sensors Article

Auxiliary Sensor-Based Borehole Transient Electromagnetic System for the Nondestructive Inspection of Multipipe Strings Bo Dang 1, * 1

2

*

ID

, Ling Yang 1 , Na Du 1 , Changzan Liu 2 , Ruirong Dang 1 , Bin Wang 1 and Yan Xie 1

Key Laboratory of Education Ministry for Photoelectric Logging and Detecting of Oil and Gas, Xi’an Shiyou University, Xi’an 710065, China; [email protected] (L.Y.); [email protected] (N.D.); [email protected] (R.D.); [email protected] (B.W.); [email protected] (Y.X.) School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China; [email protected] Correspondence: [email protected] or [email protected]; Tel.: +86-029-8838-2648

Received: 18 June 2017; Accepted: 8 August 2017; Published: 9 August 2017

Abstract: Transient electromagnetic (TEM) techniques are widely used in the field of geophysical prospecting. In borehole detection, the nondestructive inspection (NDI) of a metal pipe can be performed efficiently using the properties of eddy currents. However, with increasing concern for safety in oil and gas production, more than one string of pipe is used to protect wellbores, which complicates data interpretation. In this paper, an auxiliary sensor-based borehole TEM system for the NDI of multipipe strings is presented. On the basis of the characteristics of the borehole TEM model, we investigate the principle behind the NDI of multipipe strings using multiple time slices of induced electromotive force (EMF) in a single sensor. The results show that the detection performance of NDI is strongly influenced by eddy-current diffusion in the longitudinal direction. To solve this problem, we used time slices of the induced EMF in both the main and auxiliary sensors. The performance of the proposed system was verified by applying it to an oil well with a production casing and liner. Moreover, field experiments were conducted, and the results demonstrate the effectiveness of the proposed method. Keywords: auxiliary sensor; transient electromagnetic techniques; borehole; nondestructive inspection

1. Introduction The transient electromagnetic (TEM) technique has gained much attention over the past several decades owing to its wide range of applications, such as mineral and petroleum geophysical exploration [1], hydrogeophysical surveys [2], and geotechnical and environmental investigation [3,4]. In the field of borehole detection, TEM systems enable the rapid acquisition of broad-frequency-range data related to the electrical and geometrical parameters of each borehole’s cylindrical layer [5–7]. This technique, which is also known as transient (pulsed) eddy-current testing [8–11], enables the highly effective nondestructive inspection (NDI) of downhole casings [12]. However, unlike the conventional NDI systems, oil and gas wells require more than one string of pipe, such as casing, tubing, and liner [13], to protect a wellbore against potential damage from byproducts, which makes NDI of the thickness of metal pipes more difficult in terms of data interpretation [14–16] because of the influence of additional pipe strings. The problem associated with the NDI of the thickness of multilayer structures has been investigated extensively in numerous research fields [17–19]. In the case of borehole TEM systems, the early time data of the transient signal mainly correspond to the inner layers, whereas the late time data provide more information about the outer layers [15–17]. Consequently, the TEM data collected Sensors 2017, 17, 1836; doi:10.3390/s17081836

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collected different times correspond eachdifferent layer with different weights, andisthe response at differentattimes correspond to each layertowith weights, and the response assumed to beis assumed to be manifested as a convolution of the time decay signal, with each circular shell of metal manifested as a convolution of the time decay signal, with each circular shell of metal with increasing with increasing radiustocorresponding to a thereby “time window”, therebyseparating approximately separating the radius corresponding a “time window”, approximately the receiving signal receiving signal from different strings of pipe [15]. Similarly, using the longitudinal sensor, time from different strings of pipe [15]. Similarly, using the longitudinal sensor, time slices as well as time slices as well as timeelectromotive windows of force induced electromotive forcecoils (EMF) theas receiving are used windows of induced (EMF) in the receiving arein used a featurecoils to recognize as a feature recognize defects in thetubing NDI of casing tubing of [16]. interpretation of the defects in thetoNDI of casing through [16]. Thethrough interpretation theThe results obtained using results obtained using the aforementioned methods based on the eddy-current diffusion property of the aforementioned methods based on the eddy-current diffusion property of TEM systems in the TEM systems in the radial direction is straightforward. In the longitudinal direction, however, the radial direction is straightforward. In the longitudinal direction, however, the eddy-current diffusion eddy-current and the late time also contain more about the still exists, anddiffusion the late still timeexists, data also contain moredata information about the information regions at increasing regions at increasing distances from the borehole axis; this information will strongly influence the distances from the borehole axis; this information will strongly influence the effectiveness of the NDI effectiveness of the NDI of multipipe strings. of multipipe strings. In this paper, wepresent presentan anauxiliary auxiliary sensor-based sensor-based borehole borehole TEM TEM system system for for the the NDI NDI of of the the In this paper, we thickness of multipipe strings. On the basis of the characteristics of the borehole TEM signal model, thickness of multipipe strings. On the basis of the characteristics of the borehole TEM signal model, an auxiliary auxiliary sensor sensor isis used used to to improve improve the the longitudinal longitudinal resolution resolution of of the the NDI NDI of of the the thickness thickness of of an multipipe strings, where induced EMFs in both the main and auxiliary sensors are utilized. We multipipe strings, where induced EMFs in both the main and auxiliary sensors are utilized. We verify verify the performance of the proposed by applying to an oil–borehole TEM used system the performance of the proposed system system by applying it to an it oil–borehole TEM system forused the for the NDI an oil well with a production casing and liner. NDI of an oilof well with a production casing and liner. The rest of this paper is organized as follows. The borehole TEM signal model based on The rest of this paper is organized as follows. The borehole TEM signal model based on magnetic-core-coil sensors is presented in Section 2. The principle behind the NDI of multipipe magnetic-core-coil sensors is presented in Section 2. The principle behind the NDI of multipipe strings, i.e., using multiple time slices of induced EMF in a single sensor, is discussed in Section 3. strings, i.e., using multiple time slices of induced EMF in a single sensor, is discussed in Section 3. The diffusion property of the TEM sensor is analyzed and an auxiliary sensor-based borehole TEM The diffusion property of the TEM sensor is analyzed and an auxiliary sensor-based borehole TEM system for the NDI of the thickness of multipipe strings is presented in Section 4. The experimental system for the NDI of the thickness of multipipe strings is presented in Section 4. The experimental results are discussed in Section 5. Finally, we conclude the paper in Section 6. results are discussed in Section 5. Finally, we conclude the paper in Section 6. BoreholeTEM TEMSystem SystemModel Model 2.2.Borehole The cylindrically cylindrically layered layered structures structures of of the the borehole borehole TEM TEM system system equipped equipped with with coaxial coaxial The transmittingand andreceiving receiving coils are wound around soft magnetic are illustrated transmitting coils thatthat are wound around a soft amagnetic core arecore illustrated in Figure in 1. Figure 1. The electrical and geometrical parameters of the jth layer are defined as (μ j , ε j , σ j ) and rj, The electrical and geometrical parameters of the jth layer are defined as (µj , εj , σj ) and rj , respectively. respectively. We consider the soft magnetic core to be the innermost layer. The transmitting and We consider the soft magnetic core to be the innermost layer. The transmitting and receiving coils receiving located in the layer, with their number turns given by NT and NR, are locatedcoils in theare second layer, withsecond their number of turns given by Nof T and N R , respectively. For all respectively. For all coils, the diameter is assumed to be sufficiently small the source coils, the diameter is assumed to be sufficiently small and the source regionand is assumed toregion containis assumed to contain only the second layer. Moreover, all the other layers, such as the well liquid, only the second layer. Moreover, all the other layers, such as the well liquid, casing, liner, cement, and casing, liner, cement, and formation, are regarded as source-free regions. formation, are regarded as source-free regions. Borehole axis (z)

Hz

1 1 1

Formation

Air

2 2 2

Pipe String 2

Well liquid

4 4 4

Pipe String 1

Cement ring 1

6 6 6

Receiving coils

Tool housing

Cement ring 2

8 8 8

Magnetic core

3 3 3

5 5 5

7 7 7

J J J

Eφ Radial axis (r)

Transmitting coils

r5 r6 r7

r1

r2

r3

r4

r8

Figure1.1. Cylindrically Cylindricallylayered layeredstructures structuresof ofaaborehole. borehole. Figure

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As shown in a previous study [20], the response of a TEM system in such a multicylindrically layered geometry consists of reflection and transmission components with both standing and outgoing waves. The vector potential A is introduced, and the homogeneous and inhomogeneous Helmholtz equations are given by ∇2 A j + k2j A j = 0 j 6= 2 , (1)

∇2 A2 + k22 A2 = −Je ,

(2)

where kj 2 = µj εj ω 2 − iµj σj ω, and Je denotes the electrical source. With the introduction of variables xj and λj that satisfy xj 2 = λj 2 − kj 2 , the vector potential A can be calculated by solving the Helmholtz equations. Considering the cylindrical symmetry model in Figure 1, the electric field is located in planes perpendicular to the borehole axis, and it has only the tangential component. Thereby, directional measurement cannot be achieved by using the proposed borehole TEM system. The electric field and the vertical component of the magnetic field of the jth layer with radius r and longitude (borehole axis) distance z can thus be obtained as [20] E ϕj (r, z) = −iωµ j M Hzj (r, z) = M

Z ∞ 0

Z ∞ 0


τj K1 ( x j r ) I1 ( x j r1 ) + Cj I1 ( x j r ) + D j K1 ( x j r ) cos λ j z dλ j ,

 
x j −τj K0 ( x j r ) I1 ( x j r1 ) + Cj I0 ( x j r ) − D j K0 ( x j r ) cos λ j z dλ j ,

(3) (4)

with M = IT r1 /π, τ 2 = 1, and τ j 6=2 = 0, where IT denotes the transmitting current; I0 (·), I1 (·), K0 (·), and K1 (·) are the first and second type of modified Bessel functions of order zero and one, respectively, and Cj and Dj denote the reflection and transmission coefficients, respectively, which are related to the geometrical and electrical parameters of all layers, and can be calculated using the boundary conditions. Then, the induced EMF in the receiving coils can then be calculated by U (ω ) = −iωµ1

NT −1 NR −1 Z r1

∑ ∑

m =0 n =0

0

Hz1 (r, zmn ) · 2πrdr,

(5)

where zmn denotes the distance between the mth turn of transmitting coils and the nth turn of receiving coils along the borehole axis. Given a ramp signal with a turn-off time of t0 , the induced EMF U(t) can be obtained by converting Equation (5) into the time domain; using the Gaver–Stehfest inverse Laplace transform as an example [20], we obtain U (t) =

µ1 πr12 ln 2 12 1 K q ( e − s q t0 − 1 ) ∑ t0 t q =1 s q

Z r 1 0

Hz1 · 2πrdr,

(6)

where sq = qln2/t and Kq denotes the integral coefficient of the Gaver–Stehfest inverse Laplace transform. The tool housing is fixed, and the conductivities of the cement ring, formation, and fluids are much smaller than that of the metal pipes, whose thickness can be estimated from U(t) by ignoring the effect of the other layers. Moreover, if only one pipe string exists, a single time slice of the induced EMF, whose amplitude monotonically increases with the thickness of the metal pipe, can be used to describe the relationship between U(t) and thickness [5,16]. However, when more than one string of metal pipes is present in oil and gas wells, the coupling of the response from the additional pipe strings will strongly influence the interpretation of the NDI, where additional time slices of the induced EMF in the receiving coils must be used to interpret the logging data. 3. NDI of Multipipe Strings As shown in Section 2, the presence of more than one pipe string makes NDI data interpretation more difficult, because the TEM response is strongly influenced by additional pipe strings. In this section, we investigate the principle behind the NDI of multipipe strings using multiple time slices

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of induced EMF in a single sensor. Considering the boundary conditions of multilayered cylindrical structures that the tangential component of the electric field and the tangential component of the magnetic field are continuous across the interface in the case of r = rj , we have E ϕ,j = E ϕ,j+1 and Hz,j = Hz,j+1 [20]. Thereby, the relationship between the coefficients Cj and Dj of each layer can be written as " # " # " # " # rj r j Pj (1, 1) 0 Cj C j +1 = − Pj K1 ( x j +1 r 1 ) + , (7) − τj+1 µj µ j Pj (2, 1) −τj I1 ( x j r1 ) Dj D j +1 where Pj is the transfer matrix, with each element expressed as Pj (1, 1) = −µ j+1 x j K0 ( x j r j ) I1 ( x j+1 r j ) − µ j x j+1 K1 ( x j r j ) I0 ( x j+1 r j ),

(8)

Pj (1, 2) = −µ j+1 x j K0 ( x j r j )K1 ( x j+1 r j ) + µ j x j+1 K1 ( x j r j )K0 ( x j+1 r j ),

(9)

Pj (2, 1) = −µ j+1 x j I0 ( x j r j ) I1 ( x j+1 r j ) + µ j x j+1 I1 ( x j r j ) I0 ( x j+1 r j ),

(10)

Pj (2, 2) = −µ j+1 x j I0 ( x j r j )K1 ( x j+1 r j ) − µ j x j+1 I1 ( x j r j )K0 ( x j+1 r j ).

(11)

In Equation (7), CJ and D1 have been proved to be zero because of the absence of transmission and reflection of the innermost and outermost layers, respectively. Then, C1 can be derived using the relationship described in Equation (7), as   r1 P(1, 2) C1 = − T −V µ1 P(2, 2)

(12)

P = P1 · P2 · · · · · P J ,

(13)

T = P1 (2, 1)K1 ( x2 r1 ) − τj P1 (2, 2) I1 ( x1 r1 ),

(14)

V = P1 (1, 1)K1 ( x2 r1 ) − τj P1 (1, 2) I1 ( x1 r1 ).

(15)

with

Note that C1 is related to the electrical and geometrical parameters of the multicylindrical layers and to the diffusion time. To measure the thickness of metal pipes, we assume that the electrical parameters of all layers and the outer radius of the metal pipes are fixed. Thus, for each sampling time, the unknown variables remaining in Equation (12) are the thicknesses of the multipipe strings. Obviously, if only one string of pipes is involved, Equation (12) will contain just one unknown variable and can be solved using a single time slice of induced EMF. Correspondingly, when more than one string of pipe is utilized, multiple time slices of induced EMF must be employed to solve Equation (12). Taking two strings of pipes as an example, the relationships between the induced EMF and the thickness of the two pipes at an early time (20 ms) and a late time (50 ms) are shown as follows, where the simulation parameters are set as follows: r1 = 12 mm, r2 = 17.5 mm, r3 = 21 mm, r4 = 54.31 mm, r6 = 87.31 mm, r8 = 120.65 mm, NT = 95, NR = 980, IT = 0.5 A, and t0 = 30 µs. Notably, the liner and casing in Figures 2 and 3 represent the first pipe string and the second pipe string as shown in Figure 1, where a liner is a pipe string that does not extend to the surface, being hung from a liner hanger set inside of the previous pipe string [13]. Corresponding to Figure 1, the inner radiuses of the two pipes (r4 and r6 ) are assumed to be fixed, which can be obtained by the prior wellbore information, so that the thicknesses of the two pipe strings are related to the outer radiuses of the two pipes (r5 and r7 ), and can be calculated by r5 − r4 and r7 − r6 , respectively. In Figures 2 and 3, the thicknesses of the two pipe strings are changed within a range to show the characteristics of the borehole TEM system. Moreover, the three dashed lines denote the contour curves of the induced EMF value with respect to the three combinations of the thicknesses of two pipes (termed Cases A, B, and C) at different times. We find that the induced EMF of a single time slice corresponds to numerous solutions, which obviously makes Equation (12) unsolvable. Nevertheless, by employing

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the eddy-current diffusion property of the TEM system, where the data at different times correspond solve (12) the association of multiple timewe slices. Projecting the (12) contour curves to the Equation information of through each layer with different weights [15–17], can solve Equation through the onto the casing–liner thickness plane, we describe the characteristics of the induced EMF contour association of multiple time slices. Projecting the contour curves onto the casing–liner thickness plane, curves as shown in Figure 4. of the induced EMF contour curves as shown in Figure 4. we describe the characteristics 3.25

3.2

3.3 (V) EMF (V) Induced EMF Induced

3.25 3.2

3.15

3.15 3.1

3.1

3.05 3

3.05

2.95 16

3 14 Lin 12 er T 10 hic kne 8 ss ( mm 6 )

4

4

6

16 14 12 m) m ( 10 s nes 8 hick ng T Casi

18 2.95

Figure 2. 2. Induced Induced electromotive electromotive force force (EMF) (EMF) in in receiving receiving coils at 20 ms. Figure 1

(V) EMF (V) Induced EMF Induced

0.9 1

0.8

0.8

0.7

0.6

0.6

0.4 0.5 0.2 0.4 0 16

14 Lin 12 er T 10 hic kne 8 ss ( mm 6 )

4

4

6

16 14 12 ) m (m 10 ness 8 hick T g n Casi

18

0.3 0.2

Figure 3. 3. Induced Induced EMF EMF in in receiving receiving coils coils at at 50 50 ms. ms. Figure

Figure 4 shows that although although each each single single time time slice slice of the induced induced EMF EMF cannot cannot have have a unique unique Figure solution for for two two metal metal pipe pipe thicknesses, thicknesses, their their projections projections can can intersect intersect at at one one point point for for each each case. case. solution Since each induced EMF contour curve represents a combination of solutions of Equation (12) Since each induced EMF contour curve represents combination of solutions of Equation (12) at different times, times, the the intersection intersection point point can can be be regarded regarded as the unique unique solution solution of of Equation Equation (12) (12) that different two curves curves simultaneously. simultaneously. Thereby, Thereby, on the basis of the eddy-current diffusion property, satisfies the two two time time slices slices of of the the induced induced EMF EMF can can be be used used to to achieve achieve the the NDI NDI of of two two pipe pipe strings. strings. Specifically, Specifically, two contour curves curves according according to to the when the two time slices have been selected, the two projected contour corresponding EMF EMF values values are are then then obtained obtained with with the the simulation simulationresults resultsapproximately. approximately. As As aa result, result, corresponding the intersection intersection of of the the two two curves curves can can be be used used to to interpret interpret the the thickness thickness of of the the two two pipe pipe strings. strings. the However, the similarity of the two Theoretically, the combinations of the time slices are not unique. However, EMF curves curves for for each case is inversely proportional proportional to the difference between the two observation observation EMF times. Thereby, Thereby, although although different different combinations combinations of of the the time time slices slices may may lead lead to different inspection inspection times. performance, as long as the contour curves are not too similar, lots of combinations of time slices could be employed to obtain almost the same results. In this paper, the effectiveness of the principle of the NDI of multipipe strings is demonstrated by using the two time slices at 20 and 50 ms as an

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performance, as long Sensors 2017, 17, 1836 Sensors 2017, 17, 1836

as the contour curves are not too similar, lots of combinations of time slices could 6 of 15 6 of 15 be employed to obtain almost the same results. In this paper, the effectiveness of the principle of the NDI of multipipe using two time slices at 20 and 50 as an example shown instrings Figureis4demonstrated to ensure thatby the two the EMF curves are sufficiently farms apart to example provide example shown in Figure 4 to ensure that the two EMF curves are sufficiently far apart to provide shown in noise Figuresuppression. 4 to ensure By thatcontrast, the twoifEMF curves are sufficiently apart to provide adequate adequate the two time slices were toofar close (e.g., 35 ms and 40 ms) adequate noise suppression. By contrast, if the two time slices were too close (e.g., 35 ms and 40 ms) noise suppression. By contrast, if the two time slices were too close (e.g., 35 ms and 40 ms) as shown as shown in Figure 5, the projected contour curves will become almost parallel, which will not only as shown in Figure 5, the projected contour curves will become almost parallel, which will not only in Figure the projectedvery contour curvestowill become almost which will only make the make the5, intersection difficult distinguish, but parallel, also influence thenot ability of noise make the intersection very difficult to distinguish, but also influence the ability of noise intersection very difficult to distinguish, but also influence the ability of noise suppression. suppression. suppression. 17 17

(mm) Thickness Liner (mm) Thickness Liner

16 16

Case C Case C Intersection Intersection 16.71 mm+9.53 mm 16.71 mm+9.53 mm

20 ms-Case A 20 20 ms-Case ms-Case A B 20 20 ms-Case ms-Case B C 20 ms-Case C 50 ms-Case A 50 ms-Case A 50 ms-Case B 50 50 ms-Case ms-Case B C 50 ms-Case C

15 15 14 14 13 13 12 12 11 11 10 10 9 9 9 9

Case A Case A Intersection Intersection 9.19 mm+9.53 mm 9.19 mm+9.53 mm

10 10

11 11

Case B Case B Intersection Intersection 9.19 mm+17.86 mm 9.19 mm+17.86 mm

12 13 14 15 12 14 (mm) 15 Casing13 Thickness Casing Thickness (mm)

16 16

17 17

18 18

Figure 4. Intersection of induced EMF contour curves at 20 and 50 50 ms. ms. Figure 4. 4. Intersection Intersection of of induced induced EMF EMF contour contour curves curves at at 20 20 and and Figure 50 ms. 17 17

Case C Case C Intersection Intersection 16.71 mm+9.53 mm 16.71 mm+9.53 mm

(mm) Thickness Liner (mm) Thickness Liner

16 16

35 ms-Case A 35 35 ms-Case ms-Case A B 35 35 ms-Case ms-Case B C 35 40 ms-Case ms-Case C A 40 40 ms-Case ms-Case A B 40 40 ms-Case ms-Case B C 40 ms-Case C

15 15 14 14 13 13 12 12 11 11 10 10 9 99 9

Case A Case A Intersection Intersection 9.19 mm+9.53 mm 9.19 mm+9.53 mm

10 10

11 11

Case B Case B Intersection Intersection 9.19 mm+17.86 mm 9.19 mm+17.86 mm

12 13 14 15 12 14 (mm) 15 Casing13 Thickness Casing Thickness (mm)

16 16

17 17

18 18

Figure 5. Intersection of induced EMF contour curves at 35 and 40 ms. Figure Figure 5. 5. Intersection Intersection of of induced induced EMF EMF contour contour curves curves at at 35 35 and and 40 40 ms. ms.

In practice, when the difference between the two time slices is less than 10 ms, the intense noise In practice, when the difference between the two time slices is less than 10 ms, the intense noise In practice, when the environment difference between the two is as lesswell thanas10the ms,intersection the intense point noise due to a poor downhole will make thetime two slices curves due to a poor downhole environment will make the two curves as well as the intersection point due to a poor downholeand environment will make the curves as well as the intersection point difficult difficult to distinguish recognize. Notably, thetwo detection performance can be further improved difficult to distinguish and recognize. Notably, the detection performance can be further improved to distinguish and recognize. Notably, thetime detection can be furtherinimproved through through the optimization of the chosen slices;performance this will be investigated our future work. through the optimization of the chosen time slices; this will be investigated in our future work. the optimization the chosen timebe slices; this will be investigated work. Furthermore, Furthermore, thisofmethod can also extended to solve the probleminofour thefuture NDI of multipipe strings, Furthermore, this method can also be extended to solve the problem of the NDI of multipipe strings, this method can also be of extended to EMF solve contour the problem of the NDI of strings, where the where the dimensions induced curves should be multipipe correspondingly increased. where the dimensions of induced EMF contour curves should be correspondingly increased. dimensions of induced EMF contour curves be correspondingly increased. Unfortunately, in Unfortunately, in borehole detection, the should late time data of the TEM response contain more Unfortunately, in borehole detection, the late time data of the TEM response contain more borehole detection, the late time data of thedistance TEM response contain more information to information corresponding to increasing not only in the radial directioncorresponding but also in the information corresponding to increasing distance not only in the radial direction but also in the increasing distance not which only inwill the radial direction but detection also in theperformance longitudinalof direction, whichTEM will longitudinal direction, strongly affect the the borehole longitudinal direction, which will strongly affect the detection performance of the borehole TEM stronglyfor affect performance system the the NDIdetection of multipipe strings. of the borehole TEM system for the NDI of multipipe strings. system for the NDI of multipipe strings. 4. Auxiliary Sensor-Based NDI of Multipipe Strings 4. Auxiliary Sensor-Based NDI of Multipipe Strings On the basis of the model for the signal of the borehole TEM system for NDI, we showed that On the basis of the model for the signal of the borehole TEM system for NDI, we showed that the thickness of two pipe strings can be estimated by detecting two time slices of induced EMF in a the thickness of two pipe strings can be estimated by detecting two time slices of induced EMF in a single sensor. Now, we show how the auxiliary sensor-based borehole TEM system (Figure 6) can single sensor. Now, we show how the auxiliary sensor-based borehole TEM system (Figure 6) can

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4. Auxiliary Sensor-Based NDI of Multipipe Strings On the basis of the model for the signal of the borehole TEM system for NDI, we showed that the thickness of two pipe strings can be estimated by detecting two time slices of induced EMF in a single Sensors 2017,we 17, 1836 of 15 sensor. Now, show how the auxiliary sensor-based borehole TEM system (Figure 6) can 7be used to improve the detection performance of the NDI of multipipe strings. The measurement tool shown in be used to improve the detection performance of the NDI of multipipe strings. The measurement Figure 6 comprises two sensors and their measurement circuits, which are fixed in a waterproof tool tool shown in Figure 6 comprises two sensors and their measurement circuits, which are fixed in a housing. Each sensor consists of transmitting and receiving coils wound around a magnetic core with waterproof tool housing. Each sensor consists of transmitting and receiving coils wound around a a radius of 6 mm sensor, as A-sensor) andtermed 12 mmas(main sensor, M-sensor), magnetic core (auxiliary with a radius of 6termed mm (auxiliary sensor, A-sensor) andtermed 12 mmas(main respectively, where the main sensor is the same one discussed in Section 3. The number of turns sensor, termed as M-sensor), respectively, where the main sensor is the same one discussed in of the two Section sensors3.isThe thenumber same. of turns of the two sensors is the same. Control & Signal Processing R3 D1

R1

A-Sensor

Production Casing

C

+

R11

D2

D3

R2

R6

R5

R7

D4

R8

R9

+

R4

+

12-bits ADC

R10

Instrumentation Amplifier

H-bridge1

Liner Hanger

R3＇ Transmitting coils

Production Liner

M-Sensor

Cement Ring

D1＇

C＇

+

R11＇

D2＇ R1＇

D3＇

TEM Data Collection & Coding

MicroController

Timer H-bridge2

R2＇

R6＇

R5＇

R7＇

D4＇

Receiving coils

R4＇

+

R8＇ R9＇

+ R10＇

12-bits ADC

DC/DC coverter & DC power line communication

Surface Casing

Winch

Instrumentation Amplifier

Figure 6. Auxiliary sensor-based borehole transient electromagnetic (TEM) system in a multistring

Figure 6. Auxiliary sensor-based borehole transient electromagnetic (TEM) system in a multistring oil oil well. DC, direct current. ADC, analog-to-digital converter. well. DC, direct current. ADC, analog-to-digital converter.

The measurement circuits mainly consist of a direct current (DC)–DC converter, two transmission waveform generators two analog-to-digital converters The measurement circuits mainly(H-bridge), consist of aa microcontroller, direct current (DC)–DC converter, two transmission (ADC), generators and two instrumentation The assembled circuits have a working temperature of two waveform (H-bridge), aamplifiers. microcontroller, two analog-to-digital converters (ADC), and at least 150 °Camplifiers. for deep borehole inspection.circuits The data collected from the sensors areoftransmitted instrumentation The assembled have a working temperature at least 150to◦ C for surfaceinspection. system via The DC data power line communication in real In this to paper, we usesystem the via deepthe borehole collected from the sensors are time. transmitted the surface proposed borehole TEM system for the NDI of two strings of the pipe (production casing and liner). DC power line communication in real time. In this paper, we use the proposed borehole TEM system Figures 7 and 8 show the simulations of the eddy-current fields, which are obtained by for the NDI of two strings of the pipe (production casing and liner). converting the vertical component of the magnetic field shown in Equation (4) into the time domain, Figures 7 and 8 show the simulations of the fields, which obtained by converting and are described by magnetic flux density witheddy-current the relative permeability ofare each layer, where RLD the vertical component of the magnetic field shown in Equation (4) into the time domain, and are denotes the longitudinal diffusion range of the sensor. It is noted that since the transmitting described by magnetic with the permeability each layer, where RLD denotes multi-turn coils are flux not adensity point source, therelative total response shouldofbe calculated by summing the the response of each single turnof coil with its corresponding z coordinates. longitudinal diffusion range the sensor. It is noted that since the transmitting multi-turn coils are

Cement ring

Longitude distance (mm)

Liner

Casing

not a point source, the total response should be calculated by summing the response of each single 500 1 turn coil with its corresponding z coordinates. 400 0.9 As shown in Figures 7 and 8, the diffusion of the eddy-current fields occurs not only in the radial 300 0.8 direction but also in the longitudinal direction. In the radial direction, the influence of the casing 200 0.7 on the magnetic field at a late time (50 ms) is stronger than that at an early time (20 ms). In the M-sensor 0.6 100 longitudinal direction, the diffusion range obviously increases with observation time, where the two R =400 mm LD 0 0.5 time slices used for NDI correspond to different effective detection ranges of approximately 400 and -100 0.4 direction can help solve the 700 mm. Although the eddy-current diffusion property in the radial -200 0.3 in a substantial decrease in problem associated with the NDI of multipipe strings, it will also result 0.2 -300 both the longitudinal resolution and the accuracy for detecting changes in thickness; this may lead 0.1 -400 to a model mismatch for the borehole TEM system because of the thickness inhomogeneity of the 0 metal pipe, which means the-500 thickness of40the metal pipe is100inhomogeneous along the borehole axis -4 80 60 20 120 Radial distance (mm)

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Figure 7. Eddy-current field of the main sensor at 20 ms.

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transmission waveform generators (H-bridge), a microcontroller, two analog-to-digital converters (ADC), and two instrumentation amplifiers. The assembled circuits have a working temperature of at least 150 °C for deep borehole inspection. The data collected from the sensors are transmitted to the surface system via DC power line communication in real time. In this paper, we use the proposed TEM system for the NDI of two strings of the pipe (production casing and liner). Sensors 2017, 17,borehole 1836 8 of 15 Figures 7 and 8 show the simulations of the eddy-current fields, which are obtained by converting the vertical component of the magnetic field shown in Equation (4) into the time domain, (orand longitudinal direction), i.e., theflux thickness to thepermeability existence of of theeach collars or pipe damage. are described by magnetic densitychanges with thedue relative layer, where RLD Asdenotes an alternative, we chose to use timerange slices of induced EMFItinisboth the that mainsince sensor the auxiliary the longitudinal diffusion the sensor. noted theand transmitting multi-turn coils not a point source, the totaldiffusion responserange should be).calculated by summing thethe sensor to avoid an are excessively large longitudinal (RLD The eddy-current field of response of each coil with its corresponding z coordinates. auxiliary sensor at single 30 ms turn is shown in Figure 9.

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Figure 8. Eddy-current field of the main sensor at 50 ms. 1

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0.9 As shown in Figures 7400 and 8, the diffusion of the eddy-current fields occurs not only in the 300 0.8 radial direction but also in the longitudinal direction. In the radial direction, the influence of the casing on the magnetic field200 at a late time (50 ms) is stronger than that 0.7 at an early time (20 ms). In M-sensor the longitudinal direction, the time, where the 0.6 100diffusion range obviously increases with observation two time slices used for NDI 0correspond to different effective detection ranges of approximately 400 RLD=700 mm 0.5 and 700 mm. Although the-100 eddy-current diffusion property in the radial direction can help solve 0.4 the problem associated with the NDI of multipipe strings, it will also result in a substantial decrease -200 0.3 in both the longitudinal resolution and the accuracy for detecting changes in thickness; this may 0.2 -300 lead to a model mismatch for the borehole TEM system because of the thickness inhomogeneity of 0.1 -400 the metal pipe, which means the thickness of the metal pipe is inhomogeneous along the borehole 0 -500 i.e., the thickness changes due to the existence axis (or longitudinal direction), of the collars or pipe 40 80 60 20 100 120 ×10 -4 (T) damage. As an alternative, we chose to use time slices of induced EMF in both the main sensor and Radial distance (mm) the auxiliary sensor to avoid an excessively large longitudinal diffusion range (RLD). The Figure Eddy-current of the atat9. 5050ms. 8.8.Eddy-current ofshown the main main sensor ms. eddy-current field of theFigure auxiliary sensor at 30field ms is insensor Figure

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As shown in Figures 7500 and 8, the diffusion of the eddy-current fields occurs not only in the 1 radial direction but also in 400 the longitudinal direction. In the radial direction, the influence of the 0.9 casing on the magnetic field300 at a late time (50 ms) is stronger than that at an early time (20 ms). In 0.8 the longitudinal direction, the diffusion range obviously increases with observation time, where the 200 0.7 two time slices used for NDI correspond A- sensor to different effective detection ranges of approximately 400 0.6 100 and 700 mm. Although the eddy-current diffusion property in the radial direction can help solve RLD=400 mm 0 0.5 in a substantial decrease the problem associated with the NDI of multipipe strings, it will also result -100 0.4 in both the longitudinal resolution and the accuracy for detecting changes in thickness; this may -200the borehole TEM system because of the 0.3 lead to a model mismatch for thickness inhomogeneity of the metal pipe, which means along the borehole 0.2 -300the thickness of the metal pipe is inhomogeneous axis (or longitudinal direction), i.e., the thickness changes due to the existence of the collars or pipe 0.1 -400 damage. As an alternative, -500 we chose to use time slices of induced EMF in0 both the main sensor and -4 40 80 longitudinal 60 large 20 excessively 100 120 diffusion the auxiliary sensor to avoid an range (RLD). The ×10 (T) Radial distance (mm) eddy-current field of the auxiliary sensor at 30 ms is shown in Figure 9.

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Figure9.9.Eddy-current Eddy-current field of Figure of the the auxiliary auxiliarysensor sensoratat3030ms. ms. 1

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A comparison of Figures 7 and 9 reveals that the auxiliary sensor at 30 ms has almost the same longitudinal diffusion range300 as the main sensor at 20 ms, whereas their0.8radial diffusion properties 200 differ. On the one hand, because of their different radial properties, the 0.7 two metal pipes differently A- sensor influence the response of the100 magnetic field; thus, the principle behind the 0.6 NDI of multipipe strings, discussed in Section 3, can be Equation (12) with two unknown thicknesses. On the RLDsolve =400 mm 0 used to 0.5

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other hand, because the two time slices have approximately the same low RLD value, the mismatch of 9 of as 15 signal model at different times will be reduced, and the longitudinal resolution well as the detection accuracy will be improved. Similar to Figures 2–4, Figures 10 and 11 show the induced EMF of the two sensors for the three cases and their corresponding intersections (solutions) A comparison of Figures 7 and 9 reveals that the auxiliary sensor at 30 ms has almost the same for two thicknesses, respectively. longitudinal diffusion range as the main sensor at 20 ms, whereas their radial diffusion properties differ. On the one hand, because of their different radial properties, the two metal pipes differently influence the response of the magnetic field; thus, the principle behind the NDI 0.8 of multipipe strings, Sensors 2017, 17, 1836 9 of 15 discussed in Section 3, can be used to solve Equation (12) with two unknown thicknesses. On the other 1 0.7 hand, because the two time slices have approximately the same low RLD value, the mismatch of the other hand, because the two time slices have approximately the same low RLD value, the mismatch of borehole TEM signal model at different times will be reduced, and the longitudinal resolution as well the borehole TEM signal 0.8 model at different times will be reduced, and the longitudinal resolution as 0.6 as well the detection accuracy will bewill improved. SimilarSimilar to Figures 2–4, Figures 10 and1011and show the induced as the detection accuracy be improved. to Figures 2–4, Figures 11 show the 0.6 EMF of the two sensors for the three cases and their corresponding intersections (solutions) for two 0.5 induced EMF of the two sensors for the three cases and their corresponding intersections (solutions) thicknesses, respectively. 0.4 for two thicknesses, respectively. Induced EMF (V)

Sensors 2017, 17, 1836 the borehole TEM

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0.3 curved surface of the A comparison of Figures 2, 3, and 10 reveals that the induced EMF 0 auxiliary sensor at 30 ms differs from that of the main sensor at 20 ms, but is similar to that of the 16 0.2 18 suppression similar to that 14 main sensor at 50 ms; thus, theLinauxiliary sensor method can achieve16noise 12 er T 14 hic NDI 12 ) achieved using the single-sensor stems from the auxiliary sensor m 0.1 kne10 8 method. This capability 10 s (m s ss ( e n 8 ick mm 6 h T 6 g having a smaller radius compared with) the main sensor, thereby causing its time decay to be much n i 4 s 4 Ca shorter; thus, the observation time of 30 ms for the auxiliary sensor is already a late time, similar to 10. in the theauxiliary auxiliarysensor sensoratat3030ms. ms. Figure 10. Induced Induced the time slice of 50 ms forFigure the main sensor.EMF in

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17 2, 3, and A comparison of Figures the induced EMF curved surface of the Case10 C reveals that M-Sensor: 20 ms-Case A auxiliary sensor at 30 ms differs fromIntersection that of the main sensor ms,Bbut is similar to that of the M-Sensor:at 20 20 ms-Case 16 16.71 mm+9.53 mm M-Sensor: 20 ms-Case C main sensor at 50 ms; thus, the auxiliary sensor method can achieve noise suppression similar to that A-Sensor: 30 ms-Case A 15 A-Sensor: 30 ms-Case achieved using the single-sensor NDI method. This capability stemsB from the auxiliary sensor A-Sensor: 30 ms-Case C having a smaller radius compared with the main sensor, thereby causing its time decay to be much 14 shorter; thus, the observation time of 30 ms for the auxiliary sensor is already a late time, similar to the time slice of 50 ms for the13main sensor. 12 17 11 16

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Figure 11. 11. Intersection Intersection of the the induced induced EMF EMF curves curves using using the the auxiliary auxiliary sensor. sensor. 12 Figure of Case A

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11 Furthermore, Figure 11 shows that the projection of the induced Intersection Intersection EMF contour curves of the two A comparison of Figure 2, Figure 3, andmmFigure 10 reveals that themminduced EMF curved surface of 9.19 mm+9.53 9.19 mm+17.86 sensors at 20 and 30 ms can still 10 intersect at one point for each case. Thereby, the NDI of two strings the auxiliary sensor at 30 ms differs from that of the main sensor at 20 ms, but is similar to that of the of pipes can also be achieved using the auxiliary sensor, with better detection performance of main sensor at 50 ms; thus, the9 auxiliary sensor method can achieve noise suppression similar to that 9 10 accuracy. 11 12 13 14 15 16 17 18 longitudinal resolution and detection Casing Thickness (mm) achieved using the single-sensor NDI method. This capability stems from the auxiliary sensor having a smaller radius compared with the main sensor, EMF thereby causing itsauxiliary time decay to be much shorter; Figure 11. Intersection of the induced curves using the sensor. thus, the observation time of 30 ms for the auxiliary sensor is already a late time, similar to the time slice ofFurthermore, 50 ms for theFigure main sensor. 11 shows that the projection of the induced EMF contour curves of the two sensors at 20 and 30 ms can still intersect at one point for each case. Thereby, the NDI of two strings of pipes can also be achieved using the auxiliary sensor, with better detection performance of longitudinal resolution and detection accuracy.

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Furthermore, Figure 11 shows that the projection of the induced EMF contour curves of the two sensors at 20 and 30 ms can still intersect at one point for each case. Thereby, the NDI of two strings of pipes can also be achieved using the auxiliary sensor, with better detection performance of longitudinal resolution and detection accuracy. 5. Field Experiments 5.1. Experimental Results The validity of the auxiliary sensor method for the NDI of multipipe strings was confirmed by field experiments conducted at the Yaerxia oil production plant Yumen Oilfield, China. The experiments were conducted in a production oil well with two strings of pipes comprising a production casing and liner. In our experiment, r1 , r2 , r3 , r4 , r6 , and r8 have the same value as the simulation in the above sections. The parameters of the two sensors are shown in Table 1. Table 1. Sensor parameters for the nondestructive inspection (NDI) of multipipe strings. Parameter

Value

Radius of the main sensor Radius of the auxiliary sensor Number of transmitting coil turns Number of receiving coil turns Wire diameter of the transmitting coils Wire diameter of the receiving coils Resistance of the transmitting coils of the A-sensor Resistance of the receiving coils of the A-sensor Resistance of the transmitting coils of the M-sensor Resistance of the receiving coils of the M-sensor

12 mm 6 mm 95 980 0.46 mm 0.18 mm 1.57 Ω 52.8 Ω 3.12 Ω 105.1 Ω

In their actual sizes, the two types of metal pipe in our paper have thicknesses of 9.19 and 9.53 mm, respectively, where each liner or casing is connected by a collar with a thickness of approximately 7.52 mm (liner) and 8.33 mm (casing); thus, the corresponding thickness in the collar becomes 16.71 mm for the liner and 17.86 mm for the casing approximately as shown in [13]. Furthermore, the inner radius in the collar is the same as the pipe, while their outer radiuses are different. In this paper, the liner and casing collars that can be validated with prior and authentic knowledge are analyzed as examples to evaluate the effectiveness of the proposed method. Figures 12 and 13 show the field experiment results and theoretical values of the induced EMFs from 4110 to 4140 m and from 3970 to 4000 m, respectively. Similar to Figures 4 and 11, the experiment data in Figures 12 and 13 can be used to interpret the thickness of the two pipe strings on the basis of the NDI of the thickness of multipipe strings. Additionally, the interpreted thicknesses with the proposed auxiliary sensor method and the single-sensor method for the NDI of multipipe strings are shown in Figures 14 and 15, where the corresponding pipe string structures are also illustrated. It can be observed from Figures 12–15 that the 'peaks' are corresponding to the collars, which means that the experiment data are consistent with the pipe string structures, thereby demonstrating the feasibility of the proposed borehole TEM system. Also, as evident in the figures, all of the collars (experimental results) shown in Figures 12b and 13b appear much wider than those shown in Figures 12a,c and 13a,c; this indicates the poorer resolution performance of NDI in the borehole axis when the induced EMF in the main sensor at 50 ms is used. Moreover, at several distances between the nearby liner and casing collars (termed DNC ), the detected signals of the main sensor at a late time also do not perform well to distinguish nearby collars. Thereby, although multiple time slices of the induced EMF from a single sensor can be used to interpret the thickness of two-pipe strings, the longitudinal resolution may be influenced by large RLD at a late time.

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(a) (b) (c) Induced EMF (V) (a) (b) (c) Figure 12. Induced EMF of the sensors at different ranging from to 4140 m: (a) main (a)twosensors (b) times (c) 4110 Figure 12. Induced EMF of the two at different times ranging from 4110 to 4140 m: (a) main Figure 12.ms; Induced EMF of theattwo sensors at different from 4110 to 4140 m: (a) main sensor at 20 (b) main sensor 50 ms; and (c) auxiliarytimes sensorranging at 30 ms. sensorFigure at 20 ms; mainEMF sensor at 50 ms; and (c) sensor at 30 ms. 12. (b) Induced of the two sensors at auxiliary different times ranging from 4110 to 4140 m: (a) main sensor at 20 ms; (b) main sensor at 50 ms; and (c) auxiliary sensor at 30 ms. 3970 main sensor at 50 3970 sensor at 20 ms; (b) ms; and (c) auxiliary3970 sensor at 30 ms. Experiment

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sensor at 20 ms; (b) main sensor atsensors 50 ms; and (c) auxiliary sensor at 30 ms. Figure 13. Induced EMF of the two at different times ranging from 3970 to 4000 m: (a) main Figure Induced the two sensors at different times ranging sensor 13. at 20 ms; (b) EMF mainof sensor at 50 ms; and (c) auxiliary sensor at 30from ms. 3970 to 4000 m: (a) main sensorsensor at 20 ms; (b) main sensor at 50 ms; and (c) auxiliary sensor at 30 ms. 4110 4110 4110 at 20 ms; (b) main sensor at 50 ms; and (c) auxiliary sensor at 30 ms.

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(a) (b) (c) Casing Thickness (mm) Liner Thickness (mm) (a) (b) (c) Figure 14. Interpreted thickness using the NDI(b) of two-pipe strings ranging from 4110 to 4140 m: (a) (c) 14. Interpreted thickness using two-pipe strings ranging from 4110 to 4140 m: (a)Figure liner thickness; (b) casing thickness; andthe (c) NDI pipe of string structure. Figure 14. Interpreted thickness using the NDI of two-pipe strings ranging from 4110 to 4140 m:

thickness; thickness (b) casing thickness; (c) of pipe string structure. Figure (a) 14.liner Interpreted using theand NDI two-pipe strings ranging from 4110 to 4140 m: (a) liner thickness; (b) casing thickness; and (c) pipe string structure. (a) liner thickness; (b) casing thickness; and (c) pipe string structure.

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Figure 15. Interpreted thickness using the NDI of two-pipe strings ranging from 3970 to 4000 m: liner thickness; (b) casing thickness; and (c) pipe string structure. (a) thickness; and (c) (b) (a) liner thickness; (b) casing pipe string structure. (c) 15. Interpreted thickness using the NDI of two-pipe strings ranging from 3970 to 4000 m: (a) 5.2.Figure Analysis and Discussion

5.2. Analysis Discussion liner and thickness; (b) casing thickness; and (c) pipe string structure.

Using the experimental results, we demonstrated the effectiveness of the proposed borehole

Using the experimental results, we demonstrated the effectiveness proposed borehole system for the NDI of multipipe strings. Note that smallerofRthe LD values indicate that TEM an 5.2.TEM Analysis and Discussion systemimproved for the NDI of multipipe strings. Note smallerasRshown values indicate that an improved detection performance of NDI can that be achieved in Section 4. In this section, on LD the experimental results, we demonstrated the effectiveness thesection, proposed borehole theUsing basis of the interpreted thicknesses, we will discuss longitudinal resolution ofon the auxiliary detection performance of NDI can be achieved as shown inthe Section 4. Inofthis the basis of TEM system for the NDI of multipipe strings. Note that smaller R LD values indicate that anthe sensor-based method by analyzing the measured width of the casing or liner collars along the interpreted thicknesses, we will discuss the longitudinal resolution of the auxiliary sensor-based improved detection performance of NDI can be achieved as shown in Section 4. In this section, on borehole axis, which is related with theof thickness of the method by analyzing the measured width the casing or pipes. liner collars along the borehole axis, which the basis of the interpreted thicknesses, we will discuss the Rlongitudinal of the auxiliary In Figure 16, we describe the relationships between LD, DNC, andresolution the measured width, where is related with the thickness of the pipes. sensor-based method by analyzing the measured width of the casing or liner collars along theP4 WLC and WCC denote the actual width of the liner and casing collar, respectively. P1, P2, P3, and In Figure 16,which we describe the relationships between RLD , DNC , and the measured width, where borehole axis, is related with the thickness of the pipes. denote the four particular observation locations. Note that the liner and casing collars can be W LC andInWFigure the actual the width of the liner and casing respectively. P1, P2, P3, and P4 CC denote describe relationships between , Dcollar, NC, and the measured width, where detected only16, inwe a limited range between P1 and P2 andRLD between P3 and P4, respectively. Thus, the denote the observation locations. Note that thecollar, liner and casing collars detected WLC andfour WCCparticular denote width of the liner and respectively. P1, P2,can P3,be and P4P2 measured width of the the actual liner and casing collars can becasing represented by the distance between P1 and onlydenote inand a limited range between P1 and P2 and between P3 and P4, respectively. Thus, the can measured the four observation locations. Notethe that liner and casing collars be between P3particular and P4, respectively. We then define D NCthe as follows: width of the liner and casing collars can be represented by between the distance between P1 and P2 Thus, and between detected only in a limited range between P1 and P2 and P3 and P4, respectively. the 1follows: measured width of theWe liner anddefine casing collars represented by the distance between P1 and (16) P2 P3 and P4, respectively. then D1NCcan as be Dthe NC  WLC  WCC  RLD  DP2P3 2 define 2 the DNC as follows: and between P3 and P4, respectively. We then 1 1 where DP2P3 represents the D distance P3. As + shown W1LC + P2 RLD DP2P3in Figure 16, when DP2P3 > 0, the (16) 1Wand NC = between CC + 2 2other. D  W  WCC However, RLD  DP2P3 when the two collars are too(16) NC by each LC two sensors will not be influenced close 2 2 < 0), the two nearby collars will strongly affect each other, resulting in a substantial decrease where(D DP2P3 P2P3 represents the distance between P2 and P3. As shown in Figure 16, when DP2P3 > 0, where DP2P3 represents the distance between and P3. Asofshown in Figure 16, when DP2P3couples > 0, the of in sensors the detection accuracy of the NDI of each theP2 two strings the pipe. Taking three typical the two will not be influenced by other. However, when the two collars are too close two notinbeFigures influenced by 13 each other. However, whenthe theinversed two collars are too closethe thesensors nearbywill collars 12 and as examples, we describe thickness using (DP2P3 < 0), 0), thethe two nearby collars will strongly affect each other, resulting in a substantial decrease in (DNDI P2P3 0 forcollar the A-sensor. by almost the twothe nearby collars, where the inversed in thickness deform at the nearby side. However, auxiliary method shows300 almost sameDdetection performance in Figure 17a,b the In Figure 17e,f,the with a DNCsensor of approximately mm,the where both sensors, although P2P3 < 0 for because Dof P2P3 > 0proposed for the A-sensor. Figure 17e,f, with a Dbetter NC of approximately 300 mm, where D P2P3 performance the methodIn decreases, it remains than that of the single-sensor method.