Research On The Defect Detection Method Of Ferromagnetic Casing Based On Pulsed Eddy Current

Ferromagnetic casing has been widely used in the exploitation of downhole oil and gas since it possesses economical and reliable advantages.However,high temperature,high pressure,corrosion,and erosion cause casing distortion and even casing leakage,and lead to significant economic losses and human casualties.Thus,it is necessary to evaluate and maintain the in-service casing regularly.Nondestructive evaluation techniques are popular in the evaluation of industrial equipments since they cause no further harm to the tested object.Eddy current testing technique has been used to evaluate the downhole casings since 1960 s,as it needs no contact with the object and no couplant in the evaluation.Because the pulsed eddy current response contains a wide frequency spectrum,abundant time-domain and frequency-domain features,pulsed eddy current testing(PECT)has attracted extensive attention in metal materials evaluation.Many research findings related to PECT are published.However,there exist plenty of theory and application challenges in PECT-based ferromagnetic casing defect evaluation.Based on the deduced theoretical model of PECT,this dissertation analyzes and studies the detection method of casing defect.Numerical simulation and practical experiments of PECT are carried out to analyze and solve the theoretical problems of the defect detection of the ferromagnetic casing.In the dissertation,by applying the Green function method,the analytical solutions of transient response in an axisymmetric pickup coil are deduced in PECT on the casing,the solutions lay the foundation of the casing wall-thinning evaluation.In addition,the analytical solutions corresponding to eccentric testing coils in PECT on ferromagnetic casing are also deduced based on the second order vetor potential(SOVP),and the eccentric solutions lay the foundation of the casing local defect evaluation.Then,based on the complex frequency domain solution of transient eddy current response,the corresponding time domain solution is obtained.By simplifying the time domain solutions,a method for evaluating the annular defect of the casing is presented.Moreover,the theoretical data of eccentric array testing coils are obtained with the analytical solutions of their transient response,and a method for local defect evaluation is proposed based on the practical experiment data.The annular defect evaluation of multi-layer casings is also analyzed with the same method.The study of the dissertation enriches the basic theories and detection methods of PECT on ferromagnetic casings,and the main works and innovations of the dissertation are as follows:(1)Analytical solutions of the transient response of the detecting coils are given,the coils being located coaxially with a ferromagnetic casing under test based on pulsed eddy current.When the current source is chosen to be the power supply of the pulse excitation circuit,a huge self-induced voltage will be generated in the driver coil since the driver coil can be considered as an inductor.The self-induced voltage does no good to the evaluation and increases the design difficulty of the stability and transient power of the excitation circuit.To decrease the self-induced voltage,a voltage source is applied to generate the pulsed signal.The magnetic potential distribution in the driver coil region is obtained with the Green function method,and the expression of driver coil inductance is presented.Then,the excitation current in the driver circuit is analyzed based on Ohm’s law,and the analytical solution of the excitation current is deduced based on the Fourier series and frequency-domain expression of magnetic potential.Furthermore,the transient responses induced in the pick-up coil corresponding to ideal and non-ideal pulsed excitation signals in PECT on ferromagnetic casing are deduced based on the solution of the excitation current.The numerical simulation results of COMSOL and the practical experiment results indicate that the deduced analytical solutions are accurate.This work lays a theoretical foundation for the casing annular defect evaluation.(2)Analytical solutions of the transient response of the detecting coils are given,the coils being located eccentrically with a ferromagnetic casing under test based on pulsed eddy current.In the PECT of the ferromagnetic casing,the slight eccentricity of the driver coil is inevitable,and the array pick-up coils are eccentric in terms of the casing axis.To obtain the theoretical data that is consistent with practical data,the scalar potentials inside the casing are studied based on the SOVP.Based on the Bessel addition theorem,the expressions of the exciting magnetic field and the eddy current magnetic field are rewrriten as to different reference corrdinate systems.Additionally,the analytical solution of the transient response induced by the exciting magnetic field inside the pick-up coil in the free-space is deduced,and an approximate method for calculating the transient eddy current response in PECT is proposed.The practical experiment results indicate that the deduced solutions are accurate and the calculation method of the transient eddy current response is appropriate.The solutions lay a theoretical foundation for the casing local defect evaluation.(3)The complex frequency-domain solution of the transient eddy current response of the coaxially detecting coils in PECT on the ferromagnetic casing is studied,and a method for casing annular defect evaluation is proposed based on the time-domain solution of the response.In the dissertation,detecting coils located coaxially with the tested casing are applied for the casing annular defect evaluation.The complex frequency-domain solution of the transient eddy current response to the coil is deduced,and the corresponding time-domain expression is also obtained with the residue theorem.Then,the relationships between the transient eddy current response and the casing parameters are analyzed.Moreover,the relation between the transient response and transient eddy current response in the pick-up coil is analyzed based on the theoretical data of the PECT,and the results indicate that transient eddy current response almost equal to the transient response in the later period of the response.Further analysis of the relationships is implemented with the simulation results of COMSOL,and the results indicate that the decay rate of the logarithmic curve to the transient response is sensitive to the thickness change of the casing and is proportional to the conductivity and relative permeability of the casing,respectively.What’s more,the decay rate is insensitive to the change of the casing inner diameter and the coils’ parameters.Thus,the decay rate can be used to evaluate the annular defect of the single casing.In addition,the annular defect evaluation of multi-layers casing is also studied with the decay rate.The results of simulation experiments and practical experiments demonstrate that the proposed method can evaluate the single casing wallthinning effectively,and the method also shown proper applicability as to multi-casings annular defect detection.(4)Depending on the theoretical and experimental data of the eccentric testing coils in PECT on the ferromagnetic casing,a local defect evaluation method is proposed based on the magnitude of the transient eddy current resoponse.In casings evaluation,information on local defect is also desired.To increase the resolution ratio of the detection results,the circumferentially distributed array pick-up coils are applied for local defects detection.The analysis of theoretical and experimental data to the PECT indicates that the magnitude of the transient eddy current resoponse can evaluate the local defects correctly,and the detection mechanism of the magnitude is also analyzed.Besides,an amplifier is used to amplify the magnitude change caused by the defects.The results of practical experiments validate the proposed local defect detection method.