重力作用下轴对称非稳态渗流压强场的解析解  

Analytic Solution of Unstable Axis-ymmetrical Seepage Capillary Pressure Field Under Gravity

作　　者：刘智颖 彭文耀[3] 章成广 LIU Zhiying;PEN Wenyao;ZHANG Chengguang(Key Laboratory of Exploration Technologies for Oil and Gas Resources,Yangtze University,Wuhan 430100,China;College of Geophysics and Oil Resources,Yangtze University,Wuhan 430100,China;Logging Engineering Company of Jianghan Oil Field Authority Limited Company,Qianjiang 433123,China)

机构地区：[1]油气资源与勘探技术教育部重点实验室(长江大学) [2]长江大学地球物理与石油资源学院,湖北武汉430100 [3]江汉石油管理局有限公司测录井工程公司,湖北潜江433123

出　　处：《厦门大学学报（自然科学版）》2018年第2期243-250,共8页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(41774116)

摘　　要：平面径向稳定渗流模型是描述地层中的注水压强分布状况以及计算注水后生产井中日产量的常用理论模型.由于该模型不仅未考虑重力作用下地层注水压强随深度增大而增大的特点,也未反映注水压强随时间的变化情况,因而难以准确计算注水后生产井的日产量.因此,重新推导了重力作用下轴对称渗流场注水压强分布函数的解析解,提出了一种径向第一类非齐次边界条件和纵向第二类齐次边界条件下的二维轴对称输运方程的一般求解方法.据此,绘制了二维柱坐标系下注水压强、渗流速度的分布曲线图,并应用于生产井的日产量计算,获得了良好的效果.As a theoretical model,the radial planar stable seepage is commonly used in injection pressure distribution description and daily production of producing well after injection.The model not only ignores the effect of gravity,which increases with the depth,but also fails to reflect the variation of injection pressure with time.Hence,the accurate daily production is hardly calculated.For the purpose of solving these problem,the analytic solution of unstable axis-symmetrical seepage pressure field is derived in this paper,and a general analytic solving method of 2D axis-symmetrical transport equation with first-type non-homogeneous boundary condition of radial directional and with second type homogeneous boundary condition of vertical directional is proposed.Hereby,the paper plots the injection pressure and the seepage speed distribution graphs under 2-dimensional cylindrical coordinate system,and get good results by applying in the model calculating the daily production of producing wells.

关 键 词：注水压强 日产量 第一类非齐次边界条件 轴对称输运方程 

分 类 号：O368[理学—流体力学]