Magnetic Flux Leakage Method: Large-Scale Approximation

TL;DR

This paper develops an analytical approach for detecting and reconstructing large-scale, shallow defects in ferromagnetic tubulars using magnetic flux leakage measurements, focusing on the planar layer approximation.

Contribution

It introduces a large-scale approximation method to relate magnetic field measurements to surface defects in ferromagnetic layers, enabling defect reconstruction.

Findings

Derived analytical relations between magnetic field and surface profile.

Applicable to large-scale, shallow defects in ferromagnetic tubulars.

Provides a theoretical basis for defect detection in corrosion scenarios.

Abstract

We consider the application of the magnetic flux leakage (MFL) method to the detection of defects in ferromagnetic (steel) tubulars. The problem setup corresponds to the cases where the distance from the casing and the point where the magnetic field is measured is small compared to the curvature radius of the undamaged casing and the scale of inhomogeneity of the magnetic field in the defect-free case. Mathematically this corresponds to the planar ferromagnetic layer in a uniform magnetic field oriented along this layer. Defects in the layer surface result in a strong deformation of the magnetic field, which provides opportunities for the reconstruction of the surface profile from measurements of the magnetic field. We deal with large-scale defects whose depth is small compared to their longitudinal sizes---these being typical of corrosive damage. Within the framework of large-scale approximation, analytical relations between the casing thickness profile and the measured magnetic field can be derived.