解析几何在复杂封闭边界内流线计算中的应用

Application of Analytic Geometry in the Calculation of Streamlines in Closed Complex Boundary

通过综合保角变换,将平面上2条交叉不渗透边界内一点源(或点汇)渗流场转化为平面径向渗流场,采用解析几何方法得到2条交叉不渗透边界内一点源(或点汇)渗流场中的流线和等势线。然后通过渗流速度矢量合成方法绘制2条交叉不渗透边界内一点源和一点汇的叠加渗流场。在此基础上,应用施瓦兹-克里斯多菲变换计算三角形封闭边界渗流场流线分布。结果表明:综合保角变换方法以一点源(或点汇)的简单平面径向渗流场为基础,从解析几何角度分析复杂封闭边界内的渗流场,避开了镜像反映原理分析中的复杂求解过程,能够解决具有封闭断层的断块油藏渗流场中流线计算问题。

Through the comprehensive conformal transformation,the seepage field of a point source(or point sink)within two intersecting impermeable boundaries is transformed into a plane radial seepage field,and the streamlines and equipotential lines in the point source(or point sink)seepage field in two intersecting impermeable boundaries are obtained by the analytic geometry method.Then,the superposition seepage field of one point source and one point sink within two intersecting impermeable boundaries is drawn by the synthesis method of seepage velocity vectors.On this basis,the streamline distribution in the seepage field within triangular closed boundary is calculated by the Schwarz-Christophe transformation.The results show that based on the simple plane radial seepage field of a point source(or point sink),the seepage field within a complex closed boundary from the angle of analytic geometry is analyzed by means of the comprehensive conformal transformation method,which avoids the complex solution process in the analysis of mirror reflection principle,and can solve the streamline calculation problem in the seepage field of fault block reservoir with closed fault.