Abstract: The transient pressure analysis and morden well testing interpretation methods for multi branched horizontal wells in anisotropic formation are developed.The wellbore storage constant and the skin factor are taken into consideration.First,to use rotation of axes derive instantaneous soures functions of a linear section source which has arbitrary angle relative to x axis in xy plane.The instantaneous source function G xy of N linear sections,whose extend lines all pass origin of coordinates,are given by means of superposition.And vertical z direction source functions Gz for three cases i.e.formation top and bottom are prescribed flux,prescribed pressure and mixed boundarise in anisotropic formation are given also.The Green's functions G(x,y,z,t)=Gxy^*Gz of general multi branched horizontal wells are obtained by Newman's product method.Then the analytic expressions of dimensionless pressure PD(w) and well bottom pressure PD(w) in Laplace space are given.Finally,in Laplace space the dimensionless well bottom pressure PWD(C_D,S,s),which has taken into account the dimensionless wellbore storage C_D and the skin factor S,are obtained.Here the s is the Laplace transform variable.The expression of P_WD include PD(w) only as well as the constant C_D and S.We make use of numerical inversion of Lapalace transforms to give a set of type curves.At certain conditions the above mentioned results are also appliable for single horizontal well in wedge shaped fault.

Key words: branch, horizontal well, curve, Laplace transform, well testing, analysis

摘要： 研究了各向异性地层中分支水平井的瞬变压力分析和现代试井解释方法.考虑了井储和表皮因子,利用坐标旋转导出无限大平面中任意方向一个线段源的瞬时源函数;然后通过叠加给出任意多个线段源(其延长线均通过坐标原点)在xy平面上给出各向异性的瞬时源函数GXY.同时给出各向异性地层中上下封闭、上下定压和混合边界这三种情形在铅直方向的瞬时源函数GZ.根据Newman乘积原理得出一般情形分支水平井的Green函数GXY^*GZ.进一步给出了无量纲压力的解析表达式PD以及井底压力在Laplace空间的结果PD(w).为了计及井储和表皮影响,根据无量纲井储常数C_D和表皮因子S的定义,导出了无量纲井底压力在Laplace空间的表达式PWDD(CD,S,s),这里s是拉氏变量.这个表达式中包含PD(w).利用数值反演算出我们所需要的样板曲线,给出了若干例子.在一定条件下它对尖灭角内单个水平井同样适用.最后给出分支水平井试井解释的方法步骤.

关键词: 分支, 水平井, 曲线, 拉氏变换, 试井, 分析