HYDRUS - References. The HYDRUS Software Packages. HYDRUS models - Governing Equations. Industrial and Environmental Applications

Transcription

1 Advanced Modelng of Water Flow and Solute Transport n the Vadose Zone Usng HYDRUS models Agrcultural Applcatons Jrka Smunek Department of Envronmental Scences Unversty of Calforna Rversde George E. Brown, Jr. Salnty Laboratory, USDA, ARS Rversde, CA Unversty of Calforna, Davs May 6, 3 Industral and Envronmental Applcatons HYDRUS models - Governng Equatons Source Zone Observaton wells Control Planes Varably-Saturated Water Flow (Rchards Equaton) θ h = [ Kh ( ) Kh ( )] S z z Heat Movement Cp( θ ) T T qt = [ λθ ( ) ] Cw CwST z z z Solute Transport ( ρs) ( θ c) c + = ( θd qc) φ z z HYDRUS - References Šmunek, J., M. Šena, and M. Th. van Genuchten, The HYDRUS-D software package for smulatng one-dmensonal movement of water, heat, and multple solutes n varably saturated meda. Verson., IGWMC - TPS - 7, Internatonal Ground Water Modelng Center, Colorado School of Mnes, Golden, Colorado, pp., 998. Šmunek, J., M. Šena, and M. Th. van Genuchten, The HYDRUS-D software package for smulatng two-dmensonal movement of water, heat, and multple solutes n varably saturated meda. Verson., IGWMC - TPS - 53, Internatonal Ground Water Modelng Center, Colorado School of Mnes, Golden, Colorado, 5pp., 999. E-mal: gwmc@mnes.edu

2 HYDRUS-D - Hstory of Development Israel: Neuman [97] - UNSAT U. of Arzona: Davs and Neuman [983] Agr. U. n Wagenngen: Feddes et al. [978] Vogel [987] - SWMII USSL - SWMS-D Šmunek et al. [99] USSL - HYDRUS-D (.) Šmunek et al. [996] Prnceton U.: van Genuchten [978] MIT: Cela et al. [99] USSL - CHAIN-D Šmunek et al. [99] USSL - HYDRUS-D (.) Šmunek et al. [999] HYDRUS-D - Hstory (References) Neuman, S. P., Fnte element computer programs for flow n saturated-unsaturated porous meda, Second Annual Report, Part 3, Proect No. A-SWC-77, 87 p. Hydraulc Engneerng Lab., Technon, Hafa, Israel, 97. Davs, L. A., and S. P. Neuman, Documentaton and user's gude: UNSAT -Varably saturated flow model, Fnal Report, WWL/TM-79-, Water, Waste & Land, Inc., Ft. Collns, Colorado, 983. van Genuchten, Mass transport n saturated-unsaturated meda: One-dmensonal soluton, Research Rep. No. 78-WR-, Water Resources Program, Prnceton Unv., Prnceton, NJ, 978. Cela, M. A., and E. T. Bouloutas, R. L. Zarba, A general mass-conservatve numercal soluton for the unsaturated flow equaton, Water Resour. Res., 6(7), 83-96, 99. Vogel, T. SWMII - Numercal model of two-dmensonal flow n a varably saturated porous medum, Research Report No. 87, Dept. of Hydraulcs and Catchment Hydrology, Agrcultural Unv., Wagenngen, The Netherlands, 987. Šmunek, J., T. Vogel, and M. Th. van Genuchten. The SWMS_D code for smulatng water flow and solute transport n two-dmensonal varably saturated meda, Verson.. Research Report No. 6, 69 p., U.S. Salnty Laboratory, USDA, ARS, Rversde, Calforna, 99. HYDRUS Modular Structure HYDRUS Graphcal Interface Input, Output, Meshgen Water Flow Solute Transport Heat Transport HYDRUS Man Module Sol Hydraulc Propertes Pedotransfer Functons Root Uptake Equaton Solvers Inverse Optmzaton Water Flow - Rchards Equaton The governng flow equaton for two-dmensonal sothermal Darcan flow n a varably saturated sotropc rgd porous medum: θ = t x K ( K A h x + K A z θ - volumetrc water content [L 3 L -3 ] h - pressure head [L] K - unsaturated hydraulc conductvty [LT - ] K A - components of a ansotropy tensor [-] x - spatal coordnates [L] z - vertcal coordnate postve upward [L] t - tme [T] S - root water uptake [T - ] ) S Rchards Equaton - Assumptons Effect of ar phase s neglected Darcy s equaton s vald at very low and very hgh veloctes Osmotc gradents n the sol water potental are neglgble Flud densty s ndependent of solute concentraton Matrx and flud compressbltes are relatvely small

3 Sol Hydraulc Propertes Retenton Curve, θ(h) (Sol-water characterstc curve) - characterzes the energy status of the sol water Pressure head [cm] 5 3 Loam Sand Clay Water Content [-] Sol Hydraulc Propertes Hydraulc Conductvty Functon, K(h) - resstance of porous meda to water flow log (Hydraulc Conductvty [cm/d]) log ( Pressure Head [cm]) Loam Sand Clay Sol Hydraulc Propertes Hydraulc Conductvty Functon, K(θ) log (Hydraulc Conductvty [cm/d]) Loam Sand -8 Clay Water Content [-] Retenton Curve Brooks and Corey [96]: van Genuchten [98]: Kosug [996]: θ s - saturated water content [-] θ r - resdual water content [-] α, n, h, σ - emprcal parameters [L - ], [-], [L], [-] S e - effectve water content [-] -n α h h < -/ α S e = h -/ α S = e / ( α h n + ) n ( h h ) σ ln / Se = erfc θ θr Se = θ θ s r Hydraulc Conductvty Functon Brooks and Corey [96]: Kh ( ) = K s S / n + l + e Sol Water Retenton Curve, (h) van Genuchten [98]: (Mualem [976]) / m ( ) l K( h) = K S S S e e m Kosug [996]: (Mualem [976]) θ s - saturated water content [-] θ r - resdual water content [-] α, n, h, σ, l - emprcal parameters [L - ], [-], [L], [-], [-] S e - effectve water content [-] Κ S - saturated hydraulc conductvty [LT - ] ( h h ) σ l ln / Kh ( ) = KS s e erfc + σ θ θr Se = θ θ s r

4 Hydraulc Conductvty Functon, K() Rchards Equaton - Complcatons Hysteress n the sol water retenton functon Extreme nonlnearty of the hydraulc functons Lack of accurate and cheap methods for measurng the hydraulc propertes Extreme heterogenety of the subsurface Inconsstences between scale at whch the hydraulc and solute transport parameters are measured, and the scale at whch the models are beng appled Sol Water Hysteress Boundary Condtons: System-Independent Pressure head (Drchlet type) boundary condtons: h( x, z, t) = ψ ( x, z, t) for ( x, z) ε Flux (Neumann type) boundary condtons: Γ D h - [ K ( K + K )] n = σ ( x, z, t) for ( x, z) ε Γ x A A z N Gradent boundary condtons: A h A ( K + K z ) n = σ ( x, z, t) for ( x, z) ε Γ x G Boundary Condtons: System-Dependent Atmospherc boundary condton: h -K -K E ha h hs x Pondng Boundary Condtons: System-Dependent Seepage face (free dranng lysmeter, dke) f(h<) => q= f(h=) => q=? Tle drans D sol profle Sol surface Groundwater table Tme [days] Tme [days] Tle dran Impermeable layer

5 Root Water Uptake Bresler et al. [98] S( z,t ) = - b ( z) K( )[ h -h( z,t) ] θ Feddes et al. [978] S( z,t ) = - b ( z) α ( h( z,t )) T p r van Genuchten (987): Y / Ym ( c/ c5) = + p General structure of the system of solutes: Products Products µ g, µ w, µ s, µ g, µ w, µ s, A µ w, B µ w, C... g c s µ s, g c s µ s, k g, k s, µ g, k g, k s, µ g, γ g, γ w, γ s, γ g, γ w, γ s, Products Products Typcal examples of sequental frst-order chans: Radonucldes [van Genuchten, 985] 38 Pu 3 U 3 Th 6 Ra c s c s c 3 s 3 c s Ntrogen [Tllotson et al., 98] g N (NH ) CO NH + NO - NO - 3 c s c s c 3 c N O

6 Typcal examples of sequental frstorder chans: Pestcdes [Wagenet and Hutson, 987] Unnterrupted chan - one reacton path: Gas Parent Daughter Daughter pestcde product product Products c s c s c 3 s 3 Product Product Product (aldcarb, oxme) (sulfone, sulfone oxme) (sulfoxde, sulfoxde oxme) Interrupted chan - two ndependent reacton paths: Gas Gas Typcal examples of sequental frstorder chans: Organc Hydrocarbons Dechlornaton of chlornated ethenes [Schaerlaekens et al., 999; Casey and Smunek, ] t-dce PCE TCE c-dce VC ethylene,-dce Parent Daughter Parent pestcde product Products pestcde Products c s c s c 3 s 3 c s Product Product Product Perchloroethylene trchloroethylene dchloroethylene vnylchlorde Typcal Examples of Sequental Frstorder Chans: Pharmaceutcals and Explosves Pharmaceutcals, hormones (Estrogen, Testosterone): Estradol Estrone Estrol Explosves (TNT, RDX HMX) ADNT TNT ADNT ADNT ADNT TAT,,6 trntrotoluene -amno-,6-dntrotoluene -amno-,6-dntrotoluene,,6-trmnotoulene Governng Solute Transport Equatons θc ρs ag c g qc + + = ( θ ) + ( a )- - -( µ + µ ) -( µ + µ ) -( µ + µ ) a + + µ (, ) k k k w k g k k D,k D,k t t t x x x x x ' ' ' ' θ w,k w,k ck ρ s,k s,k sk g,k g,k g µ k w,k θck- ' ' s,k ρ sk -µ g,k a g k + γ w,kθ+ γ s,kρ+ γ g,ka Scr, k kε ns w, s, g subscrpts correspondng wth the lqud, sold and gaseous phases, respectvely c, s, g concentraton n lqud, sold, and gaseous phase, respectvely,dant;,6dant;,dnt;,6dnt Governng Solute Transport Equatons q -th component of the volumetrc flux ρ sol bulk densty a ar content S snk term n the water flow equaton c r concentraton of the snk term D w,d g dsperson coeffcent tensor for the lqud and gaseous phase, respectvely k subscrpt representng the kth chan number µ w, µ s, µ g frst-order rate constants for solutes n the lqud, sold, and gaseous phases, respectvely γ w, γ s, γ g zero-order rate constants for the lqud, sold, and gaseous phases, respectvely µ w ', µ s ', µ g ' frst-order rate constants for solutes n the lqud, sold and gaseous phases, respectvely; these rate constants provde connectons between the ndvdual chan speces. number of solutes nvolved n the chan reacton n s

7 3 3 Interactons Among Phases Lnear Adsorpton s = Rθ c t Steady-State R c t kc c = θ + φ D q c x x c c = D v z z Nonlnear Equlbrum Adsorpton + k c Equaton Model Reference s=kc+k Lnear Lapdus and Amundson [95] Lndstrom et al. [967] s=k c k Freundlch Freundlch [99] k c Langmur Langmur [98] s = + k c k k c Freundlch-Langmur Sps [95] s = k + k c k c + k c k 3 c Double Langmur Shapro and Fred [959] s= c s=k c k / k 3 Extended Freundlch Sbbesen [98] k c Gunary Gunary [997] s = + k c + k 3 c k s=kc - k Ftter-Sutton Ftter and Sutton [975] 3 s=k - + k c k 3 k { [ ] } Barry Barry [99] RT ln( ) Temkn Bache and Wllams [97] s = k c k s=k cexp( - k s) Lndstrom et al. [97] van Genuchten et al. [97] s = c modfed Kelland La and Jurnak [97] st [ c+ k( ct c)exp{ k( ct c)}] Interactons Among Phases Equlbrum nteractons between the soluton (c) and gaseous (g) concentratons (Henry s law) Nonequlbrum nteractons between the soluton (c) and adsorbed (s) concentratons A generalzed nonlnear emprcal equaton β kc d s= + c β η k d, η, β emprcal constants Non-Equlbrum Adsorpton Equatons Nonequlbrum two-ste adsorpton model [95] Equaton Model Reference s Lnear Lapdus and Amundson Oddson et al. [97] s k = α ( kc -s) Freundlch Hornsby and Davdson [973] t van Genuchten et al. [97] s kc = α - s +k c Langmur Hendrcks [97] s k3 kc = α - s Freundlch- Šmunek and van Genuchten [99] k3 +k c Langmur s s - s T Fava and Eyrng [] = α ( s -s)snh T k t s - T s s α exp( k s ){ k c exp( - k s ) -s } Lndstrom et al. [97] s = c k s k α Leenheer and Ahlrchs [97] Enfeld et al. [976] s e k s k k f s k= s e k+ sk k Type - stes wth nstantaneous sorpton Type - stes wth knetc sorpton e sk sk = f k β s k k ks,k c k k k = αk ( - f k) - µ γ β sk - s,k sk + ( - f ) + η k kck fracton of exchange stes assumed to be at equlbrum s,k

8 Two-Regon Physcal Nonequlbrum Transport +f k c = D c m ( θ m ρ D) m ( θ m m -qc )-α( c -c )-( θµ + fρ k µ ) c z z m m m l,m D s,m m cm [ θ m + ( - f) ρkd] = α( c - c )-[ θ µ + ( - f) ρ k µ ] c m m m l,m D s,m m Interacton among phases Lqud - Gas: a lnear relaton g = k gc k g,k emprcal constant equal to (K H RT A ) - K H R T A Henry's Law constant unversal gas constant absolute temperature Volatlzaton ( ρs) ( θc) ( ) + + ag = ( θd c ) φ x x +ad g w a w a -q c-q g + x Steady-State: g = kh c w ρ k ak q q D H c w a a c = D + D k - θ θ H θ x x θ a k H c x Temperature Dependence of Transport and Reacton Coeffcents Most of the dffuson (D w, D g ), dstrbuton (k s, k g ), and reacton rate (γ w, γ s, γ g, µ w ', µ s ', µ g ', µ w, µ s, and µ g ) coeffcents are strongly temperature dependent. HYDRUS_D assumes that ths dependency can be expressed by an Arrhenus equaton [Stumm and Morgan, 98]. A A E( T - T r ) at = ar exp A A RT T r a r,a T coeffcent values at a reference absolute temperature, T ra, and absolute temperature, T A, respectvely E actvaton energy of the reacton or process Solute Transport - Dsperson Coeffcent Bear [97]: q q θ D = D T q δ + ( D L - D T ) q + θ D D d - onc or molecular dffuson coeffcent n free water [L T - ] τ - tortuosty factor [-] δ - Kronecker delta functon (δ = f =, and δ = otherwse) D L, D T - longtudnal and transverse dspersvtes [L] q x q z θ D xx = D L + DT + θ Dd τ q q q z q x θ D zz = D L + DT + θ Dd τ q q q x q z θ D xz = ( D L - DT) q d τ δ

9 Solute Transport - Boundary Condtons Frst-type (or Drchlet type) boundary condtons c( x, z, t ) = c ( x, z, t ) for( x, z ) ε Γ D Thrd-type (Cauchy type) boundary condtons c - θ D n + qnc = q nc for ( x, z ) ε Γ x Second-type (Neumann type) boundary condtons c θ D n = for ( x, z ) ε Γ x C N Dspersvty as a functon of scale Governng Heat Transport Equaton Sophocleous [979] T C t = T x x - ( θ) [ λ C q T ( θ) ] w x λ (θ) apparent thermal conductvty of the sol C(θ), C w volumetrc heat capactes of the porous medum and the lqud phase, respectvely de Vres [963] C ( θ ) = C θ + C θ + C θ + C a n n o o w g θ volumetrc fracton n, o, g, w subscrpts representng sold phase, organc matter, gaseous phase, and lqud phase, respectvely. Thermal Conductvty λ ( θ ) = λt C w q δ + ( λ L -λt ) C q q w + λ( θ ) δ q λ (θ) thermal conductvty of the porous medum (sold plus water) n the absence of flow λ L, λ T longtudnal and transverse thermal dspersvtes, respectvely Chung and Horton [987] b, b, b 3 ( ) = b + b + b 5. λ θ θ w 3θ w emprcal parameters.

10 Pedotransfer Functons: Rosetta Schaap et al. () Model Input Data TXT Textural Class SSC Sand, Slt, Clay % SSCBD Same + Bulk Densty SSCBD + 33 SSCBD + at 33 kpa SSCBD Same + at 5 kpa Estmaton of Sol Hydraulc Propertes Wth Artfcal Neural Networks Log Sucton [cm] 3 Sand Retenton Clay...6 Water Content [cm 3 /cm 3 ] Sand Clay Sand % 79 8 Slt % 3 9 Clay % 8 3 Bulk d..5. Probablty Saturated Conductvty.5..5 Sand. Clay.5 Log K(h) [cm/day] Log(K s ) [cm/day ] Unsaturated Conductvty Clay 3 Sand 3 Log Sucton [cm] Parameter Estmaton n HYDRUS Parameter Estmaton: - Sol hydraulc parameters - Solute transport and reacton parameters - Heat transport parameters Sequence: - Independently - Smultaneously - Sequentally Method: - Marquardt-Levenberg optmzaton Obectve Functon Φ ( b, q, p ) = m q n q * v w, [ q = = m p n p * v w, [ p = = n b * vˆ [ b - b ] = ( x, t ) - q ( θ ) - ( x, t, b ) ] + p ( θ, b ) ] + st term: devatons between measured and calculated space-tme varables nd term: dfferences between ndependently measured, p *, and predcted, p, sol hydraulc propertes 3rd term: penalty functon for devatons between pror knowledge of the sol hydraulc parameters, b *, and ther fnal estmates, b.

11 Furrow Irrgaton Pressure Heads Dke Pressure Heads Dke - Velocty Vectors Fnte Element Mesh Cut-off Wall Solute Plume Under Dam Capllary Barrer - Materal Dstrbutons

12 Capllary Barrer - Velocty Vectors Mesh Generator Tunnel - Spectral Color Maps Tunnel - Velocty Vectors Plume Movement n a Transect wth Stream HYDRUS - Exstng Applcatons Agrcultural: Irrgaton management (FREP, LINK, Brstow et al., ) Drp rrgaton desgn (FREP, LINK, Brstow et al., ) Sprnkler rrgaton desgn (FREP, LINK) Tle dranage desgn and performance (Mohanty et al., 998, do Vos et al., ) Studes of root and crop growth (Vrugt et al.,, ) Salnzaton and reclamaton processes (Šmůnek and Suarez, 998) Ntrogen dynamcs and leachng (Ventrella et al., ; Jacques et al., ) Transport of pestcdes and degradaton products (Wang et al., 998) Non-pont source polluton Seasonal smulaton of water flow and plant response...

13 HYDRUS - Exstng Applcatons Non-Agrcultural: Leachng from radoactve waste stes at the Nevada test Ste (DRI, DOE) Flow around nuclear subsdence craters at the Nevada test ste (Pohll et al., 996; Wlson et al., ) Capllary barrer at Texas low-level radoactve waste dsposal ste (Scanlon, 998) Evaluaton of approxmate analytcal analyss of capllary barrers (Morrs and Stormont, 997; Kampf and Montenegro, 997; Heberger, 998) Landfll covers wth and wthout vegetaton (Abbaspour et al, 997; Albrght, 997; Gee et al., 999, Scanlon et al., ) Rsk analyss of contamnant plumes from landflls Seepage of wastewater from land treatment systems Tunnel desgn - flow around bured obects (Knght, 999) Hghway desgn - road constructon - seepage (de Haan, ) Stochastc analyses of solute transport n heterogeneous meda (Tseng and Jury, 993; Roth, 995; Roth and Hammel, 996; Kasteel et al. 999; Hammel et al., 999; Roth et al., 999; Vanderborght et al., 998, 999) Lake basn recharge analyss (Lee, ) HYDRUS - Exstng Applcatons Non-Agrcultural: Stream-aqufer nteractons Envronmental mpact of the drawdown of shallow water tables Analyss of cone permeameter and tenson nfltrometer experments (Grbb et al., 996; Kodesova et al., 998, 999; Šmůnek et al., 997, 998, 999) Vrus and bactera transport (Shven and Šmůnek,, Bradford et al., a,b, Yates et al., ) Hll-slope analyses Transport of TCE and ts degradaton products (Scharlaekens et al., ; Casey and Smunek, ) Multcomponent geochemcal transport (Jacques and Šmůnek, ) Analyses of rparan systems (Whtaker, ) Flud flow and chemcal mgraton wthn the capllary frnge (Sllman et al., ) Flow n hstorcal monuments (Ishzak et al., ) Flow and transport around land mnes (Das et al., ; Šmůnek et al., ) Analyses of Chlorde profles n deep vadose zones to evaluate hstorcal fluxes (Scanlon et al., 3) Current and Future Development Coupled movement of water and energy, ncludng vapor transport Modfed Rchards Equaton: θ Lh ( ) K h K Lh ( h) K LT ( h) T K h T = vh + KvT S z z z z z K Lh - hydraulc conductvty for lqud phase fluxes due to gradent n h K LT - hydraulc conductvty for lqud phase fluxes due to gradent n T K vh - sothermal vapor hydraulc conductvty K vt - thermal vapor hydraulc conductvty Energy Transport: C T p v T l v v L λ( θ ) C qt q + = qt w CwST L Cv z z z z z () () (3) () (5) () Sol heat flow by conducton () Convecton of sensble heat by water flow (3) Heat removed by root water uptake () Transfer of latent heat by dffuson of water vapor (5) Transfer of sensble heat by dffuson of water vapor Coupled Movement of Water and Energy Coupled movement of water and energy yrs Central kyr 5 kyr Hgh Plans 5 9 kyr Feld Amargosa Desert yrs kyr 3 5 kyr 6 kyr Feld Lab 5 kyr 5 kyr 9 kyr Measured kyr kyr 6 kyr Measured Depth [cm] 8 6 T= t=.5 d t= t=5 t=5 8 6 T= t=.5 d t= 8 t=5 t=5 6 T= t=.5 d t= t=5 t=5 8 6 T= t=.5 d t= t=5 t=5 5 5 Eagle Flat yrs 5 kyr kyr Feld Feld - OP kyr kyr Measured Water Content [-] Total Flux [cm/d] Temperature [C] Concentraton [-] Hueco Bolson 5 yrs kyr 5 5 kyr 3 kyr Feld kyr kyr 3 kyr Measured Smulated matrc potentals and chlorde concentratons from wet ntal condtons (pluval perod) to dfferent tmes of upward flow. (Scanlon et al. 3) Total flux=water flux+vapor flux

14 Coupled movement of water and energy, freezng/thawng cycle Modfed Rchards Equaton: θ ρ θ h T h T + = K Lh ( h) + K Lh ( h) + K LT ( h) + Kvh + KvT S ρ w z z z z z K Lh - hydraulc conductvty for lqud phase fluxes due to gradent n h K LT - hydraulc conductvty for lqud phase fluxes due to gradent n T K vh - sothermal vapor hydraulc conductvty - thermal vapor hydraulc conductvty K vt Energy Transport: C T p v T l v v L θ L f ρ + = λ( θ ) C qt q qt w CwST L C v z z z z z (6) () () (3) () (5) () Sol heat flow by conducton () Convecton of sensble heat by water flow (3) Heat removed by root water uptake () Transfer of latent heat by dffuson of water vapor (5) Transfer of sensble heat by dffuson of water vapor (6) Freezng/thawng term Coupled Movement of Water and Energy, Freezng/thawng Cycle Apparent Capacty [Jm -3 K - ] Apparent Capacty [Jm -3 K - ].E+.E+.E+.E+9.E+8.E+7.E+6..E+.E+.E+.E+9.E+8.E+7.E Temperature [ o C] Temperature [ o C] -.8 Slty clay Loam Sand -.5 Slty clay Loam Sand Apparent heat capacty for dfferent textures Coupled movement of water and energy Freezng/thawng cycle Slty Clay Depths (cm):,.5.,, 3.5, 5, Heterogenety, Layerng Tme [days] Tme [days] Tme [days] Tme [days] Nonequlbrum and Preferental Flow and Transport Dual-porosty approach (Rchards eq. for water, moblemmoble concept for solute) Dual-porosty approach (moble-mmoble concept for both water and solute) Dual-permeablty approach (two overlappng porous meda, one for matrx flow, one for preferental flow) [Gerke and van Genuchten, 993] Knematc wave approach for flow n macropores [Jarvs, 99] Smplfed frst-order approach [Ross and Smettem, ] θ θe θ = f( θθ, e) = τ Dual-porosty hydraulc property models [Durner, 99] Desgn experments that would provde parameters for above models

15 Dual-permeablty Approach Gerke and van Genuchten [993]: (two overlappng porous meda, one for matrx flow, one for preferental flow) Flux [cm/d] Fracture Flux Matrx Flux Mass Transfer Mass Transfer (-5%) Mass Transfer (+5%) Tme [d] Depth [cm] 5 5 t =. d 5 t =. d t =.8 d 3 t =.8 d (-5%) 35 t =.8 d (+5%) Water Content [-] Depth [cm] 5 t =. d t =. d t =.8 d 5 t =.8 d (-5%) t =.8 d (+5%) Water Content [-] Infltraton and mass exchange fluxes (a), water contents n the matrx (b) and fracture (c) domans Multcomponent solute transport: Couplng HYDRUS and PHREEQC [Parkhurst and Appelo, 999]) Avalable chemcal reactons: Aqueous complexaton Redox reactons Ion exchange (Gans-Thomas) Surface complexaton dffuse double-layer model and nonelectrostatc surface complexaton model Precptaton/dssoluton Chemcal knetcs Bologcal reactons Verfcaton of HYDRUS-PHREEQC Transport and Caton Exchange (maor ons and heavy metals): (catons - Ca, Mg, Na, K, Cd, Pb, Zn; anons Cl, Br, Al) a) Intally the 8-cm column contans a soluton (wth heavy metals) n equlbrum wth the caton exchanger. b) The column s then flushed wth three pore volumes of soluton wthout heavy metals. Parameters: q= cm/d, λ=. cm, CEC= mmol/cell. Intal concentratons: Al=.5, Br=.9, K=, Na=6, Mg=.75, Cd=.9, Pb=., Zn=.5 mmol/l. Boundary concentraton: Al=., Br=3.7, Cl=, Ca=5, Mg= mmol/l. Speces and Complexes: Al 3+, Al(OH) +, Al(OH) +, Al(OH) 3, Al(OH) -, Br -,Cl -, Ca +, Ca(OH) +, Cd +, Cd(OH) +, Cd(OH), Cd(OH) 3-, Cd(OH) -, CdCl +, CdCl, CdCl 3-, K +, KOH, Na +,NaOH, Mg +, Mg(OH) +, Pb +, Pb(OH) +, Pb(OH), Pb(OH) 3-, Pb(OH) -,PbCl +, PbCl, PbCl 3-, PbCl -, Zn +, Zn(OH) +, Zn(OH), Zn(OH) 3-, Zn(OH) -, ZnCl +, ZnCl, ZnCl 3-, ZnCl Exchange Speces: AlX 3, AlOHX, CaX, CdX, KX, NaX, MgX, PbX, ZnX Verfcaton of HYDRUS-PHREEQC Transport and caton exchange of maor catons and heavy metals Concentraton (mol/l) Concentraton (mol/l) Na Al Cl Ca Tme (days) ZnX CdX CaX Tme (days) Concentraton (mol/l) 8E- 6E- E- E- E+ Relatve mass balance errors (%) Pb Cd Zn Tme (days) Cl Ca Al Cd Zn Tme (days) Verfcaton of HYDRUS-PHREEQC Knetc bodegradaton of NTA (ntrylotracetate), cell growth, complexaton wth Co, and knetc sorpton Processes: Bacterally medated degradaton of an organc substrate Bacteral cell growth and death Aqueous specaton ncludng metal-lgand complexaton Knetc sorpton of Co and CoNTA Convectve dspersve transport Parameters: L=m, θ s =. m, ρ=.5 kg/m 3, v= m/h,, λ=.5 m. Intal Cond.: O =3.5e-5, Na=., Cl=. mol/l, Bomass=.36g/L Boundary Cond.: O =3.5e-5, Co=5.3e-6, NTA=5.3e-6, Na=., Cl=. mol/l Verfcaton of HYDRUS-PHREEQC Knetc bodegradaton of NTA, cell growth, complexaton wth Co, and knetc sorpton Rate equatons: NTA degradaton: RHNTA = qm X [ HNTA ] [ O ] K s + [ HNTA ] Ka + [ O ] m Bomass producton: R cell = YR HNTA Knetc sorpton (Co +,CoNTA - ): Z [ ] R Z = k m Z K d X m bomass K s, K a half-saturaton constants Z speces concentraton bx m Concentratons [mol/g].6e-9.e-9 8.E-.E-.E+ Sorbed Co - PHREEQC Sorbed CoNta Sorbed Co - HYDRUS Sorbed CoNta Bomass Bomass Tme [hours].e- 3.E-.E-.E-.E+ Bomass [g/l]

16 Verfcaton of HYDRUS-PHREEQC Knetc bodegradaton of NTA, cell growth, complexaton wth Co, and knetc sorpton Concentraton [mol/kg] CoNTA HNTA Co CoNTA HNTA Co ph ph Tme [hours] Ph Constructed Wetlands Components: Dssolved oxygen O Organc matter: readly bodegradable, slowly bodegradable, nert Ntrogen: NH +, NO -, NO 3-, N Inorganc phosphorus Heterotrophc mcro-organsms Autotropc mcro-organsms: Ntrosomonas & Ntrobacter 9 Processes: Heterotrophc Organsms Hydrolyss Aerobc growth of heterotrophs on readly bodegradable OM NO 3 -growth of heterotrophs on readly bodegradable OM NO -growth of heterotrophs on readly bodegradable OM Lyss Ntrosomonas Aerobc growth of N.somonas on NH Lyss of n-somonas Aerobc growth of N.bacter on NO Lyss of N.bacter Ntrobacter Overland Flow Knematc wave equaton: h Q + = qxt (, ) Q= αh x h - unt storage of water (or mean depth), Q -dscharge per unt wdth, q(x,t) - rate of local nput, or lateral nflows (precptaton - nfltraton) Mannng hydraulc resstance law: / S α =.9 and m = 5/ 3 n n - Mannng s roughness coeffcent for overland flow S -slope m *.5 m HYDRUS-3D - Prevew HYDRUS-3D - Prevew HYDRUS Web Ste FAQ

17 HYDRUS Web Ste Tutorals HYDRUS Web Ste Dscusson Forum HYDRUS-D User Manual Davd Rassam, Jrka Šmůnek and Ren Van Genuchten Introductory examples. A Journey Through HYDRUS Wndows.. Pre-Processng.. Post-Processng. HYDRUS Output Fles 3. Root Water Uptake. Example Applcaton 5. Inverse Soluton 6. Trouble Shootng Appendces: I. Sol Hydraulc Propertes II. Concept Related to Modellng Evaporaton III. Root Water Uptake IV. Scalng Factors V. Inverse Soluton VI. Alphabetcal Index for HYDRUS Wndows