Lumped representation in inductive measurement of metal casing properties

In low-frequency evaluation of oil-well steel casing using a transmitter coil and several receiver coils, high measurement accuracy is required to successfully resolve individual casing properties. The results of such measurements are usually only lumped parameters: casing factor and permeability-to-conductivity ratio. In this paper, we generalize the two lumped parameters into one space-frequency dependent parameter using an analytical model based on the truncated-region method and the series expansion of the vector magnetic potential. Using the generalized lumped parameter and the sensitivity analysis, we evaluate the traditional positioning of the receiver coils and discuss the frequency dependence of the measurement uncertainty of the lumped parameters.