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

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