Freiberg Online Geology FOG is an electronic journal registered under ISSN VS2DRT: Variably Saturated Two Dimensional Reactive Transport

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1 FOG Freberg Onlne Geology FOG s an electronc ournal regstered under ISSN , VOL 34 Sosna Shmeles Hale VSDRT: Varably Saturated Two Dmensonal Reactve Transport Modelng n the Vadose Zone 53 pages, 97 fgures, tables, 55 references

2 Abstract Contamnate transport n vadose s a huge concern snce the vadose zone s the man passage way for ground water recharge. Understandng ths process s crucal n order to prevent contamnaton, protect and rehabltate ground water resources. Reactve transport models are nstrumental for such purposes and there are numerous solute transport smulaton programs for both ground water and vadose zone but most of ths models are lmted to smple Lnear, Langmur and Freundlch sorpton models and frst order decay and fal to smulate more complex geochemcal reactons that are common n the vadose zone such as caton exchange, surface complexaton, redox reacton and bodegradaton. So t s necessary to enhance capabltes of solute transport models by ncorporatng well tested hydrogeochemcal models lke PHREEQC n to them to be able closely approxmate the geochemcal transport process n the subsurface. In ths PhD research a new reactve transport model called VSDRT was created by couplng exstng publc doman solute and heat transport models VSDT, VSDH wth hydrochemcal model PHREEQC usng non-teratve operator splttng technque. VSDRT was compled usng MnGW compler usng tools lke autotools and automake. A graphcal user nterface was also created usng QT creator and Argus ONE numercal development tools. The new model was tested for one dmensonal conservatve Cl transport, surface complexaton, caton exchange, dssoluton of calcte and gypsum, heat and solute transport as well as for two dmensonal caton exchange cases. Ther results were compared wth VSDT, VSDH, HP and HP models and the results are n good agreement.

3 Acknowledgement It has been a long ourney glory to the Almghty God who has made everythng possble. I would lke to take ths opportunty to express my heartfelt grattude to my supervsor Prof. Dr. habl Border J. Merkel, Head of Geology Department and Char of Hydrogeology, for gvng me the opportunty to do ths research and for hs gudance, valuable dscussons, comments, suggestons and support I receved at every stage of my work. I am also very grateful to Dr. Volkmar Dunger for hs constructve supervson. I am deeply ndebted to German Academc Exchange Servce (DAAD) and TU Bergakademe Freberg (TUBAF) for fnancng my study. I am very thankful to Mrs. Manuela Junghans, Cornela Magnus, Cornela Knep, Sabne Schrenk, Petra Kräher, Heke Beyer and Stefane Lndner from TUBAF and Studentenwerk Freberg. I would lke to thank also Jürgen Gelke and Joachm Scharfe. Specal thanks go to Mr. Tno Beer for always beng there to fx computer related problems and to all my colleagues at the Insttute of Hydrogeology TUBAF, specally Dr. Eyad Aboshnd, Dr. Samer Bachmaf, Raghd Sabr, Wondem Gezahegne, Dr. Sameh Wsam, Dr. Nar Sreeesh, Dr. Mandy Schpek, Ramadan Azz, Mustafa Almukhtar, Alreza Arab, Mohammed Omer, Omed Mustafa, Iwona Woloszyn and Zheenbek Kulenbekov. Last but not least, I am deeply oblged to my beloved mother Wude Mekonne and my father Atnafu Mengste, my brothers, frends and my husband Kehulu Ylkal for ther love, support and understandng durng my study. My dear daughter, Bethel, you are my angel, nspraton and courage we dd t together thank God. 3

4 Table of content Contents Page No. Abstract... Table of content... 4 Lst of fgures... 7 Lst of tables... Lst of abbrevatons... 3 Chapter One: Introducton Background Lterature revew Obectve....4 Methodology and materals used....5 Features and lmtatons... 3 Chapter Two: Unsaturated water flow Unsaturated Water flow equaton Temperature dependence of saturated hydraulc conductvty n sol Unsaturated sol hydraulc propertes Intal and boundary condtons for water flow Evaporaton Evapotranspraton... 3 Chapter Three: Heat transport n unsaturated zone Heat transport equaton Intal and boundary condtons for heat transport Chapter Four: Solute transport n unsaturated zone Solute transport equaton n unsaturated zone Intal and boundary condtons for solute transport Chapter Fve: Chemcal reactons n unsaturated zone Equlbrum reacton Heterogeneous on-exchange Heterogeneous surface complexaton process

5 5..3 Heterogeneous mneral dssoluton/precptaton Knetc reacton Chapter Sx: Numercal solutons for water flow, heat transport and mult-solute transport Numercal mplementaton for unsaturated water flow Spatal dscretzaton of unsaturated water flow Temporal dscretzaton of unsaturated water flow Numercal soluton Numercal mplementaton for heat transport Spatal dscretzaton of heat transport Temporal dscretzaton of heat transport Numercal soluton Numercal mplementaton for mult-solute transport Spatal dscretzaton of mult-solute transport Temporal dscretzaton of mult-solute transport Numercal soluton Numercal solutons for chemcal equlbrum and knetc reacton equatons Chapter Seven: Couplng procedure Coupled process n reactve transport Operator splttng Chapter Eght: Data nput and output for VSDRT VSDRT pre-processor for non-spatal nput Model descrpton Settng smulaton optons Settng ntal conducton and hydraulc propertes functons choce Settng recharge perod propertes Settng evaporaton parameters Settng evapotranspraton parameters Settng reactve transport smulaton Settng heat transport Settng solver parameters Settng output potons VSDRT pre-processor for spatal nput Smulaton doman outlne VSDRT Grd Textural Class

6 8..4 Intal condton for flow Intal soluton Intal temperature Observaton ponts Boundary condtons VSDRT post-processor Runnng VSDRT numercal model Presentng VSDRT output usng Argus ONE post-processor tools... 4 Chapter Nne: Model verfcaton D Conservatve sngle component transport n vadose zone Surface complexaton and equlbrum phase D reactve transport nvolvng caton exchange D reactve transport nvolvng dssoluton of calcte and gypsum D Heat and solute transport D reactve transport nvolvng caton exchange D reactve transport Chapter Ten: Concluson and recommendatons Concluson Recommendatons Reference

7 Lst of fgures Fgures Page No. Fgure. Evoluton of the scence of sol-water physcs and solute transport (Rolston, 007) 9 Fgure 6. Schematc representaton of rectangular grd block system (E.G. Lappala, R. W. Healy and E.P. Weeks, 986)...49 Fgure 6. Schematc representatons of cylndrcal grd-block system (E.G. Lappala, R. W. Healy and E.P. Weeks, 986)..50 Fgure 7 Schematc representaton of modelng approach of coupled VSDRT model...69 Fgure 8. Intatng new VSDRT proect n Argus One Envronment 70 Fgure 8.. Bref descrpton about VSDRT program 7 Fgure 8..a Settng general smulaton parameters n the Proect wndow.7 Fgure 8..b Choosng length unt Fgure 8..c Choosng tme unt Fgure 8..d Choosng heat unt...74 Fgure 8..e Choosng coordnate system.74 Fgure 8..f General smulaton opton for transport and flow.74 Fgure 8..g Choosng fnte dfferencng opton for transport smulaton...74 Fgure 8..3 Settng ntal condtons and hydraulc functons n Hydraulc wndow...75 Fgure 8..4 Recharge perod wndow to nput recharge perod parameters..77 Fgure 8..5a Inactve evaporaton wndow...78 Fgure 8..5b Selectng evaporaton to be smulated n the proect wdow...79 Fgure 8..5c Actvated evaporaton table n Evaporaton wndow...79 Fgure 8..6a Selectng evapotranspraton n proect wndow..80 Fgure 8..6b Actvated evapotranspraton table n evaporaton wndow...8 Fgure 8..6c Selectng evaporaton and evapotranspraton optons....8 Fgure 8..6d Actvated evaporaton and evapotranspraton table n Evaporaton wndow..8 Fgure 8..7a Selectng solute n the Proect wndow...83 Fgure 8..7b Database fle name and selectng solute mass balance 7

8 output n solute wndow...83 Fgure 8..7c Phreeqc nput wndow to set ntal and boundary solutons and varous chemcal reactons...84 Fgure 8..8a selectng heat transport opton n the proect wndow...84 Fgure 8..8b Heat mass balance selecton n t heat wndow.85 Fgure 8..9a Solver wndow to set solver parameters...86 Fgure 8..9b Settng smulaton to smulate heat and reactve transport...86 Fgure 8..9c Settng solver parameters for flow, heat and reactve transport...87 Fgure 8..0 Output wndow to set out optons and tme..88 Fgure 8. VSDRT pre-processor for spatal nput n Argus ONE envronment.90 Fgure 8..a Schematc representaton of selectng drawng sze...9 Fgure 8..b Drawng sze wndow...9 Fgure 8..c Schematc representaton of selectng scale and unts...9 Fgure 8..d Scale and unts wndow 93 Fgure 8..e Selectng closed contour tool to draw the doman of nterest..93 Fgure 8..f Schematc representaton of doman of nterest...94 Fgure 8..g Schematc presentaton of settng grd densty value for doman of nterest...94 Fgure 8..a Schematc representaton of selectng Magc Wand tool to generate grd n VSDRT Grd layer wndow...95 Fgure 8..b Grd angle wndow...95 Fgure 8..c Scheamtc representaton of grd generated by Magc Wand tool...96 Fgure 8..d Schematc representaton of selectng delete tool to remove unwanted grds...97 Fgure 8..e Schematc representaton of row ncertng tool to creat a one dmentoal coulm...97 Fgure 8..f Grd Lnes generaton wndow...98 Fgure 8..g Schematc representaton of D grd n column...98 Fgure 8..3a Schematc representaton of selectng Textural Class 0 Fgure 8..3b Schematc representaton of selectng closed contour to delneate a textural class...0 8

9 Fgure 8..3c Schematc representaton of settng textural class propertes.0 Fgure 8..4 Schematc representaton of settng ntal pressure head or ntal mosture content n doman of nterest..03 Fgure 8..5 Schematc representaton of settng ntal soluton.04 Fgure 8..6a Schematc representaton of settng ntal temperature n doman of nterest...05 Fgure 8..6b Settng hydraulc, thermal and geochemcal propertes of the medum along n case of heat and reactve transport..05 Fgure 8..6c Settng boundary condtons for flow, heat and reactve transport smulaton...06 Fgure 8..7 Settng observaton pont on the observaton layer...07 Fgure 8..8a Selectng boundary Condtons layer. Fgure 8..8b Schematc representaton of selectng open contour tool of Argus ONE to set the boundary condtons... Fgure 8..8c Schematc representaton of settng boundary condtons for flow and solute transport... Fgure 8.3.a Schematc representaton of selectng ExportVSDRT menu...3 Fgure 8.3.b Schematc representaton of RunVSDRT wndow..3 Fgure 8.3.a Schematc representaton of selectng the Data layer.5 Fgure 8.3.b Schematc representaton selectng Import Data menu...5 Fgure 8.3.c Schematc representaton selectng Text Fle menu of Import Data menu..6 Fgure 8.3.d Schematc representaton of Import Data wndow.6 Fgure 8.3.e Schematc representaton of choosng fle to be mported to Data layer 7 Fgure 8.3.f Schematc representaton of mported data to Data layer...7 Fgure 8.3.g Schematc representaton of selectng Output layer to plot the outputs of the smulaton.8 Fgure 8.3.h Schematc representaton of selectng Argus ONE Post-processng tools popup menu...8 Fgure 8.3. Schematc representaton of settng Color Map parameters to create color map...9 9

10 Fgure 8.3. Example color map showng spatal dstrbuton of pressure head plotted usng Argus ONE Post-processng Color Dagram tool..9 Fgure 9. Comparsons of conservatve Cl transport smulaton usng VSDRT and VSDT... Fgure 9.a Dstrbuton of mosture content at 40 and 00 days based on VSDRT smulaton.3 Fgure 9.b Dstrbuton of water content and ph at 40 (crcles) and 00 (trangles) days respectvely (L. Wssmeer and D.A. Barry, 008, page 87)..3 Fgure 9.c Dstrbuton of Na at 40 and 00 days based on VSDRT smulaton.4 Fgure 9.d Dstrbuton of Ca at 40 and 00 days based on VSDRT smulaton.4 Fgure 9.e Dstrbuton of C at 40 and 00 days based on VSDRT smulaton.4 Fgure 9.f Dstrbuton of Na, Ca and C at 40 (crcles) and 00 (trangles) days respectvely (L. Wssmeer and D.A. Barry, 008, page 87)..5 Fgure 9.3a Smulaton of caton exchange usng VSDRT...6 Fgure 9.3b PHREEQC smulaton of caton exchange n nvolvng advecton and dsperson transport...7 Fgure 9.4a Ca and S profle at 0, 0.5,,.5, and.5 days accordng to HP smulaton...8 Fgure 9.4b Ca and S profle at 0, 0.5,,.5, and.5 days accordng to VSDRT smulaton...9 Fgure 9.5a Comparson of heat smulaton of VSDRT wth that of VSDH...30 Fgure 9.5b conservatve Cl transport smulated wth heat transport usng VSDRT...3 Fgure 9.6a Schematc representaton of furrow rrgaton smulaton doman along wth fnte dfference grd...3 Fgure 9.6b Pressure head profle at tmes a) 0., b) 0.5, c) and d) days usng VSDRT smulaton 34 Fgure 9.6c Pressure head profle at tmes a) 0., b) 0.5, c) and d) days usng HP smulaton (Smunek, Jacques, Sena, & van Genuchten, 0).34 0

11 Fgure 9.6d Chlorde n mol/l profle at tmes a) 0., b), c) 3 and d) 5 days usng VSDRT smulaton...36 Fgure 9.6e Chlorde n mol/l profle at tmes a) 0., b), c) 3 and d) 5 days usng HP smulaton (Smunek, Jacques, Sena, & van Genuchten, 0).36 Fgure 9.6f Na n mol/l profle at tmes a) 0., b), c) 3 and d) 5 days usng VSDRT smulaton.38 Fgure 9.6g Na n mol/l profle at tmes a) 0., b), c) 3 and d) 5 days usng HP smulaton (Smunek, Jacques, Sena, & van Genuchten, 0)..38 Fgure 9.7a vertcal secton of smulaton doman (Lappala E.G.,Healy R.W. and Weeks E.P.,987).39 Fgure 9.7b VSDRT smulaton of evaporaton and evapotranspraton rates...4 Fgure 9.7c VSD smulaton of evaporaton and evapotranspraton rates (Lappala E.G.,Healy R.W. and Weeks E.P.,987)...4 Fgure 9.7d Pressure head profle based on VSDRT at a),b) 6,c)33 and 77days respectvely...4 Fgure 9.7e Ca profle based on VSDRT at a), b) 6, c) 33 and 77days respectvely.43 Fgure 9.5f Cl profle based on VSDRT at a), b) 6, c) 33 and 77days respectvely.44 Fgure 9.5g Ca profle based on VSDRT at a), b) 6, c) 33 and 77days respectvely.45 Lst of tables Tables Page No..a Publc doman reactve transport models...0

12 .b Commercal reactve transport models a Possble flow boundary condtons b Possble combnaton of boundary condtons for flow and heat and solute transport Hydraulc and geochemcal propertes of the loamy sand column along wth ntal and boundary condtons modfed from (Wssmeer & Barry, 008). 9. Hydraulc and geochemcal propertes of the slt loam column along wth ntal and boundary condtons Hydraulc and geochemcal propertes of sol column along wth ntal and boundary solutons Hydraulc, thermal and geochemcal propertes sol column along wth ntal and boundary condtons for heat and reactve transport Hydraulc and geochemcal propertes of smulaton doman along wth ntal and boundary solutons for furrow rrgaton problem Hydraulc and geochemcal propertes, ntal and boundary condtons for D re-actve transport Recharge perod parameters used for D reactve transport Evaporaton and evapotranspraton parameters used for D reactve transport smulaton 40 Lst of abbrevatons D one dmensonal D two dmensonal L length unt T tme unt - dmensonless C degree centgrade J oule W watt m meter cm centmeter

13 g cm/h mmol mol/kg mmol/kg m²/g Cl Ca Na C gram centmeter per hour mlmole mole per klogram mlmole per klogram meter square per gram chlorde calcum sodum carbon 3

14 Chapter One: Introducton. Background Vadose zone lays between the earth s surface and the water table playng a crucal role n earth s ecosystem. It provdes nutrents and water for plants and act as a source of contamnate and recharge water for the ground water system. It s a complex system (Healy & Ronan, 996) where all three phases gas, lqud and sold coexst and varous physcal, chemcal and bologcal actvtes take part. Human actvtes such as the use of fertlzers, pestcdes and unsafe dsposal of waste greatly affect the qualty of ground water. Clear understandng of the vadose zone processes s mportant from agrcultural, hydrogeologcal and envronmental perspectve. The present study s focused on modelng hydrogeologcal and envronmental aspects of vadose zone processes. The vadose zone processes of nterest n ths study are water flow, heat transport, solute transport and reactve transport. These processes affect both qualty as well as quantty of the ground water by affectng the chemstry and amount of recharge water. Hence, modelng of such processes could be nstrumental n predctng and estmatng qualty and quantty of ground water recharge. Such predcton could be used for plannng and mplementng sustanable ground water utlzaton and management as well as to take proper remedal measures. Although there are numerous analytcal and numercal models to smulate vadose zone processes none of them has the capacty to fully smulate ths complex system. Many of the models are focused on water flow and solute transport or heat transport. HP (Jacques & Smunek, 005), HYDROGEOCHEM (Yeh & Trpath, 990), TOUGHREACT (Xu, E.I., Spycher, & Pruess, 004) and UNSATCHEMD (Smunek & Suarez, 994) are few reac- 4

15 tve transport models avalable to do D and mult-dmensonal reactve transport smulaton n vadose zone. Ths PhD research focuses on development of D reactve transport model wth abltes to smulate water flow, heat transport, mult-solute transport and reactve transport n the vadose zone by couplng the latest versons of VSDT (Healy, 990), VSDH (Healy & Ronan, 996) wth PHREEQC (Parkhurst & Appelo, 999). Such model could have applcatons n the study of contamnate transport, acd mne dranage, nuclear repostory both n one and two dmenson. VSDT s a computer program wrtten n FORTRAN90 programmng language and smulates advectve dspersve solute transport n varably saturated porous meda n one and two dmenson. It s based on VSD (Lappala, Healy, & Weeks, 987) whch smulates flow of water n varably saturated porous meda based on Rchard s equaton. The model s a sngle solute transport wth fxed head, fxed flux, evaporaton, evapotranspraton and seepage face flow boundary condtons and fxed concentraton and flux concentraton transport boundary condtons. It consders varous source/snk terms lke root water uptake, frst order decay, Lnear, Freundlch and Langmur sotherm adsorptons. VSDH s a computer program wrtten n FORTRAN90 programmng language and smulates advectve dspersve heat transport n varably saturated porous meda n one and two dmenson. It s based on the VSDT model takng advantage of the smlarty n the advectve dspersve transport processes of solute and heat transport. The maor dfference between the two programs s the dfference n parameters presented n solute and heat transport governng equatons. VSDH s not applcable for vapor phase flow and varable densty 5

16 condtons. It can have fxed heat flux and fxed temperature boundary condtons. The source and snk term can be due the flow of water nto or out of the doman. It assumes that saturated hydraulc conductvty s a functon of temperature. PHREEQC s based on ether on-assocaton aqueous model or Specfc Interacton Theory (SIT, PITZER) wth capabltes for specaton and saturaton ndex calculaton, batch reacton, knetc reactons, one dmensonal transport and nverse modelng (Parkhurst & Appelo, 999). PHREEQC has been used as geochemcal module for reactve transport models. Some of the reactve transport models that nclude PHREEQC n ther models are PHT3D (Appelo & Rolle, 00), TACK (Källvenus & Ekberg, 003), PHAST (Parkhurst, Kpp, Engesgaard, & Charlton, 004), PHWAT (Mao, Prommer, Barry, Langevn, Pantelet, & L, 006) and HP (Jacques & Smunek, 005) for ground water and vadose zone respectvely. The man task of ths PhD research was to prepare a new two dmensonal mult-component reactve transport model called VSDRT (Varably Saturated Dmensonal Reactve Transport) for vadose zone by couplng VSDT, VSDH and PHREEQC models. The model has capabltes to smulate water flow, heat transport and mult-component reactve transport as well as equlbrum and knetc reactons n the vadose zone.. Lterature revew Vadose zone hydrology s rather a young feld of study whch nvolves multdscplnary felds of sol physcs, hydrogeology, geochemstry and deals wth physcal, chemcal and bologcal processes n the subsurface. The frst graduate courses n ths feld were offered only n early 980s (U.S. Department of Energy, 00). The vadose zone s consdered as neglected component of nature (Ronen & Sorek, 005). Most of the papers before 980s are 6

17 on sol physcs and groundwater hydrogeology aspect of the subsurface. The man mlestones studes that paved the road for vadose studes are n 856 Darcy Law concernng flow n porous medum, n 855 Fck s law for solute transport and n 8 for heat transport. In 899 Slchter publshed Theoretcal nvestgaton of groundwater, whch provded exact solutons for flow and pressure feld around a pumped wells (Tndall & Kunkel, 999; Selker, Keller, & McCord, 999). In 907 Buckngham extended Darcy s law to flow n unsaturated systems and proposed that hydraulc conductvty must be a functon of mosture content and hydraulc potental must nclude capllary pressure (Selker, Keller, & McCord, 999; Tndall & Kunkel, 999; Nmmo & Landa, 005; Raats & van Genuchten, 006). In 9 Green and Ampt made sgnfcant contrbuton on the nfltraton of water n sol (Selker, Keller, & McCord, 999; Tndall & Kunkel, 999). In 93 Rchards derved Rchard s equaton, whch s a governng equaton n unsaturated zone hydrology (Rchards, 93). In 930 Hanes ntroduced hysteress (Selker, Keller, & McCord, 999; Raats & van Genuchten, 006). In 95 Bouyoucous demonstrated that temperature affected pressure gradents n sol columns under sothermal condtons and n 940 Moore showed that temperature has a consderable effect on the sol hydraulc propertes (Nelsen, van Genuchten, & Bggar, 986). The evoluton of sol physcs and solute transport studes n the subsurface s presented n fgure.. Further comprehensve works on sol physcs aspect of vadose zone could be referred to (Phlp, 974; Raats & van Genuchten, 006). Many models of varyng degree of complexty and dmensonalty have been developed durng the past several decades to quantfy the basc physcal and chemcal processes affectng the flow and contamnate transport n the unsaturated zone (Smunek & Bradford, 008). Complaton of many analytcal solutons for convecton-dsperson equaton of solute 7

18 transport n one and mult-dmenson s presented n publc doman software package STANMOD (Studo of Analytcal MODels) (Smunek, van Genuchten, Sena, Torde, & Le, 999). It ncorporates CFITM (van Genuchten, 980), CFITIM (van Genuchten, 98), and CHAIN (van Genuchten, 985) one-dmensonal models and 3DADE (Le & Bradford, 994) and N3DADE (Le and Torde, 997) two- and three-dmensonal models. Analytcal models are only applcable to very smplfed problems and smple geometres. Analytcal solutons can usually be derved only for smplfed transport systems nvolvng lnearzed governng equatons, homogeneous sols, smplfed geometres of the transport doman, and constant or hghly smplfed ntal and boundary condtons (Smunek J., 005). To obtan more realstcally soluton to the non-lnear Rchards equaton numercal solutons are essental. Numercal models are preferable n maorty of the cases due to ther unque ablty to handle complex geometry, heterogeneous sols, more realstc ntal and boundary condtons as well as non-lnear relatonshps. VSDTI (Healy,990), DAISY (Abrahamsen & Hansen, 000), TOUGH (Pruess, Oldenburg, & Mords, 999), MACRO 5 (Larsbo, 003), SHAW (Flerchnger, 000), SWAP (Kroes, van Dam, Huygen, & Vervoort, 999), HYDRUS-D (Smunek, Sena, Sato, Saka, & van Genuchten, 009), HYDRUS-D (Sena, Smunek, & and van Genuchten, 0) and UNSATH (Fayer,000) are some of the wdely used numercal models for smulatng varably-saturated water flow and solute transport n the vadose zone. Some of currently avalable bogeochemcal models are UNSATCHEMD (Smunek & Suarez 994), PHREEQC (Parkhurst and Appelo, 999), 3DHYDROGEOCHEM (Yeh & Cheng, 999), HBG3D (Gwo, et al., 00), CrunchFlow (Steefel, 009) and HP (Jacques and Smunek, 005). A comprehensve lterature revew on transport of reactve solutes n 8

19 sol s presented n the book Advances In Porous Meda volume (Corapcoglu, 994). Table.a and.b presents selected publc doman and commercal reactve transport models respectvely. Fgure. Evoluton of the scence of sol-water physcs and solute transport (Rolston, 007) 9

20 Table.a Publc doman reactve transport models Models DFATMIC 3DFATMIC CHEMFLO CHAIN_D FEHM HydroBoGeoChem3 PESTAN RITZ SUTRA UNSATCHEM UNSATCHEM-D VLEACH HYDRUSD PHREEQC VSDI HP SWMS_D SWMS_3D RETRASO SHAW General capabltes D/D varably saturated flow and transport of mcrobes and chemcals wth smple chemcal reactons lke decay knetcs, lnear/non-lnear adsorpton D/D/3D varably saturated flow and transport of mcrobes and chemcals wth smple chemcal reactons lke decay knetcs,lnear/non-lnear adsorpton D varably saturated flow and solute transport D water flow, heat and multple solute transport n varably saturated porous meda D/D/3D multphase, multcomponent, non-sothermal, reactve flow through varably saturated porous and fractured meda D/D/3D solute transport, heat transport, mxed, heterogeneous, chemcal knetcs and equlbrum and coupled reactve transport n varably saturated porous meda D analytcal smulaton of organc solute transport n the vadose zone D analytcal smulaton of unsaturated zone flow and transport of oly wastes durng land treatment. varably saturated, varable-densty ground-water flow wth solute or energy transport D smulaton of varably saturated water flow, heat transport, CO producton and transport,multcomponent transport wth maor on equlbrum and knetc chemstry D smulaton of varably saturated water flow, heat transport, CO producton and transport,multcomponent transport wth maor on equlbrum and knetc chemstry D smulaton of lqud-phase advecton, sold-phase sorpton, vaporphase dffuson, and three-phase equlbraton n vadose zone. D smulaton of flow water, heat and multple solutes n varably saturated meda chemcal reacton and D reactve transport D/D heat or solute transport n varably saturated porous meda D smulaton of flow water, heat and multple solutes reactve transport n varably saturated meda D/D water flow and solute transport n varably saturated porous meda D/D/3D water flow and solute transport n varably saturated porous meda D/D multphase flow, heat and reactve transport n varably saturated porous meda D smulaton of water flow, heat and solute transport n varably saturated meda 0

21 Table.b Commercal reactve transport models Models 3DFEMFAT AIRFLOW-SVE BIOF&TD/3D CTRAN/W FEFLOW FRAC3DVS HYDROGEOCHEM HYDROGEOCHEM HYDRUSD/3D KYSPILL MIGRATE MODFLOW- SURFACT MOFAT POLLUTE TOUGHREACT General capabltes 3D flow and solute transport n varably saturated porous meda ncludng salt water ntrusons smulaton of vapor flow and mult-component vapor transport n unsaturated, heterogeneous and ansotropc sol D/3D smulaton of bodegradaton, flow and solute transport n varably saturated meda as well as fractured meda D/D water flow and solute transport n varably saturated porous meda D/3D smulaton of water flow, heat and solute transport n varably saturated meda D/D/3D smulaton of water flow and solute transport n varably saturated porous fractured meda D coupled smulaton of water flow, chemcal reactons and reactve solute transport n varably saturated porous meda zone D coupled smulaton of water flow, chemcal reactons and reactve solute transport n varably saturated porous meda zone D/3D smulaton of flow water, heat and multple solutes n varably saturated meda D/D/3D smulaton of water flow and solute transport n varably saturated porous meda D/D water flow and solute transport n varably saturated porous meda D/D/3D MODFLOW based smulaton of water flow and solute transport n varably saturated porous meda D/D multphase flow and transport of up to fve non-nert chemcal speces. D smulaton of water flow and solute transport n varably saturated porous meda zone D /D/3D smulaton chemcal reacton and multphase fluds,heat and reactve transport n varably saturated porous and fractured meda.3 Obectve The man obectve of ths PhD work was to develop two dmensonal reactve transport model for unsaturated zone by couplng publc doman flow, heat and solute transport models VSDT and VSDH wth PHREEQC. The specfc obectves are:

22 To modfy the solute transport model VSDT for mult-solute transport. To couple the heat and mult-solute transport. To couple the heat, mult-solute transport models wth chemcal reacton code PHREEQC. To run and test the VSDRT model wth varous publshed lterature data. To create a graphcal user nterface for VSDRT usng QT creator and Argus ONE numercal development software..4 Methodology and materals used The methodology used to acheve the above mentoned obectves are:. Lterature revew: - whch nvolves collectng and revewng varous artcles on the topc and relevant codes as well as source codes of VSDT, VSDH, PHREEQC and PHAST.. Get acquanted wth FORTRAN90, C/C++ programmng languages, Autotools, QT Creator and Argus ONE development envronment. 3. Complng, runnng and testng each program usng freely avalable complers lke MnGW whch has a capablty to comple FORTRAN and C/C++ programs. 4. Develop nterface functons between FORTRAN90 heat and mult-solute transport programs and C/C++ geochemcal program by adaptng such functons from PHAST. 5. Wrtng a confgure scrpt whch would help to create Makefle for VSDRT.

23 6. Develop pre-processor graphcal GUI for non-spatal nput data usng publc doman Qt Creator. 7. Develop pre-processor and post-processor GUI usng Argus ONE. Materals used: Varous publshed ournals, reports and books Argus ONE software MnGW compler QT Creator Source codes of VSDH, VSDT, PHREEQC and some functons from PHAST source code.5 Features and lmtatons The followng features are applcable for VSDRT model: Constant densty lqud phase flow n the porous meda The flow equaton s based on Rchards equaton The solute transport s based on advecton dsperson transport equaton The heat transport s based on advecton dsperson transport equaton Vscosty and saturated hydraulc conductvty are functons of temperature Mult-solute transport Varous chemcal equlbrum and knetc reactons 3

24 Root water uptake Heterogeneous porous meda Effect of temperature on thermodynamcs constants and rate parameters Same molecular dffuson coeffcent s used for all solute The man lmtatons of VSDRT model are: Inherted lmtatons from PHREEQC model for varous geochemcal computatons as explaned by (Parkhurst & Appelo, 999) Gaseous flow s neglected Change of porosty and hydraulc conductvty and densty due to chemcal reacton are not consdered 4

25 Chapter Two: Unsaturated water flow. Unsaturated water flow equaton The flow of water n the unsaturated zone s descrbed by Rchards equaton neglectng effects of vapor phase flow, thermal or soluton densty gradents s gven n equaton. for D flow (Suarez & Smunek, 996). t h K S z z (.) The terms h, θ, t, z, K and S n equaton. refer pressure head [L], water content [L 3 L -3 ], tme [T], spatal coordnate [L], hydraulc conductvty [LT - ] and source/snk term [T - ] respectvely. VSDRT uses modfed form of Rchards equaton for two dmensonal unsaturated flows gven n equaton. (Lappala, Healy, & Weeks, 987). v H t H x H z C ss A KK h A KK h qv 0 m s x r z r (.) The terms v, ρ, C m, s, S s, H, t, KK r, q, A x and A z refer to volume [L 3 ], lqud densty [ML -3 ], specfc mosture capacty [L - ], lqud saturaton [L 0 ], specfc storage [L - ], total pressure head, tme [T], effectve hydraulc conductvty [LT - ], volumetrc source/snk term, area [L ] n x and z faces respectvely.. Temperature dependence of saturated hydraulc conductvty n sol In case of heat transport or heat and solute transport smulaton saturated hydraulc conductvty s computed n VSDRT as functon of temperature. Equaton.3 shows that saturated hydraulc conductvty depends on vscosty and temperature. 5

26 gk K T (.3) where the terms K, ρ, g, k, T and µ refer to saturated hydraulc conductvty [LT - ], densty [ML -3 ], gravty [MT - ], ntrnsc permeablty [L ], temperature [ C] and vscosty [MLT - L - ] respectvely. Vscosty could be approxmated usng emprcal equaton.4 (Kpp, 987) T 8 T (.4) VSDRT adapts VSDTH s assumpton that temperature has much less effect on densty of water than that of vscosty over the range of pore-water pressures and temperatures typcally encountered under varably saturated feld condtons (Healy & Ronan, 996)..3 Unsaturated sol hydraulc propertes The flow of water n the vadose s hghly controlled by ts hydraulc propertes. These hydraulc propertes nclude porosty, resdual mosture content, volumetrc mosture content, specfc storage and hydraulc conductvty. In VSDRT mosture content, specfc mosture capacty and relatve hydraulc conductvty could be computed usng Brooks and Corey (Brooks & Corey, 964), Haverkamp, Van Genuchten (van Genuchten, 980) or Ross- Nmmo (Ross & Nmmo, 994) equatons. Brooks and Corey s (Brooks & Corey, 964) equatons of volumetrc mosture content, specfc mosture capacty and relatve hydraulc conductvty can be computed usng equatons.5,.6 and.7 respectvely. s e r r hb h, b h h ; (.5) 6

27 s e.0 h h, b ; c m h r hb h h b h h, b (.6) h 0 c m h h, b K ( h) r h h b 3 h h, b (.7) h 0 K r h h, b where the terms S e, θ, θ r,, h b,λ, K r (h) and C m (h) refer to effectve saturaton [-], volumetrc mosture content [-], resdual mosture content [-], porosty [-], bubblng pressure or arentry pressure potental [L], pore sze dstrbuton ndex whch s a functon of sol texture [- ], relatve hydraulc conductvty [LT - ] and specfc mosture capacty [L - ] respectvely. Haverkamp s equatons of volumetrc mosture content, specfc mosture capacty and relatve hydraulc conductvty can be computed usng equatons.8,.9 and.0 respectvely. s e h c m h h r h (.8), h 0 (.9) h c m 0, h 0 K r ( h) B' h A' (.0) 7

28 8 where the terms S e, θ r, α, β, A and B refer to effectve saturaton [-], resdual mosture content [-], porosty [-], pressure potental at whch S e =0.5 [L], slope of a log-log plot of (/S e - ) versus h [-], pressure potental at whch S e =0.5 [L], slope of a log-log plot of (/K r - ) versus h [-] respectvely. Van Genuchten s (van Genuchten, 980) equatons of volumetrc mosture content, specfc mosture capacty and relatve hydraulc conductvty can be computed usng equatons.,. and.3 respectvely. ' ' h s e (.) ' ' ' ' ' ' ) ( h h h c r m, 0 h (.) 0 h c m, 0 h ' ' ' ' ' ' ) ( h h h h K r (.3) where the terms S e, θ r,, α, β, γ, K r (h) and C m (h) refer to effectve saturaton [-], resdual mosture content [-], porosty [-], recprocal of α van Genuchten parameter [-], ((-γ) - ) [-], (-β - ) [-], relatve hydraulc conductvty [LT - ] and specfc mosture capacty[l - ] respectvely.

29 9 Ross Nmmo model (Ross & Nmmo, 994) can be used to estmate volumetrc mosture content and relatve hydraulc conductvty over the entre range of saturaton usng equatons.4 to.7. 0 c I s 0 <= ψ <=ψ 0 II s ψ <= ψ <=ψ (.4) d III s ln ψ <= ψ <=ψ d s s r I I K (.5) ) ( III I I 0 <= θ <= θ ) ( II I I θ <= θ <= θ (.6) ) ( I I I θ <= θ <= θ s exp s d I III 0 s s I II I III (.7) / / 0 / s s II I C I I θ= θ(ψ), θ= θ(ψ) where θ, θ s, ψ, ψ 0 and ψ d represents volumetrc water content [-], saturated water content [-], matrx sucton [L], ar entry value [L] and matrx sucton [L] at zero volumetrc mosture content respectvely and c, λ and α parameters.

30 .4 Intal and boundary condtons for water flow In order to smulate the flow water n a certan doman of unsaturated porous meda over a perod of tme t s necessary to know the spatal dstrbuton of pressure head n the porous meda at the begnnng of the smulaton and how t would be affected by external forces actng at the boundares of the doman of nterest and source or snk ponts n the doman of nterest. In VSDRT ntal condton for unsaturated water flow could be pressure head or volumetrc mosture n the doman of nterest at the begnnng of a smulaton. Intal condton for water flow could be mathematcally expressed n equaton.8: h(x,z,t)=h 0 (x,z) or θ(x,z,t)=θ 0 (x,z) at t=0 (.8) where h 0 and θ 0 s spatal ntal pressure head [L] and volumetrc mosture content [-] n the doman of nterest. Boundary condtons for unsaturated water flow refer to physcal stuatons lke mpermeable boundares, water table and seepage face and external forces lke nfltraton, evaporaton and evapotranspraton actng at the boundares of the doman of nterest durng the smulaton perod. In VSDRT the flow boundary condtons can be set as specfed flux across the boundary, specfed total pressure potental along the boundary or a combnaton of the two boundary condtons. Specfed flux boundary (Neumann boundary type) can be mathematcally expressed n equaton.9 as: m k H KK r ( h) f( x, z, t, H, h) n k (.9) 30

31 where the term f refers to a general functon whch depends on spatal, temporal varables as well as on gradent of total hydraulc potental across the boundary face and pressure head at the boundary face. Specfed head boundary (Drchlet boundary type) can be mathematcally expressed n equaton.0 as: x, z, t f x, z, t, H h h, (.0) where the term f refers to a general temporal varable functon. Combnaton of flux and head boundary (Cauchy boundary type) can be mathematcally expressed n equaton. as: m k H KK r ( h) f( x, z, t, H, h) n x, z, t f x, z, t, H h k h, f flux >IC where the term IC refers to the nfltraton capacty of the sol. f flux < IC (.).5 Evaporaton Evaporaton normally occurs at surface of the sol where lqud water leaves the unsaturated zone n the form of vapor gas. Evaporaton from sol surface depends manly on sol mosture content, solar radaton, wnd and vapor-pressure gradent. Moreover, evaporaton s determned by potental evaporatve demand of the atmosphere and the ablty of the sol transmts water upward to the land surface. Normally evaporaton rate decreases wth tme n sols where mosture content s due to ranfall and rrgaton. In presence of shallow groundwater evaporaton may occur more or less at constant rate dependng on clmatc 3

32 condton. In cases of wet surface sol evaporaton occurs at atmospherc evaporaton demand rate. In case of dry surface sol evaporaton depends manly on the ablty of the dry sol to transmt water to surface and t normally decreases and eventually cease. Two boundary condtons that may occur at the land surface due to evaporaton are:. Specfed lqud flux whch equals to atmospherc evaporaton demand, untl the sol cannot any longer satsfy the atmospherc evaporatve demand.. Specfed flux caused by pressure potental gradent between the sol and the atmosphere..6 Evapotranspraton Evapotranspraton occurs at the earth surface through evaporaton from sol surface and transpraton from vegetaton. Evapotranspraton depends on ar temperature, relatve humdty, sol mosture content, wnd, solar radaton, and type of vegetaton cover and the ablty of the sol to transmt water to roots. In VSDRT plant root extracton s expressed as the rato of pressure-potental dfference between the plant root and sols to combned resstance to flow mposed by the sol and roots. Evapotranspraton represents the snk term n the unsaturated flow equaton and n the model mathematcally t s expressed n equaton. (Lappala, Healy and Weeks, 987) as: vq m v R hroot hm, m R root m f hm h root (.) vq 0 m h, f m hroot ; where the terms h m, h root, R m and R rootm refer to pressure potental n the sol n volume m [ L], pressure potental n the plant roots [ L], resstance to flow n the sol towards the roots n volume m [LT], and resstance to flow n the roots occurrng n volume m [LT] respec- 3

33 tvely. In VSDRT the resstance term s computed usng equaton.3 (Lappala, Healy and Weeks, 987) as: Rm Rroot m KK z, t r hr (.3) Evapotranspraton due to plant root extracton s computed n VSDRT usng emprcal expresson (Lappala, Healy and Weeks, 987) usng equaton.4: q m hr z th h KK, r root (.4) Where the terms r(z,t) and h root refer to the root actvty functon as a functon of depth and tme and the pressure head n the root for the entre system. The total plant root extracton for a gven column of cells s gven by usng equaton.5 (Lappala, Healy, & Weeks, 987): Q m cq m m (.5) To smulate evapotranspraton usng VSDRT perodcally varable potental evapotranspraton, mnmum pressure n the roots, and depth of rootng, root actvty at the bottom of the root and root actvty at the land surface are requred. The detal mplementaton of evapotranspraton computaton can be referred from VSD documentaton (Lappala, Healy, & Weeks, 987). 33

34 Chapter Three: Heat transport n unsaturated zone Heat transport n unsaturated zone nvolves the transfer of heat n sol through thermal conducton, thermo-mechancal dsperson and advecton processes. The sol gets heated by solar radaton and transfer the heat to the subsurface by thermal conducton. Thermal conducton nvolves the transfer of heat when materals wth dfferent temperatures come n physcal contact, where heat flows from materal wth hgh temperature to materal wth low temperature. Thermo-mechancal dsperson nvolves the transfer of heat as a result of mxng due to flow of water n porous meda. Advecton nvolves the transfer of heat due to the movement of water of dfferent temperature. Natural source of heat n subsurface are solar radaton on surface of the earth, geothermal actvty form the earth s nteror, from volcanc and tectonc actvtes. Temperature varaton n the shallow vadose zone vares both wth depth and tme, whle temperature varaton n deep vadose vares only wth depth (Constantz, Tyler, & Kwcckls, 003). Temperature affects the evaporaton, nfltraton, pondng and seepage n the sol water system. Varous factors n the sol water system, such as flud vscosty, sol water content, and sol physcal and chemcal propertes, nteract wth temperature changes n the system, therefore, nfluence the temperature effects on sol water flow processes (Zhang, Zhang, & Kang, 003). 3. Heat transport equaton The governng equaton of advecton dsperson heat transport n unsaturated zone s gven n equaton 3. (Healy & Ronan, 996): t * C C T K T C D T C vt qc T w s T w H w w (3.) 34

35 Where the terms θ, C w, C s T, K T, D H, v, q, T * and t refer to volumetrc mosture content, heat capacty of water [Jm -3 o C], porosty [-], heat capacty of the sold matrx [Jm -3 o C], temperature [ o C], thermal conductvty of water [Wm - o C], hydrodynamc dsperson tensor [L T - ], water velocty [LT - ], rate of flud source [L - ], temperature of flud source [ o C ] and tme [T] respectvely. Change n energy stored n the doman of nterest over a smulaton perod s gven by the left hand sde term of equaton 3.. The frst, second, thrd and last term on the rght hand sde of equaton 3. represent thermal conducton, thermo-mechancal dsperson, advectve transport and heat sources-snk term respectvely. Advecton or convecton of heat nvolves the transport of heat by movement of flud from one place to the other at the velocty of water flow n the porous meda. The velocty of advectve transport s gven n equaton 3. as: v K r hk h (3.) where stands for drecton of flow n ths case X or Z. Peclet number s usually used to control numercal errors related to grd sze or spatal dscretzaton. Peclet number can be mathematcally expressed n equaton 3.3 as; P e v L D (3.3) where the terms v, L and D refer to the magntude of velocty vector, grd cell wdth and dsperson coeffcent respectvely. Thermal conducton occurs due to temperature gradent whle thermo-mechancal dsperson occurs due to mxng caused by local varatons n ve- 35

36 locty around some mean velocty of flow. The hydrodynamc dsperson tensor s gven n equaton 3.4 (Healy, 990): D H v T v v v L T (3.4) where α T s transverse dspersvty of the porous medum [L], α L s longtudnal dspersvty of porous medum [L], v s the magntude of hydraulc flux densty vector [LT - ], δ s Kronecker delta operator (equal to one f = otherwse t s zero) and v s th component of hydraulc flux densty vector. v / v x v z (3.5) D H XX vx L T v vz v (3.6) D H zz vz L T v vx v The source/snk term accounts for nect or removal of heat n to the doman of nterest n form of flud source or snk. The potental source can be flud nected n to the well, stream flow loss and rrgaton. The potental ways to remove heat from the porous medum are wthdrawal from the well, sprngs, evaporaton and evaporaton. 3. Intal and boundary condtons for heat transport The ntal condton for heat transport accounts for temperature dstrbuton n the unsaturated zone doman of nterest at the begnnng of smulaton and can be mathematcally wrtten as equaton 3.7. T(x,z,t)= T 0 (x,z) at t=0 (3.7) 36

37 Boundary condtons for heat transport can be set as heat flux or fxed temperature. At the nflow heat flux boundares the temperature must be specfed. At the outflow heat flux boundary cells temperature wll be set nternally by the program to the temperature of the fnte dfference cells where the water flow out. Upper boundary condton often consdered to be the average annual ar temperature and lower boundary condton can be the temperature at the water table (Constantz, Tyler, & Kwcckls, 003). 37

38 Chapter Four: Solute transport n unsaturated zone Solute transport s a process by whch solutes are manly transported n the subsurface through the movement of water. The chemcal consttutes of ground water play sgnfcant role on ts qualty and feasblty for varous purposes. The man sources of water to recharge ground water come from ranfall and snow melt. Ranfall and snowmelt have very lttle dssolved mneral matter (Schwartz & Zhang, 003). Therefore, the water that recharges the ground water pcks up most of ts dssolved mnerals on ts pathway through the sol and vadose zone. It s clear that the use of fertlzers, pestcdes and unsafe dsposal of chemcal wastes lke hazardous and radoactve wastes n unsaturated zone sgnfcantly affect the chemstry of ground water and ultmately the degree of polluton and contamnaton of ground water. Hence, t s very mportant to smulate the solute transport pattern n unsaturated zone n order to be able to see the dstrbuton and quantty of solutes n the unsaturated zone before reachng the ground water. Ths would help to map potental ground water contamnants comng from unsaturated zone whch helps to evaluate varous remedal measures desgned to protect ground water resource. 4. Solute transport equaton n unsaturated zone The advecton dsperson equaton for solute transport wthout any chemcal reacton n varably saturated condton s gven n equaton 4. (Bear, 979): C t D C vc SS h (4.) where the terms C, t,d h, and SS refer to volumetrc mosture content, concentraton of chemcal consttute [ML -3 ], tme [T], hydrodynamc dsperson tensor [L T - ], flud velocty vector [LT - ] and source/snk terms [ML -3 T - ] respectvely. 38

39 Change n solute concentraton n the doman of nterest over the perod of smulaton s gven by left hand sde term of equaton 4.. The frst, second and last term on the rght sde of equaton 4. accounts for hydrodynamc dsperson, advecton and source/snk respectvely. Hydrodynamc dsperson accounts for mechancal dsperson and molecular dffuson. Mechancal dsperson s more promnent at greater flow veloctes whle molecular dffuson s promnent at lower flow velocty. The causes of hydrodynamc dsperson are: range n pore sze whch results n the solutes to arrve at varous tmes at the end of a sol column, transverse dffuson nto stagnate pores, whle drect flow through other pores cause solutes to arrve at varous tmes and molecular dffuson ahead of the wettng front as t vares wth tme (Tndall & Kunkel, 999). Mechancal dsperson accounts for spreadng of solute through flow channel n the porous meda. Normally, dsperson takes place n longtudnal (along the flow lne) drecton and transverse drecton (n drecton perpendcular to the flow drecton) and the longtudnal dsperson s always larger than transverse dsperson. Molecular dffuson can be expressed by Fck s Law and depends on molecular dffuson coeffcent. Hydrodynamc dsperson tensor s gven n equaton 4. (Healy, 990) as: D D h D m (4.) D T v v v v L T (4.3) D m D d (4.4) 39

40 where the termd, D m, T, L, v,, v, D d and refer to mechancal dsperson [L /T], molecular dffuson [L /T], transverse dspersvty of porous medum [L], longtudnal dspersvty porous medum [L], magntude of the velocty vector [LT - ], Kronecker delta functon, whch s equal to when = and zero otherwse, th component of the velocty vector [LT - ], coeffcent of molecular dffuson of solute n water [L T - ] and tortuosty respectvely. In ths VSDRT T, L and tortuosty are constants and tortuosty s unformly algned wth the x and z axes so that xx = zz = and xz = zx = (Healy, 990). The components of hydrodynamc dsperson n D are gven n equaton 4.5 (Healy, 990): DH XX L v x v T z v v D m (4.5) D H zz L z v v T v x v D m D H XZ D H ZX v v v L T X Z The source/snk term accounts for nect or removal of solute n to the doman of nterest n form of flud source or snk. The potental source can be flud nected n to the well, polluted stream flow loss and rrgaton. 4. Intal and boundary condtons for solute transport Intal soluton condton accounts for spatal dstrbuton of solute at the begnnng of the smulaton. And mathematcally t may be represented usng equaton 4.6 as: C(x,z,t)= C 0 (x,z) at t=0 (4.6) 40

41 The boundary condtons for solute transport can be fxed concentraton or fxed mass flux of solute. The concentraton solute n the water enterng the system must be specfed and for water leavng the system concentraton of solute n the extng water s set to be equal to the concentraton of solute n cell where water s extng wth excepton of the case of evaporaton. In case of evaporaton the water assumed to be solute free (Healy, 990). 4

42 Chapter Fve: Chemcal reactons n unsaturated zone Varous chemcal reactons occur n the unsaturated zone between aqueous chemcal consttutes n porous and sold matrx as well as among aqueous chemcal consttutes. The chemcal reactons my result n the transfer of chemcal consttutes n to or from the lqud phase through desorpton, dssoluton and sorpton, precptaton and decay processes respectvely. The chemcal reactons are smulated n VSDRT based on on-assocaton aqueous model or on nteracton model wthn PHREEQC. It has capabltes to smulate both equlbrum and knetc reactons. Geochemcal databases are used to store chemcal reactons and ther correspondng equlbrum constants, as well as other parameters such as Debye-Hückel parameters, charge, molar volume, and gram-formula weght (Lchtner, 996). In PHREEQC the chemcal speces contaned n the system are dvded nto prmary and secondary speces. Prmary speces are total number of speces mnus the number of reactons. Secondary speces equals to the number of reactons. In PHREEQC chemcal reactons are wrtten n terms of prmary speces. For any lnearly ndependent set of chemcal reactons, chemcal reactons could be wrtten n canoncal form as gven n equaton 5. (Lchtner, 996): N c v~ A A (= N c +,,N) and N c = N - N r (5.) where N, N c and N r represents total number of speces nvolved n the reactons, number of prmary speces and secondary speces respectvely,v stochometrc coeffcents for th and th prmary and secondary speces, A, A represents th and th prmary and secondary speces respectvely. The stochometrc coeffcent measures the degree to whch a chemcal speces take part n a reacton. 4

43 5. Equlbrum reacton Equlbrum reactons are governed by mass acton law whch relates actvtes of the reactant and products speces to equlbrum constant. Equlbrum constant K s gven n equaton 5. as: a K a cp p cr r (5.) where a p and a r represent actvtes of th product and th reactant speces respectvely, cp and cr stand for stochometrc coeffcents of th product and th reactant speces n the chemcal reacton. Equlbrum constants are temperature dependent and the actvty of an aqueous speces s a product of ts actvty coeffcent and molalty. Actvty coeffcents of the aqueous speces are functons of speces charge and onc strength, and can be determned usng WATEQ Debye-Hückel, Daves or extended Debye-Hückel equatons 5.3, 5.4 and 5.5 respectvely. AZ log Ba 0 log AZ 0. 3 AZ log Ba 0 b for I < 0.mol/kg (5.3) for I < 0.5 mol/kg (5.4) for I < mol/kg (5.5) where Z refers to onc charge of aqueous speces, A and B are temperature dependent parameters, a o and b are on-specfc parameters whch are determned based on on radus. Ionc strength (I) s gven n equaton 5.6 as: 43

44 C Z (5.6) where C and Z are molar concentraton and charge number of the th speces. In PHREEQC the default actvty coeffcent equaton used s Daves equaton and WATEQ Debye-Hückel equatons are used for charged and uncharged speces respectvely and are set n the database or n the nput fle through SOLUTION_SPECIES data block. 5.. Heterogeneous on-exchange One of the most common reversble chemcal reactons whch occur n the unsaturated zone s on-exchange. Ion-exchange s a sorpton process whch nvolves exchange of ons between the aqueous soluton and the sold matrx. The on-exchange process n vadose zone depends on caton exchange capacty (CEC) of the sol. CEC refers to the amount of exchangeable equvalents of catonc charge per mass of dry sol. The CEC of a sol s hghly dependent on ts clay and organc matter content manly due to presence of hgh amount of charges on ther surface. In PHREEQC on-exchange s smulated based on heterogeneous mass-acton equaton and mole-balance equatons for the exchange stes. The general mass acton equaton for on-exchange can be wrtten as equaton 5.7 (Parkhurst & Appelo, 999): M m, K a a e e m C m e (5.7) where the terms a e, K e and C m,e refer to the actvty of an exchange speces, the halfreacton selectvty constant and the stochometrc coeffcent of master speces, m, n the assocaton half-reacton for exchange speces, e, respectvely. 44

45 EXCHANGE_SPECIES data block of PHREEQC s used to defne on-exchange chemcal equatons for mole-balance and mass-acton expressons, actvty coeffcent expresson for each exchange speces and other thermodynamc parameters. 5.. Heterogeneous surface complexaton process Surface complexaton s a sorpton process where ons n aqueous soluton attracted to charged sold matrx surface due to electrostatc forces. Surface complexaton can be modeled for example wth double layer model. In double layer model charges on the sold surface are neutralzed by equal and opposte charges n the aqueous soluton. In PHREEQC surface complexaton s smulated based on heterogeneous mass-acton equaton and molebalance equatons for the surface stes and charge-potental relatons for each surface. The mass acton equaton for surface complexaton reactons may nclude electrostatc potental or not. The general mass-acton equaton for surface speces can be wrtten as equaton 5.8 (Parkhurst & Appelo, 999): K nt sk a sk M m a Cm, m sk e F S z RT I sk (5.8) where the terms Z sk, K nt sk, (sk), C m,e, F, s, R and T refer to the net change n surface charge due to the formaton surface speces, the ntrnsc equlbrum constant, the th surface speces for surface-ste type k n surface s, the stochometrc coeffcent of master speces, m, n the assocaton half-reacton for surface speces, (sk), the Faraday constant, the potental surfaces (volt), the gas constant and the temperature (Kelvn) respectvely. 45

46 5..3 Heterogeneous mneral dssoluton/precptaton Heterogeneous mneral dssoluton/precptaton process nvolves transfer of chemcal speces n to and out of the aqueous soluton respectvely and could be model n VSDRT usng PHRREQC s EQULIBIRUM-PHASES data block. In general pure phase equlbra can be represented wth equaton 5.9 (Parkhurst & Appelo, 999): M aq C p a m m m, p K (5.9) where the term C m,p refers stochometrc coeffcent of master speces m n dssoluton reacton. Saturaton ndex for the mneral, SI p, s gven n equaton 5.0: M aq C p a m m m, SI log p (5.0) 5. Knetc reacton Slow homogeneous and heterogeneous chemcal reactons n unsaturated zone are controlled by the rate of knetc reactons. Frst order radoactve decay and bodegradaton can be an example for the knetc reactons n sol. PHREEQC models knetc reactons usng user defned rate equatons wrtten n Basc language statements. A general rate expresson for a knetc reacton of mnerals and other solds s gven n equaton 5. (Parkhurst & Appelo, 999): R k r k A0 mk V m 0k n (5.) 46

47 where the terms r k, A 0, V, m 0k and m k refer to the specfc rate [T - ], the ntal surface area of the sold [L ], the amount of soluton, the ntal moles of sold and the moles of sold at a gven tme respectvely. 47

48 Chapter Sx: Numercal solutons for water flow, heat transport and mult-solute transport Fnte dfference method s used to solve unsaturated water transport equaton ncludng advecton, dsperson, dffuson, equatons of heat and mult-solute transport subected to ntal and boundary condtons. Fnte dfference numercal approxmaton of unsaturated water flow results n a set of smultaneous nonlnear algebrac equatons. To obtan the soluton for unsaturated water flow and transport the smultaneous nonlnear algebrac equatons was lnearzed usng a modfed Newton-Raphson Method. Strongly mplct procedure (SIP) s used to solve the lnearzed smultaneous algebrac equatons, as well as smultaneous algebrac equatons for heat and mult-solute transports. 6. Numercal mplementaton for unsaturated water flow 6.. Spatal dscretzaton of unsaturated water flow Block centered fnte dfference approach s used to approxmate spatal dervatves of unsaturated flow. Schematc representaton rectangular and cylndrcal grd-block systems are presented n the fgure 6. and 6. respectvely. The form of unsaturated flow equaton for each grd block s gven n equaton 6. (Lappala, Healy, & Weeks, 987): v C Cˆ Cˆ m n/, n, / ss m H t H ˆ ˆ n, H n, Cn, / H n, H n, Cn /, H n, H n, H H qv 0 n, n, (6.) where the term represent the conductance and s defned as: 48

49 ^ C /, KK r A X /, (6.) ^ C ^ C, / /, KK r A Z KK r A X, / /, (6.3) (6.4) ^ C, / KK r A Z, / (6.5) where A represents block face area. Fgure 6. Schematc representaton of rectangular grd block system (Lappala, Healy, & Weeks, 987) 49

50 Fgure 6. Schematc representatons of cylndrcal grd-block system (Lappala, Healy, & Weeks, 987) Averagng the conductance terms for adacent blocks s essental whle usng block centered scheme. In VSDRT the conductance terms of the medum s represented by saturated hydraulc conductvty and relatve hydraulc conductvty. Inter-cell saturated hydraulc conductvty of adacent blocks are determned usng dstance-weghted harmonc mean of saturated hydraulc conductvty of adacent cells. Geometrc mean or weghted arthmetc mean can be used to determne the averages relatve hydraulc conductvty of adacent blocks or cells. 50

51 6.. Temporal dscretzaton of unsaturated water flow The numercal approxmaton for the tme dervatve term ( H/ t) of Rchard s equaton s gven n equaton 6.6 as: H t / H H t t (6.6) where the terms and - represent the current tme and prevous tme steps respectvely. Temporal dscretzaton can be n the form of fully mplct or backward dfference scheme form. Numercal representaton of Rchard s equaton for D flow n terms of spatal and temporal dscretzaton s gven n equaton 6. 7 (Lappala, Healy, & Weeks, 987): C v c C m / n/, / n/, ss s / H n, H n, Cn, / H n, H n, / / H H C H H qv n, / H t n, n, H t n, n, / n, n, n, (6.7) Numercally approxmaton of D Rchards s equaton could be wrtten n matrx form (Lappala, Healy and Weeks, 987) n equaton 6.8: A / H RHS (6.8) Where A s a square m by m matrx whch holds unknown parts of conductance terms, storage and source-snk terms and RHS s a vector whch holds known parts of conductance, storage and source-snk terms Numercal soluton Modfed Newton-Raphson method s used to lnearze Rchard s matrx equaton. Strongly mplct procedure s appled to solve lnearzed D Rchard s matrx equaton. 5

52 The lnearzed Rchard s matrx equaton (Lappala, Healy, & Weeks, 987) s gven n equaton 6.9 as: k k k k k A H * RHS A H s (6.9) s user defned dampng factor, HMAX In VSDRT the same teraton loop s used for both lnearzaton and matrx soluton of Rchard s equaton. Steps to solve the lnearzed Rchard s equaton are ( Lappala, Healy, & Weeks, 987):. Evaluaton nonlnear coeffcents usng the latest value of H. Determnaton of the elements of the[ ]matrx and {RHS} vector 3. Solvng lnearzed Rchard s matrx equaton for the resduals {H*} usng the SIP 4. Compute new potentals (H k ) usng the equaton H k = H k- + w k H* where w k s a dampng factor and 0 < w k <= 5. Test for convergence by checkng whether H* s less than a user specfed tolerance lmt. 6. Proceeds to the next tme step f convergence s reached, otherwse step to 5 wll be repeated untl convergence s reached durng the user specfed maxmum teraton lmt. For case where convergence could not be reached the length of tme step could be adusted to a maxmum of three tmes and repeats the steps to 5. If stll convergence s not reached the program ether proceeds to the next tme step or termnates. 5

53 6. Numercal mplementaton for heat transport 6.. Spatal dscretzaton of heat transport Spatal dscretzaton of D advecton dsperson heat transport can be wrtten n equaton 6.0 modfed from (Healy, 990): Aˆ T BT ˆ CT ˆ Dˆ T Eˆ n, n, n, n, n, T RHS (6.0) The values of coeffcents and are computed usng equatons 6.0a, 6.0b, 6.0c, 6.0d, 6.0e, 6.0f, 6.0g, 6.0h, 6.0 and 6.. RHS would be computed usng equatons 6.0rhs and 6.. Aˆ Bˆ TC TC A A K C C T xx n/, w n/, H xx n/, n /, K / D Gˆ Hˆ w n/, x n/, xn xn C C T zz n, / w n, / H zz n, / n, / / D w n, / z n, / z z v v Fˆ Iˆ (6.0a) (6.0b) Cˆ TC A K C C T xx n/, w n/, H xx n/, n /, / D Gˆ Hˆ w n/, x n/, xn xn v (6.0c) Dˆ TC A K C C T zz n, / w n, / H zz n, / n, / / D Fˆ Iˆ w n, / z n, / z z v (6.0d) ˆ ˆ ˆ ˆ ˆ V E A B C D t TC C Av Av Av Av x n/, w z n, / C s x n/, z n, / (6.0e) 53

54 V RHS T t n, C C w s TCAˆ T ˆ ˆ ˆ ˆ n, B Tn, C Tn, D Tn, E Tn, Fˆ Gˆ T, ˆ ˆ, ˆ ˆ, ˆ ˆ n H F Tn I G Tn H I T n, (6.0rhs) where A KT z XZ n, ˆ / F G A KT x / n, / ˆ ZX A KT x n C w DH XZ n/, z z / ZX n, / ˆ H n / C w D H ZX x n xn C w D H ZX n, / n, / x n xn (6.0f) (6.0g) (6.0h) A KT z XZ n, ˆ / I (6.0) TC /, for fullymplct /, for tme centered C w DH XZ n/, z z In presence of source/snk term RHS and terms would be modfed to consder source/snk effect n the smulaton. The modfcaton could be done usng equatons 6. and 6.: RHS RHS qcw T * V If qv 0 (6.) Eˆ E ˆ qcw T * V If qv 0 (6.) 6.. Temporal dscretzaton of heat transport The tme dervatve of D advecton dsperson heat transport equaton can be approxmated usng equaton 6.3 as follows: 54

55 55 / / s w w s w w s w t t T T C C t t C T t T C C t TC t T C C (6.3) Where represents current tme step, - represent prevous tme step, T, T -, θ and θ - represents current tme step temperature, prevous tme step temperature, current tme step volumetrc mosture content and prevous tme step volumetrc mosture content at a gven node respectvely. Spatal and temporal dscretzaton equatons D heat transport equaton could be gven n equaton 6.4 as: RHS T E T D T C T B T A n n n n n,,,,, ˆ ˆ ˆ ˆ ˆ (6.4) 6..3 Numercal soluton At each node n the fnte dfference grd the advecton dsperson heat transport equaton have to be solved. Fnte dfference approxmaton at each nodal pont n the fnte dfference grd gves a set of smultaneous equatons whch could be solved as matrx n equaton 6.5. RHS T A (6.5) where A s a pentagonal square coeffcent matrx T s the vector of unknown temperatures at the tme level and RHS s the vector defned above. The matrx equaton for D advecton dsperson heat transport equaton s solved usng an teratve matrx solver applyng strongly mplct procedure accordng to equaton 6.6:,, k k k AT RHS T A (6.6)

56 where, k, k, k T T T and k represents the teraton ndex Steps nvolved to solve the advecton dsperson heat transport equaton are:. Determnaton of the elements of matrx [ ] and {RHS} vector. Solvng advecton dsperson heat transport equaton for the resduals, usng the SIP. 3. Compute new temperature (T k ) usng the equaton T k = T k- +w k, where w k s a dampng factor and 0 < w k <= 4. Test for convergence by checkng whether s less than a user specfed tolerance lmt. 5. Proceed to the next tme step f convergence s reached, otherwse step to 4 wll be repeated untl convergence s reached durng the user specfed maxmum teraton lmt. For cases where convergence could not be reached the length of tme step could be adusted to a maxmum of three tmes and repeats the steps to 4. If stll convergence could not be reached the program ether proceeds to next tme step or termnates. In VSDRT there s an opton ether to use fully mplct or tme centered dfferencng. The demert of tme-centered dfferencng methods s that t can cause oscllaton. Although, fully mplct dfferencng method would avod the oscllaton problems of tmedfferencng, t s prone to numercal dsperson. 56

57 Numercal mplementaton for mult-solute transport 6.3. Spatal dscretzaton of mult-solute transport Spatal dscretzaton of D advecton dsperson mult-solute transport can be gven n equaton 6.7 modfed from (Healy, 990): RHS E C DC CC BC AC l n l n l n l n l n, ^,,,, ˆ ˆ ˆ ˆ (6.7) The values of coeffcents and are computed usng equatons 6.7a, 6.7b, 6.7c, 6.7d, 6.7e, 6.7f, 6.7g, 6.7h, 6.7 and 6.9. RHS would be computed usng equatons 6.7rhs and 6.8. x n n n h xx n n H G v x x D A TC A ˆ ˆ / ˆ, /, /, / (6.7a) z n h zzn n I F v z z D A TC B ˆ ˆ / ˆ /, /, /, (6.7b) x n n n h xx n n H G v x x D A TC C ˆ ˆ / ˆ, /, /, / (6.7c) z n h zzn n I F v z z D A TC D ˆ ˆ / ˆ /, /, /, (6.7d)

58 58 n z n x n z n x n n v A v A v A v A TC t V D C B A E /,, / /,, /,, ˆ ˆ ˆ ˆ ˆ (6.7e) n n n n n n n n n n C I H C G I C F H C G F C E C D C C C B C A TC C t V RHS,,,,,,,,,, ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ (6.7rhs) where, / / ˆ n h z z z D A F XZ (6.7f) /, / ˆ n n n n h x x x D A G ZX (6.7g) /, / ˆ n n n n h x x x D A H ZX (6.7h), / / ˆ n h z z z D A I XZ (6.7) mplct fully for tme centered for TC,, / In the presence of source/snk term RHS and need to be modfed to consder source/snk effect n the smulaton. The modfcaton could be done usng equatons 6.8 and 6.9: V T qc RHS RHS w * f 0 qv (6.8) V T qc E E w * ˆ ˆ f 0 qv (6.9)

59 6.3. Temporal dscretzaton of mult-solute transport The tme dervatve term n equaton 4. could be approxmated usng equaton 6.0 as follows: C t C C t t C / t t C C / t t (6.0) where represents current tme step, - represent prevous tme step, C, C -, θ and θ - represents current tme step l th speces concentraton, prevous tme step l th concentraton, current tme step volumetrc mosture content and prevous tme step volumetrc mosture content at a gven node respectvely. Spatal and temporal dscretzaton of mult-solute transport equaton s gven n equaton 6. as: Aˆ C Bˆ C Cˆ C Dˆ C Eˆ C n, n, n, n, n, RHS (6.) Numercal soluton At each node of the fnte dfference grd solute transport equaton s solved for each solute. Fnte dfference approxmaton at each nodal pont n the fnte dfference grd gves a set of smultaneous equatons whch could be solved as matrx equaton n equaton 6.. AC RHS (6.) where A represents pentagonal square coeffcent matrx, l th C s the vector of unknown concentraton at the tme level and RHS s the vector above. 59

60 Equaton 6. wll be solved by strongly mplct procedure teratve matrx solver n equaton 6.3:, k k, k A C RHS AC (6.3) where, k, k, k C C C and k represents teraton ndex. Determnaton of the elements of matrx [ ]and {RHS} vector. Solvng advecton dsperson solute transport equaton for the resduals, usng the SIP. 3. Compute new concentraton (C k ) usng the equaton C k = C k- + w k, where w k s a dampng factor and 0<w k <= 4. Test for convergence by checkng whether s less than a user specfed tolerance lmt. The code proceeds to the next tme step f convergence s reached, otherwse step to 4 wll be repeated untl convergence s reached durng the user specfed maxmum teraton lmt. For case where convergence could not be reached the length of tme step could be adusted to a maxmum of three tmes and repeats the steps to 4. If stll convergence could not be reached the program ether proceeds to next tme step or exts. 6.4 Numercal solutons for chemcal equlbrum and knetc reacton equatons In PHREEQC a set of functons, f, are derved by substtutng the equatons for the moles of speces nto mole- and charge-balance equatons to defne heterogeneous equlbrum. These functons nclude f HO,, f µ, f Ptotal, f p, f Pss, f Sk, f e, f Alk, f m, f z, f ψs and f z,s are gven n equatons 60

61 from 6.4 to 6.47 along wth ther total dervatves (Parkhurst & Appelo, 999). Ther correspondng master unknowns are lna Alk, lna e, n g, lna e-, lna HO, lna m, lnw aq, N gas, n p, n ss, lna sk, lna H+, μ,and lna ψs (Parkhurst & Appelo, 999). The functon used for actvty of water, f HO, n the numercal methods s gven n equaton 6.4. The total dervatve of f HO s gven n equaton 6.5: N aq a H O 0. f W 07 H O aq n N aq a H O a H O W aqd lnw aq 0. df H O WaqaH Od ln 07 dn (6.4) (6.5) where a HO s the actvty of water, W aq s the mass of solvent water n aqueous soluton and n s the moles of aqueous speces n the soluton respectvely. The functon used for onc strength, f μ, n the numercal methods s gven n equaton 6.6. The total dervatve of f μ s also gven n equaton 6.7: f df W aq W aq d ln Naq z n N aq W aqwaqd z dn (6.6) (6.7) where μ refers to the onc strength. The functon used for fxed-pressure multcomponent gases, f Ptotal, n the numercal methods s gven n equaton 6.8. The total dervatve of f Ptotal s gven n equaton 6.9: f P total P total N g g P g (6.8) 6

62 df P total N g M aq g m C m, g P d ln a g m (6.9) where P total, N g, C m,g and P g refer to total pressure, total number of gas components n the gas phase, the stochometrc coeffcent of aqueous master speces m and partal pressure of gas component g n the gas phase respectvely. The functon used for phase equlbrum, f p, n the numercal methods s gven n equaton The total dervatve of f p s gven n equaton 6.3. f df P P M aq K ln0si C lna ln p P; t arg et m, p m M aq m C m, p d ln a m m (6.30) (6.3) where K p, SI p,target and C m,p refer to pure phase equlbra, target saturaton ndex for the phase and the stochometrc coeffcent of master speces m respectvely. The functon used for each component of an deal soluton, f Pss, n the numercal methods s gven n equaton 6.3. The total dervatve of f Pss s gven n equaton f P ss ln M aq m a K Cm, Pss m Pss n ln N pss total (6.3) df P ss M aq m C m, P ss d ln a m n P ss N total N n total P ss dn P ss N, P ss ss ss ss N total dn ss (6.33) N ss N total n ss ss (6.34) 6

63 where C m,pss, K Pss, n Pss and N ss refer to the stochometrc coeffcent of master speces m n the dssoluton reacton for component p n the sold soluton ss, sold-soluton equlbra, mole of each component n each sold soluton n Pss and the number of components n sold soluton ss respectvely. The functon used for surface ste type S k, f Sk, n the numercal methods s gven n equaton The total dervatve of f Sk s gven n equaton f S k S k N S k T b, S k S k S k n S K (6.35) df S k Sk N S K T b, Sk Sk Sk dn SK (6.36) where T, N S k s k and bs, k s k refer to the moles of the surface ste type, the number of surface speces for the ste type and the number of surface stes occuped by the surface speces ( s k ) respectvely. The functon used for exchange ste, f e, n the numercal methods s gven n equaton The total dervatve of f e s gven n equaton f e Ne Te be, e e n e (6.37) df e Ne Te be, e e dn e (6.38) The functon used for alkalnty, f Alk, n the numercal methods s gven n equaton The total dervatve of f Alk s gven n equaton

64 f Alk Naq TAlk balk, n (6.39) df Alk Naq balk, dn (6.40) where T Alk and b Alk, refer to the number of equvalents of alkalnty n the soluton and the alkalnty contrbuton of aqueous speces respectvely. The functon used for mole balance of elements, f m, n the numercal methods s gven n equaton 6.4. The total dervatve of f m s gven n equaton 6.4. f S T s sk s m K k N m s k b N p p m, s k b n m, p ss g aq bm gng S, k n p N g SS ss N Pss b m, p ss S n s p ss N b m, N aq n b, s m, n E e e N e b m, e n e (6.4) df m S p s sk s K k N N p s k b b m, p dn m, sk p dn ss aq g aq bm gdng S, k ss ss N Pss N g b m, PSS dn PSS N S s N b m, b dn m, dn e, s E e N e b m, e dn e (6.4) where the terms ( ) and refer to total moles of the element n the system, the number of phases n the pure phase assemblage, the number of sold solutons n the sold-soluton assemblage, the number of sold solutons, the number of aqueous speces, the number of surface speces for surface type s k, the number of exchangers n the exchange assemblage, the number of exchange speces for exchange ste e, the number of surfaces n the surface assemblage, the number of surface types for surface s, the number of gas phase components, moles for pure phase n the pure-phase assemblage, moles of aqueous speces,moles for exchange speces of exchange ste e, moles for components n sold soluton, moles for surface speces for surface type s k, 64

65 moles for gas components, moles of aqueous speces n the dffuse layer of surface s and moles of element m per mole of each entty respectvely. The functon used for charge balance, f z, n the numercal methods s gven n equaton The total dervatve of f z s gven n equaton Naq S K N S N s sk aq f z Tz zn z ns s zn ( k ) k, s s k sk s E e e N e z e n e (6.43) df z N aq z dn S s Sk S K k N s k z dn sk sk E e e N e z e dn e (6.44) The functon used for charge potental, f ψs, n the numercal methods s gven n equaton The total dervatve of f ψs s gven n equaton f s F s RT snh RT F A surf K s sk k N sk z n s k s k (6.45) df s 8000 RT 0 F s snh d RT 8000 RT 0 F s cosh d ln a RT s F A surf K s sk k N s k z dn s k s k (6.46) where, 0,, A s surf, R and F refer to the delectrc constant of water (78.5, dmensonless), the permttvty of free space (8.854x0- CV - m - ), the potental at the surface, surface area of the materal (m ), the gas constant (8.34Jmol - K - ) and Faraday constant (96,493.5C/mol) respectvely. The functon used for charge balance whch ncludes surface charge and dffuse-layer charge, f z,s, n the numercal methods s gven n equaton The total dervatve of f z,s s gven n equaton

66 K N s s N k aq f z, s z n s z k s n, s k k s k Ks Nsk k s k s k Naq s k df z, s z dn zdn, s (6.47) (6.48) For a set of equatons f = 0, there are x sets of unknowns whch are solved usng Newton- Raphson method by teratvely revsng an ntal sets of x values. A set of equatons r s formulated as equaton 6.48 (Parkhurst & Appelo, 999) for the resduals of the equatons for the current values of x. J f r x dx (6.48) J s total number of master unknowns for a set of lnear equatons whch can be solved smultaneously for the unknowns, dx. New values of x are calculated for k th teraton step usng equaton 6.49 (Parkhurst & Appelo, 999) and then new values of r are calculated and f they are less than a specfed tolerance lmt then the process contnues teratvely untl convergence s acheved. k x k x dx (6.49) Numercal solutons of knetc reactons are controlled by rate equatons. Stff sets of equatons form as a result of many geochemcal knetc reactons n whch some rates are changng rapdly whle others are changng slowly as the reactons unfold n tme (Parkhurst & Appelo, 999). In PHREEQC- Runge-Rutta algorthm s used to solve knetc reacton equatons. 66

67 Chapter Seven: Couplng procedure 7. Coupled process n reactve transport Unsaturated zone s a complex system where varous physcal, chemcal and bologcal processes take place. These processes ntegrate n many ways and affect the reactve transport. The varous couplng processes that are ncluded n VSDRT are:. Heat transport and water flow are coupled through advecton of heat and the effect of temperature on vscosty and saturated hydraulc conductvty.. Solute transport and water flow are coupled through advecton of solute 3. Solute transport and heat transport are coupled through effect of temperature on thermodynamcs and chemcal reacton rates Addtonal couplng processes that are not ncluded n VSDRT are:. The effect of precptaton or dssoluton of mnerals on porosty and permeablty. The effect of temperature and solute concentraton on flud densty 3. The effect of chemcal reactons on heat transport. 7. Operator splttng Solute transport and chemcal reactons can be coupled through global mplct method or operator splttng method. Global mplct method nvolves solvng solute transport and chemcal reactons smultaneously. The GIMRT (Steefel & Yabusak, 996) reactve transport model uses a global mplct approach. Operator splttng nvolves solvng the solute transport and chemcal reacton equatons separately wthn a sngle tme step. Sequen- 67

68 tal teratve approach (SIA), sequental non-teratve approach (SNIA) and Strang Splttng are the maor operator splttng technques. SIA nvolves solvng the solute transport and reacton ndependently and terate between the transport and chemcal reacton untl some sort of convergence s acheved. SIA approach s used by reactve transport models lke HYDROGEOCHEM (Yeh & Trpath, 990) and OS3D (Steefel & Yabusak, 996). SNIA solves the solute transport frst followed by chemcal reacton of transported concentratons. PHAST (Parkhurst, Kpp, Engesgaard, & Charlton, 004) saturated porous meda reactve transport model use SNIA approach. Strang Splttng s type of SNIA method whch nvolves solvng the transport n the half tme step flowed by full tme step chemcal reacton and followed by half tme step transport. VSDRT uses SNIA approach and the potental problem wth SNIA method s that t assumes the addton of flud from one cell to another as beng rapd enough that the reactons only begn after the physcal transport s complete (Steefel & Yabusak, 996). SNIA ntroduces an operator-splttng error of the order of the tme-step length and ths error can be mnmzed by usng smaller tme steps (Parkhurst, Kpp, Engesgaard, & Charlton, 004; Carrayrou, Mose, & Behra, 004). SNIA can be mathematcally expressed n equatons 7. and 7. (Steefel & Yabusak, 996): C transp C t n L C n for transport step (7.) n transport C C n t n R for reacton step (7.) Schematc depcton of the couplng approach used for VSDRT s presented n fgure 7. 68

69 Fgure 7 Schematc representaton of modelng approach of coupled VSDRT model. 69

70 Chapter Eght: Data nput and output for VSDRT 8. VSDRT pre-processor for non-spatal nput To start a new VSDRT proect n Argus ONE envronment one has to open Argus ONE and then clck on PIEs menu and select New VSDRT Proect as shown n fgure 8.. Then a new VSDRT pre-processor wndow opens to set non-spatal parameters needed by the model. In ths wndow the user can set the unts for length, tme and energy to be used, choose whether to smulate heat transport, reactve solute transport, evaporaton and evapotranspraton. Addtonally, t s used to set ntal condton for flow, choce of hydraulc propertes functons, evaporaton, evapotranspraton, root-water uptake parameters, temporal parameters, solver parameters, chemcal speces, thermodynamc database choce and mass balance output optons. Fgure 8. Intatng a new VSDRT proect n Argus One Envronment 70

71 8.. Model descrpton VSDRT preprocessor conssts of About, Proect, Hydraulc, Recharge Perods, Evaporaton, Solute, Heat, Solver, Phreeqc nput and output menus whch are used to set smulaton optons, choce of hydraulc functon, recharge perod parameters, solver parameters, ntal and boundary solutons, solute, heat and flow mass balance output choces and general output setup. About wndow gves a bref nformaton and reference to VSDT, VSDH and PHREEQC- programs whch are the bass of VSDRT program and developers contact address, see fgure 8... Fgure 8.. Bref descrpton about the VSDRT program 7

72 8.. Settng smulaton optons Proect wndow shown n fgure 8..a s used to set general smulaton optons lke whether to smulate heat transport, reactve solute transport, evaporaton or evapotranspraton or any combnaton of these. Fgure 8..a Settng general smulaton parameters n the Proect wndow The nputs needed here are:. Ttle of the proect 7

73 . Geometrc unts for length, tme, heat and avalable optons of unts are shown n fgures 8..b, 8..c, and 8..d respectvely. 3. Coordnate system (Cartesan or Radan) see fgure 8..e. 4. Choose whether to smulate heat, solute, evaporaton, evapotranspraton or any combnaton of them as shown fgure 8..f. 5. Duraton of the smulaton, number of recharge perods, ntal tme and maxmum number of tme steps 6. Spatal and temporal fne dfferencng scheme choce for transport smulaton whch could be centered or backward n space and centered or backward n tme respectvely as shown fgure 8..g. Fgure 8..b Choosng length unt Fgure 8..c Choosng tme unt 73

74 Fgure 8..d Choosng heat unt Fgure 8..e Choosng coordnate system Fgure 8..f General smulaton optons for transport and flow Fgure 8..g Choosng fnte dfferencng opton for transport smulaton 74

75 8..3 Settng ntal conducton and hydraulc propertes functons choce In the hydraulc wndow shown n fgure 8..3 the user sets the ntal hydraulc condton, choce of hydraulc characterstc functons and weghtng functon for estmatng nter-cell hydraulc conductvty terms. The ntal condton could be set ether as equlbrum profle, pressure head or mosture content. Hydraulcs characterstc functons may be based on Brooks & Corey, Van Genuchten, Haverkamp or Ross-Nmmo. Inter-cell relatve hydraulc conductvty may be estmated ether usng arthmetc mean, geometrc mean or upstream weghtng method. Fgure 8..3 Settng ntal condtons and hydraulc functons n Hydraulc wndow 75

76 8..4 Settng recharge perod propertes Recharge Perods wndow s used to set recharge perod parameters for each recharge perod, as shown n fgure The recharge perod parameters that need to be set for each avalable recharge perod are:. Length of ths recharge perod (P.Length). Length of ntal tme step for ths perod (DELT) 3. Multpler for ths tme length (TMLT) 4. Maxmum allowed tme step (DLTMX) 5. Mnmum allowed tme step (DLTMIN) 6. Factor by whch tme step should be reduced n order to obtan convergence f convergence s not attaned at maxmum teratons (TRED) 7. Maxmum allowed change n head per tme step of ths recharge perod (DSMAX) 8. Steady state head crteron (STERR). The program assumes that steady state s reached when maxmum change n head between successve tme steps s less than STERR 9. Maxmum allowed heght of ponded water for constant flux nodes (POND) 0. Prnt heads, concentratons, temperature, mosture content and /or saturaton to output fle after each tme step (PRNT= true). Enter for true and 0 for false 76

77 . Smulate seepage faces for ths recharge perod (SEEP). Enter for true and 0 for false. Smulate evaporaton for ths recharge perod (BCIT). Enter for true and 0 for false 3. Smulate evapotranspraton for ths recharge perod (ETSIM). Enter for true and 0 for false The add button s used to add recharge perods, the clear button s used to clean the content of recharge table and the delete button s used delete a sngle row of a recharge perod. Note that the number of rows n the recharge perod must be equal to the number of recharge perods and flled wth value. Leavng a recharge perod cell empty wll cause error on the program. One can use the horzontal bar as well as vertcal bars to go through the recharge perods table. Fgure 8..4 Recharge perod wndow to nput recharge perod parameters 77

78 8..5 Settng evaporaton parameters By default the evaporaton wndow s nactve as shown n fgure 8..5a and t would get actvated f evaporaton or evapotranspraton or both of them are selected to be smulated n proect wdow fgure 8..5b. Parameters that are needed n evaporaton table are evaporaton perod number (perod), potental evaporaton rate (PEVAL), surface resstance to evaporaton (SRES) and pressure potental of the atmosphere (HA) at the begnnng of each evaporaton perod (fgure 8..5c). The add button s used to add an evaporaton perod, the clear button s used to clean the content of evaporaton table and the delete button s used delete a sngle row of evaporaton perod. Leavng an evaporaton perod cell empty wll cause an error of the program. One can use the horzontal bar as well as vertcal bars to go through the evaporaton perods table. Fgure 8..5a Inactve evaporaton wndow 78

79 Fgure 8..5b Selectng evaporaton to be smulated n the proect wdow Fgure 8..5c Actvated evaporaton table n the evaporaton wndow 79

80 8..6 Settng evapotranspraton parameters By default the evapotranspraton table s nactve (fgure 8..5a) and t gets actvated f evapotranspraton s selected to be smulated n the proect wdow as shown fgure 8..6a. Parameters that are needed n evapotranspraton table are evapotranspraton perod number (Perod), potental evapotranspraton rate (PTVAL), root depth, root actvty at the base of the root zone (RA Bottom), root actvty at top of root zone (RA Top) and pressure head n roots (P.Head at Root) at the begnnng of each evaporaton perod (fgure 8..6b). The add button s used to add evapotranspraton perod, the clear button s used to clean the content of evapotranspraton table and the delete button s used delete a sngle row of evapotranspraton perod. Leavng an evapotranspraton perod cell empty wll cause error on the program. One can use the horzontal bar as well as vertcal bars to get evapotranspraton perods. Fgure 8..6a Selectng evapotranspraton n the proect wndow 80

81 Fgure 8..6b Actvated evapotranspraton table n the evaporaton wndow In case of smulatng both evaporaton and evapotranspraton as shown n fgure 8..6c both evaporaton and evapotranspraton tables get actvated as shown n fgure 8..6d. Fgure 8..6c Selectng evaporaton and evapotranspraton optons 8

82 Fgure 8..6d Actvated evaporaton and evapotranspraton table n the Evaporaton wndow 8..7 Settng reactve transport smulaton In order to smulate reactve transport solute opton should be selected n the proect wndow as shown n fgure 8..7a. The thermodynamc database needed by geochemcal model PHREEQC has to be defned n solute wndow as shown n fgure 8..7b. The phreeqc.dat s the default database and should be avalable n each proect folder. The user could use other database fles as well. Solute mass balance components to be wrtten to output fles could be selected n the solute wndow as shown n fgure 8..7b as well. The ntal and boundary condton solutons and varous equlbrum and knetc reactons has to be defned n the Phreeqc nput wndow and saved to proect folder where the database fle s also saved (fgure 8..7c). The solutons and varous chemcal reactons should 8

83 be wrtten accordng PHREEQC nput format and the user should refer to the PHREEQC manual. Fgure 8..7a Selectng solute n the Proect wndow Fgure 8..7b Database fle name and selectng solute mass balance output n the Solute wndow 83

84 Fgure 8..7c Phreeqc nput wndow to set ntal and boundary solutons and varous chemcal reactons 8..8 Settng heat transport To smulate heat transport the heat opton n proect wndow has to be selected and heat unt has to be set as shown n fgure 8..8a. The heat mass balance components could be selected n Heat wndow as presented n fgure 8..8b. Fgure 8..8a Selectng heat transport opton n the proect wndow 84

85 Fgure 8..8b Heat mass balance selecton n the Heat wndow 8..9 Settng solver parameters Solver wndow s used to set solver parameters needed to solve flow, heat and solute transport equatons (fgure 8..9). These parameters are:. Relaxaton parameter for teratve soluton (HMAX). Mnmum number of teratons per tme step (MINIT) 3. Maxmum number of teratons per tme step (ITMAX) 4. Head closure crteron (EPS) 5. Temperature closure crteron (EPS) 85

86 6. Velocty closure crteron (EPS) 7. Solute closure crteron (EPS3) Fgure 8..9a Solver wndow to set solver parameters Fgure 8..9b Settng smulaton to smulate heat and reactve transport 86

87 Fgure 8..9c Settng solver parameters for flow, heat and reactve transport 8..0 Settng output potons The output wndow s used to determne whether pressure head, total head, volumetrc mosture content, saturaton, velocty, temperature and chemcal consttutes are wrtten to output fles at prnt tmes. It s also used to specfy whether mass balance components should be wrtten to output fles at prnt tme or at each tme step. Observaton pont values of pressure head, total head, volumetrc mosture content, saturaton, velocty, temperature and chemcal consttutes may be wrtten to output fles at prnt tmes or at each tme step. 87

88 Fgure 8..0 Output wndow to set out optons and tme 8. VSDRT pre-processor for spatal nput Spatal parameters needed for the smulaton should be set usng VSDRT pre-processor for spatal nput n Argus ONE envronment (fgure 8.). VSDRT pre-processor for spatal nput wndow s created based on the spatal layers created at the end of VSDRT preprocessor for non-spatal nput. 88

89 The spatal layers that are used n VSDRT are:. Doman outlne. Grd densty 3. VSDRT Grd 4. Textural class 5. Equlbrum profle/ntal pressure head/ntal mosture content 6. Intal Soluton 7. Intal temperature 8. Boundary condtons 9. Observaton ponts 0. Source_snk. Data. Outputs 89

90 Fgure 8. VSDRT pre-processor for spatal nput n Argus ONE envronment 8.. Smulaton doman outlne The spatal doman of nterest for the smulaton should be outlned n the doman outlne layer. Before drawng the doman of nterest drawng sze and scale and unts of the smulaton should be set usng Argus ONE features. To set drawng sze clck on specal menu and then select Drawng sze as shown n fgure 8..a and a Drawng sze wndow appears as presented n fgure 8..b. 90

91 Fgure 8..a Schematc representaton of selectng drawng sze. To set scale and unts clck on specal menu as show n fgure 8..c and select scale and snts and then scale and unts wndow appears as shown n fgure 8..d. To draw doman of nterest make sure the current layer s doman outlne layer. Then select closed contour by clckng on the closed contour menu as shown n fgure 8..e. After drawng a doman of nterest Informaton contour wndow wll appear to set the value of grd densty as shown n fgure 8..g. 9

92 Fgure 8..b Drawng sze wndow Fgure 8..c Schematc representaton of selectng scale and unts 9

93 Fgure 8..d Scale and unts wndow Fgure 8..e Selectng closed contour tool to draw the doman of nterest 93

94 Fgure 8..f Schematc representaton of doman of nterest Fgure 8..g Schematc presentaton of settng grd densty value for doman of nterest. 94

95 8.. VSDRT Grd Spatal dscretzaton of doman of nterest would be done n VSDRT Grd layer usng Argus ONE fnte dfference grd module. Select Magc Wand tool as shown n fgure 8..a and clck on the doman of nterest outlned and a grd angle wndow appear as shown n fgure 8..b. Set angle of nclnaton of the grd and clck ok. Automatcally a grd wll be generated as shown n fgure 8..c and could be edted by addng or deletng rows, columns usng Argus ONE delete and nsert menus as shown n fgure 8..d and 8..e respectvely. Fgure 8..a Schematc representaton of selectng Magc Wand tool to generate grd n VSDRT Grd layer wndow Fgure 8..b Grd angle wndow 95

96 Fgure 8..c Schematc representaton of grd generated by Magc Wand tool To nsert desred number of rows for D smulaton one can use row nsert tool as shown n fgure 8..e and drag t on doman of nterest and Grd lne generaton wndow opens. Grd lne generaton wndows s used to set requred number of row usng row spacng or number of rows by selectng dstance or count respectvely as shown n fgure 8..f. Based on the settng on grd lne generaton wndows automatcally a new grds wll be generated as shown n fgure 8..g. 96

97 Fgure 8..d Schematc representaton of selectng the delete tool to remove unwanted grds Fgure 8..e Schematc representaton of row nsertng tool to create a D column 97

98 Fgure 8..f Grd Lnes generaton wndow Fgure 8..g Schematc representaton of D grd n column. 98

99 8..3 Textural Class Textural class layer s used to set heterogeneous hydraulc, chemcal and thermal propertes of textural class of the doman of nterest. The hydraulc propertes needed dependng on the choce of hydraulc functons of Brooks & Corey, van Genuchten, Haverkamp or Ross- Nmmo for a partcular smulaton. General addtonal hydraulc propertes requred for water flow smulaton are:. Rato of hydraulc conductvty n the z-coordnate drecton to that of n the x- coordnate drecton (Kz_Kx). Saturated hydraulc conductvty (Saturated Kh), L/T 3. Specfc storage, L - 4. Porosty In case of Brooks & Corey models the hydraulc propertes requred are:. Bubblng pressure head whch s always has a negatve value, L.. Resdual mosture content 3. Pore-sze dstrbuton ndex In case of van Genuchten models the hydraulc propertes requred are:. van Genuchten alpha (Alpha), L.. Resdual mosture content 3. n van Genuchten parameter (Beta) 99

100 In case of Haverkamp models the hydraulc propertes requred are:. A prme Haverkamp parameter (A prme) whch s always has a negatve value, L.. Resdual mosture content 3. B prme Haverkamp parameter (B prme) 4. Alpha Haverkamp parameter (Alpha) whch s always has a negatve value, L. 5. Beta Haverkamp parameter (Beta) In case of Ross-Nmmo models the hydraulc propertes requred are:. ψ 0 Ross-Nmmo parameter (Ps_0), L.. ψ D Ross-Nmmo parameter (Ps_D), L. 3. ψ Ross-Nmmo parameter (Ross_lambda ) Thermal propertes of the textural class requred n cases of heat transport smulaton are:. Heat longtudnal dspersvty, L.. Heat transverse dspersvty, L. 3. Heat capacty of dry solds (Cs), Q/L 3 o C, where Q s unt of energy. 4. Thermal conductvty of water-sedment at resdual mosture (KTr), Q/L o C. 5. Thermal conductvty of water-sedment at full saturaton (KTs), Q/L o C. 6. Heat capacty of water (Cw ), Q/L 3 o C. 00

101 Chemcal propertes of the textural class requred n case of reactve transport smulaton are:. Longtudnal dspersvty, L.. Transverse dspersvty, L. 3. Molecular dffuson coeffcent, L /T. To set the textural propertes of doman of nterest select the actve layer as Textural Class as shown n fgure 8..3a. Dfferent textural unts would be delneated usng closed contour tool as shown n fgure 8..3b and textural propertes as well as thermal and chemcal propertes of the textural class would be set usng contour nformaton wndow dependng on the type of smulaton conducted as shown n fgure 8..3c. Fgure 8..3a Schematc representaton of selectng textural Class 0

102 Fgure 8..3b Schematc representaton of selectng closed contour to delneate a textural class Fgure 8..3c Schematc representaton of settng textural class propertes. 0

103 8..4 Intal condton for flow The ntal condton for flow smulaton could be set as pressure head wth equlbrum profle, ntal pressure head or ntal mosture content. To set ntal condton for flow the equlbrum profle, ntal pressure head or mosture content layer must be the actve layer. Closed contour tool could be used to defne the ntal flow condton n doman of nterest n the same way as t s used to delneate doman of nterest or textural class as shown n fgures 8..e and 8..3b. In case equlbrum profle s chosen as ntal condton depth of the ground water table and mnmum pressure head above the ground water table are requred. Otherwse ntal pressure head or mosture content values are requred whch s also set by the contour value. Fgure 8..4 presents Contour nformaton wndow to set value of ntal pressure head or ntal mosture content. Multple closed contours can be used f ntal flow condton s not unform n the doman of nterest. Fgure 8..4 Schematc representaton of settng ntal pressure head or ntal mosture content n doman of nterest. 03

104 8..5 Intal soluton In order to set ntal soluton n the doman of nterest the actve layer should be Intal soluton layer. Intal soluton can be defned by provdng the soluton number, pure-phases number, surface number, gas number, sold soluton number and knetcs number gven n the Phreeqc nput fle generated by VSDRT pre-processor for non-spatal nput. The default value for soluton number s and for pure-phases number, surface number, gas number, sold soluton number and knetcs number s -. Bascs of settng soluton, purephase, surface, gas, sold soluton and knetcs have to be referred from PHREEQC manual. Fgure 8..5 Schematc representaton of settng ntal soluton 8..6 Intal temperature Intal temperature layer s used to set ntal temperature dstrbuton n the doman of nterest n case of heat transport usng closed contour tool. Intal temperature layer wll be aval- 04

105 able n case of heat transport smulaton. The ntal temperature can be set usng Argus ONE contour tool n smlar ways as the ntal pressure head or soluton has been set usng contour nformaton wndow as shown n fgure 8..6a. Thermal propertes of the doman of nterest wll be set n the texture layer along wth hydraulc propertes and n case of reactve transport also wth geochemcal property of the medum as shown n fgure 8..6c. The heat transport boundary condton can be set usng boundary layer along wth flow, reactve transport boundary condtons as shown n fgure 8..6b. Fgure 8..6a Schematc representaton of settng ntal temperature n doman of nterest Fgure 8..6b Settng boundary condtons for flow, heat and reactve transport smulaton 05

106 Fgure 8..6c Settng hydraulc, thermal and geochemcal propertes of the medum along n case of heat and reactve transport 8..7 Observaton ponts Observaton ponts are used to see the output of the smulaton at chosen tme at a partcular pont n space and observaton layer s used to set one or more observaton ponts usng pont contour tool as shown n fgure

107 Fgure 8..7 Settng observaton pont n the observaton layer 8..8 Boundary condtons Boundary condtons layer s used to set flow, heat and/or solute transport boundary condtons for varous recharge perods. Possble flow boundary condtons along wth ther boundary dentfer ndex are presented n table 8..8a. The avalable heat transport boundary condtons are not specfed boundary and specfed temperature wth heat boundary dentfer ndex of 0 and respectvely. The avalable solute transport boundary condtons are not specfed boundary and specfed concentraton wth solute boundary dentfer ndex of 0 and respectvely. Specfed concentraton s set by provdng soluton number of the chemcal soluton at the boundary or chemcal soluton flux of water across the boundary. 07

108 Table 8..8a Possble flow boundary condtons Flow boundary dentfer ndex Type of boundary condton 0 No flow across the boundary Specfed pressure head Specfed flux n unts of L/T 3 Possble seepage face 4 Specfed total head 5 Evaporaton 6 Specfed volumetrc flow n unts of L 3 /T 7 Gravty dran. No flow across the boundary refers to a boundary where no water nters or leaves n to the doman of nterest.. Specfed pressure head boundary refers to a boundary where pressure head has a specfed value. 3. Specfed flux n to the doman boundary refers to a boundary where water nters n to the doman of nterest n the form of nfltraton rate from precptaton and rrgaton. Specfed flux boundary nodes may change to specfed pressure head boundary nternally by the program f pressure head at specfed flux boundary node exceeds the maxmum allowed heght of pondng provded by the user. Converted specfed pressure head boundary node may return to specfed flux boundary node nternally f computed flux exceeds the specfed flux. 08

109 4. Possble seepage face boundary refers to a boundary where seepage mght occur f pressure head along the seepage face s zero and water flow out of the doman at same tme. In case of possble seepage face only the correspondng flow boundary dentfer ndex should be provded by user. 5. Specfed total head boundary condton refers to boundary where specfc total head value s defned. If the total head boundary s above the ground water table t wll have negatve value and f t s below the ground water table t wll have a postve value. 6. Evaporaton boundary condton refers to boundary where water flow out of the doman of nterest n the form of evaporaton and evapotranspraton. In case of evaporaton boundary condton only the correspondng flow boundary dentfer ndex should be provded by the user. 7. Specfed volumetrc flow boundary refers to a boundary where water enters or leaves the doman of nterest and applcable only n cases when radal coordnate system s used. 8. Gravty dran boundary refers to a boundary where water flow out of the doman vertcally due to gravtatonal force at unt vertcal hydraulc gradent. The heat and solute transport boundary condtons at any partcular boundary depends to the correspondng flow boundary condton. Possble combnaton of boundary condtons for flow and heat and solute transport s presented n the table 8..8b. 09

110 Table 8..8b Possble combnaton of boundary condtons for flow and heat and solute transport Flow boundary condton Heat boundary condton Solute boundary condton No flow across the boundary Specfed pressure head Specfed flux n to the doman n unts of L/T Specfed temperature at the boundary Specfed temperature n nflow water Specfed concentraton at the boundary Specfed concentraton n nflow water Possble seepage face no no Specfed total head Specfed temperature at the boundary Specfed concentraton at the boundary Evaporaton no no Specfed volumetrc flow n unts of L 3 /T Gravty dran Specfed temperature nflow water Specfed concentraton n the nflow water In the boundary condton layer varous boundary condtons could be set usng open contour tool of Argus ONE as shown n fgure 8..8b. Fgure 8..8b shows how to set boundary condtons for a gven recharge perods usng open contour tool and fgure 8..8c shows contour nformaton wndow of Argus ONE for to set a boundary condtons for flow and reactve transport. In VSDRT a partcular boundary open contour s supposed to exst n all recharge perods so when a user draws the boundary segment t s requred to provde the respectve boundary condtons for flow, heat and/or solute transport for all recharge perods through contour nformaton wndow of Argus ONE. So f 0

111 a partcular flow boundary segment exst for one recharge perod and does not exst for other recharge perod then ts flow boundary dentfer ndex should be set as 0. Fgure 8..8a Selectng boundary condtons layer Fgure 8..8b Schematc representaton of selectng open contour tool of Argus ONE to set the boundary condtons

112 Fgure 8..8c Schematc representaton of settng boundary condtons for flow and solute transport 8.3 VSDRT post-processor VSDRT post-processor deals wth runnng VSDRT numercal model and presentng the output usng Argus ONE post-processor tools Runnng VSDRT numercal model To run the numercal model one need to make sure that:. Phreeqc nput fle and database are n the same proect folder. All necessary spatal, non-spatal and temporal nputs are properly provded 3. Boundary nodes are properly draw along the boundary

113 To start the smulaton the actve layer of Argus ONE envronment need to be the VSDRT Grd layer. From PIEs menu by selectng Export VSDRT one can ntate RunVSDRT dalog wndow as shown n fgure 8.3.a and fgure 8.3.b. To run RunVSDRT one has to clck frst on Run VSDRT button followed by clckng the Ok button to start numercal smulaton. Fgure 8.3.a Schematc representaton of selectng ExportVSDRT menu Fgure 8.3.b Schematc representaton of RunVSDRT wndow 3

114 8.3. Presentng VSDRT output usng Argus ONE post-processor tools After successfully runnng the VSDRT numercal model the output of the smulaton can be presented wth help of Argus ONE post-processor tools usng the Data and Output layers of VSDRT.. Make sure Data s the actve layer as shown n fgure 8.3.a.. From the fle menu select mport Data menu as shown n fgure 8.3. b and then select mport text fle menu, see fgure 8.3.c. Import Data wndow wll open to set the format of the data fle to be mported. For VSDRT one has to select grd data and read trangulaton from layer VSDRT Grd as shown n fgure 8.3.d. 3. Chose fle to mport wndow would be used to select the output of the smulaton for pressure head, temperature, mosture content, velocty, saturaton or solute concentratons fles as shown n fgure 8.3.e. 4. Then make the actve layer to be the Outputs layer by selectng outputs layer as shown n fgure 8.3.g. 5. Then select Post-processng popup menu to choose vsualzaton tool of choce, for example n fgure 8.3. h Color dagram tool to make color map for the output of the smulaton. 6. Set the color map parameters as shown n fgure 8.3. by selectng Data layer as the Layer from whch the data wll be plotted and the value wll be the value of the data on data layer. 7. Get the color map as shown n fgure

115 Fgure 8.3.a Schematc representaton of selectng the Data layer Fgure 8.3.b Schematc representaton of selectng the Import Data menu 5

116 Fgure 8.3.c Schematc representaton of selectng Text Fle menu from Import Data menu Fgure 8.3.d Schematc representaton of the Import Data wndow 6

117 Fgure 8.3.e Schematc representaton of choosng fle to be mported to Data layer Fgure 8.3.f Schematc representaton of mported data to the Data layer 7

118 Fgure 8.3.g Schematc representaton of selectng Output layer to plot the outputs of the smulaton Fgure 8.3.h Schematc representaton of selectng Argus ONE Post processng tools popup menu 8

119 Fgure 8.3. Schematc representaton of settng Color Map parameters to create color map Fgure 8.3. Example color map showng spatal dstrbuton of pressure head plotted usng Argus ONE Post-processng Color Dagram tool 9

120 Chapter Nne: Model verfcaton Model verfcaton nvolves testng coupled VSDRT model wth varous reactve transport problems from lterature to check whether the model s workng properly. For verfcaton proposes seven cases are taken from lterature nvolvng smple D conservatve sngle component transport, caton exchange, surface complexaton, dssoluton of calcte and gypsum, heat and conservatve chemcal transport, D reactve transport nvolvng caton exchange and D mult-solute reactve transport. VSDRT smulaton results were compared wth other reactve transport models lke VSDT, PHREEQC, HP, VSDH and HP. Snce VSDH, VSDT and PHREEQC are ndependently well tested programs the verfcaton problems here are more focused on the testng the couplng of ths programs. 9. D Conservatve sngle component transport n vadose zone The problem s taken and modfed from USGS Water-Resources Investgatons Report (p. 45) (Healy, 990). It deals wth chlorde transport n 40 cm sandy loam column. The smulaton s conducted for half an hour and the column s dvded n to 40 grds of cm length and hour tme step s used. Van Genuchten parameters for sandy loam sol are used as column s hydrologc propertes. Longtudnal dspersvty assumed to be 0 cm. Intal pressured head of -0 cm and zero chlorde ntal concentraton n column was assumed. Flux of 5.5 cm/h appled at the top of the column wth gm/kgw of Cl. Ths problem was smulated by both VSDT and VSDRT n order to check the lnk between PHREEQC and VSDRT. The result of the smulaton s presented n fgure 9. and shows that both VSDT and VSDRT gve dentcal result. 0

121 Cl n g/kgw 8.00E E E-0 VSDRT VSDT 5.00E E E-0.00E-0.00E E Depth n cm Fgure 9. Comparsons of conservatve Cl transport smulaton usng VSDRT and VSDT 9. Surface complexaton and equlbrum phase Ths problem s taken from (Wssmeer & Barry, 008) to demonstrate the capabltes of VSDRT to smulate surface complexaton. 5 cm column of loamy sand was dscretzed n to 50 cells of 0. cm length and smulated for 00 days wth tme step of 0.0 days. The hydraulc and geochemcal propertes of the loamy sand column along wth ntal and boundary condtons are gven n table 9. below.

122 Table 9. Hydraulc and geochemcal propertes of the loamy sand column along wth ntal and boundary condtons modfed from (Wssmeer & Barry, 008) Hydraulc propertes of loamy sand n terms of van Genuchten parameters α g 0. 4 cm - ng.8 K s cm/day θ s 0.4 θ r Geochemcal propertes (surface assembly and sold phase n equlbrum wth ntal soluton) (mol/l sol) Equlbrum phases Calcte 0.05 Surface propertes Weak adsorpton stes (Hfow) 0.0 Strong adsorpton stes (Hfos) Specfc surface area 600 m /g Total mass of surface n each cell 0.03 g Thckness of the dffuse layer Intal soluton ( mol/kg water) ph 7.6 Ca.08 x 0-3 Na x 0-7 C x 0-3 Water content m Boundary condton soluton (mol/kg water) ph 3. Na.4 x 0 - Water content 0.4 The results of VSDRT smulaton are presented n the fgure 9.a, 9.c, 9.d and 9.e for water content, Na, Ca and C respectvely at 40 and 00 days. These results were compared wth that of HP results presented n fgures 9.b and fgure 9.f (L. Wssmeer and D.A. Barry, 008). The profle of water content, Na and C at 40 days show smlar pattern for both VSDRT and HP whle Ca shows slght dfference towards the top of the column. However at 00 days the dstrbuton of water content s dfferent where VSDRT calculates full saturaton whle HP gves near full saturaton result. The profles of Na and C at 00 days are also smlar to that of HP but Ca shows slghtly dfferent towards the top of the column. The profle of Ca n top 0 and 0 cm of smulaton shows some peak values n HP smulaton

123 water content for both 40 days and 00 days respectvely whch are not observed n VSDRT smulaton. Ths varaton may be due the varaton n value of longtudnal dspersvty used n HP whch s not clearly stated on the orgnal paper. For ths smulaton longtudnal dspersvty of 0. cm used and zero molecular dspersvty was assumed depth n mm water content at 40 days water content at 00 days Fgure 9.a Dstrbuton of mosture content at 40 and 00 days based on VSDRT smulaton Fgure 9.b Dstrbuton of water content and ph at 40 (crcles) and 00 (trangles) days based on HP smulaton respectvely (Wssmeer & Barry, 008) 3

124 C n mole/kgw Ca n mole/kgw Na n mole/kgw 3.00E-0.50E-0.00E-0 Na at 40 days Na at 00 days.50e-0.00e E E depth n mm Fgure 9.c Dstrbuton of Na at 40 and 00 days based on VSDRT smulaton.50e-03.00e-03.50e-03 Ca at 40 days Ca at 00 days.00e E E depth n mm Fgure 9.d Dstrbuton of Ca at 40 and 00 days based on VSDRT smulaton 3.50E E-0.50E-0 C at 40 days C at 00 days.00e-0.50e-0.00e E E depth n mm Fgure 9.e Dstrbuton of C at 40 and 00 days based on VSDRT smulaton 4

125 Fgure 9.f Dstrbuton of Na, Ca and C at 40 (crcles) and 00 (trangles) days based on HP smulaton respectvely (Wssmeer & Barry, 008) 9.3 D reactve transport nvolvng caton exchange A D reactve transport nvolvng caton exchange was taken from PHREEQC (Parkhurst & Appelo, 999) to be smulated usng VSDRT n 8 cm column of slt loam. Intally the column s flled wth mmol NaNO 3 and 0. mmol KNO 3 soluton. Then the column was flushed wth 3 pore volume of 0.6 mmol CaCl. The smulaton was conducted for 4 hours at a tme step of hour and grd sze of 0. cm. The hydraulc and geochemcal propertes of the slt loam sol along wth ntal and boundary condtons are gven n table 9.. The results of VSDRT and PHREEQC smulaton at the outlet of the column are presented n fgure 9.3a and 9.3b respectvely. The cell length, tme step and longtudnal dspersvty used n PHREEQC smulaton are 0. cm, 70 seconds and 0.cm respectvely. Due to lack nformaton regardng hydraulc propertes of the column medum used n the ntal PHREEQC problem t was not possble to get exact result as PHREEQC n VSDRT. However, the smulaton results from VSDRT are more or less shows smlar pattern as that of PHREEQC. For example Na, Cl and Ca gve same result for both smulatons. In the case of 5

126 mole /kg of water K profle, PHREEQC and VSDRT have smlar pattern but dfferent peak values of. and 0.8 mmol/kgw respectvely. Table 9. Hydraulc and geochemcal propertes of the slt loam column along wth ntal and boundary condtons Hydraulc propertes of slt loam sol n terms of van Genuchten parameters αg cm - ng 7 Ks.7777E-04 cm/seconds θs 0.3 θr 0.7 Geochemcal propertes Caton exchanger. mmol/l of pore water Longtudnal dspersvty 0.05 cm Intal soluton ( mmol/kg water) temp 5.0 ph 7.0 charge pe.5 O (g) Na.0 K 0. N(5). Boundary condton soluton (mmol/kg water) temp 5.0 ph 7.0 charge pe.5 O (g) Ca 0.6 Cl..40E-03.0E-03.00E E E E-04.00E-04 Ca Cl K Na 0.00E E+00.00E E E E+04 tme n seconds Fgure 9.3a Smulaton of caton exchange usng VSDRT 6

127 Fgure 9.3b PHREEQC smulaton of caton exchange n nvolvng advecton and dsperson transport. 9.4 D reactve transport nvolvng dssoluton of calcte and gypsum Reactve transport nvolvng dssoluton of gypsum and calcte was smulated wth HP and s used here to show that VSDRT capabltes to smulate dssoluton of gypsum and calcte. In a 50 cm long column mmol of CaCl was nfltrated for.5 hour under steady-state saturated flow condtons. The nfltratng soluton s n equlbrum wth atmospherc partal pressure of oxygen and carbon doxde. The sol column contans calcte (CaCO 3 ) and gypsum (CaSO 4.H 0) mnerals at.76 x0 - mmol/kg sol each. The ntal soluton n the sol column s n equlbrum wth calcte, gypsum and atmospherc partal pressure of oxygen. Hydrologc and geochemcal propertes of the sol column and ntal and boundary solutons are presented n table 9.3. The results of gypsum and calcte dssoluton reactve transport smulaton usng HP and VSDRT are presented n fgures 9.4a and 9.4b respectvely. The results of the smulaton 7

128 are dentcal except a slght dfference at the bottom of the column due to dfference n solute boundary condton used. Table 9.3 Hydraulc and geochemcal propertes of sol column along wth ntal and boundary solutons van Genuchten hydraulc propertes of slt sol αg cm - ng.56 Ks 0 cm/day θs 0.35 θr bulk densty.8g/cm 3 Geochemcal propertes Calcte.76 x 0-5 mol/kg sol Gypsum.76 x 0-5 mol/kg sol Longtudnal dspersvty cm Transverse dspersvty 0.0 cm Molecular dffuson 0 cm /day Intal soluton ( mmol/kg water) Gypsum Calcte O(g) Boundary soluton ( mmol/kg water) ph 7.0 charge Cl Ca O(0) O(g) C(4) CO(g) -3.5 Fgure 9.4a Ca and S profle at 0, 0.5,,.5, and.5 days accordng to HP smulaton (Jacques & Smunek, 009) 8

129 S mol/kg water Ca n mol/kg water.00e-0.50e-0.00e E E days 0.5 days days.5 days days.5 days Z n cm (a).00e-0.50e-0.00e E E Z n cm 0 days 0.5 days days.5 days days.5 day (b) Fgure 9.4b Ca and S profle at 0, 0.5,,.5, and.5 days accordng to VSDRT smulaton 9.5 D Heat and solute transport The problem was taken from USGS Water-Resources Investgatons Report (p. 5) (Healy & Ronan, 996) wth modfcaton to smulate heat and chlorde transport. A 60 m column sol wth vertcal spacng of.0 m and smulaton tme of 0765 s was used. Hydraulc, thermal and chemcal propertes of the medum along wth ntal and boundary condtons for flow, heat and reactve transport s gven n table

130 Temperature n C Table 9.4 Hydraulc, thermal and geochemcal propertes sol column along wth ntal and boundary condtons for heat and reactve transport Hydraulc propertes n terms of van Genuchten parameters α g cm - ng 3 K s m/second θ s 0.5 θ r 0 Thermal propertes of the medum α L 0 m α T 0 m.08e+06 C s C w K tr.8 K ts.8 Geochemcal propertes α L 4.E+06 0 m.e-06 molecular dffuson Intal soluton ( g/kg water) Cl 0.0 Intal Temperature T 0 C Intal pressure head m Boundary condton soluton (g/kg water) Cl. Boundary temperature (top) T C Boundary pressure head m Fgure 9.5a shows that the spatal dstrbuton of temperature based on VSDRT and VSDH smulaton. The VSDRT smulaton result s same as that of VSDH whch show that the heat transport s properly coupled to the reactve transport. Fgure 9.5b show spatal dstrbuton of chlorde based on VSDRT model..e+0.0e+0.08e+0.06e+0.04e+0.0e+0.00e+0.98e+0 VSDRT VSDH depth n m Fgure 9.5a Comparson of heat smulaton of VSDRT wth that of VSDH 30

131 Cl n mole/kgw 3.00E-0.50E-0.00E-0.50E-0.00E E E depth n m Fgure 9.5b conservatve Cl transport smulated wth heat transport usng VSDRT 9.6 D reactve transport nvolvng caton exchange A furrow rrgaton problem presented n UNSATCHEM and HP (Smunek, Jacques, Sena, & van Genuchten, 0) manuals s used to smulate two dmensonal nfltraton of gypsum saturated water n to sodc sol. The schematc representaton of the doman of smulaton s presented n fgure 9.6a along wth the fnte dfference grd used. Intal pressure head condton of -00 cm s used. Sol hydraulc and chemcal propertes along wth chemcal ntal and boundary condtons are presented n table 9.5. It s assumed that furrow s flooded wth water and the water level n the furrow was kept at constant 6 cm. Due to symmetry, the smulaton was carred out only for the doman between the axs the two neghborng furrows. The bottom boundary consdered as free dranage and zero flux s consdered for the rest of the boundares. The smulaton was carred out for 5 days wth ntal, maxmum and mnmum tme steps of 0.00, 0.00 and days respectvely and tme multplcaton factor of.3. 3

132 Fgure 9.6a Schematc representaton of furrow rrgaton smulaton doman along wth fnte dfference grd. Table 9.5 Hydraulc and geochemcal propertes of smulaton doman along wth ntal and boundary solutons for furrow rrgaton problem van Genuchten hydraulc propertes of slt sol αg 0.06 cm - ng.37 Ks 6 cm/day θs 0.46 θr bulk densty.4g/cm 3 Geochemcal propertes Caton exchanger 0.0 mol/l of sol Longtudnal dspersvty cm Transverse dspersvty 0. cm Molecular dffuson cm /day Intal soluton ( mmol/kg water) temp 5.0 ph 7.0 charge Na 5 Ca Cl 0.0 S(6) 3.5 O(0) O (g) Boundary soluton ( mmol/kg water) temp 5.0 ph 7.0 charge Na 4.4 Ca 6.3 Cl 5.0 S(6) 6.0 O(0) O (g)

133 The results of VSDRT smulaton are presented n fgures 9.6b, 9.6d, and 9.6f for pressure head, chlorde and sodum profles at varous tmes respectvely. The results of HP smulaton are also presented n fgures 9.6c, 9.6e and 9.6g for pressure head, chlorde and sodum respectvely. Pressure head profle at 0., 0.5, and days based on VSDRT smulaton shows that pressure head ranges from to 6 cm whch s also smlar to HP smulaton result whch shows pressure head ranges from to 6 cm. (a) (b) 33

134 (c) Fgure 9.6b Pressure head profle at tmes a) 0., b) 0.5, c) and d) days usng VSDRT smulaton (d) Fgure 9.6c Pressure head profle at tmes a) 0., b) 0.5, c) and d) days usng HP smulaton (Smunek, Jacques, Sena, & van Genuchten, 0) 34

135 Chlorde profle at 0.,, 3 and 5 days based on VSDRT smulaton shows that concentraton of Cl ranges from to 0 mol/l. Hgh concentraton of Cl s observed near the furrow and concentraton of Cl s zero towards the bottom and left sde of the profle. Chlorde profle at 0.,, 3 and 5 days based on HP smulaton also show same result. (a) (b) (c) 35

136 (d) Fgure 9.6d Chlorde n mol/l profle at tmes a) 0., b), c) 3 and d) 5 days usng VSDRT smulaton Fgure 9.6e Chlorde n mol/l profle at tmes a) 0., b), c) 3 and d) 5 days usng HP smulaton (Smunek, Jacques, Sena, & van Genuchten, 0) Sodum profle at 0.,, 3 and 5 days based on VSDRT smulaton shows that concentraton of Na ranges from to mol/l. Hgh concentraton of Na s observed water 36

137 flow front and concentraton of Na s lower towards the furrow and left sde of the profle. Chlorde profle at 0.,, 3 and 5 days based on HP smulaton also show same result wth Na range of to mol/l. (a) (b) (c) 37

138 (d) Fgure 9.6f Na n mol/l profle at tmes a) 0., b), c) 3 and d) 5 days usng VSDRT smulaton Fgure 9.6g Na n mol/l profle at tmes a) 0., b), c) 3 and d) 5 days usng HP smulaton (Smunek, Jacques, Sena, & van Genuchten, 0) 38

139 9.7 D reactve transport The problem was taken from USGS Water-Resources Investgatons Report (p. 93) (Healy & Ronan, 996) and modfed to nclude reactve transport. It nvolves D nfltraton and evaporaton along wth reactve transport. The smulaton doman has 3 m wdth and. m heght and contans clay, sand and gravel textural classes as presented n fgure 9.7a. A gravel of 0.6m thck s overlad by.5m thck clay whch embeds 0.3m thck and.5m wde sand at depth of 0.4 m. The Brooks & Corey hydraulc parameters of clay, sand and gravel sols, chemcal propertes along wth the ntal flow condton and ntal soluton n the doman of smulaton s gven n table 9.6. The smulaton was conducted for 77 days wth four recharge perods and the recharge perod parameters are presented n table 9.7. Evaporaton and evapotranspraton related parameters were gven n table 9.8. The results of the smulaton are presented n fgures 9.7b, 9.7d to 9.7g for pressure head, Ca, Cl and Na at, 6, 33 and 77 respectvely. Fgure 9.5b and 9.5c depct temporal varaton of evaporaton and evapotranspraton rate smulated by VSDRT and VSD respectvely and shows that VSDRT smulaton of evaporaton and evapotranspraton are rather consstent wth that of VSD. Fgure 9.7a vertcal secton of smulaton doman (Lappala, Healy, & Weeks, 987) 39

140 Table 9.6 Hydraulc and geochemcal propertes, ntal and boundary condtons for D reactve transport Hydraulc propertes n terms of Brooks & Corey parameters Clay Sand Gravel K z /K x K s 5 cm/day 00 cm/day 300 cm/day Specfc storage e-6 e-6.e-6 θ θ r h b - 50 cm -5-8 λ 0.6. Geochemcal propertes α L m m α T molecular dffuson.e-06 Intal soluton ( mmol/kg water) Ca C Intal equlbrum head profle Water table depth at m Mnmum pressure head of - m Boundary condton soluton (mmol/kg water) Na Cl Table 9.7 Recharge perod parameters used for D reactve transport Recharge Perod Duraton (days) Type of boundary at the top Infltraton at 75mm/day rate and Pressure head of 4 m at the bottom 30 Evaporaton 3 Infltraton at 75mm/day rate 4 45 Evaporaton and Evapotranspraton Table 9.8 Evaporaton and evapotranspraton parameters used for D reactve transport smulaton Evaporaton perods PEVAL SRS HA Evapotranspraton PTVAL Root depth RA Bottom RA Top P.Head at Root perods

141 Flux cm3/days 0.00 Tme (days) Evaporaton Evapotranspraton Evaporaton + Evapotranspraton Fgure 9.7b VSDRT smulaton of evaporaton and evapotranspraton rates Fgure 9.7c VSD smulaton of evaporaton and evapotranspraton rates (Lappala, Healy, & Weeks, 987) 4

142 (a) (b) (c) Fgure 9.7d Pressure head profle based on VSDRT at a), b) 6, c) 33 and d) 77days respectvely (d) 4

143 (a) (b) (c) Fgure 9.7e Ca profle based on VSDRT at a), b) 6, c) 33 and d) 77days respectvely (d) 43

144 (a) (b) (c) Fgure 9.7f Cl profle based on VSDRT at a), b) 6, c) 33 and d) 77days respectvely ( d) 44

145 ( a) (b) (c) Fgure 9.7g Na profle based on VSDRT at a), b) 6, c) 33 and d) 77days respectvely (d) 45