Three-Dimensional Finite Element Numerical Simulation and Physical Experiment for Magnetism-Stress Detecting in Oil Casing

MENG Fanshun, ZHANG Jie YANG Chaoqun, YU Weizhe and CHEN Yuxi

1)College of Marine Geo-science,Ocean University of China,Qingdao266100,P.R. China

2)Shenzhen Branch Company of China National Offshore Oil Corporation,Shenzhen518067,P.R. China

Three-Dimensional Finite Element Numerical Simulation and Physical Experiment for Magnetism-Stress Detecting in Oil Casing

MENG Fanshun1),*, ZHANG Jie1), YANG Chaoqun2), YU Weizhe1), and CHEN Yuxi1)

1)College of Marine Geo-science,Ocean University of China,Qingdao266100,P.R. China

2)Shenzhen Branch Company of China National Offshore Oil Corporation,Shenzhen518067,P.R. China

The casing damage has been a big problem in oilfield production. The current detection methods mostly are used after casing damage, which is not very effective. With the rapid development of China’s offshore oil industry, the number of offshore oil wells is becoming larger and larger. Because the cost of offshore oil well is very high, the casing damage will cause huge economic losses. What’s more, it can also bring serious pollution to marine environment. So the effective methods of detecting casing damage are required badly. The accumulation of stress is the main reason for the casing damage. Magnetic anisotropy technique based on counter magnetostriction effect can detect the stress of casing in real time and help us to find out the hidden dangers in time. It is essential for us to prevent the casing damage from occurring. However, such technique is still in the development stage. Previous studies mostly got the relationship between stress and magnetic signals by physical experiment, and the study of physical mechanism in relative magnetic permeability connecting the stress and magnetic signals is rarely reported. The present paper uses the ANSYS to do the three-dimensional finite element numerical simulation to study how the relative magnetic permeability works for the oil casing model. We find that the quantitative relationship between the stress’s variation and magnetic induction intensity’s variation is： Δδ=K*ΔB,K= 8.04×109, which is proved correct by physical experiment.

oil casing damage; magnetism-stress detecting; magnetic anisotropy; finite element analysis; physical experiment; relative magnetic permeability; ANSYS; three-dimensional numerical simulation

1 Introduction

Casing damage has caused huge economic losses in offshore oilfield production, becoming the urgent problems in oil and gas exploration. Currently, domestic and foreign researchers focus on detecting the tube geometry factors, develop and improve logging equipment and logging techniques, and detection of casing damage under various conditions (Yanget al., 2013). However, these methods only work when the deformation occurs. None of these methods measure the casing damage from the view of stress mechanism, so the results are not very satisfactory. With the rapid development of China offshore oil industry, the number of offshore oil wells is becoming larger and larger. Because of the cost of offshore oil well is very high, if the casing damage occurs, it will cause huge economic losses. What’s more, it can also bring serious pollution to marine environment. So the effective method of detecting casing damage is required badly to reduce the offshore oil well casing damage rate. Casingdamage occurs mainly because of the accumulation of stress; if the stress changes in the casing can be directly measured, hidden dangers can be found. So managerial staff can take actions timely to prevent casing damage from occurring, solving the casing damage problems fundamentally.

There are many methods of stress detecting. The magnetic method is one of them which includes a metal magnetic memory testing method and the magnetic anisotropy detection method. These two methods are based on the counter magnetostriction effect of ferromagnetic materials (Jianget al., 2006).This effect refers to the phenomenon that the relative magnetic permeability of ferromagnetic material will change when subjected to external force, thus affecting the magnetic field (Wanget al., 2005; Laguerreet al., 2002). Ferromagnetic material stress variation can be obtained by analysising the changes in the magnetic field. Oil casing wall material is ferromagnetic materials, so the above-described method is applicable.

Currently, few studies on this method are reported at home and abroad. Liu at China University of Geosciences studied the metal magnetic memory testing method in his PhD thesis, and developed the corresponding detection device based on this principle to detect the casing stress(Liu, 2006). Its disadvantage is that different geographical locations will impact magnetic memory phenomenon, making the measurement results appear randomly. This method is not ideal. However, magnetic anisotropy detection method does not have this disadvantage, and represents the development direction of the magnetic stress measurement techniques. Wanget al.(2007, 2012) did some exploring work from engineering practice, creating a MST-II well casing stress testing instruments based on this method. But its core components, the stress sensor, rely on foreign devices and technology. The relevant paper did not make it clear that the stress sensor output signal is which kind of magnetic signals, just generally giving a qualitative relationship between the signal and stress. The method was preliminarily used in oil production, and played a role in the prevention of the occurrence of casing damage. However, it did not help much to understand the deeper relationship between stress and magnetic signals; it just proved that it is meaningful to study such a relationship. There are a lot of work to do about mechanism of the stress magnetic measurements technology.

Advance in magnetic anisotropy stress detection method is relatively slow, scholars can not make a perfect explanation of the nature of the ferromagnetic material. Not many scholars at home and abroad study the problem.

Pulnikovet al.(2003, 2004）used magnetic flux and the change of relative magnetic permeability to characterize the change of stress and its distribution by physical experiment. Sakaiet al. (2004) developed a measurement system with stress sensor to measure the pipe stress under bending. Their paper briefly introduced the technique tha the stress sensors were placed on the outer surface of the

t pipe, getting the change of the stress by analyzing the voltage changes, and it was proved effective by physical experiments. Mohammedet al.(2004) found the magnetic induction intensity increases with the increase of stress by measuring solid object. ?ureket al.(2005) used the changes in the magnetic field strength to characterize changes in stress and its distribution. Baudendistelet al.(2007) developed a stress sensor which can analyze changes in the electrical impedance of the sensor inside to perceive pressure changes when it is close to the measured object. Ekreemet al.(2007) pointed out that the changes of relative magnetic permeability will lead to the change of the magnetic flux. It can get the changes of the stress by receiving the changes of magnetic flux in the coil. Bechtoldet al.(2010) placed the object to be measured at the middle of the excitation coil and receiving coil, analyzing the measured object deformation by receiving the magnetic signals in the receiving coil.

In a word, the research results of the magnetic anisotropy analysis at home and abroad at present just show the qualitative relation between the magnetic signals and stress or the quantitative relation between the magnetic signals and stress on the basis of the physical experiment. Such results indicate that the magnetic anisotropy detection method based on counter magnetostriction effect is feasible (Evangelos and Aphrodite, 2007; Olabi and Grunwald, 2007; Raffertyet al., 2009; Auslenderet al., 2013). There are few papers that elaborate how relative magnetic permeability works which connects the stress and magnetic signal. If the intermediate process is not clear, the relationship between stress and magnetic signal is also at the fuzzy qualitative understanding stage. So we must understand the process if we want to apply this technology to the detection of stress of oil casing accurately. There are two aspects we must make clear. One is that we must figure out how the stress influence the relative magnetic permeability, for which there are theoretical derivation and experimental verification can be consulted. The other is that we must figure out how the changes of the casing wall’s relative magnetic permeability affect the magnetic signal. For petroleum casing pipe model, how the relative magnetic permeability of the casing wall affect the magnetic signal is equivalent to how an irregular ferromagnetic material with relative magnetic permeability not evenly distributed affect the magnetic field around. Because there exists no analytical solution to solve this problem, we use the finite element method to describe the distribution of magnetic field inside the casing pipe wall effectively if its relative magnetic permeability is not uniformly distributed. Finally physical experiment is to be done to verify the correct understanding of the intermediate process. In the present work, such a process is revealed by numerical simulation, in which the approach of FEM is for the first time applied to the problem and tested with physical experiment.

2 The Relationship Between Stress and Permeability

Permeability is one of important basic features of magnetic materials, it is changing with crystal structure in the material (Tian, 2001). The forces can change the crystal structure, so the stress results in the change of relative magnetic permeability of magnetic materials.

On the one hand，the specific relationship between stress and permeability can be analyzed based on power conversation law. Wanget al.(2005) gave a model about the relationship between stress and the change of relative magnetic permeability of magnetic materials. He concluded that the relative change in stress and permeability is proportional, which has been generally recognized by academic. On the other hand, the relationship between them can be obtained by physical experiments. Karlet al.(2000) described a pressure sensor and found that the relative magnetic permeability decreases as the stress increases in physical experiments. The experiments of Pulnikovet al.(2004) showed that the relative magnetic permeability increases with the increase of the tensile stress. Sakaiet al.(2004) also pointed out the increase of relative magnetic permeability under tensile stress. Sun (2011) did experiments using steel for his PhD thesis and found that the relative magnetic permeability gradually reduces under pressure and increases under tensile stress. Xu (2011) obtained the specific linear relationship between the tensile stress and the relative magnetic perme-ability by using advanced experiment technique for steel with the result：

herek1= 4.596×106,m1= - 6.356×109, stress unit being Pa. This relationship further provides evidence that the stressinduced permeability change is an objective reality, and proves the correctness of theoretical deduction of Wanget al. (2005). Stress and relative magnetic permeability are inherent characteristics of material. For the same type of ferromagnetic material, the value ofk1should be consistent and worth being considered. The value of m1relates to residual stress and experimental environment and has no worth to be considered. Therefore, the relationship between the change of stress and the change of relative magnetic permeability can be got from (1)：

The object of the experiment is steel, which is just the steel of oil casing. So (2) will be referred to in the research of oil casing model.

3 Experimental Method

In most cases，the casing is subject to deformation, offset and fracture under the external pressure extrusion, so the focal point of the numerical experiment is the magnetic signal changes of casing wall under compressive stress. The oil casing is made from stainless steel with inner diameter 0.263 m, outer diameter 0.272 m and length 0.6 m. The same size is used in the numerical experiment.

3.1 Numerical Experiment

The variation range of relative magnetic permeability of oil casing wall is approximately from 600 to 1000, so we simulated the transformation situation of magnetic induction intensity around the casing wall in the variation range. The analytical method cannot reveal the effect of change of relative permeability on electromagnetic field in casing and this can only be solved by numerical solution. The finite element method can efficiently solve the distribution of electromagnetic field in casing when the relative magnetic permeability of casing wall is not evenly distributed.

In reality, we should consider the manufacture of measuring instrument. In the process of oil casing stress magnetic survey, we designed four probes to get the magnetic signal distribution of casing wall as shown in the cross section of Fig.1. It is faster to get the distribution of magnetic signals around the casing with many rotating probes than with one probe at some water depth. But if too many probes are used, the measuring results are not accurate because they are affected by each other. In addition, the cost is higher. The design of four probes is best, for it reduces the time of measurement because of the absence of interference between probes during work. In order to evaluate the measurement results, the four probes have the same small distance from the inner surface of oil casing. The relative results based on one of the probe’s measurements are evaluated to know where is the abnormality of the relative magnetic permeability.

Fig.1 Cross section of four probe measurement.

To recognize the nature of the problem and avoid the influence of many factors, we simulated the situation when the whole casing wall relative magnetic permeability is changed and what changes of the magnetic induction intensity in the probe. The conclusion is that with the decrease of the casing wall relative magnetic permeability, magnetic induction intensity increases. But changing the whole casing wall relative magnetic permeability is not consistent with the actual situation. In fact, not the whole casing tube wall relative magnetic permeability are changed when oil casing wall are under external force somewhere. The relative magnetic permeability changes where there is the force. Then we simulated the situation that the probe A is facing the casing wall under compressive stress. We want to find out the changing process of magnetic induction intensity at that point where the compressive stress increases gradually and the relative magnetic permeability in gradually reduced. The geometric model is shown in Fig.2. The blue part represents the air; the purple part represents the part of casing wall, where permeability is fixed; the red part represents the part which the probe is facing. Changing the size of the relative magnetic permeability of the red part and getting the value of the magnetic induction intensity form probe A. The mesh generation is shown in Fig.3. The grid of region of interest was deliberately arranged to be relatively close to make the results more accurate. Boundary conditions and load are applied for modeling after meshing.

Fig.2 Geometric model with abnormality in relative magnetic permeability.

Fig.3 Meshing of model with abnormality in relative magnetic permeability.

Fig.4 is the simulated result. The magnetic induction intensity and relative magnetic permeability have an inverse linear relationship. This is consistent with the situation that by changing the whole relative magnetic permeability of all casing wall, fitting equation is as follows：

Herek2= - 0.000547,m2= 51.436. The constantk2should be consistent for a given model of oil casing, andm2is related to parameter settings of measuring instruments. The parameter settings of numerical simulation are different from the those of real situation. Usually, the numerical modeling is simplified. To make sure that the result of numerical simulation is not affected and can be used in actual situation, the relationship between the variable value of magnetic induction intensity and the variable value of relative permeability can be given as follows：

Combing Eqs.(2) and (4), the relationship between the variable value of casing wall stress and that of a probe’s magnetic induction intensity can be given as follows：

In the formulaK=k1/k2. The casing is under pressure, so the value ofk1is negative andK= 8.40×109.

Fig.4 The relationship between probe A’s magnetic induction intensity and casing wall’s relative magnetic permeability with abnormality.

3.2 Physical Experiment

The magnetic survey experiment under external force on the casing wall was carried out based on the numerical experiment. The steel pipe’s relative magnetic permeability decreases with the increases of compressive stress. The experiment was conducted in the Mechanics of Materials Laboratory of OUC. We used the WE-1000A hydraulic universal tester as the pressure instruments and ZGF-4 NDT sorter as the magnetic signal measurement instruments. In the experiment setup shown in Fig.5, while increasing the external force continuously, a probe over against the force position on the other side can record the magnetic flux data. The measured data and curve fitting is shown in Fig.6. The fitted curve of the measured magnetic fluxФand external forceFis

Herep1=2.9164×10-3,q1=58.09, The unit of external force is N and the unit of magnetic flux is Wb.

Fig.5 Physical experiment setup with four probes.

Fig.6 The measured data and fitted relationship between flux and load.

We can calculate the stress at the point subjected to external force by simulating with the ANSYS structural stress module. The simplified geometric model of the simulation is shown in Fig.7. The red arrow indicates where external force is applied, the yellow arrows indi-cate where the displacement is to be constrained. Changing external force through the APDL language, the simulated data and the fitting curve are shown in Fig.8. The fitted curve equation for the stressδand external forceFis：

Herep2=30367,q2=0.00074251. The unit of load is N and the unit of stress is Pa. By combing Eqs.(6) and (7), the relation between the variation of stress and the variation of magnetic flux can be given as follows：

In the physical experiment, the existing stress in the steel pipe is not considered because Eq. (8) is the relative variation relationship between stress and magnetic flux, we need not to know the existing stress.

Fig.7 Load and displacement constraint.

Fig.8 The fitted relationship between stress and load.

4 Result Analysis

The relationship between the magnetic flux and the magnetic induction intensity isφ=NBS,Nrepresenting the number of coil turns andSrepresenting coil area which are constant in physical experiments. Based on this, Eq.(8) can also be expressed as the relation between the stress variation and the magnetic induction intensity variation as follows：

We next analyze whether there is consistency between (5) and (9). IfPis multiplied byNandSis almost the same asK, it can be showed that theKvalue is accurate. But the manufacturer did not provide the parameters of the probe used in the physical experiment, so the parameters obtained from the numerical simulation of the accuracy ofKcan not be accurately verified. The value ofKin numerical simulation is 8.04×109and that ofPin the physical experiment is 1.04×107.Kis greater thanP; they are of the order of magnitude of 100. In fact, on the one hand, number of turns of coilNmultipled with area of the coilSis 100 times easier to meet the situation. On the other hand, even if the constantsNandSare unknown, the physical experiment results can prove the numerical simulation result that the stress variation is proportional to the magnetic induction intensity variation. In addition, for all the ferromagnetic materials, Xiong Erganget al. (2011) obtained the same relationship with theoretical derivation based on micro-magnetic energy theory, which also proves the validity of the numerical simulation result. HoweverKin theoretical derivation is a constant which is not easy to determine. The method in this paper can determineKeasily.

5 Conclusions

Oil casing wall is made of ferromagnetic material. The relative magnetic permeability decreases with the increase of compressive stress and increases with the increase of tensile stress. According to the result of ANSYS numerical simulation, the obtained relation between the variation of stress and the variation of magnetic induction intensity is：Δδ=K*ΔB. The physical experiment and theoretical derivation verify the validity of the relation. But the method in this paper that can determine the key parameterKeasily is much better than theoretical derivation for the oil casing model, the value ofKbeing given as 8.04×109. In this way, the variation of casing wall stress can be determined by measuring the variation of the magnetic induction intensity ifKhas been determined.

The value of magnetic induction intensity around the casing wall increases with the increase of compressive stress and decreases with the increase of tensile stress. The stress at each point on the casing wall can be judged from the change of magnetic induction intensity. With theKvalue the stress variation can be determined. When the probe passes by the casing wall where the permeability is abnormal, magnetic induction intensity records will be abnormal. There is a positive anomaly in the part of the permeability decrease, which means the compressive stress is increasing. There is negative anomaly in the part of the permeability increase, which means the tensile stress is increasing. Abnormal peak corresponds to the largest concentration of stress. The peak amplitude reflects the magnitude of stress. Separation point between abnormal line and the baseline reflects the stress range. Therefore, this technique is able to make a comprehensiveevaluation for the distribution of stress in the casing pipe. In the application of this technology, the key parameterKcan be obtained with the ANSYS numerical simulation method, which has important practical value and can help us to apply this technique for detecting the stress of oil casing accurately.

Acknowledgements

The study was supported by the National Natural Science Foundation of China (No. 41174157).

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(Edited by Ji Dechun)

(Received May 13, 2014; revised July 12, 2014; accepted December 28, 2014)

? Ocean University of China, Science Press and Springer-Verlag Berlin Heidelberg 2015

* Corresponding author. Tel： 0086-532-66781905 E-mail： mengfsh@ouc.edu.cn