水平井两相非达西椭球渗流特征线解与差分解

水平井开采油气田是一种有效的增产技术。它生产时在地层中激发旋转椭球三维渗流， 即形成以其端点为焦点的共轭等压旋转椭球面和双曲面流线族。基于旋转椭球的概念和等价发展圆柱面的思想，建立了油水两相非达西椭球三维渗流数学模型。它属于具有活动边界的非线性问题。分别运用特征线法和有限差分法求解，得到了（ 可动）含油（水）饱和度分布和活动边界的变化规律。为水平井注水开发低渗油田的数值模拟研究奠定了基础。还研究了非活塞驱替理论。并进行了实例计算分析，分别讨论了启动压力梯度和注入率对含水率、（ 可动） 含油（ 水） 饱和度分布、水驱油活动边界变化规律的影响。

CHARACTERISTIC LINEAR AND FINITE DIFFERENCE SOLUTIONS OF TWO-PHASE NON-DARCY SPHEROIDAL FLOWING THROUGH POROUS MEDIA FOR HORIZONTAL WELL

Horizontal well technology is an effective one of increasing production. A horizontal well can bring out three-dimensional flow in the direction of normal of developing and revolving spheroids-conjugate equal-pressure spheroids and hyperboloid streamline bunches whose focal points are the two ends of the well when it works. A mathematical model of oil and water two-phase fluid non-darcy flow in the direction of normal of the spheroids with starting pressure gradient (spg) taken into account, which is a nonlinear equation with a moving boundary, is established according to concepts of revolving spheroids and equivalent developing cylinders. Characteristic linear and finite difference solutions to the model are derived respectively and water saturation distribution curves are presented. And the law of the moving boundary is found. Results show good agreement between the characteristic linear and finite difference solution. Influence of spg and injection rate on water cut and its derivative, saturation distribution and the laws is discussed respectively. The paper provides numerical simulation of water flood development to low permeability oil fields in the case of horizontal wells with theoretical basis. The mathematical model is also fit for water flood development of bingham viscous oil fields in the case of horizontal wells.