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Sensors and Actuators A 111 (2004) 154–165 New distributed optical sensor for detection and localization of liquid hydrocarbons Part II: Optimization of the elastomer performance Mónica Mendoza, Antonio Carrillo, Alfredo Márquez Centro de Investigación en Materiales Avanzados, Miguel de Cervantes #120, Complejo Industrial Chihuahua, Chihuahua, Chih. 31109, Mexico Received 20 March 2003; received in revised form 7 October 2003; accepted 31 October 2003 Abstract This paper reports the second part of a work that introduces and describes the testing of a new optical distributed sensor. This new sensor is capable of detecting and locating liquid hydrocarbon leaks on long pipelines. In the first part of this work a number of advantages of this new design were presented. The present part deals specifically with the influence of elastomer preparation on the performance of this sensor, and in a more general way, with the performance of any distributed optical sensor based on optical fiber bending by a swelled elastomer. The results show that the optimal sensor response is obtained when the osmotic pressure developed by the elastomer due to hydrocarbon absorption and the swelling of the elastomer are balanced. Therefore, by modifying the cross-linking density of the elastomer, it is possible to optimize the sensor performance, by finding the condition where the pressure against the fiber is large enough to surpass the resistance of the optical fiber to be bended and, at the same time, the elastomer absorbs enough solvent to bend the fiber at an optimum level. © 2003 Elsevier B.V. All rights reserved. Keywords: Distributed leakage sensors; Optical fiber bending; Polymer swelling 1. Introduction One of the currently relevant areas of application for optical sensors is the fast detection and exact location of hydrocarbon leakages in storage tanks and pipelines. Based on optical fibers, different optical sensors have been developed to detect liquid leaks, which may be grouped as sensors where the optical fiber interacts directly [1–5] or indirectly [6–19] with the spilled liquid. In a previous work, [20] a new design of an optical distributed sensor was introduced and its main characteristics described. The present design is a modification of the bending distributed sensors that work by means of an optical fiber attached to an elastomeric cable through a helicoidal wire [15–17]. This type of sensors work in the following way: when a liq- uid or gas compatible with the elastomer comes in contact with the sensor, the elastomer absorbs the liquid and swells compressing the optical fiber against a helicoidal wire. The previous phenomena produce a sinusoidal bending of the fiber, thus generating the attenuation of an optical signal Corresponding author. Tel.: +6-14-4391133; fax: +6-14-4391112. E-mail address: [email protected] (A. M´ arquez). traveling through the fiber. The signal attenuation allows the detection of a specific liquid in contact with the sensor, and, in turn, the reflection of the same signal allows pinpointing this event. The new design (see Fig. 1) has several advan- tages over its predecessors: the swelling of the elastomeric cable is conducted in a preferential direction allowing that the osmotic pressure concentrates towards to the optical fiber, improving its response speed. Furthermore, the fiber is positioned in a channel eccentrically located within the elastomer cable. In this way, the optical fiber is protected from the environment thus making an external coating layer or jacket unnecessary. Of greater importance, the fiber is free of stress and deformation produced by the contact with other sensor parts (particularly with the helicoidal wire). These characteristics reduce the initial losses and permit to have a longer range of detection. This sensor uses an optical fiber, which is connected to an optical time domain reflec- tometer (OTDR) and a PC with an acquisition data system. In the first part of this work [20], we have studied the influence of the thread spacing of the helicoidal wire on the optical fiber bending and consequently on the response of this new sensor. Also, in that paper the effect of the elastomer aromaticity and a test of the sensor response to a number of organic solvents (hexane, THF, benzene, ethylic 0924-4247/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2003.10.061

New distributed optical sensor for detection and localization of liquid hydrocarbons: Part II: Optimization of the elastomer performance

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Page 1: New distributed optical sensor for detection and localization of liquid hydrocarbons: Part II: Optimization of the elastomer performance

Sensors and Actuators A 111 (2004) 154–165

New distributed optical sensor for detection andlocalization of liquid hydrocarbons

Part II: Optimization of the elastomer performanceMónica Mendoza, Antonio Carrillo, Alfredo Márquez∗

Centro de Investigación en Materiales Avanzados, Miguel de Cervantes #120, Complejo Industrial Chihuahua,Chihuahua, Chih. 31109, Mexico

Received 20 March 2003; received in revised form 7 October 2003; accepted 31 October 2003

Abstract

This paper reports the second part of a work that introduces and describes the testing of a new optical distributed sensor. This new sensoris capable of detecting and locating liquid hydrocarbon leaks on long pipelines. In the first part of this work a number of advantages of thisnew design were presented. The present part deals specifically with the influence of elastomer preparation on the performance of this sensor,and in a more general way, with the performance of any distributed optical sensor based on optical fiber bending by a swelled elastomer.The results show that the optimal sensor response is obtained when the osmotic pressure developed by the elastomer due to hydrocarbonabsorption and the swelling of the elastomer are balanced. Therefore, by modifying the cross-linking density of the elastomer, it is possibleto optimize the sensor performance, by finding the condition where the pressure against the fiber is large enough to surpass the resistanceof the optical fiber to be bended and, at the same time, the elastomer absorbs enough solvent to bend the fiber at an optimum level.© 2003 Elsevier B.V. All rights reserved.

Keywords: Distributed leakage sensors; Optical fiber bending; Polymer swelling

1. Introduction

One of the currently relevant areas of application foroptical sensors is the fast detection and exact locationof hydrocarbon leakages in storage tanks and pipelines.Based on optical fibers, different optical sensors have beendeveloped to detect liquid leaks, which may be groupedas sensors where the optical fiber interacts directly[1–5]or indirectly [6–19] with the spilled liquid. In a previouswork, [20] a new design of an optical distributed sensorwas introduced and its main characteristics described. Thepresent design is a modification of the bending distributedsensors that work by means of an optical fiber attachedto an elastomeric cable through a helicoidal wire[15–17].This type of sensors work in the following way: when a liq-uid or gas compatible with the elastomer comes in contactwith the sensor, the elastomer absorbs the liquid and swellscompressing the optical fiber against a helicoidal wire. Theprevious phenomena produce a sinusoidal bending of thefiber, thus generating the attenuation of an optical signal

∗ Corresponding author. Tel.:+6-14-4391133; fax:+6-14-4391112.E-mail address: [email protected] (A. Marquez).

traveling through the fiber. The signal attenuation allows thedetection of a specific liquid in contact with the sensor, and,in turn, the reflection of the same signal allows pinpointingthis event. The new design (seeFig. 1) has several advan-tages over its predecessors: the swelling of the elastomericcable is conducted in a preferential direction allowing thatthe osmotic pressure concentrates towards to the opticalfiber, improving its response speed. Furthermore, the fiberis positioned in a channel eccentrically located within theelastomer cable. In this way, the optical fiber is protectedfrom the environment thus making an external coating layeror jacket unnecessary. Of greater importance, the fiber isfree of stress and deformation produced by the contact withother sensor parts (particularly with the helicoidal wire).These characteristics reduce the initial losses and permit tohave a longer range of detection. This sensor uses an opticalfiber, which is connected to an optical time domain reflec-tometer (OTDR) and a PC with an acquisition data system.

In the first part of this work[20], we have studied theinfluence of the thread spacing of the helicoidal wire onthe optical fiber bending and consequently on the responseof this new sensor. Also, in that paper the effect of theelastomer aromaticity and a test of the sensor response to anumber of organic solvents (hexane, THF, benzene, ethylic

0924-4247/$ – see front matter © 2003 Elsevier B.V. All rights reserved.doi:10.1016/j.sna.2003.10.061

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Fig. 1. Sensor model.

ether, etc.) at different temperatures were evaluated. Thepresent work deals with the influence on the performance ofthe same sensor due to the elastomer cross-linking densityand additives content. It is important to stress that theseparameters are not only valid for our design but also forother sensors that use the same principle.

In this type of sensors, the main force to bend the fiber isthe osmotic pressure produced into the elastomer by the ab-sorption of the liquid. The magnitude of this pressure is dic-tated by the interaction constantχ12 of the elastomer-solventsystem as well as the cross-linking density of elastomermolecules (ρc-l ). The first parameter is inherent to the typeof polymer chosen and cannot be modified during the pro-cess. In contrast, the cross-linking density could be changedduring the sensor manufacture process. At this respect, itis important to mention that a high cross-linking density(reticulation density) diminishes significantly the absorptioncapacity of the elastomer but also increases its mechanicalproperties and its osmotic pressure. This last pressure isused in the sensor to exert a force to bend the fiber. Thefiber bending is dependent of its mechanical properties,the osmotic pressure of the elastomer and the thread spac-ing of the helicoidal wire. When the elastomer has a highcross-linking density it does not swell enough to bend thefiber, because the polymeric chains are too close betweenthem and do not permit a large absorption of solvent insidethe elastomer. In contrast, a low reticulation density pro-motes a larger swelling of the elastomer, but the osmoticpressure remains at a very low level because the polymerchains are rarely bonded producing an insufficient osmoticpressure to bend the fiber. Also, the elastomer could remainso soft that instead to deform the fiber it circumvents thisone diminishing the effective pressure exerted against it.

Concerning the role of the additives, it is important tomention that an elastomer is rarely processed in its originalstate; normally, some processing aids are used as plasticiz-ers, lubricants, antioxidants, etc. These substances allow aconvenient flow during the processing and reduce the ma-terial degradation. However, these additives may also havean influence on the behavior of the sensor. This influence isspecially considered in the present study.

2. Experimental

The basic design of the sensor is shown inFig. 1. The sen-sor is formed by an elastomeric cable reinforced by a steelwire of 1900±15�m in diameter. An optical fiber is placedinto the cable at 1500±5�m of its center. The hole diameteris 250± 2�m. The characteristics of the optical fiber usedare reported inTable 1. In the opposite side of the opticalfiber aluminum mesh is also placed. Finally, a stainless steelwire of 370.0± 5.0�m in diameter is coiled at the exterior

Table 1Optical fiber characteristics

Optical fiber Newport F-MLD

Operating wavelength 850/1300 nm.Index profile GradedNA 0.29Core refraction index 1.46Core diameter 100± 4�mCladding diameter 140± 15�mCoating diameter 200± 15�mAttenuation 850/1300 nm 4.0/1.5 dB/kmBandwidth 850/1300 nm 100/100 MHz/km

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Table 2Poly-butadiene characteristics

Polybutadiene solprene 200

Type Mediumcis partiallybranched

Mooney viscosity Mll+ 4 (100◦C) 49Voltatile matter 0.75Tg (◦C) −9.2Ash content (% maximum) 0.2Organic acid 0.03Free soap (% maximum) 0.03Specific gravity 0.90Antioxidant (%) 0.6

of the cable. The experimental prototypes were designedto detect gasoline leaks; therefore, a low polarity elastomerwas chosen for this study. A ramified Polybutadiene (BR),commercialized by “Negromex S.A.”, as Solprene-200, waschosen for this purpose. The main characteristics of thisrubber are reported inTable 2. A dicumyl peroxide (DCP),provided by Vanderbilt Inc., was employed to reticulate theBR. Five different concentrations of DCP were used: 0.05,0.1, 0.15, 0.2 and 0.25% (w/w). Three different series offormulations were prepared: the first without additives, thesecond has two plasticizers; stearic acid (2% (w/w)) andcalcium stearate (4% (w/w)), and the third has the sameproportion of plasticizers that the previous one plus 5%(w/w) of naftenic oil.Table 3resumes the composition ofeach formulation. In order to manufacture the sensor, aBrabender single-screw laboratory extruder was employedusing a coating die with a mouth of 5.0 mm in diameter.This die was specially designed to deposit eccentrically anoptical fiber into the sensor and to coat a reinforcementsteel wire as depicted inFig. 1. A sensor of approximately6.0 mm in diameter was obtained, with the optical fiber andreinforcement wire already integrated. In order to achievethe cross-linking reaction, the cable was heated at 175◦Cduring 20 min in a forced-convection stove.

In order to assess the optimal thread spacing of the ex-ternal wire of the sensor, we simulated the fiber deforma-tion into the sensor using a lab jack. The experimental set isshown inFig. 2. In this set the optical fiber is connected to aTektronix OTDR model TPF2A. The wavelength of the sig-nal used was 850 nm. An indicator of stage was employed tomeasure the displacement of the lab jack. The copper wiresshown in the figure were disposed in various intervals from6.0 to 10.0 mm.

Table 3Additive contents for each series

Additive PHR

Series 1 Series 2 Series 3

Stearic acid 0 2 2Calcium stearate 0 4 4Naftenic oil 0 0 5

Fig. 2. Lab jack used to bend the optical fiber.

Furthermore, forty-five sensor samples of 300.0 m werefabricated using cables prepared with previous formulations(three samples for each formulation). The samples weretested by direct immersion in gasoline at room temperature.The test zone was 30.0 cm long and was always located at adistance of 150.0 m from the beginning of the sensor. Eachtest was stopped after 60 min of immersion. The gasolineemployed was provided by PEMEX S.A., which commer-cializes it under the name of “Magna”.

Moreover, small portions of samples of 10.0 mm longproduced with each formulation were swelled with hexaneto evaluate their cross-linking density. These last mea-sures were performed employing hexane, because thereis no information about the interaction parameterχ12 ofgasoline and the elastomer. The hexane was provided byAldrich Inc.. The swelling evaluation was performed usinga thermo-mechanical analyzer (TMA), from TA Instruments(model 2940). Each test was carried out for 48 h.

Finally, the resistance of the sensor to weather conditionswas evaluated employing an accelerated weathering cham-ber, QUV/ITSELF Q-panel, from “Lab Products”. The testcycle conditions were: (1) Exposition to radiation ultravi-olet for 6 h to a temperature of 50◦C with an intensity of0.63 W/m2/nm, and (2) a cycle of condensed of 4 h of du-ration to a temperature of 50◦C. The type of lamp utilizedwas UV-B-313 B with a wavelength interval from 315 to290 nm.

3. Evaluation of the osmotic pressure

The effect of the cross-linking density over the osmoticpressure and equilibrium swelling of a gel has been ap-proximately described by Flory and coworkers[21,22].These models establish that the osmotic pressure (π) of aswelled gel is approximately evaluated by the followingexpression:

π = k T Nv(φ1/3 − aφ/2) (1)

wherek is the Boltzmann constant,T the temperature in◦K,φ the equilibrium swelling (V0/Vf ) which is defined as therelation between the elastomer original volume (V0) and theswelled one (Vf ), Nv is the number of elementary chains ina unit cube. Finallya is a constant, that in the present workwill be taken as 2. Furthermore, we have considered that the

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cross-linking density could be evaluated as:

ρc-l = M0

Mc= NvM0

Navρ(2)

whereM0 is the molecular weight per structural unit,Mc themolecular weight per cross-linked unit,Nav the Avogadronumber andρ is the elastomer density.

The osmotic pressure has the following dependence to thecross-linking density:

π = ρc-l(kTρ Nav)(φ1/3 − aφ/2)

M0(3)

From the previous expression is evident that for a specificvalue ofφ andT, the osmotic pressure increases whenρc-laugments.

Furthermore, the equilibrium swelling may be evaluatedwith the following expression:[

ln(1 − φ) + φ + χ12φ]

V1(φ1/3 − aφ/2)

]= −ρc-l

(kT Navρ

RM0

)(4)

whereV1 is the solvent molar volume andR is the ideal gasconstant. A numerical evaluation of the previous expressionshows that when the cross-linking densityρc-l increases, theequilibrium swelling diminishes. This suggest that it mustbe an optimal cross-linking density that produces the largerswelling possible but maintaining a pressure high enough tobend the optical fiber at the best possible level.

4. Results

Figs. 3 and 4illustrate the attenuation of the optical fiberinto the sensor when is bended with the lab jack. InFig. 3two lineal regions are observed, with a slope change at adisplacement of 1.5 mm. InFig. 4, it is observed that the

Fig. 3. Optical fiber attenuation vs. lab jack displacement using different wire spacing.

wire interval that causes the largest attenuation is 7.0 mm.This last result agrees very satisfactorily with those reportedpreviously employing multi-mode optical fibers[20,26–28].Indeed, the results of Fields et al.[26,27], show a very impor-tant maximum at short intervals (approximately of 1.5 mm)and one smaller at intervals around 5.0 mm. Also, in our pre-vious results using a similar fiber[20], we found this secondmaximum situated at an interval close to 7.0 mm. However,it is important to mention that the previous results differ fromthe tests performed on single-mode optical fibers where nomaximum is observed when the bend period is increased[25].

Concerning the results of Fields et al.[26,27], it is appar-ent that obtaining the maximum fiber attenuation at shortbending intervals (∼1.5 mm) would be optimal for our pur-poses. Unfortunately, the pressure necessary to bend thefiber at very short radius of curvature is beyond of the levelprovided by the osmotic pressure of our swelled elastomers.Therefore, we have chosen to coil the external wire of thesensor with a thread spacing of 7.0 mm (seeFig. 1).

Fig. 5 illustrates the variation in diameter of the extrudedsamples as a function of the percentage of DCP. It is notedthat even though the die mouth have 5 mm in diameter, thefinal cable diameters are around 6 mm. This swelling processis due to the visco-elastic nature of the elastomer used. Also,it is interesting to note that the diameters of the series 1 and3 show a random behavior while the diameter of the series2 seems to go wider with the content of DCP.

Fig. 6shows the swelling of samples after to be submergedin gasoline during 24 h. As expected, the swelling of all thesamples diminishes when the DCP content increases. Thisis due to the reticulation increase and the consequent de-crease of the intermolecular space to accommodate the sol-vent. Maximum swellings (Vf /V0) of 11 and 10 are attainedby sample of series 2 and 3, respectively, with a 0.05% (w/w)

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Fig. 4. Optical fiber attenuation vs. wire spacing at different lab jack displacements.

of DCP content, while the samples of series 1 have a max-imum of 5.5. It is apparent that the additives integrated toseries 2 and 3 interact with the cross-linking agents impair-ing their effect, while the samples of series 1 were more ef-ficiently reticulated. However, when the percentage of DCPrises to 0.25% (w/w), the series present approximately thesame swelling level, situated around 4.0.

The results of the swelling with hexane are reported inFig. 7. It is noted that the sample swelling diminishes bya half with this solvent in comparison to gasoline. Usingthe previous data, and a value forχ12 of 0.54 [23], thecross-linking density was calculated employingEq. (2). Theresults are plotted inFig. 8. The cross-linked densities mea-sured vary from 0.1×10−2 to 3.5×10−2, and, as expected,their value increases conforming the content of DCP raises.

Fig. 5. Sensor diameter after extrusion.

It is important to observe that the error bars of the previouscurves are broader than those corresponding toFig. 7. Thisis because the evaluation of the cross-linking density fromEq. (4) is very sensitive to the measured error of swelling.

Fig. 9shows a sensor sample (where the aluminum meshwas removed to improve the view of the fiber position). InFig. 9a the original sensor is shown, while inFig. 9b itis observed after 20 min of direct submersion in gasoline.In the first photograph, a very light bending of the opticalfiber is observed inside the sensor, which produces a smallinitial attenuation, while inFig. 9b it is observed how theoptical fiber bends at the area directly below of the helicoidalwire, maintaining practically its form through the sectionbetween each wire pitch. It is important to mention thatwithout a mesh the attenuation diminishes almost a half.

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M. Mendoza et al. / Sensors and Actuators A 111 (2004) 154–165 159

Fig. 6. Swelling (Vf /V0) of samples submerged in gasoline.

Therefore, the optical fiber bending of the following resultsmust be more important that that observed in the presentfigure.

Figs. 10–12show the attenuation in the optical fiber dueto sensor swelling by gasoline as a function of the DCPcontent, at different immersion times. In all the cases, it isobserved the existence of an optimal reticulation level forwhich the response is the fastest. The percentage of DCP forwhich the attenuation has a maximum is roughly of 0.15%(w/w) for series 1 and 2, and of 0.20 for series 2.

Significant differences between the attenuation obtainedby each series are apparent. Indeed, after 60 min of immer-sion, the maximum attenuation of series 1 is 2.5 dB, while

Fig. 7. Swelling (Vf /V0) of samples submerged in hexane.

it is 1.7 dB for series 2, and 1.4 dB for series 3. It is notedthat the first series are the best. However, it is also the mostdifficult to manufacture. Moreover, it is interesting to ob-serve, in all the curves, that the attenuation evolution is nogradual but grows more rapidly in the last 30 min. This lastpoint agrees with the results reported inFig. 3, where af-ter a threshold, the fiber attenuation is more sensitive to thebending level. Apparently, this threshold is obtained after30 min of swelling.

Finally, as previously mentioned the sensor was submit-ted to an accelerated weathering test. After this test no ap-preciable degradation was observed in the fiber or polymer,only the helicoidal steel wire was deteriorated, therefore it

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Fig. 8. Cross-linking density as a function of the dicumyl peroxide (DCP) content.

Fig. 9. Photographs of the sensor before and after to immersion in gasoline; (a) Original state, (b) after 20 min of immersion.

is recommended to use a nylon fiber instead of a steel wirefor industrial applications of this sensor.

5. Discussion

The performance of this type of sensors depends of anumber of factors, such as its geometry, the kind of opti-

cal fiber (multi or single mode), the wavelength of the opti-cal signal, the wire pitch, the elastomer characteristics, etc.Of all these factors, perhaps the less studied is the elas-tomer (or more generally the polymer). Indeed, in almost allworks related to this subject, the authors only mention thepolymers used but no reference are made about their mor-phologies. In the present work, we stressed the importanceof this factor, which is determinant for an optimal perfor-

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Fig. 10. Attenuation of sensors of series 1; after 15, 30 and 60 min of immersion in gasoline.

mance of this type of sensors, and in particular, its level ofreticulation.

There are a number of different ways to reticulate anelastomer. Reticulation could be done by physical means(for example irradiating the elastomer with beta rays) orby chemical ones (for example using peroxides as the DCPemployed in this work). However, the fundamental struc-tural factor, as previously mentioned, is the cross-linkingdensityρc-l , obtained. This parameter tells us how muchan elastomer has been reticulated and it is independentof the method employed. Indeed polymers with the samecross-liking density have the same properties no matter if itwas physically irradiated or chemically treated. Therefore,

Fig. 11. Attenuation of sensors of series 2; after 15, 30 and 60 min of immersion in gasoline.

in order to explain the behavior of our elastomer we willemploy this density as the main variable in the subsequentgraphs.

Figs. 13–15, summarize the results on fiber attenuation,elastomer swelling (1/φ) and the corresponding osmoticpressure due to the absorption of gasoline as function of thereticulation densityρc-l . It is important to mention that theosmotic pressure was evaluated by employing the swellingand cross-linking values, reported in previous figures, andEq. (3).

The data corresponding to series 1 are plotted inFig. 13.A maximum attenuation is obtained for a reticulation den-sity (ρc-l ) of 2.1 × 10−2. It is interesting to note that, until

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Fig. 12. Attenuation of sensors of series 3; after 15, 30 and 60 min of immersion in gasoline.

this point, the attenuation rises when the osmotic pressureincreases; this is normal because at larger pressures the fiberbending is more important. However, at higher values ofρc-lthe elastomer swells less and then it fails to deform the fiber.Similar conclusions could be drawn from the subsequentFig. 14. It is interesting to observe that for the two first se-ries, the attenuation grows when osmotic pressure rises untilthat the swelling falls bellow a value of 4, and at this pointthe attenuation falls when the swelling diminishes. There-fore, under this threshold the increase in volume of the elas-tomer starts to be insufficient to bend the fiber at an optimallevel.

Fig. 13. Attenuation, swelling and osmotic pressure developed after 60 min of immersion in gasoline of the samples of series 1.

Similarly, for series 3 the decrease of the attenuation startswhen the swelling falls below a value of 6. It must be men-tioned, however, that the mineral oil introduced in series 3 isuseful to reduce the viscosity of the melt but also imparts ahigh flexibility to the solid elastomer. In the case of the lastsamples, a visual inspection of the bending process revealsthat the elastomer circumvents the optical fiber instead ofbending it, producing a lower response. Also, it is interest-ing to note that the samples of series 1 apparently keeps alarge attenuation on the optical fiber even when the swellingis low. The previous visual inspection also revealed that thesurface of the elastomer of this last series remains practically

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Fig. 14. Attenuation, swelling and osmotic pressure developed after 60 min of immersion in gasoline of the samples of series 2.

undeformed due to the rigidity imparted by the reticulation.Indeed, this could be evaluated by the increase of its elastic(E) and shear (G) modulus. This modulus varies with thecross-linking densityρc-l in the following way[24]:

E = 3ρc-lRTρ

M0; G = ρc-lRTρ

M0(5)

Therefore, it is normal that the samples with a large reticu-lation are also the ones that more efficiently bend the opticalfiber.

Considering all the previous points, it is apparent thatthese phenomena are dictated by the cross-linking density.Of course, the previous analysis is clearly qualitative, be-cause the actual pressure on the fiber depends on the equi-

Fig. 15. Attenuation, swelling and osmotic pressure developed after 60 min of immersion in gasoline of the samples of series 3.

librium of forces between the fiber and the elastomer, andthe larger portion of the deforming potential of the osmoticpressure is employed to deform the elastomer itself, spe-cially when it is highly reticulated. However, this analysisshows very well the leading mechanisms of the signal atten-uation into the sensor.

At the light of the previous results, it is observed that theformulation without additives (Series 1) is the one that bet-ter results provides, however it is very difficult to process.For example, the extrusion rate to obtain the sensor withthis formulation descends from 5 to 0.1 cm/s. Thus, this for-mulation is interesting as a maximum standard but not forcommercial proposes. Concerning the other two formula-tions, the best is probably the number 3 since it produces a

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Fig. 16. Attenuation of the optical fiber at different curvature radius, with different loops.

sensor more homogeneous and reliable. Of course, the bestformulation depends on the specific uses of this device, aswell as of its final design and geometry.

Moreover, to evaluate in a quantitative fashion the previ-ous phenomena, currently we are developing an algorithmwhich taking in consideration the interaction constantχ ofthe elastomer/liquid system and the geometry of the sen-sor, could predict the sensor performance on the basis ofthe elastomer cross-linking density. This algorithm will beproperly introduced in a subsequent paper.

Also, it is important to mention that the attenuation re-ported in the previous results is produced by the additionof all the contributions of fiber bends produced in the testarea, and not only by the first one. However, during ourtests unexpectedly a very small change in the attenuationwas observed when the length of the test zone was dimin-ished or increased by a factor of ten. Then only the firstbend produces the irradiation of modes inside the fiberthat provokes the attenuation of the optical signal at anspecific curvature radius, and the subsequent bending nolonger contributes in a significant way to this attenuation.To verify this observation, the optical fiber was coiled tosteel cylinders of specific diameters and the produced atten-uation was measured. The results are reported inFig. 16;for one, two and three loops of the optical fiber. It is notedthat the larger attenuation is obtained with three loops;however, the difference with the other curves is almostnegligible.

Finally, it is important to mention that using a thinnerelastomeric cable a more rapid response of the sensor isobserved, as shown by Culshaw et al.[2,3,15,16]. However,considering the heavy-duty conditions in the petroleum andoil industries, we have preferred to use a thicker cable eventhough a slower response is expected.

6. Conclusions

In the present study, the performance of distributed opti-cal sensors based on fiber bending by a swelled elastomerwas studied. More specifically, the influence of the elas-tomer micro-morphology on the sensor performance was ex-amined. It has been found that the sensor performance maybe optimized by finding the condition where the developedosmotic pressure is large enough to surpass the resistanceof the optical fiber to be bended, and where the elastomermay absorb enough solvent to bend the fiber at the levelrequired.

Acknowledgements

The authors are grateful to “Instituto Mexicano delPetroleo” by financial support under the grant No.FIES97-04-IV, and to “Consejo Nacional de Ciencia y Tec-nologıa” for the grant No. G25866-A. Also we acknowledgeto Prof. Daniel Glossman for useful advises, and M.Sc.Cesar Leyva and Dr. Citlalli Gaona for technical support.

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Biographies

Monica Mendoza received her BS in Chemical Engineering in 2002 fromInstituto Tecnológico de Chihuahua, México. Currently she is a researchassistant at CIMAV and her research interest area includes polymer pro-cessing and chemical sensors.

Antonio Carrillo received his BS in Mechanical Engineering in 1995from Instituto Tecnológico de Mérida, México, and his MS in Materi-als Science from the Centro de Investigación en Materiales Avanzados(CIMAV), México, in 2001. Currently he is at Akron University as a PhDstudent, and his research interest area includes polymer processing andchemical sensors.

Alfredo Márquez is the Head of the Engineering Division at the “Cen-tro de Investigación en Materiales Avanzados”, Chihuahua, México. Heobtained his PhD in Materials Science, from the “Institut National Poly-technique de Lorraine, France, in 1986. Professor A. Marquez joinedthe “Sherbrooke University” in 1986 and the Industrial Materials Re-search Institute Boucherville, Canada in 1988. In 1990 he returned toMéxico to join the “Conacyt Research System”. He is the author of fivepatents, 42 papers in journals and 49 papers in proceedings. His currentresearch interest is the development of chemical sensors for the petro-chemical industry. He is a member of the SPIE, the American ChemicalSociety, the Mexican Society of Physics and the Mexican Associationof Institutions for the Applied Research and Technological Development(ADIAT).