Integral equation of relationship on the apparent conductivity and true conductivity in induction logging

作     者：LI JianHao Li J H

作者机构：China Petroleum Logging Co.Ltd 

出 版 物：《Science China Earth Sciences》 (中国科学（地球科学英文版）)

年 卷 期：2014年第57卷第5期

页      面：1972-1978页

核心收录：

学科分类：081801[工学-矿产普查与勘探] 081802[工学-地球探测与信息技术] 08[工学] 0818[工学-地质资源与地质工程] 

基　　金：supported by the National Science and Technology Major Project (Grant No. 2011ZX05020) 

主　　题：electric-field intensity induction logging formation apparent conductivity true conductivity integral equation 

摘      要：This paper investigates the relation between the induced electromotive force measured by induction logging tool and the apparent conductivity, and the relation between the apparent conductivity and the formation true conductivity. Assuming the conductivity in Green s function to be the function of the field point coordinate, the apparent conductivity expression of electric-field intensity is derived using Green s formula, and the integral equation has been established representing the relationship of the apparent conductivity with the true conductivity under this condition. The integral equation is analyzed and then leads to the conclusion that the equivalent conductivity is the apparent conductivity and the values of the apparent conductivity function contain the true conductivity, and the method derived the true conductivity from the apparent conductivity around the well axis is put forward. The validity of the approach given in this paper is verified through numerical calculation. On the basis of above means, the transmitter coil produces an electric-field distribution in formation at every point where the induction logging tool moves along a wellbore, and a number of the receiving coils obtain an apparent conductivity distribution; this is what induction electric-field logging is.