|1Myrontsov, ML |
Stas, iv, OS
1Institute of Telecommunications and Global Information Space of the NAS of Ukraine, Kyiv
|Dopov. Nac. akad. nauk Ukr. 2020, 2:58-67|
The example of solving the multiprobe induction logging inverse problem in the small-diameter well filled with a non-conductive drilling fluid (300 Ohm·m) is presented. Such parameters of the well allow us to consider its effect on the logging to be absent. As a skin effect correction, we used the analytical relationship between the apparent conductivity and the specific conductivity of a homogeneous infinite medium. We use solutions of the Fredholm equation of the first kind of the convolution type to account for the shoulder-beds effect. This equation connects the apparent conductivity with the spatial distribution of the specific conductivity in the Doll linear theory. A low-frequency (100 KHz) induction four-probe logging complex was selected. It is shown that the skin effect correction for thick formations allows us to determine the true conductivity of impermeable formations. In addition, the use of a solution of the Fredholm equation of the first kind of the convolution type allows us to eliminate the influence of the shoulder-beds on the determination of the parameters of the studied low-power bed completely. The boundary between the sedimentary rocks and the crystalline basement that fell into the logging interval allows us to estimate the accuracy of the determination of the resistivity of low-con ductivity rocks determining.
|Keywords: Fredholm equation of the first kind of the convolution type, induction logging, inverse problem, oil and gas well, skin effect|
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