Power losses in steel pipe delivering very large currents

This paper presents a finite difference time domain solution for the electromagnetic fields in ferromagnetic conducting steel pipes of the type used to deliver large currents for in situ heating of heavy oil reservoirs and for in situ environmental decontamination. A method is described whereby a single measured hysteresis loop can be used to deduce the family of hysteresis loops that governs the variable magnetic behavior throughout the pipe wall. Hysteresis and eddy current losses are calculated, and it is shown that hysteresis effects greatly alter the eddy current distribution and can more than triple the total power losses in the steel pipe when compared to the power losses that would be present if hysteresis effects are ignored and magnetic permeability is assumed constant.