Application of Toroidal Coils to Obtain Electrical Resistivity of Core Samples: Mathematical Modeling

Abstract

We consider the capability of evaluating the specific electrical resistivity of a cylindrical core by means of a transmitter-receiver system with toroidal coils placed around it. An algorithm for two-dimensional finite-difference modeling of electrical and magnetic signals from an external circular magnetic harmonic current equivalent to a toroidal coil has been developed and verified. We perform twodimensional numerical modeling of the real (in-phase) and imaginary (quadrature) part of the vertical component of the electric field and the tangential component of the magnetic field for a practically-significant range of core resistivities, the sample being located within an insulating or highly conductive tube with toroidal coils. Following the results of numerical simulation, the optimal length of the measuring system is selected, as well as the operating frequency and type of measured signals. The transformation of the latter into the apparent resistivity values of vertically inhomogeneous samples is proposed. Moreover, criteria have been established for the correspondence of the measured signals in thinlayered and equivalent electrically macroanisotropic samples when changing the resistivity contrast and thickness of the interlayers.

Keywords

• toroidal coil
• core material
• specific electrical resistivity
• mathematical modeling
• finite difference method
• two-dimensional model
• signal transformation