Far-Field Current Model for Carbon Steel Gas Pipes

The far-field eddy current effect refers to an observed phenomenon in electrically conducting tubular material in which the amplitude of an electromagnetic field induced at one location decays relatively slowly with distance along the tube. This effect and its usefulness for nondestructive evaluation of ferromagnetic pipe were noted as early as 1951 [1]. However, no published work of which the authors are aware has attempted more than a qualitative explanation of the far-field effect [2]. This paper presents a semi-empirical model, verified in laboratory experiments, that describes the behavior quantitatively. The experiments and model show that the far-field effect is due to the presence of a directly coupled wave that is rapidly attenuated by the pipe geometry. The directly coupled wave, in turn, excites eddy currents that travel through the pipe wall and then along the outer surface of the pipe with relatively low attenuation. The model allows an understanding of how the effect scales for varying pipe diameters, wall thicknesses, conductivity, and permeability as well as some aspects of probe design.