Leakage Detection in Buried Pipes by Electrical Resistance Imaging

Transcription

1 st World Congress on Industrial Process Toograp Buxto Greater Mancester, April -7, 999 Leakage Detection in Buried Pipes by Electrical Resistance Iaging Josep Jordana, Manel Gasulla and Raón Pallás-Areny Divisió d'instruentació i Bioenginyeria, Departaent d Enginyeria Electrònica Universitat Politècnica de Catalunya Jordi Girona -, Edifici C- 8 Barcelona, SPAIN Pone Fax E-ail: jordana@eel.upc.es Abstract: Tis work describes a non-invasive etod to detect leaks in buried pipes tat uses a surface linear electrode array perpendicular to te pipe axis. Two electrodes inject current and te reaining electrodes detect te drop in voltage. We ave used bot te dipole-dipole array and a odified Scluberger array. A single step reconstruction algorit based on te sensitivity teore yields D iages of te cross section. Te corresponding sensitivity atrices are ill posed. Neverteless, te reconstructed iages allow us to detect leaks witout needing any regularisation paraeter because it is possible to replace te inverse of te sensitivity atrix by teir transposed. A personal coputer controls current injectio electrode switcing and voltage detectio wic enables us to easily test different electrode arrays. Te syste as been first tested in te laboratory using a stainless steel tube iersed in water and covered by a rubber sleeve to siulate a non-conductive leak. By taking reference easureents wit te iersed bare pipe, it is possible to reconstruct iages sowing te siulated leak using 6 electrodes and even 8 electrodes onl toug wit reduced resolution. Field easureents ave involved siulated water leaks fro a plastic tube, 8 c in radius buried at about c dept in a far field. Te syste injected kh, V peak-to-peak square wavefors, tus avoiding electrode polarisation effects. Iages reconstructed fro an eigt electrode array sow te leak if te iage before te leak is used as reference. Keywords: Geoelectrics, resistance toograp leak detectio syncronous sapling.. INTRODUCTION Electrical resistivity surveying is a versatile prospecting etod applicable to groundwater locatio arcaeological evaluation and containant onitoring. It is a coon etod in sallow subsurface investigations, especially for groundwater studies []. Leak detection etods based on soil sapling and boreole toograpy are expensive. Hence, we are considering subsurface resistivity easureents to detect leakage fro buried pipes because tey do not need soil drilling. Toograpic iaging of geopysical data as becoe increasingly iportant because of te need for a ig-resolution approac to delineate buried structures, ainly in near-surface exploration. Resistance toograpy is gaining iportance as alternative to soil studies based on apparent resistivity curves. Tis advance is fueled by progress in instruentation and data processing. Electrical ipedance toograpy (EIT) ais to iage ipedance distribution in an object s cross section fro surface easureents. EIT arose in edical iaging but as found broader application in industrial processes. Dines and Lytle [] proposed EIT for geopysical applications. in inverse geopysical probles are not very sensitive to target paraeters. As a result, inverse geopysical probles are unstable, and two different targets can yield siilar easureents. Terefore, te ai is to find an approxiate solutio as close as possible to te actual situation. Regularisation tools elp in tose inversion probles. According to Tikonov and Goncarsky [], te efficiency in geopysical prospecting depends ore on te efficiency in data processing and interpretation tan on ore accurate instruentation. Resistive geoelectrical prospecting often uses stratified odels because any geopysical cross sections consist of oogeneous layers wit given resistivity and tickness []. 8

2 st World Congress on Industrial Process Toograp Buxto Greater Mancester, April -7, 999 In any toograpy syste an iage reconstruction algorit obtains iages fro te easured data. Tere are several D algorits able to iage underground resistivity distributions. Many of te derive fro EIT for edical applications [] [6]. Noel and Xu [7] proposed an algorit to iage sallow underground objects, applicable to arcaeology. Using atrices, an inverse proble can be described by d..., were [ ] t G = d () = d, d, d M is te data =,..., P is te paraeter vector (target), and G is te Jacobian atrix [8] or data Kernel, wose order is M P. Geopysical data inversion ais to estiate te paraeters of an eart odel fro a series of observations. Ofte tere is not a single solution and two or ore solutions fit te observations witin a given error argin. Geopysical odels consider several ground layers or strata, wose tickness and resistivity ust be deterined. Tere are several inversion tecniques tailored to tose odels, wic are based on fitting easured to teoretical apparent resistivity profiles []. Noel and Xu [7] iage twolayer distributions using a reconstruction algorit based on electrical resistivity toograpy (ERT). Solving () by te least-squares etod yields an estiate vector, [ ] t t t ( G G) G d = () est Tis solutio tered Gauss-Newton solution [8], suits equation systes tat are overdeterined, i.e., tere are ore observations tan paraeters in te odel (M > P). In order to acieve an acceptable solution using te leastsquares etod, underdeterined systes need additional (a priori) inforation [9]. Tis inversion proble is in trouble wen G t G is a singular atrix. G is an ill-conditioned atrix and tis copounds te proble because sall data variations affect iage reconstruction. Hence, easureent noise odifies odel paraeters according to G + ) = d + d ( () d cond ( G) () d were cond ( G) = µ µ N, and µ, µ N are, respectively te largest and te sallest eigenvalues of G. Fro (), te largest cond(g) is, te worst te influence of easureent noise on calculated odel paraeters. Lascaux and Teodor [] analyse atrix conditioning and solve different probles using te least-squares etod. In order to alleviate soe of te difficulties in inverting G t G, we solve an alternative proble using te least-squares etod. Many inverse probles are neiter copletely deterined nor copletely underdeterined. Teir solution can be ten written as [9] t t ( G G + I ) G d = λ () est Te daping factor λ attenuates te contribution of te underdeterined part to te solution. Tis etod, tered Marquardt- Levenverg [8] overcoes te difficulty in inverting G t G because λ prevents singularities by offsetting values in te diagonal of G t G, so tat any of te is ero. Loke and Torleif [] copare different iterative etods to invert geolectric data using te least-squares etod. Te Marquardt- Levenverg algorit yields a distorted solution wen tere are any paraeters. Furterore, te solution depends on λ. We are interested on reconstruction algorits tat do not need any regularisation paraeter and tat are not iterative, tus saving coputation tie.. IMAGING ALGORITHM Iaging subsurface resistivity distributions needs te placeent of a series of electrodes for current injection and voltage detection. Figure sows electrode placeent to iage successive vertical iage distributions. Electrodes A and B constitute injection pair and electrodes M and N are detection pair n. y x A B M N n l = l = l =N Te relative sensitivities of easured data and paraeter odels are related by te condition nuber of G, cond(g), [] according to Figure : Electrode arrangeent for iaging vertical, underground resistivity distributions. 9

3 st World Congress on Industrial Process Toograp Buxto Greater Mancester, April -7, 999 In order to solve te inverse proble in (), we need to know G, wic caracterises te ediu. G is tered sensitivity atrix because its coefficients result fro applying te sensitivity teore []. Te proposed algorit relies on te following assuptions: -Measured data is te real part of te ipedance. Hence, iages correspond to underground conductivity or resistivity distributions. -Electrode separation is unifor. -Te initial conductivity distribution is assued to be unifor. -Conductivity canges to be iaged are not very different fro te unifor distribution. Neverteless, te algorit can detect igcontrast anoalies. -Te region to iage is bidiensional. Practical situations do not et all te above assuptions. In edical applications, for exaple, te electrical conductivity in a cross section of te uan body is not unifor. Neverteless, several autors ave obtained useful iages [] [6]. We propose to use te algorit developed by Kotre [6] because it is fast and does not need any regularisation paraeter. According to [6] wen te resistivity canges, te cange in voltage corresponding to an injecting detecting electrode pair n as a function of te sensitivity coefficients obeys to V V V n ρ ρ S x y ρ = S x y ( ) (6) V are te easured voltages wen tere is te anoal V are te easured voltages for an oogeneous ediu and S is te sensitivity coefficient relating te easureent (n) to te position (). For several injecting detecting pairs, (6) leads to an equation syste relating sall conductivity canges to voltage canges easured on te surface. Te noralised resistivity is ten [] V V S n V ( n) P( ) = (7) S n Tis reconstruction etod approxiates te inverse sensitivity atrix by its transposed, wose values (reconstructed pixels) are ( ρ( ) ) ln( ρ ) P( ) ln = (8) were ρ is te reference resistivity (oogeneous ediu) and ρ( ) is te actual resistivity distributio sligtly different fro te oogeneous distribution. Soe experiental easureents later described involve ig-contrast objects, but te algorit detects te too. Te initial algorit was intended for edical applications involving a circular perieter []. Later, Kotre [] considered geolectric applications and te detection of abandoned land ines [6]. Tis reconstruction algorit yields blurred iages tat can be restored by a spatial frequency filter derived fro te algorit s pointspread-function (PSF). Iage restoration is particularly useful to iage strata parallel to te easureent surface []. Leak detectio owever, only needs to distinguis between iages sowing an intact pipe and iages sowing a leaking pipe. Tere is no need for neat iages, and experiental results witout any restoration filter are acceptable.. INSTRUMENTATION Figure sows te instruentation syste tat we ave designed for field easureents. A function generator (HPA) injects a kh, V peak-to-peak square wavefor. Syncronously sapling te flat one of square signals reduces interference [7]. Te voltage detector [8] ipleents syncronous deodulation using te floating capacitor tecnique [9]. A portable PC controls tis detector via te serial port (EIA). A Daqbook- plug-in card (Iotec) acquires te deodulated dc voltage. Te portable coputer also controls four switcing plug-in cards wit 8 relays eac tat allow us to ipleent any injection detection strategy using 8 electrodes []. HPA Syncronisation PARALLEL PORT LCUR HCUR P Switcing cards (x8 crosspoint array) 8 ELECTRODES a RS- LVOLT HVOLT PARALLEL PORT Vt P DAQBOOK- Ri t electrode P VOLTAGE DETECTOR Figure : Measureent syste for current injection and voltage detection.

4 st World Congress on Industrial Process Toograp Buxto Greater Mancester, April -7, 999. EXPERIMENTAL MEASUREMENTS Te reconstruction algorit as been first tested in te laboratory by iersing different objects into a c x c x c water tank. A non-conductive sleeve (rubber) around a cylindrical conductor siulates a leaking pipe []. Te cylinder radius was c and te iersion dept c. Gasulla et al. [] describe te easureent syste used in te laboratory. We ave considered two different electrode arrays: dipole dipole, including end electrodes, and a odified Scluberger array [], using 6 and 8 electrodes uniforly spaced along te sae distance ( c). Figure sows te reconstructed cylinder using 6 electrodes. Bot electrode arrays yield siilar iages, in spite of te larger nuber of independent easureents for te dipole dipole array () tan for te odified Scluberger array (9). easureent far fro te pipe. Neverteless, te uncertainty in electrode placeent yields large errors. Sánce [] as sown tat iages obtained fro voltage canges relative to a oogeneous ediu yield siilar iages. Using 8 electrodes instead of 6 electrodes yields lower-resolution iages. Neverteless, figures and 6 respectively sow tat it is possible to detect te pipe and te leak Figure : Reconstructed iages for a etal cylinder c in radius iersed c in water, fro voltages easured wit 8 electrodes spaced c using a) te dipole-dipole array and b) te odified Scluberger array Figure 6: Te reconstructed iages for te cylinder in figure cange wen a. c rubber sleeve covers te cylinder Figure : Reconstructed iage for a etal cylinder c in radius iersed c in water, fro voltages easured wit 6 electrodes spaced c using a) te dipole-dipole array and b) te odified Scluberger array. Figure sows te corresponding iages wen a rubber sleeve. tick covers te cylinder in figure. Iages worsen for deeper objects. Te algorit allows us to detect leaks fro pipes buried at four ties te inter-electrode distance approxiately []. We ave carried out field easureents at a far in Sta Eulàlia de Ronçana (Barcelona, Spain). We buried a PVC tube 6 c in lengt and 8 c in radius, at a c dept (figure 7). Te top soil was about c tick and rested on rocky layer sligtly tilted towards te west. 6 c N W E S c Figure : Te reconstructed iages for te cylinder in figure cange wen a. c rubber sleeve covers te cylinder. c c PVC TUBE ROCKY LAYER 8 c 8 c Figures and sow tat bot electrode arrays allow us to detect a siulated leak, even toug te odified Scluberger array places te anoaly (cylinder) closer to te surface and te dipole-dipole array places te anoaly deeper. Reference voltages in figure are tose leading to figure, i.e., correspond to a ediu tat includes te pipe. Tis resebles te actual situation because it is ipossible to obtain reference voltages corresponding to a ediu witout pipe ( oogeneous ediu). It would certainly be possible to take a reference Figure 7: Tube diensions and arrangeent for field easureents. Because te soil was extreely dr we watered a.9. area around te tube using about l/ (figure 8). A close area easuring. x. provided reference easureents. Tis reference area does not include any know object.

5 st World Congress on Industrial Process Toograp Buxto Greater Mancester, April -7, 999 HOMOGENOUS MEDIUM c c 9 c Figure : Ideal iages for te cross section in figure 9. a) Insulating object. b) Conductive object.. Results wit te odified Scluberger array c 6 c Figure 8: Top view of te tube placeent in te experiental field. Te circle next to te tube sows te site of te siulated leak. Te easureent syste was tat in figure using 8 stainless-steel electrodes c in lengt and c in diaeter inserted about c in te ground and spaced c. Figure 9 sows a vertical section across te tube and its position relative to te electrode array. Te section is divided in square pixels c in side. Te tube is under te fift electrode and belongs to two pixels. However, given tat ost of te tube falls inside te second row of pixels, te reference (ideal) iage is tat in figure, wic sows bot an insulating anoaly (PVC tube) and a conductive anoaly (water). Figure sows te detected voltages using te odified Scluberger array and te reconstructed iage for te buried tube. Te circles, joined by a tin line, correspond to te voltages detected in te reference area. Te tick line corresponds to te voltages easured along an iaginary surface line across te tube centre and perpendicular to its axis Figure : a) Reconstructed iage for te buried tube using te odified Scluberger array. b) Measured voltages in te oogeneous area (circles) and along a surface line across te tube c c Figure sows te iage corresponding to te siulated water leak. Te cange in colour wit respect to figure for te pixels close to te area were tere is te tube, suggest a ediu ore conductive tan te insulating tube c Figure 9: Tube positio electrode array and pixel assignent for te vertical cross section to iage. Pouring l of water into a tube 7 c in diaeter tat reaced te buried tube fro te surface (figure 8) siulated te leak. Because of terrain tilt, ost of te water accuulated at te west of te buried tube. We used two electrode arrays: a odified Scluberger array ( independent voltage easureents) and dipole dipole wit endelectrode easureents ( independent voltage easureents) Figure : a) Reconstructed iage for te leak using te odified Scluberger array. b) Measured voltages wen tere is a conductive leak (tick line). Figure sows apparent resistivities for te tube alone and for te tube plus te siulated leak, and te noralised apparent resistivity. Negative values iply tat te leak is conductive.

6 st World Congress on Industrial Process Toograp Buxto Greater Mancester, April -7, 999 Noralised apparent resistivity Apparent resistivity (O.).. Noralised apparent resistivity Apparent resistivity (O.) Figura : Measured apparent resistivities. a) Noralised apparent resistivity. b) Apparent resistivity for te tube (tin line) and for te tube plus siulated water leak (tick line) Figure 6: Measured apparent resistivities.a) Noralised apparent resistivity. b) Apparent resisitivity for te tube (tin line) and te siulated leak (tick line)... Results using te dipole-dipole array Figure sows te reconstructed iages and easured voltages for te tube alone using te dipole dipole arra including voltages easured by te end electrodes. Circles correspond to voltages easured on te reference area. Te tick line corresponds to voltages easured along an iaginary surface line across te tube and perpendicular to its axis. All easured voltages are saller tan tose easured using te odified Scluberger array (figure b) Bot electrode arrays yield siilar results. Bot locate te tube in its approxiate position and te presence of a leak close to it. (Voltage easureents were taken iediately after pouring water, and terefore te leak did not ave tie to spread.) Te leak as been detected using as reference easureents tose corresponding to te tube alone. Hence, te electrodes stayed in place, wic guarantees siilar easureent conditions. Bot te reconstructed iages and te apparent resistivity curves indicate tat te leak is ore conductive tan te tube. Te availability of apparent resistivity curves elps in ensuring tat te reconstructed iages are not te result of soe uncontrolled artefact CONCLUSIONS Figure : a) Reconstructed iage for te tube using te dipole dipole array. b) Measured voltages for te reference area (circles) and on te area were tere is te buried tube (tick line). Figure sows te easured voltages and te reconstructed iage for te siulated water leak. Te iage area close to te tube again canges in colour, pointing to a ore conductive ediu as result of te leak Figure : a) Reconstructed iage for te siulated leak using te dipole dipole array. b) Measured voltages wen tere is a siulated leak (tick line). Figure 6 sows easured apparent resistivities for te tube and te siulated leak, and te noralised apparent resistivity. Here too, negative apparent resistivity values iply a leak tat is ore conductive tan te tube. Kotre [6] proposed a reconstruction algorit to iage ipedance distributions based on te sensitivity teore tat does not need any regularisation paraeter. We ave applied tis algorit to detect underground leaking pipes using 6 and 8 electrodes, and te dipole dipole and a odified Scluberger array. Laboratory easureents for a siulated non-conductive leak sow tat leak detection is possible by using as reference voltages tose easured for te non-leaking pipe. Tis is convenient because sall canges in electrode position ave a strong influence in te reconstructed iages. Field easureents ave allowed us to detect a siulated conductive leak fro an insulating tube. Te siilitude between iages reconstructed fro eac electrode array validates te etod. Increasing te nuber of electrodes and reducing teir separation would iprove iage resolution. Bidiensional arrays could provide data to iage oriontal layers.

7 st World Congress on Industrial Process Toograp Buxto Greater Mancester, April -7, 999 REFERENCES [] R. H. Burger, Exploration geopysics of te sallow subsurface, Englewood Cliffs (NJ): Prentice Hall, 99. [] K.A. Dines, R.J. Lytle, Analysis of electrical conductivity iaging, Geopysics, 98, 6, 7, pp. -6. [] A.N. Tikonov, A.V. Goncarsk Ill-posed probles in te natural sciences, Moscow: MIR [] E. Orellana, Prospección Geoeléctrica en corriente continua, nd ed. Madrid: Paraninfo, 98. [] D.C. Barber, Quantification in ipedance iaging, Clin. Pys. Pysiol. Meas., 99, supl. A, pp. -6. [6] C.J. Kotre, Studies of iage reconstruction etods for electrical ipedance toograpy, PD tesis. University of Newcastle-Upon-Tyne, UK. 99. [7] M. Noel, B. Xu, Arcaelogical investigation by electrical resistivity toograpy: a preliinary study, Geopys. J. Int., 99, 7, pp. 9-. [8] L.R. Lines, S. Treitel, Tutorial. A review of least-squares inversion and its application to geopysical probles, Geopysical Prospecting, 98,, pp [9] W. Menke, Geopysical data analysis: discrete inverse teory, London: Acadeic Press, 989. [] D. Kaaner, C. Moler, S. Nos, Nuerical Metods and Software. Englewood Cliffs (NJ): Prentice Hall, 989. [] P. Lascau R. Teodor, Analyse nuérique atricielle appliquée à l art de l ingénieur, Paris: Maso986. [] M.H. Loke, Torleif Dali A coparison of different least-squares forulations for te inversion of resistivity and IP Data, IV Meeting of te Environental and Engineering Geopysical Society. Barcelona -7.septeber, 998, pp [] D.B. Geselowit, An application of electrocardiograpic lead teory to ipedance pletysograpy, IEEE Trans. Bioed. Eng., 97,8, pp. 8-. [] C.J. Kotre, EIT iage reconstruction using sensitivity weigted filtered backprojection. Pysiol. Meas., 99,, pp. A-A6. [] C.J. Kotre, Subsurface electrical ipedance iaging using ortogonal linear electrode arrays IEE Proc, Meas. Tecnol., 996, vol.,, pp. -6. [6] C.J. Kotre, Detection of sub-surface objects by electrical ipedance toograpy. Detection of abandoned land ines, IEE Conference Publicatio 7-9 october 996, pp [7] M. Gasulla, J. Jordana, R. Pallás-Aren J.M. Torrents, Subsurface resistivity easureents using square wavefors, IEEE Instruentation and Measureent Tecnology Conference, May 9-, 997, Ottawa, Canada, pp. -6. [8] I. García, Differential syncronous detector for soil electrical resistivity easureent, Projecte fi de carrera, ETSETB, UPC, (In Spanis), 998. [9] M. Gasulla, J. Jordana, R. Pallás-Aren J.M. Torrents, A fully differential syncronous deodulator. Proceedings DCIS 96, Noveber -. Sitges, Barcelona, 996. [] F. LL. Llorens, Autoated syste for soil resitivity easureent, Projecte final de carrera, ETSETB, UPC, (In Catalan), 998. [] J. Jordana, M. Gasulla, R. Pallás-Areny. Dept and sie deterination of concentric cylindrical anoalies applied to leak detection in buried pipes, IV Meeting of te Environental and Engineering Geopysical Societ Septeber -7, Barcelona, 998, pp. -6. [] M. Gasulla, J. Jordana, R. Pallás-Aren Autoated electrical ipedance easuring systes to detect leaks fro buried pipes, IV Meeting of te Environental and Engineering Geopysical Society. Barcelona, Septeber -7, 998, pp [] M. Gasulla, J. Jordana, R. Pallás-Aren Subsurface resistivity iaging using two single-step algorits, IV Meeting of te Environental and Engineering Geopysical Societ Barcelona, Septeber -7, 998, pp [] J. Sánce. Iaging underground ipedance distributions to detect leaking buried pipes and tanks, Projecte final de carrera, ETSETB, UPC, (In Spanis), 998.