MEASUREMENT OF WALL LOSS IN PRESSURE VESSELS

USING FBG SENSORS

H. Adldoost

Sharif University of Technology, Int’l Campus, School of Science and Engineering,

Kish Island (Iran) adldoost@kish.sharif.edu

A. Zabihollah

Sharif University of Technology, Int’l Campus, School of Science and Engineering,

Kish Island (Iran) zabihollah@sharif.edu

S. J. Fattahi

Sharif University of Technology, Int’l Campus, School of Science and Engineering,

Kish Island (Iran) fattahi@kish.sharif.edu

Abstract

Pressure vessels including high pressure pipelines

carrying petrochemical fluids seen to be opposed to wall

degradation in some early period of their operational years.

Measurement of pipe wall thickness provides engineers

valuable information on failure probability. This work

presents designing and application of FBG as a wall loss

continuous, electromagnetic immune and trendable sensor for

this approach. The proposed design includes two FBGs for

measurement of Hoop and axial strains and also one FBG for

measurement and compensating temperature. The presented

result is a relation for the amount of wall loss by FBGs

wavelength shift. At rest of this article numerical results for

the designed sensor are presented.

Index terms- FBG sensor, pressure vessel, strain

measurement

NOMENCLATURES

Symbol Definition p

b, r

E

�

�

�

operational pressure Pressure vessel thickness, radius

young modulus temperature

thermal coefficient Poisson ratio

���� Effective refraction index �

�

�

� � � �

Grating period Bragg wavelength

Length of FBG Length of grating

Strain optic tensor components

INTRODUCTION

Pipe wall thinning (PWT) is a future failure symptom to pressure vessels. There is a specific level of pressure at any wall thickness that leads to burst. The failure pressure of pipe with wall thinning is previously studied by many researchers. Kamaya et. al. [1] studied FEA of several types of steel pipes by three dimensional analysis; declaring lowest failure pressure for line pipe steel. Bond et. al. [2] studied pipelines for various range of internal pressure and reported the rehabilitation of corroded pipes by putting steel back into pipelines as a suitable method for promoting burst pressure. Pipe inside pressure induces strain on the pipe wall. This has been worked by many researchers and their results are published including graphs and tables that indicate circumferential (Hoop) and axial stresses versus imposed pressure [3, 4]. The accurate measurement of pipe strain is accomplished by the use of strain sensors. The first strain sensor is invented in 1938 by Edward E. Simmons which is based on resistivity change of micro-wires when went under strain. During previous decades advances in micro electromechanical systems offered several types of strain sensors namely piezoresistive sensors [5, 6]. The structure consists of four p-type poiezoresistives comprising of a Wheatstone bridge [7]. Recent achievements present multilayer polymer structures using capacitive thin film PCBs and flexible surface sensors [9, 10]. Trends on design of strain sensors in the area of laser and optic have yield design of MOEMS devices, by patterning polymethylmethacrylate (PMMA) lens on a silica wafer [11]. After discovery of fiber Bragg grating as a strain sensor many researches forwarded through fiber optic sensor design in several applications such as airspace, aircraft, civil structures, underground pipes, etc., [12-14]. Novel achievements in micro optical sensors include construction of a micro hollow glass sphere embedded on the tip of a micro optic *Corresponding author, Email: adldoost@kish.sharif.edu

fiber. In this sensor the measured parameter is taken as strain and the diffraction wavelength � is found from,

�� � � �� � (1)

m is an integer and d the sphere diameter; some strain changes cause deformation of the sphere so this gives shift in wavelength as,

�� � ������ � ������� (2)

Where ����� indicates incremental change in inner diameter, ��, for small strain change of , ��, [20]. Among numerous fiber optic sensors, FBGs are the most popular. Since these sensors use wave division multiplexing (WDM) scheme so they provide distributed sensing capability. The demodulation technique for such sensors is based on detection of wavelength shift of sensor peaks [8]. FBGs are immune to environmental electromagnetic noise, are flexible, and reveal much less attenuation in long distance sensor data transferring systems. In this research we have designed a sensor based on two FBGs, orienting in vertical and horizontal directions for measurement of pipe wall strain and consequently the wall loss and one FBG for temperature compensation.

ANALYSIS OF PRESSURE VESSELS

Cylindrical computational model is the most appropriate one for analysis of pressure vessels [15]. As shown in Fig.1, the three existing stresses are Hoop, axial and radial stresses [19]. Considering a thin-walled pressure vessel of radius r, and thickness b, Hoop or circumferential stress and the resulting strain are,

�� � ��� � !� � ��

�" (3)

And the axial ones are,

�# � ����� !# � ��

��" (4)

The amount of circumferential wall deformation of the vessel is,

�$ � %!� � �&� ���" (5)

The radial stress in a thin-walled pressure vessel is much less than axial and circumferential ones, so in this work we neglect this issue.

�' � � (6)

From above stress and strain calculations a nominal wall thickness for pressure vessels could be obtained,

� � ()�"� � *

(7)

Where P is pipe pressure, D is the diameter, E is the weld joint factor (efficiency), S is 72% of specified minimum yield strength and A denotes sum of allowance for threading, grooving, corrosion and others as required [16].

We can consider two portions of pipes, restrained and unrestrained. A pipe buried or above ground has both portions. Unrestrained portions gradually start imposing bending stress to the pipe. Pressurizing or heating of pipe creates soil friction force that is proportional with the moving length. This force is against movement of the pipe. The restrained pipeline is stopped from movement by anchors and soil friction forces therefore extra longitudinal stress will appear. By considering the effect of anchors and friction, the longitudinal stress is obtained as,

�+ � ���� , �-�" � ���� , . ��

� (8)

Similarly hoop stress is,

�/ � ���� , �-�" � ��� , � ��

�� (9)

Respectively the strains are obtained from above equations using Hook’s law.In Fig. 2 and 3, the linear increment of hoop and axial strains versus temperature and pipe internal pressure is illustrated.

Figure 1. Hoop Axial and radial stresses

Figure 2. Hoop strain vs. temperature change

1

2

3

4

5

x 106

0

20

40

600

0.2

0.4

0.6

0.8

1

1.2

x 10-3

INNER PRESSUREDELTA T

HO

OP

ST

RA

IN

Figure 3. Axial strain vs. temperature change

FIBER BRAGG GRATING SENSOR Fundamentally a fiber optic sensor works with modulation of one or few properties of propagating light, including intensity, frequency, phase and polarization.

Any FBG sensor is compromised of at least a wideband light source, a coupler and a detector. Fiber grating works in a way that reflects a so-called Bragg wavelength and transmits others. The reflected wavelength depends on the grating period. Any variation in the grating period will result in shift of Bragg wavelength. Mostly the propagation of light inside fiber optic (Fig. 4) is studied by use of coupled mode theory [17],

The peak Gaussian reflected wavelength is,

0��� � -�12�& 345 �,�� , 61��

��1� � (10)

Where � is wavelength, 61 is center wavelength and �1 is the width of Gaussian curve. The Bragg wavelength is proportional to grating period,

� � ������ (11)

� is grating period and ���� is effective index of refraction.

The relation between the imposed strain, temperature variation and the shifted Bragg wavelength is obtained from,

7� � ��- , ����8��9�� � :�;� (12)

<=3>3 �� � �� and �8 are respectively Bragg wavelength shifth, strain optic constant and the axial strain change along the lengthwise direction of the fiber optic. � is thermal expansion, : is thermo-optic coefficients of the fiber and �� is obtained from,

�� � �����

� ?� � , ��� @� ��A (13)

Where � and � �are components of strain optic tensor and � is the Poisson’s ratio of fiber core [18, 21].

Figure 4. Forward and backward FBG wave propagation

ANALYSIS OF WALL THINNING RATE USING

FBG

In the present work the methodology for measuring rate of strain in two main directions on the optic fiber is by employing a vertical and a horizontal FBG on a lamina attached to the pipeline (Fig. 5). The Hoop strain on pipe wall is,

8/ � ���� , �-� � ���" , � ��

��" () (14)

This is proportional to the pipe inner pressure so that for the pipeline system with the operational properties in table 2, we achieved maximum strain of 2500 micro-strain. This amount of strain will impose shift in Bragg wavelength of 4 nm in the vertical optic fiber. The horizontal FBG sensor measures longitudinal strain induced in the fiber. Longitudinal strain of pipeline is achieved from,

8B � ���� , �-� � ����" , . ��

�" (15)

As illustrated in Fig. 6, strain on the pipe wall is extreme for over 90% of wall loss, respectively Fig. 7 shows shift in wavelength. By simulation for FBG and the pipe of properties shown in table 1 and 2, we obtained shift in wavelength of 3.29 nm in vertical FBG for 2000 micro strain (Fig. 8) and respectively a shift of 0.82 nm in horizontal FBG due to 500 micro strain (Fig. 9).

TABLE 1. PARAMETERS OF FBG SENSOR

Parameter Value CDEE 1.5

F GH IC J

JK LMM LMN CDEE

O

530nm 1537nm 7P -QRS 58mm

0.72758mm 0.113 0.252 1.482 0.87

�

1

2

3

4

5

x 106

0

20

40

600

2

4

6

8

x 10-4

INNER PRESSUREDELTA T

AX

IAL S

TR

AIN

TABLE 2. OPERATIONAL PROPERTIES OF CARBON STEEL PIPELINE

Property Value p

r

b

E

7T

U

O

5MPa 500 mm

1~20 mm 200 GPa 0~20oC

-Q�V P -QRS /o C 0.27

We studied effect of 0.95% wall loss in 5MPa operational pressure and in constant temperature in a way that the Hoop strain of 10800 microstrain gives an equivalent shift of 13.86 nm in reflected Bragg wavelength. Fig 10 shows a comparison for strain in 1mm through 19 mm wall loss for a pipe of 20 mm thickness with other given properties in table 2 versus pressure range of 1 to 5 MPa.

The shifted wavelength has a linear relation with applied strain as shown in Fig. 11, for 500 to 2000 micro strain shifted wavelength range is 0.6 to 2.42 nm.

(a) (b)

Figure 5. Sensor patch on pipe (a), vertical, horizontal and temperature FBGs (b)

Figure 6. Hoop and axial strain vs. wall loss in pressure of 1MPa

Figure7. Wavelength shift of vertical and horizontal FBGs vs. wall loss in pressure of 1 MPa.

Figure 8. Bragg wavelength shift of 3.29 nm in vertical FBG, due to 2000 micro strain.

Figure 9. Bragg wavelength shift of 0.82 nm in horizontal FBG due to 500 micro strain. 0 10 20 30 40 50 60 70 80 90 100

0

0.5

1

1.5

2

2.5x 10

-3

WALL LOSS %

ST

RA

IN

HOOP STRAIN

AXIAL STRAIN

0 10 20 30 40 50 60 70 80 90 1000

0.5

1

1.5

2

2.5

3

3.5

4x 10

-9

WALL LOSS %

WA

VE

LE

NG

TH

SH

IFT

FPG V

FPG H

1.53 1.532 1.534 1.536 1.538 1.54 1.542

x 10-6

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

RE

FLE

CT

IVIT

Y

WAVELENGTH

MAIN SPECTRUM

REFLECTED STRAIN

1.53 1.532 1.534 1.536 1.538 1.54 1.542

x 10-6

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

RE

FLE

CT

IVIT

Y

WAVELENGTH

�MAIN SPECTRUM

REFLECTED STRAIN

h v

Figure 10. Wall strain vs. percent of wall loss for the range of 1~5 MPa operational pressure.

Figure 11. Shifted wavelength vs. strain, linear relation.

COMPENSATION OF TEMPERATURE EFFECT

Temperature directly changes the Bragg wavelength of reflected light. Temperature variation effect is measured for 20oC in reflected wavelength. This is illustrated in Fig. 12, which the same degree shifts the both wavelengths. The use of third FBG as a temperature sensor handles the problem. This FBG is not tightly attached to the pipe but aside it so that measures only the temperature. The shift in wavelength of this FBG is subtracted from vertical and horizontal ones.

Figure 12. wavelength shift of 0.2 n.m due to 20o increment of temperature

CALCULATION OF WALL LOSS

MEASUREMENT USING FBG Always there exists a relation between pipe thickness and induced strain. From Hoop strain, Eq. (14), we obtain the thickness,

� � ��"?8/ , ���� , �-�A �- , Q�W��

(16)

Similarly from axial strain, Eq. (15), we obtain,

� � ���"?8B , ���� , �-�A �- , ��� (17)

In equations (16, 17), b is the pipe wall thickness, � is the operational pressure, � is the pipe radius, " is the modulus of elasticity and 8/ and 8B are the Hoop and axial strains. The obtained relation for wall thickness is a function of wall strain. Assuming in constant operational pressure, the shift in wavelength of FBGs would indicate the amount of wall loss. From previous relations for shift in Bragg wavelength of vertical FBG and hoop strain we obtain,

8/ � ;�X�YZ[\��- , ���

(18)

]^ � �_ , ��" ` ;�X�YZ[\

��- , ��� , ���� , �-�a�- , Q�W��

(19)

]b � �_ , ���" ` ;�c�YZ[\

��- , ��� , ���� , �-�a�- , ���

(20)

In Eq. (19) dX denotes the amount of wall loss by shift in wavelength of vertical FBG with consideration of temperature compensation, respectively 7�c�YZ[\, and �_ denote the degree

020

4060

80100

1

2

3

4

5

x 106

0

0.002

0.004

0.006

0.008

0.01

0.012

Percent of wall losspressure

Wall

sra

in

0 0.5 1 1.5 2 2.5

x 10-3

0

0.5

1

1.5

2

2.5

3

3.5

4x 10

-9

STRAIN

WA

VE

LE

NG

TH

SH

IFT

1.53 1.532 1.534 1.536 1.538 1.54 1.542

x 10-6

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

RE

FLE

CT

IVIT

Y

WAVELENGTH

MAIN SPECTRUM

STRAIN REFLECTED

of wavelength shifted and the initial thickness of the pipe. Respectively in Eq. (20), ]b gives the amount of wall loss by horizontal FBG signal interpretation.

CONCLUSION A specific design of an FBG sensor for measurement of hoop and axial strains of pressure vessels is studied. This technique is most appropriate and cost effective for smart pipeline systems. Due to narrow band width of FBG, this sensor handles accurate measurements of strain in both directions on pressure vessel. WDM multiplexing scheme makes use of several of such sensor patches to attach to several segments and being connected to each other in piping network system. The obtained relation for wall thickness of pressure vessels gives online thickness information by measurement of hoop and axial strains.

REFERENCES

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