Magnetic Flux Leakage Detection Technology for Well Casing on Neural Network

Jinzhong Chen1, Lin Li1, Jinan Shi2 1China University of Petroleum，Beijing 102249, China

23H（ShangHai）Petroleum Equipment Co.，Ltd E-mail：chenbeiter@yahoo.com.cn

Abstract

Well casing integrity is vital for the safe operations of oil wells, and also significant to detect well casing defects. Magnetic Flux Leakage (MFL) Detection Technology is widely-used in detecting the defects of various pipelines. Owing to the very complicated environment where well casing is laid in, the system which based on magnetic flux leakage technology is not mature yet to detect well casing defects. The technology of defects detection with RBF neural network based on Gaussian kernel is employed, by which parameters of well casing defects can be recognized. The training data samples were selected from both the simulated data sets for 3-D finite element model and measured MFL data. Detection system suitable to casing inspection is established. The experiment result indicates that defects of well casting can be detected and also its parameters can be identified effectively by detection system. 1. Introduction

Well casing integrity is a very important component for the safe operations of oil and gas wells nowadays [1]. In drilling and production operations, the well casing subject to tension, distortion, Corrosion, stresses and mechanical damage of well casing can cause Great accident and economic loss. So it is important to detecting well casing defects. Magnetic Flux Leakage (MFL) Detection Technology has been widely used to detect the defects of various pipelines. The well casing wall is magnetized to near saturation flux density. In the region where the thickness of wall is reduced because of a corrosion defect or crack, the magnetic flux leaks into air [2]. This leakage flux, which is correlated with the size and location of defect, can be detected by magnetic sensor. The parameters of defect can be identified with leakage flux signals [3] [4] [5].

In this paper, Magnetic Flux leakage (MFL) inspecting system is established which based on Magnetic Flux Leakage technology for Well Casing. The data analysis system is developed to identify the type of defect, based on RBF neural network. Finally the experiment result indicates that the system can detect the defect and identify its parameters effectively. 2. The establishment of MFL testing system for well casing

MFL testing system for well casing is made up detecting probe, data collection and storage system, surface system of data analysis and defect recognition, as shown in Fig.1. The well casing wall is magnetized to near saturation flux density by the magnetic circuit of detecting probe. Hall Effect sensors are mounted in detector probe to collect MFL signals. The detecting probe of variable diameter structure maintains the magnetizing part and sensors close to well casing wall. High-speed data collection and real-time data storage are realized by using double MCU configuration. Data collection system is configured to convert the signal into digital data and to write it with correlated time to the dual-port RAM. Data storage systems read the data and write it into electronic hard disk as file system. The electronic hard disk with IDE interface controller can be used to record a great quantity of real-time data. File system operation on embedded system enables general computer to operate data on electronic hard disk. The design of detector, data collection and storage system should meet defined applications of downhole environment. The ground system acquires the position data of detector and stores it with correlated time, while the downhole instruments acquire MFL data. When the downhole instruments return surface, surface analysis system integrate the downhole acquired MFL data and surface position data, then the surface analysis system captures the defect signal and recognizes the parameters of defect.

International Symposium on Intelligent Information Technology Application Workshops

978-0-7695-3505-0/08 $25.00 © 2008 IEEE

DOI 10.1109/IITA.Workshops.2008.67

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Figure 1. The diagram of MFL testing system for well casing

2.1. Magnetic circuit design of detecting probe

The magnetic circuit is comprised of back-iron, magnet, well casing wall and pole shoe. Fig.2 shows diagram of magnet circuit, as follows: 1 back-iron, 2 magnet, 3 pole shoe, 4 well casing wall. The permanent magnet is made from NdFeB alloy, which exhibits very high magnetic properties. The structural dimensions of magnetic circuit can be calculated by magnetic conductance method, and then be validated based on 3-D Finite Element Method. Fig.3 shows the equivalent magnetic circuit.

Figure 2. The structure diagram of probe

magnetic circuit

Figure 3. Equivalent magnetic circuit

Rj –the magnetic resistance of back-iron and pole shoe, Rg – the magnetic resistance of air gap between the pole shoe and well casing wall , Ri、Rb – the main leakage magnetic flux of magnetic circuit, Rz – the magnetic resistance of the well casing wall, rm –the internal resistance of magnet, F–magnetomotive force of magnet, ф–magnetic flux of magnet.

2.2. Defect recognition system based on gauss kernel RBF neural network

The identification of defect geometrical parameters is difficult point of magnetic flux leakage testing method. Through experiment and consulting data, We got the typical features of MFL signal related to defect geometrical parameters, such as peak to peak value of axial MFL, waveform area of axial MFL, the distance of two axial MFLpp, the ratio of waveform area and peak to peak value, the ratio of waveform area and the distance of two axial MFLpp, which were expressed by MFLpp, S, p-p, S/ MFLpp and S/p-p. The relationship between defect geometrical parameters and MFL signal is nearly definite, but it is difficult to express in function. By using nonlinear approaching ability of the neural network, the nonlinear relation between defect geometrical parameters and MFL signal can be obtained.

The Radial Basis Function Network (RBF) based on gauss kernel is a kind of feed forward network, which has the characteristics of best approximation and against local minimum problem, and has shorter training period and high forecast accuracy. Fig.4 shows the structure of neural network based on gauss kernel. The function of neurons in hidden layer is Gaussian function.

jic jidjiw

X Y

Figure 4. the structure of RBF neural network

based on gauss kernel The transfer function of RBF network can be

written as follows:

2xey −= (1)

Where jCX − is an independent variable of

transfer function. [ ]jnjjj cccC ,, 21= is central

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vector of hidden layer, which can be calculated by the following formula:

piij

piiicji

minmax)1(2

minmaxmin −−+−+= (2)

Where p is the number of neurons in hidden layer, imax is the maximum value of input vector, and X is

input vector. With increasing distance between input vector and central vector, the network output is increasing. This indicates that RBF neural network based on gauss kernel has the capability of local approximation.

The training process contains unsupervised learning step and supervised learning step. Unsupervised learning can determine the weight of input layer jC

and the weight of hidden layer jD in first step. jD

can be calculated by the formula (3), and fd is parameters to adjust the width of the original radial basis function. Supervised learning can determine the connection weight jW of hidden layer and output layer

by formula (4), kmax is the expected maximum value of neuron output, and kmin is the expected minimum of neuron output.

( )∑=

−=N

kji

kifji cx

Ndd

1

1 (3)

1minmax

2minmaxmin

+−+−+=

qkkj

qkkkwkj （4）

The neuron output of hidden layer can be obtained by following formula:

pjD

CXz

j

jj ,,2,1exp

2

=⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −−= (5)

The weight parameters of RBF neuron network are updated based on gradient descent algorithm, the iterative calculation are as follows:

)]2()1([)1(

)1()( −−−+−∂

∂−−= twtwtwEtwtw kjkj

kikjkj αη

)]2()1([)1(

)1()( −−−+−∂

∂−−= tctctcEtctc kjkj

kjkjkj αη

)]2()1([)1(

)1()( −−−+−∂

∂−−= tdtdtdEtdtd kjkj

kjkjkj αη

η is learning factor,α is momentum term, and E is evaluation function of RBF neuron network[8].

The system of ground data analysis and defect identification is established by labview. It includes ground data acquisition system, data playback system and defect recognition system based on gauss kernel RBF neural network. Its core is defect recognition system. The sample data of training neural network should contain various signals of defects as much as possible, by which the neural network can recognize the defect size effectively. It is expensive and difficult to obtain different sets of sample. But it can be solved with the results of three-dimensional finite element method (FEM) calculation as sample database[6][7].

3. Main title Experimental MFL results 3.1 .The recognition of simulated defect

The system is designed for inspecting Well casings in 139.7mm diameters and 7.72mm wall thickness. By finite element theory, the defect model of well casing is created and the relationship between the defect geometric parameters and MFL signal are simulated, finally the relationship sample database is set up. The defect length are respectively 1, 2, …, 7 times of wall thickness of well casing, and defect depth 10%, 20%, …, 60% of wall thickness. 20 sets of MFL signals are simulated as test sets, the characteristic quantity of some testing data, the Comparison of design value and identification result of defect size of which are shown in table 1.

From table 1 we find that design value and identification result of defect size are well approximate, and the maximum error is 2.2%. The result show that the RBF neural network based on gauss kernel has good recognition capability

Table 1. the Comparison of design value and identification result of defect size Numbering

of defect the features of MFL signal design value and of

defect size identification result of

defect size MFLpp S p-p S/ MFLpp S/ p-p l(mm) H(mm) l(mm) H(mm)

1 0.6475 0.8732 9 1.348571 0.097022 5 10 4.89 9.96 2 0.6955 6.1436 15 8.833357 0.409573 10 15 10.03 14.9

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3 0.7029 11.161 18 15.8785 0.620056 15 20 19.8 20.14 4 0.7034 12.432 22.5 17.67415 0.552533 20 25 20.15 24.87 5 0.7685 13.737 24.5 17.87508 0.560694 25 30 25.24 30.25 6 0.8294 16.098 25 19.40921 0.64392 30 35 30.50 34.72

3.2. Prototype experiment

Figure 4. MFL signal waveform of groove

shape defect

Figure 5. MFL signal waveform of hole defect

The prototype of the MFL inspecting system for well casing is established, which contains hardware and software system. In order to evaluate the performance of the system, experiments were carried out. As Fig.5 show, it was MFL signal waveform of hole defect with the diameter of 5mm, and Fig.6 show MFL signal waveform of groove shape defect with the width and depth of 5mm and 2.5mm.It was transformed into the data of leakage magnetic field strength and corresponding position data, after compensation, which was input into RBF neural network based on gauss kernel. The experiment result indicates that the system can detect the defect and recognize its parameters effectively. 4. Conclusions

Considering that it is difficult to identify well casing defect quantitatively, the method of quantitative recognition defect based on RBF neural network based on gauss kernel was studied in this paper, and the prototype of the MFL inspecting system for well casing was developed. Then performance of prototype that can detect and recognize the parameters of well

casing was verified, and the pass ability of prototype through 5.5 inch well casing was also verified. But this capability has previous not been available to the industry. However prototype still needs further improvement, so that the series of instruments for inspecting well casing with series diameter could be developed and be up to the requirements of field operation. 5. References [1]D.C. Vogtsberger, Baker Atlas, and B. Girrell, J. Miller, and D. Spencer, Microline Technology Corp: Development of High-Resolution Axial Flux Leakage Casing-Inspection Tools, SPE Eastern Regional Meeting held in Morgantown. W.V. 14-16 September 2005 (SPE paper 97807). [2]Jin Tao, Que Peiwen, and Tao Zhengsu. Magnetic Flux Leakage Device for Offshore Oil Pipeline Defect Inspection. Materials Performance. Oct 2005, 44:48-51 [3]Kang Yihua, Liu Bin, and Tan Bo. Study on Flux Leakage Detection Method for Tubing/Casing of Various Sizes .Steel Pipe, 2007,36 [1]:50-53. [4]A.A. Carvalho, J.M.A. Rebello, L.V.S. Sagrilo, C.S. Camerini, and I.V.J. Miranda. MFL signals and artificial neural networks applied to detection and classification of pipe weld defects. NDT & E International, Volume 39, Issue 8, December 2006:661-667 [5]Jiang Qi. Quantitative Technology and Application Research on Magnetic Flux Leakage Inspection of Pipeline Defects. Tianjin University, 2002. [6]F.I. Al-Naemi, J.P. Hall, A.J. Moses FEM modelling techniques of magnetic flux leakage-type NDT for ferromagnetic plate inspections. Journal of Magnetism and Magnetic Materials, Volume 304, Issue 2, September 2006:790-793 [7]Huang Zuoying, Que Peiwen, and Chen Liang 3D FEM analysis in magnetic flux leakage method. NDT & E International, Volume 39, Issue 1, January 2006: 61-66 [8] Yin Yong, and Qiu Ming. A Learning Algorithm of RBF Neural Networks Based on Gaussian Kernel Function. Computer Engineering and Applications, 2002[21]:118-12

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