Abstract: In this paper,a non-linear model for two dimension and two phases unsteady state flow through a porous medium is solved by a variational finite element method.Because of this model being non-elliptic a,its energy functional form can not be salved directly.However,it is successful to treat the non-elliptic model equation by the use of a breaking up unsteady state flow tecnique.The numerical solution of the equation is given by iso-par-ameter element of second order with eight nodal points.An example of a field developed by water injection is illustrated in this paper and the results are satisfactory.

摘要： 本文用变分有限元方法处理了两维两相非线性不稳定渗流模型.因为该模型是非椭圆型的,不能直接得到其能量泛函数.本文用非稳定流分解法处理这种非椭圆型方程,却获得了成功.文中采用八结点二次等参数单元给出了方程的数值解,对油田注水开发的实例,进行了计算,其结果令人满意.

关键词: 压力, 饱和度, 二维二相, 不稳定流动, 变分法, 有限元法, 数学模型