有限元法求解油藏渗流问题的精度影响因素

Discussion on Affecting Factors of Accuracy of Flow Through Porous Media in Reservoir Solved With Finite Element Method

建立了单相流体在均质油藏中不稳定渗流条件下的有限元方程,在空间上用三角形网格进行剖分,将井壁视为内边界,用线性函数描述网格结点的压力变化,通过求解有限元方程获得地层压力的变化规律。以内边界定产、外边界封闭的不稳定径向流模型为例,讨论网格数、边长比例、时间步长及差分格式对计算精度的影响。结果表明,有限元法用于求解不稳定渗流问题是方便有效的。

In this paper,the finite element equations are established under the condition of unsteady flow in the uniform formation.Section the region with triangle grid.Treat the well face as internal boundary.Describe the pressure variation of node in grid with linear function.Obtain the pressure distribution by solve the finite element equation.Discuss the affection on accuracy of the solution because of the grid num,the proportion of the triangle sides' length,the time step and the differencing scheme with the illustration of radial unsteady flow model that has an constant-flow internal boundary and a closed external boundary.It has shown that finite element methods is available and convenient to solve the problem of unsteady flow in porous media.