Fast electromagnetic modeling in cylindrically layered media excited by eccentred magnetic dipole

Abstract

We developed a fast algorithm to calculate a response of cylindrically layered media excited by the vertical magnetic dipole eccentred with respect to the axis of symmetry. The algorithm calculates response in the range of frequencies typical for induction and dielectric logging. The media conductivity and dielectric constant are described by piecewise‐constant functions. The corresponding boundary value problem is solved by method of separation of variables. Fourier transform is applied to Maxwell equations and boundary conditions to express field components through Fourier transforms of vertical components of an electrical and magnetic field. In addition, an expansion of vertical components into an infinite series with respect to angular harmonics is used to reduce the original problem to a series of 1‐D problems that only depend on the radial coordinate. The solution to each 1‐D radial problem for the angular harmonics is presented as a linear combination of modified Bessel functions. Finally, inverse Fourier transformation is applied to the angular harmonics of vertical components to derive electrical and magnetic field of the original boundary value problem. We provide detailed discussion on the elements that are critical for the numerical implementation of the algorithm: a proper normalization, convergence, and integration. Specifically, we show how to perform integration in the complex plane by avoiding intersection of the integration pass with the cuts located on the Riemann surface. Numerical results show the usefulness of the algorithm for solving inverse problems and for studying the effect of eccentricity in induction and dielectric logging.

Boundary detection capability and influencing factors of electromagnetic resistivity while using drilling tools in a horizontal well

“…Conventional LWD electromagnetic logging tools adopt single-transmitting and dual-receiving antennas, symmetrically compensated dual-transmitting and dualreceiving antennas, or multiple-transmitting and multiple-receiving array antennas (Nikitenko et al, 2020;Rodney et al, 1983;Clark et al, 1988;Bittar et al, 1991;Zhou et al, 2016;Fan et al, 2019). All transmitting and receiving antennas are axial, which means that they cannot measure azimuth information.…”