Lumped representation in inductive measurement of metal casing properties

Abstract

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 truncatedregion 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.

Eddy Current Measurement for Planar Structures

“…to as the sensitivity/Jacobian matrix. If the influences of various variables on measurements are correlated, for example, coupling effect of permeability and conductivity on inductance [64][65][66] and correlation between the derivatives in terms of thickness and electromagnetic parameters [61], the condition number of the Hessian matrix will be large, and the function convexity can hardly be satisfied. Furthermore, the variable correlation renders the optimization process unstable when the inversion of the Hessian matrix is required [67].…”