Semi-analytical solutions for the problem of the electric potential set in a borehole with a highly conductive casing

Aralar Erdozain, Ignacio Muga, Victor Péron, Gabriel Pinochet

Research output: Contribution to journalArticlepeer-review

Abstract

Highly conductive thin casings pose a great challenge in the numerical simulation of well-logging instruments. Witty asymptotic models may replace the presence of casings by impedance transmission conditions in those numerical simulations. The accuracy of such numerical schemes can be tested against benchmark solutions computed semi-analytically in simple geometrical configurations. This paper provides a general approach to construct those benchmark solutions for three different models: one reference model that indeed considers the presence of the casing; one asymptotic model that avoids computations in the casing domain; and one asymptotic model that reduces the presence of the casing to an interface. Our technique uses a Fourier representation of the solutions, where special care has been taken in the analytical integration of singularities to avoid numerical instabilities.

Original languageEnglish
Article number6
JournalGEM - International Journal on Geomathematics
Volume13
Issue number1
DOIs
StatePublished - Dec 2022
Externally publishedYes

Keywords

  • Asymptotic models
  • Boreholes with casing
  • Electric potential
  • Semi-analytical solutions

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