Detectng Leas from Waste Storage Ponds usng Electrcal Tomographc Methods Andrew Bnley #, Wllam Daly ## & Abelardo Ramrez ## # Lancaster Unversty, Lancaster, LA1 4YQ, UK ## Lawrence Lvermore Natonal Laboratory, Lvermore, CA 9455, USA Abstract Methods for detectng and locatng leas n lned waste dsposal ponds have been establshed based on njectng electrcal current through the lner nto the surroundng sol and then, wth the ad of an under-lner array of electrodes, mappng electrcal potental. Hgh potental gradents then reveal lely locaton of lea spots wthn the lner. The approach s very expensve and s clearly not applcable n exstng stes, where retrofttng s not an opton. A tomographc varant of ths electrcal lea locaton method has been developed whereby electrcal potentals are collected around the permeter of the ste and then wth sutable data processng the locatons of a lea wthn the pond s computed. Applcatons on a controlled laboratory scaled model and a feld scale test ste have shown promsng results. Keywords: lea locaton, electrcal magng 1. INTRODUCTION Large quanttes of sold and lqud wastes are stored n ponds and lagoons world-wde. In many cases synthetc lners are used to protect the waste from leang out of the storage facltes and enterng the envronment, whch could have devastatng affects on the qualty of local groundwater and thus publc water supply. Snce these man-made lners wll degrade eventually wth tme naturally and are prone to damage throughout the worng lfe of the waste faclty t s essental that technques are avalable to assess the ntegrty of lners and locate possble leas. In some cases, such leas may be small n terms of flow rate but sgnfcant n terms of mass flux of contamnants. Snce many stored wastes have a hgh electrcal conductvty contrast wth sol water resstvty magng has been used n a number of studes to reveal leaage from surface and subsurface storage facltes, see for example [1], [2]. These methods rely on assessng changes n the subsurface resstvty to montor contamnant plumes. In most cases an assessment of the ntegrty of an envronmental barrer s requred over a short term perod, wthout 'before plume' data. Leas from barrers may also be relatvely small n dscharge, mang resstvty contrasts undetectable, but stll sgnfcant from the potental polluton threat. In addton, there has been relatvely recent nterest n leaage from water storage facltes and ppelnes, n many such cases resstvty magng wll not provde conclusve results, agan due to the mnor changes lely to result n the bul resstvty of the subsurface. Relatvely new lea locaton methods have been establshed based on njectng electrcal current through the lner nto the surroundng sol and then, wth the ad of an under-lner array of electrodes, mappng electrcal potental. The methods are based on the orgnal wor of [3] and [4]. Hgh potental gradents reveal lely locaton of lea spots wthn the lner. Example recent applcatons nclude [5] and [6]. The approach s very expensve to mplement and s clearly not applcable n exstng stes, where retrofttng s not an opton. A tomographc varant of ths electrcal lea locaton method was frst proposed by [7]. In ths new approach electrcal potentals are collected around the permeter of the ste and then wth sutable nverse methods the locatons of leas wthn the pond are computed. Fgure 1 llustrates the general procedure. To date applcatons of ths method has employed reasonably complex nverson methods to determne the lea locatons. In an attempt to derve more robust, hence practcal data processng technques we report here on recent experments usng ths method of determnng the locaton of leas n waste storage ponds usng only boundary measured data. 6
I I Lea Lea Pond Fgure 1: Schematc of measurement procedure. Electrodes (shown as sold crcles) may be also located outsde the pond. 2. METHODOLOGY The dstrbuton of electrcal potental (v) wthn the system shown n fgure 1 can be represented by: v v 2 σ + σ λ vσ x x y y = Iδ( x) δ ( y) V (1) Here λ s the Fourer transformaton varable, x and y are co-ordnates, σ s the electrcal conductvty (assumed varable), I s the current appled and δ s the Kronecer delta. Ths dfferental equaton may be solved usng the fnte element method for gven boundary condtons. Inverse Fourer transform and approprate superposton of the calculated potentals yelds the voltages of an arbtrary electrode confguraton n the consdered plane. The nverse soluton of (1) for the problem here requres the determnaton of the dstrbuton of current (I) gven the conductvtes (σ) and voltages (v). In practce, transfer resstances are measured and thus the tas of an nverse soluton s the determnaton of the dstrbuton of unt current. If the regon of nterest s dscretsed nto node ponts for soluton of the forward problem any number of these node ponts may be selected as possble current source nodes. The nverse soluton may then be consdered as the determnaton of the magntude of current at all of these possble source nodes. Varous approaches to the nverse problem may be taen. Conventonal gradent-based least squares technques may appear approprate, however, they requre constrants wthn the nverson snce the current magntude must be postve. In addton the soluton must be stablsed n some manner, such as through regularsaton (as n the case of nverse methods for resstvty tomography). Such regularsaton may be so such that sgnfcant over-smoothng of the fnal result occurs. Alternatves to gradent methods are the ncreasng range of 'global optmum' methods based on controlled Monte Carlo samplng wthn the parameter space. Method such as Smulated Annealng and Genetc algorthms may be consdered wthn ths class of technques. These methods are reasonably straghtforward to apply and deally suted to constraned problems such as the one posed here. Our ntal experences wth ths type of approach was encouragng (see [7]) however contnued expermentaton wth a range of nverse methods revealed a small number of cases where apparently optmum results were nconsstent wth nown lea locatons. The cause of ths s beleved to be the non-unqueness of the soluton coupled wth nevtable, yet poorly assessed, data errors. In other words the soluton of the nverse method may ndeed ft the data well but many other solutons (ncludng those representng the real case) whch have been rejected by the nverson procedure may ft the data equally well. For successful ndustral applcaton of ths method the magng procedure must ndcate some degree of 'trust' assocated wth the result. Incorrect assessment of lea locatons have severe fnancal mplcatons, n partcular when waste materal (sold or lqud) has to be removed temporarly n order to repar the lner materal. In addton, data processng must not requre expert nowledge of nverson parameters and the consequence of napproprate choce of such factors. In addton, the dstrbuton of electrcal conductvty wthn the regon s unlely to be nown. Waste dsposal ponds wll often contan a wde range of materals and thus be hghly heterogeneous n electrcal propertes. The spatal dstrbuton of waste depths has the same nfluence as varaton n waste type. Depths may be estmated but wll often be poorly now. Inverse methods whch rely on accurate nowledge of these factors are unlely to have practcal value n ndustry. Gven these constrants our ams are to determne what useful and relable nformaton may be derved from electrcal lea locaton surveys usng only boundary data. Our approach here s to adopt smple robust data processng technques n an attempt to assess ther vablty n 7
practcal stuatons, rather than more elaborate nverse methods sutable only for research stes. Rather than approach the measure of msft between the model and the data n terms of a least squares ft, the correlaton of data to model may be used. The product-moment correlaton s expressed here as: r = ( D ( D D )( F ( I D ) 2 ( F ( I ) F( I )) ) F ( I )) 2 (2) where D s the th measured transfer resstance and F (I ) s the th transfer resstance computed due to unt current at locaton. For M possble current source nodes the value of r may then me computed. We therefore expect that, for the case of a sngle lea, the hghest postve correlaton wll be assocated wth the source node closest to locaton of the lea. A map of the spatal pattern of the correlaton functon should then reveal the lea locaton. For cases where more than one lea occurs a map of the correlaton functon n (2) s napproprate snce only one 'optmum' wll be apparent. It s therefore essental that the relablty of the correlaton functon, produced n ths way, can be made. Calculaton of the correlaton functon s not computatonally demandng once the forward solutons have been determned for the M possble source nodes. It s, therefore relatvely trval to carry out a search usng pars of source nodes to assess the mprovement n correlaton n comparson to usng only one source node. The search must contan all possble pars due to possble non-unqueness, as explaned earler. The magntude of current n each of the two possble sources may dffer and so the search must also account for ths by samplng varous permutatons of the same source par. The mplementaton of such a search s trval. By selectng a suffcent number of combnatons of source node pars and a suffcent number of permutatons n ther relatve current strengths t s possble, wth very lttle computatonal effort, to assess whch combnatons resulted n mprovement over usng one sngle source node. By smply dsplayng the dstrbuton of the number of occurrences that each source node, when combned wth another, mproved the correlaton wth the data, t s possble to reveal the level of unrelablty n the locaton of optmum correlaton from one source node alone. Hgh relablty wll be shown by a dstnct pea n ths count functon, centred on the pea of the correlaton functon. Low relablty wll be revealed by more than one possble source node showng hgh counts. Ths wll be llustrate by two examples, one usng a controlled laboratory test, the other usng measurements at a feld scale test ste. 3. APPLICATION TO A SCALED MODEL 3.1 Expermental setup A scale model was desgned as follows. Twenty stanless steel electrodes were located around the permeter of a shallow plastc contaner, 9cm by 42cm n plan, flled wth mans water. Fgure 2 shows the basc setup. To represent a lea, another stanless steel electrode was located at stes A, B and C n fgure 2. Combnatons of these stes were also consdered usng two electrodes smultaneously. The electrode stes A, B and C thus represent deal leas n the contaner (equvalent to a current source placed outsde the tan). 4 2 C B A 2 4 6 8 Fgure 2: Expermental setup for laboratory lea tests (sold dots show electrode stes) To model the system a fnte element mesh contanng 64 elements, 693 node ponts was used. To represent possble current source locatons 135 of these fnte element nodes were used as shown n fgure 3. 4 2 2 4 6 8 Fgure 3: Dstrbuton of possble source nodes used for laboratory experment. 8
For each of the three possble 'lea' sources plus a number of combnatons of sources, transfer resstances were collected by usng the source(s) as one current electrode and one of the boundary electrodes as the other current electrode. Resstances were then measured between varous pars of other boundary electrodes. The procedure was repeated by usng each boundary electrode n turn as a current electrode. In total 36 measurements were collected for each possble 'lea' source. The njected waveform used was a swtched DC type, 4Hz frequency, typcal of geophyscal applcatons. Current magntudes vared but were typcally approxmately 1mA. 3.2 Results Fgure 4 shows the correlaton functon n (2) plotted for two of the cases consdered. Snce correlaton shows a reasonably flat surface the response has been exaggerated by plottng r 1 rather than r. In fgure 4a the correlaton functon s shown for a sngle 'lea' at pont B (see fgure 2). For ths case the optmum goodness of ft clearly matches the actual source locaton. For a combnaton of two sources (at A and C n fgure 2) fgure 4b shows that the correlaton s poorly suted, as would be expected. For cases wth one major source locaton (one domnatng lea) smply plottng the correlaton may then be a robust soluton. A measure of relablty s requred, as dscussed earler. Fgure 5 llustrates one possble way of addressng ths by plottng the number of occasons each of the possble 135 sources nodes, when used wth any other, mproves the correlaton wth the data, when compared to the optmum from usng one sngle source node. For reference the search conssted of approxmately 2, combnaton of source node pars. Also shown n fgure 5 s the locaton of the source node(s) for optmum goodness of ft (defned by maxmum correlaton), observed durng search. For the sngle source node case n fgure 5a the relablty measure shows a dstnct pea close to the locaton of the sngle lea. Ths can then be nterpreted as confrmaton that the correlaton functon n fgure 4a does n fact locate the lea well and confrms that the sgnal s domnated by a sngle source. For the dual source n fgure 5b the response s sgnfcantly dfferent. Here, although a maxmum can be seen, the mportant feature s that a large number of source nodes can be used n combnaton wth each other and result n an mprovement over a sngle source node. Note that here no sgnfcance s placed on the extent of that mprovement. 4 3 2 1 (a) 1 2 3 4 5 6 7 8 9..1.2.3.4 4 3 2 1 r 1 (b) 1 2 3 4 5 6 7 8 9..1.2.3.4 Fgure 4: Example results of laboratory experments showng correlaton functon plotted for two cases: (a) sngle lea, (b) dual lea. Crcles ndcate actual source locaton. 4 3 2 1 r 1 (a) 1 2 3 4 5 6 7 8 9 5 1 15 2 25 Search count 9
4 3 2 1 (b) 1 2 3 4 5 6 7 8 9 5 1 15 2 25 3 35 Search count Fgure 5: Relablty measured plotted for the two cases n fgure 4: (a) sngle lea, (b) dual lea. Crcles ndcate actual source locaton, crossed square shows optmum source node combnaton resultng from the search. Snce t s possble to select the optmum par of source nodes (defned as those producng the maxmum correlaton wth the data) encountered durng the search, ther locatons are shown n fgure 5a and 5b for the two cases. Even for the dual source case n fgure 5b the optmum soluton corresponds well wth the true locaton of the sources. 4. FIELD SCALE DEMONSTRATION 4.1 Expermental setup Feld scale experments were conducted durng summer, 1998 at a storage pond n Lvermore, CA, USA. The applcaton permtted tests to be performed under more realstc condtons. Besdes the obvous ssue of scale other factors are relevant: the electrcal conductvty s lely to be hghly varable wthn the pond due to the lqud stored and varablty n depth; the pond has an rregular boundary mang modellng errors more sgnfcant. An array of 36 electrodes was nstalled just wthn the permeter of the pond, as shown n fgure 6. Measurements of resstance were made usng a smlar arrangement to that used n the laboratory scale experment. The magntude of current appled was typcally 2mA. Two source locatons were selected, as shown n fgure 6. In order to model the response the regon was dscretsed nto 288 fnte elements, 2997 nodes. 16 of these nodes were used as possble source nodes. 4.1 Results Fgure 7 shows sample results from the expermental programme. In fgure 7a the correlaton functon n (2) s plotted for the sngle 'lea' case. In fgure 7b, correlaton between model and data for each possble source node s shown for the dual 'lea' case. The results are consstent wth the fndngs of the laboratory scale pond: for the sngle source case the correlaton functon wors well but clearly s napproprate for more than one lea. B A 1m 1m Fgure 6: Expermental setup for feld scale lea tests. Sold dots show electrode stes, A and B ndcate locatons of current sources. 1
As n the small scale test searches were performed to nvestgate the relablty of the result from usng only the correlaton functon. Fgure 8 llustrates the result of ths search for the two cases. In fgure 8a a well peaed response ndcates good relablty, whereas n fgure 8b the unrelablty of the correlaton functon result n fgure 7b s clearly shown by a much wder pea. (a) 1m 1m..2.4.6.8.1.12 (b) r1 1m 1m..5.1.15.2.25.3.35 r 1 Fgure 7: Correlaton maps for feld scale lea tests (a) sngle lea, (b) dual lea. Whte crcles show locatons of current sources. 11
(a) A 1m 1m 25 5 75 Search count (b) B A 1m 1m 2 4 6 8 1 12 14 Search count Fgure 8: Search counts showng relablty for feld scale lea tests (a) sngle lea, (b) dual lea. Whte crcles show locatons of current sources. 5. CONCULSIONS To our nowledge the experments reported here are the frst attempts to determne lea locatons n storage ponds usng measurements obtaned from electrodes located wthn the permeter of a storage pond. The results ndcate that t s possble to derve nformaton about the locaton of a major electrcal (and hence flud) lea through electrcally nsulatng lners wthout resortng to complex nverson methods. By dsplayng maps of the correlaton between data and the response of a numercal model usng a number of possble source locatons the locaton of a sngle lea can be estmated wth accuracy. The relablty of the lea locaton mpled by the correlaton functon can be easly assessed by an extensve search of combnatons of two or more source locatons. Snce the forward model s only computed once the computaton cost of the procedure s mnmal and certanly possble on ste mmedately followng data collecton. Such tools may then be used to help locate not the exact locaton of a lea but reasonably small areas of suspected damage to the envronmental barrer, the exact locaton beng determned by more thorough nvestgatons wthn such areas. Non-robust nverson methods have lttle practcal value for detectng leas from the many waste dsposal stes world-wde. Data processng tools must assess levels of relablty or uncertanty n the fnal response due to the fnancal mplcatons of false assessments. We antcpate more nvestgatons nto smplstc approaches, such as the type utlsed here. 12
REFERENCES [1] Van, G.P., Par, S.K. and Hamlton, P., 1992, Use of resstvty montorng systems to detect leas from storage ponds, n Proc. Symp. on the Applcaton of Geophyscs to Engneerng and Envronmental Problems: EEGS, Chcago, 629-647. [2] Ramrez, A., Daly,W., Bnley,A., LaBrecque, D. and Roelant,D., 1996, Detecton of Leas n Underground Storage Tans Usng Electrcal Resstance Methods, J. Env. and Eng. Geophyscs, Vol. 1 (3), 189-23. [3] Para, J.O., 1988, Electrcal response of a lea n a geomembrane lner, Geophyscs, 53, 1445-1452. [4] Frangos, W., 1992, Electrcal detecton of leas n lned waste dsposal ponds, MSc thess, Dept. geology and Geophyscs, Unversty of Utah, 78pp. [5] Falcone, G. and Agostn, A., Electronc lea detecton system (ELDS), In: Proc. 1st Meetng European Secton of the Envronmental and Engneerng Geophyscs Socety, Torno, Italy, 4-42. [6] Taylor, S., Barer, R. and Whte, C., The UK's frst landfll below-lner montorng system: The frst year of montorng, In: Proc. 2nd Meetng of the Envronmental and Engneerng Geophyscs Socety, Nantes, France, 177-18. [7] Bnley, A., Daly, W. and Ramrez,A., 1997, Detectng Leas from Envronmental Barrers usng Electrcal Current Imagng, J. Env. and Eng. Geophyscs, Vol. 2.(1), p11-19. 13