Uncertainty in measured biodegradation rate constant for heterogeneous aquifers

Transcription

1 Uncertanty n meaured bodegradaton rate contant for heterogeneou aqufer Amr H Hoen, Clayton V Deutch Department of Cvl and Envronmental Engneerng, Unverty of Alberta, Edmonton, AB, Canada Carl A Mendoza Department of Earth and Atmopherc Scence, Unverty of Alberta, Edmonton, AB, Canada Kevn W Bggar BGC Engneerng, Edmonton, AB, Canada ABSTRACT The bodegradaton rate contant of organc contamnant are partcularly mportant for decon makng and management of contamnated te. A number of feld approache that etmate the rate contant by ung concentraton dtance relaton along the plume centerlne are commonly ued. However, the etmated rate contant wll be affected by heterogenety n tranmvty, uncertanty n hydraulc head meaurement and uncertanty n ource geometry. Th tudy attempt to quantfy the reultng uncertanty n the rate contant. Frt, a ynthetc aqufer wth known hydrogeologcal and tranport properte created and tranport of dolved BTEX mulated acro the te. The frt-order bodegradaton rate contant then etmated ung the method of Bucheck and Alcantar (995) and compared to the known value ued n the tranport mulaton. Next, uncertanty n head meaurement and t effect on the etmated frt-order rate contant nvetgated. For th purpoe, multple realzaton of the tranmvty feld are generated condtoned to a number of hydraulc conductvty meaurement (tatc data) and hydraulc head obervaton (dynamc data). Thee realzaton are then combned wth the realzaton of ource geometry obtaned by a dtance-functon approach to create multple jont realzaton of tranmvty and ource geometry. In a Monte Carlo Smulaton framework, tranport of dolved BTEX mulated for all jont realzaton and the frt-order bodegradaton rate contant etmated by the method of Bucheck and Alcantar. The reult of the mulaton how that the frt-order bodegradaton rate contant can be ealy overetmated due to mng the centerlne of the plume n heterogeneou aqufer. Uncertanty n head meaurement alo affect the etmated frt-order rate. In th cae the method of Bucheck and Alcantar may overetmate the frt-order rate contant by more than one order of magntude. RÉSUMÉ La contante de vtee de bodégradaton de contamnant organque ont partculèrement mportante pour la pre de décon et la geton de te contamné. Un certan nombre d'approche domane etmer que le taux contante en utlant la concentraton - le relaton à dtance le long de l'axe du panache ont couramment utlé. Toutefo, le taux etmé contante eront touché par l'hétérogénété dan tranmvté, l'ncerttude dan le meure hydraulque et de l'ncerttude dan la ource la géométre. Cette étude tente de quantfer l'ncerttude qu en réulte pour le taux de contante. Tout d'abord, un aqufère de ynthèe dont on connaît hydrogéologque et proprété de tranport et créé et le tranport de BTEX dou et mulé à traver le te. Le premer ordre de bodégradaton contante de vtee et alor etmée en utlant la méthode de Bucheck et Alcantar (995) et par rapport à la valeur connue utlée pour le tranport de mulaton. Enute, l'ncerttude de meure dan la tête et on effet ur l'etmaton du premer ordre et contante de vtee d'une enquête. À cet effet, de multple réalaton de la tranmvté domane ont généré condtonné à un certan nombre de meure de la conductvté hydraulque (donnée tatque) et hydraulque obervaton (donnée dynamque). Ce réalaton ont enute combné avec le réalaton de la ource géométre obtenu par une dtance foncton de créer plueur réalaton conjonte de tranmvté et la ource la géométre. Dan une mulaton Monte Carlo cadre, le tranport de BTEX dou et mulée pour toute le common partare et le réalaton de premer ordre bodégradaton contante de vtee et etmé par une concentraton communément utlé dtance technque. Le réultat de mulaton montrent que le premer ordre de bodégradaton contante de vtee peut être faclement ou-etmée en raon de l'abence de l'axe du panache dan le aqufère hétérogène. Incerttude ur la tête meure nflue également ur l'etme de premer ordre. Dan ce ca, la méthode de Bucheck et Alcantar ma uretmer le premer ordre contante de vtee de plu de un ordre de grandeur. INTRODUCTION Actve clean up of uptream ol and ga contamnated te ha both practcal and fnancal lmtaton, whch ha led to extenve nteret n remedaton technque that utlze the natural attenuaton (NA) capacty of the uburface. Reducton n concentraton of organc contamnant n the uburface due to combnaton of phycal, geochemcal and bochemcal procee (Fgure ). Among thee, aerobc and anaerobc bodegradaton are the man procee for the detructve removal of organc contamnant (Chang et al. 989). 563

2 Etmatng the amount of tme requred for NA procee to lower contamnant level to gven regulatory goal requred when aeng montored natural attenuaton (MNA) a a remedal alternatve. The need for quanttatve aement of th tme of remedaton problem ha reulted n the development of numercal model that mulate complex knetc and multcomponent nteracton (Zheng 990, Rfa et al. 997 and Chapelle et al. 2003). Unfortunately, many of the knetc parameter and electron acceptor data requred by thee model are ether qute uncertan or very dffcult to determne ung the current natural attenuaton gudelne and protocol (Rfa and Rttaler 2005). When electron acceptor data are uncertan or do not ext, one approach to ue a frt-order bodegradaton rate, whch can be determned ung the concentraton veru dtance technque or mcrocom tude (Chapelle et al. 996, Wdemeer et al. 999). In a concentraton veru dtance approach, contamnant concentraton are plotted along the centerlne of the plume, whch aumed to be n the drecton of groundwater flow. The bodegradaton rate contant are then calculated by matchng the frt-order curve to the oberved concentraton. The method of Bucheck and Alcantar (995) a concentraton dtance approach commonly ued n practce. It baed on the teady-tate oluton for a D tranport equaton, ncorporatng advecton, longtudnal dperon and frt-order bodegradaton. An etmate of longtudnal dpervty requred for th approach, whch may ntroduce addtonal uncertanty n etmaton of bodegradaton rate contant. bodegradaton rate contant a a drect reult of uncertanty n a heterogeneou tranmvty feld. Smlar to the tudy of Bauer et al. (2006), n th work we nvetgate the uncertanty n meaured bodegradaton rate contant n a Monte Carlo Smulaton framework. However, there are two mprovement to the work of Bauer et al. (2006): () n th work tranmvty realzaton are condtoned to head obervaton (dynamc data) a well a drect tranmvty meaurement (tatc data), and (2) the effect of uncertanty n ource geometry alo nvetgated. The frt mprovement enure that we can tudy the effect of uncertan hydraulc head meaurement on the etmated frt-order rate. The econd mprovement ueful to nvetgate the effect of uncertanty n ource geometry on the reult. The propoed mprovement render the mulaton more realtc. To evaluate the performance of the method of Bucheck and Alcantar (995) n heterogeneou aqufer, a ynthetc aqufer wth a known tranmvty feld condered and teady-tate preure (head) repone mulated. For a gven montorng well confguraton, a few tranmvty meaurement and head obervaton are then recorded from the ynthetc aqufer. In a realworld applcaton, thee tranmvty meaurement and head obervaton are uually the only te-pecfc data avalable about the hydrogeologc regme of the te. So, n th work we only ue thee data to model the uncertanty n tranmvty feld. In the next tep, a dtance functon baed approach ued to model the uncertanty n ource geometry; and multple combned ource-tranmvty realzaton are created. Fate and tranport of dolved BTEX then mulated for all combned realzaton wth pre-pecfed value of bodegradaton rate contant and dpervty. The method of Bucheck and Alcantar (995) then appled to etmate the bodegradaton rate contant for all mulated plume. To nvetgate the effect of uncertan ource geometry alone, the mulaton are repeated for a fully characterzed ource zone geometry wth uncertan tranmvty feld, and the varablty n the rate contant are compared for the two et of mulaton. Source zone Fgure. Conceptual llutraton of mportant natural attenuaton procee that affect the fate of petroleum hydrocarbon n aqufer (Bekn et al. 200) The concentraton dtance technque are affected by the level of heterogenety of aqufer materal. In fact, the centerlne of a plume can ealy be med by montorng well ntalled baed on aumed (but ncorrect) groundwater flow drecton (Wlon et al. 2004). The uncertanty nherent n ource zone geometry may alo contrbute to uncertanty n the etmated bodegradaton rate contant. It ha been alo oberved that, n the method of Bucheck and Alcantar (995), etmaton of dpervte by common approache may alo ntroduce large uncertante n the bodegradaton rate etmate (Bauer et al. 2006). The work of Bauer et al. (2006) a mlar work whch nvetgate the uncertanty n the meaured 2 SYNTHETIC AQUIFER 2. Modelng doman and parameter The ynthetc aqufer developed for th work a farly heterogeneou two-dmenonal aqufer wth 300m length and 60m wdth. The well confguraton and modelng doman aocated wth the ynthetc aqufer hown n fgure 2. The heterogeneou tranmvty feld (Fgure 3) created by a ngle uncondtonal realzaton mulated by equental Gauan mulaton (Deutch and Journel 997). Thu, tranmvty condered a a lognormally dtrbuted random varable wth a mean of m/ and a tandard devaton of 2. (n natural logarthmc unt). The correlaton tructure of the heterogeneou feld follow a phercal varogram model wth a range of 25m and wth 5% nugget effect. The tattcal properte of the ynthetc aqufer are mlar to 564

3 that of Columbu Ar Force Bae te (Rehfeldt et. al. 992) wth lght modfcaton. A hown n Fgure 2, there are a total of 38 montorng well at whch teady-tate hydraulc head are to be recorded. The confguraton of well choen mlar to a natural attenuaton tudy te n wet-central Alberta wth ome modfcaton. Tranmvty value are recorded at 4 well marked n Fgure 2. Alo hown n Fgure 2 the locaton of well deemed nde the ource zone. Boundary condton of the ynthetc aqufer nclude contant head boundary condton on the north and outh boundare and no-flow boundary condton on the eat and wet boundare. A hydraulc gradent equal to % ha been mpoed to the ynthetc aqufer through the contant head boundary condton on the north and outh boundare. For all mulaton, bodegradaton rate contant, and longtudnal and tranvere dpervte are et at day -,.0 m and 0.2 m, repectvely. plotted a hown n Fgure 2. In practcal applcaton, a number of well are often ntalled along the preumed centerlne of the plume to record the concentraton for ubequent concentraton-veru-dtance calculaton. There are a total of 6 well along the centerlne of the plume that are ued n the calculaton of frt-order bodegradaton rate contant. In remedaton project aocated wth petroleum hydrocarbon, dtrbuton of moble L (lght-nonaqueou-phae-lqud) ttng on top of groundwater table often delneated by obervaton well. A few ource removal technque are avalable to ubequently reduce the volume of moble L n a practcal way. After removal of much of moble L tll there may be a large plume of redual L n ol n the ource zone area. The focu of th work on contamnaton of groundwater expoed to redual L. In th work, we aume that the redual L concentraton n ol equal to 27 mg/kg and t unformly dtrbuted wthn the ource geometry hown n Fgure 2. Due to lmted number of amplng pont, there alway uncertanty n the ource zone geometry. Th uncertanty wll be addreed n ubequent ecton of th work through a dtance-functon algorthm. The other mportant ource zone property doluton rate. In general, the doluton rate of nto groundwater depend on nterfacal area between the and water (Imhoff 993), aqufer heterogenety (Mayer and Mller 996), the ze and hape of the blob (Power et al. 994) and groundwater velocty (Pfannkuch 984). Thu, f tranport procee occur at a hgh rate relatve to the doluton rate, aqueou concentraton ( C ) may reman lower than -water equlbrum concentraton ( C eq ). Th effect can be decrbed mathematcally (Parker et al. 99, Imhoff et al. 993) by a ma tranfer rate coeffcent (k ), uch that the doluton nto groundwater can be explaned by: R eq = max[0, k ( C C )] [] Fgure 2. Well confguraton and modelng doman aocated wth the ynthetc aqufer In practcal applcaton, approprate detecton of the centerlne of the plume mportant when the ntenton to ue any one of the concentraton-veru-dtance technque. In our ynthetc contamnated aqufer, we aume that the centerlne of the plume tart omewhere n the mddle of the ource zone wth oberved non-aqueou-phae-lqud () n the obervaton well (old crcle n Fgure 2). The drecton of the centerlne of the plume the ame a the drecton of groundwater flow n the vcnty of the ource zone whch uually detected ung a hydrogeologc trangle, early n lfe of a remedaton project. Followng the ame procedure, the preumed centerlne of the plume can be eq Accordng to Raoult law, C can be calculated a: eq ol C = f C [2] where, f the mole fracton of the ubtrate (e.g. BTEX) ol n and C olublty of the pure ubtrate n water. Average BTEX olublty n water and t mole fracton n are et to 500 mg/l and 0.26, repectvely. The ma tranfer rate coeffcent (k ) ha been et to day - for all mulaton (Waddll and Wddowon 998). The concentraton of redual n ol alo dependent on rate of ma tranfer between the ol and groundwater. Th rate of change n concentraton of redual n ol may be expreed by: dc dt = T [3] b R 565

4 n whch, C the ma of ubtrate per unt ma of dry ol, θ T total poroty and ρ b the bulk denty of porou medum. θ T and ρ b are et to 0.35 and 600 kg/m 3, repectvely. 2.2 Reactve ma tranport mulaton The governng ma-conervaton equaton for fate and tranport of dolved BTEX n groundwater may be expreed by (Chapelle et al. 2003): ( C) C = D j ( vc) + R + R n t x x [4] j x where, C dolved concentraton of BTEX, θ the effectve poroty, x the dtance along the repectve Cartean coordnate, D j the hydrodynamc dperon coeffcent tenor, v pore water velocty, R doluton term (Equaton ) and R the chemcal n reacton term. A tated prevouly, the chemcal reacton term aumed to be a frt-order rreverble reacton gven by ( - C ), where the frt-order bodegradaton rate contant et to day mg/l 50 mg/l 5 mg/l 0.5 mg/l 0.05 mg/l mg/l Fgure 3. Synthetc tranmvty feld (left) and dolved BTEX plume n teady tate condton (rght) The partal dfferental equaton decrbng the reactve tranport of dolved hydrocarbon (Equaton 4) mathematcally olved by the method of charactertc (KonKow and Bredhoef 978). The method of charactertc (MOC) ue a conventonal partcle trackng technque for olvng the advecton term. At the begnnng of the mulaton, a large number of movng partcle are dtrbuted n the flow feld wth a random or fxed pattern. A concentraton and poton n the Cartean coordnate ytem are aocated wth each of thee partcle. Partcle are tracked forward through flow feld ung a mall tme ncrement. At the end of each tme ncrement, the average concentraton at each cell evaluated from the concentraton of movng partcle whch are located wthn that cell. Change n cell concentraton due to dperon, nk/ource mxng and chemcal reacton are then mulated by mplct or explct fnte dfference method (FDM). The mulaton cell are m m. Th conderably maller than the range of phercal varogram (25m) that ued to create the tranmvty feld and jutfe the ue of mall dpervty value (Fernandez-Garca and Gomez-Hernandez 2007). The method of Bucheck and Alcantar (995) baed on the oluton to onedmenonal teady-tate tranport equaton. To reach to a teady-tate condton, all tranport mulaton are run for 7 year. Fgure 3 how the ynthetc heterogeneou tranmvty feld and aocated teady-tate dolved BTEX plume. 2.3 Etmaton of bodegradaton rate contant There are everal method to determne the te pecfc bodegradaton rate coeffcent (Alvarez and Illman 2006). Thee method nclude ma balance, the technque of Bucheck and Alcantar (995), normalzaton of contamnant concentraton to thoe of a recalctrant cocontamnant that wa preent n the ntal releae, the ue of n tu mcrocom and drect puh tet. The method of Bucheck and Alcantar baed on an analytcal oluton to one-dmenonal, teady-tate contamnant tranport that conder advecton, longtudnal dperon, orpton and frt-order bodegradaton: /2 x 4 ( ) + L C x = C 0exp [5] 2L vc where, C(x) concentraton at a dtance x downtream of the ource, C 0 the ource concentraton, α L longtudnal dpervty, and v c the contamnant velocty. Bucheck and Alcantar (995) recognzed that contamnant concentraton uually decreae exponentally along the centerlne of the plume a a functon of dtance from the ource: kx v ( x) = C exp C 0 where k the decay coeffcent, whch ncorporate bodegradaton, dluton, etc. The varable x n Equaton 6 repreent the dtance from the ource, and x / v the tme t take groundwater to travel a dtance x. Bucheck and Alcantar (995) equated Equaton [5] and [6] and olved for λ: 2 v c k = + 2 [7] L 4L v n whch, k/v the negatve of the lope of a lne obtaned from a log-lnear plot of the (centerlne) contamnant concentraton veru dtance downgradent along the flow path. Accordng to Equaton 7, determnaton of λ ung th approach requre knowledge of the longtudnal dpervty (α L) and contamnant (retarded) [6] 566

5 velocty (v c). A tated prevouly, orpton condered to be neglgble n th work. Alo, a reaonable aumpton would be to conder that bodegradaton occur olely n aqueou phae. Thu, v c can be replaced by groundwater eepage velocty (v por). In a real-world applcaton, eepage velocty can be determned baed on Darcy law and by ung the meaured hydraulc conductvte, effectve poroty and oberved hydraulc gradent. In th work, hydraulc conductvte have been meaured at 6 well locaton (Fgure 2). ln C (mg/l) HHHH y = x R 2 = Dtance from the ource (m) Fgure 4. Determnaton of k / v by lnear regreon, to be ued n the method of Bucheck and Alcantar A repreentatve value for hydraulc conductvty can be obtaned a geometrc average of all hydraulc conductvty meaurement, whch equal to m/ n th work. Gven that hydraulc gradent equal to 0.0 and the effectve poroty equal to 0.3, the average eepage velocty wll be m/. In practce, longtudnal dpervty often etmated a 0. tme the maxmum oberved plume length. Conderng a BTEX concentraton value of mg/l a the end of the BTEX plume and baed on the well confguraton dplayed n Fgure 2, the maxmum oberved plume length wll be 235 m, whch gve an etmated value of 23.5 m for α L. A hown n fgure 3, the BTEX concentraton can be meaured at x well n the mulated teady-tate plume along the preumed centerlne. Fgure 4 how thee concentraton meaurement plotted agant the dtance from the ource. When appled n the ynthetc aqufer, the method of Bucheck and Alcantar (995) reult n a bodegradaton rate contant equal to day - and overetmate the actual known frt-order rate ued n tranport mulaton whch day -. The hgher value of the frt-order rate contant by the method of Bucheck and Alcantar largely due to mng the centerlne of the plume a well a overmplfyng aumpton of D tranport. Thee effect have been explaned to ome extent by Zhang and Heathcote (2003) and Wlon et al. (2004). So far, we have etmated the frt order bodegradaton rate contant for the 2D ynthetc aqufer whle aumng no uncertanty ext n tranmvty fled, head meaurement and areal extent of the redual zone. In the ret of th work, we nvetgate the uncertanty n the etmated frt-order rate a a reult of uncertanty n tranmvty feld and ource geometry. 3 MONTE CARLO SIMULATIONS In real-world applcaton, we have acce nether to the exhautve dtrbuton of tranmvty feld nor to the true dtrbuton and geometry of redual ource zone. The only data often avalable are pont meaurement of hydraulc conductvty (e.g. by lug tet), hydraulc head obervaton and pare ol ample n the ource area. Accordng to tochatc hydrogeology prncple, the avalable data cannot unquely characterze the contamnated aqufer. In other word, there are multple plauble cenaro that jontly honour all avalable data. In addton to th, we know that hydraulc head meaurement alway ncorporate ome level of uncertanty. Th uncertanty uually come nto play motly due to eaonal groundwater table fluctuaton. The uncertanty n hydrogeologcal and ource zone properte tranlate nto uncertanty n etmated frt-order bodegradaton rate contant. A large number of jont realzaton of ourcezone/tranmvty-feld have been bult by geotattcal technque to determne the potental uncertanty n the etmated frt order rate. The contructed realzaton honour all avalable data and ncorporate uncertanty n hydraulc head meaurement. Performng Monte Carlo Smulaton, fate and tranport of dolved BTEX then mulated for every jont realzaton and concentraton are recorded at the locaton of x montorng well along the preumed centerlne of the contamnant plume (Fgure 2). Ung the method of Bucheck and Alcantar, frt-order bodegradaton rate contant then etmated for all realzaton and compared to the orgnal value ued n mulaton. 3. Characterzng uncertanty n the tranmvty feld A hown n Fgure 2, hydraulc conductvty meaured at 4 locaton acro the ynthetc aqufer. Hydraulc head are recorded at all 38 well ntalled for te nvetgaton. A tated earler, head meaurement are alway prone to varablty due to eaonal groundwater fluctuaton. Uncertanty n head meaurement coupled wth the non-unquene problem that are from pare hydraulc conductvty meaurement motvate u to contruct multple realzaton for the tranmvty feld. Sequental Gauan mulaton (Deutch and Journel 997) performed ung 4 hydraulc conductvty meaurement a condtonng data. The correlaton tructure defned by a phercal varogram wth the range of 25m and wth 5% nugget effect. Th the ame a the varogram ued to contruct the ynthetc aqufer. The root mean of quared redual error (RMS) crteron ued to evaluate the goodne of ft to oberved hydraulc head and gven by (Zheng and Bennet 2002): 567

6 N RMS = N = cal ob 2 ( h h ) /2 cal ob where, h and h are calculated and oberved hydraulc head, and N the number of head obervaton. It aumed that all 38 head obervaton are uncertan and the dtrbuton of error normal wth a mean of zero and a tandard devaton of 0. m. Thu, the calculated RMS hould be le than 0. m for every geotattcal realzaton to be accepted and ued n ubequent mulaton. To accomplh th, 4000 realzaton of tranmvty feld were generated and flow mulated; and ultmately 00 realzaton wth RMS < 0. m were elected for ubequent MCS. 3.2 Characterzng the uncertanty n ource geometry The model of uncertanty for the geometry of the redual ource contructed by the dtance functon (DF) approach. Detal of the DF approach and t applcaton n modelng the dtrbuton of redual dcued n Hoen et al. (2008). In th work, we only apply the methodology to model the uncertanty n areal lmt of the ource zone. Frt, ntal codng of the avalable ample data n term of beng nde or outde the ource zone mplemented and DF value are calculated (Fgure 5). It hould be noted that the area hown n Fgure 5 the upected ource zone area n the ynthetc aqufer hown n Fgure 2. Fgure 5. Codng the well locaton and calculatng DF value for well nde and outde of the ource zone An nterpolaton technque employed to defne the boundary nterface n the preence of pare ample data. A dcued n Hoen et al. (2008), a data value dependent nvere dtance approach ued for th purpoe: Z * ID Z(u ) N Z(u ) Z(u = ) (u 0) = ID(u ) Z(u ) + Z(u ) [8] [9] where, α and β are calng and eparaton factor, repectvely. Z(u ) repreent the DF value at amplng locaton u, N the number of data pont ued n nterpolaton, and ID(u ) nvere dtance weght calculated by: ( d( u )) + c ID (u ) = N [0] d u c where, ( ) j ( ( ) = j + d u the Eucldan dtance between the etmaton locaton u 0 and Z(u ) ample data, ω dtance exponent (et to.5) and c a mall contant. The calng and eparaton factor α and β control the centerlne and wdth of an uncertanty band condtoned to the calculated et of DF value. For a gven well arrangement, an uncertanty band defned a a probabltc areal nterval that nclude the actual boundary whch unknown. The α and β value are calbrated agant a large number of ynthetc plume ung the followng objectve functon: S q [ ] 2 M * (,, R) Pj Pj (,, R) = [] j= q where, P repreent the true probablte correpondng to quantle j q,..., q ued n optmzaton. The calculated M P * j,, R are defned a the proporton of probablte ( ) ynthetc plume (R) whoe area completely fall nde the q,..., q quantle map. Thee quantle map are M derved from the condtonal cumulatve dtrbuton functon (CCDF) of an uncertanty band calculated for ome α and β value. A downhll mplex optmzaton algorthm then adapted to mnmze the objectve functon gven n [] and to calbrate the value of α and β. A a reult, n th tudy, the calbrated value of α and β are determned to be.44 and 2., repectvely. Fgure 6 how the calbrated uncertanty band and correpondng p0, p50 and p90 map. A total of 00 equ-probabale realzaton of ource geometry are drawn from the uncertanty band hown n Fgure 6 to be ued n ubequent MCS. 3.3 Uncertanty n etmated frt-order rate contant A explaned earler, uncertanty n the tranmvty feld of the heterogeneou aqufer and the ource zone geometry reult n uncertanty n the etmated frt-order bodegradaton rate contant. To nvetgate th uncertanty, we generated 00 realzaton of the hydraulc conductvty feld and 00 realzaton of the ource zone geometry. Thee realzaton are then randomly combned to create 00 jont ourcetranmvty realzaton. Then, n a Monte Carlo 568

7 Smulaton framework, contamnant tranport mulaton are mplemented for the realzaton and the frt-order bodegradaton rate contant etmated by the method of Bucheck and Alcantar (995). Except for the tranmvty dtrbuton and ource geometry, all other parameter reman the ame a the parameter ued for the ynthetc aqufer. Fgure 7 how the htogram of the etmated frtorder bodegradaton rate contant, where the tranmvty feld, hydraulc head obervaton and ource zone geometry are uncertan. It can be oberved that for heterogeneou aqufer, even when there no uncertanty n head obervaton (Fgure 7 ynthetc aqufer), the method of Bucheck and Alcantar conderably overetmate the true bodegradaton rate contant, n th ntance by 7%. Accordng to Fgure 7, the etmated frt-order bodegradaton rate contant for the ynthetc aqufer day -, whle the prepecfed value day -. Th overetmaton largely due to mng the centerlne of the plume by the obervaton well. Fgure 7. Htogram of etmated bodegradaton rate contant under uncertan tranmvty dtrbuton, hydraulc head obervaton and ource zone geometry Fgure 6. Calbrated uncertanty band (top-left) and p90 (top-rght), p50 (bottom-left), and p0 (bottom-rght) map. The tuaton become even wore when there uncertanty n head obervaton (Fgure 7 MCS). In th cae the frt-order bodegradaton rate contant can ealy be over-etmated by one order of magntude or more. In th cae the mean etmated frt-order rate wll be day - whch one order of magntude hgher than the pre-pecfed value beng day - that wa ued n the mulaton. The htogram of the etmated frt-order rate under uncertan tranmvty feld and head obervaton hown n Fgure 8. Comparng Fgure 7 and 8, we oberve that uncertanty n geometry of the ource zone appear to have a mnor mpact on the dtrbuton of etmated frt-order rate. In th cae, the mean etmated frt-order rate contant day -. The varablty n th cae lghtly lower a t could be expected. The coeffcent of varaton for the cae 2 (no uncertanty n ource geometry) wherea that for cae Fgure 8. Htogram of etmated bodegradaton rate contant under uncertan tranmvty feld and hydraulc head obervaton 4 CONCLUSIONS The method of Bucheck and Alcantar (995) a wdely ued feld technque for etmaton of frt-order bodegradaton rate contant baed on the meaured feld data. Uncertanty n the frt-order contant etmated by the method of Bucheck and Alcantar wa nvetgated ung a ynthetc heterogeneou aqufer wth known properte. It wa ntally aumed that there no uncertanty n the head obervaton and ource geometry. Under th condton, the method of Bucheck and Alcantar wa ued to etmate the frt-order rate 569

8 contant. The etmated value conderably overetmated the true value by 7%. To nvetgate the performance of the Bucheck and Alcantar methodology under uncertan head obervaton, t wa aumed that head obervaton are uncertan and the unknown error are normally dtrbuted wth a mean of zero and tandard devaton of 0 cm. One hundred realzaton of the tranmvty feld were then generated condtoned to a number of tranmvty meaurement. For all realzaton the root mean quared error wa maller than the tandard devaton of obervaton error. The realzaton of the tranmvty feld were then combned wth the realzaton of ource geometry to create 00 jont tranmvty-ource geometry realzaton. Then, the tranport of dolved BTEX wa mulated for all jont realzaton n a Monte Carlo Smulaton framework, and frt-order rate contant wa etmated ung the Bucheck and Alcantar approach. The reult how that uncertanty n head obervaton can reult n overetmaton of the frt-order rate by more than one order of magntude. The reult alo how that, for the gven hydrogeologcal ettng, uncertanty n the geometry of the ource zone doe not play an mportant role n propagaton of uncertanty n the etmated frt-order rate. However, th may not be the more general cae. Further nvetgaton hould be carred out to tudy the effect of uncertan ource geometry on the frt order rate n more tagnant aqufer. AKNOWLEDGEMENT The frt author would lke to acknowledge the Alberta Ingenuty Fund for provdng upport for th reearch. REFERENCES Alvarez, P. J. J., and Illman, W.A. 2006: Boremedaton and Natural Attenuaton: Proce Fundamental and Mathematcal Model. John Wley & Son, 609 pp. Bauer, S., Beyer, C. and Koldtz, O. 2006: Aeng meaurement uncertanty of frt order degradaton rate n heterogeneou aqufer. Water Reource. Reearch, 42(): W0420. Bekn, B., Rttmenn, B.E. and MacDonald, J.A Natural Attenuaton: a groundwater remedaton trategy baed on demontratng caue and effect. EOS, Tranacton, AGU 82, Bucheck, T.E. and Alcantar, C.M Regreon technque and analytcal oluton to demontrate ntrnc boremedaton. Proc. of 995 Battelle Int. Conference on In Stu and On Ste Boreclamaton, San Dego, CA. Battelle Pre, Columbu, OH. Chapelle, F.H., Bradley, P., Lovely, D.R. and Vrobleky, D.A. 996: Meaurng rate of bodegradaton n a contamnated aqufer ung feld and laboratory method. Ground Water 34, Chapelle, F.H., Wddowon, M.A., Brauner, J.S., Mendez, E. and Caey, C.C Methodology for etmatng Tme of Remedaton Aocated wth Montored Natural Attenuaton. Water-Reource Invetgaton Report , US Geologcal Survey, Columba, SC. Chang, C.Y., Salantro, J.P., Cha, E.Y., Colthart, J.D. and Klen, C.L Aerobc bodegradaton of benzene, toluene, and xylene n a andy aqufer: data anal. and comp. modelng. Groundwater. 27, Deutch, C.V. and Journel, A.G GSLIB: Geotattcal Software Lbrary and Uer Gude, Oxford Unverty Pre, New York, NY, 396 pp. Hoen, A.H., Deutch, C.V. Bggar, K.W. and Mendoza, C.A Uncertanty n patal dtrbuton of redual and t downtream mpact. 6th Annual Canadan Geotechncal Conf. and 9th Jont CGS/IAH-CNC Conference, September 2-24, Edmonton, AB, Canada. Imhoff, P.T., Jaffe, P.R. and Pnder, G.F An expermental tudy of complete doluton of a nonaqueou phae lqud n aturated porou meda. Water Reource Reearch, 30(2): Mayer, A.S. and Mller, C.T The nfluence of ma tranfer charactertc and porou meda heterogenety on nonaqueou phae doluton. Water Reource Reearch, 32(6): Pfannkuch, H.O Determnaton of contamnant ource trength from ma exchange procee at the petroleum-ground-water nterface n hallow aqufer ytem. Proc. NWWA/API Conf. on Petroleum Hydrocarbon and Organc Chemcal n Groundwater, NWWA, 5-7 Nov, Worthngton, Oho. Power, S.E. Abrola, L.M. and Weber, W.J An expermental nvetgaton of nonaqueou phae lqud doluton n aturated uburface ytem: Tranent ma tranfer rate. Water Re. Re., 30(2), Rehfeldt, K.R., Bogg, J.M. and Gelhar, L.W Feld tudy of dperon n a heterogeneou aqufer: 3. Geotattcal analy of hydraulc conductvty, Water Reource Reearch, 28(2): Rfa, H. S., Newell, C.J. Gonzale, J.R. Dendrou, S. Kennedy, L. and Wlon, J.T Boplume III Natural Attenuaton Decon Support Sytem, veron.0, uer' manual. EPA/600/R-98/00. Rfa, H.S., and Rttaler, T Modelng natural attenuaton of benzene wth analytcal and numercal model. Bodegradaton, 6, Wedemeer, T. H., Rfa, H.S., Newell, C.J. and Wlon, J.T Natural Attenuaton of Fuel Hydrocarbon and Chlornated Solvent n the Suburface. John Wley & Son, Hoboken, N.J. Wlon, R.D., Thornton, S.F. and Mackay, D.M Challenge n montorng the natural attenuaton of patally varable plume. Bodegradaton, 5: Zhang, Y.K., and Heathcote, R.C An mproved method for etmaton of bodegradaton rate wth feld data. Groundwater Mon. & Remed, 23, 2-6. Zheng, C MT3D: A Modular, 3D Tranport Model for Smulaton of Advecton, Dperon and Chemcal Reacton of Contamnant n Groundwater Sytem. Report to the U.S. EPA, Ada, OK, 70 pp. Zheng, C., Bennett, G.D Appled Contamnant Tranport Modelng: Theory and Practce. Van Notrand Renhold Pub., New York, 440 pp. 570