Abstract: Hydraulic parting,which can form a symmetrical and vertical plane of fracture in the ormation thaft surrounds a well is an effective measure of increasing production.A vertical fractured well can bring out two-dimensional flow in the direction of normals of developing ellipse-conjugate equal-pressure ellipse and hyperbola streamline bunches whose focal points are the two ends of the fracture when it works.A mathematical model of oil and water two-phase fluid flow in the normal direction of the ellipses,which is a nonlinear equation with a moving boundary is established according to concepts of turbulent ellipses and equivalent developing regulations.Characteristic solution and finite difference solution to the model are derived respectively and water saturation distribution curves are presented.And the variation of regularity moving boundary is found.Results showed good agreement between the characteristic solution and finite difference solution.Moreover,formula of water-flooding development indexes for vertical fractured wells are derived. Laws of change of production and pressure difference with time are recognized.The paper provides numerical simulation, dynamic analysis and prediction of water-flooding development of oilfields in the case of vertical fractured wells with theoretical basis.

Key words: vertical fractured well, two-phase fluid, moving boundary, nonlinear equation, finite difference method, development index

摘要： 水力压裂是一种有效的增产技术,它能使油井周围地层形成一个对称的垂直裂缝面.垂直裂缝井工作时在地层中诱发平面二维椭圆渗流,即形成以裂缝端点为焦点的共轭等压椭圆和双曲线流线族.基于扰动椭圆的概念和等价的发展矩形的思想,建立了油水两相随圆二维渗流数学模型.它属于具有活动边界的拟线性问题.分别运用特征线法和有限差分法求解,得到了含水饱和度分布和活动边界的变化规律.结果表明,特征线法和有限差分法获得的结果吻合得较好.从而为用数值模拟的方法研究垂直裂缝井注水开发油田提供了理论依据,还为垂直裂缝井注水开发低渗油田的数值模拟研究奠定了基础.此外,研究了非活塞驱替理论,导出了垂直裂缝井注水开发油田时产油量和压差及井排见水时间的计算公式,并进行了实例计算分析,得出了产油量及压差随时间变化的规律.

关键词: 垂直裂缝井, 两相流体, 活动边界, 非线性方程, 有限差分法, 开发指标