HYDRUS Lecture - Nevada Agricultural Experiment Station

Transcription

Advanced Modeling of Water Flow and
Solute Transport in the Vadose Zone
Agricultural
Applications
Using HYDRUS models
Jirka Simunek
Department of Environmental Sciences
University of California Riverside
George E. Brown, Jr. Salinity Laboratory, USDA, ARS
Riverside, CA
University of California, Davis
May 26, 2003
Industrial and Environmental Applications
HYDRUS models - Governing Equations
Variably-Saturated Water Flow (Richards Equation)
∂θ
∂
∂h
= [ K ( h) − K ( h)] − S
∂t ∂z
∂z
Observation wells
Heat Movement
∂C p (θ )T
∂t
Source Zone
=
∂
∂T
∂qT
− C w ST
[λ (θ ) ] − C w
∂z
∂z
∂z
Solute Transport
Control Planes
The HYDRUS Software Packages
Variably-Saturated Flow (Richards Eq.)
Root Water Uptake (water, salinity stress)
Multiple Solutes (decay chains, ADE)
Nonlinear Sorption
Two-Site Nonequilibrium Sorption
Mobile-Immobile Water
Heat Transport
Pedotransfer Functions (hydraulic properties)
Parameter Estimation
Interactive Graphics-Based Interface
∂ ( ρ s ) ∂ (θ c ) ∂
∂c
+
= (θ D − qc ) − φ
∂t
∂t
∂z
∂z
HYDRUS - References
Šimunek, J., M. Šejna, and M. Th. van Genuchten, The HYDRUS-1D
software package for simulating one-dimensional movement of water, heat,
and multiple solutes in variably saturated media. Version 2.0, IGWMC - TPS
- 70, International Ground Water Modeling Center, Colorado School of
Mines, Golden, Colorado, 202pp., 1998.
Šimunek, J., M. Šejna, and M. Th. van Genuchten, The HYDRUS-2D
software package for simulating two-dimensional movement of water, heat,
and multiple solutes in variably saturated media. Version 2.0, IGWMC - TPS
- 53, International Ground Water Modeling Center, Colorado School of
Mines, Golden, Colorado, 251pp., 1999.
E-mail: [email protected]
http://www.mines.edu/igwmc
http://www.ussl.ars.usda.gov/models/hydrus2d.HTM
http://www.pc-progress.cz
HYDRUS-2D - History of Development
Israel: Neuman [1972] - UNSAT
U. of Arizona: Davis and Neuman [1983]
Princeton U.:
van Genuchten [1978]
MIT:
Celia et al. [1990]
Agr. U. in Wageningen:
Feddes et al. [1978]
Vogel [1987] - SWMII
USSL - SWMS-2D
Šimunek et al. [1992]
USSL - HYDRUS-2D (1.0)
USSL - CHAIN-2D
USSL - HYDRUS-2D (2.0)
HYDRUS –Modular Structure
HYDRUS-2D - History (References)
Neuman, S. P., Finite element computer programs for flow in saturated-unsaturated
porous media, Second Annual Report, Part 3, Project No. A10-SWC-77, 87 p.
Hydraulic Engineering Lab., Technion, Haifa, Israel, 1972.
Davis, L. A., and S. P. Neuman, Documentation and user's guide: UNSAT2 - Variably
saturated flow model, Final Report, WWL/TM-1791-1, Water, Waste & Land, Inc., Ft.
Collins, Colorado, 1983.
van Genuchten, Mass transport in saturated-unsaturated media: One-dimensional
solution, Research Rep. No. 78-WR-11, Water Resources Program, Princeton Univ.,
Princeton, NJ, 1978.
Celia, M. A., and E. T. Bouloutas, R. L. Zarba, A general mass-conservative numerical
solution for the unsaturated flow equation, Water Resour. Res., 26(7), 1483-1496, 1990.
Vogel, T. SWMII - Numerical model of two-dimensional flow in a variably saturated
porous medium, Research Report No. 87, Dept. of Hydraulics and Catchment
Hydrology, Agricultural Univ., Wageningen, The Netherlands, 1987.
Šimunek, J., T. Vogel, and M. Th. van Genuchten. The SWMS_2D code for simulating
water flow and solute transport in two-dimensional variably saturated media, Version
1.1. Research Report No. 126, 169 p., U.S. Salinity Laboratory, USDA, ARS,
Riverside, California, 1992.
HYDRUS Graphical Interface
Input, Output, Meshgen
HYDRUS – Main Module
Water Flow
Soil Hydraulic Properties
Pedotransfer Functions
Solute Transport
Heat Transport
Root Uptake
Equation Solvers
Inverse Optimization
Water Flow - Richards’ Equation
The governing flow equation for two-dimensional isothermal
Darcian flow in a variably saturated isotropic rigid porous medium:

∂θ
∂ 
A ∂h
=
+ K izA )  − S
 K ( K ij
∂t
∂ x i 
∂x j

θ
- volumetric water content [L3L-3]
h - pressure head [L]
K - unsaturated hydraulic conductivity [LT-1]
KijA - components of a anisotropy tensor [-]
xi - spatial coordinates [L]
z - vertical coordinate positive upward [L]
t
- time [T]
S - root water uptake [T-1]
Nonlinear Sorption
Heat Transport
Richards Equation - Assumptions
Effect of air phase is neglected
Darcy’s equation is valid at very low and very high
velocities
Osmotic gradients in the soil water potential are negligible
Fluid density is independent of solute concentration
Matrix and fluid compressibilities are relatively small
Retention Curve, θ(h)
Hydraulic Conductivity Function, K(h)
(Soil-water characteristic curve)
- resistance of porous media to water flow
- characterizes the energy status of the soil water
log (Hydraulic Conductivity [cm/d])
4
500
Loam
|Pressure head| [cm]
400
Sand
Clay
300
200
100
2
Loam
Sand
0
Clay
-2
-4
-6
-8
-10
0
0
0
0.1
0.2
0.3
0.4
1
2
3
4
5
log (|Pressure Head| [cm])
0.5
Water Content [-]
Retention Curve
Hydraulic Conductivity Function, K(θ)
Brooks and Corey [1964]:
log (Hydraulic Conductivity [cm/d])
4
van Genuchten [1980]:
2
0
-2
 |α h |- n
Se = 
 1
Se =
Kosugi [1996]:
-4
Se =
-6
Loam
θs - saturated water content [-]
θr - residual water content [-]
α, n, h0, σ - empirical parameters [L-1], [-], [L], [-]
Sand
-8
Clay
-10
0
0.1
0.2
0.3
0.4
0.5
Se - effective water content [-]
W a ter Content [-]
Brooks and Corey [1964]:
K (h) = K s S e2 / n + l + 2
van Genuchten [1980]:
(Mualem [1976])
K ( h ) = K S S el 1 − 1 − S e1 / m



2
Kosugi [1996]:
(Mualem [1976])
 ln ( h / h0 )
 
 1
+ σ 
K (h) = K s Sel  erfc 
2σ

 
 2
2
θs - saturated water content [-]
θr - residual water content [-]
α, n, h0, σ, l - empirical parameters [L-1], [-], [L], [-], [-]
Se - effective water content [-]
ΚS - saturated hydraulic conductivity [LT-1]
Se =
θ − θr
θs − θr
1
n
(1 + α h )1−1/ n
 ln ( h / h0 ) 
1
erfc 

2
2σ 

Se =
θ − θr
θs − θr
Soil Water Retention Curve, 2(h)
Hydraulic Conductivity Function
(
h < -1/α
h ≥ -1/α
)
m
Hydraulic Conductivity Function, K(2)
Richards Equation - Complications
Hysteresis in the soil water retention function
Extreme nonlinearity of the hydraulic functions
Lack of accurate and cheap methods for measuring
the hydraulic properties
Extreme heterogeneity of the subsurface
Inconsistencies between scale at which the
hydraulic and solute transport parameters are
measured, and the scale at which the models are
being applied
Soil Water Hysteresis
Boundary Conditions: System-Independent
Pressure head (Dirichlet type) boundary conditions:
h ( x, z, t ) = ψ ( x, z, t )
for ( x, z ) ε Γ D
Flux (Neumann type) boundary conditions:
- [ K ( K ijA
∂h
+ K izA )] n i = σ 1( x, z , t )
∂x j
for ( x , z ) ε Γ N
Gradient boundary conditions:
( K ijA
Boundary Conditions: System-Dependent
∂h
- K |≤ E
∂x
for ( x , z ) ε Γ G
Boundary Conditions: System-Dependent
Seepage face (free draining lysimeter, dike)
if(h<0) => q=0
if(h=0) => q=?
Atmospheric boundary condition:
|- K
∂h
+ K izA ) n i = σ 2 ( x , z , t )
∂xj
h A ≤ h ≤ hS
Tile drains
Ponding
0
-20
-20
-25
Soil surface
1D soil profile
-30
-40
Groundwater table
-35
-40
-60
-45
-80
Tile drain
-50
-100
0
0.025
0.05
Time [days]
0.075
0.1
-55
0.00
0.05
0.10
Time [days]
0.15
0.20
Impermeable layer
Root Water Uptake
Nonlinear Sorption
Heat Transport
van Genuchten (1987):
Y / Ym =
Bresler et al. [1982]
S ( z, t ) = - b1 ( z ) K (θ ) [ hr - h( z, t ) ]
Feddes et al. [1978]
S ( z ,t ) = - b 2 ( z ) α 1 ( h ( z ,t )) T
1
1 + (c / c 50) p
p
Nonlinear Sorption
Heat Transport
General structure of the system of solutes:
Products
Products
µg,1 µw,1 µs,1
µg,2 µw,2 µs,2
A
g1 c1 s1
kg,1 ks,1
γg,1 γw,1 γs,1
Products
µw,1
µs,1
µg,1
B
g2 c2 s2
kg,2 ks,2
γg,2 γw,2 γs,2
Products
Typical examples of sequential
first-order chains:
Radionuclides [van Genuchten, 1985]
238Pu
234U
230Th
c1 s 1
µw,2
µs,2
µg,2
C
...
c2 s 2
c3 s 3
226Ra
c4 s 4
Nitrogen [Tillotson et al., 1980]
g2
(NH2) 2CO
c1 s1
NH4+
c2 s2
N2
NO2c3
NO3c4
N2O
Typical examples of sequential firstorder chains: Pesticides [Wagenet and Hutson, 1987]
Uninterrupted chain - one reaction path:
Dechlorination of chlorinated ethenes
Gas
Parent
pesticide
c1 s1
Product
(aldicarb, oxime)
Daughter
product 1
Daughter
product 2
c2 s2
Typical examples of sequential firstorder chains: Organic Hydrocarbons
[Schaerlaekens et al., 1999; Casey and Simunek, 2002]
Products
c3 s3
Product
t-DCE
Product
PCE
(sulfone, sulfone oxime) (sulfoxide, sulfoxide oxime)
Interrupted chain - two independent reaction paths:
Gas
Parent
pesticide 1
c1 s1
Product
c-DCE
VC
ethylene
1,2-DCE
Gas
Daughter
product 1
Products
c2 s2
c3 s3
Product
Parent
pesticide 2
Products
Product
Pharmaceuticals, hormones (Estrogen, Testosterone):
Estradiol
Perchloroethylene trichloroethylene dichloroethylene vinylchloride
c4 s4
Typical Examples of Sequential Firstorder Chains: Pharmaceuticals and Explosives
Estrone
Estriol
4ADNT
4ADNT
2ADNT
4ADNT
TNT
∂q c
∂θ c k ∂ρ s k ∂ag k
∂
∂
g ∂gk
w ∂c k
(θ D ij,k
)+
(a D ij,k
)- i k +
+
=
∂t
∂t
∂t
∂ xi
∂ x j ∂ xi
∂x j
∂ xi
'
'
− µ s,k
−1 ρ s k −1 - µ g,k −1a g k −1 + γ w,kθ + γ s,k ρ + γ g,ka − Scr , k
TAT
2-amino-4,6-dinitrotoluene
Governing Solute Transport Equations
'
-( µ w,k + µ w,k ' )θ c k - ( µ s,k + µ s,k ' ) ρ s k - ( µ g,k + µ g,k ' )a g k + µ w,k
−1θ c k -1 +
Explosives (TNT, RDX HMX)
2,4,6 trinitrotoluene
TCE
4-amino-2,6-dinitrotoluene
2,4,6-triminotoulene
w, s, g
c, s, g
kε (2, ns )
subscripts corresponding with the liquid, solid and gaseous phases,
respectively
concentration in liquid, solid, and gaseous phase, respectively
2,4DANT; 2,6DANT; 2,4DNT; 2,6DNT
Governing Solute Transport Equations
qi
i-th component of the volumetric flux
soil bulk density
a
air content
S
sink term in the water flow equation
concentration of the sink term
cr
w
g
Dij , Dij
dispersion coefficient tensor for the liquid and gaseous phase, respectively
k
subscript representing the kth chain number
µw, µs, µg first-order rate constants for solutes in the liquid, solid, and gaseous phases,
respectively
γw, γs, γg
zero-order rate constants for the liquid, solid, and gaseous phases,
respectively
µw', µs', µg' first-order rate constants for solutes in the liquid, solid and gaseous phases,
respectively; these rate constants provide connections between the individual
chain species.
number of solutes involved in the chain reaction
ns
ρ
Nonlinear Sorption
Heat Transport
Interactions Among Phases
Equation
s = k1c + k 2
Linear Adsorption
s =
∂ Rθ c
∂t
Nonlinear Equilibrium Adsorption
kc


R
s = k 1 c k2
Freundlich
k 1 c
1 + k 2 c
k 1 c k3
s =
1 + k 2 c k3
k3c
k1c
+
s =
1+ k2c
1+ k4c
Langmuir
Langmuir [1918]
Freundlich-Langmuir
Sips [1950]
Double Langmuir
Shapiro and Fried [1959]
k2/ k3
Extended Freundlich
Sibbesen [1981]
k 1 c
c + k
Gunary
Gunary [191970]
s = k1 ck2 - k 3
Fitter-Sutton
Fitter and Sutton [1975]
s = k 1 { 1 - [ 1 + k 2 c k 3 ] k4 }
Barry
Barry [1992]
Temkin
Bache and Williams [1971]
s = k1cc
Steady-State
s =
∂c
∂t
=
D
∂ 2c
∂c
−v
∂ z2
∂z
Reference
Lapidus and Amundson [1952]
Lindstrom et al. [1967]
Freundlich [1909]
s =

∂ 
∂c
θD
− q i c  + φ
∂ x i  ij ∂ x j
=
Model
Linear
s =
1 + k
RT
k
2
3
ln ( k 2 c )
c
1
s = k 1 c exp( -2 k 2 s )
modified Kielland
s
c
=
sT [ c + k1 ( cT − c )exp{ k2 ( cT − 2c )}]
Interactions Among Phases
Equilibrium interactions between the solution (c)
and gaseous (g) concentrations (Henry’s law)
Nonequilibrium interactions between the solution
(c) and adsorbed (s) concentrations
Nonlinear Sorption
Heat Transport
A generalized nonlinear empirical equation
s=
kd , η , β
kd cβ
1+η cβ
empirical constants
Non-Equilibrium Adsorption Equations
Nonequilibrium two-site adsorption model
e
Equation
∂s
= α ( k1 c + k 2 - s )
∂t
Model
Linear
∂s
= α ( k1 ck2 - s )
∂t
Freundlich
 kc

∂s
= α  1 - s 
∂t
 1+ k 2 c 
 k1 c k 3

∂s
= α 
- s 
k
∂t
 1+ k 2 c 3 
Langmuir
FreundlichLangmuir
Reference
Lapidus and Amundson [1952]
Oddson et al. [1970]
Hornsby and Davidson [1973]
van Genuchten et al. [1974]
Hendricks [1972]
Fava and Eyring [42]
∂s
= α exp ( k 2 s ){ k1 c exp ( -2 k 2 s ) - s}
∂t
∂s
= α c k1 s k 2
∂t
Leenheer and Ahlrichs [1971]
Enfield et al. [1976]
k
sk = sk + sk
sk e
sk k
Šimunek and van Genuchten [1994]
 sT - s 
∂s

=α(sT -s)sinh k1
 s - si 
∂t
 T

van Genuchten et al. [1974]
Lai and Jurinak [1971]
Type - 1 sites with instantaneous sorption
Type - 2 sites with kinetic sorption
∂ s ek
∂ sk
= f
∂t
∂t


∂ skk
k cβ k
= α k (1- f k ) s,k k β - skk  - µs,k skk + (1- f )γ s,k
k
∂t
1+ηk ck


f
fraction of exchange sites assumed to be at equilibrium
Nonlinear Sorption
Heat Transport
Interaction among phases
Liquid - Gas: a linear relation
g = k gc
k g,k
KH
R
TA
empirical constant equal to (KHRTA)-1
Henry's Law constant
universal gas constant
absolute temperature
Temperature Dependence of Transport
and Reaction Coefficients
Most of the diffusion (Dw, Dg), distribution (ks, kg), and reaction
rate (γw, γs , γg , µw', µs', µg', µw , µs , and µg) coefficients are
strongly temperature dependent. HYDRUS_2D assumes that
this dependency can be expressed by an Arrhenius equation
[Stumm and Morgan, 1981].
 E (T A - T rA) 
aT = a r exp 
A A 
 RT T r 
ar, aT coefficient values at a reference absolute temperature,
TrA, and absolute temperature, TA, respectively
E
activation energy of the reaction or process
Two-Region Physical Nonequilibrium Transport
∂
∂
∂c
(θ m + fρ k D) cm = (θ m Dm m - qcm) - α (cm - cim) - (θ µ l,m + fρ k D µ s,m) cm
∂t
∂z
∂z
[θ im + ( 1 - f ) ρ k D]
∂ cim
= α (cm - cim) - [θ im µ l,im + ( 1 - f ) ρ k D µ s,im] cim
∂t
Volatilization
∂( ρ s) ∂(θ c) ∂(ag) ∂
∂c
∂g w
+
+
=
(θ Dijw
+ aDija
- qi c - qia g) +φ
∂t
∂t
∂t
∂xi
∂x j
∂x j
g = kH c
Steady-State:
2
qw + qa k ∂c
 ρ kD akH  ∂c  w
i H
1 +
 =  D + D a k a  ∂ c - i
+
ij H θ ∂x ∂x

 ∂t  ij
θ
θ
θ
∂xi
 i j


Solute Transport - Dispersion Coefficient
Bear [1972]:
θ D ij = D T | q | δ ij + ( D L - D T )
q j qi
|q |
+ θ Dd τ δ
[L2T-1]
Dd - ionic or molecular diffusion coefficient in free water
τ - tortuosity factor [-]
δij - Kronecker delta function (δij =1 if i=j, and δij =0 otherwise)
DL , DT - longitudinal and transverse dispersivities [L]
2
2
qx
q
+ DT z + θ D d τ
|q|
|q |
2
2
q
q
θ D zz = D L z + DT x + θ D d τ
|q|
|q |
q q
θ D xz = ( D L - DT ) x z
|q |
θ D xx = D L
ij
Solute Transport - Boundary Conditions
First-type (or Dirichlet type) boundary conditions
c ( x, z, t ) = c 0( x, z, t )
for ( x, z ) ε Γ D
Third-type (Cauchy type) boundary conditions
- θ D ij
∂c
n i + q i n i c = q i 0 n i c 0 for ( x, z ) ε Γ C
∂ xj
Second-type (Neumann type) boundary conditions
θ D ij
∂c
ni = 0
∂ xj
for ( x, z ) ε Γ N
Dispersivity as a function of scale
Nonlinear Sorption
Heat Transport
Thermal Conductivity
λ ij (θ ) = λ T C w |q| δ ij + ( λ L - λ T ) C w
q j qi
| q|
+ λ 0 (θ ) δ ij
λ0(θ) thermal conductivity of the porous medium (solid plus water)
in the absence of flow
λL, λT longitudinal and transverse thermal dispersivities,
respectively
Chung and Horton [1987]
λ 0 (θ ) = b1 + b 2 θ w + b 3 θ 0w.5
b1, b2, b3
empirical parameters.
Governing Heat Transport Equation
Sophocleous [1979]
C(θ )
λij(θ)
C(θ), Cw
∂
∂T
∂T
∂T
=
[λij (θ )
] - Cw qi
∂t ∂ xi
∂ xj
∂ xi
apparent thermal conductivity of the soil
volumetric heat capacities of the porous medium and the liquid phase,
respectively
de Vries [1963]
C (θ ) = C n θ n + C o θ o + C w θ + C g a
θ
volumetric fraction
n, o, g, w subscripts representing solid phase, organic matter, gaseous phase, and
liquid phase, respectively.
Nonlinear Sorption
Heat Transport
Pedotransfer Functions: Rosetta
Estimation of Soil Hydraulic Properties With
Artificial Neural Networks
Retention
Schaap et al. (2001)
Saturated Conductivity
0.25
TXT
Textural Class
Clay
2
1
Sand, Silt, Clay %
SSCBD
Same + Bulk Density
SSCBD + 233
SSCBD + 2 at 33 kPa
SSCBD + 233 + 21500
Same + 2 at 1500 kPa
0.2
0.2
Sand
0.15
0.1
Clay
0.05
Sand
0
SSC
Probability
Input Data
3
0.4
0
0.6
Water Content [cm 3/cm 3]
1
2
3
4
Log(Ks) [cm/day ]
Unsaturated Conductivity
Sand %
Silt %
Clay %
Bulk d.
Sand
79
13
8
1.45
Clay
28
29
43
1.44
Log K(h) [cm/day]
Model
Log Suction [cm]
4
2
Sand
0
-2
Clay
-4
-6
1
2
3
4
Log Suction [cm]
Nonlinear Sorption
Heat Transport
Objective Function
Φ ( b,q, p )=
mq
nq j
∑v ∑w
j
j= 1
mp
∑v ∑w
j
j= 1
nb
∑ vˆ
i, j
[ q *j ( x, t i ) - q j ( x, t i , b ) ] 2 +
i, j
[ p *j (θ i ) - p j (θ i , b ) ] 2 +
i= 1
npj
i= 1
*
j [b j
- b j ]2
j= 1
1st term: deviations between measured and calculated space-time
variables
2nd term: differences between independently measured, pj*, and
predicted , pj, soil hydraulic properties
3rd term: penalty function for deviations between prior knowledge
of the soil hydraulic parameters, bj*, and their final
estimates, bj .
Parameter Estimation in HYDRUS
Parameter Estimation:
- Soil hydraulic parameters
- Solute transport and reaction parameters
- Heat transport parameters
Sequence:
- Independently
- Simultaneously
- Sequentially
Method:
- Marquardt-Levenberg optimization
Nonlinear Sorption
Heat Transport
Furrow Irrigation – Pressure Heads
Dike - Velocity Vectors
Solute Plume Under Dam
Dike – Pressure Heads
Finite Element Mesh – Cut-off Wall
Capillary Barrier - Material Distributions
Capillary Barrier - Velocity Vectors
Tunnel - Spectral Color Maps
Plume Movement in a Transect with Stream
Mesh Generator
Tunnel - Velocity Vectors
HYDRUS - Existing Applications
Agricultural:
Irrigation management (FREP, LINK , Bristow et al., 2002)
Drip irrigation design (FREP, LINK, Bristow et al., 2002)
Sprinkler irrigation design (FREP, LINK)
Tile drainage design and performance (Mohanty et al., 1998, do Vos et al., 2000)
Studies of root and crop growth (Vrugt et al., 2001, 2002)
Salinization and reclamation processes (Šimůnek and Suarez, 1998)
Nitrogen dynamics and leaching (Ventrella et al., 2001; Jacques et al., 2002)
Transport of pesticides and degradation products (Wang et al., 1998)
Non-point source pollution
Seasonal simulation of water flow and plant response
...
Non-Agricultural:
Non-Agricultural:
Stream-aquifer interactions
Leaching from radioactive waste sites at the Nevada test Site (DRI, DOE)
Flow around nuclear subsidence craters at the Nevada test site (Pohll et al., 1996;
Environmental impact of the drawdown of shallow water tables
Wilson et al., 2000)
Analysis of cone permeameter and tension infiltrometer experiments
Capillary barrier at Texas low-level radioactive waste disposal site (Scanlon, 1998)
Evaluation of approximate analytical analysis of capillary barriers (Morris and
(Gribb et al.,
1996; Kodesova et al., 1998, 1999; Šimůnek et al., 1997, 1998, 1999)
Virus and bacteria transport (Shijven and Šimůnek, 2002, Bradford et al., 2002a,b, Yates et al., 2000)
Hill-slope analyses
Transport of TCE and its degradation products (Scharlaekens et al., 2000; Casey and
Stormont, 1997; Kampf and Montenegro, 1997; Heiberger, 1998)
Landfill covers with and without vegetation (Abbaspour et al, 1997; Albright, 1997; Gee et al.,
1999, Scanlon et al., 2002)
Simunek, 2002)
Risk analysis of contaminant plumes from landfills
Seepage of wastewater from land treatment systems
Tunnel design - flow around buried objects (Knight, 1999)
Highway design - road construction - seepage (de Haan, 2002)
Stochastic analyses of solute transport in heterogeneous media (Tseng and Jury, 1993;
Multicomponent geochemical transport (Jacques and Šimůnek, 2002)
Analyses of riparian systems (Whitaker, 2000)
Fluid flow and chemical migration within the capillary fringe (Silliman et al., 2002)
Flow in historical monuments (Ishizaki et al., 2001)
Flow and transport around land mines (Das et al., 2001; Šimůnek et al., 2001)
Analyses of Chloride profiles in deep vadose zones to evaluate historical fluxes
Roth, 1995; Roth and Hammel, 1996; Kasteel et al. 1999; Hammel et al., 1999; Roth et al., 1999; Vanderborght et
al., 1998, 1999)
Lake basin recharge analysis (Lee, 2000)
(Scanlon et al., 2003)
Coupled movement of water and energy,
including vapor transport
Modified Richards Equation:
∂θ
∂ 
∂h
∂T
∂h
∂T 
=
+ K Lh ( h ) + K LT ( h )
+ K vh
+ K vT
−S
K Lh ( h )
∂t
∂ z 
∂z
∂z
∂z
∂ z 
KLh
KLT
Kvh
KvT
Current and Future Development
- hydraulic conductivity for liquid phase fluxes due to gradient in h
- hydraulic conductivity for liquid phase fluxes due to gradient in T
- isothermal vapor hydraulic conductivity
- thermal vapor hydraulic conductivity
Energy Transport:
∂C pT
∂θ v
∂q T
∂q
∂q T
∂ 
∂T 
+ L0
=
λ (θ )
− C w l − C w ST − L0 v − C v v
∂t
∂t
∂ z 
∂ z 
∂z
∂z
∂z
(1)
(2)
(3)
(4)
(5)
(1)
(2)
(3)
(4)
(5)
Coupled Movement of Water and Energy
-1000
-500
0
0
1000
2000
3000
4000
10
15
20
0 yrs
1 kyr
5 kyr
9 kyr
Field
0
Amargosa Desert
0
10
20
30
40
50
0 yrs
5 kyr
Field
2000
4000
6000
0
Eagle Flat
8
8000 10000
5 kyr
10 kyr
16 kyr
Measured
10 kyr
16 kyr
Lab
2000
4000
6000
8000 10000
5
15
20
Hueco Bolson
0
5
15
20
0 yrs
5 kyr
Field
10 kyr
13 kyr
5000
10000
15000
20000
5 kyr
10 kyr
13 kyr
Measured
Simulated matric potentials and chloride
concentrations from wet initial conditions
(pluvial period) to different times of
upward flow. (Scanlon et al. 2003)
10
T=0
t=0.25 d
t=1
t=0.25 d
8
t=1
t=5
t=5
t=25
t=25
t=25
6
T=0
t=0.25 d
8
t=5
6
t=5
4
4
4
2
2
2
2
0
0
0.05
0.1
0.15
0.2
0
Total flux=water flux+vapor flux
0.02
0.04
Total Flux [cm/d]
0.06 0
t=1
t=25
6
4
Water Content [-]
5 kyr
12 kyr
Measured
0
10
6
0
0 yrs
5 kyr
12 kyr
Field
Field - OP
10
T=0
8
t=1
0
0
10
10
T=0
t=0.25 d
1 kyr
5 kyr
9 kyr
Measured
Central
High Plains
Depth [cm]
5
Coupled movement of water and energy
5000
0
10
Soil heat flow by conduction
Convection of sensible heat by water flow
Heat removed by root water uptake
Transfer of latent heat by diffusion of water vapor
Transfer of sensible heat by diffusion of water vapor
0
10
20
Temperature [C]
30
0
2
4
6
Concentration [-]
8
10
Coupled movement of water and energy,
freezing/thawing cycle
Coupled Movement of Water and Energy,
Freezing/thawing Cycle
Modified Richards Equation:
(1)
(2)
(3)
(4)
(5)
(6)
Soil heat flow by conduction
Convection of sensible heat by water flow
Heat removed by root water uptake
Transfer of latent heat by diffusion of water vapor
Transfer of sensible heat by diffusion of water vapor
Freezing/thawing term
-1
-3
1.00E+09
1.00E+08
1.00E+07
1.00E+06
0.02
0.00
-0.02
-0.04
-0.06
-0.08
-0.10
o
Te mpe rature [ C]
1.00E+12
Silty clay
Loam
1.00E+11
Sand
1.00E+10
1.00E+09
1.00E+08
Apparent heat capacity
for different textures
1.00E+07
1.00E+06
0.50
0.00
-0.50
-1.00
-1.50
-2.00
o
Te mpe rature [ C]
Coupled movement of water and energy
Freezing/thawing cycle
Silty Clay
Depths (cm):
0, 0.5. 1, 2, 3.5, 5, 10
Sand
1.00E+10
-1
Energy Transport:
∂C pT
∂θ v
∂θ i
∂q T
∂q
∂q T
∂ 
∂T 
λ (θ )
+ L0
− L f ρi
=
− C w l − C w ST − L0 v − C v v
∂t
∂t
∂t
∂ z 
∂ z 
∂z
∂z
∂z
(6)
(1)
(2)
(3)
(4)
(5)
Silty clay
Loam
1.00E+11
-3
- hydraulic conductivity for liquid phase fluxes due to gradient in h
- hydraulic conductivity for liquid phase fluxes due to gradient in T
- isothermal vapor hydraulic conductivity
- thermal vapor hydraulic conductivity
Apparent Capacity [Jm K ]
KLh
KLT
Kvh
KvT
Apparent Capacity [Jm K ]
1.00E+12
ρ ∂θ i
∂θ
∂ 
∂h
∂T
∂h
∂T 
K Lh ( h )
+ i
=
+ K Lh ( h ) + K LT ( h )
+ K vh
+ K vT
−S
∂t
ρ w ∂t
∂ z 
∂z
∂z
∂z
∂ z 
Heterogeneity,
Layering
0
4
2
- 20 000
0
- 40 000
-2
- 60 000
-4
-6
- 0.5
0.0
0.5
1.0
1.5
2 .0
- 80 000
- 0.5
0 .0
0.5
1.0
1.5
2.0
T ime [d ays]
T ime [d ays]
0.36
1.5
1.4
0.34
1.3
0.32
1.2
0.30
1.1
1.0
0.28
0.9
0.26
0.24
- 0.5
0.8
0.0
0.5
1.0
T ime [d ays]
1.5
2 .0
0.7
- 0.5
0.0
0.5
1 .0
1.5
2 .0
T ime [d ays]
Nonequilibrium and Preferential Flow and Transport
Dual-porosity approach (Richards eq. for water, mobileimmobile concept for solute)
Dual-porosity approach (mobile-immobile concept for both
water and solute)
Dual-permeability approach (two overlapping porous media, one
for matrix flow, one for preferential flow) [Gerke and van
Genuchten, 1993]
Kinematic wave approach for flow in macropores [Jarvis, 1991]
Simplified first-order approach [Ross and Smettem, 2000]
∂θ
θ −θ
= f (θ ,θ e ) = e
∂t
τ
Dual-porosity hydraulic property models [Durner, 1994]
Design experiments that would provide parameters for above
models
Dual-permeability Approach
Multicomponent solute transport:
Coupling HYDRUS and PHREEQC [Parkhurst and
Appelo, 1999])
Gerke and van Genuchten [1993]: (two overlapping porous
media, one for matrix flow, one for preferential flow)
60
0
50
0
5
5
10
10
t = 0.01 d
t = 0.04 d
t = 0.08 d
15
t = 0.08 d (-25%)
t = 0.08 d (+25%)
Fracture Flux
Matrix Flux
Mass Transfer
Mass Transfer (-25%)
Mass Transfer (+25%)
20
15
20
t = 0.01 d
25
t = 0.04 d
t = 0.08 d
30
0
0.04
0.06
0.08
25
30
t = 0.08 d (+25%)
35
0.02
20
t = 0.08 d (-25%)
10
0
Depth [cm]
30
Depth [cm]
F lux [cm /d ]
40
0.1
40
0.25
Time [d]
35
40
0.3
0.35
0.4
0.45
0.5
0
Water Content [-]
0.005
0.01
0.015
0.02
0.025
Water Content [-]
Infiltration and mass exchange fluxes (a), water contents in the matrix
Available chemical reactions:
Aqueous complexation
Redox reactions
Ion exchange (Gains-Thomas)
Surface complexation – diffuse double-layer model and nonelectrostatic surface complexation model
Precipitation/dissolution
Chemical kinetics
Biological reactions
(b) and fracture (c) domains
0.01
a)
Initially the 8-cm column contains a solution (with heavy metals) in equilibrium with the
cation exchanger.
b) The column is then flushed with three pore volumes of solution without heavy metals.
Exchange Species:
Verification of HYDRUS-PHREEQC
Kinetic biodegradation of NTA (nitrylotriacetate), cell growth,
complexation with Co, and kinetic sorption
Processes:
Bacterially mediated degradation of an organic substrate
Bacterial cell growth and death
Aqueous speciation including metal-ligand complexation
Kinetic sorption of Co and CoNTA
Convective dispersive transport
Parameters:
L=10m, θs=0.4 m, ρ=1.5 kg/m3, v=1 m/h, , λ=0.05 m.
Iinitial Cond.:
O2=3.125e-5, Na=0.001, Cl=0.001 mol/L, Biomass=0.000136g/L
Boundary Cond.: O2=3.125e-5, Co=5.23e-6, NTA=5.23e-6, Na=0.001, Cl=0.001
mol/L
Na
0.006
Ca
0.004
0.002
Al
Zn
6E-004
4E-004
Pb
2E-004
Cd
0E+000
0
3
6
9
Time (days)
12
15
0.005
0.004
CaX2
0.003
0.002
ZnX2
0.001
CdX2
0
0
3
6
9
Time (days)
12
15
0
3
6
9
Time (days)
12
15
Cl
Ca
Al
Cd
Zn
1.5
1.2
0.9
0.6
0.3
0
0
3
6
9
Time (days)
12
15
Kinetic biodegradation of NTA, cell growth, complexation with Co, and kinetic sorption
Rate equations:
1.6E-09
NTA degradation:
RHNTA2− = −qm X m
[HNTA ] [O ]
K + [HNTA ] K + [O ]
4.0E-04
Sorbed Co - PHREEQC
Sorbed CoNta
Sorbed Co - HYDRUS
Sorbed CoNta
Biomass
Biomass
2−
2
2−
s
a
2
Biomass production:
R cell = − YR HNTA 2 − − bX
Kinetic sorption (Co2+, CoNTA-):

Z 

R Z = − k m  [Z ] −
K d 

m
1.2E-09
8.0E-10
2.0E-04
4.0E-10
1.0E-04
0.0E+00
0.0E+00
0
Xm – biomass
Ks, Ka– half-saturation constants
Z – species concentration
3.0E-04
10
20
30
40
Time [hours]
50
60
70
80
Biomass [g/L]
Boundary concentration:
Species and Complexes:
0.008
0
q=2 cm/d, λ=0.2 cm, CEC=11 mmol/cell.
Al=0.5, Br=11.9, K=2, Na=6, Mg=0.75, Cd=0.09, Pb=0.1, Zn=0.25
mmol/L.
Al= 0.1, Br=3.7, Cl=10, Ca=5, Mg=1 mmol/L.
Al3+, Al(OH)2+, Al(OH)2+, Al(OH)3, Al(OH)4-, Br-, Cl-, Ca2+,
Ca(OH)+ , Cd2+, Cd(OH)+, Cd(OH)2, Cd(OH)3-, Cd(OH)42-, CdCl+,
CdCl2, CdCl3-, K+, KOH, Na+, NaOH, Mg2+, Mg(OH)+, Pb2+,
Pb(OH)+, Pb(OH)2, Pb(OH)3-, Pb(OH)42-, PbCl+, PbCl2, PbCl3-,
PbCl42-, Zn2+, Zn(OH)+, Zn(OH)2, Zn(OH)3-, Zn(OH)42-, ZnCl+,
ZnCl2, ZnCl3-, ZnCl42
AlX3, AlOHX2, CaX2, CdX2, KX, NaX, MgX2, PbX2, ZnX2
Concentration (mol/l)
Parameters:
Initial concentrations:
8E-004
Cl
Transport and cation
exchange of major cations
and heavy metals
Relative mass balance errors (%)
(cations - Ca, Mg, Na, K, Cd, Pb, Zn; anions – Cl, Br, Al)
Concentrations [mol/g]
Transport and Cation Exchange (major ions and heavy metals):
0.000004
7
6
CoNTA
HNTA
Co
CoNTA
HNTA
Co
pH
pH
0.0000025
0.000002
0.0000015
9 Processes:
5
4
Heterotrophic Organisms
Hydrolysis
Aerobic growth of heterotrophs on readily biodegradable OM
NO3-growth of heterotrophs on readily biodegradable OM
NO2-growth of heterotrophs on readily biodegradable OM
Lysis
Nitrosomonas
Aerobic growth of N.somonas on NH4
Lysis of n-somonas
Aerobic growth of N.bacter on NO2
Lysis of N.bacter
Nitrobacter
Ph
0.000003
Concentration [m ol/kg]
Dissolved oxygen O2
Organic matter: readily biodegradable, slowly biodegradable, inert
Nitrogen: NH4+, NO2-, NO3-, N2
Inorganic phosphorus
Heterotrophic micro-organisms
Autotropic micro-organisms: Nitrosomonas & Nitrobacter
8
0.0000035
3
0.000001
2
0.0000005
1
0
0
0
10
20
30
40
50
60
70
Constructed Wetlands
12 Components:
Kinetic biodegradation of NTA, cell growth, complexation with Co, and kinetic sorption
80
Tim e [hours]
Overland Flow
HYDRUS-3D - Preview
Kinematic wave equation:
∂h ∂Q
+
= q ( x, t )
∂t ∂x
h
Q
q(x,t)
Q = α hm
100*0.5 m
- unit storage of water (or mean depth),
- discharge per unit width,
- rate of local input, or lateral inflows (precipitation - infiltration)
Manning hydraulic resistance law:
α = 1.49
n
S
S 1/ 2
n
and
m = 5/3
- Manning’s roughness coefficient for overland flow
- slope
HYDRUS-3D - Preview
HYDRUS Web Site – FAQ
HYDRUS Web Site – Tutorials
HYDRUS-2D – User Manual
David Rassam, Jirka Šimůnek and
Rien Van Genuchten
Introductory examples
1. A Journey Through HYDRUS Windows
1.1. Pre-Processing
1.2. Post-Processing
2.
3.
4.
5.
6.
HYDRUS Output Files
Root Water Uptake
Example Application
Inverse Solution
Trouble Shooting
Appendices:
I. Soil Hydraulic Properties
II. Concept Related to Modelling Evaporation
III. Root Water Uptake
IV. Scaling Factors
V. Inverse Solution
VI. Alphabetical Index for HYDRUS Windows
HYDRUS Web Site – Discussion Forum

HYDRUS Lecture - Nevada Agricultural Experiment Station

Transcription

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