关于求解二相渗流的平面问题的一类新方法

本文提出一类求解二相平面渗流问题的新方法:用有限元法求解关于压力分布的椭圆型方程,然后利用所得的对压力梯度的半解析解,根据已有的饱和度沿流线传播的精确公式求得饱和度场.其主要特点和优点是能克服通常的数值模拟方法所具有的数值弥散,给出准确清晰的水驱油前沿饱和度间断面的位置,并且完全避免了通常必须与压力方程联立求解或交替求解的饱和度方程,从而使计算工作量大大减少.

On a New Kind of Methods to Solve the Plane Problems of Two-Phase Flow Through Porous Media

This paper presents a new kind of method for solving the plane problems of two-phase flow in porous media. The elliptical partial differential equation for pressure distribution is solved by the finite element method, and then the semi-analytical solution for pressure gradient is used to determine the new saturation field according to the existing exact formula describing the saturation propagation along the streamlines. The main distinguishing feature and advantage of this kind of method are the ability to overcome the numerical dispersion which is inherent in the ordinary numerical simulation methods, and thereby, to give a precise and clear-cut position of the saturation discontinuity in the water-oil displacement front. Moreover, the saturation equation, which should commonly be solved simultaneously or alternatively with the pressure equation, is completely avoided, so that the computing time is greatly reduced.