EFFECT OF GROUNDWATER PUMPING SCHEDULE VARIATION ON ARRIVAL OF TETRACHLOROETHYLENE (PCE) AT WATER-SUPPLY WELLS AND THE WATER TREATMENT PLANT

Transcription

1 EFFECT OF GROUNDWATER PUMPING SCHEDULE VARIATION ON ARRIVAL OF TETRACHLOROETHYLENE (PCE) AT WATER-SUPPLY WELLS AND THE WATER TREATMENT PLANT Jnjun Wang and Mustafa M. Aral Multmeda Envronmental Smulatons Laboratory School of Cvl and Envronmental Engneerng Georga Insttute of Technology Atlanta, Georga, USA MESL January 2007

2 EFFECT OF GROUNDWATER PUMPING SCHEDULE VARIATION ON ARRIVAL OF TETRACHLOROETHYLENE (PCE) AT WATER-SUPPLY WELLS AND THE WATER TREATMENT PLANT by Jnjun Wang and Mustafa M. Aral Multmeda Envronmental Smulatons Laboratory School of Cvl and Envronmental Engneerng Georga Insttute of Technology Atlanta, Georga, USA The work on whch ths report s based was supported by the School of Cvl and Envronmental Engneerng, Georga Insttute of Technology. The project was admnstered through the Multmeda Envronmental Smulatons Laboratory of the School of Cvl and Envronmental Engneerng, Georga Insttute of Technology. MESL January 2007

3 Authors Mr. Jnjun Wang s a graduate student at Multmeda Envronmental Smulatons Laboratory n the School of Cvl and Envronmental Engneerng, Georga Insttute of Technology. Dr. Mustafa M. Aral (PhD, PE) s a Professor and the Drector of Multmeda Envronmental Smulatons Laboratory n the School of Cvl and Envronmental Engneerng, Georga Insttute of Technology. Acknowledgments Ths report s based on the work conducted n Multmeda Envronmental Smulatons Laboratory n the School of Cvl and Envronmental Engneerng, Georga Insttute of Technology. The authors are grateful for the contnued support provded by Agency for Toxc Substances and Dsease Regstry (ATSDR) and the School of Cvl and Envronmental Engneerng, Georga Insttute of Technology n the actvtes of Multmeda Envronmental Smulatons Laboratory. Computatonal servces were provded by the Multmeda Envronmental Smulatons Laboratory facltes. Jnjun Wang and Mustafa M. Aral Effect of Groundwater Pumpng Schedule Varaton on Arrval of Tetrachloroethylene (PCE) at Water-Supply Wells and the Water Treatment Plant Research report No.: MESL-01-07; January 2007, 91p. Keywords Groundwater, Exposure-dose reconstructon, hydrogeology, coupled smulaton-optmzaton model.

4 Table of Contents Table of Contents...v Lst of Fgures... v Lst of Tables... v Glossary of Acronyms and Abbrevatons... x Abstract Introducton A Revew of ATSDR Camp Lejeune Study Background Introducton to smulaton tools and nput data MODFLOW model and nput data MT3DMS model and nput data Water-supply well nformaton Smulaton results of ATSDR modelng study Optmzaton of the Pumpng Schedules Formulaton of the optmzaton model Selecton of the optmzaton method The Downhll Smplex method The Steepest Descent method The Conjugate Gradent method Genetc Algorthms Introducton to PSOpS Methodology of PSOpS The rank-and-assgn method The mproved gradent method Improvement of computatonal effcency Input data for PSOpS Smulaton Results and Dscusson Optmzaton and smulaton results for the Maxmum Schedule PCE dstrbuton n the groundwater system PCE concentraton n the water-supply wells PCE concentraton n the WTP Optmzaton and smulaton results for the Mnmum Schedule I PCE dstrbuton n the groundwater system PCE concentraton n the water-supply wells PCE concentraton n the WTP Optmzaton and smulaton results for the Mnmum Schedule II v

5 4.3.1 PCE dstrbuton n the groundwater system PCE concentraton n the water-supply wells PCE concentraton n the WTP Summary of smulaton results Pumpng rate n well TT PCE concentraton n well TT PCE concentraton n the WTP Conclusons Summary of Results References v

6 Lst of Fgures Fgure 2.1. Water-supply well locatons at Tarawa Terrace and vcnty, U.S. Marne Corps Base Camp Lejeune, North Carolna...6 Fgure 2.2. PCE concentratons n water-supply wells under the Orgnal Schedule...13 Fgure 2.3. PCE concentratons n the WTP under the Orgnal Schedule...15 Fgure 2.4. PCE concentratons n the WTP under the Orgnal Schedule for the perod of nterest...16 Fgure 3.1. Flowchart for PSOpS...25 Fgure 3.2. Flowchart for the mproved gradent method...32 Fgure 4.1. Pumpng rate and pumpng capacty of well TT-26 under Maxmum Schedule...36 Fgure 4.2. Comparson of PCE dstrbuton n Layer 1 under the Orgnal Schedule and the Maxmum Schedule...37 Fgure 4.3. Comparson of PCE dstrbuton n Layer 3 under the Orgnal Schedule and the Maxmum Schedule...38 Fgure 4.4. Comparson of PCE dstrbuton n Layer 5 under the Orgnal Schedule and the Maxmum Schedule...39 Fgure 4.5. PCE concentratons n water-supply wells under the Orgnal Schedule and the Maxmum Schedule...40 Fgure 4.6. PCE concentratons n well TT-26 under the Orgnal Schedule and the Maxmum Schedule for perod of nterest...42 Fgure 4.7. PCE concentratons n WTP under the Orgnal Schedule and the Maxmum Schedule...43 Fgure 4.8. PCE concentratons n the WTP under the Orgnal Schedule and the Maxmum Schedule for the perod of nterest...44 Fgure 4.9. Pumpng rate and pumpng capacty of well TT-26 under the Mnmum Schedule I...46 Fgure Comparson of PCE dstrbuton n Layer 1 under the Orgnal Schedule and the Mnmum Schedule I...48 Fgure Comparson of PCE dstrbuton n Layer 3 under the Orgnal Schedule and the Mnmum Schedule I...49 Fgure Comparson of PCE dstrbuton n Layer 5 under the Orgnal Schedule and the Mnmum Schedule I...50 Fgure PCE concentratons n water-supply wells under the Orgnal Schedule and the Mnmum Schedule I...51 Fgure PCE concentratons n water-supply wells under the Orgnal Schedule and the Mnmum Schedule I for the perod of nterest...53 Fgure PCE concentratons n the WTP under the Orgnal Schedule and the Mnmum Schedule I...54 Fgure PCE concentratons n the WTP under the Orgnal Schedule and the Mnmum Schedule I for the perod of nterest...55 Fgure Pumpng rate and pumpng capacty of well TT-26 under the Mnmum v

7 Schedule II...57 Fgure Comparson of PCE dstrbuton n Layer 1 under the Orgnal Schedule and the Mnmum Schedule II...59 Fgure Comparson of PCE dstrbuton n Layer 3 under the Orgnal Schedule and the Mnmum Schedule II...60 Fgure Comparson of PCE dstrbuton n Layer 5 under the Orgnal Schedule and the Mnmum Schedule II...61 Fgure Comparson of PCE dstrbuton n Layer 1 under the Mnmum Schedule I and the Mnmum Schedule II...62 Fgure Comparson of PCE dstrbuton n Layer 3 under the Mnmum Schedule I and the Mnmum Schedule II...63 Fgure Comparson of PCE dstrbuton n Layer 5 under the Mnmum Schedule I and the Mnmum Schedule II...64 Fgure PCE concentratons n water-supply wells under the Orgnal Schedule and the Mnmum Schedule II...65 Fgure PCE concentratons n the major water-supply wells under the Orgnal Schedule and the Mnmum Schedule II for the perod of nterest...66 Fgure PCE concentratons n the major water-supply wells under the Mnmum Schedule I and the Mnmum Schedule II for the perod of nterest...67 Fgure PCE concentratons n the WTP under the Orgnal Schedule, the Mnmum Schedule I, and the Mnmum Schedule II...68 Fgure PCE concentratons n the WTP under the Orgnal Schedule, the Mnmum Schedule I, and the Mnmum Schedule II for the perod of nterest...69 Fgure Percentage of pumpng rate relatve to ts pumpng capacty n well TT-26 under the Orgnal and the updated pumpng schedules...71 Fgure Percentage of pumpng rate relatve to ts pumpng capacty n well TT-26 under the Orgnal and updated pumpng schedules for the perod of Fgure PCE concentratons n well TT-26 under the Orgnal and updated pumpng schedules...73 Fgure PCE concentratons n the WTP under the Orgnal and the updated pumpng schedules...75 Fgure PCE concentratons n the WTP under the Orgnal and the updated pumpng schedules for the perod of nterest...76 v

8 Lst of Tables Table 2.1. Input fles used for the MODFLOW smulaton code...9 Table 2.2. Input fles used for the MT3DMS smulaton code...11 Table 2.3. Locatons and servce perods of water-supply wells n the Tarawa Terrace area...12 Table 3.1. Summary of the optmzaton status for the maxmum PCE concentraton...33 Table 4.1. PCE concentratons n well TT-26 under the Orgnal Schedule and the Maxmum Schedule for the perod of nterest...42 Table 4.2. PCE masses wthdrawn under the Orgnal Schedule and the Maxmum Schedule...45 Table 4.3. PCE concentratons n the WTP under the Orgnal Schedule and the Maxmum Schedule for the perod of nterest...45 Table 4.4. PCE masses wthdrawn under the Orgnal Schedule and the Mnmum Schedule I...56 Table 4.5. PCE concentratons n the WTP under the Orgnal Schedule and the Mnmum Schedule I for the perod of nterest...56 Table 4.6. PCE masses wthdrawn under the Orgnal Schedule, the Mnmum Schedule I, and the Mnmum Schedule II...70 Table 4.7. PCE concentratons n the WTP under the Orgnal Schedule, the Mnmum Schedule I and the Mnmum Schedule II for the perod of nterest...70 Table 4.8. PCE concentratons n well TT-26 under the Orgnal and updated pumpng schedules for the perod of nterest...74 Table 4.9. PCE MCL arrval tmes n well TT-26 under the Orgnal and the updated pumpng schedules...74 Table PCE concentratons n the WTP under the orgnal and the updated pumpng schedules for the perod of nterest...75 Table PCE MCL arrval tmes n the WTP under the Orgnal and the updated pumpng schedules...76 Table PCE masses wthdrawn under the Orgnal and the updated pumpng schedules...77 v

9 Glossary of Acronyms and Abbrevatons ATSDR: CEE: DIS: FTL: GA: GT: KTC: Max. Sche.: Mn. Sche. I: Mn. Sche. II: MCL: MESL: OBS: Org. Sche. PCE PSOpS: S/O: USGS: WEL: WTP: Agency for Toxc Substances and Dsease Regstry School of Cvl and Envronmental Engneerng Dscretzaton fle for MODFLOW Flow-transport lnk Genetc algorthm Georga Insttute of Technology Kuhn-Tucker condton Pumpng schedule yeldng the early arrval tme Pumpng schedule yeldng the late arrval tme wth no condtons on the well TT-26 schedules Pumpng schedule yeldng the late arrval tme wth condtons on the well TT-26 schedules Maxmum contamnant level Multmeda Envronmental Smulatons Laboratory Concentraton observaton fle for MT3DMS Orgnal pumpng schedule used by ATSDR Tetrachloroethylene Pumpng Schedule Optmzaton System Smulaton optmzaton U.S. Geologcal Survey Well package for MODFLOW Water treatment plant x

10 Effect of Groundwater Pumpng Schedule Varaton on Arrval of Tetrachloroethylene (PCE) at Water-Supply Wells and the Water Treatment Plant Jnjun Wang and Mustafa Aral Multmeda Envronmental Smulatons Laboratory School of Cvl and Envronmental Engneerng Georga Insttute of Technology Atlanta, Georga, USA Abstract The Agency for Toxc Substances and Dsease Regstry (ATSDR) s conductng an epdemologcal study to evaluate whether exposures (n-utero and durng nfancy up to 1 year of age) to volatle organc compounds that contamnated the drnkng water at the U.S. Marne Corps Base Camp Lejeune, North Carolna, were assocated wth specfc brth defects and chldhood cancers that are observed at the ste. The study ncludes the brths that occurred to women who were pregnant whle they resded n the famly housng at the base durng the perod There s no exposure data and very lmted ste-specfc contamnaton data are avalable to support the epdemologcal study. As a result, ATSDR s usng modelng technques to estmate the hstorcal and present-day contamnaton condtons n the groundwater and the water treatment plant at Camp Lejeune, North Carolna. Owng to the complexty of the hstorcal reconstructon process, a number of reports are beng prepared to provde a comprehensve descrpton of nformaton and data used n hstorcal reconstructon and present-day analyses at Tarawa Terrace and vcnty. To complement these studes, ths report descrbes the effect of groundwater pumpng schedule varatons on the arrval tmes of Tetrachloroethylene (PCE) at water-supply wells and the water treatment plant (WTP). Durng the hstorcal reconstructon study, as descrbed n varous ATSDR reports accompanyng ths report, the groundwater flow and fate-and-transport of contamnants n the Tarawa Terrace area of the Camp Lejeune base and ts vcnty have been smulated to evaluate the contamnant concentraton n the WTP. Due to the uncertanty resdng n the reconstructed nput data used n these smulatons, uncertanty may be present n the smulated contamnant concentratons n the water-supply wells and the WTP, hence the tmes for contamnant concentratons to reach the maxmum contamnant level (MCL) at these locatons. A major cause and contrbutor to ths uncertanty s the pumpng schedules used n the ATSDR model, therefore, n ths study the focus s on the uncertanty assocated wth the pumpng schedules. The study ncluded the development of a smulaton and optmzaton (S/O) procedure dentfed as PSOpS (Pumpng Schedule Optmzaton System), whch combnes smulaton models and optmzaton 1

11 technques to optmze the pumpng schedules for maxmum or mnmum contamnant concentratons n the WTP. Based on the optmzed pumpng schedules, varatons of PCE concentraton and the maxmum contamnant level (MCL, 5 ppb for PCE) arrval tme at water-supply wells and the WTP are evaluated. The results of ths study ndcate that the varaton of pumpng schedules may cause sgnfcant changes n the contamnant concentraton levels and MCL arrval tme at the WTP. 2

12 1 Introducton The Agency for Toxc Substances and Dsease Regstry (ATSDR) s conductng an epdemologcal study to evaluate whether exposures (n-utero and durng nfancy up to 1 year of age) to volatle organc compounds (VOC) that contamnated drnkng water at the U.S. Marne Corps Base Camp Lejeune, North Carolna, were assocated wth specfc brth defects and chldhood cancers. To provde the epdemologcal study wth quanttatve estmates of exposure, characterzaton of envronmental contamnaton and the frequency and duraton of exposure to contamnated drnkng water s beng conducted usng the hstorcal reconstructon process [Masla et al., 2001]. The ste nvestgaton at the base concluded that groundwater was the sole source of water to the WTP. The contamnant source was the ABC One-Hour Cleaners located n the Tarawa Terrace area, and the major contamnants at the ste ncluded Tetrachloroethylene (PCE) and ts degradaton by-products. Contamnants released from the ABC One-Hour Cleaners mgrated nto the groundwater system and eventually nto the WTP through several water-supply wells n the Tarawa Terrace area of the base. Based on the study of the hydrogeologc and the hstorcal data from the Tarawa Terrace area and ts vcnty, the ATSDR modelng team has reconstructed and smulated the multlayer groundwater flow at the ste usng MODFLOW, a groundwater flow smulaton model [McDonald and Harbaugh, 1988]. The smulaton model MT3DMS [Zheng and Wang, 1999] was then used to evaluate the fate-and-transport of contamnants n the subsurface. Based on ths analyss, the concentraton dstrbuton and the arrval tme of contamnants n the WTP were determned hstorcally. Due to ts nature, the hstorcal reconstructon modelng process conducted by ATSDR has uncertantes assocated wth t. These uncertantes could have a sgnfcant effect on the epdemologcal study. One uncertanty s assocated wth the pumpng schedules used n groundwater flow smulatons because there are lmted hstorcal records of the pumpng rates at the water-supply wells. In ths study, the focus s on the evaluaton of the uncertanty caused by the pumpng schedules and ts effect on the smulaton results. For ths purpose, a methodology was developed to yeld the earlest/latest contamnant arrval tmes at the water-supply wells and the Tarawa Terrace WTP assocated wth the allowable varatons n groundwater pumpng schedules throughout the hstorcal operaton of the ste. As t was developed n ths study, ths methodology uses a combnaton of smulatons and optmzaton methods to adjust the pumpng schedules whle mantanng the hstorcal total pumpng demands at the Tarawa Terrace WTP that were dentfed by the ATSDR modelng team. The study presented here ncludes the followng assumptons:. Tetrachloroethylene (PCE) s the only contamnant of concern at the ste, although other contamnants such as degradaton by-products of PCE exsted n the groundwater and at the WTP. In ths study, the use of the term contamnant 3

13 . mples PCE, unless otherwse specfed; Pumpng schedule s the only varable consdered to be uncertan n ths analyss. Some other factors, such as hydrogeologc varables, may also cause varatons n contamnant transport process and may affect the contamnant concentraton and arrval tme at the water-supply wells and the WTP. The uncertantes assocated wth these varables are treated n other parallel studes conducted by ATSDR, and, therefore, are not consdered n ths study. Ths study used two smulaton models:. MODFLOW: MODFLOW s a three-dmensonal groundwater smulaton model, whch can be used n the soluton of governng equatons of multlayer groundwater flow systems. The model uses the fnte-dfference method n ths process [McDonald and Harbaugh, 1984]. The model s developed by U. S. Geologcal Survey and s an open source code. MODFLOW-2000 (also dentfed as MF2K), a fourth generaton of MODFLOW, s employed n ths study. In ths report, all MODFLOW related nformaton was adopted from the report authored by Harbaugh et al. [2000] unless otherwse dentfed. The executable fle and the source codes of MODFLOW were downloaded from: MT3DMS: MT3DMS s a modular three-dmensonal multspeces contamnant transport model. It can be used n the smulaton of advectve, dffusve, and reactve transport of contamnants n multlayer groundwater systems [Zheng and Wang, 1999]. All the MT3DMS related nformaton n ths report was obtaned from the reports authored by Zheng and Wang [1999] and Zheng [2005] unless otherwse dentfed. The verson of MT3DMS model employed n ths study s verson 5.1. The executable fle and the source codes of MT3DMS were downloaded from the webste at: In ths study, all nformaton regardng the Camp Lejeune Marne Corps Base and the nput data used for the models prevously descrbed above were obtaned from ATSDR. Detals of the framework and the bass of the data can be found n other ATSDR reports, and wll not be dscussed n detal here. The organzaton of ths report s as follows. In Chapter 2, a revew of the study conducted by the ATSDR modelng team s provded, ncludng a revew of the background and the smulaton models used n the hstorcal reconstructon study. A groundwater smulaton and optmzaton procedure, dentfed as PSOpS (Pumpng Schedule Optmzaton System), developed by the researchers at Multmeda Envronmental Smulatons Laboratory (MESL), Georga Tech (GT), s ntroduced n Chapter 3. The smulaton results and a dscusson of these results are presented n Chapter 4, whch s followed by a summary secton n Chapter 5. 4

14 2 A Revew of ATSDR Camp Lejeune Study 2.1 Background The Agency for Toxc Substances and Dsease Regstry (ATSDR), U. S. Department of Health and Human Servces, s currently (2007) conductng a hstorcal reconstructon of contamnant occurrences n water-dstrbuton networks at Marne Corps Base Camp Lejeune, North Carolna. Camp Lejeune s located n the Coastal Plan of North Carolna, n Onslow County, southeast of the Cty of Jacksonvlle and about 70 mles northwest of the cty of Wlmngton, North Carolna. The purpose of ths study s to determne f there s an assocaton between the exposure to contamnated drnkng water and the brth defects and the chldhood cancers n chldren born to women who lved at the base whle they were pregnant durng the perod 1968 to Due to lmted exposure data avalable for the perod of nterest ( ), ATSDR has undertaken a reconstructon of the hstorcal data. ATSDR s nvestgaton focuses on the Tarawa Terrace area and ts vcnty (Fgure 2.1). The Tarawa Terrace area s bounded on the east by Northeast Creek, and to the south by New Rver and Northeast Creek. On the west and north, t s bounded by the dranage boundares of these streams. The hstorcal reconstructon ncludes the groundwater system reconstructon, contamnant source characterzaton, and contamnant fate-and-transport smulaton n the groundwater system and the water dstrbuton system servng the Tarawa Terrace area. The ATSDR study concluded that groundwater was the sole source of water to the WTP and water dstrbuton system servng the Tarawa Terrace area. The source of contamnants n the groundwater was the ABC One-Hour Cleaners located to the north of several water-supply wells at Tarawa Terrace (Fgure 2.1). Accordng to the ATSDR study, Tetrachloroethylene (PCE) was contnuously released to the subsurface system at a rate of 1,200 gram/day durng the perod January 1953 to December PCE released from ABC One-Hour Cleaners mgrated nto the groundwater system and was then pumped nto the WTP by the water-supply wells shown n Fgure 2.1. Usng the reconstructed hydrogeologc data and the contamnant source characterzaton, the ATSDR modelng team was able to smulate the groundwater flow and contamnant fate-and-transport n the subsurface system of the Tarawa Terrace area to obtan the hstorcal exposure data. Due to the nature of hstorcal reconstructon, uncertantes are assocated wth the reconstructed data, whch wll n turn cause uncertantes n the resultng exposure data. The uncertantes n the exposure outcome may have a sgnfcant effect on the epdemologcal study. In partcular, the uncertanty caused by the groundwater pumpng schedule used n the smulatons has been ponted out to be mportant. Therefore, n ths study, there s an evaluaton of the varaton n PCE concentratons and the arrval tme of maxmum contamnant level (MCL, 5 ppb for PCE) at the water-supply wells and the WTP that could be caused by the varaton of groundwater pumpng rates at the water-supply wells. 5

15 Fgure 2.1. Water-supply well locatons at Tarawa Terrace and vcnty, U.S. Marne Corps Base Camp Lejeune, North Carolna. 2.2 Introducton to smulaton tools and nput data In the ATSDR study, the contamnant concentraton n the WTP was evaluated by employng the followng steps:. MODFLOW model was used to smulate the groundwater flow n the Tarawa Terrace area and ts vcnty. The MODFLOW smulaton also generated the flow-transport lnk (FTL) fle to be used n the MT3DMS smulaton;. Usng the FTL fle, along wth other nput fles, MT3DMS smulaton was conducted to obtan the contamnant concentratons n the water-supply wells; and,. The contamnant concentraton dstrbuton obtaned from MT3DMS smulaton was used to calculate the PCE concentraton n the WTP through a volumetrc mxng model. In the followng sectons, MODFLOW and MT3DMS models and ther nput fles are brefly descrbed, as they are used n the ATSDR study and ths study MODFLOW model and nput data MODFLOW s a computer program that was desgned to solve the three-dmensonal equaton, Equaton (2.1), governng groundwater flow by usng the fnte-dfference 6

16 method [McDonald and Harbaugh, 1988] for both steady state and transent flow applcatons: h h h h ( K xx ) + ( K yy ) + ( K zz ) + W = Ss (2.1) x x y y z z t n whch K xx, K yy, and K zz are hydraulc conductvty values along the x-, y-, and z-coordnate axs drectons (L/T); h s the pezometrc head (L); W s a volumetrc flux per unt volume that represents sources and/or snks at the ste (T -1 ); S s s the specfc storage of the porous medum (L -1 ); t s tme (T); and x, y, z are the Cartesan coordnate drectons (L). MODFLOW was orgnally developed by McDonald and Harbaugh [1984]. Snce then t has been modfed numerous tmes, and several versons exst n the lterature. The second verson s dentfed as MODFLOW-88 [McDonald and Harbaugh, 1988]. the thrd verson s dentfed as MODFLOW-96 [Harbaugh and McDonald, 1996a and 1996b]. The latest verson, whch s used n ths study, s dentfed as MODFLOW-2000 [Harbaugh et al., 2000]. Also snce ts ncepton, the followng authors Prudc [1989], Hll [1990], Leake and Prudc [1991], Goode and Appel [1992], Harbaugh [1992], McDonald et al. [1992], Hseh and Freckleton [1993], Leake et al. [1994], Fenske et al. [1996], Leake and Llly [1997], and Hll et al. [2000] have made several mprovements to MODFLOW. In the ATSDR study, as well as ths study, MODFLOW model was appled to generate the flow-transport lnk (FTL) fle for the MT3DMS smulaton. In addton, MODFLOW s also a component of the newly developed PSOpS model. In MODFLOW smulatons, a fundamental component of the tme dscretzaton data s the tme step. A group of tme steps are dentfed as a stress perod [Harbaugh et al., 2000]. In ths study, from the frst month of year 1951 through the last month of year 1994, each month s dentfed as a stress perod, and there are a total of 528 stress perods n the overall smulaton perod. January of 1951 s stress perod 1, February s stress perod 2, and so forth. Wthn a stress perod, the tme dependent varables, such as the groundwater pumpng rates of pumpng wells, are constant, therefore, the update of the pumpng schedule, as reconstructed n ths study, occurs monthly. In MODFLOW the basc spatal smulaton unt used n the fnte-dfference calculatons s called a fnte-dfference cell or cell. In the ATSDR study, the groundwater system n the Tarawa Terrace area and ts vcnty s modeled as a zone that contans 200 rows, 270 columns, and 7 layers of cells. In other words, a total of 378,000 cells are used to dealze the three-dmensonal groundwater flow regon at the ste. The nput data for the MODFLOW smulaton can be dvded nto two categores: () global process nput data fle and, () groundwater flow process nput data fle. Global process nput fles contan basc nformaton that s appled to the whole 7

17 smulaton. As for the groundwater flow process nput fles, a group of related nput data are put together nto a fle as the nput for a specfc package. For example, dscretzaton (DIS) fle s a global process nput fle. It contans data such as number of rows, columns and layers n the model, cell wdths etc. In comparson to that, the well (WEL) fle s a fle that contans nput data for the Well Package, ncludng the locatons and pumpng rates of water-supply wells n each stress perod. Based on these types of classfcatons, the MODFLOW nput fles, as used n the ATSDR study, are gven below and are summarzed n Table 2.1. There are two global process fles used n the study:. Fle type: NAM Fle contents: The name and Fortran unt of each fle used n the smulaton;. Fle type: DIS Fle contents: Basc dscretzaton nformaton, ncludng number of rows, columns, and layers of the model; number of stress perods; confnng layers nformaton; wdth of each cell along rows and columns; elevaton of each cell; perod length, number of tme steps, and the state (steady or transent) of each stress perod. The followng nne groundwater flow process fles are also used n the study:. Fle type: BAS6 Package: Basc Package Fle contents: Boundary condtons; pezometrc head value n nactve cells; ntal head dstrbuton;. Fle type: BCF6 Package: Block-Centered Flow Package Fle contents: Wet-dry cell nformaton; layer type nformaton (whether the layer s confned or not, and how the nterblock transmssvty wll be calculated); transmssvtes or hydraulc conductvtes; horzontal ansotropy factors; prmary and secondary storage coeffcents; vertcal hydraulc conductvtes dvded by thckness of cells;. Fle type: DRN Package: Dran Package Fle contents: Number of dran parameters; maxmum number of dran cells used n any stress perod; number of parameters used n each stress perod; locaton and elevaton of each dran cell, and factors used to calculate the dran conductance n that cell; v. Fle type: GHB Package: General-Head Boundary Package Fle contents: Number of general-head boundary parameters; maxmum number of general-head-boundary cells used n any stress perod; number of parameters used n each stress perod; locaton of each constant head cell, and the heads n 8

18 the cell at the begnnng and end of each stress perod; v. Fle type: OC Package: Output Control Opton Fle contents: Informaton on whether the computed head, drawdown and water budget wll be saved for each stress perod; where to save and n what format; v. Fle type: PCG Package: Precondtoned Conjugate-Gradent Package Fle contents: Maxmum number of outer and nner teratons; matrx condtonng method; head change crteron and resdual crteron for convergence; relaxaton parameter; prntout nterval; v. Fle type: RCH Package: Recharge Package Fle contents: Recharge dstrbuton type; recharge flux (f applcable); v. Fle type: LMT6 Package: Lnk-MT3DMS Package [Zheng et al., 2001] Fle contents: The name, unt, header, and format of the flow-transport lnk (FTL) fle for MT3DMS smulaton; x. Fle type: WEL Package: Well Package Fle contents: Maxmum number of operatng wells n each stress perod; number, locaton and pumpng rate of each well n each stress perod. Table 2.1. Input fles used for the MODFLOW smulaton code Process Fle Type Package Global NAM N/A DIS N/A Groundwater BAS6 Basc Flow BCF6 Block-Centered Flow DRN Dran GHB General-Head Boundary OC Output Control Opton PCG Precondtoned Conjugate-Gradent RCH Recharge LMT6 Lnk-MT3DMS WEL Well MT3DMS model and nput data MT3DMS s a modular three-dmensonal mult-speces transport model that can be used n the smulaton of advectve, dspersve, and reactve transport of contamnants n groundwater flow systems [Zheng et al., 2001]. In the MT3DMS model, three major classes of transport soluton technques are appled so that the best approach can be offered for varous transport problems for effcency and accuracy. These three technques nclude: the standard fnte-dfference method, the partcle-trackng-based 9

19 Euleran-Lagrangan methods, and the hgher-order fnte-volume total-varaton-dmnshng method. The governng equaton used n the MT3DMS smulaton model can be gven as: k k ( θc ) C k k = ( θdj ) ( θνc ) + qscs + Rn (2.2) t x x x j where θ s the porosty of subsurface system; C k s the concentraton of speces k n aqueous phase (ML -3 ); t s tme (T); x and x j are the dstances along the three-dmensonal Cartesan coordnate axs drectons (L); D j s the dsperson coeffcent (L 2 T -1 ); ν s pore velocty (LT -1 ); q s s the flow rate per unt volume of aqufer representng snks and sources (T -1 ); k C s s the concentraton of speces k n snk or source flux (ML -3 ); and Rn s the chemcal reacton term (ML -3 T -1 ). In the ATSDR study, as well as ths study, MT3DMS s used to smulate the fate-and-transport of PCE n the groundwater system of the Tarawa Terrace area and ts vcnty. The output of MT3DMS smulaton provdes PCE concentraton n the water-supply wells. Smlar to the nput fles of MODFLOW, the nput fles of MT3DMS nclude one name fle and some other nput fles used for varous packages. These nput fles are descrbed below and n Table Fle type: NAM Fle contents: The name and Fortran unt of each fle employed n the smulaton;. Fle type: BTN Package: Basc Transport Package Fle contents: Basc model nformaton (number of rows, columns, layers, and stress perods); number of chemcal speces; transport and soluton optons; confnng layer propertes; cell wdth along rows and columns of each cell; porosty n each cell; boundary condton nformaton; startng concentratons of each chemcal speces (ntal condtons); prntng optons; output frequency; number of observaton ponts and ther locatons; mass balance output optons; and stress perod nformaton;. Fle type: ADV Package: Advecton Package Fle contents: Advecton soluton opton; and other advectve transport smulaton varables, f applcable; v. Fle type: DSP Package: Dsperson Package Fle contents: Longtudnal dspersvtes; rato of horzontal transverse dspersvty to longtudnal dspersvty; rato of vertcal transverse dspersvty to 10

20 longtudnal dspersvty; effectve molecular dffuson coeffcents; v. Fle type: SSM Package: Snk and Source Mxng Package Fle contents: Snk and source term optons; maxmum number of snks and sources; concentraton read-n optons; concentraton of evapotranspraton flux (f applcable); concentraton n specfed cells; v. Fle type: RCT Package: Chemcal Reacton Package Fle contents: Type of reacton; type of knetc reacton; bulk denstes of the aqufer medum for each cell; porostes of mmoble doman (f applcable); ntal concentraton of the sorbed phase (f applcable); sorpton parameters; reacton rates; v. Fle type: GCG Package: Generalzed Conjugate-Gradent Solver Package Fle contents: Maxmum numbers of nner and outer teratons; relaxaton factor; convergence crteron; v. Fle type: FTL Package: Flow-Transport Lnk Package Fle contents: The groundwater flow related nformaton. Table 2.2. Input fles used for the MT3DMS smulaton code Fle Type Package NAM N/A BTN Basc Transport ADV Advecton DSP Dsperson SSM Snk and Source Mxng RCT Chemcal Reacton GCG Generalzed Conjugate-Gradent Solver FTL Flow-Transport Lnk Water-supply well nformaton The purpose of ths study s to examne the effect of the updated pumpng schedules on the PCE concentraton and 5 ppb arrval tme at the water-supply wells and the WTP. In ths study, among all the nput data used n the ATSDR study, only the groundwater pumpng rates of the water-supply wells are consdered to be uncertan and are vared based on an optmzaton procedure developed n ths study. Therefore, t s necessary to present more detaled nformaton about the water-supply system n the Tarawa Terrace area. In the ATSDR study, a total of 16 water-supply wells were used to supply groundwater to the Tarawa Terrace WTP. Thrteen of these wells are located n the Tarawa Terrace area and ts vcnty (Fgure 2.1). The other three wells, dentfed as well 6, well 7, and well 11

21 TT-45, are located outsde of ths area and, therefore, are not shown n Fgure 2.1. In both the ATSDR study and ths study, t s assumed that well 6, well 7, and well TT-45 had zero contamnant concentraton, whch mples that these wells contrbuted only water but no contamnant mass to the WTP. In MODFLOW and MT3DMS smulatons, the locaton of a pumpng well s dentfed n terms of the coordnates of the cell n whch the well les (x, y, z). In the smulaton codes the x, y, and z values correspond to the layer number, row number, and column number of the cells respectvely. Accordng to the well-constructon logs, some wells penetrate more than one layer of aqufer, therefore n MODFLOW smulatons some well dscharges are splt nto two or more vrtual wells whch extract water from dfferent layers. For example, n the MODFLOW nput used by the ATSDR, well TT-52 s splt nto TT-52A and TT-52B, where the extenson A refers to Layer-1 and B refers to Layer-3. Wells TT-31 and TT-54 also are splt ths way. In ths study well TT-53 and TT-67 are splt to satsfy ther pumpng capactes, wth respect to dry- and wet-cell condtons observed at the cell. Locatons and servce perods of these water-supply wells are lsted n Table 2.3. Table 2.3. Locatons and servce perods of water-supply wells n the Tarawa Terrace area Well Layer Row Column Start Date End Date TT / /1985 TT / /1987 TT / /1985 TT / /1961 TT / /1971 TT / /1958 TT / /1985 TT-31A / /1987 TT-31B / /1987 TT-52A / /1987 TT-52B / /1987 TT-53A / /1984 TT-53B / /1984 TT-54A / /1987 TT-54B / /1987 TT / /1971 TT-67A / /1987 TT-67B / /1987 Durng the smulaton perod ( ), the pumpng rates of the water-supply wells vared, and some wells were out of servce for some stress perods. Usng the hstorcal records, the pumpng rates and the pumpng capactes of each water-supply well were 12

22 generated for all the stress perods. 2.3 Smulaton results of ATSDR modelng study Usng nput fles lsted n Table 2.1, a MODFLOW smulaton was performed to generate the flow-transport lnk (FTL) fle for the follow-up MT3DMS smulaton. The PCE concentraton dstrbuton n the water-supply wells was then obtaned from an output fle of MT3DMS smulaton, the concentraton observaton (OBS) fle, and these results are shown n Fgure TT-26 TT TT TT-54A PCE Conc. (ppb) TT-67 TT-54B 0.01 TT-31A Org. Sche. PCE MCL TT-53 TT-31B Jan-51 Jan-55 Jan-59 Jan-63 Jan-67 Jan-71 Jan-75 Jan-79 Jan-83 Jan-87 Date Fgure 2.2. PCE concentratons n water-supply wells under the Orgnal Schedule In Fgure 2.2 the PCE concentratons n the water-supply wells are shown durng ther servce perods as lsted n Table 2.3. Although 16 pumpng wells were operatng n the Tarawa Terrace area n ATSDR s smulaton, only wells TT-26, TT-23, TT-25, TT-67, TT-54A and TT-54B had PCE concentratons hgher than the MCL. Among them, well TT-26 had a much longer perod of exposure to PCE concentratons over 5 ppb the PCE MCL arrval tme n well TT-26 s January 1957, whle the second-earlest PCE 13

23 MCL arrval n a water-supply well occurred durng January 1983 at well TT-54A. PCE concentraton n well TT-26 s always much hgher than n the other water-supply wells, ndcatng that TT-26 conveyed the majorty of PCE mass ntroduced nto the WTP. Ths s probably because of proxmty of well TT-26 to the contamnant source and the well s long pumpng hstory. Employng the PCE concentraton data n the water-supply wells, along wth the pumpng rates n these wells, the PCE concentraton n the Tarawa Terrace WTP was calculated by usng the followng mxng model: n qc j j j= 1 C = (2.3) QT n whch C s the PCE concentraton n the WTP at stress perod (ML -3 ); n s the total number of actve water-supply wells n stress perod ; q j s the pumpng rate of well j at stress perod (L 3 T -1 ); c j s the PCE concentraton n the water-supply well j at stress perod (ML -3 ); and Q T s the total water demand at stress perod (L 3 T -1 ). The PCE concentraton n the Tarawa Terrace WTP s shown n Fgure 2.3. To dstngush t from other updated pumpng schedules that were developed and are dscussed n later chapters, the pumpng schedule used n the ATSDR study s dentfed as the Orgnal Schedule (Org. Sche.) n the fgures as well as throughout the remander of ths report. Accordng to Fgure 2.3, the PCE concentraton n the Tarawa Terrace WTP frst exceeded the MCL n November When ths outcome s compared to the results presented n Fgure 2.2, only well TT-26 had a PCE concentraton over ppb by November Therefore, well TT-26 s crtcal n assessng the PCE MCL arrval tme n the WTP. As shown n Fgure 2.4, for the perod of nterest (January 1968 December 1985), the maxmum PCE concentraton n the WTP s ppb and the mnmum PCE concentraton s 0.72 ppb. Durng ths perod, however, there are only 15 months when the PCE concentraton n the WTP s lower than ppb. Therefore, for most of the perod of nterest (201 months out of 216 months), the PCE concentraton n the Tarawa Terrace WTP ranges between ppb and ppb, and the average PCE concentraton s about ppb, whch s much hgher than the 5 ppb MCL for PCE. The tme perods n whch the PCE concentraton n the WTP s lower than ppb are: July 1980 August 1980, January 1983 February 1983, and February 1985 December These also are the tme perods durng whch well TT-26 was out of servce. As can be seen n Fgure 2.2, durng these tme perods, the PCE concentratons n other water-supply wells were much lower than those n well TT-26. Stoppng well TT-26 from supplyng water to the WTP therefore caused the sudden PCE concentraton drops as shown n Fgure 2.3 and Fgure

24 For the PCE concentraton drop at the end of 1961 n Fgure 2.3, the reason s smlar to the one descrbed prevously. At that tme, the pumpng rate of well TT-26 decreased from 28,715 ft 3 /day to 18,959 ft 3 /day, whle the total water suppled was to the WTP kept unchanged (116,199 ft 3 /day). Snce the PCE concentratons n the other water-supply wells were neglgble (less than ppb) and the well TT-26 was the only source of PCE n the WTP at that tme, a decrease of PCE concentraton s expected n the WTP / / PCE Conc. (ppb) 1 11/ / / / Org. Sche. PCE MCL Jan-51 Jan-55 Jan-59 Jan-63 Jan-67 Jan-71 Jan-75 Jan-79 Jan-83 Jan-87 Date Fgure 2.3. PCE concentratons n the WTP under the Orgnal Schedule 15

25 PCE Conc. (ppb) 10 02/ / /1980 Org. Sche. PCE MCL 0.1 Jan-68 Jan-70 Jan-72 Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Date Fgure 2.4. PCE concentratons n the WTP under the Orgnal Schedule for the perod of nterest 16

26 3 Optmzaton of the Pumpng Schedules As ntroduced n Chapter 2, the PCE concentraton n the Tarawa Terrace WTP was obtaned through consecutve applcaton of the followng three steps:. Smulaton of groundwater flow usng the MODFLOW model;. Smulaton of PCE fate-and-transport usng the MT3DMS model; and. Calculaton of PCE concentraton n the WTP usng the MT3DMS output, the pumpng schedules, and the WTP mxng model. Throughout these steps, pumpng schedules are used both n MODFLOW smulaton and durng the calculaton of PCE concentraton n the WTP when the mxng model s used. Moreover, as stated earler, pumpng schedules are the only uncertan varables n ths study. Therefore, to evaluate the change n PCE arrval tme at the water-supply wells and the WTP, pumpng schedules that may cause that change must be obtaned frst accordng to certan crtera. In ths study, a pumpng schedule optmzaton procedure, dentfed as PSOpS (Pumpng Schedule Optmzaton System), s developed usng the smulaton/optmzaton (S/O) approach. In PSOpS, the smulaton models (MODFLOW and MT3DMS) are combned wth optmzaton technques to generate the optmal pumpng schedules that would yeld the earlest or the latest PCE MCL arrval tmes at the WTP. 3.1 Formulaton of the optmzaton model To evaluate the PCE arrval tme at the WTP caused by a varaton of pumpng schedules, models must be dentfed to lnk the contamnant arrval tme and the pumpng schedules. Currently, several smulaton models (or a combnaton of smulaton models), whch may be used n ths analyss, are avalable n the lterature. Among the models, one straght forward choce s the combnaton of MODFLOW and MODPATH [Pollock, 1994]. MODPATH s a partcle trackng model that computes the three-dmensonal pathlnes and the partcle arrval tmes at the pumpng wells based on the advectve transport output of MODFLOW. A combnaton of MODFLOW and MODPATH can provde contamnant arrval tme at the water-supply wells. However, several lmtatons n the MODPATH model restrct ts use n ths study. Frst, MODPATH only smulates the advectve transport of contamnants n the groundwater system. In a MODPATH smulaton, the advecton of water s consdered to be the only drvng force of contamnant movement, whle other factors whch may also affect the movement of contamnants, such as dffuson and dsperson, are not consdered. Second, n a MODPATH smulaton, the contamnant s treated as a tracer, whch mples no chemcal reacton or degradaton that maybe assocated wth the contamnant can be accounted for. Fnally, although MODPATH smulaton can provde contamnant arrval tme at a pumpng well, ths tme s only recorded for the frst contamnant partcle that arrves at the well. No concentraton nformaton s assocated wth ths smulaton output. 17

27 In ths study, however, a more precse smulaton of contamnant fate-and-transport s requred, and the tme for contamnant concentraton that reaches a specfc level s requred for exposure evaluaton purposes. Consderng all these restrctons, the combnaton of MODFLOW and MT3DMS was selected for ths study. As ntroduced n the prevous sectons, MT3DMS s a subsurface contamnant fate-and-transport smulaton model. Usng the FTL fle obtaned from MODFLOW, the MT3DMS can be run on the same groundwater system. MT3DMS does not have the restrctons assocated wth the MODPATH model. The output fle of MT3DMS provdes contamnant concentratons at specfed tmes and locatons. Usng ths nformaton, the arrval tme at the water-supply wells of certan concentraton levels can be evaluated. Other benefts of the coupled smulaton of MODFLOW and MT3DMS nclude:. By usng the output of MT3DMS, the contamnant concentraton n the WTP also can be calculated and evaluated; and,. By usng the combnaton of MODFLOW and MT3DMS, all the orgnal nput fles obtaned from the ATSDR study can be appled drectly and only a few complementary fles need to be added wthn the PSOpS framework. The followng steps are used to evaluate the change of PCE arrval tme caused by varatons n pumpng schedules:. Optmze the pumpng schedules for the earlest and the latest PCE arrval tmes usng a combnaton of smulaton models (MODFLOW and MT3DMS) and optmzaton technques (S/O);. Smulate the groundwater flow and the contamnant fate-and-transport at the ste usng the optmal pumpng schedules obtaned from step ();. Calculate PCE concentraton at the WTP usng Equaton (2.3) and the optmal pumpng schedules; and, v. Evaluate the earlest and the latest PCE arrval tmes at the WTP. In step (), the optmzaton of pumpng schedule for the earlest or the latest PCE arrval tme s equvalent to optmzng the pumpng schedule for the maxmum or mnmum PCE concentratons n the WTP because the observaton of a hgher concentraton at the WTP mples an earler contamnant arrval tme, and vce versa. To optmze the pumpng schedule for maxmum or mnmum PCE concentratons n the WTP, one approach s to optmze the pumpng schedules for the maxmum or mnmum PCE concentratons for each stress perod ndvdually. After the maxmum or mnmum concentratons are obtaned for each stress perod, a relatonshp can be obtaned between maxmum or mnmum concentraton versus stress perod (tme). Ths approach, however, s assocated wth sgnfcant computatonal burden. The large scale of the smulaton model 200 rows, 270 columns, 7 layers, and 528 stress perods clearly ndcates that ths approach wll requre a hgh end PC computer years of calculaton tme to complete the smulatons and, therefore, s unacceptable. 18

28 Another possble approach s to combne the stress perods wth same characterstcs (pumpng rates, pumpng capactes, pumpng demands, recharge, and so forth) together to reduce the sze of the overall model. Ths approach, however, wll lose some detal durng optmzaton, whch mples that t may not be as precse as the orgnal model, and, thus, may affect the optmzaton results. Consderng the computaton power and memory of the desktop workstatons avalable for ths study (64 bt dual processor PC boxes), along wth the need to obtan an acceptable result n a tmely manner wthout losng any detal and accuracy, the optmzaton problem needs to be formulated n a more computatonally cost-effcent manner. To create such a model, the followng observatons were made about the ste data used n these smulatons:. The contamnant was contnuously released from the same source pont;. Well TT-26 was the only major contamnant contrbutor to the Tarawa Terrace WTP; and,. Well TT-26 was n operaton durng most of the perod of nterest. Wth these observatons n mnd, the optmzaton problem s reformulated as follows. Optmze each successve stress perod for a maxmum or mnmum PCE concentraton n the WTP n stress perod whle keepng all of the prevously optmzed pumpng rates constant. In other words, n the reformulaton, the pumpng schedule of stress perod 1 s frst optmzed for optmal (maxmum or mnmum) PCE concentraton n the WTP n stress perod 1. Then the pumpng schedule of stress perod 2 s optmzed for optmal PCE concentraton n stress perod 2 keepng the optmzaton results from stress perod 1 constant, and so on. In ths manner, at the end of the smulaton/optmzaton process an optmal pumpng schedule, under whch the PCE concentraton n the WTP can be maxmzed or mnmzed, s obtaned for all the stress perods. The reformulated optmzaton problem for maxmum PCE concentraton n the WTP can be expressed mathematcally as: Max C = f ( q,..., q ) n q R st.. 0 q n j= 1 j q = q ( k = 1,..., 1) k q * k w = Q T 1, (3.1) where C s the PCE concentraton n the WTP at stress perod (ML -3 ); n s the number of actve water-supply wells n stress perod ; q s an n-dmensonal vector of pumpng rates at stress perod (L 3 T -1 ); w s an n-dmensonal vector of the upper bound of q at 19

29 stress perod (pumpng capactes) (L 3 T -1 ); Q T s the total water demand at stress perod (L 3 T -1 ); and q k * s the optmal pumpng schedule for stress perod k (L 3 T -1 ). In the optmzaton problem gven n Equaton (3.1), q 1,, q -1 are known, and C s only a functon of q. Thus, to obtan the maxmum PCE concentraton C, only the pumpng schedule of stress perod needs to be optmzed based on the optmal pumpng schedules of the prevous stress perods. By formulatng the problem n ths way, the dmensons of the problem are reduced sgnfcantly, and the computatonal demand becomes manageable. The optmzaton model for the mnmum PCE concentraton n the WTP s smlar: Mn C = f ( q,..., q ) n q R st.. 0 q n j= 1 j q = q ( k = 1,..., 1) k q w * k = Q T 1. (3.2) The explanatons used for ths equaton s the same as gven for Equaton (3.1). Problem (3.2) can be easly solved by usng the same method as used n the soluton of the optmzaton problem gven n Equaton (3.1), because t can be re-wrtten as: ' Max C = C = f( q,..., q ) n q R st.. 0 q n j= 1 j * k 1 T q = q ( k = 1,..., 1) k q w = Q. (3.3) Therefore, n ths report only the maxmzaton problem gven n Equaton (3.1) s used as an example when descrbng the optmzaton method. 3.2 Selecton of the optmzaton method For optmzaton problems gven n Equatons (3.1) and (3.2), the PCE concentraton n the WTP s calculated by usng the followng governng equatons: h h h h ( K xx ) + ( K yy ) + ( K zz ) + W = Ss ; (3.4) x x y y z z t and, k k ( θc ) C k k = ( θdj ) ( θνc ) + qscs + Rn ; (3.5) t x x x j 20

30 n qc j j j= 1 C =. (3.6) QT For the defnton of the terms used n these equatons, please refer to the text followng Equatons (2.1), (2.2), and (2.3). Among Equatons (3.4), (3.5), and (3.6), Equaton (3.4) s used n MODFLOW smulaton for obtanng pezometrc head dstrbuton and groundwater flow velocty between adjacent nodes; Equaton (3.5) s used n MT3DMS smulaton to obtan the PCE concentraton dstrbuton; and Equaton (3.6) s used to calculate the PCE concentraton n the WTP. A study of these three equatons shows that optmzaton problems gven n Equatons (3.1) and (3.2) are multdmensonal nonlnear optmzaton problems wth lnear constrants, whch are much harder to solve and more computatonally ntensve than the lnear optmzaton problems. Moreover, the objectve functons are nonconcave or nonconvex, whch mposes more dffculty n fndng a global optmal soluton. Sgnfcant lterature exsts on optmzaton methods for the soluton of nonlnear optmzaton problems. Some of these methods are ntroduced brefly n the followng sectons The Downhll Smplex method The Downhll Smplex method s an optmzaton method for multdmensonal nonlnear problems that does not requre evaluatng the dervatve of the objectve functon but uses only the objectve functon values [Press et al., 1989]. For an N-dmensonal mnmzaton problem, the Downhll Smplex Method starts wth N+1 ntal ponts (feasble solutons), whch defne an ntal smplex, and then moves step by step towards the optmal soluton. Each step s called a reflecton. For a mnmzaton problem, n each reflecton the pont of the smplex whch has the largest value s found and moved through the opposte face of the smplex to a lower pont, untl the soluton meets the termnaton crteron. In the Downhll Smplex method, although dervatves are not requred, ths approach s stll not qute effcent consderng the number of objectve functon evaluatons t requres The Steepest Descent method The Steepest Descent method s a non-lnear optmzaton method that uses the dervatve nformaton of the objectve functon [Press et al., 1989]. To solve a mnmzaton problem by usng ths method, startng from an ntal pont, the downhll gradent at that pont s calculated, and a mnmzaton pont along the gradent drecton s found. From that pont, the downhll gradent s calculated, and another pont along the gradent drecton s found. By followng ths gradent drecton on the objectve functon, an optmal soluton that meets termnaton crteron can be found. The problem wth the Steepest Gradent method s that the terated solutons may move 21

31 n a drecton of reversed gradent paths because the gradent at a new pont can be perpendcular to the prevous gradent. Ths ncreases the computatonal burden and may lead to an neffcent method. Another problem for ths method s that often the soluton wll be trapped n a local optmal soluton The Conjugate Gradent method Smlar to the Steepest Descent method, the Conjugate Gradent method uses the dervatve nformaton to fnd the optmal soluton for a non-lnear optmzaton problem [Press et al., 1989]. Ths method dffers from the Steepest Descent method n the followng sense. The Conjugate Gradent method s mproved n such a way that, for each movement towards the soluton, the drecton of movement s constructed to be conjugate to the old gradent. By dong ths, an optmal soluton can be acheved more effcently. Even though the Conjugate Gradent method s more effcent than Steepest Descent method, the calculaton of dervatves of the objectve functon at each teraton step s stll a heavy computatonal burden. Also smlar to the Steepest Decent method, the possblty for the soluton of the Conjugate Gradent method to be a local optmum nstead of a global optmum s very hgh Genetc Algorthms Genetc Algorthms (GA) get ther name snce the computatonal steps used are based on the evolutonary process observed n nature [Chnneck, 2006]. Ther applcaton requres the soluton to be expressed as a strng. Usng a populaton of strngs, an objectve functon value can be calculated for each strng for ts ftness evaluaton. Durng a GA process, frst an ntal populaton s generated and the ftness of each strng s evaluated. Then, a matng pool s generated from the current populaton usng several GA operatons. For example, crossover operaton (two parent strngs obtaned from the matng pool exchange part of ther strngs to form two new chld strngs) and mutaton operaton (values at some ponts of some strngs are changed randomly) are appled to generate the new populaton. After the generaton of new populaton, the ftness of each new strng s evaluated agan. Ths evolutonary process leads to the most ft strngs to reman and accumulate n the populaton. If the termnaton crteron s met, the process s stopped. Otherwse, the process wll start agan based on the new generaton of populaton. A good aspect of GA s that the process can yeld better and better solutons wthout relance on gradents. Another advantage of GA s that they search the optmal soluton globally and, thus the soluton s sometmes better than those obtaned from other methods mentoned prevously. However, consderng the computaton power requred for the evaluaton of ftness of each strng, f the computaton tme of the smulaton tools requred to solve the problem s large and f the matng pool s also large, then GA can be 22

32 more computatonally demandng than the other methods dscussed earler. Based on the revew gven above one can conclude that, for a complex nonlnear optmzaton problem, any of the methods dscussed above can be computatonally qute demandng. To reduce computatonal demand, a new optmzaton method dentfed as rank-and-assgn method, whch wll be ntroduced n detal n the next secton, has been developed unquely for the problem dscussed n ths study. The few cases that can not be solved by the rank-and-assgn method are optmzed by the mproved gradent method. 3.3 Introducton to PSOpS Based on the two optmzaton technques (rank-and-assgn and mproved Conjugate gradent methods) and smulaton models (MODFLOW and MT3DMS), a procedure dentfed as PSOpS (Pumpng Schedule Optmzaton system) has been developed to optmze the pumpng schedule for the earlest or the latest PCE arrval tme at the Tarawa Terrace WTP usng the smulaton/optmzaton approach. In PSOpS, MODFLOW and MT3DMS are used to smulate the groundwater flow and contamnant fate-and-transport condtons for the dervatve calculatons that are necessary n the soluton of the optmzaton problem, and the optmzaton technques are used wthn the same procedure to optmze the pumpng schedules Methodology of PSOpS The pumpng schedule adjustment necessary to acheve the maxmum PCE concentraton level n the WTP, whch s analogous to the earlest arrval tme soluton we are seekng, s solved by the procedure descrbed n Fgure 3.1. The varables and abbrevatons used n Fgure 3.1 are defned as follows: Q T : total pumpng demand for the stress perod ; ( k ) C : PCE concentraton n the WTP n the stress perod after the k th teraton; q j : the pumpng rate of the water-supply well j at the stress perod ; C ( ): the change of PCE concentraton n the WTP for the stress perod caused by the ( ) k q j unt change of q j after the k th teraton; ( k ) q : the pumpng schedule vector for the stress perod after the k th teraton whch conssts of q j of all water-supply wells at the stress perod ; ( k ) C( q ): the concentraton gradent vector for q ( k ) whch conssts of C ( ) ( ) k of all qj actve water-supply wells at the stress perod ; ( k ) ( k ) C( q ) : the norm of C( q ), whch s the maxmum absolute value of C ( ) ( ) k ; q w : pumpng capacty vector for the stress perod ; j 23

33 SQ : the sequence of C ( ); and, ( k ) ( ) k q j ε : a pre-defned termnaton crteron. If C q s less than ε, the pumpng ( k ) ( ) schedule of the stress perod s consdered to be optmal. The assumptons made n PSOpS are as follows: ( k ). When C ( q ) s less than ε, the pumpng schedule for the current stress.. v. perod s optmal, and no further update s requred; The total pumpng rate of all water-supply wells at stress perod s equal to the total pumpng demand of that stress perod; Pumpng rate n a water-supply well s always less than or equal to ts pumpng capacty; and, Water-supply wells outsde of the smulated regon (well 6, well 7, and well TT-45 n ths case) are consdered as one well wth zero C value. In other words, the pumpng rates n these wells can be adjusted but they do not provde contamnant mass nto the WTP. u j 24

34 Read data for stress perod Q = 0? T C C Calculate C and ( ), sort ( ) for SQ N (0) (0) (0) (0) qj qj C q < (0) ( ) ε? N (1) (0) Create q accordng to SQ, w and QT C C Calculate C and ( ), sort ( ) for SQ (1) (1) (1) (1) qj qj SQ (0) (1) = SQ? Y N C q < (1) ( ) ε? Y N (2) (1) Create q accordng to SQ, w and QT Y q (1) (2) = q? Y N C = C, q = q (0) (1) (1) (2) SQ = SQ (0) (1) Y C (0) (1) < C? Y N Improved gradent method Save result, go to next S.P. Fgure 3.1. Flowchart for PSOpS Followng the procedure gven n Fgure 3.1, PSOpS optmzes the pumpng schedules for maxmum PCE concentraton levels n the WTP at stress perod as outlned n the step-by-step process gven below: 25

35 . Read nput data for the stress perod, such as the total pumpng demand (Q T ),. the pumpng capactes (w ), and the ntal pumpng schedule ( q ); If Q T s equal to zero, no pumpng schedule update s requred, go to step (x); otherwse go to step ();. Run MODFLOW and MT3DMS for stress perod to obtan C (0), then run MODFLOW and MT3DMS for another n tmes, where n s the number of actve wells n the stress perod, wth a unt change n pumpng rate to calculate the C (0) C (0) gradents ( ) for each actve well. After ths computaton, sort the ( ) q q j (0) j values for (0) SQ ; v. If C q s less than ε, no update for the stress perod s requred, then (0) ( ) go to step (x); otherwse go to step (v); v. Update the pumpng schedule of stress perod to (1) q usng rank-and-assgn v. method accordng to detaled nformaton on these varables); Smlar to step (), update (0) SQ, w, and Q T (please refer to secton for a C usng q (1), calculate (1) C ( ) q j (1) values and sort these values to obtan (1) SQ ; v. v. Compare (0) SQ and SQ. If they are the same, q (1) s the optmal pumpng (1) schedule for the stress perod, then go to step (x); otherwse go to step (v); If C q s less than ε, (1) ( ) otherwse go to step (x); (1) q s the optmum, then go to step (x); x. Smlar to step (v), update q (1) to q (2) usng the rank-and-assgn method accordng to (1) SQ, w, and Q T ; x. Compare x. to step (x); Compare (1) q and (0) (2) q. If they are the same, then go to step (x); otherwse go C and C (1). If C (0) s less than C (1), use C (1), SQ, and q (2) (1) to replace (0) C, (0) SQ, and (1) q, then go to step (v) and update agan; otherwse 26

36 go to step (x); x. x. Optmze (2) q usng the mproved gradent method (please refer to for detaled nformaton); Run MODFLOW and MT3DMS smulatons usng the optmal pumpng schedule for the stress perod agan, and save pezometrc head and concentraton dstrbuton nformaton at the end of the stress perod for optmzaton of pumpng schedule of the next stress perod. Optmzaton of the pumpng schedule to obtan the mnmum PCE concentraton n the WTP s equvalent to the optmzaton of the pumpng schedule for the maxmum PCE concentraton n the WTP wth the objectve functon multpled by mnus one, and therefore wll not be dscussed here The rank-and-assgn method The rank-and-assgn method was specally developed for PSOpS. Ths method updates the pumpng schedule for maxmum or mnmum contamnant concentraton levels n the WTP based on the dervatve, pumpng capacty, and the total pumpng demand nformaton avalable for the system. The name of ths method reflects the steps t follows to update the pumpng schedule t frst ranks the gradents, and then assgns the pumpng rates to each water-supply well accordng to ths rankng. Steps () to step (x) shown n Fgure 3.1 descrbe the rank-and-assgn optmzaton technque. In step (v), by assumng an (0) SQ wth the followng rankng, C C C ( )... ( )... ( ) q q q (0) (0) (0) 1 k n, (3.7) the procedure below s followed to assgn the q (1) to yeld the maxmum PCE concentraton n the WTP:. Assgn the pumpng capacty of the frst well n.. (0) SQ as ts pumpng rate. If the total pumpng demand s less than the pumpng capacty of that well, assgn the total pumpng demand as ts pumpng rate, and go to step (v); If the remanng pumpng demand s greater than the pumpng capacty of the next well n (0) SQ, assgn the pumpng capacty of that well as ts pumpng rate, and repeat step (), otherwse go to step (); Assgn the remanng pumpng demand as the pumpng rate of the next well n (0) SQ ; and, v. Assgn zero pumpng rates to all other wells that are left n the (0) SQ lst. 27

37 In the rank-and-assgn method, the optmzed pumpng schedule satsfyng the condton SQ = (0) (1) SQ s at least a local optmum because t satsfes the Kuhn-Tucker condton [Kuhn and Tucker, 1951]. The Kuhn-Tucker condton s descrbed below. Consder the problem: Mn f ( x) n x R st.., (3.8) g ( x) 0 h ( x) = 0 j where g (x) ( = 1,,m) s the non-equalty constrants; h j (x) (j = 1,,l) s the equalty constrants; m s the number of non-equalty constrants; and, l s the number of equalty constrants. Suppose that the objectve functon f : R n R and the constrant functons g : R n R and h j : R n R are contnuously dfferentable at a pont x* S. If x* s a local mnmum, then constants λ 0 ( = 1,, m) and μ j ( j = 1,, l) exst such that m f(*) x + λ g (*) x + μ h (*) x = 0 j j = 1 j= 1 λ g ( x*) = 0 for all = 1,..., m l. (3.9) To prove that a soluton from the rank-and-assgn method satsfes the Kuhn-Tucker condton, the problem for one stress perod s reformulated as: Mn C = f( q) n q R st.. q 0 ( = 1,..., n), (3.10) q w 0 ( = 1,..., n) n = 1 q Q = 0 T where C s the PCE concentraton n the WTP; n s the number of actve water-supply wells; q s an n-dmensonal vector of pumpng rates; q s the pumpng rate of well ; w s the pumpng capacty for well ; and, Q T s the total water demand. The Kuhn-Tucker condtons for the problem gven n Equaton (3.10) are, 28

38 f λ + ω + μ = 0 ( = 1,..., n) q λ q = 0 ( = 1,..., n) ω ( q w) = 0 ( = 1,..., n) λ 0 ( = 1,..., n) ω 0 ( = 1,..., n). (3.11) Suppose the optmal soluton from the rank-and-assgn method s = w ( = 1,..., k 1) q w ( = k), (3.12) = 0 ( = k + 1,..., n) whle the followng condton s satsfed, f f f q q q 1 k n. (3.13) For k, snce q > 0, to satsfy λ q = 0, there s: f Accordng to equaton: λ + ω + μ = 0, there s: q λ = 0 ( = 1,..., k). (3.14) f ω = μ ( = 1,..., k). (3.15) q Let f μ =, there s: q k ω = 0. (3.16) k Snce f q f q k for < k, there s: f f ω = 0 ( = 1,..., k 1). (3.17) q q k For > k, snce q =0, to satsfy ω ( q w) = 0, there must be: ω = 0 ( = k+ 1,..., n). (3.18) f Accordng to equaton λ + ω + μ = 0 q there s: 29

39 λ f f f = μ = ( = k+ 1,..., n). (3.19) q q q k Snce f q k f q for > k, t s known that, f f λ = 0 ( = k+ 1,..., n) q q k (3.20) Therefore, the Kuhn-Tucker condtons are satsfed. The Kuhn-Tucker condtons are the necessary condtons for a soluton to be optmal. For an optmzaton problem wth convex (mnmzaton problem) or concave (maxmzaton problem) objectve functon, the Kuhn-Tucker condtons are also suffcent condtons for the soluton to be a global optmum. However, snce the objectve functon n ths problem s nonconvex (or nonconcave), the soluton obtaned from the rank-and-assgn method s not guaranteed to be the global optmum, whch s same as the stuaton assocated wth many other nonlnear optmzaton methods. In ths sense, the rank-and-assgn method trades computatonal effcency wth global optmalty The mproved gradent method As shown n Fgure 3.1, n PSOpS applcaton, the rank-and-assgn method s appled frst to each stress perod. If the optmal soluton can not be obtaned from the rank-and-assgn optmzaton process, an mproved gradent method s used for the optmal soluton. The mproved gradent method s smlar to the steepest descent method ntroduced prevously. In PSOpS, the steepest descent method s further mproved from two aspects: (1) reducng the dmenson of the optmzaton problem and, (2) projectng the gradent to satsfy the equalty constrant. In the mproved gradent method, the rankng of actve pumpng wells n (0) SQ and (1) SQ obtaned from the rank-and-assgn method are compared, and wells wth same rankngs n both sequences are exempted from the optmzaton process. Thus, the dmenson of the optmzaton problem can be reduced sgnfcantly along wth the computatonal cost. For example, assumng that there are fve pumpng wells wth (0) SQ and (1) SQ as, SQ SQ C C C C C :( ) ( ) ( ) ( ) ( ) (0) (0) (0) (0) (0) (0) q 1 q2 q3 q4 q5 C C C C C :( ) ( ) ( ) ( ) ( ) (1) (1) (1) (1) (1) (1) q1 q4 q2 q3 q5 ; (3.21). (3.22) 30

40 Between the two sequences gven above, only wells 2, 3, and 4 have dfferent rankngs. Therefore, n the mproved gradent method, only wells 2, 3, and 4 are consdered as varables for optmzaton, and the dmenson of the problem s reduced from 5 to 3, accordngly. Ths varable-elmnaton step s logcal. Usng the maxmzaton process as an example, after (0) SQ s obtaned the pumpng schedule would be updated accordng to the procedure descrbed n the rank-and-assgn method. Then, accordng to Equaton (3.22), (1) SQ ndcates that well 1 stll has the most potental to ncrease the contamnant concentraton by ncreasng ts pumpng rate. However, the pumpng rate n well 1 has reached ts pumpng capacty and can not be ncreased any further. Therefore, t s exempted from optmzaton. The case for well 5 s smlar to ncrease the contamnant concentraton ts pumpng rate s supposed to be decreased, whle ts pumpng rate s already zero. (If the pumpng rate of well 5 s not zero, then accordng to the descrpton of the rank-and-assgn method we know that the pumpng rates of wells 2, 3, and 4 are at ther pumpng capactes, respectvely, and the pumpng schedule can not be updated any more.) After elmnatng water-supply wells wth same rankngs n both sequences, the gradent of the remanng wells s then projected to the feasble soluton space by subtractng the same amount from all the dervatves to make the summaton of the resultng dervatves to be zero. The equalty constrant of the optmzaton problem can be elmnated by applyng ths gradent projecton because the process guarantees the summaton of the resultng pumpng rates to be constant. The mproved gradent method works through the steps shown n Fgure 3.2. Some varables are the same as defned for Fgure 3.1, the others are defned below. ( k ) d : The search drecton of the optmal soluton for the k th teraton. Its dmenson s the same as the dmenson of the pumpng rate vector. λ k : The step sze of the soluton ncrement for the k th teraton. ( k ) C ( q ): The projecton of C ( q ) n the feasble soluton space. * ( k ) Computatonal steps of the mproved gradent method n obtanng the maxmum PCE concentraton levels at the WTP at stress perod are:. Elmnate the decson varables wth the same rankngs n (0) (1) SQ and SQ ;. Set (1) d to be equal to * (1) C( q ) ; 31

41 ( k) ( k). Fnd λk to maxmze C( q + λd ) method; usng the one-dmensonal lne search v. Update ( k ) q q + ; to ( k 1) v. If C ( q + ) * ( k 1) q + ( k 1) s less than ε, otherwse go to the next step; s the optmum, then go to step (v); v. v. ( k ) Update d to d ( k + 1), go to step () for another teraton; and Save the optmal soluton. Elmnate decson varables wth same rankngs n SQ and SQ (0) (1) d = C ( q ) (1) * (1) ( ) ( ) ( ) ( ) Fnd λ to satsfy ( k k ) ( k k k C q + λkd = MaxC q + λd ) λ q = q + λ d ( k+ 1) ( k) ( k) k C ( q ) < ε? * ( k + 1) N d = C ( q ) ( k+ 1) * ( k+ 1) Y Save result, stop Fgure 3.2. Flowchart for the mproved gradent method Improvement of computatonal effcency The goal of the development of PSOpS s to mprove the computatonal effcency and ths has been acheved as follows.. The reducton of the dmensons of the problem: By reformulatng the problem, only the pumpng schedule of the current stress perod needs to be updated to obtan the optmal contamnant concentraton n the WTP. A problem that can not 32

42 .. be solved by the rank-and-assgn technque and can be solved by the mproved Conjugate Gradent method whch further reduces the dmenson of the problem; The reducton of the number of teratons for the optmzaton: Smulaton results of ths study ndcate that most rank-and-assgn optmzatons converge wthn two teratons; and, Elmnaton of repeated smulatons: At the end of optmzaton for each stress perod, the pezometrc head and concentraton dstrbutons are updated and saved as the startng pont of the optmzaton of the next stress perod. By applyng PSOpS, an optmal pumpng schedule for the problem can be obtaned wthn four to fve days on a desktop workstaton wth 2 GHz CPU and 1 GB memory. A summary of the optmzaton status for the maxmum PCE concentraton levels n the WTP s gven n Table 3.1. In 106 of 528 stress perods, no water was suppled to the WTP (January 1951 December 1951 and March 1987 December 1994). Among the remanng 422 stress perods, the pumpng schedules n 417 stress perods were updated by the rank-and-assgn method, whch accounts for 98.8% of the soluton. Ths percentage ndcates that the rank-and-assgn method works effcently for ths problem. Table 3.1. Summary of the optmzaton status for the maxmum PCE concentraton Optmzaton status Number of cases Percentage C q < ε, no update (0) ( ) (1) ( ) SQ = SQ (0) (1) C q < ε, no second update q = q (1) (2) Optmzaton usng mproved gradent method No pumpng and no update Total Input data for PSOpS As ntroduced before, PSOpS was developed based on the smulaton/optmzaton (S/O) approach. In PSOpS the groundwater smulaton model MODFLOW and the contamnant fate-and-transport model MT3DMS are used as the smulators. Therefore, the orgnal nput fles of MODFLOW and MT3DMS obtaned from the ATSDR study can be used as nput for PSOpS drectly. Other than these fles, only three fles are requred to provde smulaton type, pumpng capactes, and total pumpng demand nformaton as gven below.. Fle type: INFO Fle contents: optmzaton type ( 1 for maxmzaton of the contamnant 33

43 .. concentraton and 2 for mnmzaton of the contamnant concentraton); Fle type: PCP Fle contents: Pumpng capactes of each water-supply well at each stress perod; Fle type: TPD Fle contents: Total pumpng demand for each stress perod. Drect applcaton of nput fles for MODFLOW and MT3DMS as nput for PSOpS makes the generaton of nput fles very effcent and convenent. 34

44 4 Smulaton Results and Dscusson In ths study, PSOpS was run three tmes: () the frst run was to obtan the early PCE arrval tme n the Tarawa Terrace WTP; () the second run was to obtan the late PCE arrval tme n the WTP; and, () the thrd run was also to obtan the late PCE arrval tme wth a restrcton that the pumpng rate n well TT-26 was not to be assgned less than 25% of ts pumpng capacty. In all PSOpS applcatons the pumpng rates n the water-supply wells are consdered to be the only unknown varables. In ths report, the optmal pumpng schedules obtaned from the three PSOpS runs are dentfed as the Maxmum Schedule (Max. Sche.); the Mnmum Schedule I (Mn. Sche. I); and, the Mnmum Schedule II (Mn. Sche. II), respectvely. The orgnal pumpng schedule obtaned from the ATSDR study s dentfed as the Orgnal Schedule (Org. Sche). In the followng sectons, results for these three optmzed pumpng schedules are dscussed. 4.1 Optmzaton and smulaton results for the Maxmum Schedule In the Maxmum Schedule obtaned from PSOpS the pumpng rates of 419 stress perods are updated. Among them, the pumpng rates from 417 stress perods are updated by the rank-and-assgn method, whch reduces the computatonal tme sgnfcantly. Accordng to the ATSDR study, the water-supply wells n the Tarawa Terrace area started to pump n January 1952, whle ABC One-Hour Cleaners started operatons durng January The output of PSOpS ndcates that the frst three-months of pumpng n 1952 had neglgble effect on the PCE concentraton n the WTP after ABC One-Hour Cleaners started to release contamnants nto the groundwater system. Except for those three stress perods, well TT-26 always pumped at ts maxmum pumpng rates (pumpng capactes) n the Maxmum Schedule soluton. Ths fact may be caused by the proxmty of the locaton of well TT-26 to the ABC One-Hour Cleaners relatve to the other wells (Fgure 2.1) and ts locatng n the downstream groundwater flow drecton relatve to the locaton of ABC One-Hour Cleaners. A hgher pumpng rate n well TT-26 wll generate a hgher hydraulc gradent between the contamnant source and well TT-26. Ths would result n faster movement of contamnants from the source to well TT-26 and, thus, an early contamnant arrval tme at the pumpng well and the WTP. Pumpng rates of well TT-26 under the Maxmum Schedule are compared to ts pumpng capactes n Fgure

45 40000 Pumpng Rate Pumpng Capacty Pumpng Rate (ft 3 /day) Jan-51 Jan-55 Jan-59 Jan-63 Jan-67 Jan-71 Jan-75 Jan-79 Jan-83 Jan-87 Date Fgure 4.1. Pumpng rate and pumpng capacty of well TT-26 under the Maxmum Schedule PCE dstrbuton n the groundwater system Whle keepng the other nput data unchanged, and usng the Maxmum Schedule as nput for the WEL package, an MF2K smulaton and an MT3DMS smulaton were conducted to smulate the groundwater flow and PCE transport under the Maxmum Schedule. As expected, a varaton n the pumpng schedule changes the groundwater flow n the subsurface system, thus the PCE fate-and-transport n the aqufer doman also s changed. To llustrate ths change, a comparson of the PCE dstrbuton n the groundwater system of the Tarawa Terrace area and ts vcnty under the Orgnal Schedule and the Maxmum Schedule are shown n Fgures 4.2, 4.3 and 4.4. Only PCE dstrbutons at stress perods 100, 200, 300, and 400 n layers 1, 3, and 5 are shown n these fgures. The text at the bottom left corner of each llustraton n these fgures ndcates the pumpng schedule, the stress perod, and the layer number. For example, Org_SP100_L1 dentfes a plot for PCE dstrbuton n layer 1 at stress perod 100 under the Orgnal Schedule. 36

46 Fgure 4.2. Comparson of PCE dstrbuton n Layer 1 under the Orgnal Schedule and the Maxmum Schedule (Unts: ppb) 37

47 Fgure 4.3. Comparson of PCE dstrbuton n Layer 3 under the Orgnal Schedule and the Maxmum Schedule (Unts: ppb) 38

48 Fgure 4.4. Comparson of PCE dstrbuton n Layer 5 under the Orgnal Schedule and the Maxmum Schedule (Unts: ppb) 39

49 The results gven n Fgures 4.2, 4.3, and 4.4 ndcate that, when compared to the Orgnal Schedule, the PCE contamnant plume under the Maxmum Schedule s aggregated nto a smaller doman and the front of the plume s drected more towards the locaton of well TT-26. Ths s because, under the Maxmum Schedule, the hgher pumpng rate n well TT-26 creates a hgher pezometrc head gradent towards the locaton of well TT-26, whch causes a faster groundwater flow towards and more contamnant mass enterng nto the well TT-26. Therefore, a hgher PCE concentraton n well TT-26 s expected under the Maxmum Schedule PCE concentraton n the water-supply wells From the concentraton observaton fle obtaned from the MT3DMS smulaton, the PCE concentraton n water-supply wells s acqured. The results are compared to the PCE concentraton dstrbuton under the Orgnal Schedule as shown n Fgure Org. Sche. Max. Sche. PCE MCL 100 TT-26 TT-23 TT-25 PCE Conc. (ppb) 10 1 TT-67 TT-31A 0.1 TT-54A 0.01 TT-54B TT-53 TT-31B Jan-51 Jan-55 Jan-59 Jan-63 Jan-67 Jan-71 Jan-75 Jan-79 Jan-83 Jan-87 Date Fgure 4.5. PCE concentratons n water-supply wells under the Orgnal Schedule and the Maxmum Schedule 40

50 The results presented n Fgure 4.5 lead to the followng observatons for PCE concentratons n the water-supply wells under the Maxmum Schedule:. Instead of nne water-supply wells whch had PCE concentratons hgher than ppb (well TT-26, TT-23, TT-25, TT67, TT-54A, TT-54B, TT-31A, TT-31B, and TT-53) under the Orgnal Schedule, under the Maxmum Schedule there are only fve pumpng wells that had PCE concentratons hgher than ppb. These wells are TT-26, TT-23, TT-25, TT-54A, and TT-54B;. Throughout the smulaton perod, PCE concentratons n well TT-26 were always hgher under the Maxmum Schedule when compared to the concentratons obtaned under the Orgnal Schedule. More specfcally, as shown n Fgure 4.6, PCE concentratons n well TT-26 were much hgher under the Maxmum Schedule when compared wth the Orgnal Schedule results durng the perod of nterest ( );. PCE concentraton n well TT-25 was hgher under the Maxmum Schedule when compared wth the Orgnal Schedule results before October 1985 and was lower after that; v. For well TT-23, TT-54A, and TT-54B, the PCE concentratons were lower under the Maxmum Schedule when compared wth the concentratons obtaned under the Orgnal Schedule; v. Under the Maxmum Schedule, only three water-supply wells had PCE concentratons over 5 ppb. They are wells TT-26, TT-23, and TT-25. Among them, PCE concentraton n well TT-26 was much hgher than the MCL throughout the perod of nterest. The other two wells had PCE concentratons hgher than the MCL only for a very short perod of tme; v. PCE concentraton n well TT-26 was much hgher than those obtaned n other wells throughout the smulaton perod. Snce well TT-26 always pumped at ts full capacty (except for the frst three months of 1952), t was the major water-supply well that transported contamnants nto the WTP under the Maxmum Schedule. Based on the observatons gven above, the dfference of the PCE concentratons obtaned n well TT-26 from dfferent pumpng schedules s further evaluated, and the followng observatons can be made:. PCE concentraton n well TT-26 reached 5 ppb n May 1956 under the Maxmum Schedule, whch was eght months earler than the PCE MCL arrval tme under the Orgnal Schedule (January 1957). Snce well TT-26 was the major contrbutor of PCE nto the WTP, the PCE concentraton n the WTP would also reach the MCL earler under the Maxmum Schedule;. PCE concentraton n well TT-26 was much hgher under the Maxmum Schedule when compared to the concentraton obtaned under the Orgnal Schedule durng the perod of nterest. Between these two pumpng schedules, the mnmum dfference of PCE concentraton n well TT-26 s ppb, the 41

51 maxmum dfference s ppb and the average dfference s ppb (Table 4.1) PCE Conc. (ppb) Org. Sche. Max. Sche. 100 Jan-68 Jan-70 Jan-72 Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Date Fgure 4.6. PCE concentratons n well TT-26 under the Orgnal Schedule and the Maxmum Schedule for perod of nterest Table 4.1. PCE concentratons n well TT-26 under the Orgnal Schedule and the Maxmum Schedule for the perod of nterest* (Unts: ppb) Maxmum Mnmum Average Org. Sche Max. Sche Dfference * Data for July 1980 August 1980, January 1983 February 1983, and February 1985 December 1985 are not ncluded. 42

52 4.1.3 PCE concentraton n the WTP Usng the mxng model descrbed n Equaton (2.3), the PCE concentraton n the Tarawa Terrace WTP under the Maxmum Schedule was calculated and compared to that obtaned under the Orgnal Schedule. These comparsons are shown n Fgures 4.7 and /1956 PCE Conc. (ppb) 1 11/ / / Org. Sche. Max. Sche. PCE MCL 07/ Jan-51 Jan-55 Jan-59 Jan-63 Jan-67 Jan-71 Jan-75 Jan-79 Jan-83 Jan-87 Date Fgure 4.7. PCE concentratons n WTP under the Orgnal Schedule and the Maxmum Schedule Results gven n Fgures 4.7 and 4.8 lead to the followng observatons:. The PCE concentraton n the WTP under the Maxmum Schedule s sgnfcantly hgher than that obtaned from the Orgnal Schedule except for the tme perod after February 1985, when well TT-26 was out of servce. The hgher PCE concentraton n the WTP s caused by the hgher pumpng rate and the hgher PCE concentraton n well TT-26 under the Maxmum Schedule;. The hgher PCE concentraton n the WTP s equvalent to the earler 43

53 . contamnant arrval tme the PCE concentraton n the Tarawa Terrace WTP reached 5 ppb n December 1956, whch s eleven months earler than the Orgnal Schedule (November 1957); There are three sudden drops n PCE concentraton n the WTP under the Maxmum Schedule: July 1980 August 1980, January 1983 February 1983, and February 1985 December Ths s smlar to what was observed under the Orgnal Schedule and also s caused by well TT-26 beng out of servce durng these perods PCE Conc. (ppb) 1 02/ / Org. Sche. Max. Sche. PCE MCL 07/ Jan-68 Jan-70 Jan-72 Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Date Fgure 4.8. PCE concentratons n the WTP under the Orgnal Schedule and the Maxmum Schedule for the perod of nterest Results gven n Fgures 4.7 and 4.8 also ndcate that after the well TT-26 was shut down n February 1985, the PCE concentraton n the WTP was lower than that obtaned under the Orgnal Schedule, although the absolute dfference s small (less than 4 ppb). Ths phenomenon s caused by the presence of lower PCE concentratons n the other 44

54 water-supply wells. Ten pumpng wells were stll n servce after February 1985 under the Maxmum Schedule: well TT-25, TT-23, TT-67A, TT-67B, TT-52A, TT-52B, TT-31A, TT-31B, TT-54A, and TT-54B. Results shown n Fgure 4.5 ndcate that, besdes water-supply wells wth PCE concentratons lower than ppb and not shown n the fgure, the PCE concentratons n all the remanng wells were lower under the Maxmum Schedule when compared wth the results obtaned under the Orgnal Schedule durng ths perod. The lower PCE concentratons n these pumpng wells may be attrbuted to the followng:. Accordng to results gven n Fgures 4.2, 4.3, and 4.4, the hgher pumpng rate n well TT-26 under the Maxmum Schedule causes the PCE plume to aggregate nto a smaller regon, whch n turn causes lower PCE concentratons n the water-supply wells other than TT-26;. More contamnant mass s wthdrawn and less mass s left n the groundwater system under the Maxmum Schedule. Accordng to the ATSDR study, grams of PCE was released nto the groundwater system from January 1953 to December By the tme all the pumpng operatons were termnated (February 1987), grams of PCE was dscharged through the water-supply wells under the Orgnal Schedule, whle grams of PCE was dscharged under the Maxmum Schedule as ndcated n Table 4.2. Table 4.2. PCE masses wthdrawn under the Orgnal Schedule and the Maxmum Schedule Total Mass Released (g) Mass Wthdrawn (g) Percentage (%) Org. Sche Max. Sche As dscussed before, there are 15 months durng the perod of nterest when well TT-26 was out of servce and the PCE concentraton n the WTP was lower than 5 ppb. In all the other 201 months, PCE concentraton n the WTP was hgher than the MCL under both the Orgnal Schedule and the Maxmum Schedule. A comparson of PCE concentratons n the WTP durng those 201 months s summarzed n Table 4.3. Table 4.3. PCE concentratons n the WTP under the Orgnal Schedule and the Maxmum Schedule for the perod of nterest* (Unts: ppb) Maxmum Mnmum Average Org. Sche Max. Sche Dfference * Data for July 1980 August 1980, January 1983 February 1983, and February 1985 December 1985 are not ncluded. 45

55 4.2 Optmzaton and smulaton results for the Mnmum Schedule I Smlar to the Maxmum Schedule, PSOpS was run to obtan the Mnmum Schedule I to obtan the latest PCE MCL arrval tme n the Tarawa Terrace WTP. The results obtaned under the Mnmum Schedule I ndcate that well TT-26 pumped at a lowest possble rate for most of the tme perod (Fgure 4.9), whch mples that well TT-26 was not put nto operaton unless no other water-supply well was avalable to provde the requred total demand. The reason for ths s clear snce the PCE concentraton n well TT-26 s sgnfcantly hgher than those n other pumpng wells. For most of the smulaton perod, the lower PCE concentraton n the WTP can be realzed by reducng the pumpng rate of well TT-26. However, there are exceptons to ths durng the perod of late 1970s and early 1980s, whch wll be dscussed n the followng secton Pumpng Rate Pumpng Capacty Pumpng Rate (ft 3 /day) Jan-51 Jan-55 Jan-59 Jan-63 Jan-67 Jan-71 Jan-75 Jan-79 Jan-83 Jan-87 Date Fgure 4.9. Pumpng rate and pumpng capacty of well TT-26 under the Mnmum Schedule I 46

56 4.2.1 PCE dstrbuton n the groundwater system Smlar to the Maxmum Schedule results presented n Fgures 4.2, 4.3, and 4.4, the PCE dstrbutons n the subsurface system around the Tarawa Terrace area and the vcnty under the Orgnal Schedule and the Mnmum Schedule I are compared n Fgures 4.10, 4.11 and The notaton used n these fgures s the same as used for Fgures Results presented n Fgures 4.10, 4.11, and 4.12 ndcate that the Mnmum Schedule I also causes a change of PCE dstrbuton n the groundwater system. Opposte to what has been observed under the Maxmum Schedule, the contamnant plume under the Mnmum Schedule I s dspersed to a larger area, and the front of the plume s more away from the locaton of well TT-26. Therefore, PCE concentratons n some wells other than well TT-26 are expected to be hgher, and the PCE concentraton n TT-26 s expected to be lower. Accordng to the results presented n these fgures, the PCE concentraton near well TT-26 s stll relatvely hgh due to ts closeness to the contamnant source, whch causes a hgher PCE concentraton n well TT-26 when compared to the other wells. Therefore, as dscussed n prevous secton, well TT-26 was pumped at the lowest possble rates for most of the tme under the Mnmum Schedule I to lower the PCE concentraton n the WTP. 47

57 Fgure Comparson of PCE dstrbuton n Layer 1 under the Orgnal Schedule and the Mnmum Schedule I (Unts: ppb) 48

58 Fgure Comparson of PCE dstrbuton n Layer 3 under the Orgnal Schedule and the Mnmum Schedule I (Unts: ppb) 49

59 Fgure Comparson of PCE dstrbuton n Layer 5 under the Orgnal Schedule and the Mnmum Schedule I (Unts: ppb) 50

60 4.2.2 PCE concentraton n the water-supply wells The output of the MT3DMS smulaton under the Mnmum Schedule I provde PCE concentratons n the water-supply wells. These results show hgher PCE concentratons n some of the pumpng wells other than TT-26. Due to the large number of pumpng wells wth PCE concentratons hgher than ppb, only wells wth PCE concentratons hgher than 5 ppb are shown n Fgure Another verson of ths fgure emphaszng the perod of nterest s shown n Fgure TT TT-26 TT-67A 10 TT-67B PCE Conc. (ppb) 1 TT TT-54A TT-25 TT-54B TT-31B 0.01 Org. Sche. Mn. Sche. I TT-31A PCE MCL Jan-51 Jan-55 Jan-59 Jan-63 Jan-67 Jan-71 Jan-75 Jan-79 Jan-83 Jan-87 Date Fgure PCE concentratons n water-supply wells under the Orgnal Schedule and the Mnmum Schedule I From the results gven n Fgures 4.13 and 4.14, one may observe the followng:. Instead of sx water-supply wells (TT-26, TT-23, TT-25, TT-67, TT-54A, and TT-54B) havng PCE concentratons hgher than 5 ppb as seen wth the Maxmum Schedule, nne pumpng wells have PCE concentratons more than 5 ppb under the Mnmum Schedule I. These wells are TT-26, TT-23, TT-25, 51

61 TT-31A, TT-31B, TT-54A, TT-54B, TT-67A, and TT-67B. As dscussed n the prevous secton, ths s caused by the generaton of a more dspersed contamnant plume under the Mnmum Schedule I;. PCE concentraton n well TT-26 s always lower under the Mnmum Schedule I when compared to that obtaned under the Orgnal Schedule throughout the smulaton perod;. Well TT-26 s the frst well to have a PCE concentraton over PCE MCL. Durng the frst half of the smulaton perod, well TT-26 s the only well wth a PCE concentraton hgher than 5 ppb. Therefore, well TT-26 s stll crtcal to the PCE MCL arrval tme n the WTP; v. PCE concentraton n well TT-26 exceeded 5 ppb n August 1959 under the Mnmum Schedule I, whch s 31 months later than the case for the Orgnal Schedule (January 1957). Ths delay would cause a late PCE MCL arrval tme n the WTP as well; v. The PCE concentraton n well TT-26 s no longer domnant durng the second half of the smulaton perod under the Mnmum Schedule I. PCE concentratons n well TT-23, TT-67A, and TT-67B are sometmes hgher than that n well TT-26. Hgher PCE concentratons n these pumpng wells also explan why well TT-26 s not always pumpng at the lowest possble rates towards the end of the smulaton perod wth several pumpng wells havng hgh PCE concentraton n them, the Mnmum Schedule I s managed n a way that the plume front s not led to any partcular water-supply well. 52

62 TT-26 TT-67A 10 PCE Conc. (ppb) 1 TT-67B 0.1 TT-54A TT TT-54B TT-67 TT-31A Org. Sche. PCE MCL TT-31B Mn. Sche. I Jan-68 Jan-70 Jan-72 Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Date Fgure PCE concentratons n water-supply wells under the Orgnal Schedule and the Mnmum Schedule I for the perod of nterest PCE concentraton n the WTP The PCE concentraton n the Tarawa Terrace WTP under the Mnmum Schedule I s calculated usng Equaton (2.3) and s shown n Fgures 4.15 and

63 / / /1977 PCE Conc. (ppb) 1 06/ / / / Org. Sche. Mn. Sche. I PCE MCL Jan-51 Jan-55 Jan-59 Jan-63 Jan-67 Jan-71 Jan-75 Jan-79 Jan-83 Jan-87 Date Fgure PCE concentratons n the WTP under the Orgnal Schedule and the Mnmum Schedule I The results presented n Fgures 4.15 and 4.16 lead to the followng observatons:. The PCE concentraton n the WTP under the Mnmum Schedule I s lower than that obtaned under the Orgnal Schedule except for the perod after February 1985;. The PCE concentraton n the WTP reached 5 ppb n June 1960 under the Mnmum Schedule I, whch s 31 months later than the arrval tme of the Orgnal Schedule. Ths s due to the lower PCE concentraton and lower pumpng rate n well TT-26 under the Mnmum Schedule I. Accordng to Fgure 4.13, by the tme the PCE concentraton n the WTP reached 5 ppb, the PCE concentratons n the supply wells other than TT-26 were stll neglgble. Therefore, well TT-26 s the crtcal well affectng the PCE MCL arrval tme n the WTP;. Under the Mnmum Schedule I, the PCE concentraton n the WTP ncreased 54

64 v. steadly untl December 1961, when the PCE concentraton dropped below trace levels due to zero-pumpng n well TT-26. The concentraton reached 5 ppb agan n November Between January 1962 and December 1971, the PCE concentraton n the WTP was lower than ppb and therefore s not shown n these fgures; The sudden PCE concentraton drops that were observed durng perods of July 1980 August 1980, January 1983 February 1983, and February 1985 December 1985 under the Orgnal Schedule were not obvous under the Mnmum Schedule I for two reasons. Frst the overall PCE concentraton level n the WTP s very low under the Mnmum Schedule I. Second, the PCE concentraton n well TT-26 s no longer domnant as shown n Fgure /1977 PCE Conc. (ppb) 1 07/ / / Org. Sche. Mn. Sche. I PCE MCL Jan-68 Jan-70 Jan-72 Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Date Fgure PCE concentratons n the WTP under the Orgnal Schedule and the Mnmum Schedule I for the perod of nterest Another observaton that can be made from the results presented n Fgures 4.15 and

65 s that durng the last 11 months of the perod of nterest the PCE concentratons n the WTP under the Mnmum Schedule I are slghtly hgher than those obtaned under the Orgnal Schedule, whch s n contrast to the results obtaned under the Maxmum Schedule. The reason for ths s the hgher PCE concentratons n some water-supply wells other than well TT-26 (.e., well TT-67A and TT-67B). The hgher PCE concentratons n these pumpng wells may be caused by the followng factors:. As shown n Table 4.4, by the end of the perod of nterest, less contamnant mass was extracted from the groundwater system under the Mnmum Schedule I, and more mass was left n the aqufer, whch causes hgher PCE concentratons n the water-supply wells;. The Mnmum Schedule I causes a more dspersed contamnant plume n the groundwater system. Whle PCE concentraton n well TT-26 s decreased, the PCE concentratons n some other wells are ncreased. Table 4.4. PCE masses wthdrawn under the Orgnal Schedule and the Mnmum Schedule I Total Mass Released (g) Mass Wthdrawn (g) Percentage (%) Org. Sche Mn. Sche. I The Mnmum Schedule I yelds lower PCE concentratons n the WTP durng the perod of nterest (Table 4.5). To keep ths comparson consstent wth the prevous comparson made for the Maxmum Schedule, the concentraton dstrbuton obtaned from the 15 months when well TT-26 was out of servce was not ncluded n ths analyss. The results shown n Table 4.5 ndcate that the average PCE concentraton n the WTP under the Mnmum Schedule I s 5.01 ppb, whch s qute close to the 5 ppb MCL of PCE. Table 4.5. PCE concentratons n the WTP under the Orgnal Schedule and the Mnmum Schedule I for the perod of nterest* (Unts: ppb) Maxmum Mnmum Average Org. Sche Mn. Sche. I Dfference * Data for July 1980 August 1980, January 1983 February 1983, and February 1985 December 1985 are not ncluded. 4.3 Optmzaton and smulaton results for the Mnmum Schedule II The late PCE MCL arrval tme n the WTP can be obtaned through MODFLOW and MT3DMS smulatons usng the Mnmum Schedule I developed earler. These results ndcate that under Mnmum Schedule I, well TT-26 was out of servce for a long perod of tme, whch s unrealstc based on the hstorcal records and also consderng that well 56

66 TT-26 was one of the major water-supply wells n the Tarawa Terrace area. Therefore, a thrd PSOpS smulaton was conducted to obtan a pumpng schedule whch may stll yeld the latest arrval tme but at the same tme be closer to the hstorcal data on the schedule of operatons at the ste. To acheve ths, one more constrant was added to the optmzaton model. The pumpng rate n well TT-26 s restrcted not to be less than 25% of ts pumpng capacty at any tme when the pumpng well was n servce. The pumpng rate of well TT-26 obtaned for ths case s shown n Fgure Smlar to the Mnmum Schedule I, the Mnmum Schedule II pumpng rate for well TT-26 also s the lowest possble durng the frst half of the smulaton perod Pumpng Rate Pumpng Capacty Pumpng Rate (ft 3 /day) Jan-51 Jan-55 Jan-59 Jan-63 Jan-67 Jan-71 Jan-75 Jan-79 Jan-83 Jan-87 Date Fgure Pumpng rate and pumpng capacty of well TT-26 under the Mnmum Schedule II PCE dstrbuton n the groundwater system The PCE dstrbuton n the subsurface system n the Tarawa Terrace area and vcnty under the Orgnal Schedule and the Mnmum Schedule II are compared n Fgures 4.18, 4.19, and 4.20 for dfferent stress perods. A comparsons of PCE dstrbutons obtaned under the Mnmum Schedules I and II are shown n Fgures 4.21, 4.22, and The 57

67 notatons used n these fgures are the same as used n Fgure 4.2. A comparson of Fgures 4.10, 4.11, and 4.12 and Fgures 4.18 through 4.23 ndcate that the Mnmum Schedule II also causes the PCE plume to be more dspersed than the Orgnal Schedule, but not as much as the Mnmum Schedule I. Ths s because the average pumpng rate n well TT-26 under the Mnmum Schedule II s lower than that obtaned under the Orgnal Schedule, but hgher than the average pumpng rate obtaned under the Mnmum Schedule I. Therefore, one may expect the PCE concentratons n well TT-26 and the WTP under the Mnmum Schedule II to be between those obtaned under the Orgnal Schedule and the Mnmum Schedule I. 58

68 Fgure Comparson of PCE dstrbuton n Layer 1 under the Orgnal Schedule and the Mnmum Schedule II (Unts: ppb) 59

69 Fgure Comparson of PCE dstrbuton n Layer 3 under the Orgnal Schedule and the Mnmum Schedule II (Unts: ppb) 60

70 Fgure Comparson of PCE dstrbuton n Layer 5 under the Orgnal Schedule and the Mnmum Schedule II (Unts: ppb) 61

71 Fgure Comparson of PCE dstrbuton n Layer 1 under the Mnmum Schedule I and the Mnmum Schedule II (Unts: ppb) 62

72 Fgure Comparson of PCE dstrbuton n Layer 3 under the Mnmum Schedule I and the Mnmum Schedule II (Unts: ppb) 63

73 Fgure Comparson of PCE dstrbuton n Layer 5 under the Mnmum Schedule I and the Mnmum Schedule II (Unts: ppb) 64