Abstract: The seepage flowing pattern of a gas well with hydraulic fractures was transferred to a simple single direction flowing one by using the conformal transformation principle.The conformal transformation can transfer a complicated seepage flowing problem into a relative simple one.The transferred patterrn can describe the contribution of the complicated seepage flowing pattern near the well bore to the productivity of the fractured gas well.The closed boundary condition at the fracture tip is more rational after transformation.According to the comprehensive applications of material balance theory and non-Darcy's law and the theory of pressure coupling in matrix,a second order differential equation for expressing the pressure of mass-variable seepage flowing in fractures was derived on the basis of seepage flowing analysis on microelements.Then an equation for estimating gas productivity of a hydraulic fractured well with various fracture lengths and conductivities (finite and infinite conductivity) were obtained.Comparison of calculated result with the real production of a hydraulically fractured gas well in a certain field shows an excellent agreement.This method is simple and feasible for field application.

Key words: gas well, fracturing, conformal transformation, vertical fracture, single flowing pattern, stable production, calculation method

摘要： 应用保角变换原理,将求解带垂直裂缝的气井产量问题转化为简单的单向渗流问题.保角变换方法能将Z平面上特别复杂的渗流问题转化为W平面上相对简单和易于求解的渗流问题.变换后,可用于描述井筒附近较为复杂的流动型态(裂缝内流动和非裂缝区域拟径向流动)对压裂后产能的贡献.变换后假设的缝端封闭边界条件更符合实际.然后再根据微元体流动分析,综合应用物质守衡原理、非达西运动方程和压力耦合原理,导出了裂缝内变质量流动时压力满足的二阶微分方程,进而推导出不同缝长和导流能力(包括无限导流能力和有限导流能力)裂缝井的产能公式.将计算结果与现场某气井压裂后产量相比,两者吻合程度较好.该计算方法简单易行,便于现场应用.

关键词: 气井, 压裂, 保角变换原理, 垂直裂缝, 单向渗流, 稳态产能, 计算方法