PROTECTING WELLHEAD QUALITY AND QUANTITY IN A CONTAMINATED AQUIFER

Transcription

1 57ème CONGRÈS CANADIEN DE GÉOECHNIQUE 5ème CONGRÈS CONJOIN SCG/AIH-CNN 57H CANADIAN GEOECHNICAL CONFERENCE 5H JOIN CGS/IAH-CNC CONFERENCE PROECING WELLHEAD QUALIY AND QUANIY IN A CONAMINAED AQUIFER J. F. Sykes, Department of Cvl Engneerng, Unversty of Waterloo, Waterloo, Ontaro, Canada S. D. Norman, Department of Cvl Engneerng, Unversty of Waterloo, Waterloo, Ontaro, Canada M. I. Jyrkama, Department of Cvl Engneerng, Unversty of Waterloo, Waterloo, Ontaro, Canada ABSRAC he protecton of water qualty and quantty at the Parkway Wellfeld n oms Rver, New Jersey requres careful management of pumpng rates at the feld s seven wells. o support ths management, a detaled, three-dmensonal, transent, hghly calbrated groundwater model has been developed for the Cohansey aqufer. Well pumpng rates as well as groundwater recharge have changed seasonally and yearly over the 32 year perod snce contamnants were llegally dumped at the Rech Farm Superfund ste, north of the wellfeld. he evoluton of the wellfeld combned wth the spatally and temporally varable recharge n the Cohansey aqufer results n the fact that tradtonal steady-state capture zones may not permt the optmal management of the water quantty and qualty at the Parkway wells. Rather, fully transent capture zones and analyses are requred for wellhead management. he adjont method appled to the contamnant transport equaton s also used to defne capture zones that nclude the effect of dsperson. Further, t s shown that whle capture zones defned by average water partcle paths can be used to manage water qualty, other technques such as the Frst-Order Relablty Method (FORM) combned wth the adjont senstvty method provde the necessary nput for the management of water quantty. RÉSUMÉ La protecton de la qualté de l eau et sa quantté au champs de puts de Parkway à oms Rver, New Jersey, exge la geston actve des taux de pompage pour leurs sept puts. Pour ader à la geston de la ressource, un modèle détallé, fortement calbré, trdmensonnel, et varable en temps a été développé pour l aqufère Cohansey. Au cours d une pérode de 32 ans depus que des contamnants ont été llégalement déchargés sur la ste Superfund de la ferme Rech au nord du champs de puts, les taux de pompage ans que les taux d almentaton des eaux souterranes ont changé annuellement avec des varatons sasonnères. L évoluton du champs de puts ans que la varaton spatalle et temporelle de l almentaton de l aqufère Cohansey sgnfe que les méthodes tradtonelles pour dentfer les zones de capture en état statonnare ne permettront pas la geston optmale de la qualté et quantté de l eau des puts de Parkway. Plutôt, la modélsaton et l analyse des zones de capture en temps sont nécessares pour la geston des têtes de puts. La méthode d'adjont (adjont method) applquée à l'équaton de transport de contamnants est auss employée pour défnr les zones de capture qu ncluent l'effet de la dsperson. De plus, tands que des zones de capture défnes par les chemns moyens des partcules d'eau peuvent être employées pour gérer la qualté de l'eau, d'autres technques telles que la méthode de fablté du premer ordre combnée avec la méthode d'adjont fournssent les données nécessares pour la geston de sa quantté. 1. INRODUCION A statstcally sgnfcant chldhood cancer cluster has been dentfed n oms Rver, New Jersey (see Fgure 1). A case-control epdemologcal study nto the cause of the cancer ncluded an nvestgaton of the qualty of the groundwater used to supply the muncpal water dstrbuton system. Hstorcally, groundwater for the water dstrbuton system was suppled by numerous wells ncludng fve wells that are part of the Parkway Wellfeld. he Parkway wells are approxmately 16 m down gradent from the Rech Farm Superfund ste. he contamnants that mgrated from the ste, through the Cohansey aqufer, and entered one or more of the Parkway wells ncluded trchloroethylene (CE), perchloroethylene (PCE) and a styrene-acrylontrle (SAN) trmer. An addtonal well was nstalled at the wellfeld to further control the contamnant plume enterng some Parkway wells and to maxmze the quantty of water pumped from the aqufer. he water from three wells s treated usng an ar strpper and carbon adsorpton columns, and then dscharged to the ground surface n an area southwest of the wellfeld. Water from the remanng Parkway wells s used to supply the muncpal water dstrbuton system. 2. SIE DESCRIPION 2.1 Spatal Doman he modellng doman s bounded on the west by the oms Rver, on the south by the oms Rver estuary, on the east by Barnegat Bay and along the north by a surface water dvde and assumed groundwater dvde. he top of the model s defned by a Dgtal Elevaton Model (DEM) obtaned from the New Jersey Geologcal Survey, whle the bottom of the doman represents the nterface between the bottom of the Cohansey-Krkwood aqufer and the top of a basal clay layer as defned by Zapecza Page 1

2 Fgure 1. Ste map showng locaton of oms Rver n New Jersey, the modellng doman, and the locaton of the Rech Farm Superfund ste and the varous muncpal pumpng wells (1989). he nterface between the Cohansey and Krkwood aqufers s nterpolated from drller s logs that entered the Krkwood formaton, where the Krkwood formaton s dentfed by fne gray sands and slts, and gray clays. he locatons of these wells were determned from a combnaton of nformaton provded on the well records, well permts, tax maps, a tax database, property locatons by street address and lot/block, as well as the 1995/97 aeral dgtal orthophotography from the New Jersey Department of Envronmental Protecton (NJDEP). he use of ArcVew GIS was ntegral to the management of the data and determnaton of well coordnates. he MODFLOW model s comprsed of columns, 8 rows, and 4 layers; of whch the top three layers represent the hgher conductvty Cohansey aqufer, whle the bottom layer represents the lower conductvty Krkwood aqufer. categores as shown n Fgure 2 are represented n the model usng the MODFLOW rver package. he surface water bodes n the model were descrbed usng rver wdth and length n a grd block, conductance, stage elevaton, and water depth. Stage elevatons of rvers and 2.2 Boundary Condtons Boundary condtons for the top surface of the model doman were represented by prescrbed ype I Drchlet boundary condtons (general head boundary (GHB) condton as mplemented n MODFLOW), leakance from surface water bodes such as rvers, lakes, and ponds, and recharge from precptaton. Fgure 2 depcts the varous boundary condtons that were assgned to the layer 1 grd blocks. he oms Rver estuary and Barnegat Bay were represented usng a general head boundary condton (see Fgure 2). Head elevatons for these grd blocks were set to zero feet AMSL, and a hgh conductance was selected for these blocks. he Rvers and Surface Water Fgure 2. Boundary condtons appled to layer 1 of the groundwater flow model Page 2

3 lakes or ponds were estmated from the USGS 7.5 mnute quadrangle maps as the DEM was not suffcently accurate to determne the elevaton of surface water bodes. GIS layers for rvers, ponds and lakes were obtaned from the NJDEP. Some of these GIS layers were corrected to reflect the actual locatons of water features as shown n the USGS quadrangle maps for the area. ArcVew GIS was used to facltate the calculaton of the grd block propertes and to create some MODFLOW nput fles. Stage elevatons, surface water body areas, and conductances were assumed to be temporally nvarant. Recharge for the doman vares both spatally and temporally. A combnaton of land use, sol maps, daly precptaton and temperature over a 3+ year tme span, and the HELP3 (Hydrologc Evaluaton of Landfll Performance) model were used n a database / ArcVew framework to develop monthly recharge values (that vary n tme and n space) for each recharge grd block. hs approach s documented n Jyrkama (2). Fgure 3 shows the average monthly recharge for the ten year perod from 1981 to Pumpng Wells Eght muncpal pumpng wells that pump water from the Cohansey aqufer are shown n Fgure 1. he Parkway Wellfeld s comprsed of Wells 22, 24, 26, 26B, 28, and 29. Pumpng volumes for the eght wells from 1981 to 1 are shown n Fgure 4. he eght wells shown on Fgure 1 have not operated n a contnuous manner as demonstrated n Fgure 4. Some wells such as 26B and 44 are relatvely new, whle Well has ceased operaton as of md he remanng Parkway wells have operated at varable rates dependng on the consumer demand for water, whch vares from season to season. Wells 22 and 28 have steadly ncreased ther pumpng rates over the years, whle Well 26 s pumpng rates decreased durng the 199 s. he well was redeveloped, thereby ncreasng ts capacty. Fgure 3. en year temporally averaged, spatally varable recharge for 1981 through 199 Well Well Well Well Well 26B Well Well Well Fgure 4. Monthly pumpng volumes for varous wells from 1981 to 1 Page 3

4 3. WAER QUALIY 3.1 Capture Zones In order to better protect groundwater resources, capture zone analyss s typcally performed usng steady state reverse partcle trackng. Although ths practce s common, t does not account for the transent behavour of wells, the evoluton of groundwater flow systems, or the effects of seasonally and/or annually varyng ranfall and temperature. he temporally averaged recharge and pumpng rates from 1981 to 199 were used to model the steady state capture zones for the 1991 to 1 tme perod. ransent capture zones were also modelled usng the recorded precptaton, temperature, and well pumpng rates. he modellng llustrates the dfferences between the steady state and the transent analyses Steady State Capture Zones Well pumpng rates for the January 1981 to December 199 perod were averaged to obtan the steady state pumpng rates for the steady state capture zone analyss. Monthly spatally varable recharge was averaged over the same ten year perod to yeld the temporally averaged, spatally varable recharge shown n Fgure 3. Reverse partcle trackng was performed usng MODPAH to yeld Fgure 5. Fgure 5. en year steady state capture zones for wells ransent Capture Zones he transent capture zone analyss was performed by generatng a grd of partcles (151 rows by 131 columns) on a 3.48 m (1 ft) grd at the begnnng of each month, from October 1971 to December for a total of 6,83,589 partcles (some partcles were not wthn the actve modellng doman and are excluded). Each partcle was tracked to determne ts destnaton, whether to a well or otherwse. Fgure 6 demonstrates all partcles released n January 1991 that entered one of the eght wells wthn 1 years. As can be seen, the capture zones are slghtly dfferent as compared to Fgure 5. Some notable dfferences can be seen wth Well, as t was shutdown a few years nto the future, as vewed from the perspectve of when these partcles were released. he capture zones for Well 22 and Well 24 are relatvely stable and can be traced back to the fact that the pumpng rates for these wells are mostly mantaned at steady state values durng the 199 s. Other wells show a marked dfference, namely Wells 26B and 44 whch dd not exst n 1991 and whose presence was not antcpated. hs has the effect of changng the capture zones of neghbourng wells 26, 28, and 29. Some partcles n the vcnty of Rech Farm can be seen to enter Well 26B wthn 1 years, although Well 26B does not yet exst n Varatons n the pumpng rates at the varous wells s demonstrated n the jaggedness of the capture zones. he capture zone for Well 22 contans partcles that wll be captured by Well 28, snce Well 22 wll be shutdown at some pont n the future (late 1996). he same can be sad of Well 28 partcles dspersed wthn the Well 29 or Well 26 capture zones. Fgure 6. Average water partcles released n January 1991 that arrved n a well wthn ten years Gven that a partcle released at a partcular locaton may enter dfferent wells dependng on when t was released, partcle lkelhood maps have been generated to demonstrate the lkelhood that an average water partcle entered a partcular well. he lkelhood s calculated as Page 4

5 the number of average water partcles enterng a gven well dvded by the number of average water partcles that entered any well. hs approach would exclude partcles that have not yet reached a destnaton; ether a well, or snk such as a rver or lake. Average water partcles move wth the ntersttal groundwater flow velocty and do not represent the mgraton of contamnants, many of whch are affected by adsorpton, dffuson, and dsperson mechansms. to pump. Average water partcles that had mgrated toward Well 22 whle t was pumpng, whch were close to beng captured, were not as the well was turned off. Snce Well 28 was nearby and pumpng, these average water partcles were captured by Well 28. Fgure 7 represents the lkelhood of an average water partcle enterng Well from October 1971 to December. In the vcnty of Rech Farm, the lkelhood ncreases n a westerly drecton because Well was n operaton several years pror to the development of the Parkway Wellfeld. As the groundwater flow system evolved due to pumpng at the Parkway Wellfeld, average water partcles that would have orgnally mgrated to Well, then mgrate to Wells 26, 26B, or 28 (see Fgures 8, 9, and 1). he lkelhood map for Well 26 (see Fgure 8) s relatvely stable and conforms qute well to the capture zones n Fgures 5 and 6. Well 26B n Fgure 9 shows a low lkelhood of average water partcle capture because Well 26B was placed nto operaton n he lkelhood s greatest at the ends of the capture zones, as ths allows more travel tme for the average water partcles and they are more lkely to be captured by Well 26B as t develops ts capture zone nto the future. Fgure 1 llustrates the lkelhood of capture for Well 28. As can be seen, Well 28 wll, on occason, capture average water partcles that orgnate n Well 22 s capture zone. A few nstances exst a whereby Well 22 was turned off, whle Well 28 contnued Fgure 8. Lkelhood of an average water partcle enterng Well 26 from Oct to Dec. Fgure 7. Lkelhood of an average water partcle enterng Well from Oct to Dec. Fgure 9. Lkelhood of an average water partcle enterng Well 26B from Oct to Dec. Page 5

6 Fgure 1. Lkelhood of an average water partcle enterng Well 28 between Oct and Dec. Fgure 12. Lkelhood of an average water partcle enterng Well 44 between Oct and Dec. be seen n Fgure 13. he majorty of these partcles arrved pre-1985 as compared to post Approxmately.56% of average water partcles orgnated northwest of Well 29. For Well 44 (see Fgure 14), approxmately.82% of average water partcles orgnated north of Well 44 and entered between July 1998 and Aprl Backward Advectve Dspersve ransport he forward advectve dspersve solute transport equaton s defned as: C C C D j q t x x [1] j x where s the porosty, D j s the dspersvty tensor, q s the darcy flux, t s tme and C s the concentraton. he adjont of the advectve dspersve solute transport equaton s: * * * f(,c) D j q [2] t x x x C j Fgure 11. Lkelhood of an average water partcle enterng Well 29 between Oct and Dec. Fgures 11 and 12 llustrate that partcles whch would mostly be captured by Wells 26, 26B, or 28, can be captured, under some crcumstances, by Wells 29 and 44. An analyss of when these partcles arrved at Well 29 can where * s the adjont state varable, or mportance functon, and s any model nput varable. Equaton 2 s solved backward n tme from a prescrbed fnal state. o nvestgate the senstvty to the concentraton n a pumpng well, Page 6

7 Fgure 13. Fracton of average water partcles that arrve at Well 29 n each month from the northwest Fgure 14. Fracton of average water partcles that arrve at Well 44 n each month from the northwest f(,c) C C w Q C for w Q for w In other words, the concentraton appled to the backwards problem s unty at the specfed pumpng well, and zero elsewhere. he adjont of the forward advectve dspersve equaton represents the backward advectve dspersve equaton. A beneft of usng an advectve dspersve smulaton s that dsperson and dffuson are accounted for, whereas average water partcle trackng does not nclude these transport processes. M3DMS was used to perform the backward solute transport smulatons. he nput data fles for M3DMS were processed to reverse the tme step order, as well as reversng the fluxes, veloctes, and storage terms calculated from the forward transent groundwater flow smulatons. One smulaton was performed for each well wth a unt concentraton appled to the approprate well. he ten year results for several wells are descrbed n the followng paragraphs. Fgure 15 shows the mportance functon for Well 26. As n the comparson for Well, we can see that dsperson tends to lengthen the zone of mpact and make t wder. A small lobe can also be seen northeast of the well. [3] Fgure 15. Importance functon for Well 26 n January 1991 Smlarly, Well 26B s shown n Fgure 16; snce Well 26B was nstalled n 1999, regons of greater mportance are shown to be further away from the well. Fgure 17 for Well 28 also demonstrates the effects of Well 22 beng turned off as prevously shown n Fgure 1. Fgure 18 for Well 29 shows that Well 29 obtans most of ts water from the east although some comes from the west, and s dfferent than the steady state capture zones shown n Fgure WAER QUANIY Management of a well requres the consderaton of both water qualty and quantty aspects. Whle land use management wthn the well capture zone s an effectve way of protectng the well from contamnaton, the head and hence, producton at the well s not controlled only by the well capture zone, but by the wder aqufer system. Groundwater flow s nfluenced both by the physcal characterstcs of the aqufer, as well as the recharge boundary condton. Whle recharge s affected by a multtude of factors, such as clmatc condtons and the nature of the unsaturated zone, t s also nfluenced by land surface parameters such as land use and vegetaton (Sharma, 1989). herefore, any changes n land use wll not only nfluence the groundwater flow system,.e. heads at specfc locatons, through the recharge mechansm, but wll also mpact the extent and confguraton of well capture zones. In the present study, the hghly varable recharge boundary condton for the groundwater model ncorporated detaled nformaton about the land use and land cover n the study area. he mpact of the recharge Page 7

8 Fgure 16. Importance functon for Well 26B n January 1991 Fgure 18. Importance functon for Well 29 n January Relablty Analyss Relablty analyss (e.g. the frst- and second-order relablty methods FORM and SORM) are based on the formulaton of falure crtera whch s flexble and applcable to a wde spectrum of problems and events (e.g. Star, 1987 and Jang, 1994). he man advantage of the method over other approaches, besdes hgh computatonal effcency, s that t not only provdes senstvty nformaton as an ntegral part of the soluton, but t also determnes the combnaton of model parameters that are most lkely to result n the falure condton. hs s very useful for studes wth a large number of uncertan varables, such as grd based groundwater modellng nvestgatons. he senstvty nformaton also dentfes parameters that have the hghest nfluence on the soluton, whch can be used to assess the mpact of the recharge boundary condton on the groundwater flow system. Consder the lmt-state equaton, or performance measure M as S h M g( X ) w( u) h ( u) [4] Fgure 17. Importance functon for Well 28 n January 1991 boundary condton, and hence land use, on the head or flow rate at a pumpng well are therefore nvestgated by ntegratng the relablty analyss method wth MODFLOW. where X denotes the uncertan boundary recharge fluxes, w(u) s an arbtrary weghtng functon denotng the locaton of mportance, u s the locaton vector, h S s the smulated head, and h s the specfed target head. he lmt-state equaton s therefore solely a functon of pezometrc head and only ndrectly related to recharge through the heads. o smplfy the analyss, we select a Page 8

9 sngle locaton of nterest concdng wth the locaton of a pumpng well (.e. Well 22) such that w PW 22 ( u ) ( u u ) [5] where denotes the Drac delta. he falure condton assocated wth the lmt-state equaton, therefore, ndcates the probablty that the head at Well 22 would fall below a certan specfed level h, due to uncertantes n the estmated recharge dstrbuton. Or n other words, the probablty assocated wth exceedng a specfed drawdown at the well. he probablty of falure s obtaned by ) P g( X f ( x) dx [6] x g( X) where f X (x) s the jont PDF of X ntegrated over the entre falure doman. he frst-order approxmaton of the probablty of falure s estmated as P f ( ) [7] where s the standard normal CDF and s the relablty ndex. he relablty ndex s defned as the closest dstance from the orgn to the falure surface n standard normal space, also known as the desgn pont Y*, and s estmated accordng to the non-lnear constraned optmzaton problem 1 Yk 1 G( Yk ) Yk G( Yk ) G( Yk ) [8] 2 G( Y ) k whch can be solved usng the effcent and robust HL-RF algorthm (Hasofer, 1974 and Rackwtz, 1978). he senstvty of wth respect to equally lkely changes n the random varables s descrbed by the unt gamma senstvty vector as ( ) D [9] ( ) D where D s the dagonal matrx of standard devatons. he evaluaton of the gradent senstvty vector G(Y) n grd based numercal models can become very demandng computatonally, due to the potentally large number of random varables resultng from model dscretzaton. hs challenge s overcome by mplementng the adjont method for flow n MODFLOW. 4.2 Adjont Method he equatons used to solve the groundwater flow problem n MODFLOW are descrbed n matrx form as A(, h q( ˆ) [1] where A s the symmetrc matrx of head coeffcents, are system parameters, h are the head values, and q s the vector of constant terms, or RHS, whch s a functon of the model boundary condtons ˆ (McDonald, 1996). In ths study, only the recharge rates are assumed to be random or uncertan, whle all other model parameters are assumed to be constant (.e. determnstc). he soluton of the frst-order relablty problem requres the senstvty of the lmt-state equaton wth respect to the recharge boundary condton. he margnal senstvty of the performance measure M wth respect to the recharge rates X s M M( h X h X [11] Expressng the flow problem n terms of head and recharge only, and dfferentatng wth respect to X gves A( h h X h [ I h] A( X q( X) X [12] where I s the dentty matrx and * denotes the Kronecker or outer product. Representng the state senstvty d{h} / d{x} } as, the adjont equatons of the partal dfferental equatons are formulated by multplyng [12] by an arbtrary dfferentable constant ~ and subtractng the result from [11] to gve M M( ~ A( ~ ~ q( X) [ I h] A( X h h X [13] Collectng terms, M M( ~ X h Snce ~ s arbtrary, we let A( ~ ~ q( X) [ I h] A( h X [14] M( ~ A( [ ] ~ ( ) I h A h h h herefore, [15] A( ~ M( A( [ I h] [16] h h where ~ represents the adjont state or mportance functon (Sykes, 1985). As shown n [4], the performance functon s formulated n terms of the pezometrc head and the weghng functon w(u). he load term on the rght hand sde of [16] therefore becomes Page 9

10 M( w( u) h [17] As ndcated by [5] the weghng functon s equal to 1 at the pumpng well, and zero elsewhere. he second term on the left hand sde of [16] can be shown to have a neglgble mpact on the convergence of the relablty soluton, and s therefore gnored. hs smplfes [16] to A( ~ w( u) [18] he mportance functon, therefore, represents the ncrease of head at all locatons n the doman due to a unt volumetrc nflux of water at the well. Because q s formulated n terms of recharge volume n MODFLOW, the margnal senstvty of the performance measure wth respect to the system parameters smplfes to M X g( X) ~ rc [19] where r and c denote the dmensons of the fnte dfference grd blocks n the row and column drectons, respectvely. he senstvty of head at the well wth respect to the recharge boundary condton g(x) s therefore smply equal to the value of the mportance functon n each grd block multpled by the horzontal grd block area. 4.3 MODFLOW Implementaton Evaluaton of the gradent senstvty vector requres the soluton of [1] whch s termed the forward problem and s solved frst for the coeffcent matrx A and the head dstrbuton h, whle [18] s defned as the backward problem and s used to calculate the mportance functon for a gven performance functon M. he backward problem can be readly solved usng MODFLOW by: 1) runnng MODFLOW (forward problem) to obtan the A matrx, 2) settng the RHS vector equal to zero, except for the grd cell contanng the pumpng well, whch s set to one, and 3) re-runnng MODFLOW usng the new RHS to obtan the mportance functon. he senstvty of head wth respect to the recharge boundary condton can therefore be obtaned n a sngle MODFLOW run. Whle the forward problem s non-lnear, the adjont problem s lnear wth passve boundary condtons. hat s, there s no loadng except at the node of nterest. he method was mplemented n MODFLOW- 96 (McDonald, 1996), wth only mnmal addtons to the exstng code. 4.4 Model Applcaton As dscussed prevously, the recharge boundary condton for the groundwater model was estmated usng the physcally based recharge methodology, whch consdered detaled nformaton about the land use and sols n the study area. he land use and sol based recharge rates were then averaged over the model grd to obtan the recharge boundary condton for the groundwater flow model. Usng the same analogy, the senstvtes n [19] can be related back to the orgnal land use and sol based recharge rates through the chan rule as M R M X X R n 1 ~ rc â [] where R are the land use and sol based recharge rates, n s the number of grd blocks ntersectng each unque land use and sol area, and â s the proporton of the area wthn each of the ntersected grd blocks. Equaton [] therefore allows the assessment of the mpact of recharge on the groundwater flow system ndependent of the groundwater model dscretzaton. he land use and sol based recharge rates (a total of 7357 unque combnatons) were assumed to be lognormally dstrbuted, whle the coeffcent of varaton (COV) was used to reflect uncertanty n the estmates. he same COV was assumed for all recharge rates n each smulaton. he objectve of the relablty analyss was to fnd the dstrbuton of recharge (wth a specfed level of uncertanty) that would cause the head n the well to be less than or equal to a specfed target level. All smulatons were run untl the lmt-state equaton,.e. the head dfference n the well was less than.1 m. o smplfy the analyss, all smulatons were done under steady-state condtons. he steady-state pumpng rate at Well 22 was equal to 2715 m 3 /day. he algorthm was computatonally very effcent as convergence was generally obtaned n only a few teratons. he mean pont n the standard normal space was used as the startng pont for all smulatons. 4.5 Results and Dscusson Fgure 19 shows the mportance or mpulse functon obtaned from the backward problem. he value of the functon decreases exponentally wth dstance from the well as a result of the unt njecton of water nto the system at the well. A typcal result of the relablty analyss s shown n Fgure. In ths case, the target head was assumed to be.6 m below the mean value, wth a COV of.3 for the recharge rates. he plot llustrates the dfference n recharge between the mean condton (.e. average annual recharge dstrbuton) and the dstrbuton of recharge that resulted n falure (.e. the most lkely realzaton of recharge that resulted n the head beng equal to.6 m below the mean value at Well 22). Page 1

11 Fgure 19. Importance functon for groundwater flow for Well 22 Fgure 21. Unt gamma senstvty for Well 22 greater than or equal to.6 m below the mean condton, was equal to.17. he relatve mportance of each of the nput parameters,.e. ndvdual recharge rates, on the probablstc outcome are shown by the unt gamma senstvtes n Fgure 21. he steady-state capture zone for Well 22 s also ncluded n Fgure 21. As ndcated by [9], the unt gamma senstvty s scaled by the standard devatons and measures the senstvty of the relablty ndex wth respect to equally lkely changes n the random varables,.e. the recharge rates. he negatve sgns ndcate an nverse relatonshp, that s, ncreasng the recharge rates wll result n a decrease n the probablty of falure. In other words, ncreasng recharge wll ncrease the relablty of the head at the well. Fgure. Dfference n recharge for Well 22 resultng from a recharge COV of.3. It s evdent from Fgure that areas wth hgher ntal recharge rates have a hgher nfluence on the head at the well, whle areas such as hghways wth low ntal recharge rates have a smaller mpact. he estmated probablty of falure,.e. the probablty that the head s he most mportant feature of Fgure 21 s that t dentfes areas that have the most mpact on the probablty of falure (or relablty) at the well. Darker areas contrbute more to the probablty of falure, or the probablty that the head at the well wll decrease by.6 m. It s evdent that areas that are qute dstant from the pumpng well (and also down-gradent and outsde the steady-state well capture zone) can have a sgnfcant mpact on the head at the well. herefore, Fgure 21 demonstrates how land use plannng and management decsons based purely on the water qualty crtera (as dctated by the wellhead protecton programs) may not protect the head, and hence, producton at a well. he probablty of falure ncreases wth ncreased uncertanty n the estmated recharge dstrbuton. For example, for COV of.5 there s an 83% probablty that the head at the well s less than or equal to.5 m below Page 11

12 the mean level (.e. the drawdown at the well exceeds.5 m), whle the probablty s 38% for COV of.4 and 3% for COV of.3. Increasng the confdence n the estmated recharge dstrbuton wll therefore decrease the probablty of falure (or ncrease the relablty) of the smulated head at the well. 5. CONCLUSIONS Both the transent forward average water partcle trackng method and the backward advectve dspersve transport method demonstrate the effect of transents upon capture zones. It s not uncommon that average water partcles n one well s capture zone, would mgrate to a dfferent well once the frst well s taken out of servce. It s also evdent that an average water partcle departng from the same locaton, but at dfferent tmes, can ultmately be captured by varous wells, as can be seen by the lkelhood plots for partcles departng from the vcnty of Rech Farm. he relablty analyss method was ntegrated wth MODFLOW to study the nfluence of the recharge boundary condton on the groundwater flow system. he spatally varyng mean recharge dstrbuton was derved from detaled sol and land use nformaton, whle the coeffcent of varaton was used to reflect uncertanty n the estmates. he performance functon was formulated n terms of the head or flow rate at a pumpng well. he heavy computatonal burden of calculatng the gradent senstvty vector n the relablty analyss was overcome effcently by mplementng the adjont method n MODFLOW. Consequently, the senstvty of the performance functon to recharge n all the grd blocks n the model could be computed n a sngle MODFLOW run wth only mnmal changes to the orgnal MODFLOW code. he nfluence of the orgnal physcally based recharge dstrbuton on the performance functon was furthermore obtaned usng the grd block margnal senstvtes. hs allowed the assessment of the mpact of recharge on the groundwater flow system ndependent of the groundwater model dscretzaton. References Hasofer, A.M., and N. Lnd An exact and nvarant frst-order relablty format. Journal of Engneerng Mechancs, 1(1), pp Jang, Y.-S., N. Star, and A. Der Kureghan Relablty analyss of contamnant transport n saturated porous meda. Water Resources Research, 3(8), pp Jyrkama, M.I., J.F. Sykes, S.D. Norman. 2. Recharge Estmaton for ransent Ground Water Modelng. Groundwater, (6), pp McDonald, M.D., and A.W. Harbaugh A Modular hree-dmensonal Fnte Dfference Groundwater Flow Model. Unted States Geologcal Survey. Rackwtz, R., and B. Fessler Structural relablty under combned load sequences. Computers and Structures, 9, pp Sharma, M.L. (ed.) Groundwater Recharge. Proceedngs of the Symposum on Groundwater Recharge, Mandurah, Australa, 6-9 July 1987, A.A. Balkema, Rotterdam. Star, N., J.D. Cawlfeld, and A. Der Kureghan Frst-Order Relablty Approach to Stochastc Analyss of Subsurface Flow and Contamnant ransport. Water Resources Research, 23(5), Sykes, J.F., J.L. Wlson, and R.W. Andrews Senstvty analyss for steady state groundwater flow usng adjont operators. Water Resources Research, 21(3), Zapecza, Otto S., Hydrogeologc Framework of the New Jersey Coastal Plan Regonal Aqufer System Analyss - Northern Atlantc Coastal Plan, U.S. Geologcal Survey Professonal Paper 14-B It was concluded that the senstvty of head at the well s not only dependent on dstance, but also on the sze of the fnte dfference grd blocks and hence total recharge for the grd block. Whle areas wth hgher ntal recharge rates had a hgher nfluence on the smulated head at the well, dstant land use areas that were outsde the tradtonal well capture zone also had a sgnfcant mpact on the head at the well, as dentfed by the normalzed gamma senstvty coeffcent. herefore, land use plannng and management decsons based purely on the water qualty crtera (as dctated by the tradtonal wellhead protecton programs) may not necessarly protect the head, and hence, producton at a well. Although the methodology was subject to some assumptons and lmtatons, t clearly demonstrated the potental of usng the relablty method n probablstc groundwater flow modellng. Page 12