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Ｌａｐｌａｃｅ变换域（Ｌ域）中的试井模型具有诸多优点：如容易处理并筒储集效应；多层和双重介质油藏的渗流模型与 单层均质之间不存在本质差异等。因此在试井分析中常常是先求解Ｌ域中的试井模型，然后利用Ｓｔｅｈｆｅｓｔ数值反演计算 井底不稳定压力响应。为给Ｌ域中试井模型的求解提供最一般化的手段，本文引入Ｇｒｅｅｎ函放方法并建立求解试井模型 的通用积分公式。Ｇｒｅｅｎ函数只依赖于渗流区域的形状以及边界类型，与视为源汇的井筒边界条件无关。通过导出一些典 型区域的Ｇｒｅｅｎ函数，重点研究了局部打开井、垂直及水平压裂井、水平井等各种复杂井筒边界模型下的均匀流量压力 解。文中的Ｇｒｅｅｎ函数方法较好地解决了现代试井分析中所遇到的复杂试井模型和复杂井筒边界模型下的求解问题。
The well testing model in Laplace transform domain (L-domain) has many advantages such as ease of handling and barrel-stacking effect; there is no essential difference between seepage model and monolayer homogenization in multi-layer and dual-medium reservoirs. Therefore, it is often the first solution to the well test analysis of the well test model in the L domain, and then use the Stehfest numerical inversion to calculate the bottom hole instability pressure response. In order to provide the most generalized method to solve the well testing model in L domain, this paper introduces Green’s method and builds a general integral formula to solve well testing model. The Green function depends only on the shape of the seepage area and the type of boundary, irrespective of the wellbore boundary conditions considered as sinks. By deriving the Green function of some typical regions, we focus on the uniform flow pressure solution under various wellbore boundary models such as partially open well, vertical and horizontal fracturing wells, horizontal wells and so on. The Green function method in this paper is a good solution to the problem of complex well testing and complicated wellbore boundary model encountered in modern well testing.