on mixed finite element method of numerical simulation for the simulation of anisotropic reservoir has theoretical and applied value.