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

LIU Fu-Ping~(1,4),GAO Jie~2,SUN Bao-Dian~3,BAO De-Zhou~3,YANG Chang-Chun~41 Beijing Institute of Graphic Communication,Beijing 102600,China2 China University of Petroleum,Beijing 102249,China3 Technological Center,Chinese Petroleum Logging Corporation,Xi′an 710021,China4 Institute of Geology and Geophysics,Chinese Academy of Sciences,Beijing 100029,China  
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.
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