【摘要】 复杂源汇边界矩形区域的流动是工程领域中的典型问题。通过椭圆函数保角变换.矩形区域变为全平面空间,一部分源汇变成无限大圆形边界,另一部分被组合存一起置于圆的中心。再利用全平面空间中圆形边界到圆心组合汇流动的分析,得到原问题的解析解。该方法应用于石油工程.解决了水平井网渗流问题,得到了渗流压力分布和井的产量,并给出了流线分布图。考虑了纵向和横向井距及水平井长度等因素的影响.随水平井长度增加,水平井产量增加,但面积波及系数下降,同时主流线与水平井的交点向水平井端点靠近。该方法对于相关工程问题具有普遍适用性。更多还原

【Abstract】 The flow in a rectangular area with complex sources and sinks boundaries is a typical problem in engineering. By conformal transformation with elliptical function, the rectangular area is transformed to the whole plane. Parts of the sources and sinks are changed to an infinite circular boundary, and the others are integrated and located it the center of the circular boundary. The analytic solution of the oniginal problem is obtained by analysis of the flow between the circular boundary and the integrated sources or sinks. Utilizing the above method in the petroleum engineering, the problem of the flow through horizontal well networks is solved. The pressure distribution and well production rate are obtained. The figures showing the streamline distribution are presented. The longitudinal and transverse well spaces, and the length of the horizontal wells are considered. When the horizontal well length increases the producing rate goes up but the flood conformance goes down, the intersection point of the principal streamline and the horizontal well goes closer to the end of the horizontal well. The above meth- od is applicable to all the similar problems in related engineering fields.更多还原