modelling and simulation of fbg for oil and gas based sensing

8/10/2019 Modelling and Simulation of FBG for oil and gas based sensing

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Modelling and Simulation of Fiber Bragg Grating Characterizationfor Oil and Gas Sensing Applications

Solomon Udoh, James Njuguma, Radhakrishna Prabhu

Institute for Innovation, Design and SustainabilityRobert Gordon University

Aberdeen, UKEmail: [email protected]

Abstract In this paper, modelling, simulation and charac-terization of optical bre Bragg grating (FBG) for maximumreectivity for oil and gas sensing applications are presented.The bre grating length and the refractive index prole are keyparameters for effective and high performance optical Bragggrating. The spectral reectivity, bandwidth and sidelobes wereanalysed with changes in grating length and refractive index.Modelling and simulation of the Bragg grating which are basedon solving the Coupled Mode Theory (CMT) equation by usingthe transfer matrix method were carried out using MATLABand the results show that the changes in grating length andrefractive index prole affect the bandwidth as the demand forbandwidth and high-speed transmission grows in oil and gassensing applications.

Keywords Fiber Bragg grating (FBG); Reectivity; Coupled Mode Theory (CMT); Transfer Matrix Method

I. INTRODUCTION

Fiber Bragg grating (FBG) as an important sensing el-ement for measuring multi-parameters measurands such asstrain, temperature, pressure and ow has been extensivelystudied over the past 20 years [1]. FBG has its origin fromthe discovery of the photosensitivity of germanium-dopedsilica ber by Hill et al in 1978 [2, 3]. In 1989, Meltz et al[4] further demonstrated that a permanent refractive indexchange occurred when a germanium-doped ber is exposedto direct single photon ultraviolet (UV) light.

FBG is the periodic perturbation of the refractive indexalong the optical bre length which is formed by exposingthe core of the optical bre to a periodic pattern of intenseUV light [5]. This exposure introduces a permanent changeto the refractive index of the core of the bre. At certain

wavelengths, the constructive interference of the reectedband results in a band rejection which is known as the Braggwavelength [6]. The Bragg wavelength is dependent on therefractive index and the grating period, so any changes onthe physical structure on any of these will cause a shifton the Bragg wavelength. This makes the above mentionedparameters to be sensed using the FBG. On this basis, howkey parameters affect the quality of the rejected band in FBGis presented.

FBG has been successfully applied in diverse range of

areas which include structural health monitoring, telecom-munications and chemical sensing [7-11]. For the past 30years, the oil and gas industry has relied on the use of electronic retrievable sensors that are driven down into thewellbore or reservoir for measurement of key parameterssuch as temperature, pressure, ow and vibration. Unfor-tunately, these electronic systems suffer huge limitationssuch as drastic reduction in reliability, corrosion of electricalparts and susceptibility to electromagnetic interference whenused in harsh extreme conditions. Also, the huge number of electronic sensors make the downhole sensing and monitor-ing application very challenging and complex [12-14]. Tooptimize the recovery or production efciency of oil andgas, the industry is gearing towards the implementation of intelligent well and hence there is a need for more sensorycapabilities in the wellbore.

The FBG technology is now gaining wide applicationin oil and gas sensing due the numerous advantages overthe electronic sensors which are: electrically passive de-vice (no downhole electronics), intrinsically safe (does notcause explosion when used in harsh environments), highsensitivity, immune to electromagnetic interference (as thereare no electrical current owing at the sensing point),suitable for high temperature operation, distributed sensingcapabilities and their relatively small size and light weight[15, 16]. The FGB also have a distinctive advantage overother optical bre congurations due to its multiplexingcapability that allows a single bre optic cable with tensof gratings to measure a large range of parameters in oiland gas production not limited to downhole productionmonitoring but also for downstream process monitoring,

platform structural monitoring and pipeline monitoring usingwavelength division multiplexing (WDM) technique [17].FBG are generalised distributed reectors whose char-

acteristic are wavelength-dependent that can accurately beadjusted by proper design. One important feature of the FBGis the relative narrow bandwidth of the reection spectrum[18]. However, some certain applications such as seismicsensing in the oil and gas industry need large bandwidth[19]. In this paper, using the CMT, a short grating lengthis needed to achieve a large bandwidth and it was also


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found that the refractive index change will also affect thebandwidth.

I I . P ROPERTIES AND P RINCIPLES OF FGB S ENSING

The refractive index prole, grating length and the grat-ing strength are basically the three qualities that control

the properties of FBG. And the properties that need tobe control in an FBG are reectivity, bandwidth and thesidelobe strength. Parameters like strain, temperature andpressure simultaneously act on FBG sensor [20]. The Braggwavelength of the FBG will vary with changes in any of these parameters experienced by the bre optic sensor andthe corresponding wavelength shifts are as follows:

A. Strain

The shift in Bragg wavelength due to the applied longi-tudinal strain B | S is given by [20]

B | S = B (1 P e )z (1)where B is the Bragg wavelength, z is the applied strainalong the longitudinal axis and P e is an effective strain-opticconstant dened as

P e = n2 eff

2 [P 12 (P 11 + P 12 )] (2)

P 11 and P 12 are the components of the ber optic straintensor also known as the Pockels constants of the ber, de-termined experimentally [21], neff is the effective refractiveindex and is the Poissons ratio.

B. Temperature

The shift in Bragg wavelength B | T as a result of tem-perature changes T is described by [20]

B | T = B ( + ) T (3)

= 1

( T

) (4)

= 1n ef f

(n eff

T ) (5)

where T is the change in temperature, is the gratingperiod, is the thermal expansion coefcient for the berand is the thermo-optic coefcient.

C. PressureThe shift in Bragg wavelength B | P as a result of pressure

changes P is described by [20, 22]

P = B [(1 2)

E +

n 2 eff 2E

(1 2)(2P 12 + P 11 )] P (6)

where E is the Youngs modulus of the bre. Equation 6shows the wavelength shift and is directly proportional tothe pressure change P .

III . M ODELS OF FBG

A. Coupled Mode Theory (CMT)

To model the FBG, the CMT will be considered since it isone of the best tools in understanding the optical propertiesof gratings. The CMT is a powerful mathematical tool toanalyze the wave propagation and interactions with materialsin optical waveguide. The CMT sees the grating structure asperturbation to an optical waveguide [23]. CMT have beenused to successfully model numerous bre grating structuresand the results show excellent match with experimentalworks. The fabrication of FBG results in a perturbationon the effective refractive index nef f of the guided modeswhich is given by [6]

n ef f (z) = n ef f (z){1 + cos[2

z + (z)]} (7)where n eff is the dc index change, is the fringevisibility of the index change, is the grating period and(z) denotes the grating chirp. For a single mode FBG, thesimplied coupled mode equations are given as [6]

dRdz

= iR (z) + iS (z) (8)

dS dz

= iS (z) iR(z) (9)where R(z) and S (z) are the amplitudes of forward-propagating and backward-propagating modes respectively. is the ac coupling and is the general dc couplingcoefcient. They are dened as

= +

1

2

d

dz (10)

= =

n ef f (11)

The detuning and in Equation 10 are dened as

=

= 2n (1

1D

) (12)

= 2

n ef f (13)

For a uniform FBG, in which is the mode propagationconstant, neff is a constant and the grating chirp ddz = 0 ,and thus , and in Equations 10, 11 and 13 are con-stants. By specifying the appropriate boundary conditions,the analytical expression of the reectivity is obtained as[6]

r = sinh2 ( 2 L )

cosh2 ( 2 L ) 2 2

(14)

The transfer matrix method is applied to solve the coupledmode theory equations and to obtain the spectral response of FBG. The FBG with grating length L is divided into sections


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Figure 1. The transfer matrix method applied to obtain the spectralcharacteristics of a FBG.

of M as shown in Figure 1 and the larger the number of M , the more accurate this method is. During design, careshould be taken not to make M arbitrary too large as thecoupled mode theory is difcult to implement for a uniformgrating section with just few periods long [24].

The amplitude of the forward-propagation mode andthe backward-propagation mode before and after the ithuniform sections are represented in a matrix of the form F i

as;

R iS i

= F iR i 1S i 1

= F 11 F 12F 21 F 22R i 1S i 1

(15)

where Ri and S i are the amplitudes of the forward-propagation mode and backward-propagation mode after thei th uniform sections and R i 1 and S i 1 are the amplitudesof the forward-propagation mode and backward-propagationmode before the ith uniform sections. The elements in thetransfer matrix are represented as;

F 11 = F 22 = cosh( B z) i B

sinh ( B z) (16)

F 11 = F 22 = i B

sinh ( B z) (17)

where z is the length of the ith uniform section, B = 2 is the imaginary part for which || > [6] , and* represent the complex conjugate. The output amplitudeare obtained by multiplying all the matrices for individualsections as

RM S M

= F R 0S 0 (18)

where F = F M .F M 1 ...F 1 .The output amplitudes for the non-uniform FBG are ob-

tained by applying the boundary conditions, R0 = R(L) = 1and S 0 = S (L) = 0 . The amplitude reection coefcient = RM /S M , and the power reection r = ||

2 arecalculated by the transfer matrix method.

IV. R ESULTS AND A NALYSIS

The spectral response of a uniform FBG is obtained,the simulation was carried out using MATLAB and theparameters of the uniform FBG used for the simulation arelisted in Table 1.

TABLE IS IMULATION PARAMETERS OF FBG

Parameters Symbols ValuesEffective refractive index n ef f 1.447Grating length changes L 1 - 8 mm

Bragg wavelength B 1550 nmChange in refractive index n 0.0005 - 0.002

Grating period 535.59 nm

A. Spectral reectivity dependence on grating length

The spectral response of a uniform FBG is affected asthe length of the grating is altered by external perturbationsuch as strain, temperature and pressure. The dependencyof spectral reectivity on different grating lengths wereobserved and analysed by varying the grating length from1 10 mm . Figure 2 shows the simulated results of thereectivity as a function of wavelength for different lengthsof the grating. Clearly from the graphs, the reectivity of theuniform FBG increases with increase in the grating length.When the grating length L = 1 mm , 2 mm , 3 mm , 4 mmand 5 mm the maximum reectivity is 58.83%, 93.28%,99.09%, 99.88% and 99.98% respectively. At L = 6 mm ,the reectivity reaches 100%. When the grating length isincreased further to L = 10 mm , it is observed that themaximum reectivity maintains at 100%.

Figure 3 shows a linear relationship between the changein grating length and the shift in centre wavelength. It isobserved from the graph, as the grating length changes, thereis a corresponding shift in the centre wavelength.

B. Spectral Reectivity Dependence on Refractive Index

Figure 4 shows the results of the simulation of a uniformFBG with grating length of L = 1 mm as the changein refractive index is varied from n = 0 .0005 0.002.For grating with refractive index of n = 0 .0005, 0.0006,0.0007, 0.0008, 0.0009 and 0.001 the maximum reectivityis 58.83%, 70.28%, 79.07%, 85.51%, 90.09% and 99.01%

respectively. 100% maximum reectivity was achieved at n = 0 .002 and maintains this value when the refractiveindex is further increased. Figure 5 shows the linear rela-tionship between the refractive index change and the shiftin centre wavelength. As the change in refractive indexincreases, there is a corresponding increase in the centrewavelength which is in agreement with the ndings of Sunita and Mishra [25]. The shifts in centre wavelength isused for calculating the external perturbations like strain,temperature, pressure etc.


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Figure 2. Spectral reectivity characteristics of FBG for different gratinglengths 1 - 8 mm from a to h

Figure 3. Effect of grating length on FBG

C. Bandwidth dependence on grating length and refractiveindex

The dependence of bandwidth on grating length wasobserved and analysed, the bandwidth values of a FBG withdifferent grating lengths were calculated from Figure 2 andplotted in Figure 6. It can be observed that the bandwidthreduces with increase in grating length but increases withincrease in change in refractive index of a FBG.

Figure 4. Spectral reectivity characteristics of FBG for different refractiveindex change 0 . 0005 0 . 003 from a to h

Figure 5. Effect of refractive index change on centre wavelength

In Figure 6, it can be seen that when the grating lengthis 5 mm with a refractive index change of 0.0005 thebandwidth is 0.6 nm . As the grating length reduces to 2mm , the bandwidth increases to 0.75 nm . Theoretically,larger bandwidth of a FBG can be achieved with smallergrating length. Thus, for a strong grating with a largebandwidth to be achieved, the grating length has to be smalland the refractive index change must be large. However,for a strong grating with smaller bandwidth, the grating


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[25] S. P. Ugale and V. Mishra, Optimization of ber Bragg grating length for maximum reectivity, in Communications and Signal Processing(ICCSP), 2011 International Conference on, 2011, pp. 28-32.

[26] J. Albert, K. O. Hill, B. Malo, S. Theriault, F. Bilodeau, D. C. Johnson,and L. E. Erickson, Apodisation of the spectral response of bre Bragg gratings using a phase mask with variable diffraction efciency,Electronics Letters, vol. 31, pp. 222-223, 1995.

modelling and simulation of fbg for oil and gas based sensing

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