Mathematical Modeling of the Electromagnetic Field from a Solenoidal Coil in the Frequency Domain

Abstract

AbstractNumerical estimates of the measured electromotive force (EMF) for the electric field excited by a multi-turn solenoidal coil depend on the way the field source is approximated. The simple representation of the source as a point dipole is correct for measurements in the far field. For measurements in the vicinity of the field source, this method of approximation may give unreliable results. This paper proposes two ways of approximating a multi-turn solenoidal coil: surface approximation or single-coil approximation. Here we present the numerical simulation of the downhole logging procedure. As a result, we show the three-dimensional electromagnetic field, an electromotive force (EMF) induced in the receiver coils, and the phase difference of EMF depending on the method of source approximation. To calculate the three-dimensional electromagnetic field, the vector finite element method on the tetrahedral unstructured partition was used. The difference in the electromagnetic field configuration for different source approximation methods is shown. The effect of the number of cores on the time of solving a finite element system of linear algebraic equations is demonstrated. The use of a larger number of processor cores makes it possible to significantly reduce the time of solving the problem.KeywordsVector finite element methodSLAEElectromagnetic fieldSolenoidal source approximationHelmholtz equation