实际井眼条件下过套管电阻率测井响应的传输线方程正演算法

过套管电阻率测井通过测量套管壁电势实现测量地层视电阻率，不同的地层模型对过套管电阻率测井会有不同的测井响应. 在传输线方程系数中本文考虑了径向含多个界面地层的影响，对轴向（井轴方向）呈层状、径向阶跃变化地层模型，给出了电势分布递推公式，计算了过套管电阻率测井响应，绘出了测井响应曲线. 算例表明，该方法有较强的轴向地层界面分辨能力；对径向均匀地层计算结果非常接近地层模型电导率，能较好地反映实际地层特征；对高电导地层，低电导水泥环有明显的测井响应；当径向存在多个地层界面时计算结果则为径向各层电导率的综合反映，不是某一径向层的电导率；算例显示该方法有较快（算例运行时间在1s内）的计算速度.

Forward calculation of the resistivity logging response through casing by transmission line equation for multi-layer formations

Since the difference in the formation model affects the potential distribution on the metal casing,the resistivity logging response can be obtained through casing by measuring the potential distribution on the metal casing.Logging response generally portrays a comprehensive effect of complex formation and the metal casing.Therefore,we have carefully considered the effect of formation model in radial-direction in setting the coefficients of the transmission line equation(TLE),and then formulated the recurrence formulae for potential distribution in axial-direction,and step-in radial-direction to compute the resistivity logging response through casing.The computed results show that this method has a strong capability to distinguish layer boundaries in axial-direction,while in the radial-direction the computed conductivity for the formation is very close to that from formation model.Results from this method reflect more closely to the actual formation.They show distinctively different logging response for the high conductive formation layer and the low conductive cement layer.It is also found that when multiple layers are encountered in the radial-direction,the computed conductivity is a composite result of all layers in this direction,and not for any one particular layer.A group of resistivity logging response curves from these computations are included in this paper.This method has a fast computing speed with an average run time of less than one second.