3-D Finite-Difference Modeling for MWD Logging Development

Abstract

This paper presents a 3-D finite-difference method (FDM) for analysis of electromagnetic measurement- while-drilling (MWD) tool response. The FDM is formulated with cylindrical coordinates, enabling accurate simulation of a cylindrical tool geometry. The algorithm allows the simulation of inhomogeneous media with arbitrary conductivity and magnetic permeability distributions. Material averaging is applied to both conductivity and magnetic permeability based on a mixture of harmonic and arithmetic averages. With the use of an irregular finite-difference grid, a complex MWD antenna with cavities and slots is accurately modeled. The system of linear equations is solved with the Lanczos decomposition method or the quasi-minimum-residual method, depending on the volume of output data. Our results show the 3-D FDM can accurately predict the tool response. It is shown that ferrite inserted in antenna slots increases the effective radiating length of the slots. The ferrite also helps reduce the eddy currents in the metal. However, it is not necessary to use ferrite with a relative magnetic permeability greater than 200 for the particular antenna geometry considered. For typical MWD tool spacings of 1 m or so, the field by a slotted antenna can be well approximated by that of a dipole antenna.