Modeling on Ground Magnetic Anomaly Detection of ... - ASCE Library

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Modeling on Ground Magnetic Anomaly Detection of Underground Ferromagnetic Metal Pipeline* Zhiyong Guo1, Dejun Liu2*, Zhuo Chen3 and Hao Meng4 1 Doctoral, College of Geophysics and Information Engineering, China University of Petroleum (Beijing); No.18, Fuxue Road, Beijing 102249; Tel: 18810267641; Email: [email protected]; 2* Professor, College of Geophysics and Information Engineering, China University of Petroleum (Beijing); No.18, Fuxue Road, Beijing 102249; Tel: 010-89731868; Email: [email protected]; 3 Engineer, Research Institute of Pipeline Transportation Technology; No.44, Jinguang Road, Langfang 065000; Tel: 15933631597; Email: [email protected]; 4 Master, College of Geophysics and Information Engineering, China University of Petroleum (Beijing); No.18, Fuxue Road, Beijing 102249; Tel: 010-89731868; Email: [email protected]; ABSTRACT Underground Pipeline is an integral part of the urban construction, as there are various pipelines in our city. These pipelines usually distribute in a special environment. Underground ferromagnetic metal pipeline which is magnetized by the earth's magnetic field can generate new magnetic field. The new magnetic field can change the original magnetic field distribution and lead to the formation of geomagnetic anomaly. Based on the magnetic dipole model and pipeline volume division, the underground pipeline ground remote detection model and close detection model are established. Through numerical simulation, the detection plane’s magnetic flux density distribution curved surface can reveal intensity distribution characteristics of magnetic anomaly. The magnetic anomaly is caused by the single straight pipe. The geomagnetic abnormal data sampled by magnetic-resistance sensor can be used to judge whether underground pipeline exist or not, and indicate its orientation. KEYWORDS Pipeline Modeling; Magnetic Dipole; Magnetic Anomaly Detection; Magnetic Field Distribution INTRODUCTION Underground pipelines play an important role in linking a secure and growing supply

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of national oil and gas resources with the largest refining markets in the urban area, significantly improving urban security supply and drainage. For most people, the underground pipelines project is the way of the future. They’re the infrastructure in people's daily life. All the techniques were non-destructive pipe locating procedures that provide approximations to the depth and location of underground-buried pipe. These underground pipelines can be located at depths ranging from 0.5 to 3 meters. Therefore, these locators are best suited for low moisture, low saline soils with small pipes when economics is a primary concern. The data of underground pipeline are often incomplete or inconsistent with the actual situation because of historical or other reasons (Niu, 2006). Therefore, the locations of underground pipelines are eventually inconsistent with the original situation. According to the previous observation, the accident such as oil and gas leakage or electricity and water supply shortage often occur in some field operations such as city construction, plant construction. What’s more, oil and gas transmission pipeline lay under encryption brings great harm to people's normal life. Leakage of cooking gas, accompanied by a spark around the leakage could cause fire. These are typically very dangerous. Therefore, it is very necessary to provide accurate underground pipeline distribution information for excavation before construction. A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, and attracts or repels other magnets. Materials that can be magnetized, which are also the ones that are strongly attracted to a magnet, are called ferromagnetic. Since most buried oil and gas pipelines are completely made of steel or something containing iron, it is a kind of ferromagnetic metal. These ferromagnetic metals which were magnetized by the Earth's magnetic field will produce the magnetizing field. And in turn, it has impact on the natural magnetic field distribution and engender local magnetic anomaly (Blakely, 1996). In a word, these ferromagnetic metals can be used to determine the presence or absence of underground pipes. Through the detection of magnetic anomaly caused by underground pipelines, the distribution of characteristics of these ferromagnetic metals can be obtained. And in order to verify the feasibility of underground pipeline detection, it needs to establish detection plane magnetic anomaly model and study the planar abnormal distribution. The result can be used to analysis and interpret the magneto-resistive sensor collection data. MAGNETIC DIPOLE THEORY DERIVATION Since a magnet has two poles, it is sometimes called a magnetic dipole, being analogous to an electric dipole, composed of two opposite charges. The magnetic dipole is the basic model for the research of magnetic field and is widely used in the location of target object and the determination of status (Billings, 2004; El Tobelyl et

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al., 2005 and Nara et al., 2006). The magnet in nature can be regarded as a combination of a large number of different shapes and sizes of the magnetic dipole (Xu, 2009). According to the magnetic field superposition principle, the surrounding magnetic field can be regarded as a combination of all the magnetic field superimposed in space. Fig. 1 shows the 3-D (three-dimensional) Cartesian coordinate system. It places the magnetic dipole in the origin of coordinate system, in that way, the magnetic field generated by magnetic dipole at the space point P is:

Bp =

0  3  m  r  r m   3  4  r5 r 

（1）

Where, B p is the magnetic flux density of the point P generated by the magnetic dipole at the space point P, m is the magnetic dipole magnetic moment, r is the vector from the magnetic dipole to the point P and r is the size of the vector. The μ0 is the permeability of vacuum and its value is 4107 H / m .

z P(x2,y2,z2)

z

Bp

Bp

m(mx,my,mz)

r m

r

O(x1,y1,z1) x

0

0

x

y Figure 1. Magnetic dipole is located in Figure 2. The B p is magnetic flux the origin of the Cartesian coordinate density of the point P generated by the system magnetic dipole at the point O y

Vector B p , m and r expressed in the form of three-component is B p   Bpx , Bpy , Bpz  ,





m =  mx , m y , mz  and r = rx , ry , rz respectively, so (1) can be expressed as (Ren et al.,

2007 and Zhou et al., 2008):

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    3  m x rx  m y ry  m z rz  rx Bpx  0 3   m x 4r  r2        0  3  m x rx  m y ry  m z rz  ry (2)  m    Bpy  y 4r 3  r2        0  3  m x rx  m y ry  m z rz  rz B   m   pz z 4r 3  r2    When the magnetic dipole is not located in the origin of the Cartesian coordinate system but is placed in the point O  x1 , y1 , z1  that is shown in fig.2 and the point P is





expressed as  x 2 , y2 , z 2  , therefore r = rx , ry , rz   x 2  x1 , y2  y1 , z 2  z1  and (2) can have the flowing transformation (Ren et al., 2007 and Zhou et al., 2008):      3  m x  x 2  x1   m y  y 2  y1   m z  z 2  z1    x 2  x1  Bpx  0 3    mx  2 4r  r      3  m x  x 2  x1   m y  y 2  y1   m z  z 2  z1    y 2  y1   0      my   Bpy  3  2 4r  r       0   3  m x  x 2  x1   m y  y 2  y1   m z  z 2  z1    z 2  z1  B   m   pz z 4r 3  r2   

Where, r 

 x 2  x1 

2

(3)

  y2  y1    z 2  z1  , therefore, in the Cartesian coordinate 2

2

system, the relationship among the coordinate value of magnetic dipole at the point O, magnetic moment, the coordinate value of the point P and the magnetic flux density B p of point P can be established. Magnetization vector M is the total amount of the atomic magnetic moment per unit volume of magnet material (Ulaby, 2004); Assuming that the total amount magnetic moment of the magnet with per unit volume V is m , then m = V  M . According to the static magnetic field theory (Ulaby, 2004), the magnetization vector of the magnetic material is the product of the magnet susceptibility  m and the magnet in which the external magnetic field strength H , and then M = m H , and m  r  1 , so M =  r  1 H . After pipes buried in the ground and fixed, the residual magnetization is several orders smaller than induced magnetization (Huang et al., 2007). And the Earth's magnetic field can be regarded as a constant magnetic field at tens of meters detection range and during a few hours short period of time in the MAD (magnetic anomaly detection) process. Let the isotropic magnetization of the ferromagnetic material and then pipeline magnetization can be considered as a linear process. The essence of ferromagnetic material contained in underground pipelines is Low-carbon steel and their relative permeability is about 2000 (Ulaby, 2004).That M  r H due to r ? 1 , therefore, the relationship between the total magnetic

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moment m of the magnet which volume is V and the magnetic field strength H can be interpreted as flowing: (4) m  V r H The H is expressed as a three-component form of 3-D Cartesian coordinate system is  H x , H y , H z  , flowing substituting (4) into (3) let the equations directly take the equal sign to get:     V   3  H x  x 2  x1   H y  y 2  y1   H z  z 2  z1    x 2  x1  Bpx  0 r 3    H x 4r  r2      3  H x  x 2  x1   H y  y 2  y1   H z  z 2  z1    y 2  y1    0 r V      Hy   Bpy   3 2 4r  r        0 r V   3  H x  x 2  x1   H y  y 2  y1   H z  z 2  z1    z 2  z1  B   H   pz z 4r 3  r2   

(5)

Here, the combined magnetic flux density of the point P is Bp  B2 px  B2 py  B2 pz . The equation (5) shows that the magnetic flux density of point P in the form of three-component, which generated by iron magnet with the volume V , the relative permeability  r and placed in point O in 3-D Cartesian coordinate system. UNDERGOUND PIPELINE MAD REMOTE MODELING When doing numerical simulation of space magnetic field generated by pipe, it needs to divide underground ferromagnetic pipe into a mass of small patch and then it can be classified as a magnetic dipole (Ren et al., 2007 and Zhou et al., 2008). In the space of more than 2.5 times length of the magnet, the magnetic field generated by magnet is approximately equivalent to what is regarded as a mass of magnetic dipole does (Zhou et al., 2008 and Zhang et al., 2010). Let the pipeline axial as x-axis, pipe midpoint as the origin and the vertically upward as z-axis to establish 3-D Cartesian coordinate system shown in Fig.3.

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z

Detection Plane P

r m

0 Pipeline L

x

y

Figure 3. Establish Remote MAD 3-D Cartesian coordinate system Let the outside diameter of a single straight pipe is a , the inside is b and the length of the pipe is L. Divide the pipe into equal N sections so the coordinate of each 2n  1  N  section center is On   x1n , y1n , z1n    L, 0, 0  , and then using (5) to 2N   calculate the magnetic dipole moment of each section, that is: L  2 a  2 b  m r H (6) 4N According to (5) the magnetic flux density of the point P generated by ferromagnetic metal pipeline is defined as following: N 1   L 2  2  0 r  a b   3  H  rn  rn Bp    H (7)  3 2 16Nrn rn n 0   Where, rn 

2 2 2  x 2n  x1n    y2n  y1n    z2n  z1n  and rn   x 2n  x1n , y2n  y1n , z2n  z1n  .

Divide the detection flat into uniformity mesh to calculate the superimposed magnetic field, which is formed by all of the magnetic dipole from the pipeline subsection. As a result, it can be used to analyze the distribution of the magnetic field intensity of the detection plane. For instance: The length of a single straight underground ferromagnetic metal pipeline is 10m; Dividing the pipeline into uniform 100 sections, the outside diameter of the pipe is 10cm and the inside is 9cm. Let material relative permeability is to take 2000 and the relative permeability of ambient soil and air is 1.The distance from detection area to the pipe is 20m and to the top of pipe is 1m. Assuming that buried underground pipeline is laid in East-West where the size of the nature geomagnetic field is 46865nT, geomagnetic inclination is 41.21° and geomagnetic declination is 11.5° respectively (Ren et al, 2007), so the three-component of geomagnetic field H is (5.5936, -27.4932, -24.5703) A / m in 3-D Cartesian coordinate system accordingly. The equation (7) is decomposed as the form

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of a three-component (5) to calculate the magnetic flux density generated by each magnetic dipole in the detection network. And then Fig.3 shows the superposition of all magnetic dipole magnetic flux density for the detection plane magnetic field intensity distribution. Along the direction of x=0 and in the range of y= [-10, 10] to get the magnetic field intensity values for drawing a curve shown in Fig.4.

Figure 4. The magnetic flux density distribution surface generated by remote pipeline

Figure 5. The magnetic flux density profile curve generated by remote pipeline

The MAD signal consists of three components which are the geomagnetic field, the magnetic anomaly generated by underground pipeline and noise. Without considering the impact of noise on the detection signal, and superimpose geomagnetic background in the pipeline magnetic field, we can get the distribution of detection plane magnetic field strength in Fig. 6. On the detection plane, let a magneto-resistive sensor to collect geomagnetic anomaly data along the direction of x=0 and the range of y=[-10,10], it will get a detection curve shown in Fig.7. The range of magnetic anomaly intensity is from 33530nT to 61150nT. There are both raised magnetic anomaly and sunken magnetic anomaly on the magnetic anomaly curve.

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Figure 6. The magnetic anomaly distribution surface of remote pipeline

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Figure 7. The magnetic anomaly detection curve of MAD remote model emulation data

UNDERGOUND PIPELINE MAD CLOSE MODELING When the distance from the detection plane to the top interface of the pipeline relative to the pipe diameter is less than 2.5 times, it is inapplicable to let each segment of segmented pipeline along its axial as a magnetic dipole for the modeling (Zhang et al., 2010). Thereby, the pipe must be further divided. Let the pipeline axial as y-axis, pipe midpoint as the origin, and the vertically upward as z-axis to establish 3-D Cartesian coordinate system. Supposing that the length of the pipeline is L and in the x-z plane coordinate system shown in Fig.8, let the outside diameter of a single straight pipe is a and the inside is b , furthermore the distance from the detection plane to the top interface of the pipe is h. Divide the pipe into equal N L sections along its axial, so the L length of each segment is .For each segmented pipeline, divide it into equal N  NL  portions along its circumference, which makes the length of each arc is a . N 5 h L The  2.5 in underground pipeline MAD close modeling, N L  2h b 5a and N   . That is because the divided small bulk of pipe must be regarded as 2h the magnetic dipole (Blakely, 1996).

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Detection Plane

z P

h

r m

a

θ

b

0

On

Pipe Cross-section

x

Figure 8. The x-z profile of close pipeline MAD modeling As shown in Fig.8, assuming that the magnetic moment of divided pipeline segmentation is focused on the point O n , which is the geometric center of pipeline 2n  segmentation, and the angle between the straight line 0 O n and z-axis is   , so N    2n  2n  1  N L a  b  2n    is  a b sin    , L L, cos    ,  2 2N L 2  N   N    and n   0,1, N  1, n L  0,1, NL  1 .The volume V of divided pipeline fragments

the

is

coordinates

L  2 a  2 b  4N L N 

fragments is

of

On

and the corresponding magnetic moment m of the divided pipeline

L  2a  2 b  4N L N 

 r H which can be used to calculate the magnetic flux

density of the point Pn  x 2n , y2n , z 2n  on the close detection plane, that is:

0r L  2a  2 b   3  H  rn  rn  Bp     H  3 2 16N  N L rn rn n L 0 n  0   N L 1 N 1

(8)

Where,   2n    2n     b   b 2n L  1  N rn   x 2n  a sin  L, z 2n  a cos   , y2n    and rn is 2 2N 2  N   N    the size of rn .

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The following is a numerical simulation instance of the underground pipeline MAD close modeling, where the three-component of geomagnetic field H is (0, -27.4932, -24.5703) A / m in 3-D Cartesian coordinate system without considering the impact of soil and air. Let a single straight underground ferromagnetic metal pipe lay in North-South direction and its length is 10m. The outside diameter of the pipe is 80cm and the inside is 79cm. Let material relative permeability of the pipe to take 2000 and the distance from detection area above the pipe with the length and width of 20m to the top of pipe is 1m. Divide the pipeline into 200 segments along its axes and 80 segments along its circumference. Next decompose (8) into the form of the three-component (5) to calculate the magnetic flux density generated by each magnetic dipole in the detection plane network. And then Fig. 9 shows the superposition of all magnetic dipole magnetic flux density. The result can be used to get the distribution of the detection plane magnetic field. Fig. 10 is a curve which shows the values of magnetic field intensity along the direction of y=0 and the range of x= [-10, 10].

Figure 9. The magnetic flux density distribution surface generated by close pipeline

Figure 10. The magnetic flux density distribution curve generated by close pipeline

Without considering the impact of noise on the detection signal and superimposed geomagnetic background in the pipeline magnetic field, we can get the distribution of detection plane magnetic field shown in Fig.11. Let a magneto-resistive sensor collect geomagnetic anomaly data along the direction of y=0 and the range of x= [-10, 10] on the detection plane, it will get a detection curve shown in Fig.12. The range of magnetic anomaly intensity is from 38710nT to 158500nT and there are one raised magnetic anomaly and two sunken magnetic anomaly on the magnetic anomaly curve.

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Figure 11. The magnetic anomaly distribution surface of close pipeline

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Figure 12. The magnetic anomaly detection curve of MAD close model emulation data

DISCUSSION Because of the limitation of the computing ability, this paper does not simulate the case of magnetic anomaly distribution generated by an infinite pipe. However, when the length of pipeline is long enough and the length of detection plane is less than a certain pipeline length, the magnetic anomaly surface is truncated at both ends. The formation of magnetic anomaly surface is closer to the real magnetic anomaly detection. Fig. 13 shows the magnetic anomaly distribution. It is a case calculated by remote MAD model, in which the pipeline with 20m length lay in x-axial. The length and width of the detection plane are both 16m, the total field strength of geomagnetic background field is 46865nT and its inclination and declination is 41.21°and 11.5° respectively (Ren et al, 2007). The case shown in Fig.14 is calculated by close MAD model, in which the pipeline with 20m length lay in y-axial, the length and width of the detection plane are both 14m, and the three-component of earth's background magnetic field H is (0, -27.4932, -24.5703) in the established coordinate system.

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Figure 13. An instance simulation of magnetic anomaly distribution by remote MAD model

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Figure 14. An instance simulation of magnetic anomaly distribution by close MAD model

When the pipeline is short enough and it is calculated by remote magnetic anomaly detection model, the magnetic flux density distribution formed by the pipe is similar to a magnetic dipole magnetic flux density on the detection plane. The case shown in Fig.15 is calculated by remote MAD model in which the length of pipe is 0.1m.

Figure15. The 0.1m-long pipeline magnetic anomaly distribution simulated by remote MAD model In the 3-D Cartesian coordinate system, let the pipeline axial as the axis. Assuming that the pipe is horizontal toward for the convenience of calculation of the pipeline magnetic field, so the earth’s original magnetic field need to be transformed for the pipeline MAD model. In fact, the pipeline and the detection plane may not be horizontal. Therefore, the magnetic dipole coordinate of pipeline need to be further transformed in the process of detection plane MAD model. CONCLUSION This paper establishes the calculation model of the detection plane for the

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ferromagnetic pipe through the derivation of the magnetic dipole model and the pipeline division. After superimposing the geomagnetic field on pipe magnetic field, the formulation of magnetic anomaly distribution of detection plane reflects the distribution characteristic of magnetic anomaly generated by underground ferromagnetic pipe. The obtained magnetic anomaly detection curve can be used to determine the presence or absence of underground ferromagnetic pipeline through the magneto-resistive sensor MAD simulation.

Figure16. The magnetic flux density distribution pseudo-color image generated by remote pipeline

Figure17. The magnetic flux density distribution pseudo-color image generated by close pipeline

As it is shown in Fig.16 and Fig.17, the magnetic anomaly zone can be distinguished from the detection plane magnetic anomaly distribution in the pseudo-color images. The distribution characteristic of magnetic anomaly can be used to judge whether underground pipeline exist or not, and indicate the orientation of the underground pipeline. REFERENCES

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