Magnetic flux leakage (MFL), a pipeline internal detection, is the mainstream technology for international oil and gas pipeline safety maintenance. To address the problem of large errors in the assessment of defects in pipeline inspection by existing theoretical analysis models, this paper introduces the charge density parameter to establish a mathematical model of non-uniform magnetic charge for pipeline leakage detection and calculates the non-uniform distribution pattern of magnetic charge on the defect side wall. The contour plot method is proposed to visually analyze the size of defects. To compare the error between uniform and non-uniform models, and verify the correctness of the theoretical model, experiments were systematically conducted on the X70 pipeline with internal MFL technology. The results show that: the magnetic charge distribution curve is symmetrically shaped at the center of the defect, with a valley at the center and two peaks at the defect edge. As the defect depth and width increase, the magnetic charge density increases sharply near the surface and edge. The peak-to-valley spacing and peak-to-valley values in the contour map of the magnetic flux leakage signal can directly reflect the location and size of defects. The signal characteristic values follow the trend of a first-order decreasing exponential function as the value of the lift-off increases. The first-order derivative of the signal characteristic value tends to decrease and then increase as the mesh size decreases, and the extreme point of the derivative curve is the best mesh size.

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In order to solve the problem of the quantification of detection signals in the magnetic flux leakage (MFL) of defective in-service oil and gas pipelines, a non-uniform magnetic charge model was established based on magnetic effects. The distribution patterns of magnetic charges under different stresses were analyzed. The influences of the elastic load and plastic deformation on the characteristic values of MFL signals were quantitatively assessed. The experimental results showed that the magnetic charge density was large at the edges of the defect and small at the center, and approximately decreased linearly with increasing stress. The eigenvalues of the axial and radial components of the MFL signals were compared, and it was found that the eigenvalues of the radial component exhibited a larger decline rate and were more sensitive to stress. With the increase in the plastic deformation, the characteristic values of the MFL signals initially decreased and then increased, and there was an inflection point. The location of the inflection point was associated with the magnetostriction coefficient. Compared with the uniform magnetic charge model, the accuracy of the axial and radial components of the MFL signals in the elastic stage of the improved magnetic charge model rose by 17% and 16%, respectively. The accuracy of the axial and radial components of the MFL signals were elevated by 9.15% and 9%, respectively, in the plastic stage.

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